Document [original]

Temperature-Stable, Energy-Efficient,

and High Bit-Rate 980 nm VCSELs

vorgelegt vom

Master of Science Physik

Hui Li

geb. in Rizhao

von der Fakultät II - Mathematik und Naturwissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

Dr. rer. nat.

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Michael Lehmann

Berichter/Gutachter: Prof. Dr. Dieter Bimberg

Berichter/Gutachter: Prof. Dr. Gadi Eisenstein

Berichter/Gutachter: Prof. Dr. James A. Lott

Tag der wissenschaftlichen Aussprache: 30. Juli 2015

Berlin 2015

D 83

Abstract

For over 30 years, vertical-cavity surface-emitting lasers (VCSELs) have been the

subject of intensive worldwide research, due to their many applications in optical

data communications, optical and spectroscopic sensing, printing, and displays.

Most notably VCSELs are the key enabling technology for short-reach optical inter-

connects (OIs) across multimode fiber in modern data centers and petaflop-scale to

exaflop-scale supercomputers. VCSELs have replaced edge-emitting laser diodes

as the preferred light sources for short-reach OIs due to their significant advantages,

including high bit-rates, low energy consumption, high beam quality, low manufac-

turing cost, and more. Optical communications provide the only reliable means of

transferring large volumes of data at the ultra-high bit-rates needed in data centers.

Considering cost, long-term system sustainability, and reliability, future OIs must

be suited for operation without extra cooling, implying the VCSELs must be capable

of operating perpetually and reliably at elevated temperatures (e.g. at 85 °C). Tem-

perature stability can also contribute to the low energy consumption of OIs, because

high bit-rate operation at constant current and voltage driving parameters provides

the opportunity to dispose of cooling systems and to use simpler driver circuits. In

addition to temperature insensitivity one also seeks to concurrently improve the

energy efficiency and to increase bandwidth via an increased single-channel bit

rate to reduce the total life cycle cost of a given VCSEL-based OI system. Future

exaflop-scale supercomputers will require billions of OIs and are predicted to require

high bit-rate interconnects operating at 25 Gb/s per channel or beyond. This leads

to the firm requirement for future OI systems of increased bit rate and lower energy

dissipation.

This work experimentally demonstrates that 980 nm VCSELs can achieve high

bit-rate, temperature-stable, and energy-efficient operation concurrently with one

epitaxial wafer design for the first time. It is shown that this is a result of high-speed

device fabrication and careful wafer design, including the active region design,

the quantum well gain-to-etalon wavelength offset design, the distributed Bragg

reflector design, and a careful thermal design. Systematic experimental temperature-

dependent and oxide-aperture diameter-dependent characterization are presented,

including static measurements, small-signal analysis, and data transmission experi-

ments. It is also demonstrated that VCSELs with oxide-aperture diameters between

~3 and ~4 µm are most suitable to achieve energy-efficient, temperature-stable, and

high bit-rate operation at the same time. Error-free data transmissions at 38 Gb/s

at 25, 45, 65 and 85 °C are achieved without any change of working point and

modulation condition by using VCSELs with oxide-aperture diameters smaller than

5 µm. Moreover, error-free data transmission at a bit rate of 42 Gb/s at room tempera-

ture is achieved, as is 38 Gb/s at 85 °C by using small oxide-aperture VCSELs. These

maximum achievable data transmission bit rates match very well with the prediction

from small-signal analysis. Record low energy dissipation of 139 and 177 fJ/bit for

35 and 38 Gb/s error-free data transmission at 85 °C are achieved by using ~3 µm

oxide-aperture diameter VCSELs. These VCSELs are the most energy efficient

VCSELs operating at 85 °C at any wavelength to date. At room temperature, only 145,

147, and 217 fJ/bit of dissipated heat energy per transferred bit are needed for 35, 38,

and 42 Gb/s error-free data transmission by using a ~3 µm oxide-aperture diameter

VCSEL, which are all record low heat energy dissipation for 980 nm VCSELs. A

temperature-dependent and oxide-aperture diameter-dependent impedance analysis

are performed to better understand the data bit rate limitations and to understand

what improvements should and can be made for the next generation 980 nm VCSEL

device design. Relative intensity noise (RIN) values are also given, which are low

enough to satisfy the application requirements of the 32 GFC Fibre Channel standard.

During the course of this dissertation, small oxide-aperture diameter (smaller than

5 µm) 980 nm VCSELs are demonstrated to be especially well suited for use in short-

reach optical interconnects in high performance computers, and in board-to-board

and chip-to-chip integrated photonics systems.

Table of Contents

Chapter 1 ...........................................................................................................1

Introduction

1.1 A Brief History of VCSELs ..........................................................................1

1.2 VCSELs for Short-Reach Optical Communication ......................................3

1.2.1 Advantages of VCSELs ....................................................................5

1.2.2 High Bit-Rate VCSELs .....................................................................6

1.2.3 High Operating Temperature VCSELs .............................................7

1.2.4 Energy-Efficient VCSELs .................................................................9

1.3 More Applications of VCSELs ...................................................................10

1.4 Dissertation Overview ................................................................................11

Chapter 2 .........................................................................................................13

Design and Modeling of 980 nm VCSELs

2.1 Theoretical Background ..............................................................................14

2.1.1 Static VCSEL Properties .................................................................14

2.1.2 Dynamic VCSEL Properties ...........................................................16

2.2 Active Region Design .................................................................................19

2.2.1 Critical Layer Thickness.................................................................19

2.2.2 Compressively strained InGaAs QWs ............................................20

2.2.3 Strain-Compensated InGaAs/GaAsP QWs ....................................26

2.2.4 Summary ........................................................................................28

2.3 DBR Design ................................................................................................28

2.3.1 Electrical Design of DBR Mirrors ..................................................29

2.3.2 Optical Design of the DBR Mirrors ...............................................32

2.4 QW Gain-to-Etalon Wavelength Offset Design .........................................33

2.4.1 The Effect on Static Properties .......................................................33

2.4.2 The Effect on High Bit-Rate Modulation Properties ......................35

2.4.3 Summary ........................................................................................37

2.5 Thermal Design ..........................................................................................37

2.5.1 Theoretical Background .................................................................37

2.5.2 Thermal Simulation ........................................................................39

2.5.3 Summary ........................................................................................43

Chapter 3 .........................................................................................................44

Fabrication and Measurements

3.1 The 980 nm VCSEL Structure ................................................................... 44

3.1.1 Mode Characterization ....................................................................46

3.1.2 QW Active Region ..........................................................................48

3.1.3 Photon Lifetime Optimization ........................................................48

3.2 VCSEL Fabrication .....................................................................................49

3.2.1 Process Techniques .........................................................................50

3.2.2 High-Speed VCSEL Processing .....................................................55

3.3 VCSEL Measurements ................................................................................57

3.3.1 LIV Measurements .........................................................................57

3.3.2 Spectral Measurements...................................................................57

3.3.3 Small-Signal Measurements ...........................................................59

3.3.4 Data Transmission Measurements ..................................................61

Chapter 4 .........................................................................................................63

Impedance Characteristics

4.1 Motivation and Applications .......................................................................63

4.1.1 Equivalent Circuit Model for VCSELs ........................................... 64

4.1.2 Measurement of Impedance ............................................................66

4.2 Experimental Results ..................................................................................67

4.2.1 Impedance vs. Temperature ............................................................67

4.2.2 Impedance vs. Oxide-Aperture Diameter ......................................70

4.3 Summary ....................................................................................................72

Chapter 5 .........................................................................................................73

980 nm VCSEL Noise Characteristics

5.1 Semiconductor Laser RIN ..........................................................................73

5.1.1 Laser Diode RIN Measurement ......................................................75

5.1.2 RIN Specification Trend for the Fibre Channel Standard ..............76

5.2 980 nm VCSEL RIN Characteristics ..........................................................76

5.2.1 980 nm VCSEL RIN versus Bias Current ......................................77

5.2.2 980 nm VCSEL RIN versus the Oxide-Aperture Diameter ...........78

5.3 Summary.....................................................................................................80

Chapter 6 .........................................................................................................81

Temperature-Stable 980 nm VCSELs

6.1 Temperature-Dependent Static Analysis ....................................................81

6.1.1 Temperature-Dependent LIV Results .............................................82

6.1.2 Spectral Characteristics ..................................................................84

6.2 Small-Signal Modulation Analysis .............................................................87

6.3 Highly Temperature-Stable VCSELs ..........................................................90

6.4 Summary ....................................................................................................93

Chapter 7 .........................................................................................................94

Energy-Efficient High Bit-Rate 980 nm VCSELs

7.1 Static Characteristic ....................................................................................94

7.1.1 Static LIV Characteristics ...............................................................95

7.1.2 Spectral Characteristics ..................................................................99

7.2 Room Temperature Energy Efficiency .....................................................101

7.2.1 Small-Signal Analysis at Room Temperature ...............................101

7.2.2 High Bit-Rate Data Transmission .................................................103

7.2.3 Energy-Efficient Data Transmission .............................................104

7.3 High Temperature Energy Efficiency .......................................................107

7.3.1 Small-Signal Analysis at High Temperature ................................107

7.3.2 High Bit-Rate Data Transmission ................................................. 111

7.3.3 Energy-Efficient Data Transmission ............................................. 114

7.4 Summary ................................................................................................... 116

Chapter 8 .......................................................................................................117

Conclusions and Outlook

8.1 Conclusions ............................................................................................... 117

8.2 Outlook .....................................................................................................119

References ......................................................................................................121

Appendix A ....................................................................................................133

High Bit-Rate VCSEL Process Flow

Appendix B ....................................................................................................137

Abbreviations

Appendix C ....................................................................................................138

Symbols

Acknowledgments .........................................................................................139

List of Publications .......................................................................................140

Chapter 1

Introduction

1.1 A Brief History of VCSELs

The basic concept of a “surface-emitting injection laser” [1] that later evolved into

what is now call the vertical-cavity surface-emitting laser (VCSEL), as shown in

Fig. 1-1, was proposed in 1977 by Haruhisa Soda and Kenichi Iga at the Tokyo In-

stitute of Technology [2]. The modern VCSEL structure that grew from this original

idea contains a top distributed Bragg reflector (DBR) mirror, a bottom DBR mirror,

and an optical cavity active region. Prof. Iga was awarded the 2013 Franklin Institute

Award, the Bower Award and Prize specifically for the conception and development

of the vertical-cavity surface-emitting laser and its multiple applications in opto-

electronics [3]. In 1979, Prof. Iga’s group demonstrated the first surface-emitting

injection laser that lased under pulsed operation at 77 K [1]. This predecessor to

the modern VCSEL was based on InP/GaInAsP materials, had a relatively long

~90 µm vertical optical cavity, and used thin semitransparent gold and tin layers as

the top mirror and gold and zinc layers as the bottom mirror. The idea of making

an all-semiconductor AlGaAs DBR via epitaxial growth by MBE originated from a

paper by Jan P. van der Ziel and M. Ilegems from AT&T Bell laboratories in 1975 [4].

This pioneering work on semiconductor DBRs was followed by a similar work on

20 repeating pairs of GaAs/AlxGa1–xAs “multilayer reflectors” (or MLRs) grown by

molecular beam epitaxy (MBE) by Matsuo Ogura et al. at the Electrotechnical Labo-

ratory in Japan in 1983 [5]. In 1984 Ogura et al. reported an MBE-grown “surface

emitting laser diode” or SLED that used 20 top periods and 30 bottom periods of

Si-doped (n-doped) Al0.3Ga0.7As/GaAs DBR layers surrounding a half-lambda-thick

GaAs “phase shifter layer” and zinc diffusion to form a lateral p-n junction in every

GaAs layer in the DBRs [6]. The SLED emitted with pulsed excitation at about

840 nm from about 54 to 150 K. Dr. Ogura moved to the University of California

2 Chapter 1 Introduction

Berkeley and with his new colleagues in 1987 demonstrated a similar vertical-cavity

laser diode grown by metal-organic chemical vapor deposition (MOCVD) that

consisted of 20 top pairs and 60 bottom pairs of undoped Al0.3Ga0.7As/GaAs DBRs

surrounding a half-lambda-thick GaAs “phase shifter layer” (about 118 nm-thick)

that in fact served as an optical cavity [7]. The device structure was etched forming

a rectangular pillar and then surrounded by n-type and p-type Al0.4Ga0.6As cladding

re-growth layers that were grown by liquid-phase epitaxy. In 1989, Fumio Koyama

et al. at the Tokyo Institute of Technology reported the room temperature operation

of quantum well (QW) VCSELs emitting at 894 nm [8]. The bulk GaAs optical

cavity length was ~5.5 µm-thick and included a 2.5 µm-thick GaAs active layer that

was surrounded by GaAs/AlGaAs layers. The vertical cavity laser diode wafer was

grown by a two-step MOCVD process. The optical cavity was surrounded by SiO2/

TiO2 dielectric DBRs on the top and bottom. The lowest threshold current achieved

was 30 mA at 20 °C, and the highest achieved output power was 1.6 mW [8]. Also in

1989 Dr. Yong H. Lee (now a Prof. at Korea Advanced Institute of Science and Tech-

nology) working at AT&T Bell Laboratories with colleagues from Bellcore including

Dr. Jack L. Jewell and Dr. Axel Scherer reported a ~983 nm QW VCSEL [9]. This

was the first modern VCSEL with all-semiconductor DBRs as reported by Dr. Ogura

but with a QW active region – a critical advance for the future success of VCSELs.

The VCSEL operated continuous wave (CW) at room temperature with electrical

injection. A single In0.2Ga0.8As QW with a thickness of 10 nm was used in the active

region, and the threshold current was 1.5 mA [9]. Subsequently the performance of

VCSELs improved rapidly during the 1990’s due in large part to the development of

the molecular beam epitaxy and MOCVD semiconductor growth techniques, which

make the growth of DBRs with high power reflectance possible (e.g. with R > 0.99)

by precisely controlling the epitaxial layers thicknesses and material compositions,

but also the spatial doping profiles. The golden age of VCSEL development included

many pioneering contributions by research groups at the Technische Universität

Berlin, the University of California Santa Barbara (UCSB), the University of Texas

Austin, the University of Ulm, the Tokyo Institute of Technology, the University of

New Mexico, Sandia National Laboratories, Chalmers University of Technology, the

University of California Berkeley, the Ferdinand Braun Institut, and many others.

The introduction of selective wet oxidation technology [10, 11] by the use of a thin

oxide aperture layer buried inside an epitaxial structure in 1994 greatly improved the

VCSEL performance, and made it easier to achieve room temperature CW operation

with wall-plug efficiencies of 50 % or higher. The first commercial VCSELs came

on the market in the middle 1990s [12, 13]. In 1990, Prof. Larry Coldren’s group at

UCSB achieved room temperature CW lasing operation of a 979 nm VCSEL with

1.2 VCSELs for Short-Reach Optical Communication 3

a single In0.2Ga0.8As QW, with a threshold current of only 0.7 mA [14]. In 1993, the

first near room temperature (14 °C) CW operation of a 1.3 µm GaInAsP/InP VCSEL

was report by Prof. K. Iga’s group [15]. A buried heterostructure and MgO/Si heat

sink mirror were used. The 1.3 µm VCSEL’s threshold current was reduced to 22 mA.

In 1993, the first AlGaInP visible light VCSELs (620 – 680 nm) operating pulsed

and CW room temperature were demonstrated by James A. Lott at Sandia National

Laboratories in Albuquerque, New Mexico [16–18]. Follow up work in 1995 using

selective wet oxide technology to confine current and the optical modes led to red

VCSELs with low threshold currents (0.66 mA) and low threshold voltages (150 mV

above the photon bandgap energy of about 1.9 V at 650 nm) [19]. The first 1.54 µm

VCSELs operating at room temperature were realized by the groups of Prof. Evelyn

Hu and Prof. John Bowers at UCSB in 1995 [20].

Optical and Current

confinement

DBR

Active region

Substrate

Transverse

Mode Field

Longitudinal

Mode Field

DBR

Fig. 1-1. Model of a VCSEL as described by Prof. K. Iga in [2]. The structure contains a top DBR, a

bottom DBR, and an active region within an optical cavity. The QWs that comprise the gain media are

placed at the center of the optical cavity formed between the two DBR mirrors. Oxidized or proton-im-

planted regions provide the lateral confinement for both the current and the optical mode. Carriers are

injected through the metal contacts at the top and bottom of the structure and light is emitted from the

top mirror. The beam profile is governed primarily by the diameter of optical and current confinement.

1.2 VCSELs for Short-Reach Optical Communication

The exponential growth in computer performance and Internet traffic has prompted

the great interest in optics technologies to replace conventional electronics in data

communication links. Optical interconnects (OIs) have been widely used for data

centers and supercomputers, due to their advantages of higher bandwidth, lower

energy consumption, and a smaller physical footprint and volume as compared to

4 Chapter 1 Introduction

conventional copper-based electrical interconnects [21]. One of the main challenges

in data centers is to satisfy the increased bandwidth capacity while keeping a moder-

ate level of required energy consumption, module cost, complexity, and physical

space. The VCSEL-based short-reach (SR) optical links for data communication

have been used since their commercial introduction by Honeywell Inc. in 1996

[12, 13]. These VCSELs have found important applications in data communications

as the light-sources for optical interconnects. The demand for OIs in data centers and

supercomputers is estimated to reach a market revenue of $520 million by 2019 [22].

VCSELs have become a main laser source for short-range high-speed optical links,

and VCSEL light sources are a key component for the development of other OI

systems including on-chip photonics. The GaAs-based VCSEL technology is pres-

ently extensively utilized in short-reach optical communication links. 850 nm

VCSELs are now in volume production and are used for 10 to 28 Gb/s, multimode

fiber transceivers for the ANSI Fibre Channel and Gigabit Ethernet IEEE 802.3

standards [13]. Future optical interconnects such as those envisioned in large scale

integration (LSI) chips, optical circuit boards and backplanes, and multiple-core fiber

systems as in supercomputers and personal computers (PCs) will continue the great

demand for high performance VCSELs for the next several decades [23].

Direction

of epitaxial

growth

Edge-Emitting Laser (EEL)

VCSEL

Light output Light output

(circular beam)

(elliptical beam)

P-contact

N-contact

Active region

P-DBR

N-DBR

Fig. 1-2. Comparison between a VCSEL and an edge-emitting laser (EEL). The VCSEL has a circular

output light beam of low divergence, and the beam direction is perpendicular to the epitaxial layers.

The edge-emitting laser has an elliptical output light beam, and the beam direction is parallel with

the epitaxial layers.

Table 1-1. Comparison of typical parameters between EELs and VC-

SELs as in [2]

Parameter EEL VCSEL

Active layer thickness (d) 10 nm – 0.1 µm 8 nm – 0.5 µm

Active Volume (V) 60 µm30.07 µm3

Cavity Length (L) 300 µm ≈ 1 µm

Reflectivity (Rm) 0.3 (uncoated) 0.99 – 0.999

Relaxation frequency (fR) < 5 GHz > 10 GHz

1.2 VCSELs for Short-Reach Optical Communication 5

1.2.1 Advantages of VCSELs

Different compared to conventional edge-emitting lasers (EELs), the VCSEL’s

vertical cavity is formed by the surfaces of epitaxial layers and light output is taken

from one of the DBR mirror surfaces. The comparison of an EEL and a VCSEL [24]

is shown in Fig. 1-2. For the VCSEL, the active layer is sandwiched between two

DBRs. The light oscillates perpendicular to the epitaxial layers and exits the top or

bottom mirror stack in a circular, low-diverging beam. Edge-emitters are made up of

cleaved bars diced from the wafers. The two cleaved facets act as mirrors. The light

oscillates along the epitaxial layers and exits through the coated cleaved facets in a

high-diverging elliptical beam. Selected parameters for typical directly modulated

EELs and VCSELs for data communication are given in Table 1-1 for comparison.

Table 1-2. Advantages of VCSELs compared to EELs and communication LEDs [26]

VCSELs vs. EELs VCSELs vs. LEDs

Low threshold current High modulation bandwidth

High efficiency at low power Focused output beam

Slowly divergent circular beam Narrow spectrum

Wafer-level testing, low cost Small operating current

Simplified mounting and packaging High output power

Two-dimensional arrays High power conversion efficiency

Compared to conventional EELs and light-emitting diodes (LEDs) for data com-

munications across optical fiber [25], VCSELs have many advantages as listed in

Table 1-2 [26]. To satisfy the requirements for optical interconnect applications,

VCSELs offer superior characteristics including [26]: 1) low threshold currents and

correspondingly small driving currents to produce optical output powers in the

milliwatt range, thus minimizing energy consumption and making the design of

an electronic driver circuit easier; 2) excellent modulation behavior for data rates

approaching 64 Gb/s [27]; 3) high power conversion efficiencies; 4) circular beam

profiles with small divergence angles; 5) a wide ambient temperature range that

enables uncooled operation; 6) the straightforward formation of homogeneous laser

arrays that is the key to compact space division multiplexed data transmission; 7)

on wafer-level device testing, yielding an enormous cost reduction; 8) the use of

mounting and packaging technology that is well known from light-emitting diode

production; and 9) very high reliability with projected lifetimes on the order of ten

million hours at room temperature.

6 Chapter 1 Introduction

1.2.2 High Bit-Rate VCSELs

Future supercomputers capable of operating at tens to 100s of exaflops will require

billions of optical interconnects and are predicted to require high bandwidth optical

interconnects operating at single-channel bit rates of at least 25 Gb/s before 2020

[28, 29]. Google Inc. stated in 2011 that 40 Gb/s would be the desired bandwidth for

their new generation datacenters [30]. Recently, 16 Gb/s Fibre Channel has begun

to replace the 8 Gb/s Fibre Channel lasers, and the next major speed milestone is

deployment at 25 Gb/s for the new Ethernet standard and at 28 Gb/s for the Fibre

Channel standard [12]. Many industrial companies, universities, research centers,

and institutes have focused their activity on the development of high bit-rate VCSELs

for data communication across standard 850 nm multimode optical fiber, and signifi-

cant progress has been made due to these intensive research efforts. In the following

an overview of the state-of-the-art high bit-rate GaAs-based VCSEL results is pre-

sented, including the wavelengths of 850, 980, and 1100 nm.

The wavelength 850 nm is the standard for local area network (LAN) and Fibre

Channel serial links. Unstrained GaAs QWs with AlGaAs barrier layers are com-

monly used for the active region of 850 nm VCSELs. The highest data rate achieved

with GaAs QWs is 30 Gb/s at a bias current of 8 mA using 6 µm oxide-aperture

diameter devices [36]. By adding indium to the GaAs active layers, compressive

strain is introduced to increase the differential QW gain [37]. 32 Gb/s error-free data

transmission (defined as a bit error ratio (BER) < 1 × 10−12) was achieved in 2009

[38]. The same year, our group at the Technische Universität Berlin reported the first

39 Gb/s error-free transmission and open eye diagram at 40 Gb/s [39]. Prof. Anders

Larsson’s group at Chamlers achieved 40 Gb/s error-free data transmission in 2011

[40]. In 2013, 57 Gb/s was achieved by reducing the optical cavity thickness to λ/2 to

increase the photon density at the QWs and by optimizing the cavity photon lifetime

[32]. By using similar 850 nm VCSELs with a bandwidth of ~26 GHz packaged in

a module with a SiGe-based driver integrated circuit that incorporates feed forward

equalization (FFE) and a custom-built highly sensitive and fast photoreceiver, error-

free operation at 64 Gb/s was demonstrated [27].

The 980 nm high-speed VCSELs typically employ strained InGaAs/GaAs QWs.

Compared with 850 nm VCSELs, 980 nm VCSELs typically have deeper QWs that

suppress the escape of non-equilibrium carriers and thus have improved temperature

stability. The operating voltage of 980 nm VCSELs is lower due to smaller energy

bandgaps, which is important for the low voltage complementary metal oxide

semiconductor (CMOS) drivers. In addition, the 980 nm VCSELs may be bottom-

emitting structures due to the transparency of the GaAs substrate at 980 nm. But the

1.2 VCSELs for Short-Reach Optical Communication 7

absorption loss is higher at 980 nm because the free carrier absorption coefficient

of the AlGaAs material increases with the wavelength. In 2007, error-free data

transmission at 35 Gb/s was achieved [41] using a 3 µm diameter VCSEL with a

bias current of 4.4 mA. This VCSEL employed a tapered oxide aperture, multiple

deep oxide layers, and a spatially modulated doping profile in the DBRs to lower the

capacitance and the resistance, leading to a larger than 20 GHz maximum −3 dB

modulation bandwidth. Our group achieved 44 Gb/s error-free operation at 25 °C in

2011 [42, 43] , and 42 Gb/s error-free operation with a 1.5λ-thick optical cavity active

region [34]. Our most recent generation of 0.5λ-thick optical cavity 980 nm VCSELs

achieve a −3 dB modulation bandwidth of 23.9 GHz and demonstrate error-free

operation at 50 Gb/s at 25 °C [33].

For VCSELs emitting at 1100 nm their energy bandgaps are even smaller thus

their operating voltages are lower than for the 980 nm VCSELs. However, the

1100 nm VCSELs typically have higher free carrier losses as compared to VCSELs

emitting at shorter wavelengths. The NEC System Device Research Laboratory dem-

onstrated 1100 nm oxide-confined VCSELs operating at bit rates of up to 25 Gb/s at

25 °C in 2006 [44], and up to 30 Gb/s [36] and 40 Gb/s [37] both in 2007 by using a

buried tunnel junction [45].

Table 1-3. Selected state-of-the-art optical data transmission parameters of VCSELs

at room temperature

Affiliation UIUC

[31]

CHT

[32]

TUB

[33]

TUB

[34]

NEC

[35]

Wavelength (nm) 850 850 980 980 1100

Bit Rate (Gb/s) 40 57 50 42 40

Oxide-Aper. Dia. (µm) 4 ~8 4.5 − 5 ~4 6

Current Density (kA·cm–2)51.7 25.86 ~50.3 43.77 17.68

Year of Publication 2014 2013 2014 2014 2007

1.2.3 High Operating Temperature VCSELs

Optical communications provide a reliable means of transferring the large volumes

of data at the ultra-high bit-rates needed in data centers. Using VCSELs for data

communication requires operation in an environmental temperature of up to 85 °C

or higher, making reliable operation at high temperature an essential element for the

development of optical components. Considering cost, energy consumption, and

long-term system sustainability and reliability, optical interconnects ideally must

8 Chapter 1 Introduction

be able to operate without cooling at up to 85 °C or higher temperatures with low

sensitivity to temperature variations. The stable performance of VCSELs against

temperature variation is an important criterion of a high performance light source

in optical interconnect applications.

Table 1-4. Selected state-of-the-art optical data transmission performance of

VCSELs at high temperatures

Affiliation NEC

[46]

TUB

[47]

TUB

[48]

TUB

[50]

TUB

[33]

Wavelength (nm) 1100 980 980 980 980

Temperature (°C) 100 85 120 85 85

Bit Rate (Gb/s) 25 25 25 38 46

Year of Publication 2010 2010 2012 2014 2014

In 2001, data transmission at 12.5 Gb/s was measured at temperatures up to 100 °C

using an 850 nm VCSEL [51]. In 2007, 20 Gb/s eye diagrams at 70 °C was reported

by Agilent [52]. In 2008, our group reported 20 Gb/s error-free operation between 0

and 120 °C without any adjustment of the driving conditions using 980 nm VCSELs

[53]. In 2010, the NEC System Device Research Laboratories reported 25 Gb/s error-

free operation at 100 °C [46]. These device show extremely long lifetime of about

10000 hours MTTF (mean time to failure) under an ambient temperature of 150 °C

and a current density of about 19 kA/cm2. Also in 2010, our group reported error-free

data transmission at 980 nm at 25 Gb/s at temperature of 25 and 85 °C without any

change of working point and modulation condition [47]. In 2012, our group achieved

40, 38, 25 and 12.5 Gb/s at temperatures as high as 75, 85, 120 and 155 °C, respec-

tively, with short 0.5λ-thick optical cavity 980 nm VCSELs [48, 54]. The Chalmers

University of Technology group reported the first 40 Gb/s 850 nm VCSELs operating

at up to 85 °C in 2013 [49]. The results were achieved at a modulation bandwidth

of 27 GHz at 25 °C and at 21 GHz at 85 °C. In this dissertation, error-free data

transmission at 38 Gb/s at 25, 45, 65 and 85 °C without any change of working point

and modulation condition are achieved by using 1.5λ-thick optical cavity 980 nm

VCSELs. Our new generation short 0.5λ-thick cavity 980 nm VCSELs can achieve

46 Gb/s error-free data transmission at 85 °C with a record high −3 dB modulation

bandwidth of 23 GHz [33].

1.2 VCSELs for Short-Reach Optical Communication 9

1.2.4 Energy-Efficient VCSELs

VCSELs will continue to be a key part of the optical interconnects market at 28 Gb/s

and beyond [12]. Another key technology now under development in optical com-

munications is Silicon Photonics. For VCSELs and multimode fiber to continue to

compete favorably with Silicon Photonics, it is important to continue to focus on

lower energy consumption, low cost multimode optical interconnections, and low

cost packaging. The energy consumption of VCSELs is typically 2 to 10 times lower

than Silicon Photonics when the total energy consumption of the entire transmit-

ter chain is included [12]. A complete energy consumption accounting calculated

by Finisar reveals the “value proposition” for using VCSELs in the data center for

short reach applications [12]. The very rapid growth of global Internet traffic over

the past two decades and the perpetually increasing demand for raw computational

power has led to an exponential increase of energy consumption in data centers

and supercomputers [55]. The efforts for “green photonics” set rigorous demands

on achieving the smallest possible energy consumption. It is thus vitally important

to optimize the performance and energy efficiency of high-speed VCSELs for use

in optical interconnects and as the low-cost and integrated light sources for Silicon

Photonics and on-chip OI systems. According to estimates and predictions based on

the International Technology Roadmap for Semiconductors, laser diodes for optical

interconnects must operate with a maximum energy dissipation of ~100 femtojoules

(fJ) per bit by circa 2015 [56].

To compare the energy efficiency of different VCSEL designs, the electrical

energy-to-data ratio (EDR) and the dissipated heat-to-bit rate ratio (HBR) are defined

as [57]:

EDR P

= (fJ/bit) (1.1a)

HBR P

P P

diss el opt

= =

−

(fJ/bit) (1.1b)

where Pel = I ∙ V is the input CW electrical power, I is the bias current, V is the

operating voltage of the VCSEL, Pdiss = I ∙ V − Popt is the dissipated power, Popt is the

optical output power, and BR is the bit rate. Table 1-5 summarizes the state-of-the-

art high-speed 850 nm and 980 nm VCSELs performance. For 850 nm VCSELs, the

best reported energy efficiency is 108 fJ/bit at room temperature for 40 Gb/s error-

free data transmission [58]. For high temperature operation, 477 fJ/bit is needed for

40 Gb/s error-free data transmission using 850 nm VCSEL [49]. For 980 nm VCSELs,

the best previously published power dissipation is 233 fJ/bit for 35 Gb/s error-free

10 Chapter 1 Introduction

operation at 25 °C [54]. In this dissertation record low 139 fJ/bit [34] and 177 fJ/bit

[50] for 35 and 38 Gb/s error-free data transmission at 85 °C with a ~3 µm oxide-

aperture diameter VCSEL are reported. To date, these VCSELs are still the most

energy efficient VCSELs operating at 85 °C at any wavelength. At room temperature,

only 145, 147, and 217 fJ/bit of dissipated energy are needed for 35, 38 and 42 Gb/s

error-free data transmission with a ~3 µm oxide aperture diameter VCSEL [59],

which are record low energy dissipations for 980 nm VCSELs.

Table 1-5. Selected state-of-the-art optical data transmission with 850 nm and

980 nm VCSELs

Affiliation UIUC

[31]

TUB

[54]

TUB

[59]

CHT

[49]

TUB

[50]

TUB

[34]

Wavelength (nm) 850 980 980 850 980 980

Temperature (°C) 20 25 25 85 85 85

Bit Rate (Gb/s) 40 35 35 40 38 35

EDR (fJ/bit)1~435 287 178 ~578 230 168

HBR (fJ/bit)2~395 233 145 ~477 177 139

Aperture dia. (µm) 4 4 ~3 7 ~4 ~3

Current Density (kAcm–2) 51.7 32 38.2 25 28.6 38.2

1EDR: electrical energy-to-bit rate ratio. 2HBR: heat-to-bit rate ratio.

1.3 More Applications of VCSELs

VCSELs are used in many different consumer products including in laser printers,

computer mice, as sources for optical sensors, and more as depicted in Fig. 1-3 [23,

60]. One mass application of VCSELs besides optical interconnects is their use in

optical mice and sensing. VCSELs offer a better performance than LEDs as illumina-

tion sources for sensing applications [61]. The market of lasers for computer mice

and optical finger navigation devices, like smartphones exceeds the data communica-

tion laser market in numbers and is the second largest laser market. VCSELs are ideal

illumination source for optical mice [61], because the emission profiles of the VCSEL

is circular and maybe designed for a small divergence and fixed polarization, which

reduces the requirements on the optics in the illumination path and allows a simple

system. Additionally, VCSELs offer very low threshold currents and low energy

consumption, which is especially important for battery powered devices. Single-

mode VCSEL arrays are used as a light source for laser printing systems [62 – 64].

The world’s first VCSEL-based electrophotographic printer was launched utilizing a

780 nm single-mode 8×4 VCSEL array. This printer features 2400 dots per inch (dpi)

1.4 Dissertation Overview 11

resolution, which is still the highest level in the industry [65]. The laser wavelength

was chosen to be 780 nm where the organic photoconductor materials have a

maximum sensitivity. Each VCSEL must emit a Gaussian beam profile and operate

in a single transverse mode [66]. Also, each VCSEL must emit sufficient output

power to produce a latent image at the photoconductor [62]. The concept of VCSELs

has also been expanded into the nanophotonics and photonic crystals fields. The ultra

parallel and ultrahigh-speed photonics based upon sophisticated VCSELs including

MEMS and integrated optics will begin a new era of VCSEL research [23].

1.4 Dissertation Overview

This dissertation consists of eight chapters. The first chapter is an overview of the

VCSEL concept, history, and applications, especially the application for short-reach

optical communication, including the requirements and the state-of-the-art of

VCSELs. The second chapter includes the necessary theoretical background and

design considerations, including active region design, DBR design, and suitable

QW gain-to-etalon wavelength offset design, and careful thermal design. The third

chapter elucidates the device structure studied in this dissertation in detail, and

the simulated optical, electrical, and gain properties. In addition, the fabrication

techniques, main measurements, and evaluation methods are presented. The fourth

chapter presents a detailed temperature-dependent and oxide-aperture diameter-de-

pendent impedance analysis. The impedance study provides a better understanding

Fig. 1-3. Example application areas of VCSELs [23, 60].

PrintingDatacom

Display Interconnects

optical mouse

The Optoelectronics Co. Ltd.

Novalux Inc. IBM Inc. / Agilent Inc.

Sensing

VCSEL Photonics

Philips

Active Optical cables

12 Chapter 1 Introduction

of the data bit rate limitations and helps us to understand what improvements should

and can be made for the next generation 980 nm VCSEL device design. In the fifth

chapter, noise characteristics are investigated. These VCSELs can satisfy the require-

ments of bandwidth and relative intensity noise (RIN) of the 32 GFC Fibre Channel

standard. In the sixth chapter, highly temperature-stable VCSELs are experimentally

demonstrated. Systematic experimental characterization of 980 nm VCSELs are

presented, including static measurements, small-signal analysis, and data transmis-

sion experiments. In the seventh chapter, 980 nm VCSELs that can simultaneously

achieve temperature-stable, energy-efficient, and high bit-rate operation are ex-

perimentally demonstrated for the first time. From the experimental results, 980 nm

VCSELs with ~3 to ~4 µm oxide-aperture diameter have small threshold currents,

large mode spacing, and large D-factors at room temperature and at high tempera-

tures. These results lead to low energy dissipation, and to temperature-stable and

high bit-rate operation. Finally, in chapter eight, the main results are summarized and

an outlook on future work based on the results of this dissertation is given.

Chapter 2

Design and Modeling of 980 nm VCSELs

A 980 nm quantum well (QW) VCSEL consists of an optical cavity active region

surrounded by a top DBR and a bottom DBR, all epitaxially grown upon a GaAs

substrate. A proper VCSEL epitaxial design is critical for the production of high

performance devices for both commercial applications and for research. A theoreti-

cal design study of VCSEL structures is necessary to establish a first understanding

of the design trade-offs, the expected device performance, and to set the goals of

the research work. The active region simulation can provide an estimate of the

required QW material composition and thickness, plus an understanding of the ef-

fective layer-by-layer QW spatial strain, the overall strain of the composite QW and

barrier system, the theoretical differential gain, and the emission wavelength for a

given set of materials. Via an AlxGa1–xAs/AlyGa1–yAs DBR modeling and simulation

analysis, the number of DBR periods required for a given top and bottom DBR power

reflectance can be determined, and also the impact of various compositional DBR

hetero-interfacial grading and doping schemes on DBR resistance and free carrier

absorption losses can be studied. One or more AlxGa1–xOy aperture layers of various

thicknesses and various AlAs mole fractions x may furthermore be added to reduce

mesa capacitance and thus increase the parasitic cutoff frequency. Many other at-

tributes of the VCSEL may be investigated theoretically prior to planning a series of

experiments with device structures grown by an epitaxial growth technique includ-

ing the trade-offs between the –3 dB modulation bandwidth, the photon lifetime, and

the QW gain-to-etalon wavelength offset.

In this Chapter, important aspects of 980 nm VCSEL designs are presented

via a theoretical framework. In Section 2.1 the basic theoretical background is

reviewed, including static VCSEL equations relating cavity gain versus losses, and

the theoretical dynamic properties of VCSELs as modeled by the standard laser

diode rate equations. Section 2.2 presents a numerical study of strained InGaAs QW

active regions. Next in Section 2.3 important aspects of DBR design are examined,

14 Chapter 2 Design and Modeling of 980 nm VCSELs

including optical calculations of the power reflectance of multilayer semiconduc-

tor DBRs, and the electrical properties of the same structure via a description of

heterostructure energy band offsets, DBR heterointerface grading, and DBR doping

schemes. In Section 2.4 the impact of QW gain-to-etalon wavelength offset are in-

vestigated, as it relates to the temperature performance of 980 nm VCSELs. Finally,

in Section 2.5 the theoretical concepts useful for a study of the thermal performance

of 980 nm VCSELs are presented.

2.1 Theoretical Background

2.1.1 Static VCSEL Properties

The lasing threshold is the lowest excitation level at which a laser’s output is domi-

nated by stimulated emission. If the gain is high enough to compensate the optical

losses due to the mirrors, absorption, and scattering, the transparency condition is

reached, and the laser will emit coherent light through the output mirror. The lasing

condition of a one-dimensional (1D) Fabry-Pérot cavity with cavity length of L (cm)

and for simplicity considering only propagating plane waves parallel to the flat op-

posing mirrors can be expressed as:

1 2 exp[( )2 ] 1

R R g L− α =

(2.1)

where R1 and R2 (both unitless and ranging from 0.0 to 1.0) are the mirror power

reflectance, g (cm

–1

) is the gain and is taken as acting uniformly over the entire cavity

length L, and α

(cm

–1

) is the internal loss. The optical loss is typically nearly constant

especially close to the lasing threshold. The threshold gain gth (cm–1) condition can

be rearranged under this assumption as:

1 2

1 1

ln( )

th i

gLR R

= +

(cm–1) (2.2)

The 1D VCSEL cavity can be treated as an effective Fabry-Pérot resonator by using

an effective resonator length Leff, which is composed of the cavity length Lc plus the

effective penetration depths of the resonant optical field intensity into the top and

the bottom DBRs, given by leff,t and leff,b, respectively. The penetration depth into a

DBR is derived from a simplified model of the given DBR mirror. A DBR is replaced

by a thickness of optical cavity material (leff) with an effective (average) refractive

2.1 Theoretical Background 15

index <n> for the multiple-layer DBR that accounts for the linear phase-shift of the

optical field intensity that travels over the distance leff in the given DBR and a fixed

discrete mirror with a power reflectance equal to the power reflectance of the actual

DBR at the resonance wavelength [67, 68]. The threshold condition for the VCSEL

cavity can then be expressed as:

( )

th i m i t b

eff

g R R

α α α

Γ = + = − (2.3)

where

, ,eff eff t eff b

L L l l= + +

and

Bragg

eff

Bragg

≈∆

(2.4)

where Rt and Rb are top- and bottom-mirror power reflectance, λBragg is the center

wavelength of the Bragg-mirror, and ∆nBragg is the refractive index contrast. For a

VCSEL cavity, the cavity gain region does not extend over the full cavity length Leff

but is enclosed by larger bandgap layers to form typically a double-heterostructure.

In Equation (2.3) the confinement factor Γ (unitless) is introduced to obtain the

average gain in the cavity. The terms Γ

and Γ

are the traditional lateral confinement

factors (along the x- and y-axis directions), which are self-aligned by the VCSEL’s

aperture and therefore can be assumed to be unity [67]. The terms can be combined

as a product term Γx · Γy = Γxy ≈ 1.0. A final term Γz is the longitudinal (along the

z-axis for a VCSEL) confinement factor.

(z)

act

eff

xy z z

E dz

Γ = Γ Γ ≈ Γ ≡ ∫

∫

(2.5)

where Lact is the total thickness of the active layers (i.e. the QWs), and |E(z)|2 is the

electrical filed intensity. Once the laser reaches lasing threshold, the carrier density

N and gain g may be assumed to be fixed to their threshold values Nth and gth [69].

Under this approximation the threshold current density J

(A cm

−2

) and the threshold

current Ith (A) can be expressed as [26]:

act

th th

J N

ητ

and

th a th

I A J=

(2.6)

where q (1.602 × 10-19 C) is the electronic charge, τ (ps) is the carrier lifetime, ηi (unit-

less) is the injection efficiency, and Aa (cm2) is the active area. Above the threshold

current, the optical output power P (mW) from the mirrors increases linearly with

driving current I [69]:

( )

d th

P I I

= −

(2.7)

16 Chapter 2 Design and Modeling of 980 nm VCSELs

where η

(unitless) is the differential quantum efficiency, which can be obtained from

a measurement of the slope of the output power-current (PI) characteristic. The ηd

defined as the number of photons out per electron [69], contains the current injec-

tion efficiency ηi and the photonic quantum efficiency ηp. The term ηp is the fraction

of the generated coherent light that is available for top (or bottom) emission, which

determined by the ratio of τp (s) and τp,m (s):

1ln( )

1ln(

)

p eff

d i p i i i

T B

p m i m m i t b

eff

R R

h h h h h h

ta a a a

= = » =

+ + -

(2.8)

where τp is the photon lifetime which is related to the internal cavity loss rate αi(rate)

(s–1), and τp,m is the photon lifetime which is related to the coupling mirror loss rate

αm(rate) (s–1) (in this example the top (T) DBR mirror is used as the coupling mirror),

as expressed [26]:

(rate) (rate) (rate)

pT B

i m m

τα α α

≈+ + (s) and

(rate)

p m T

τα

≈

(s) (2.9)

Equation (2.9) is for top-emitting VCSELs. For bottom-emitting VCSELs, αm(rate)

for the top mirror should be replaced by the bottom (B) mirror loss rate. Note that

α(rate) = <vg> · α, thus relating a power loss rate to a power loss per distance. The wall

plug efficiency is defined as the ratio of coherent light output power and electrical

input power, and can be expressed as:

WPE

I V

=⋅

(unitless) (2.10)

2.1.2 Dynamic VCSEL Properties

Rate equations are used to analyze the intrinsic dynamic behavior of semiconductor

lasers. The single mode equations that describe the supply and the loss of the carriers

and photons within the active region [69] are:

g p

dN N gN

dt qV

ην

= − −

(2.11a)

p p

g p sp sp

dN N

gN R

ν β τ

= Γ + Γ −

(2.11b)

2.1 Theoretical Background 17

where N (cm–3) is the carrier density, Np (cm–3) is the photon density, ηi is the injec-

tion efficiency or internal quantum efficiency, I (mA) is the injection current, q is the

electronic charge, Va (cm3) is the active region volume, τ (s) is the carrier lifetime, vg

is the group velocity of the lasing mode, g is the gain, Γ is the optical confinement

factor, βsp is the spontaneous emission factor, Rsp is the spontaneous recombination

rate, and τp is the photon lifetime. Equation (2.11a) is for the carrier density in the

active region, and (2.11b) is for the photon density of the lasing mode in the cavity.

Interestingly the single mode rate equations can be used to describe and understand

the intrinsic dynamic modulation behavior of multimode VCSELs, because the

dynamic behavior of index-guided multimode VCSELs with highly overlapping

transverse intensity fields have approximately uniform transverse carrier and photon

densities and thus exhibit a single relaxation resonance frequency very similar to a

single mode VCSELs [70–72]. The small-signal response can be obtained by super-

imposing a small sinusoidal modulating current on the bias current. The modulation

transfer function Hi(ω) is defined as [69, 73]:

2 2

( ) R

ωω ω ωγ

≡− + (2.12)

where ωR = 2π fR is the relaxation resonance angular frequency, and γ (s-1) is the

damping factor. This transfer function is in the form of a second-order low pass filter

with a damped resonance peak [69, 73]. The relaxation resonance frequency is the

natural oscillation frequency between the carriers and photons in the laser cavity and

can be approximately expressed as [69]:

( ) ( )

2 2 .

i g

R th

vg N

f I I

π π χ

Γ∂ ∂

= = −

(2.13)

where ∂g/∂N (cm2) is the differential gain, Ith (mA) is the threshold current, and χ

(unitless) is the transport factor. The D-factor [74] characterizes the dependence of

the relaxation resonance frequency on the driving current, and can be expressed as:

I I

q V

g N

i g

−

( )

=⋅⋅∂ ∂

( )

(GHz/(mA1/2)) (2.14)

The modulation current efficiency factor (MCEF) is another commonly used figure-

of-merit to evaluate and compare the overall high-speed performance of one or more

VCSELs, as given in equation (2.15) [75].

( )

3dB

MCEF

I I

−

(2.15)

18 Chapter 2 Design and Modeling of 980 nm VCSELs

where f–3dB is the –3 dB bandwidth of the modulation response, which is defined as

the frequency when:

2 2

( ) / (0) 1/ 2

H f H

−= (2.16)

The damping represents the rate of energy loss in the cavity, which effectively

reduces the strength of the resonance peak. The damping γ (s-1) increases linearly

with the square of fr. The proportionality is the K-factor

K f

γ γ

= ⋅ +

( )

Kv g N

ε χ

π τ

 

⋅

= +

 

∂ ∂

 

(s-1) (2.17)

The bandwidth of a VCSEL is also determined by the extrinsic electrical parasitic

response besides the intrinsic laser response. The effects of parasitic equivalent

circuit elements can be approximated by a single-pole low-pass filter function with

a cut-off frequency fP. Then the overall small signal modulation response of a laser

diode may be approximated by a three-pole transfer function, by introducing the ad-

ditional effects due to the parasitic elements into the intrinsic laser transfer function.

2 2

( ) ( ) ( )

i par

H f H f H f f

f f j f jf

= ⋅ = ⋅

   

− + ⋅ ⋅ + ⋅

   

   

(2.18)

According to equation (2.18) the small signal modulation response and thus the high

speed physical properties of a laser diode can be described using three parameters:

the relaxation resonance frequency fR, the damping factor γ, and the parasitic cut-off

frequency fP. Accordingly, there are three physical limits that restrict speed perfor-

mance of VCSELs: thermal limits, damping limits, and parasitic limits. The general

approach toward increasing the speed of a laser diode is to increase fR by increasing

the differential gain and by reducing the active region volume. The reduction of

mode volume can be accomplished by reducing the oxide-aperture diameter or by

reducing the penetration depth of the optical field into the VCSEL mirrors. Based

on these methods to overcome the limitation of the fR, several optimization consid-

erations of high-speed VCSELs are as follows:

reduction of electrical parasitics by minimizing the resistance and capacitance;

2. optimization of the active layer to provide a high differential gain;

3. improvement of thermal conductivity and a reduction of heat generation;

4. improvement of the optical confinement; and

5. optimization of the photon lifetime (i.e. the trade-off between the relaxation

resonance frequency and the damping).

2.2 Active Region Design 19

2.2 Active Region Design

High bit-rate and temperature-stable VCSELs are required for short-reach (up

to about 300 m) optical data transmission. As discussed in section 2.1.2, a larger

differential gain for the QWs in the active region generally leads to a higher modula-

tion bandwidth. In addition, an increase of the relaxation resonance frequency can

be obtained with a larger differential gain, which in turn enables a higher –3 dB

modulation bandwidth to be reached. In this section, a detailed numerical study is

presented for selecting QW and barrier layer designs that can satisfy the require-

ments for the active regions of 980 nm VCSELs.

Table 2-1. Parameter values of selected binary semiconductors GaAs, InAs, and GaP

at room temperature [78]

Parameter GaAs InAs GaP

Lattice constant a0 (Å) 5.65325 6.0583 5.4505

Elastic stiffness constant C11 (1011dyn cm−2) 11.879 8.329 14.05

Elastic stiffness constant C12 (1011dyn cm−2) 5.376 4.526 6.203

Luttinger parameter γ1 (unitless) 6.98 20.0 4.05

Luttinger parameter γ2 (unitless) 2.06 8.5 0.49

Luttinger parameter γ3 (unitless) 2.93 9.2 1.25

Hydrostatic deformation potential a (eV) –8.33 –6.08 –9.9

Shear deformation potential b (eV) –2.0 –1.8 –1.6

2.2.1 Critical Layer Thickness

For the epitaxial growth of lattice mismatch material, the theoretical maximum

thickness for an epitaxial layer should be below a certain critical layer thickness in

order for this layer not to experience misfit dislocations. The dislocations form at

the interface between the strained layer and the lattice-matched layer or layers (the

lattice-matched layer or layers are taken to be infinitely thick). The critical layer

thickness h

(Å) can be calculated for a zinc-blende III-V semiconductor by using the

standard Matthews-Blakeslee mechanical equilibrium model as [76]

1 0.25 (ln 1)

epi c

epi

hv a

fk p

= +

(2.19)

20 Chapter 2 Design and Modeling of 980 nm VCSELs

where aepi is the natural relaxed (unstrained) lattice constant of the epitaxial layer, asub

is the lattice constant of the substrate layer. f = (a

epi

– a

sub

) / a

epi

is the misfit strain, and

v (unitless) is the Poisson ratio, defined as v = C12 / (C11 + C12), where C11 and C12 are

the elastic stiffness constants. The term κ is a constant with the value of 1, 2, and 4

for a superlattice structure, a single QW surrounded on both sides by infinitely-thick

lattice-matched layers, and a single strained layer on an infinitely-thick substrate,

respectively [76]. Linear interpolation [77] from the binary material endpoints are

used to obtain the basic parameters for ternary compound semiconductor materials.

In Table 2-1, useful parameters of relevant binary semiconductors are shown [78].

2.2.2 Compressively-strained InGaAs QWs

Compressively-strained InGaAs QWs are commonly used for the active region of

980 nm VCSELs, and GaAs and GaAsP are two candidate barrier materials. The

compressive strain of InGaAs for different indium compositions and the tensile

strain of GaAsP grown on GaAs with different phosphorus compositions are show

in Fig. 2-1(a), which shows the strain increase with the increase of the compositions

of indium and phosphorus. The critical layer thickness hc for a single pseudomorphic

InxGa1–xAs QW surrounded on both sides by infinitely-thick GaAs barrier layers, is

calculated with the mechanical equilibrium model [76] in Equation (2.26). The result

is shown in Fig. 2-1(b). These values should not be exceeded in order to prevent the

formation of misfit dislocations. Multiple (usually five QWs) compressively-strained

InGaAs layers surrounded by GaAs barrier layers or tensile-strained GaAsP layers

are usually used for 980 nm VCSEL active regions, and thus the resultant critical

thickness of the QW and barrier layers in the active region is more complicated than

for a single strained epitaxial layer on an infinite substrate.

0.00 0.10 0.20 0.30

0.0

0.4

0.8

1.2

1.6

2.0

2.4

GaAs(1-x)Px

InxGa(1-x)As

compositon x

Compressive Strain (%)

(a)

0.0

0.4

0.8

1.2

1.6

2.0

Tensile Strain (%)

0.00 0.10 0.20 0.30

100

1000

Critical Thickness (Å)

compositoon x of In

(1-x)

(b)

Fig. 2-1. (a) Compressive-strain change with the indium-arsenide composition x of InxGa1–xAs layer

and tensile strain change with phosphorus composition x of GaAs1–xPx layer, both realtive to the lattice

constant of GaAs, and (b) calculated critical layer thickness hc change with indium composition x by

using κ = 2 in equation (2.26) according to the mechanical equilibrium model.

2.2 Active Region Design 21

The calculated emission wavelength (i.e. the energy transition between the n = 1

electron level and the n = 1 heavy-hole level) as a function of QW thickness for

In0.17Ga0.83As, In0.18Ga0.82As, and In0.19Ga0.81As single QWs surrounded on both sides

by GaAs barrier layers (for modeling purposes taken to be infinitely-thick) are shown

in Fig. 2-2(a). The emission wavelength increases toward longer wavelengths with

increasing QW thickness. The emission wavelengths are 955 and 970 nm for 5 and

9 nm-thick In0.17Ga0.83As/GaAs QWs, respectively. For QWs with the same thickness,

the expected peak emission wavelength increases with increasing indium content,

which is because the energy bandgap decreases with increasing indium content. For a

6 nm-thick QW, the emission wavelengths are 960, 967 and 974 nm for In0.17Ga0.83As,

In0.18Ga0.82As, In0.19Ga0.81As QWs, respectively. This means the thickness of QWs

should be decreased to maintain a certain constant emission wavelength when

increasing the indium composition x in the InxGa1–xAs QWs. For strain compensa-

tion of the InxGa1–xAs QW by using tensively strained GaAs1–xPx barrier layers,

different phosphorus content x of the GaAs1–xPx barrier layers are considered in the

calculations to determine the influence on the emission wavelengths. Calculated

results for In0.21Ga0.79As/GaAs1–xPx and In0.20Ga0.80As/GaAs1−xPx QW/barrier systems

are shown in Fig. 2-2(b) and 2-2(c). For a fixed indium content and thickness in the

QWs, the emission wavelength shifts to shorter wavelengths with an increase of the

phosphorus content x. When the tensively strained GaAs1–xPx barrier layers are fixed

in composition and taken to be infinitely thick, the emission wavelength increases

with an increase of the thickness of InGaAs QWs. The final emission wavelength of

a QW and barrier layers depends on the net results of three impact factors, which

are the indium content, the thickness of the QW, and the particular barrier material

(i.e. the resultant conduction and valence band offsets, effective masses, QW-barrier

Wavelength(nm)

QW thickness (nm)

4 6 8 10

0.94

0.95

0.96

0.97

0.98

0.99

0.17

0.18

0.19

(a)

Wavelength(nm)

GaP mole fraction in GaAsP

0.08 0.16 0.24

0.95

0.96

0.97

0.98

3.8 nm

4.2 nm

5.0 nm

(b)

Wavelength(nm)

GaP mole fraction in GaAsP

0.08 0.16 0.24 0.32

0.94

0.95

0.96

0.97

0.98

4.0 nm

5.0 nm

6.0 nm

(c)

In0.20Ga0.80As/GaAs1-xPx

In0.21Ga0.79As/GaAs1-xPx

InxGa1-xAs/GaAs

Fig. 2-2. Peak emission wavelengths versus the QW thickness for (a) In0.17Ga0.83As/GaAs, In0.18Ga0.82As/

GaAs, and In0.19Ga0.81As/GaAs QW/barrier materials, and the peak emission wavelengths as a func-

tion of the GaP content for (b) In0.21Ga0.79As/GaAs(1–x)Px and (c) In0.20Ga0.80As/GaAs1–xPx QW/barrier

materials.

22 Chapter 2 Design and Modeling of 980 nm VCSELs

interface sharpness, etc.). Additionally, the use of coupled multiple strained QWs and

barriers further complicates the calculation of emission wavelength, net gain, overall

average strain of the QW/barrier active region, and more.

2.2.2.1 The Influence of Strain on QWs

As already mentioned, the indium concentration of compressively strained InGaAs

QWs surrounded by GaAs barrier layer can be varied to reach certain emission

wavelengths. A more detailed study of the effects of compressive strain on the gain

properties of InGaAs QWs are conducted to determine the change of the gain peak

wavelength, and transparency carrier density as a function of strain. Five InxGa1–xAs

QWs are investigate here, including In0.17Ga0.83As, In0.18Ga0.82 As, In0.19Ga0.81As,

In0.20Ga0.80As, and In0.21Ga0.79As, each surrounded by infinitely-thick GaAs barrier

layers. These compressively-strained QWs lattice-matched to GaAs have corre-

sponding compressive strains of 1.20, 1.27, 1.34, 1.41 and 1.48 %, respectively. The

QWs used in the following study have the same 6 nm thickness and same GaAs

barrier layers. The band alignment diagrams of the InxGa1–xAs/GaAs QWs are

calculated using the model-solid theory [79, 80]. This theory may be used to predict

reliable values for the experimentally observed energy band lineups in a wide variety

of test cases and can be used to explore which combinations and configurations of

strained and unstrained epitaxial materials layers will lead to the desired electronic

properties for an active QW gain region as used in a semiconductor laser diode. The

principal feature of the model-solid theory consists of assuming the alignment of

band structure on an absolute energy scale. This puts all calculated energies on an

absolute energy scale, and allows us to derive the energy band lineups by simply

subtracting values for individual semiconductors. For the real-space energy band

diagrams plotted in Fig. 2-3, the In0.21GaAs/GaAs QW/barrier system has the largest

conduction and valence band offsets, which is beneficial for hole and electron con-

finement [81]. Note that in Fig. 2-3 there are separate band offsets for the heavy-holes

In0.17Ga0.83As

0 5 10 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z (nm)

(a)

EHH

ELH

In0.18Ga0.82As

0 5 10 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z (nm)

ELH

EHH

(b)

In0.19Ga0.81As

0 5 10

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z (nm)

ELH

EHH

(c)

In0.20Ga0.80As

05 10 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z (nm)

ELH

EHH

(d)

In0.21Ga0.79As

0 5 10 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z (nm)

ELH

EHH

(e)

Fig. 2-3. Real-space charge neutral energy-band diagrams showing the conduction and valence bands

for (a) In0.17Ga0.83As/GaAs; (b) In0.18Ga0.82As/GaAs; (c) In0.19Ga0.81As/GaAs; (d) In0.20Ga0.80As/GaAs; and

(e) In0.21Ga0.79As/GaAs QWs.

2.2 Active Region Design 23

(solid lines) and the light holes (dashed lines). The valence subbands are calculated

using the k•p theory [82, 83]. An advanced three-dimensional simulator Crosslight

(PICS3D) [84] is used for the calculations in this work, which self-consistently com-

bines quantum well band structure calculations by using the k•p theory, radiative

and nonradiative carrier recombination, carrier drift and diffusion, and optical mode

computation. Based on the k•p theory, the valence subbands, optical gain spectra,

transparency carrier densities, and maximum differential gain for the InGaAs QW

with different compressive strains are calculated. The valence subbands for the

InxGa1–xAs/GaAs QWs are shown in Fig. 2-4. The QWs with higher strain (increasing

indium) have a larger energy separation between the first heavy hole HH1 and first

light hole LH1 subband at the Γ point (Wave Vector = 0). This leaves more carriers

for the C1-HH1 (conduction band n = 1 quantized electron energy level to heavy-hole

n = 1 quantized energy level) transitions to improve the material gain, as shown in

Fig. 2-5(a).

The gain spectra are calculated at a fixed carrier density of 3 × 1018 cm–3 for trans-

verse-electric (TE) polarization at 300 K. The gain peak shifts to longer wavelengths

as the strain in the QW increases (thus as the amount of indium increases). Fig. 2-5(b)

In0.20Ga0.80AsIn0.19Ga0.81AsIn0.18Ga0.82AsIn0.17Ga0.83As In0.21Ga0.79As

0.00 0.03 0.06

-0.21

-0.14

-0.07

0.00

HH3

LH1

HH2

HH1

Energy(eV)

Wave Vector

(a)

0.00 0.03 0.06

-0.21

-0.14

-0.07

0.00

HH3

LH1

HH2

HH1

Energy(eV)

Wave Vector

(b)

0.00 0.03 0.06

-0.21

-0.14

-0.07

0.00

LH1

HH2

HH1

Energy(eV)

Wave Vector

(c)

HH3

0.00 0.03 0.06

-0.21

-0.14

-0.07

0.00

LH1

HH2

HH1

Energy(eV)

Wave Vector

(d)

HH3

0.00 0.03 0.06

-0.21

-0.14

-0.07

0.00

LH1

HH2

HH1

Energy(eV)

Wave Vector

HH3

(e)

Fig. 2-4. K-space dispersion of the valence heavy-hole and light-hole subbands for (a) In0.17Ga0.83As/

GaAs; (b) In0.18Ga0.82As/GaAs; (c) In0.19Ga0.81As/GaAs; (d) In0.20Ga0.80As/GaAs; and (e) In0.21Ga0.79As/

GaAs QWs with the hole subband energies versus the in-plane (transverse) wave vector kt normalized

by 2π/a0 (Å–1), where a0 = 5.6533 Å is the lattice constant.

0.17 0.18 0.19 0.20 0.21

1.8

2.0

2.2

2.4

2.6

In composition x

Gain peak 103 (1/cm)

0.95

0.96

0.97

0.98

0.99

Gain peak

Well width=6nm

(a)

0.16 0.18 0.20 0.22

1.5

1.6

1.7

1.8

In composition x

Transparency carrier

density (1/cm3)

(c)

1 2 3 4 5 6 7

In0.17Ga0.83As

In0.18Ga0.82As

In0.19Ga0.81As

In0.20Ga0.80As

In0.21Ga0.79As

Gain peak 103 (1/cm)

Carrier density 1018 (1/cm3)

300K

TE mode

(b)

Wavelength(µm)

Fig. 2-5. (a) Gain peak and gain peak wavelength change with indium composition, (b) peak gain as

a function of carrier density, and (c) transparency carrier density versus the indium composition for

In0.17Ga0.83As/GaAs, In0.18Ga0.82As/GaAs, In0.19Ga0.81As/GaAs, In0.20Ga0.80As/GaAs, and In0.21Ga0.79As/

GaAs QWs, all at room temperature.

24 Chapter 2 Design and Modeling of 980 nm VCSELs

shows the calculated peak material gain as a function of carrier density for the single

InxGa1–xAs/GaAs QW/barrier structures at 300 K. The QWs with a larger strain have

smaller transparency carrier density due to the higher valence band curvature (as

in the E versus k diagrams in Fig. 2-4), which leads to a smaller joint densities of

states, making it easier to achieve a population inversion. The gain characteristics

of InxGa1–xAs QWs can be improved by adding a certain compressive strain (emis-

sion wavelength and critical thickness should be considered). Higher compressively

strained InxGa1–xAs QWs have a higher material gain and lower transparency carrier

concentration.

2.2.2.2 The Influence of QW Thickness

The QW thickness is another important factor that influences the peak emission

wavelength and gain properties. The QW thickness needed to maintain good

electron and hole wave-function overlap is from 2 to 10 nm. In addition, the QW

thickness cannot exceed the critical layer thickness limit hc to avoid misfit disloca-

tions. Fig. 2-6(a) shows the gain peak and the gain peak wavelength as a function

of the thickness of In0.19Ga0.81As QWs that are surrounded by GaAs barrier layers at

a fixed carrier density of 3 × 1018 cm–3 for TE polarization at 300 K. The emission

wavelength shifts to a longer wavelength with increasing the QW thickness. Also,

the material gain increases rapidly when QW thickness increases from 4 to 6 nm,

and achieves a maximum value at a QW thickness of 6.5 nm, then the emission

wavelength decreases with further increases of the QW thickness. When the QW

thickness is thin (less than ~6.5 nm), the L energy band valley will also fill with elec-

trons, which reduces the number of available carriers that can fill the Γ energy band

valley. As the Γ band valley has the larger impact on QW material gain, the reduced

number of available carriers for Γ energy band valley filling leads to a lower material

gain of the thinner In0.19Ga0.81As QWs. In contrast when the QW thickness further

increases (i.e. ~6.5 nm and thicker), the injected carrier confinement in the eakens

4 5 6 7 8 9 10

1.0

1.5

2.0

2.5

QW thickness (nm)

Gain peak 103 (1/cm)

0.95

0.96

0.97

0.98

0.99

0 1 2 3 4 5 6 7

5 nm

6 nm

6.5 nm

7 nm

5.0 6.0 7.0

1.4

1.6

1.8

2.0

QW thickness (nm)

Gain peak 103 (1/cm)

Carrier density 10

(1/cm

)

300K

TE mode

(b) (c)

In0.19Ga0.81As/GaAs

(a)

Transparency carrier

density (1/cm3)

Gain peak

Wavelength(µm)

Fig. 2-6. (a) Gain peak and gain peak emission wavelengths versus QW thickness, (b) peak gain

as a function of carrier density, and (c) transparency carrier density change with QW thickness for

In0.19Ga0.81As/GaAs QWs.

2.2 Active Region Design 25

and this leads to a decrease of material gain. Fig. 2-6(b) shows the peak material

gain of the TE mode as a function of carrier density for QW structures at 300 K. The

thicker QW has a smaller transparency carrier density. An In0.19Ga0.81As/GaAs QW

with a thickness of 6.5 nm has a large material gain and a small transparency carrier

density. For QWs with a fixed strain, an optimized QW thickness can be chosen to

achieve a high material gain and a low transparency carrier density.

2.2.2.3 Comparison of InGaAs QW designs for 980 nm VCSELs

Based on the analysis in the previous sections, the following QW structures are

chosen to analyze as candidates for the active region of 980 nm VCSELs, as listed in

Table 2-2. The indium concentration varies from 17 to 19 % for these InGaAs QWs

with GaAs barrier layers. The thicknesses of the QWs are chosen to set the gain peak

wavelength close to 965 nm. The resultant QW thicknesses do not exceed the critical

layer thickness limit.

Table 2-2 The QW structures chosen to analyze and compare

QW material Barrier

material

thickness

(nm)

Barrier

thickness

(nm)

In0.17Ga0.83As GaAs 7.0 3.5

In0.18Ga0.82As GaAs 5.6 4.7

In0.19Ga0.81As GaAs 4.5 5.6

The gain spectra of the candidate QWs at a fixed carrier density of 3 × 1018 cm–3

for TE polarization at 25 and 85 °C are plotted in Fig. 2-7. The In0.17Ga0.81As QW

(7.0 nm-thick) has a higher material gain than the other two structures at both 25

and 85 °C. This result is the combination of the effects of strain and QW thickness.

The effect of QW thickness is overwhelmed by the effect of strain. With increasing

indium content from 0.17 to 0.19, the material gain increases as the strain increases,

but in order to keep the same emission wavelength, the QW thickness is decreased

from 7.0 to 4.5 nm, leading to a decrease in material gain. Also, the QW peak gain

wavelengths shift into longer wavelength for all three studied QW structures, and

the peak material gain decreases when temperature increases from 25 to 85 °C. Thus,

both strain and layer thickness of the QWs are very important for high gain QWs, and

both influences should be considered. The In0.177Ga0.823As/GaAs QWs are used for the

active region of one of our 980 nm VCSEL designs [43, 54] , and achieved reasonable

performance both at room temperature and at high temperature.

26 Chapter 2 Design and Modeling of 980 nm VCSELs

2.2.3 Strain-Compensated InGaAs/GaAsP QWs

GaAs barrier layers [85, 86] are commonly used to surround the compressively

strained InGaAs QWs for the active region of GaAs-based 980 nm VCSELs. GaAsP

is another candidate barrier material [33, 47], where the GaAsP layers are in tensile

strain and serve to partially counter the compressive QW strain. In order to show

the difference, GaAs0.88P0.12 barrier layers with 0.43 % tensile strain and no-strain

GaAs barrier layers are chosen to surround the In0.21Ga0.79As QWs. The QW thick-

ness is chosen to be 4.2 nm, the barrier thickness is 6 nm, and thus the combined

single GaAs0.88P0.12/In0.21Ga0.79As/GaAs0.88P0.12 QW structure lattice-matched to GaAs

is below the critical layer thickness limit. The band alignment of In0.21Ga0.79As/

GaAs

0.88

0.12

and In

0.21

0.79

As/GaAs QWs are calculated using the model-solid theory

[79], and the results are shown in Fig. 2-8. The use of GaAsP barrier layers results

in a better band alignment of the strain-compensated QWs compared to standard

In0.21Ga0.79As/GaAs QWs. For In0.21Ga0.79As/GaAs the conduction band offset is

0.15 eV. The conduction band offset of In0.21Ga0.79As/GaAs0.12P0.88 QWs is 0.18 eV,

20 % larger than the In0.21Ga0.79As/GaAs QWs. An increased conduction band offset

and valence band offset is beneficial for the electron and hole confinement [81] and

also can reduce the thermal escape of carriers [88]. VCSELs with strain compensated

In0.21Ga0.79As/GaAs0.88P0.12 QWs will have less temperature sensitivity, enabling the

VCSELs to have a better performance at high temperature, which has been proven

by experimental comparison [89]. The valence subbands are calculated using the

k•p theory [82, 83]. The results are shown in Fig. 2-8(c) and 2-8(d). One can see that

In0.21Ga0.79As/GaAs0.88P0.12 QWs have a larger energy separation at the Γ point than

the standard In0.21Ga0.79As/GaAs QWs, between the first heavy hole HH1 and the first

light hole LH1 subband. Also the in-plane effective mass of the holes become lighter

0.94 0.96 0.98 1.00 1.02 1.04

300

600

900

1200

1500

1800

Material gain(1/cm)

Wavelength (µm)

25 °C

TE mode

(a)

0.96 0.98 1.00 1.02 1.04

300

600

900

1200

Material gain(1/cm)

Wavelength (µm)

85 °C

TE mode

(b)

In0.17Ga0.83As

In0.19Ga0.81As

In0.18Ga0.82As

In0.17Ga0.83As

In0.18Ga0.82As

In0.19Ga0.81As

(7 nm)

(5.6 nm)

(4.5 nm)

(7 nm)

(5.6 nm)

(4.5 nm)

N=3x1018cm-3 N=3x1018cm-3

Fig. 2-7. Calculated material gain spectra for In0.17Ga0.83As/GaAs (7 nm-thick QW), In0.18Ga0.82As/

GaAs (5.6 nm-thick), and In0.19Ga0.81As/GaAs (4.5 nm-thick) QWs at a fixed injected carrier density of

3 × 1018 cm−3 for TE polarization at (a) 25 °C and (b) 85 °C.

2.2 Active Region Design 27

[90]. The carrier filling is mainly related to the in-plane (perpendicular to the growth

direction) effective mass of the holes, and thus the density of states in the valence

and conduction bands are more closely matched, the population inversion is earlier

achieved at lower injection carrier density, resulting in a higher differential gain and

lower transparency carrier density [91, 92].

The optical gain spectra calculated at a fixed carrier density of 3 × 1018 cm–3 for

TE polarizations at 300 K are shown in Fig. 2-9(a). Partially strain-compensated

In0.21Ga0.79As/GaAs0.88P0.12 QWs have higher material gain than normal In0.21Ga0.79As/

GaAs QWs. The peak material gain as a function of carrier density at 300 K are

shown in Fig. 2-9(b). The partially strain-compensated In0.21Ga0.79As/GaAs0.88P0.12

QW has a slightly smaller transparency carrier density, which is beneficial for low

threshold current, and has a higher material gain and differential gain (larger in-

crease of slope of the gain versus the carrier density). As discussed in section 2.1.2,

Wavelength (µm)

N=3x10

-3

Peak gain (1/cm)

25 °C

TE mode

(a)

25 °C

TE mode

(b)

Carrier density 10

(1/cm

)

2 4 6 8

1000

2000

3000

4000

5000

0.21

0.79

As/GaAs

0.88

0.12

0.21

0.79

As/GaAs

0.21

0.79

As/GaAs

0.88

0.12

0.21

0.79

As/GaAs

Material gain (1/cm)

0.94 0.96 0.98 1.00

400

800

1200

1600

Fig. 2-9. Calculated material gain spectra (a) and peak material gain as a function of carrier density

(b) for In0.21Ga0.79As/GaAs and strain-compensated In0.21Ga0.79As/GaAs0.88P0.12 QWs at a fixed injected

carrier density of 3 × 1018 cm−3 for TE polarization at 25 °C, both QWs have the thickness of 4.2 nm.

0 3 6 9 12 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z(nm)

ELH

EHH

(a)

0 3 6 9 12 15

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

Energy (eV)

Z(nm)

ELH

EHH

(b)

0.01 0.03 0.05

-0.28

-0.21

-0.14

-0.07

0.00

Energy(eV)

Wave vector

HH3

LH1

HH2

HH1

(d)

0.01 0.03 0.05

-0.28

-0.21

-0.14

-0.07

0.00

Energy(eV)

Wave vector

HH3

LH1

HH2

HH1

(c)

In0.21Ga0.79As/GaAs In0.21Ga0.79As/GaAsIn0.21Ga0.79As/GaAs0.88P0.12

In0.21Ga0.79As/GaAs0.88P0.12

Fig. 2-8. Real-space energy-band diagram showing the conduction and valence bands of an

In0.21Ga0.79As (4.2 nm-thick) QW with GaAs0.88P0.12 barrier layers (a) and GaAs barrier layers (b). k-

space dispersion of the valence heavy-hole and light-hole subbands for In0.21Ga0.79As QWs surrounded

by GaAs0.88P0.12 barriers (c) and GaAs barriers (d) with the hole subband energies versus the in-plane

wave vector normalized by 2π/a0 (Å–1), where a0 = 5.6533 Å is the lattice constant of GaAs at 25 °C.

28 Chapter 2 Design and Modeling of 980 nm VCSELs

larger differential gain is very important for high bit-rate performance, not only

essential for higher –3 dB modulation bandwidth, but also indicates the ability to

achieve high modulation bandwidth at low bias current.

2.2.4 Summary

The peak gain wavelength is determined by the composition of the QW material,

barrier material, and QW thickness. An optimized QW design for the active region

of 980 nm VCSELs should have large band offsets, high material gain, low transpar-

ency carrier density, and high differential gain, which will result in a large relaxation

resonance frequency, and ultimately a large –3 dB modulation bandwidth.

2.3 DBR Design

DBR mirrors composed of AlxGa1–xAs/AlyGa1-yAs are commonly used for GaAs-

based VCSELs. VCSELs have a limited round-trip gain due to their short cavity

and therefore rely on highly reflective mirrors, where the power reflectance usually

is 0.99 (99 %) or higher for the output coupling mirror and 99.9 % or higher for

the other high-reflector mirror. The DBR mirrors consists of a stack of quarter-

wavelength layers with alternating high- and low- refractive index to reach a very

high power reflectance above 99 %. At 980 nm with AlGaAs/GaAs DBR layers more

than 20 DBR periods are generally needed to achieve a power reflectance higher than

99 %. There will be more than 40 total DBR periods in the top and bottom DBRs,

which is the main part of the entire VCSEL epitaxial wafer structure that also con-

tains the largest number of hetero-interfaces of the VCSEL structure. Therefore, a

proper and careful electrical design of the DBR mirrors is very important. Since the

thicknesses of the DBR layers are defined by the lasing wavelength, the main goal

of the electrical simulations is to improve the conductivity of the mirrors, mainly by

reducing potential barriers at the interfaces, which arise from the different material

compositions and thus different energy band gaps of the corresponding materials

used in the DBR mirrors. Increasing the doping level can reduce the electrical resis-

tances, but will generally increase free carrier absorption losses, which means the

doping level needs to be chosen to carefully balance the trade-off of resistance and

loss simultaneously. The DBR mirrors for 980 nm VCSELs are used as an example to

show the effect of grading the DBR interface layers and the effect of various doping

levels on the DBR’s electrical and optical properties.

2.3 DBR Design 29

2.3.1 Electrical Design of DBR Mirrors

A lot work has been done before seeking to optimize the interfaces inside a DBR

mirror. Different schemes were investigated [93], for example composition linear

grading, step grading [94], biparabolic grading [95], uniparabolic grading [95],

modulation doping [96], or delta-doping (δ-doping) at the interfaces to lower the

resistance of the DBR. Linear compositional grading layers are used in this work

to improve the mirror conductivity because these can be easily grown by standard

MOCVD techniques. Additionally, no significant differences are found between the

previously listed grading schemes. The thicknesses of linear compositional grading

layers are important, and the exact sequence and spatial density of dopants within

the DBRs is found to be indeed important as well.

2.3.1.1 The Influence of Grading Layer Thickness

The Al-composition for Al0.12Ga0.88As/Al0.90Ga0.10As DBR mirrors without and with

10, 16, and 20 nm linear compositional grading is shown in Fig. 2-10(a). Only one

and a half periods of the DBR are shown for more clarity. As electron mobility is ap-

proximately 20 times higher than hole mobility, the main source of serial resistance is

the p-DBR layers, and it is thus important to lower the resistance of the p-DBR layers.

The energy band diagrams are calculated using Nextnano software [97] in this work.

The energy band diagram results for a p-doping level of 2 × 1018 for Al0.12Ga0.88As/

Al0.90Ga0.10As DBR mirrors without and with 20 nm-thick compositional linear

grading is showed in Fig. 2-10(b) and 2-10(c), in which energies of different minima

and maxima in the conduction and the valence bands are shown. The energy band

gap of AlxGa1–xAs is direct for aluminum-arsenide compositions x from 0 up to

~0.41 − 0.45 (the lowest energy occurs at the Γ-point), while for higher compositions

(x > 0.45), AlGaAs becomes an indirect semiconductor with the X-valley minima

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

0 nm

10 nm

16 nm

20 nm

Al-composition

Distance (nm)

Energy (eV)

Distance (nm)

0 50 100 150 200

-1

4no grading

HH LH

(b)

Energy (eV)

Distance (nm)

0 50 100 150 200

-1

420 nm grading

(c)

HH LH

(a)

Fig. 2-10. Aluminum composition (x) for Al0.12Ga0.9As/Al0.9Ga0.1As DBR mirrors with 0, 10, 16, 20 nm

linear grading layer (a), and band diagram including Γ, X and L conduction bands and heavy-hole

HH, light-hole LH and split-off SO valence bands of p-doping level of 2 × 1018 for the Al0.12Ga0.9As/

Al0.9Ga0.1As DBR without (b) and with 20 nm (c) grading layers.

30 Chapter 2 Design and Modeling of 980 nm VCSELs

having the lowest energy in the conduction band. In Fig. 2-10(b), the potential bar-

riers between two different aluminum composition materials (Al0.12Ga0.88As and

Al0.90Ga0.10As) for holes in the valence band is considerably large for DBRs without

grading layers. This downward peak barrier adds to the difficulty to move holes,

which makes this barrier the main source of series resistance for the p-DBR. In addi-

tion, these barriers in the p-DBR increase the voltage drop of the VCSELs. By using

a 20 nm-thick compositional linear grading layer, this barrier is reduced obviously,

which means a huge improvement of conductivity and smaller resistance.

In order to see the improvement in conductivity of a DBR with different thick-

ness grading layers, a zoomed-in view of the heavy-hole band minimum is shown

in Fig. 2-11. The height of the potential barrier for holes reaches ~0.4 eV with an

ungraded DBR, and decreases into ~0.1 eV for the DBR with 20 nm-thick graded

layers, which means the potential barriers can be effectively suppressed by adding a

grading layer at every hetero-interface in the DBR. Moreover, the height of the po-

tential barrier has a large decrease of ~0.27 eV by adding 10 nm grading layers, but a

slower decrease with a further increase of the thickness of the grading layers. When

the grading layer thickness is larger than 16 nm, the decrease of the potential barrier

becomes very small, which means extra-thick grading layers will not noticeably

further improve the hole conductivity, but will degrade the optical properties of the

DBR. The compositional linear grading layers used for AlGaAs DBR mirrors with

thickness between 16 to 20 nm are thus suitable for low resistance 980 nm VCSELs.

2.3.1.2 The Influence of Doing Level

Increased doping levels is another method to increase the conductivity of DBRs. The

energy of the heavy-hole band minimum for Al0.12Ga0.9As/Al0.9Ga0.1As DBR with

20 nm linear compositional grading layers is shown in Fig. 2-12, including the cases

of different p-type doping levels of 5 × 1017, 1 × 1018, 2 × 1018, and 3 × 1018 cm−3. By

Fig.2-11. Heavy-hole HH valence band

diagram of p-doping level of 2 × 1018

for the Al0.12Ga0.9As/Al0.9Ga0.1As DBR

without and with 10, 16 and 20 nm

grading layers.

0 50 100 150 200

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0 nm

10 nm

16 nm

20 nm

HH-Energy (eV)

Distance (nm)

grading layer

thickness:

Al0.12Ga0.9As/Al0.9Ga0.1As DBR

2.3 DBR Design 31

increasing the p-doping level from 5 × 1017 to 2 × 1018 cm−3, the interface improves

drastically. The height of the potential barriers for holes decreases significantly, and

a further increase to 3 × 1018 cm−3 results in smaller improvement, but at the same

time higher doping levels increase free carrier absorption losses.

Figure 2-12 shows that increased doping levels can reduce the downward peak

barriers and lower the electrical resistance, but potentially introduce more carrier

absorption loss. Modulation doping profiles can be used to simultaneously achieve

low resistance and low loss. The p-doped DBR for the VCSELs structure used in this

work is chosen as an example to show the effect of a modulation doping profile. Two

different doping levels are used in the VCSEL structure. For the first 5 DBR pairs

near the active region where the electric filed intensity is high relatively low doping

levels are used to avoid strong optical losses, which is 2 × 1018 cm–3 for the high re-

fractive index layers, low refractive index layers, and grading layers. Higher doping

levels are used for the next 19 DBR mirror pairs where the electric filed intensity is

lower. The doping level is 3 × 1018 cm–3 for the high refractive index layers and the

low refractive index layers, and 4 × 1018 and 5 × 1018 cm–3 for the two graded layers

in each period, as show in Fig. 2-13(a). Fig. 2-13(b) shows that the hole concentration

has two peaks, one is in the node of the optical standing cavity wave, which won’t

add to the optical absorption loss, as they are located at the intensity nulls. However,

the other peak is in the position of the grading layer when the aluminum-arsenide

composition x increases from 0.12 into 0.9. This high hole concentration will add

optical absorption loss. A lower doping level for this grading layer (from low

aluminum-arsenide composition x increasing to high composition x) in the future

design should be used to further lower the optical loss.

Fig. 2-12. Heavy-hole valence band

diagram of p-doping level of 5 × 1017,

1 × 1018, 2 × 1018, and 3 × 1018 for the

Al0.12Ga0.9As/Al0.9Ga0.1As DBR with

20 nm linear compositional grading

layers.

0 50 100 150 200

-0.20

-0.15

-0.10

-0.05

0.00

0.05

5x1017

1x1018

2x1018

3x1018

HH-Energy (eV)

Distance (nm)

Al0.12Ga0.9As/Al0.9Ga0.1As DBR

20 nm-thickness

linear compositional grading layers

32 Chapter 2 Design and Modeling of 980 nm VCSELs

2.3.2 Optical Design of the DBR Mirrors

The optical properties of multilayer dielectric structures can be calculated using

the 2 × 2 transfer matrix method [69, 80]. Crosslight software [84] is used for the

calculations in this work. Increasing the number of DBR pairs and the refractive

index contrast between the high refractive index and low refractive index materials

increases the mirror power reflectance. For the 980 nm VCSEL structure used in this

work, Al0.12Ga0.9As/Al0.9Ga0.1As layers with a refractive index difference ∆n = 0.4391

at 980 nm are used for both top- and bottom-DBR mirrors. The high refractive

index layer is Al0.12Ga0.9As, with a real refractive index at 980 nm of n = 3.4433 and

a quarter-layer thickness of 71 nm. The low refractive layer is Al0.9Ga0.1As, with a

refractive index at 980 nm of n = 3.0042 and a quarter-layer thickness of 81.5 nm.

The power reflectance for the top- and bottom-DBRs is calculated using the transfer

matrix method [69]. Fig. 2-14(a) shows the calculated power reflectance of the top 24

period DBR including two Al0.98Ga0.02As layers placed within two of the low-index

layers for the wet oxidation, using transfer matrix method. The power reflectance at

980 nm is R = 0.9975 for 24 DBR pairs with 20 nm-thick DBR grading layers. For

comparison, the power reflectance for a 24 period DBR without the grading layers

is also shown, which is R = 0.9978, a little higher than for the DBR with the 20 nm-

thick grading layers. In addition, the stop-band width is slightly decreased. The

grading layers thus have a small impact on the optical property. Fig. 2-14(b) shows

the power reflectance for the 37.5 period bottom DBR, where the power reflectance

at 980 nm is R = 0.9998 for the 37.5 period DBR with 20 nm-thick grading layers.

For comparison, R = 0.9999 for the DBR without the grading layers. The stop-band

width is also slightly decreased when grading layers are used.

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

Al composition

Distance(nm)

low doping

high doping

P doing level (10

-3

)

0 50 100 150 200

-0.3

0.0

0.3

0.6

0.9

1.2

Hole concentration (10

-3

)

Electric field intensity (a.u.)

Distance (nm)

low doping

high doping

Fig. 2-13. Aluminum-composition and doping level (a) for first 6 pair low-doped and 19 pair high-

doped p-type Al0.12Ga0.9As/Al0.9Ga0.1As DBR with 20 nm grading layers, and corresponding normal-

ized electric field intensity and free hole concentration (b).

2.4 QW Gain-to-Etalon Wavelength Offset Design 33

2.4 QW Gain-to-Etalon Wavelength Offset Design

In this section, the reason why a –15 nm QW gain-to-etalon wavelength offset is

particularly suitable for temperature-stable VCSELs is briefly explained. The effects

of the gain-to-etalon wavelength offset on both the static and high-speed modulation

properties of VCSELs are discussed. The research goal is to achieve high bit-rate

operation from 25 to 85 °C and highly temperature stable operation across a large

temperature range simultaneously.

2.4.1 The Effect on Static Properties

The three-dimensional cavity resonant modes determine the emission wavelengths

of VCSELs. Due to the typically short horizontal planar cavity with perpendicular,

z-direction optical thickness of an integer multiple of λ/2 the VCSEL’s free-spectral

range is typically larger than the spectral width of the QW gain, thus only one

longitudinal resonant cavity etalon mode overlaps with the gain. As is well known

a room temperature offset between the QW’s gain peak wavelength and the cavity

etalon wavelength can be introduced in VCSELs such that these wavelengths align

at elevated operating temperatures [98]. The result may be a relatively flat threshold

current versus temperature behavior across a broad range of temperatures and

a highly temperature insensitive output power-current (L-I) characteristic from

threshold up to several mA of forward bias. Fig. 2-15(a) shows the calculated material

gain based on the k•p theory [82] for the In0.21Ga0.79As QWs with GaAs0.88P0.12 barrier

layers at a fixed carrier density of 3 × 1018 cm–3 for TE polarization at temperatures

850 900 950 1000 1050 1100

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

R=0.9975

no grading layer

20 nm linear grading layer

Power reflectance

Wavelength(nm)

R=0.9978

24 pairs Top-DBR

850 900 950 1000 1050 1100

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

R=0.9998

Power reflectance

Wavelength(nm)

R=0.9999

37.5 pairs Bottom-DBR

no grading layer

20 nm linear grading layer

(a) (b)

∆n = 0.4391 ∆n = 0.4391

Fig. 2-14. Power reflectance as a function of the wavelength of the 24 pair Al0.12Ga0.9As/Al0.9Ga0.1As

top-DBR without and with 20 nm grading layers including two Al0.98Ga0.02As layers for the wet oxi-

dation (a). Power reflectance as a function of the wavelength of the 37.5 pair Al0.12Ga0.9As/Al0.9Ga0.1As

bottom-DBR without and with 20 nm grading layers (b).

34 Chapter 2 Design and Modeling of 980 nm VCSELs

from 300 to 380 K. The QW gain peak wavelengths change with active region tem-

perature as shown in Fig. 2-15(b), with a calculated gain shift rate of 0.396 nm/K.

Fig. 2-16(a) shows the calculated power reflectance of a 980 nm VCSEL as a function

of increasing temperature. The corresponding extracted cavity resonance wavelength

shift with temperature is depicted in Fig. 2-16(b), with the shift rate of 0.061 nm/K.

The cavity resonance wavelength shifts to longer wavelengths as the temperature

increases, as does the QW peak gain, but at a smaller rate of 0.061 nm/K compared

to 0.396 nm/K for the QW gain peak. Given these rates of wavelength-shift versus

temperature one can choose a gain-to-etalon wavelength offset at room temperature

so the offset is equal to zero at a certain elevated temperature to facilitate highly

temperature stable or possibly temperature insensitive operation within a limited op-

erating range. The peak QW gain wavelength change of the In

0.21

0.79

As/GaAs

0.88

0.12

QW system and the 1D fundamental longitudinal etalon resonance wavelength

change for three different VCSEL cavities with a gain-to-etalon wavelength offset

at 300 K of 0, –15, and –25 nm is shown in Fig. 2-17. The intersection between the

300 340 380

977

978

979

980

981

982

983

984

985

Cavity resonance

Active region temperature (K)

dλcavity/dT = 0.061 nm/K

(b)

900 950 1000 1050

0.0

0.5

1.0

1.5

2.0

2.5

3.0

380 K

360 K

340 K

320 K

Power reflectance (unitless)

Wavelength (nm)

300 K

(a)

wavelength (nm)

Fig. 2-16. Calculated power reflectance at normal incidence for the full 980 nm VCSEL epitaxial struc-

ture at different temperatures (a) and the resultant cavity longitudinal resonance (etalon dip) wave-

length (b) versus the active region temperature.

940 960 980 1000 1020

200

400

600

800

1000

1200

380 K

360 K

340 K

320 K

Material gain (1/cm)

Wavelength (nm)

300 K

N = 3 × 10

−3

TE mode

(a)

300 340 380

960

965

970

975

980

985

990

995

1000

1005

Gain peak wavelength (nm)

Active region temperature (K)

(b)

dλgain/dT = 0.396 nm/K

Fig. 2-15. Calculated material gain spectra (a) at different temperatures for a fixed injected carrier den-

sity of 3 × 1018 cm–3, and peak gain wavelength (b) versus temperature for a single In0.21Ga0.79As QW

(4.2 nm-thick) surrounded by GaAs0.88P0.12 barrier layers.

2.4 QW Gain-to-Etalon Wavelength Offset Design 35

QW gain peak and the cavity resonance occurs at a specific temperature, which is

300, 347, and 376 K for 0, –15 and –25 nm offset, respectively. This temperature

corresponds to the threshold, i.e. the best static working point for efficient operation.

2.4.2 The Effect on High Bit-Rate Modulation Properties

The QW gain-to-etalon wavelength offset not only has an important influence on the

static performance, but also a large impact on the high-speed modulation proper-

ties [99], as the change of the differential QW gain upon a temperature increase is

noticeably reduced. This effect can be predicted based on temperature dependent

calculations of the differential gain. The differential gain versus wavelength at the

threshold-gain-point for different temperatures is calculated by: 1) determining the

threshold gain of the VCSELs at a given temperature accounting for mirror losses

and absorption; 2) using the same approach as in Fig. 2-15(a) to determine the param-

eters for the specific required QW gain; and 3) calculating the differential gain at this

threshold-gain-point. The threshold gain is calculated to be here 472 cm–1 at 300 K.

As expected, the calculations show that the differential gain peak moves to longer

wavelengths with elevated temperatures and at the same time, the maximum gain

decreases slowly, as shown in Fig. 2-18(a). An active region with high differential

gain is desired for high bit-rate VCSELs. A higher differential gain leads to a larger

D-factor and thus a faster increase of relaxation resonance frequency with current.

This enables the VCSEL to reach a larger modulation bandwidth before it is limited

by damping or thermal effects [69]. In order to illustrate the importance of the change

in differential gain with temperature to the temperature stability of the devices, the

results for gain-to-etalon wavelength offsets of 0, –15, and –25 nm are depicted

in Fig. 2-18(b). For this calculation, the 1D cavity etalon resonance wavelength

values from Fig. 2-16 were used. The highest differential gain is obtained when the

300 320 340 360 380 400

960

970

980

990

1000

1010

1020

0 nm

-15 nm

QW gain peak

Etalon wavelength

Wavelength (nm)

Active region temperature (K)

-25 nm

Fig. 2-17. Stimulated peak gain

wavelength of a single In0.21Ga0.79As/

GaAs0.88P0.12 QW/barrier active re-

gion and the etalon resonance wave-

length of 980 nm VCSELs ver-

sus temperature for gain-to-etalon

wavelength offsets fixed at 300 K

at 0, –15, and –25 nm relative to the

peak QW gain.

36 Chapter 2 Design and Modeling of 980 nm VCSELs

gain-to-etalon wavelength offsets is 0 nm and the active region temperature is 300 K,

and the differential gain decreases rapidly with increasing temperature. The active

region temperature Tactive increases fast with increasing operating bias current, and

can be estimated for the linear LI region using Tactive = Tambient + Rth ∙ (I ∙ V − Pout) [100],

where Rth is the thermal resistance, I and V are bias current and voltage, and Pout is

the optical output power. By taking the ~4.0 µm oxide-aperture diameter 980 nm

VCSEL measured in Chapter 6 as an example, using an ambient temperature of 25 °C,

a bias current and voltage of 5.4 mA and 2.59 V, respectively, an optical output power

of 1.78 mW, and a measured thermal resistance of 4.68 K/mW, the active region

temperature is estimated to be 82.1 °C (355.25 K), which is 57.1 °C higher than the

ambient temperature. The temperature of the active region is always higher than the

ambient temperature, thus a large differential gain at elevated temperatures is clearly

important for a temperature robust VCSEL. The –15 nm gain-to-etalon wavelength

offset design has a smoother change of the differential gain across the temperature

range of 25 − 85 °C compared to offsets of 0 nm and –25 nm. The –15 nm offset also

results in higher differential gain at temperatures above ~350 K as compared to a

VCSEL with a 0 nm gain-to-etalon wavelength offset. This is clearly beneficial for

operation at high bit-rate at high temperatures for temperature stability. Also, this

larger differential gain results in a larger D-factor, which is an important factor for

VCSELs to reach a certain bandwidth at a low bias current, to enable a low operating

energy consumption. A larger offset, for example –25 nm, results in a lower differ-

ential gain at 300 – 340 K. In addition, the differential gain at from ~360 – 385 K is

less than what is possible with a –15 nm offset.

920 940 960 980 1000

420 K

400 K

380 K

340 K

320 K

360 K

Differential gain × 10

-16

(cm

)

Wavelength (nm)

300 K

300 320 340 360 380 400

-15 nm

0 nm

Differential gain × 10

-16

(cm

)

Temperature (K)

-25 nm

(a) (b)

Fig. 2-18. Calculated differential gain spectra for our QW active region designed for a room tempera-

ture gain peak of 965 nm. The curves are shown for active-region temperatures ranging from 300 to

420 K (a), and differential gain versus temperature for 300 K gain-to-etalon wavelength offsets of 0,

–15, and –25 nm.

2.5 Thermal Design 37

2.4.3 Summary

The temperature dependence of the QW differential gain for several 980 nm

active region designs are numerically investigated. The influence (both on static

performance and on high bit-rate modulation performance) of QW gain-to-cavity

etalon wavelength offset for 980 nm VCSEL is theoretical analyzed. By introducing

a −15 nm QW gain-to-cavity etalon wavelength offset, the temperature-stability,

the maximum bit rate at high temperature (~85 °C), and the energy efficiency of

VCSELs can be simultaneously improved. VCSELs designs with –15 nm gain-to-

etalon wavelength offset are shown to be well suited for temperature-stable static

and high-speed modulation operation.

2.5 Thermal Design

The temperature sensitivity of VCSELs is related to their structure and thermal con-

ductivity of the constituent materials. The use of high thermal conductivity materials

for DBR mirrors is helpful to achieve high thermal performance VCSELs. Therefore,

the optimization of the parameters that influence the thermal performance is of great

importance in designing high temperature performance VCSELs.

2.5.1 Theoretical Background

Heat transport in semiconductor lasers can be simulated by numerically solving the

heat conduction equation using the finite-element method (FEM). The mathematical

equation for heat transfer by conduction is the heat equation:

( )

C k T Q

r¶+ Ñ× - Ñ =

(2.20)

where T (K) is the temperature, Q (W/m3) is a heat source, ρ (kg/m3) is the material

density, Cp (J/kg·K) is the heat capacity and k (W/m·K) is the thermal conductivity

of the medium. If the thermal conductivity is isotropic, the equation (2.20) becomes:

C k T Q

r¶- Ñ =

(2.21)

38 Chapter 2 Design and Modeling of 980 nm VCSELs

Owing to the very large-scale difference in the vertical and radial directions, the

effective thermal conductivity of active region layers and DBR layers is different in

the two directions. For active region layers, the equivalent thermal conductivity of

the multilayer in the lateral (kL) and the vertical (kv) directions are determined from

the following two expressions [101]:

n n

d k

n n

(2.22)

where dn and kn represent the thickness and the thermal conductivity of the nth layer,

N is the number of layers. The effective thermal conductivity for a DBR can be

expressed as [102]:

1 1 2 2

1 2

d k d k

kd d

1 2

1 1 2 2

/ /

d d

kd k d k

(2.23)

Table 2-3. Material parameters at 300K [102, 105, 106]

Material 1Cp 2ρ 3k 4Thickness

GaAs

(P-contact layer) 327 5.32 44 20

Al0.12GaAs/ Al0.9GaAs

(Top DBR) 378.2 4.48 kL = 22.27

kv = 21.07

71/81.5

(22.5 pairs)

AlxOy850 3.96 0.7 30

Al0.98Ga0.02As

(Selective oxidation) 448 3.79 58.43 30

Al0.9GaAs/ Al0.12Ga0.88As

(Top DBR) 378.2 4.48 kL = 22.27

kv = 21.54 52.3/71

AlxOy850 3.96 0.7 30

Al0.98Ga0.02As

(Selective oxidation) 448 3.79 58.43 30

Al0.9GaAs/ Al0.625GaAs/

Al0.35Ga0.65As (Cladding layer) 400.25 4.08 kL = 19.7

kv = 17.237 75.5/70/20

In0.21Ga0.79As/ GaAs0.88P0.12

(QWs) 328.12 5.26 kL = 14.44

kv = 10.78

6/(4.2/6)

(5 QWs)

Al0.35Ga0.65As/ Al0.625GaAs/

Al0.9GaAs (Cladding layers) 400.25 4.08 kL = 19.7

kv = 17.237 20/70/104.6

Al0.12GaAs/ Al0.9GaAs

(Bottom DBR) 378.2 4.48 kL = 22.27

kv = 21.54

71/81.5 (37.5

pairs)

GaAs/AlAs

(Bottom DBR) 382.9 4.44 kL = 63.27

kv = 58.66

69.2/83.1

(37.5 pairs)

GaAs (Subtract) 327 5.32 44 2000

1Cp is in unit of J/kg·K; 2ρ is in unit of 103 kg/m3; 3k is in unit of W/m∙K; 4thickness

is in unit of nm.

2.5 Thermal Design 39

2.5.2 Thermal Simulation

The thermal behavior of semiconductor lasers is very complex, since many param-

eters are functions of temperature. To simplify the calculation the variations of the

threshold current, differential quantum efficiency, thermal conductivities, and resis-

tivity with temperature is neglected in the following simulations. Since VCSELs are

symmetric with respect to the z-axis in the cylindrical coordinate system with three

curvilinear coordinates (r, φ, z), a two-dimensional FEM simulation in the r and z

directions for an arbitrary azimuth angle φ are used to simplify the problem. The

cross section of our simulated VCSEL is shown in Fig. 2-19. As shown in equation

(2.21), three parameters are important, which are density ρ (kg/m3), heat capacity Cp

(J/kg·K), and thermal conductivity k (W/m∙K). These three parameters need to be

defined for each material for the heat transfer simulation. Table 2-3 lists the param-

eter values used in following simulations.

The heat sources in VCSELs are more complicated than those in edge-emitting

lasers, where the non-radiative recombination of charge carriers in the active region

is the dominating heat source. Important heat sources of VCSELs are non-radiative

recombination and reabsorption of spontaneous emission in the active region and

Joule heating. The heat flux distribution in the device is related to the voltage drop

across the active region and DBRs [103]. The voltage drop across the active region is

1.2653 V for 980 nm VCSEL (calculated through the average bandgap energy). The

voltage drop across the DBRs is caused by interface barriers, which increase the

Axis symmetry

Bottom-DBR

Top-DBR

GaAs Substracte

Oxide layer

Active region

(AlxOy)

Fig. 2-19. Two-dimensional GaAs-based top emitting 980 nm VCSEL structure employing a rotational

structural symmetry along the z-axis used in the simulation.

40 Chapter 2 Design and Modeling of 980 nm VCSELs

resistance and threshold voltage [104]. The heat transfer problem is solved by defin-

ing an initial value of constant temperature T0 for all domains and as the temperature

boundary condition for keeping all outer sides of the device at T0 at any time.

2.5.2.1 Active region temperature vs. current

Contour plots of the temperature distribution in a cross sectional plane (r-z plane) of

the 4 µm oxide-aperture diameter 980 nm VCSEL are given in Fig. 2-20. The con-

tinuous wave (CW) injection current is 1 mA, the voltage is 1.93 V, and the output

power is 0.29 mW. So the total heat flux in the VCSEL is 1.64 mW. Based on the

voltage drop across the active region and DBRs, the active region heat source is cal-

culated to be 1.5 × 1015 W/m3. So 1 mA CW injection current leads to a temperature

rise of 3.437 K in the active region. The contour plots of the temperature distribution

at higher injection current of 4 mA is shown in Fig. 2-21, which leads to a higher

temperature rise of 13.75 K in the active region.

2.5.2.2 Thermal resistance vs. oxide-aperture diameter

From this thermal simulation, the thermal resistance Rth (K/mW) of the device can

easily be obtained by using Rth = ΔT / ΔPdiss. The same heat flux of 4 mW across

the active region for different oxide-aperture diameter VCSELs is applied to study

the influence of oxide-aperture diameter on the thermal performance, which corre-

sponds to active region heat sources of 2.23 × 1016, 9.95 × 1015, 5.59 × 1015, 3.5 × 1015,

2.48 × 1015, and 1.82 × 1015 W/m3 for VCSELs with oxide-aperture diameter of 2, 3,

4, 5, 6, and 7 µm, respectively. The contour plots of the temperature distribution for

298 K

298.5 K

299 K

299.5 K

300 K

300.5 K

301 K

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm oxide-aperture Ø

1 mA

Tmin:298K Tmax:301.43K

25°C

Al0.12Ga0.88As/Al0.9Ga0.1As

Fig. 2-20. Simulated temperature dis-

tributions T(r,z) in a 4 µm oxide-aper-

ture diameter 980 nm VCSEL at CW

current of 1 mA with Tmin = 298 K

(dark blue) and Tmax = 301.37 K (dark

red).

Fig. 2-21. Simulated temperature dis-

tributions T(r,z) in a 4 µm oxide-aper-

ture diameter 980 nm VCSEL at CW

current of 4 mA with Tmin = 298 K

(dark blue) and Tmax = 311.75 K (dark

red).

298 K

300 K

302 K

304 K

306 K

308 K

310 K

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm oxide-aperture Ø

4mA

min

:298 K T

max

:311.75 K

25°C

0.12

0.88

As/Al

0.9

0.1

2.5 Thermal Design 41

2 and 7 µm oxide-aperture diameter 980 nm VCSELs are shown in Fig. 2-22, with

the maximum active region temperature of 326.529 and 304.361 K, respectively. This

translates into a thermal resistance of 7.13 and 1.59 K/mW, respectively.

The same thermal simulations are performed for VCSELs with oxide-aperture

diameter of 3, 4, 5, 6 µm by applying the same heat flux of 4 mW across the active

region. The maximum active region temperatures are 315.985, 310.81, 307.566, and

305.771 K for 3, 4, 5, and 6 µm oxide-aperture diameter VCSELs, respectively, as

shown in Fig. 2-23(a). The thermal resistance is calculated to be 4.49, 3.2, 2.39, and

1.94 K/mW for 3, 4, 5, 6 µm oxide-aperture diameter VCSELs, respectively, as show

in Fig. 2-23(b). As expected, small oxide-aperture VCSELs have higher active region

temperature under a given heat flux due to the smaller volume of the heat source.

This higher active region temperature increase for a given heat flux leads to a higher

thermal resistance for the small oxide-aperture VCSELs.

2.5.2.3 Active region temperature vs. bottom-DBR material

Ternary alloys have lower thermal conductivity compared with binary material, due

to the strong scattering of phonons caused by the random distribution of alloy atoms.

To study how much improvement of the thermal performance of VCSELs is pos-

sible when a binary GaAs/AlAs bottom DBR is used compared to a Al0.12Ga0.88As/

300 K

305 K

310 K

315 K

320 K

325 K

Top-DBR

Bottom-DBR

GaAs Substrate

2 µm aperture Ø

4 mW

Tmax: 326.529 K

25°C

Al0.12Ga0.88As/Al0.9Ga0.1As

Top-DBR

Bottom-DBR

GaAs Substrate

7 µm aperture Ø

4 mW

Tmax: 304.361 K

25°C

Al0.12Ga0.88As/Al0.9Ga0.1As

298 K

299 K

300 K

301 K

302 K

303 K

304 K

(a) (b)

Fig. 2-22. Simulated temperature distributions T(r,z) at the heat flux of 4 mW across the active re-

gion for 2 µm (a) and 7 µm (b) oxide-aperture diameter 980 nm VCSELs with Tmin = 298 K and

Tmax = 326.529 K for the 2 µm oxide-aperture diameter VCSEL (a), and Tmax = 304.361 K for the 7 µm

oxide-aperture diameter VCSEL (b).

Tmax (K)

980-nm VCSEL

25 °C

4 mW

(a)

Oxide-aperture diameter (µm) Oxide-aperture diameter (µm)

Rth (K/mW)

980-nm VCSEL

(b)

2468

300

320

340

2468

Fig. 2-23. Simulated maximum active region temperature (a) at the same heat flux of 4 mW across the

active region, and the thermal resistance (b) for VCSELs with oxide-aperture diameter of 2, 3, 4, 5,

6, and 7 µm, respectively.

42 Chapter 2 Design and Modeling of 980 nm VCSELs

Al0.9Ga0.1As DBR, the temperature distributions for 4 µm oxide-aperture diameter

980 nm VCSELs with two different DBRs are calculate at the same heat flux of

4 mW across the active region at room temperature. The contour plots are shown in

Fig. 2-24. The maximum active region temperatures are 310.80 and 306.456 K for the

Al0.12GaAs/Al0.9GaAs DBR and for the GaAs/AlAs DBR. The binary bottom DBR

can reduce the active region temperature by 4.3 K when the heat flux is 4 mW, which

means the thermal resistance can be reduced by 1.05 K/mW when binary GaAs/AlAs

mirrors replace Al0.12Ga0.88As/Al0.9Ga0.1As mirrors in 4 µm oxide-aperture diameter

980 nm VCSELs.

2.5.2.4 Active region temperature vs. oxide-layer thickness

Oxide-layer thickness can influence the static and high bit-rate modulation perfor-

mance of VCSELs, because the index-step, parasitic capacitance, and electrical path

vary with oxide-layer thickness. The temperature distributions for 4 µm oxide-aper-

ture diameter 980 nm VCSELs with different oxide-layer thicknesses are calculated

at the same heat flux of 4 mW across the active region at room temperature, in order

to see if the oxide-layer thickness change will influence the active region temperature

or not. The contour plots for 4 µm oxide-aperture diameter VCSELs with 10 nm-

thick and 50 nm double oxide layers are shown in Fig. 2-25(a) and 2-25(b). The

contour plots for 30 nm-thick oxide layer VCSELs is already shown in Fig. 2-24(a).

298 K

300 K

302 K

304 K

306 K

308 K

310 K

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm aperture Ø

4 mW

Tmax: 310.88 K

Al0.12Ga0.88As/Al0.9Ga0.1As

(a)

Oxide-layer: 10 nm

298 K

300 K

302 K

304 K

306 K

308 K

310 K

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm aperture Ø

4 mW

Tmax: 310.74 K

Al0.12Ga0.88As/Al0.9Ga0.1As

Oxide-layer: 50 nm

(b)

Fig. 2-25. Simulated temperature distributions at the heat flux of 4 mW across the active region for

4 µm oxide-aperture diameter VCSELs with Tmax = 310.88 K with 10 nm-thick double oxide layers (a),

and Tmax = 310.74 K with 50 nm-thick double oxide layers (b).

298 K

300 K

302 K

304 K

306 K

308 K

310 K

298 K

299 K

300 K

301 K

302 K

303 K

304 K

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm aperture Ø

4 mW

Tmax: 310.80 K

25°C

Al0.12Ga0.88As/Al0.9Ga0.1As

Top-DBR

Bottom-DBR

GaAs Substrate

4 µm aperture Ø

4 mW

Tmax: 306.546 K

25°C

(a) (b)

305 K

306 K

GaAs/AlAs

Fig. 2-24. Simulated temperature distributions at the heat flux of 4 mW across the active region for

4 µm oxide-aperture diameter VCSELs with Tmax = 310.80 K with Al0.12Ga0.88As/Al0.9Ga0.1As bottom

DBR (a), and Tmax = 306.546 K with GaAs/AlAs bottom DBR (b). The two Al0.98Ga0.02As oxide layers

are 30 nm-thick.

2.5 Thermal Design 43

The maximum active region temperatures are 310.88, 310.80, and 310.74 K for 10,

30, 50 nm-thick oxide-layers VCSELs, respectively. The active region temperature

only increases 0.14 K when the oxide layer thickness is decreased form 50 to 10 nm

when the heat flux is 4 mW.

2.5.3 Summary

Thermal simulations are performed on 980 nm VCSEL structures. The temperature

distribution of the active region is studied, and the thermal resistance is obtained by

thermal simulation for different oxide-aperture diameter VCSELs. Also, the thermal

performance improvement by the use of binary bottom DBRs is numerically dem-

onstrated. The increase of active region temperature decreases the differential gain

of the QWs. With an improved thermal performance design combined with a room

temperature QW gain-to-etalon wavelength offset design, a given 980 nm VCSEL’s

high-speed and temperature-stable static and high-speed modulation performance

can be greatly improved.

Chapter 3

Fabrication and Measurements

The fabrication of devices is as important as the wafer epitaxial design and wafer

growth to achieve high performance devices. In this Chapter, the main processing

techniques and measurement techniques are presented. In Section 3.1 the detailed

information of the epitaxial structure used in this work is given, and the simulated

mode and gain characteristics of this structure are given. Section 3.2 briefly describes

the main processing techniques used for 980 nm VCSELs fabrication, and the main

equipment used for these fabrication steps are briefly introduced with the process

results. Next Section 3.3 presents the VCSEL characterization methods, including

static and high bit-rate modulation measurements. Also the evaluation methods are

briefly shown with several measurement results.

3.1 The 980 nm VCSEL Structure

The epitaxial structure designed for high-speed, temperature-stable, and energy-

efficient operation at an emission wavelength of 980 nm, is grown by MOCVD

on GaAs-substrates by IQE plc (Cardiff, UK), a well-known commercial epitaxy

foundry. The active region contains five ~4.2 nm-thick In0.21Ga0.79As QWs with

~6 nm-thick GaAs

0.88

0.12

barrier layers. An approximately room temperature –15 nm

QW gain-to-etalon wavelength offset is introduced. A QW calibration wafer is grown

just before the growth of the full 980 nm VCSEL structure. The photoluminescence

(PL) of this calibration wafer is measured at room temperature and the result is a 2D

PL map of the wafer surface. The QW gain-to-etalon wavelength offset is determined

from this PL map, and a 2D power reflectance map that is produced after the growth

of the full VCSEL structure. The QWs together with the strain compensating layers

are surrounded by two 20 nm-thick Al

0.35

0.65

As barrier layers to improve carrier lo-

calization in the active region. The optical thickness of the cavity is 3λ/2. In addition,

3.1 The 980 nm VCSEL Structure 45

a 70 nm-thick linear grading from the Al0.35Ga0.65As barrier to the first Al0.90Ga0.10As

low-index layers is implemented for fast carrier transport and capture times. A 24-

period p-doped top distributed Bragg reflector (DBR) and a 37.5-period n-doped

bottom DBR are employed. Both DBRs are composed of alternating AlxGa1–xAs

layers with the AlAs mole fractions of x = 0.12 and x = 0.90 for the high and low

refractive index layers, respectively. The AlxGa1–xAs regions between the low and

high index layers are linearly graded over a distance of 20 nm. The doping through

the DBRs is spatially varied to minimize the VCSEL’s series resistance but at the

same time to minimize any free-carrier absorption. In order to reduce electrical para-

sitics, two 30 nm-thick (as grown before selective oxidation) oxide aperture layers

are formed in the first two low-index (p)DBR layers adjacent to the optical cavity by

selective wet thermal oxidation of the aluminum-rich (p)Al0.98Ga0.02As layers using

a proprietary TU Berlin-designed and built oxidation furnace.

Real refractive index (unitless)

Electric field intensity (a.u.)

Distance from wafer surface (µm)

oxide layers

3.2 3.4 3.6 3.8 4.0 4.2 4.4

2.8

3.0

3.2

3.4

3.6

3.8

-20

5 QWs Al0.12Ga0.88As

Al0.12Ga0.88As

Al0.90Ga0.10As

Fig. 3-2. Zoomed-in view of the refractive index profile and electric field intensity versus distance from

the top epitaxial surface of the 980 nm VCSEL epitaxial structure.

0 2 4 6 8 10

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Real refractive index (unitless)

Distance from wafer surface (µm)

Electric field intensity (a.u.)

3λ/2 cavity

top DBR bottom DBR

Fig. 3-1. 1D refractive index profile and electric field intensity versus distance from the top epitaxial

surface of the 980 nm VCSEL epitaxial structure.

46 Chapter 3 Fabrication and Measurements

3.1.1 Mode Characterization

The cavity resonant modes determine the emission wavelengths of the VCSELs.

Optical field confinement in the longitudinal direction is accomplished by the highly

reflective DBRs positioned below and above the active region. Due to the short cavity,

a VCSEL’s free-spectral range is larger than the spectral-width of the QW gain and

thus only one longitudinal resonant cavity etalon mode may lase. The refractive

index profile and electric-field intensity distribution of a 980 nm VCSEL epitaxial

structure is shown in Fig. 3-1. A zoomed-in view is shown in Fig. 3-2.

Although in a typical VCSEL only one longitudinal resonant mode can lase,

several transverse modes can be supported due to the large lateral dimensions. Trans-

verse modes of circular-shaped VCSELs can be approximated by linearly polarized

(LPlp) modes. The indices l and p are the azimuthal and radial transverse-mode

numbers, respectively. In cylindrical coordinates, the electric field amplitude of an

LPmn mode can be expressed as:

( ) ( )

, ,

j z

mn m mn

E r z e e J u r

F µ

r a<

(core) (3.1a)

( ) ( )

, ,

j z

mn m mn

E r z e e K v r

F µ

r a>

(cladding) (3.1b)

2 3 4 5 6 7

975

977

979

981

983

Wavelength (nm)

Oxide-aperture diameter (µm)

LP01

LP11

LP01 LP11

LP01

LP20

LP21

LP11

(b)

0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

0.6

0.8

1.0

LP01

LP11

LP21

LP02

Intensity (a.u.)

Radius (μm)

Oxide-aper. Ø

3µm

(a) (c)

Fig. 3-3. The four lowest transverse mode profiles in the radial direction for a 3 µm oxide-aperture di-

ameter 980 nm VCSEL (a), and intensity distributions for the four lowest LPmn modes of a cylindrical

step-index waveguide in the transverse plane (b). Calculated cold cavity emission wavelengths of the

LP01 and LP11 modes of 980 nm VCSELs as a function of oxide-aperture diameter (c), and calculated

2D plots of the optical field intensity of the LP01 mode and LP11 mode [107] for a 980 nm VCSEL

with an oxide-aperture diameter of 4 µm.

3.1 The 980 nm VCSEL Structure 47

where r, Φ, and z are the cylindrical coordinates, βmn is the propagation constant, Jm

and Km are mth order first kind and second kind Bessel function. The parameters umn

and vmn are given in equation (3.2), where k0 is the propagation constant in vacuum.

The propagation constants can be obtained by applying the boundary conditions as

expressed in equation (3.3).

2 2 2 2

0 1mn eff

u k n b= -

and

2 2 2 2

0 2mn eff

k nn b= -

(3.2)

( ) ( ) ( ) ( )

1 1

/ /

m m m m

u J ua J ua v K va K va

- -

× = - ×

(3.3)

The mode intensities, which are proportional to the square of the electric field

amplitudes, of the first four lowest order LPmn modes are shown in Fig. 3-3(a). The

spatial intensity distributions are different for different transverse modes, which

means the threshold of the higher order modes can be increased by introducing a

spatially varying loss, in order to achieve single mode operation [108]. Calculated

LP01 and the LP11 mode wavelength results as a function of oxide-aperture diameter

[107] are shown in Fig. 3-3(c). The VCSEL resonant wavelength blue-shifts as the

oxide-aperture diameter decreases [109]. For 980 nm VCSELs if the oxide-aperture

diameter is ~10 µm or larger the resonant wavelength is nearly constant [107]. The

wavelengths and 2D field intensities of the LP01 and LP11 modes are calculated using

2D simulation model and plotted in Fig. 3-3(c) [107].

0.92 0.94 0.96 0.98 1.00

1000

2000

3000

4000

N=3x1018 cm-3

N=3.5x1018 cm-3

N=4x1018 cm-3

N=4.5x1018 cm-3

Material gain (1/cm)

Wavelength (µm)

N=5x1018 cm-3

25 °C

TE mode

0.94 0.96 0.98 1.00 1.02

1000

2000

3000

N=3x1018 cm-3

N=3.5x1018 cm-3

N=4x1018 cm-3

N=4.5x1018 cm-3

Material gain (1/cm)

Wavelength (µm)

N=5x1018 cm-3

TE mode

85 °C

Fig. 3-4. Calculated gain spectra for In0.21Ga0.79As/GaAs0.88P0.12 QWs/barries used for the active region

of the 980 nm VCSELs at an injected carrier density of 3 × 1018 to 5 × 1018 cm−3 for TE polarization at

(a) 25 °C, and (b) 85 °C.

48 Chapter 3 Fabrication and Measurements

3.1.2 QW Active Region

Fig. 3-4 shows the calculated optical gain spectra of In0.21Ga0.79As/GaAs0.88P0.12 QWs

at carrier densities of 3, 3.5, 4, 4.5, and 5 × 1018 cm–3 for TE polarization at 25 and

85 °C. The room temperature gain peak wavelength is close to 965 nm at 25 °C, as an

–15 nm QW gain-to-etalon wavelength offset is introduced to improve temperature

stability. This gain peak wavelength shifts to the longer wavelength of ~990 nm

when the temperature is increased to 85 °C. The peak material gain decreases with

increasing active region temperature.

3.1.3 Photon Lifetime Adjustment

Adjustment of the photon lifetime by changing the mirror power reflectance, thus

changing the penetration depth of the optical field energy into the mirrors, is another

way to increase the modulation bandwidth of VCSELs [110]. The VCSEL’s photon

lifetime τp (in s) is related to cavity loss, and can be expressed as:

(rate) (rate) (rate)

pT B

i m m

τα α α

≈+ +

(s) (3.4)

where αi(rate) (s–1) is the internal cavity loss rate, and αm(rate) (s–1) is the top (T) or bottom

(B) DBR mirror loss rate. The loss rate can be calculated using power loss per unit

distance according to α(rate) = <vg> · α, where <vg> (cm s−1) is the average photon

group velocity in the VCSEL. The mirror loss is

1ln( )

T B

m m m t b

eff

R R

α α α

= + = −

(cm–1) (3.5)

-160 -120 -80 -40 0 40 80 120

0.97

0.98

0.99

1.00

1.5

2.0

2.5

3.0

3.5

4.0

100

1.5

2.0

2.5

3.0

3.5

4.0

Top DBR Reflectance R

Refractive index n

Thickness of coating/Etch depth into DBR (nm)

SixNy DBR

Mirror loss α

(cm

-1

)

Refractive index n

Thickness of coating/Etch depth into DBR (nm)

SixNy DBR

-160 -120 -80 -40 0 40 80 120

Fig. 3-5. Calculated top DBR power reflectance (a) and mirror loss (b) as function of SixNy thickness

and etch depth into the top DBR calculated for the 980 nm VCSEL structure. The refractive index is

also shown.

3.2 VCSEL Fabrication 49

where

, and

are the total mirror loss, the top-DBR mirror loss, and the

bottom-DBR mirror loss. Rb is the bottom-DBR power reflectance as seen from the

optical cavity looking down toward the substrate, which is 0.9998 for the DBR with

37.5 mirror pairs and with 20 nm-thick grading layers. Rt is the top-DBR power re-

flectance as seen from the optical cavity looking up toward air. Rt can be changed by

etching away part of the top-most DBR layer or by coating the VCSEL with a thin

layer, for example, SixNy. The change of Rt versus the coating thickness of added

SixNy and versus the etch depth of the top-most GaAs layer in the top DBR are show

in Fig. 3-5(a). The mirror loss change can be calculated using equation (3.5), and the

results are shown in Fig. 3-5(b). The effective internal loss is calculated to be 9.1 cm–1

by using free carrier absorption loss coefficients, which are assumed to be 11.5 and

5 cm–1 at 980 nm for holes and electrons, respectively [73]. The photon lifetime can

be calculated with equation (3.4), and the results are shown in Fig. 3-6. The output

power can be increased by decreasing the photon lifetime at a cost of slightly increas-

ing the threshold current. As the photon lifetime decreases the –3 dB modulation

bandwidths of VCSELs are generally expected to increase [111].

3.2 VCSEL Fabrication

In this section, the main processing techniques used in this work for the fabrication

of 980 nm VCSELs is briefly described, including lithography, metal contact deposi-

tion, mesa etching, selective wet thermal oxidation, annealing, BCB planarization,

and pad metallization. Also, the main equipment used for these fabrication steps,

such as the photoresist spinner, UV contact mask aligner, e-beam deposition system,

Photon lifetime (ps)

Thickness of SixNy coating (nm) Etch depth into top-DBR (nm)

SixNy DBR

-160 -120 -80 -40 0 40 80 120

Fig. 3-6. Photon lifetime as function of SixNy thickness (dashed line) and etch depth into the top DBR

(solid line) calculated for the 980 nm VCSEL structure.

50 Chapter 3 Fabrication and Measurements

thermal evaporation system, ICP-RIE etching machine, RIE etching machine, and

the oxidation furnace are shortly introduced by showing example processing results

from this work.

3.2.1 Process Techniques

3.2.1.1 Lithography

Lithography is used to transfer small feature size patterns onto the wafer. Standard

UV contact photolithography can be used for feature sizes down to approximately

1 µm, and is used in this work due to its simplicity. Electron-beam lithography can

be used for smaller patterns with sub-10 nm resolution [112], but takes longer time

and costs more. The standard UV photolithography process starts with spinning a

photoresist onto the wafer piece at a few thousand revolutions per minute (rpm) to

form a thin film where the viscosity of the resist and the spin speed determine the

thickness of the resulting film. The photoresist is then baked on a hotplate. Then the

sample is exposed to UV radiation through a patterned mask. For positive photore-

sist, the exposed areas are removed using a developer solution, leaving a pattern on

the sample, as shown in Fig. 3-7(b), while for negative photoresist, the unexposed

resist areas are removed, as shown in Fig. 3-7(a) and 3-7(c). The mask pattern is thus

transferred onto the sample. The patterned resist can then be used to protect parts of

the surface during etching or metal deposition.

3.2.1.2 Metal Contact Deposition

Lift-off processes are used for metal contacts, which proceed as follows: 1) a contact

pattern is defined in a spun-on photoresist using standard contact UV photolithogra-

phy; 2) the metal layers are deposited over the entire patterned wafer using a series

(a) (c)

(b)

Fig. 3-7. Microscope images of a VCSEL structure at various stages of processing after the develop-

ment of the photoresist (a negative photoresist) for the top p-metal contact (a); after development of

the photoresist (a positive photoresist) for the mesa one etch (b); and after the development of the pho-

toresist (a negative photoresist) for the bottom n-metal contact (c).

3.2 VCSEL Fabrication 51

of thermal evaporations or electron-beam evaporations; 3) the wafer is placed in a

solvent (N-Methyl-2-pyrrolidinone (NMP) (Microposit Stripper 1165) [113]) where

the patterned photoresist is dissolved, lifting off the metal that lies on the photoresist,

but leaving the metal that lies directly on the semiconductor. What is left is a metal

pattern on the surface of the wafer where no photoresist was present during the

metal deposition. The Ni/Ge/Au metal layers are used for n-contacts, deposited by a

Vecco thermal evaporation system. A quartz crystal monitor controls the thickness.

The Ti/Pt/Au and Cr/Pt/Au metal layers are used for p-contacts and pad contacts,

deposited by an electron-beam evaporation system. In an electron-beam evaporation

system, an electron beam is generated by thermionic emission and accelerated and

directed onto a source of metal that lies in a crucible where the kinetic energy of the

electrons is converted to thermal energy, thus heating the metal and causing metal

atoms to evaporate and form a thin metal film on the wafer. A noticeable advantage

of electron-beam evaporation over thermal evaporation is the possibility to add a

larger amount of energy into the source material. This yields a higher density film

with an increased adhesion to the wafer. The deposition system utilizes a quartz

(b)(a) (c)

Fig. 3-8. Microscope images of a VCSEL structure after the top-metal contact lift-off step (a); after

the bottom-metal contact lift-off step (b); and after the ground-signal-ground pad lift-off step (c).

Etch time (s)

0 200 400 600 800 1000

100

Reletive intensity

Mesa one etch

Measured

0 1000 2000 3000 4000

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Power reflectance

Etch depth (nm)

Mesa one etch

Simulated

0 1000 2000 3000 4000 5000

0.20

0.25

0.30

0.35

0.40

0.45

Power reflectance

Etch depth (nm)

Mesa two etch

Simulated

0 200 400 600 800 1000

100

110

Reletive intensity

Etch time (s)

Mesa two etch

Measured

(unitless)

Fig. 3-9. Simulated power reflectance and measured relative intensity monitor profiles at a wavelength

of 632.5 nm for the mesa one and the mesa two etching.

52 Chapter 3 Fabrication and Measurements

crystal monitor to accurately display the thickness and deposition rate of the metal

deposition process. A shutter is used to block the evaporated metal from hitting the

wafer until everything is ready for the deposition. Microscope images of a VCSEL

structure after various metal lift-off processing steps including after lift-off of the

top-metal contact, the bottom-metal contact, and the ground-signal-ground pads are

shown in Fig. 3-8.

3.2.1.3 Etching

Etching is an important micro-fabrication technique to remove material using a pat-

terned mask for protection. Two different types of etching technology can be used,

wet or dry etching techniques [114]. Wet etching is inexpensive, typically causes no

damage to the wafer, and may be highly selective. Dry etching techniques, using an

energetic ion beam or a plasma, is currently used in semiconductor fabrication due

to its unique ability over wet etching to remove material anisotropically to create

high aspect ratio structures. Inductively coupled plasma reactive ion etching (ICP-

RIE) is a more advanced reactive ion etching technique that uses two independent

RF sources. One RF source is coupled inductively to a low-pressure gas mixture

creating a high-density plasma, and another RF source is applied to a lower electrode

to produce a substrate bias to extract and accelerate the reactive species from the

plasma to the sample being etched. Separate RF generators for the plasma and the

Fig. 3-10. SEM images of a 980 nm VCSEL wafer after the mesa one etch.

0 50 100 150 200 250 300

-12

-10

-8

-6

-4

-2

Hight (µm)

Distance (µm)

After Mesa one etch

5.004 µm

0 50 100 150 200 250 300

-12

-10

-8

-6

-4

-2

6.034 µm

5.004 µm

Hight (µm)

Distance (µm)

After Mesa two etch

(a) (b)

Fig. 3-11. Profile measurement results of a 980 nm VCSEL after the first mesa etch and after the sec-

ond mesa etch.

3.2 VCSEL Fabrication 53

lower electrode allow independent control of ion density and energy. To monitor the

etch depth in situ, a 632.5 nm He-Ne laser is directed onto the wafer and the reflected

power is recorded, all during the etching process. The simulated and measured etch

monitor profiles for a mesa one etch and a mesa two etch for 980 nm VCSELs are

shown in Fig. 3-9. As the DBRs are multi-layer structures, the signal monitored by

the laser interferometer has periodic reflected intensity oscillations as a function of

etch depth. The etch depth at a given instant during the etching process can be deter-

mined by the reflected oscillatory profile, so a precise control of the etching depth can

be achieved. Scanning electron microscope (SEM) images of VCSELs after a mesa

one etch are shown in Fig. 3-10. The profilometer measurement results after a mesa

one etch and a mesa two etch are shown in Fig. 3-11. These measurements indicate

that the heights of the first mesa and the second mesa are 5 and 6 µm, respectively.

3.2.1.4 Selective Wet Oxidation

The oxide apertures for current and transverse optical mode confinement are defined

by the selective wet oxidation of two aluminum-rich Al0.98Ga0.02As layers with our

home-built oxidation furnace, where the sample is exposed to a purified water steam

atmosphere at a temperature of 420 °C. The schematic diagram of our oxidation

furnace is shown in Fig. 3-12. Inert nitrogen is used as a carrier gas to transport water

steam into the furnace. The furnace heater is kept at a constant temperature and the

flow of nitrogen and water steam as well as the chamber pressure are regulated to

achieve a stable and reproducible process. The oxidation rate of AlxGa1−xAs is very

sensitive to the aluminum composition. Precise control of the stop time for a desired

oxide-aperture diameter is very important. The oxidation rate is first determined

by running a calibration test using the same VCSEL epitaxial structure. The SEM

image of the side view of a cleaved 980 nm VCSEL wafer is shown in Fig. 3-13(a),

where two oxide apertures can be clearly seen as partially darkened layers. The

Baratron

Throttle Valve

Pump

H2ON2

Microscope + Camera

Mass Flow ControllerLiquid Flow Meter

Heater

Mixing Valve + Evaporator

Controlled Evaporation and

Mixing-System

H2O/N2 Gas

Fig. 3-12. Schematic diagram of the oxidation furnace.

54 Chapter 3 Fabrication and Measurements

oxidation rate can be determined by measuring the depth of these oxide layers for the

given oxidation time. The approximate oxidation time needed for the desired oxide-

aperture diameters on the subsequent VCSEL wafer piece to be fully processed can

be calculated using the oxidation rate. During the wet oxidation procedure, an in-situ

monitoring system, consisting of a silicon CCD camera and a microscope with an

appropriate illumination wavelength of 850 nm to produce a high contrast between

oxidized and unoxidized AlxGa1−xAs material is used to control the size of the oxide

apertures. Fig. 3-13(b) shows one of the structures that are used to monitor the oxi-

dation depth, illustrating the contrast difference between oxidized and unoxidized

AlGaAs attainable with the monitoring system.

3.2.1.5 RTA Annealing

Low resistance ohmic contacts are required for low threshold, high-speed VCSELs.

The ohmic contact is the contact of a metal and a semiconductor, which neither the

metal or the semiconductor generate significant additional resistance or significantly

change the equilibrium carrier concentration in the semiconductor. Ohmic contacts

have a significant impact on the resistance of the VCSELs, and further affect the

usable operating lifetime and reliability of the devices. Low resistance ohmic con-

tacts can help to reduce the threshold current, improve the efficiency, and prolong the

lifetime of the VCSELs. A SSI Solaris 150 Rapid Thermal Processing System [115]

is used for the metal contact annealing. Using the optimized rapid thermal anneal

(RTA) conditions in N2 with an annealing temperature of 380 °C and an annealing

time duration of 60 s, good ohmic contacts are obtained for the processed VCSELs.

Fig. 3-14 (a) shows the voltage-current (VI) characteristics of one VCSEL before and

after the RTA annealing step, which shows a clear improvement, as the resistance

decreases after the annealing step.

top DBR

bottom DBR

oxide apertures

active region

Stop point

(a) (b)

Fig. 3-13. A SEM image of the side view of a cleaved 980 nm VCSEL wafer test oxidation piece after

oxidation (a) and a microscope image of one of the structures used to monitor the oxidation depth (b).

3.2 VCSEL Fabrication 55

3.2.2 High-Speed VCSEL Processing

The processing is started by cleaving the as-grown 3-inch diameter wafer into four

equal pieces and using one-quarter wafer for the following steps (Fig. 3-15(a)). Top

p-contact metal (Ti/Pt/Au) rings are deposited by e-beam evaporation (Fig. 3-15(b)).

The first circular mesas with diameters from 18 to 31 µm are defined by photolithog-

raphy and etched using ICP-RIE with Cl2/BCl3, and the etch depth is monitored by

an in-situ laser interferometer (Fig. 3-15(c)). Different oxide-aperture diameters are

obtained after the selective wet thermal oxidation due to the different mesa diameters.

The oxide depth is monitored using the in-situ microscope and an 850 nm illumina-

tion source (Fig. 3-15(d)). Next the second mesa etch is performed. The mesa two

etch proceeds into the bottom (n+)GaAs contact layer after oxidation using the same

recipe as for the first mesa etch (Fig. 3-15(e)). Double mesas are used to improve

heat dissipation. The bottom Ni/Ge/Au n-contacts with the shape of a three-quarter

ring are deposited by thermal evaporation and annealed for 60 s at 380 °C in an N2

atmosphere (Fig. 3-15(f)). Thick dry-etched bisbenzo-cyclobutene (BCB) is used

for producing a relatively flat dielectric layer to reduce the parasitic capacitance and

provide a clean surface for the radio frequency (RF) coplanar contact pads. The BCB

is photosensitive enabling the opening of the BCB that covers the n-contact and first

mesa by using UV photolithography. Since the UV photolithography typically does

not fully open and remove all of the thick BCB, RIE etching was used to remove

the remaining BCB above the first mesa and above the bottom metal contact with

CF4/O2 (Fig. 3-15(g)). The coplanar ohmic Cr/Pt/Au contact pads for on-wafer radio

frequency probing are evaporated by electron-beam deposition to achieve a good step

coverage into the n-contact trench in the shape of a high-speed ground-signal-ground

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

before anneling

after anneling

Voltage (V)

Current (mA)

(a) (b)

(c)

Fig. 3-14. The voltage-current (VI) characteristics (a) before and after annealing for a 980 nm VCSEL,

and the layout (b) of the SSI Solaris 150 Rapid Thermal Processing System, also the screen (c) show-

ing the run process menu [117].

56 Chapter 3 Fabrication and Measurements

(a) wafer as grown (b) top contact deposition

(f) bottom contact deposition(e) mesa two etch

(g) BCB processing (h) GSG pad deposition

Fig. 3-15. The 980 nm VCSEL processing scheme showing the primary individual steps: (a) the wafer

as grown; (b) top contact deposition; (c) mesa one etch; (d) wet oxidation; (e) mesa two etch; (f) bottom

contact deposition and annealing; (g) BCB processing; and (h) GSG contact pad deposition.

3.3 VCSEL Measurements 57

(GSG) configuration, Fig. 3-15(h). The device pitch and contact sizes are designed

to facilitate fast automatic continuous wave on-wafer characterization. Additional

processing details may be found in Appendix A.

3.3 VCSEL Measurements

A detailed analysis of the static and high frequency characteristics are performed

for the 980 nm VCSELs, including measurements of the static light output power-

current-voltage (LIV), emission spectra, small-signal frequency response, and high

bit rate data transmission measurements. This section present how these measure-

ments are performed and the evaluation methods, and several results are given as

examples. A more detailed analysis can be found in Chapters 6 and 7.

3.3.1 LIV Measurements

Static characteristics give the basic information of a VCSEL’s performance. The

static LIV characteristics are measured and evaluated using our home-built au-

tomated wafer mapping system. For LIV measurements, VCSELs are driven by

the digital source meter Keithley 2400-LV [117] and the output light is collected

by a calibrated integrating sphere. The photocurrent from the integrating sphere

is measured by a second digital source meter. A LabVIEW program controls both

source meters. The temperature is controlled by a vacuum thermochuck Temptronic

TP03010 [118]. Fig. 3-16(a) shows one example set of LIV measurement results for

a ~7.0 µm oxide-aperture diameter 980 nm VCSEL as a function of the heat-sink

temperature from 25 to 95 °C. The range of currents is chosen to be larger than the

rollover current. Several important parameters can be extracted from the LIV curves,

including threshold current Ith, threshold electrical power Pth, rollover current Irollover,

maximum output power Pmax, maximum differential quantum efficiency DQEmax,

and maximum wallplug efficiency WPEmax, as shown in Fig. 3-16(b) − (g).

3.3.2 Spectral Measurements

To measure the emission spectra, the VCSELs are driven by the digital source meter

(Keithley 2400-LV) and the output light is coupled into a multimode fiber with a

62.5 µm core diameter connected to an optical spectrum analyzer HP 70951B. The

58 Chapter 3 Fabrication and Measurements

-60

-40

-60

-40

-60

-40

-60

-40

-60

-40

974 976 978 980 982 984

-60

-40

25 °C

35 °C

0.4mA

45 °C

Relative intensity (dB)

55 °C

65 °C

85 °C

Wavelength (nm)

-40

970 972 974 976 978 980 982 984

-40

1 mA

3 mA

25 °C

5 mA

Relative intensity (dB)

7 mA

9 mA

11 mA

Wavelength (nm)

(a) (b)

Fig. 3-17. Measured emission spectra at different heat-sink temperatures (a) at 0.4 mA and at different

bias current (b) at 25 °C for a ~7 µm oxide-aperture diameter 980 nm VCSEL.

0 10 20 30

979

981

983

985

20 40 60 80

979

981

983

985

Wavelength (nm)

Dissipated electrical power (mW)

25 °C

Heatsink Temperature (°C)

0.4 mA

∆λ/∆Pdiss

=∆λ/∆T=

Wavelength (nm)

(a) (b)

0.17948 nm/mW 0.06236 nm/K

5 15 25 35 30 50 70 90

980

982

984

986

980

982

984

Fig. 3-18. Measured emission wavelength (fundamental LP01 mode) as a function of dissipated elec-

trical power (a) and measured peak emission wavelength (fundamental LP01 mode) as a function of

heat-sink temperature (b) for the ~7 µm oxide-aperture diameter 980 nm VCSEL.

0 2 4 6 8 10 12 14 16 18

Power (mW)

Current (mA)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Voltage (V)

~7 µm oxide-aperture Ø

55 °C

65 °C

75 °C

85 °C

95 °C

25 °C

35 °C

45 °C

20 40 60 80 100

0.5

0.6

0.7

0.8

0.9 (b)

Ith (mA)

20 40 60 80 100

6(e)

Pmax (mW)

20 40 60 80 100

0.8

1.0

1.2 (c)

Pth (mW)

20 40 60 80 100

16 (d)

Irollover (mA)

20 40 60 80 100

32 (f)

DQEmax (%)

Temperature (°C) 20 40 60 80 100

21 (g)

WPEmax (%)

Temperature (°C)

(a)

Fig. 3-16. Static L-I-V characteristics (a) at 25 to 95 °C for a ~7 µm oxide-aperture diameter 980 nm

VCSEL, and the basic parameters versus temperature including: (b) threshold current Ith; (c) threshold

electrical power Pth; (d) rollover current Irollover; (e) maximum output power Pmax; (f) maximum differ-

ential quantum efficiency DQEmax; and (g) maximum wallplug efficiency WPEmax.

3.3 VCSEL Measurements 59

temperature is controlled by the vacuum thermochuck (Temptronic TP03010B).

Fig. 3-17(a) shows the measured continuous wave (CW) emission spectra for a

~7 µm oxide-aperture diameter VCSEL at a fixed forward bias current of 0.4 mA as

a function of heat-sink temperature from 25 to 85 °C. The measured CW emission

spectra from the same VCSEL at 25 °C as a function bias current from 1 to 11 mA

are shown in Fig. 3-17(b). The cavity etalon resonance wavelength shift rate versus

the dissipated power Δλ/ΔPdiss (Pdiss = I ∙ V − Popt is the dissipated power, Popt is the

optical output power) and versus the heat-sink temperature Δλ/ΔT can be obtained

from the spectral results, which are 0.17948 nm/mW and 0.06236 nm/K, respectively,

as shown in Fig. 3-18(a) and 3-18(b). In addition, the thermal resistance can be calcu-

lated by using Rth = (Δλ/ΔPdiss) / (Δλ/ΔT) [100], which is 2.878 K/mW for the ~7 µm

oxide-aperture diameter VCSEL.

3.3.3 Small-Signal Measurements

Small-signal modulation response (S21) and reflection (S11) measurements can be

measured at the same time. The operating currents are determined by a digital source

meter (Keithley 2400-LV), which is connected via an HP 8722C Network Analyzer

0 3 6 9 12 15 18 21 24

-28

-21

-14

-7

Modulation response (dB)

Frequency (GHz)

25 °C

0 3 6 9 12 15 18 21 24

-28

-21

-14

-7

Modulation response (dB)

Frequency (GHz)

45 °C

0 3 6 9 12 15 18 21 24

-28

-21

-14

-7

Modulation response (dB)

Frequency (GHz)

65 °C

0 3 6 9 12 15 18 21 24

-28

-21

-14

-7

Modulation response (dB)

Frequency (GHz)

85 °C

(a) (b)

(d)(c)

1 mA

2 mA

3 mA

4 mA

1 mA

2 mA

3 mA

4 mA

1 mA

2 mA

3 mA

4 mA

1 mA

2 mA

3 mA

4 mA

Fig. 3-19. Magnitude of the small-signal modulation response S21 for different applied bias currents

and the corresponding fits by using a transfer function at 25 °C (a), 45 °C (b), 65 °C (c), and 85 °C (d)

for a ~2.5 µm oxide-aperture diameter 980 nm VCSEL.

60 Chapter 3 Fabrication and Measurements

to the VCSEL under test. The constant signal from the source meter is overlapped

with a small harmonic signal from the network analyzer and delivered to the device

under test. The output optical signals from the VCSELs are coupled into a multi-

mode optical fiber and guided to a calibrated photodetector (New Focus 1434-50-M

[119, 120] with a bandwidth of 25 GHz), which is connected to the second port of the

network analyzer. After measurement, the response of the detector is subtracted to

eliminate its influence on the measured response. A small-signal electrical equivalent

circuit model [121, 122] is used for the S11 reflection measurements data fitting, in

order to obtain the parasitic cut-off frequencies. With these pre-determined parasitic

cut-off frequencies, the S21 modulation responses are fitted using a transfer function

to extract the relaxation resonance frequency fr and the damping factor γ [69].

The measured S21 curves with corresponding fits for different currents at 25, 45,

65 and 85 °C for a ~2.5 µm oxide-aperture diameter 980 nm VCSEL are shown in

Fig. 3-19. The extracted –3 dB bandwidth and relaxation resonance frequency versus

the square root of bias current minus threshold current and damping rate versus the

squared relaxation resonance frequency are shown in Fig. 3-20. The MCEF can be

obtained from the slope of the linear dependence of the –3 dB bandwidth versus the

square root of the quantity bias current minus the threshold current. The D-factor

can be obtained from the linear fit of the relaxation resonance frequency versus the

square root of the quantity bias current minus threshold current. The K-factor can be

obtained from the relationship of damping and the square of the relaxation resonance

frequency.

0.0 0.4 0.8 1.2 1.6 2.0

25 °C

45 °C

65 °C

85 °C

Frequency (GHz)

frf-3dB

(a)

0 100 200 300 400

120

25 °C

45 °C

65 °C

85 °C

Damping (GHz)

(Resonance frequency)2 (GHz2)

(b)

(I-Ith)1/2 (mA1/2)

( )

3dB

MCEF

I I

−

( )

I I

−

K f

γ γ

= ⋅ +

Fig. 3-20. –3 dB bandwidth and relaxation resonance frequency versus the square root of bias current

minus threshold current (a) and damping rate versus squared relaxation resonance frequency (b) at 25,

45, 65 and 85 °C for the ~2.5 µm oxide-aperture diameter VCSEL.

3.3 VCSEL Measurements 61

3.3.4 Data Transmission Measurements

For data transmission measurements, VCSELs are driven by a combined signal

consisting of a constant bias signal and an amplified bit pattern. A digital source

meter is used for the constant bias signal, and the pseudorandom bit patterns are

generated by a 12100B bit pattern generator from SHF Communication Technologies

AG (Berlin, Germany) followed by an 8 dB amplifier and a 3 dB electrical attenuator

to compensate for the losses of the electrical wires. After amplification, the signal

is superimposed onto the DC biased VCSEL using a 65-GHz SHF bias-tee and a

67 GHz-rated coplanar GSG probe. Simple fiber-to-VCSEL butt-coupling is used to

couple the light into a 5 m long OM2 multi-mode optical fiber. A variable optical

attenuator is used in front of the photoreceiver for both the determination of the bit

error ratio (BER) and for measurements of the eye diagrams. Eye diagrams and bit

error ratio measurements are studied using a 70 GHz Agilent sampling oscilloscope

86100C and a SHF 11100B error analyzer. An u2t Photonics AG photoreceiver with

an integrated limiting transimpedance amplifier is used for recording the optical

eye diagrams and for measuring the BERs. The bandwidth of this photoreceiver is

~28 GHz. A standard non-return to zero (NRZ) modulation scheme with a 27−1 bit

word-length in a pseudorandom binary sequence (PRBS) is used for all transmission

measurements. Fig. 3-21 shows eye diagrams for a ~7 µm oxide-aperture diameter

40 Gb/s 25 °C 40 Gb/s 45 °C

25 Gb/s 25 °C 35 Gb/s 25 °C

Fig. 3-21. Eye diagram for a ~7 µm oxide-aperture diameter VCSEL operating at 25 and 35 Gb/s at

25 °C, and 40 Gb/s at 25 °C and at 45 °C.

62 Chapter 3 Fabrication and Measurements

980 nm VCSEL operating at 25, 35, and 40 Gb/s at 25 °C, and at 40 Gb/s at 45 °C. In

Fig. 3-21 it can be seen that clear open eyes can be obtain at 40 Gb/s at 25 and 45 °C

for the ~7 µm oxide-aperture diameter 980 nm VCSELs. BER test results for 20, 30,

36 and 40 Gb/s error-free data transmission are shown in Fig. 3-22, which shows

error-free data transmission at 40 Gb/s at room temperature can be achieved using a

~7 µm oxide-aperture diameter 980 nm VCSEL.

Fig. 3-22. Bit error ratio (BER)

versus received optical power for

a ~7 µm oxide-aperture diameter

980 nm VCSEL operating at 24,

30, 36 and 40 Gb/s at 25 °C.

-14 -12 -10 -8 -6 -4 -2 0 2

25 °C

20 Gb/s

30 Gb/s

36 Gb/s

40 Gb/s

-log(BER)

Received Optical Power (dBm)

~7 µm oxide-aperture diameter

980 nm VCSEL

Chapter 4

Impedance Characteristics

In this Chapter, the temperature dependence of the impedance characteristics is

studied for high bit-rate, highly temperature-stable 980 nm oxide-aperture VCSELs.

A small-signal equivalent circuit model is fitted to measured small-signal reflection

S11 parameters across a large range of operating bias currents, temperatures, and

oxide-aperture diameters to extract the circuit elements and parasitic cutoff fre-

quency for each particular operating condition. The parasitic cutoff frequencies of

small oxide-aperture diameter VCSELs is highly temperature-insensitive from room

temperature up to 85 °C, and does not limit the VCSELs’ maximum data transmis-

sion rate. Finally, the dependence of the impedance characteristics and modulation

bandwidth on the oxide-aperture diameter is analyzed at 25 and 85 °C. The results

show that the larger capacitance is the main reason larger oxide-aperture diameter

VCSELs, compared to smaller aperture VCSELs, have a lower parasitic cutoff

frequency. The results are useful for the device-, circuit-, and microsystem- level

modeling of VCSELs, optical interconnect subassemblies, and hybrid integrated

photonics systems that employ VCSELs. The results are also useful for analyzing

the performance of state-of-the-art visible and infrared (~600 − 1600 nm) VCSELs

to further understand the device design and performance trade-offs and to improve

the performance of future device iterations.

4.1 Motivation and Applications

The VCSEL is a cost-effective, energy-efficient, and reliable light source for short-

reach optical interconnects in datacenters and supercomputers [123–125]. Vast arrays

of VCSELs are envisioned for use in photonic integrated circuits for chip-to-chip

and on-chip optical computer communications, where the intrinsic temperatures

of the VCSELs placed close to silicon processor cores, memories, and input-output

64 Chapter 4 Impedance Characteristics

circuits may soar. The continuous operating temperature may be 85 °C or higher in

future commercial optical interconnect applications, and furthermore the VCSELs

may be operated in and out of an idle-mode, sleep-mode, or at various bias currents

to optimize the energy efficiency of the system. Given the desire to reduce operating

costs and energy consumption by not cooling the system components the VCSELs

must thus perform well over a large range of temperatures from near zero to 85 °C.

There are three primary factors that can limit the intrinsic modulation bandwidth

of VCSELs including: 1) thermal effects; 2) over damping; and 3) extrinsic parasitic

elements [69]. Several groups have investigated the thermal effects [69, 86, 126]

and damping limitations [111] of VCSELs, and therefore in this work a detailed

systematic study and analysis of the third critical factor, the influences of parasitic

elements on the modulation bandwidth is performed, seeking techniques to optimize

the epitaxial design, the device structure and geometry, and thus the high frequency

performance. In particular parasitic elements at room temperature and at high tem-

peratures and with variations of oxide-aperture diameter are analyzed in detail for

high-speed, highly temperature-stable 980 nm VCSELs. Thus, the key factors that

limit the performance for different oxide-aperture diameter VCSELs versus tempera-

ture are analyzed to determine how to minimize the impact of these elements on the

high bit-rate modulation performance of VCSELs.

4.1.1 Equivalent Circuit Model for VCSELs

In order to better understand how the extrinsic electrical properties of VCSELs affect

their modulation bandwidth, the reflection coefficient S11 and the S21 scattering

parameter are measured and analyzed for a large range of currents, oxide-aperture

diameters, and heat-sink temperatures. Through small-signal equivalent-circuit

modeling [121, 127–129] where the reflection coefficient S11 data are fitted to an

equivalent circuit model to obtain the circuit capacitances and resistances. The

parasitic cutoff frequency fp can then be determined. With this pre-determined value

of parasitic cutoff frequency fp, and using the measured S21 data, the resonance

relaxation frequency fr and the intrinsic damping coefficient γ can then be deter-

mined. Furthermore, with this modeling information the parasitic influence can be

de-embedded [121] to obtain the estimated intrinsic frequency response of VCSELs.

This also can determine intrinsic parameters including the gain slope coefficient,

photon lifetime, and spontaneous emission recombination lifetime [130]. The result

is a more detailed understanding of the devices and insight on how to improve the

performance of subsequent device iterations.

4.1 Motivation and Applications 65

Fig. 4-1(a) shows a cross-sectional schematic view of the VCSEL structure including

the electrical parasitic capacitance and resistance elements. Cp and Rp represent the

contact pad capacitance and resistance between the p-contact and n-contact. The

term Rp and all inductive elements are neglected as these elements are determined to

be negligible in S-parameter fittings and may be replaced by zero impedance wires.

The circuit element Rmirror is the combined series mirror resistance of the p-DBR and

the n-DBR, the circuit element Rsheet is the sheet resistance in the n-contact layer,

and the circuit element Rcontact is the combined p-contact and n-contact resistances.

These resistances are grouped together into Rm (where Rm = Rmirror + Rsheet + Rcontact)

as shown in Fig. 4-1(b). Rj represents the junction resistance. The mesa capacitance

Cmesa consists of the oxide-aperture capacitance Coxide in series with the intrinsic

region layers capacitance Cintrinsic. Thus the mesa capacitance can be expressed as

Cmesa = (Coxide−1 + Cintrinsic−1)−1. The circuit element Cj is the capacitance of the junction

region. This term combine with the mesa capacitance into Cm = Cmesa + Cj. The final

resulting simplified electrical small-signal equivalent circuit model for VCSELs after

combining several of the original electrical elements is shown in Fig. 4-1(b), along

with a microwave voltage source Vs and the characteristic source output impedance

of the measuring equipment Z0, which is 50 Ω.

The load impedance [128, 131] of the electrical equivalent circuit in Fig. 4.1(b) is:

( )

1 2

1 1

( )Z f Z Z

−

= +

(4.1)

where

1 m

(2)

Z R i fC

−

= + +

, and

( )

22p

Z i fC

−

= (4.2)

The complex reflection 2-port S-parameter S11 can be expressed with the imped-

ances as:

( ) ( )

( )

Z f Z

S f Z f Z

(4.3)

Rmirror

Cmesa

CjCintrinsic

Coxide

Signal

Rsheet Rcontact

Ground

(a) (b)

Fig. 4-1. Cross-sectional schematic of the VCSEL structure including electrical parasitic capacitances

and resistances (a), and a simplified electrical equivalent-circuit model (b).

66 Chapter 4 Impedance Characteristics

where Z0 is the characteristic source output impedance of the measuring equipment

(50 Ω). Therefore, the equivalent impedance of the VCSEL can be determined from

the measured reflection coefficient S11 using:

( ) ( )

( )

S f

Z f Z S f

(4.4)

The transfer function due to the electrical parasitic effects [127] is:

par s

( ) ( )H f i f V=

(4.5)

where i(f) is the current through Rj, and Vs is the source voltage. The parasitic cutoff

frequency fp is defined as the frequency where:

| ( ) | 1/ 2

| (0) |

par

H f

H= (4.6)

4.1.2 Measurement of Impedance

The impedance is obtained by measuring the real part and the imaginary part of the

complex impedance vector using a reflection coefficient measurement S11 with an

HP 8722C Network Analyzer. The S21 scattering parameter data are measured at

the same time by the same measurement setup. For the S11 reflection measurement,

a pre-measurement system calibration is very important, as both the magnitude

and phase information are needed. So the entire measurement setup is calibrated to

the radio frequency (RF) probe tip to avoid any electrical delay, otherwise the RF

probe will add an extra frequency-dependent phase shift to the measured data. A

full two-port calibration procedure is used. This calibration uses the short, open,

and broadband load standards on a calibration substrate. Due to system drift, the

calibration must be performed immediately before the S11 measurement to ensure

the accuracy of the results. The values of the equivalent-circuit elements for the sim-

plified model (given in Fig. 4-1(b)) are determined by fitting the simulated results to

the measured scattering parameters. Fig. 4-2 shows one fitting example for a ~2.5 µm

oxide-aperture diameter 980 nm VCSEL with a forward bias current of 2 mA at room

temperature. The fit shows very good agreement with the measured data, and this

helps to verify the validity of the equivalent-circuit model. The same measurements

and evaluations are completed for many different oxide-aperture diameter VCSELs

at different bias currents, and at different operating temperatures.

4.2 Experimental Results 67

4.2 Experimental Results

4.2.1 Impedance vs. Temperature

The 980 nm VCSELs in this work show highly temperature-stable large-signal

modulation performance and high bit-rates, and energy efficient data transmission at

high temperatures, as detailed discussed in Chapter 6. To show how the small-signal

reflection response changes with increasing temperature, complex S11 values are

measured for a ~4 µm oxide-aperture diameter VCSEL operating at forward bias

currents ranging between 1 to 8 mA at room temperature and at 85 °C. The S11 data

are then plotted on a Smith Chart over a frequency range from 50 MHz to 30 GHz as

shown in Fig. 4-3. The curve fits using the equivalent circuit model from Fig. 4-1(b)

are also shown. The measured real and imaginary parts of S11 and the corresponding

curve fits are shown in Fig. 4-4 on linear-linear plots. The curve fits of the real and

the imaginary parts of S11 match very well to the measured data.

The small-signal reflection coefficient S11 and the scattering parameter S21 are

measured for a small oxide-aperture diameter 980 nm VCSEL over a wide range

of currents at 25, 45, 65, and 85 °C to further understand the influence of parasitic

device parameters at different temperatures. First the electrical reflection S11 data

are fitted to the equivalent circuit model [129]. The values of the equivalent-circuit

elements can be obtained through this fitting and the parasitic cutoff frequency can

be determined through the parasitic response. The capacitance values extracted at

25, 45, 65, and 85 °C are plotted in Fig. 4-5(a). The Cm values (the combination of

0.2 1.0 5.0

-0.5j

0.5j

-1.0j

1.0j

-2.0j

2.0j

2 mA

0 5 10 15 20 25 30

0.4

0.5

0.6

0.7

0.8

0.9

Real (S11)

Frequency (GHz)

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Imag (S11)

Real part

fit

Imag part

fit

measurement

(a)

(b)

Fig. 4-2. Measured S11 values for a ~2.5 µm oxide-aperture diameter 980 nm VCSEL operating at

2 mA at 25 °C plotted on a Smith Chart over a frequency range from 50 MHz to 30 GHz (a), and the

real and the imaginary parts of S11 versus frequency (b). The curve fits using the simplified equiva-

lent circuit model are shown as solid lines, whereas the measured data are shown as the open symbols.

68 Chapter 4 Impedance Characteristics

capacitance of the intrinsic region layer and the mesa capacitance) are shown as solid

symbols, and the contact pad capacitances Cp are shown as hollow symbols. The

Cm increase with increasing current at all temperatures. In addition, the values of

Cm at low currents are higher at room temperature compared to their values at high

temperatures. The resistance values extracted at 25, 45, 65, and 85 °C are shown in

Fig. 4-5(b). The junction resistances Rj are shown as solid symbols, and the Rm data

(combination of series mirror resistance, sheet resistance, and contact resistances)

are shown as hollow symbols. The Rj decrease fast with increasing current at all

temperatures. The R

values also decrease with increasing current, but this reduction

is relatively small. The Rm values are higher at room temperature compared to their

values at high temperatures. The VCSEL’s mirror resistance is higher than desired,

with Rm greater than 150 Ω at room temperature, although this is not unusual for such

25 °C

0 4 8 12 16 20 24

0.4

0.5

0.6

0.7

0.8

0.9

Real (S11)

Frequency (GHz)

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Image (S11)

0 4 8 12 16 20 24

0.4

0.5

0.6

0.7

0.8

0.9

Real (S11)

Frequency (GHz)

85 °C

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

1 mA

2 mA

3 mA

5 mA

8 mA

Image (S11)

1 mA

2 mA

3 mA

5 mA

7 mA

(a) (b)

Fig. 4-4. Measured real (circles) and the imaginary (triangles) parts of S11 for a ~4 µm diameter oxide

aperture 980 nm VCSEL operating at different currents at 25 °C (a) and at 85 °C (b). The curve fits

using the equivalent circuit model are shown as solid lines, whereas the measured data are shown as

the open symbols.

(a)

0.2 0.5 1.0 2.0 5.0

-0.2j

0.2j

-0.5j

0.5j

-1.0j

1.0j

-2.0j

2.0j

-5.0j

5.0j

1 mA

2 mA

3 mA

5 mA

8 mA

25 °C

~4 µm Oxide Aperture Diamter

980 nm VCSEL

0.2 0.5 1.0 2.0 5.0

-0.2j

0.2j

-0.5j

0.5j

-1.0j

1.0j

-2.0j

2.0j

-5.0j

5.0j

85 °C

~4 µm Oxide Aperture Diamter

1 mA

2 mA

3 mA

5 mA

7 mA

980 nm VCSEL

(b)

Fig. 4-3. Measured complex S11 values for a ~4 µm oxide-aperture diameter 980 nm VCSEL operat-

ing at different currents at 25 °C (a) and at 85 °C (b) plotted on a Smith Chart over a frequency range

from 50 MHz to 30 GHz. The curve fits using the equivalent circuit model are shown as solid lines,

whereas the measured data are shown as the open symbols.

4.2 Experimental Results 69

small oxide-aperture diameter (~2.5 µm) VCSELs. This leaves room to improve the

DBRs to lower the series resistance in future designs via perhaps improved grading

and doping schemes.

The transfer function, which is described in [69], is used to fit the measured

modulation response. The response of the photoreceiver is subtracted to eliminate

its influence on the measured data. The relaxation resonance frequency fr and the

damping factor γ are extracted using the standard single-mode emission rate equa-

tion model for semiconductor diode lasers [69]. The –3 dB modulation bandwidth

f–3dB is also extracted from the transfer function fits of the modulation response. The

parasitic cutoff frequency f

is reasonably temperature insensitive, as seen in Fig. 4-6.

There is only a small increase in fp with an increase of bias current. By comparing

the f–3dB and fp values at a given current and temperature, fp is higher than f–3dB from

25 to 85 °C (Fig. 4-6) across the entire measured current range. Thus parasitics are

not limiting the high frequency performance of the small oxide-aperture 980 nm

0123456

100

110

Capacitance (fF)

Current (mA)

(a)

0123456

100

150

200

250

300

350

Resistance (Ω)

Current (mA)

(b) RjRm

Fig. 4-5. Extracted values of the equivalent-circuit elements as a function of current for a ~2.5 µm ox-

ide-aperture diameter 980 nm VCSEL at 25, 45, 65, and 85 °C. (a) The Cm (combination of the capaci-

tance of the intrinsic region layer and the mesa capacitance) are shown as solid symbols, and the Cp

(the contact pad capacitance between the p- and n-contacts) are shown as unfilled symbols. (b) The Rj

(junction resistance) are shown as solid symbols, and the Rm (combination of the series mirror resis-

tance of the p-DBR and n-DBR, the sheet resistance in the n-contact layer, and the p- and n-contact

resistances) are shown as unfilled symbols.

Fig. 4-6. Extracted small-signal modu-

lation response and reflection measure-

ments including the parasitic cut-off

frequency fp (solid symbols), the –3 dB

frequency f–3dB (hollow symbols), and the

relaxation resonance frequency fr (half-

solid symbols) as a function of current

for a ~2.5 µm oxide-aperture diameter

980 nm VCSEL at 25, 45, 65, and 85 °C.

012345

f-3dB fr

Frequency (GHz)

Current (mA)

70 Chapter 4 Impedance Characteristics

VCSELs. In fact, the f

increases when moving from 25 to 85 °C, and this benefits the

VCSELs’ temperature stable high bit-rate performance. The given extracted values

of fr, fp, and f–3dB show that the high bit-rate performance of the small oxide-oxide

aperture VCSELs are limited by thermal effects, and partially by over damping.

4.2.2 Impedance vs. Oxide-Aperture Diameter

The maximum achievable bit rate and minimum possible energy dissipation per bit

for error-free data transmission are both strongly dependent on the oxide-aperture

diameter of the VCSEL, which will be discussed in further detail in Chapter 7.

The VCSELs with oxide-aperture diameters of ~3 to 5 µm are most suitable for

energy-efficient and high-speed operation at high temperatures. It is interesting

to determine how the parasitic cutoff frequency and the values of the small-signal

0 20 40 60 80

-100

100

200

300

100

200

300

400

500

0 20 40 60 80

-100

100

200

300

400

500

600

100

120

140

160

180

(fF)

Cp (fF)

Rj (Ω)

Rm (Ω)

Current density (kA/cm

) Current density (kA/cm

)

2.5

3.5

Aperture dia. (µm)

25 °C

25 °C 2.5

3.5

Aperture dia. (µm)

(a) (b)

Fig. 4-7. Extracted values of the equivalent-circuit elements as functions of current density for ~2.5,

3.5, 5, 6, and 7 µm 980 nm oxide-aperture diameter VCSELs at 25 °C; (a) the Cm are shown as filled

symbols, and the Cp are shown as unfilled symbols; (b) the Rj are shown as filled symbols, and the Rm

are shown as solid symbols.

2.5

3.5

Aperture dia. (µm)

Cm (fF)

(a)

Cp (fF)

85 °C

Rj (Ω)

(b)

2.5

3.5

Aperture dia. (µm)

85 °C

Rm (Ω)

0 20 40 60 80

-100

100

200

300

400

500

600

100

120

140

160

180

0 20 40 60 80

-100

100

200

300

100

200

300

400

500

Current density (kA/cm

) Current density (kA/cm

)

Fig. 4-8. Extracted values of the equivalent-circuit elements as functions of current density for ~2.5,

3.5, 5, 6, and 7 µm 980 nm oxide-aperture diameter VCSELs at 85 °C; (a) the Cm are shown as filled

symbols, and the Cp as unfilled symbols; (b) the Rj are shown as filled symbols, and the Rm are shown

as solid symbols.

4.2 Experimental Results 71

equivalent-circuit elements change with the VCSEL’s oxide-aperture diameter. Thus

oxide-aperture diameter-dependent small-signal measurements are performed. The

extracted capacitance results of ~2.5, 3.5, 5, 6, and 7 µm oxide-aperture diameter

VCSELs at 25 °C are shown in Fig. 4-7(a). The Cm increases with increasing current

density for all VCSELs. In addition, the value of Cm is larger for large oxide-

aperture diameter VCSELs, which have larger mesa diameters compared to small

oxide-aperture VCSELs. For the entire current density range, small oxide-aperture

diameter VCSELs have a smaller Cm at the same current density. The values of Cp

have a negligible change with increasing current density. The extracted capacitance

results at 85 °C are shown in Fig. 4-8(a), which shows a similar change as at 25 °C,

only with different values. The value of Cm is lower at 85 °C than at 25 °C for the

entire current range investigated here, which is the same as observed for the ~2.5 µm

oxide-apertures diameter VCSEL as shown in 4-5(a). The resistance results (as shown

in Fig. 4-7(b)) for ~2.5, 3.5, 5, 6, and 7 µm oxide-apertures diameter VCSELs at 25 °C

show that small oxide-aperture diameter VCSELs have larger Rj and Rm than the large

oxide-aperture diameter VCSELs at the same current density as is expected due to

current crowding. The VCSEL resistances at 85 °C follow the same general trend as

the resistances at 25 °C, as shown in Fig. 4-8(d). The junction resistance Rj is higher

at 85 °C than at 25 °C for the entire current range investigated here. This is also the

same as what has been observed before for the ~2.5 µm oxide-apertures diameter

VCSEL as shown in 4-5(b). The opposite change trends of the capacitance and the

resistance offset each other, which leads to a highly temperature-stable parasitic

cutoff frequency for the different oxide-aperture VCSELs.

Thus, as expected larger oxide-aperture diameter VCSELs have a higher capaci-

tance and a lower resistance compared to smaller VCSELs, and at the same current

density, the capacitance Cm increases faster with growing oxide-aperture diameter.

0 20 40 60 80

Frequency (GHz)

Current density (kA/cm

)

-3dB

2.5

3.5

Aperture dia. (µm)

25 °C

(a)

Frequency (GHz)

(b)

2.5

3.5

Aperture dia. (µm)

85 °C

0 20 40 60 80

-3dB

Frequency (GHz)

Current density (kA/cm

)

Fig. 4-9. Parasitic cut-off frequency fp extracted from small-signal modulation response and reflection

measurements at increasing bias current density for ~2.5, 3.5, 5, 6, and 7 µm oxide aperture diameter

980 nm VCSELs at 25 °C (a) and at 85 °C (b).

72 Chapter 4 Impedance Characteristics

This is in contrast to the resistance Rj and its slower decrease with increasing oxide-

aperture diameters. The net result is a near-stable fp with increasing current density.

Fig. 4-9 shows the extracted parasitic cutoff frequency at room temperature and at

high temperature. The ~3.5 µm oxide-aperture diameter 980 nm VCSEL has the

highest parasitic cutoff frequency both at room temperature and at high temperature.

With further increases of the oxide-aperture diameter, the parasitic cutoff frequency

starts to decrease. Large oxide-aperture diameter VCSELs have a noticeably lower

parasitic cutoff frequency. This is because the resistances decrease slowly while the

capacitance rapidly increases as the device area increases. This high capacitance

and its faster change with increasing bias current is the main reason for a reduced

parasitic cutoff frequency. Thus, the capacitance can be further decreased to improve

the parasitic cutoff frequency, by for example reducing the mesa area, by adding ad-

ditional deep oxide layers without increasing mirror resistance, or perhaps by using

an added proton implantation.

4.3 Summary

The temperature-dependent and oxide-aperture diameter-dependent impedance

characteristics are investigated for high-speed, highly temperature-stable 980 nm

VCSELs. The values of the small-signal equivalent-circuit elements (capacitances

and resistances) over a large range of currents at different temperatures are com-

pared. The analysis shows that small oxide-aperture diameter VCSELs are not

limited by parasitics at temperatures from 25 to 85 °C. The study of oxide aperture-

dependent impedance also shows that the larger capacitance of larger oxide-aperture

VCSELs limits the VCSELs’ parasitic cutoff frequency. This work provides a better

understanding of the direct current modulation rate limitation of VCSELs at dif-

ferent temperatures, and gives insight on how to maximize 980 nm VCSELs’ high

frequency performance.

Chapter 5

980 nm VCSEL Noise Characteristics

Semiconductor laser relative intensity noise (RIN) is the major source of data com-

munication system noise. RIN characterizes the relative amplitude of optical power

fluctuation around the average optical power level, which is often associated with

transmission of optical data, as it limits the maximum available signal-to-noise ratio

(S/N) of the laser during signal modulation. In high-speed digital systems, RIN can

limit the bit-error ratio and the system performance under certain conditions. This

makes the RIN value an important parameter for characterizing optical communica-

tion systems.

5.1 Semiconductor Laser RIN

Relative intensity noise in a laser diode is caused by random carrier and photon

recombination and generation events, producing instantaneous time variations in

the carrier and photon densities. The intensity noise mainly comes from the laser

diode mode competition, as well as the optical interference between the coherent

laser modes and the spontaneous light emission. A laser with low RIN is essential

in the pursuit of high fidelity optical transmission. According to [132], the RIN

needs to be below −128 dB/Hz for reliable 28 Gb/s optical data transmission. As

RIN changes with bias current and with the oxide-aperture diameter of VCSELs, it

is useful to know the RIN value at the bias conditions for high bit-rate and energy

efficient operation.

The variation in photon density causes a variation in output power. The intensity

noise (optical power fluctuations) is quantified using the relative intensity noise,

which is the power noise normalized to the average power level. Optical power is

74 Chapter 5 980 nm VCSEL Noise Characteristics

detected with a fast photodetector, and thus the optical power fluctuations are trans-

formed into electrical power fluctuations, which are measured with an electrical

spectrum analyzer (ESA). RIN can be expressed through the electrical values:

, ,

laser th PD shot

total

avg elec avg elec

N N N

RIN P P

+ +

= =

(dB/Hz) (5.1)

where Ntotal (dBm/Hz) is the overall noise and Pavg,elec is the average electrical power.

The overall noise Ntotal has three noise components: the VCSEL noise Nlaser, the

thermal noise Nth, and shot noise NPD,shot. The total amplified system noise power

spectrum N

total

is measure by the ESA with the laser diode on. By turning off the laser

and keeping the operation of the photodetector and amplifiers, the signal analyzer

measures only the thermal noise power spectrum Nth(f). Ntotal and Nth are weighted

using the power spectral density per unit bandwidth with the unit of dBm/Hz, which

can be calculated from noise power (dBm) and the resolution bandwidth (RBW)

of the ESA using 1 dBm/Hz = 1 dBm − 10 log(BW). G(f) (dB) is the frequency-

depended amplifier power gain. Shot noise NPD,shot = 2qIphRL is the shot noise power

of the photodetector under the average input laser power P0, Iph is the photocurrent

out of the photodetector, RL is the load resistance of the amplifier input port. NPD,shot

appears at the photodetector and rises proportionally to the detected optical power.

The average electrical power Pavg,elec = Iph2 RL. After subtracting the system thermal

noise and the photodetector shot noise, the intrinsic laser RIN can be extracted as:

( ) ( ) ( ) ( )

total th PD shot

laser

avg elec

N f N f G f N

RIN f P

é ù

- -

ë û

(5.2)

RIN corresponding to shot noise can be calculated as:

RIN N

qI R

I R

PD shot

avg elec

ph l

ph L ph

= = =

(5.3)

From a small-signal analysis of the rate equations for a single-mode laser diode,

the transfer function describing the RIN spectrum attains the following frequency

dependence [69, 133]:

( )

2 2 2

/ 2

Af B

RIN f

f f fg p

- +

(5.4)

which shows that RIN peaks at the relaxation resonance frequency, and A and B are

given in Ref. [133].

5.1 Semiconductor Laser RIN 75

5.1.1 Laser Diode RIN Measurement

The laser diode RIN is characterized with the measurement setup in Fig. 5-1. The

VCSEL under test is biased at constant DC currents, and the output light is directly

coupled into a 5 m-length lensed multimode fiber. The optical fiber is connected to

a high speed New Focus 25 GHz photodetector 1434-50, and the signal is amplified

by two cascaded amplifiers SHF 100AP and SHF 804EA with a gain of 19 and

20 dB to produce enough amplification to raise the signal above the noise floor of

our spectrum analyzer. The frequency-dependent total amplifier power gain G(f)

of the two cascaded amplifiers is measured using a Network Analyzer. This factor

G(f) is subtracted from the noise measured by the ESA to compensate for the gain

and the frequency response of the amplifiers. The New Focus photodetector has a

build in bias monitor to measure the average photocurrent during the measurements.

The average DC photocurrent can be calculated using a gain factor of 1 mV/μA to

determine the average optical power. To measure one RIN value at a specific diode

current, the first measurement is performed with the VCSEL turned on to determine

the amplified overall noise Ntotal by using a Hewlett-Packard (HP) 8562A Spectrum

Analyzer. Then a second measurement is performed with the VCSEL turned off,

while leaving unchanged the photodetector and amplifiers, to determine the thermal

noise Nth. The thermal noise does not depend on the optical power, which can be

simply subtracted from the total noise. The resolution bandwidth of the ESA should

be set low enough for the highest possible measurement precision with still enough

sensitivity. The measurement precision is set at 30 kHz for the following measure-

ments. The VCSEL RIN can be extracted by fitting to the theoretical small signal

model using equation (5.4) as described in [69, 133].

ESA

GPIB

Current source

Amplifier 2

Amplifier 1

Multimode Fiber

PhotodetectorVCSEL

Fig. 5-1. Schematic view of the RIN measurement setup for 980 nm VCSELs

76 Chapter 5 980 nm VCSEL Noise Characteristics

5.1.2 RIN Specification Trend for the Fibre Channel Standard

VCSELs have attractive features that have made these laser diodes the most popular

transmitter choice in short-range optical communication links. The Fibre Channel

standard is one of the most important standards in short-range communications

across optical fiber [132]. A summary of the Fibre Channel standards that have been

ratified to date is shown in Tab. 5-1 [132, 134, 135]. Obviously, the criteria specified

for RIN has become more and stricter as the bit rate increases. It is interesting to

investigate whether VCSELs can satisfy the requirements of the relative intensity

noise performance. In addition, the knowledge learned from RIN data can be used

to better construct next generation designs to improve the performance of these

VCSELs for specific low-noise applications

Tab. 5-1. RIN specifications in the different Fibre Channel standards to date

[133, 135, 136], [137, 138]*

Standard Line Rate

(GBaud)

VCSEL RIN

(dB/Hz)

Market Avail-

ability (Year)

1 GFC 1.0625 −116 1997

2 GFC 2.125 −117 2001

4 GFC 4.25 −118 2005

8 GFC 8.5 −128 2008

16 GFC 14.025 −128 2011

32 GFC 28.5 −131*2014

5.2 980 nm RIN Characteristics

Laser diode RIN depends on many device performance and measurement test con-

dition parameters, the most important are test frequency, laser diode output power,

the operating temperature, modulation frequency, modulation signal time delay, the

magnitude of any optical feedback, the side-mode-suppression ratio of the emission

spectra, and the relaxation oscillation frequency.

5.2 980 nm RIN Characteristics 77

5.2.1 980 nm RIN versus Bias Current

Fig. 5-2 (a) shows the measured RIN spectra for different bias currents above the

threshold current at room temperature for a ~3 µm oxide-aperture diameter 980 nm

VCSEL as well as the calculated shot noise level for the highest bias current. The

threshold current is 0.33 mA. Fitted theoretical curves using equation (5.4) are in-

cluded for four of the curves. The behavior is as expected [69], with maximum noise

intensity at the relaxation oscillation frequency, an increasing relaxation frequency

with bias current, and a decrease in the RIN with an increase in bias current. This

is because the predominant source of RIN is usually spontaneous emission. Hence,

RIN reaches a maximum just above threshold when the spontaneous emission is

typically at a maximum, and then the RIN decreases with increasing bias current,

when the noise power does not increase too much while the optical power increases

fast at high currents. These high-frequency RIN spectra contain well-defined peaks

and reach the maximum RIN value at the relaxation oscillation frequency. The RIN

decreases with increasing bias current, reaching a theoretical minimum level of

−152 dB/Hz at a bias current of 3 mA. From the measured photocurrent of 0.55 mA,

the shot noise level can be calculated into −152.3 dB/Hz, which is nearly the same

as the measured minimum level. At this bias point (3 mA), the measurements are

already very close to the measurement system noise. Fig. 5-2(b) shows the maximum

RIN value at different currents. The maximum RIN value at measured bias current

decreases with increasing current. In order to indicate the achievable speed, the

–3 dB bandwidth obtained from S21 measurements at different currents are also

shown. For the applied bias current of 3 mA, the –3 dB bandwidths reaches a high

value of 19.85 GHz where the RIN is as low as –141 dB/Hz, which is lower than the

requirement for the 32 GFC standard [136, 137]. The shot noise limit can be reached

by further increasing the forward bias current. The RIN data shows that 980 nm

1 mA

1.5 mA

2 mA

2.5 mA

3 mA

25 °C

~3 µm oxide aperture Ø

980 nm VCSEL

2 4 6 8 10 12

-160

-150

-140

-130

-120

-110

-100

Laser RIN (dB/Hz)

Frequency (GHz)

4 mA

012345

-160

-150

-140

-130

-120

-110

-100

RINmax (dB/Hz)

current (mA)

f3dB (GHz)

25 °C

~3 µm oxide aperture diameter

19.85 GHz

-141.377 dB/Hz

-131dB/Hz

shot noise limit:152.3dB/Hz (Iph=0.55mA)

Fig. 5-2. RIN spectra (a) for different bias conditions at room temperature for a ~3 µm oxide-aperture

diameter 980 nm VCSEL, and (b) the maximum value of RIN and the –3 dB bandwidth at the maxi-

mum RIN versus the bias current.

78 Chapter 5 980 nm VCSEL Noise Characteristics

VCSELs can be operated at high bit-rates with low noise. VCSELs may be operated

at the lowest currents where still error-free data transmission is observed to improve

energy efficiency. Fig. 5-2 shows that low current usually means a high RIN value,

so it is necessary to know whether the RIN is low enough at low currents to also

achieve energy efficiency operation. Chapter 7 shows that error-free data transmis-

sion at 35, 38, and 42 Gb/s with low power dissipation of 145, 147, and 217 fJ/bit

are achieved using the same VCSEL employed here. The bias currents are 2.7, 2.9,

4.1 mA, respectively. According to [132], the requirement of RIN for the 32 GFC

Standard is below −131 dB/Hz. Fig. 5-2(b) shows that this RIN requirement can be

met with a current larger than 2.2 mA. The current for record energy efficient 35, 38,

and 42 Gb/s error-free data transmission are all larger than 2.2 mA, which means

RIN is lower than the requirement for the 32 GFC Standard. So this VCSEL can be

operated at high bit-rates with low energy dissipation and with low noise.

5.2.2 980 nm RIN versus the Oxide-Aperture Diameter

The same measurements and evaluation as in Fig. 5-2(a) are performed for different

oxide-aperture diameter 980 nm VCSELs. Fig. 5-3 and Fig. 5-4 show the RIN spectra

for different bias currents above threshold at room temperature for ~4 to ~7 µm

oxide-aperture diameter 980 nm VCSELs as well as the calculated shot noise level

for the highest bias current and the theoretical fitting of the RIN data (the smooth

lines). The results are similar to the RIN behavior of the ~3 µm oxide-aperture diam-

eter VCSEL. However, there is one difference at the high bias current. For the small

oxide-aperture diameter (~3 µm) VCSEL, the noise saturates at the shot noise floor,

but the noise of the large oxide-aperture diameter (~6 and 7 µm) VCSELs is higher

due to mode competition. Due to much larger photocurrent, the shot noise level is

also lower for larger oxide-aperture diameter VCSELs. Also, larger oxide-aperture

2 4 6 8 10 12

Frequency (GHz)

Laser RIN (dB/Hz)

-160

-150

-140

-130

-120

-110

-100

shot noise limit at Iph= 0.45mA: 151.5 dB/Hz

0.5 mA

1 mA

1.5 mA

2 mA

3 mA

4 mA

25 °C

~4 µm oxide aperture Ø

2 4 6 8 10 12

-160

-150

-140

-130

-120

-110

-100

shot noise limit at Iph= 0.48mA: 151.7 dB/Hz

25 °C

~5 µm oxide aperture Ø 0.5 mA

1 mA

1.5 mA

2 mA

3 mA

4 mA

5 mA

Laser RIN (dB/Hz)

Frequency (GHz)

Fig. 5-3. RIN spectra for different bias conditions at room temperature for ~4 µm (a) and ~5 µm (b)

oxide-aperture diameter 980 nm VCSELs.

5.2 980 nm RIN Characteristics 79

diameter VCSELs are faster (small percentage of rollover current) to achieve low

RIN compared to small ones despite higher order mode competition, as shown in

Fig. 5-5, where maximum RIN values and the output power versus current are shown.

For the same low RIN value of −141 dB/Hz, the bias current needs to be larger than

3 and 6.1 mA for ~3 and 7 µm oxide-aperture diameter VCSELs, respectively. The

rollover currents are 6 and 16 mA for ~3 and 7 µm oxide-aperture diameter VCSELs.

The bias current needs to be larger than 49 % of the rollover current to have a low

RIN of −141 dB/Hz with ~3 µm oxide-aperture diameter VCSELs, but only 37.6 % of

the rollover current to have a low RIN of −141 dB/Hz by using ~7 µm oxide-aperture

diameter VCSELs. So larger oxide-aperture diameter VCSELs are faster to reach a

low RIN value, leading to a lower RIN for high-bit rate operation.

The maximum value of laser diode RIN is at the relaxation resonance frequency.

Fig. 5-6 shows these maximum RIN values versus bias current for VCSELs with ~3,

4, 5, 6 and 7 µm oxide-aperture diameters. It is clear that for a given constant current

larger oxide-aperture diameters VCSELs have higher RIN values than smaller ap-

erture ones. This is because the photon density is higher for smaller oxide-aperture

diameter VCSELs due to the smaller optical mode volume. The relaxation resonance

frequency and the damping both increase with an increase in photon density, which

Fig. 5-5. Maximum RIN value and the out-

put power versus current for ~3 and ~7 µm

oxide-aperture diameter 980 nm VCSELs.

0 2 4 6 8 10 12 14 16 18

-160

-150

-140

-130

-120

-110

-100

current (mA)

3µm

7µm

Optical power (mW)

RINmax (dB/Hz)

-141dB/Hz

25 °C

980 nm VCSEL

2 4 6 8 10 12

-160

-150

-140

-130

-120

-110

-100

Frequency (GHz)

25 °C

~6 µm oxide aperture diameter

1 mA

1.5 mA

2 mA

3 mA

4 mA

6 mA

Laser RIN (dB/Hz)

shot noise limit at Iph= 0.73mA: 153.6 dB/Hz

2 4 6 8 10 12

-160

-150

-140

-130

-120

-110

-100

Frequency (GHz)

25 °C

~7 µm oxide aperture diameter

1.5 mA

2 mA

2.5 mA

4 mA

6 mA

8 mA

shot noise limit at Iph= 0.9mA: 154.48 dB/Hz

Laser RIN (dB/Hz)

Fig. 5-4. RIN spectra for different bias conditions at room temperature for ~6 µm (a) and ~7 µm (b)

oxide-aperture diameter 980 nm VCSELs.

80 Chapter 5 980 nm VCSEL Noise Characteristics

leads to lower RIN values for smaller oxide-aperture diameter VCSELs. At the same

time, smaller oxide-aperture diameter VCSELs need smaller currents to achieve the

same bandwidth, as show in Fig. 5-6. Small currents lead to a high RIN value. To

achieve a high –3 dB bandwidth of 18.9 GHz, the RIN is only –141 and –151 dB/

Hz for ~3 and ~4 µm oxide-aperture diameter VCSELs, and reaches the shot noise

limit for larger VCSELs. So small oxide-aperture diameter VCSELs not only benefit

from a higher –3 dB bandwidth and lower energy dissipation, but they also have suf-

ficiently low noise, that enables the use of these VCSELs in future high-speed and

low noise optical links with low energy consumption.

5.3 Summary

The relative intensity noise is investigated for high-speed and energy-efficient

980 nm VCSELs. Measurements are performed at different bias currents at room

temperature for different oxide-aperture diameter VCSELs. The VCSELs can satisfy

the requirements of bandwidth and RIN for the 32 GFC Fibre Channel standard.

Larger oxide-aperture diameter VCSELs have higher RIN values than smaller oxide-

aperture diameter VCSELs when biased at the same current. To achieve a certain

high bandwidth, small oxide-aperture diameter VCSELs can be used for high-speed

and energy-efficient data transmission with sufficiently low noise, thus enabling the

use of small oxide-confined 980 nm VCSELs in future high bit-rate and low noise

optical links with low energy consumption.

reach the shot noise limit

-151dB/Hz

-141dB/Hz

0 3 6 9 12 15

-160

-140

-120

-100 0 3 6 9 12 15

Current (mA)

f3dB (GHz)

RINmax (dB/Hz)

µm

25 °C

980 nm VCSEL

Fig. 5-6. Comparison of maximum RIN value for 980 nm VCSELs with different oxide-aperture di-

ameters operated at room temperature, and the −3 dB bandwidth versus bias current. The −3 dB band-

width is extracted from the S21 measurements and may be used to estimate the maximum achievable

non-return-to-zero error-free bit rate.

Chapter 6

Temperature-Stable 980 nm VCSELs

Vertical-cavity surface-emitting lasers are cost-effective, energy-efficient, and reli-

able light sources for optical interconnects in datacenters and supercomputers [124,

125, 138]. Highly temperature-stable operation against the temperature variation is a

highly desired attribute for high-speed lasers for optical interconnects, because the

operating temperature can reach 85 °C or higher in datacenters and supercomputers.

These optical interconnects should operate without extra cooling to reduce the cost.

This requires that VCSELs are capable of operating over a large temperature range

with relatively stable and energy-efficient performance. The experimental results of

temperature-stable 980 nm VCSELs will be presented in this Chapter. In Section 6.1

the temperature-dependent static characteristics are shown, including output power,

threshold current, wallplug efficiency, and emission spectra. The temperature-depen-

dent small signal modulation analysis is in Section 6.2. Highly temperature-stable

data-transmission results are presented in Section 6.3.

6.1 Temperature-Dependent Static Analysis

Introducing a certain gain-to-etalon wavelength offset into the cavity design can

improve the static performance of VCSELs at high temperatures. The calculation

results of the static performance for different gain-to-etalon wavelength offset

designs have been presented in Chapter 2. In this section, the experimental static

results of 980 nm VCSELs with a –15 nm quantum well gain-to-etalon wavelength

offset will be presented. These VCSELs are demonstrated to be particularly well

suited for temperature-stable operation from 25 to 85 °C.

82 Chapter 6 Temperature-Stable 980 nm VCSELs

6.1.1 Temperature-Dependent LIV Results

LIV results between 25 and 95 °C for ~3.5 µm oxide-aperture diameter 980 nm

VCSEL are shown in Fig. 6-1(a). The approximate oxide-aperture diameters can be

determined with the model described in [139] by measuring the emission spectra.

The device has very temperature-stable output power, which is nearly constant for

the temperature range from 25 to 95 °C for bias current smaller than 2 mA, as shown

in Fig. 6-1(b). The differential quantum efficiency DQE, wall plug efficiency WPE,

and differential resistance R

change with current. Fig. 6-2 shows the WPE,DQE, and

Rd versus current at 25, 45, 65, and 85 °C for the ~3.5 µm oxide-aperture diameter

980 nm VCSEL. The WPE reaches the maximum value with a current increase then

decreases with a further increase of current. This change trend with current is the

same for room temperature and high temperature operation. The WPE is very tem-

perature-stable, and the maximum values are very close at 25 to 85 °C. The current

for maximum WPE is smaller at 85 °C than at room temperature. The maximum

differential quantum efficiency DQE is lower at the high temperature than at room

02468

0.0

0.5

1.0

1.5

2.0

2.5

Power (mW)

Current (mA)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

~3.5 µm oxide-aperture ø

Voltage (V)

20 30 40 50 60 70 80 90

0.0

0.5

1.0

1.5

2.0

2.5 0.5 mA

2 mA

4 mA

6 mA

output

(mW)

Temperature (°C)

55 °C

65 °C

75 °C

85 °C

95 °C

25 °C

35 °C

45 °C

(a)

(b)

Fig. 6-1. Static L-I-V characteristics at 25 to 95 °C (a) of a ~3.5 µm oxide-aperture diameter 980 nm

VCSEL, and the output power versus temperature at different bias currents (b).

01234567

DQE (%)

Current (mA)

012345678

WPE (%)

Current (mA) 01234567

200

400

600

800

~3.5 µm aperture Ø

Rd (Ω)

Current (mA)

~3.5 µm aperture Ø

25 °C

45 °C

65 °C

85 °C

(a) (b) (c)

25 °C

45 °C

65 °C

85 °C

25 °C

45 °C

65 °C

85 °C

Fig. 6-2. Wall plug efficiency (WPE) (a), differential quantum efficiency (DQE) (b), and differential

resistance (Rd) (c) versus current at 25, 45, 65, and 85 °C for the ~3.5 µm oxide-aperture diameter

980 nm VCSEL.

6.1 Temperature-Dependent Static Analysis 83

temperature, and needs a slightly higher current to reach the maximum value at

25 °C. The differential resistance is quite stable with temperature, and only slightly

decreases at lower temperature.

Figure 6-3 shows the static parameters extracted from the LIV curves of the

~3.5 µm oxide-aperture diameter 980 nm VCSEL. At 25 °C the threshold current

Ith is 0.388 mA, and decreases to a minimum value of 0.259 mA at 75 °C, then

increases slightly to 0.271 mA at 85 °C, with a relative change of –30 % when the

temperature increases from 25 to 85 °C. The measured threshold current reaches a

minimum value at around 75 °C, which matches with the QW gain-to-etalon offset

design to improve the temperature stability. The threshold voltage Uth approximately

linearly decreases with temperature and the change is very small, thus the threshold

electrical power Pth (Pth = Ith × Vth) has a similar change as the threshold current.

The maximum output power Pmax and the rollover current Irollover also approximately

linearly decrease with increasing temperature. The maximum optical output power

is 2.05 mW at room temperature with a rollover current of 7.36 mA, and reduces

20 40 60 80 100

0.2

0.3

0.4 (a)

20 40 60 80 100

1.2

1.5

1.8

2.1 (b)

20 40 60 80 100

1.4

1.6

1.8 (c)

20 40 60 80 100

0.4

0.6

0.8 (d)

20 40 60 80 100

Temperature (°C)

(e)

20 40 60 80 100

1.0

1.5

2.0

Temperature (°C)

(f)

20 40 60 80 100

Temperature (°C)

(g)

20 40 60 80 100

15.0

15.5

16.0

16.5

Temperature (°C)

(h)

Ith (mA)

Pmax (mW)

Pth (mW)

DQEmax (%)

Irollover (mA)

WPEmax (%)

Jth (KA/cm2)

Uth (V)

Temperature (°C) Temperature (°C) Temperature (°C) Temperature (°C)

Fig. 6-3. Extracted parameters of the ~3.5 µm oxide-aperture diameter 980 nm VCSEL versus temper-

ature: (a) threshold current Ith; (b) threshold current density Jth; (c) threshold voltage Uth; (d) threshold

electrical power Pth; (e) rollover current Irollover; (f) maximum output power Pmax; (g) maximum differ-

ential quantum efficiency DQEmax; and (h) maximum wallplug efficiency WPEmax.

0123456789

0.0

0.5

1.0

1.5

2.0

2.5

Power (mW)

Current (mA)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Voltage (V)

20 30 40 50 60 70 80 90

0.5

1.0

1.5

2.0

2.5 1 mA

3 mA

5 mA

7 mA

Temperature (°C)

output

(mW)

~4 µm oxide-aperture ø ~4 µm oxide-aperture ø

55 °C

65 °C

75 °C

85 °C

95 °C

25 °C

35 °C

45 °C

(a) (b)

Fig. 6-4. Static LIV characteristics at 25 to 95 °C (a) of a ~4 µm oxide-aperture diameter 980 nm

VCSEL, and the output power versus temperature at different bias currents (b).

84 Chapter 6 Temperature-Stable 980 nm VCSELs

to 1.36 mW with a rollover current of 5.96 mA at 85 °C. The maximum differential

quantum efficiency decreases with the temperature increases. The maximum WPE

is quite stable, and slightly increases with the temperature up to 55 °C, then slowly

decreases as the operating temperature further increases.

Fig. 6-4 shows the LIV results for a slightly larger VCSEL with ~4.0 µm oxide-

aperture diameter between 25 and 95 °C. The LIV curves are similar to the LIV

curves for the ~3.5 µm oxide-aperture diameter VCSEL. The output power is

higher due to the larger oxide-aperture diameter. The extracted parameters also

show a similar change trend, only with different values. The threshold current Ith

and threshold electrical power Pth decrease with increasing temperature reaching a

minimum and then increase in a parabolic shape as shown in Figs. 6-5(a) and 6-5(d).

The measured threshold current reaches a minimum value at around 75 °C. At 25 °C

the threshold current is 0.33 mA, and decreases to a minimum value of 0.25 mA at

75 °C, then increases slightly to 0.26 mA at 85 °C, with a relatively small change of

only −24 % when the temperature increases from 25 to 85 °C.

6.1.2 Spectral Characteristics

Emission spectra are measured to determine the thermal resistance of the 980 nm

VCSELs, and to determine the approximate oxide-aperture diameter as mentioned

in section 3.3.2. Figure 6-6(a) shows the measured CW emission spectra for the

980 nm VCSEL with an oxide aperture diameter of ~2.5 µm at a fixed forward

bias current of 0.4 mA as a function of heat-sink temperature from 25 to 85 °C.

Figure 6-6(b) shows the measured CW emission spectra from the same VCSEL at

20 40 60 80 100

0.2

0.3

0.4 (a)

20 40 60 80 100

1.6

2.0

2.4

2.8 (b)

20 40 60 80 100

1.4

1.5

1.6

1.7 (c)

0.8

20 40 60 80 100

0.2

0.4

0.6

(d)

Temperature (°C)

20 40 60 80 100

9(e)

20 40 60 80 100

1.0

1.5

2.0

2.5 (f)

Temperature (°C)

20 40 60 80 100

30 (g)

Temperature (°C)

20 40 60 80 100

15.0

15.5

16.0

16.5

17.0 (f)

(mA)

Pmax (mW)

Pth (mW)

DQEmax (%)

Irollover (mA)

WPEmax (%)

Jth (KA/cm2)

Uth (V)

Temperature (°C)

Temperature (°C) Temperature (°C) Temperature (°C)Temperature (°C)

Fig. 6-5. Parameters of the ~4 µm oxide-aperture diameter 980 nm VCSEL versus temperature: (a)

threshold current Ith; (b) threshold current density Jth; (c) threshold voltage Uth; (d) threshold electrical

power Pth; (e) rollover current Irollover; (f) maximum output power Pmax; (g) maximum differential quan-

tum efficiency DQEmax; and (h) maximum wallplug efficiency WPEmax.

6.1 Temperature-Dependent Static Analysis 85

25 °C as a function bias current from 1 to 6 mA. From the fundamental mode LP01,

the cavity etalon resonance wavelength shift rate versus the dissipated power Δλ/

ΔPdiss (Pdiss = I ∙ V − Popt is the dissipated power, Popt is the optical output power) and

the cavity etalon resonance wavelength shift rate versus the heat-sink temperature

Δλ/ΔT can be obtained, which are 0.367 nm/mW and 0.064 nm/K, respectively, as

shown in Fig. 6-7. The thermal resistance Rth [100] is then determined to be 5.73 K/

mW for the ~2.5 µm oxide-aperture diameter VCSEL. The larger Δλ/ΔPdiss value of

0.367 nm/mW is the reason of high thermal resistance for the small oxide-aperture

diameter VCSEL. Figure 6-8(a) shows the emission intensity of the fundamental

mode LP01 and the first higher-order mode LP11 as a function of the bias current

for the ~2.5 µm oxide-aperture diameter VCSEL at 25, 35, 45, 65, and 85 °C. The

intensity of the fundamental mode is nearly temperature independent, but the inten-

sity of the first higher-order mode decreases with increasing the temperature. The

side-mode-suppression-ratios (SMSRs) obtained from the values in Fig. 6-8(a) are

shown in Fig. 6-8(b). The SMSR slightly increases as the temperature increases. At

85 °C the SMSR is ~40 dB across the entire current range.

972 974 976 978 980 982

-60

-50

-40

-30

-20

-10

25 °C

45 °C

65 °C

85 °C

~2.5 µm oxide-aperature Ø

Relative intensity (dB)

Wavelength (nm)

0.4 mA

(a)

972 976 980 984

-60

-50

-40

-30

-20

-10

1 mA

3 mA

5 mA

6 mA

25 °C

Relative intensity (dB)

Wavelength (nm)

(b) ~2.5 µm oxide-aperature Ø

Fig. 6-6. Measured emission spectra (a) at 0.4 mA and at different bias currents (b) at 25 °C for the

~2.5 µm oxide-aperture diameter 980 nm VCSEL.

Wavelength (nm)

Heatsink Temperature (°C)

∆λ/∆P

diss

=∆λ/∆T=

0 5 10 15 20

976

980

984

25 °C

(a)

Dissipated electrical power (mW)

20 40 60 80

977

979

981

0.4 mA

(b)

0.367 nm/mW 0.064 nm/K

Fig. 6-7. Measured wavelength of the LP01 mode as a function of the dissipated electrical power (a),

and as a function of the heat-sink temperature (b) for the ~2.5 µm oxide-aperture diameter 980 nm

VCSEL.

86 Chapter 6 Temperature-Stable 980 nm VCSELs

The measured LP01, LP11, and LP21 peak wavelengths as a function of the forward

bias electrical power Pel (I ∙ V) are plotted in Fig. 6-9 for ~3 and ~4 µm oxide-

aperture diameter VCSELs. The wavelengths of the modes toward zero electrical

power (no heating) are extrapolated by fitting the data with a straight line, and the

resultant wavelengths at zero electrical power are called the “cold cavity modes”.

The measured cold cavity optical emission wavelengths for the LP01, LP11, and LP21

modes as a function of oxide-aperture diameter from ~2.5 to 7.0 µm for the 980 nm

VCSELs are shown in Fig. 6-10(a). The VCSEL resonant wavelength shifts to the

shorter wavelength as the oxide-aperture diameter decreases. As the oxide-aperture

diameter increases beyond about 10 µm the peak wavelengths of the LP01, LP11, and

LP21 modes reach a constant value. In Fig. 6-10(b) the mode spacing between the

fundamental mode LP01 and the first higher-order mode LP11 is shown as a function

of the oxide-aperture diameter. The small oxide-aperture diameter VCSELs have a

larger mode spacing, which is beneficial for a low single-mode emission threshold

current [139].

Fundamental mode

Second-order mode

Single-mode

Multi-mode

~2.5 µm oxide-aperature Ø ~2.5 µm oxide-aperature Ø (a) (b)

01234567

-60

-50

-40

-30

-20

-10

Relative Intensity (dB)

Current (mA)

0123456

25 °C

35 °C

45 °C

65 °C

85 °C

SMSR (dB)

Current (mA)

980 nm VCSEL

25 °C

35 °C

45 °C

65 °C

85 °C

Fig. 6-8. Emission intensities for the fundamental (LP01) and first higher-order (LP11) modes as a

function of the bias current (a), and the side-mode-suppression-ratio (SMSR) versus the bias current

(b) for the ~2.5 µm oxide-aperture diameter VCSEL at 25, 35, 45, 65, and 85 °C.

25 °C 25 °C

~3 µm aperature Ø ~4 µm aperature Ø

(a) (b)

0 2 4 6 8 10 12 14 16 18 20

972

975

978

981

984

LP01

LP11

LP21

Wavelength (nm)

Electrical power (mW)

0 5 10 15 20 25

974

976

978

980

982

984

986

LP01

LP11

LP21

Wavelength (nm)

Electrical power (mW)

Fig. 6-9. Measured emission wavelengths of the LP01, LP11, and LP21 modes against applied electri-

cal power at 25 °C for ~3 µm (a) and ~4 µm (b) oxide-aperture diameters 980 nm VCSELs. The cold

cavity wavelengths are determined by extrapolating the measured results to 0 mW.

6.2 Small-Signal Modulation Analysis 87

6.2 Small-Signal Modulation Analysis

To understand how temperature affects the high bit-rate modulation performance of

VCSELs, the temperature-dependent small-signal analysis is performed. In Fig. 6-11,

the measured small-signal modulation response curves with corresponding fittings

are shown for different currents at 25, 45, 65, and 85 °C for the ~4 µm oxide-aperture

diameter VCSEL. All the fittings match very well with the measurement data. The

−3 dB bandwidth is an important parameter to determine the high-speed capability

of VCSELs, since it is generally directly related to the maximum achievable bit rate.

The −3 dB bandwidth increases with increasing the current, and eventually saturates

and decreases. The −3 dB bandwidth decreases typically due to thermal limitations.

The change of −3 dB bandwidth with the current at high temperatures is the same as

at room temperature, and high values of f–3dB can be achieved over a large range of

temperatures. 4 and 5.4 mA are taken as typical currents to show the influence of the

temperature on the high-speed modulation performance. The measured small-signal

modulation response curves with the corresponding fittings at the bias currents of 4

and 5.4 mA at 25, 45, 65, and 85 °C for the ~4 µm oxide-aperture diameter VCSEL

are shown in Fig. 6-12. The modulation response is very temperature-stable. For

the bias current of 4 mA, the modulation response stays nearly the same when the

temperature increases from room temperature to high temperatures. For the 5.4 mA

bias current, the −3 dB bandwidth is 20.5, 20.7, 19.6, and 18.3 GHz at temperatures

of 25, 45, 65, and 85 °C, respectively, with a small change of only 2.2 GHz when the

temperature increases from 25 to 85 °C.

Fig. 6-13(a) plots the −3 dB bandwidth versus the bias current for temperatures

of 25, 45, 65, and 85 °C for the ~4 µm oxide-aperture diameter 980 nm VCSEL. The

plot shows that the VCSELs can achieved higher bandwidths at 85 °C compared

to 25 °C for currents smaller than 3 mA. The f−3dB is higher at 25 °C than at higher

Δλ=λLP11-λLP01

2345678

968

972

976

980

984

LP01

LP11

LP21

Wavelength (nm)

Oxide-aperture diameter (µm)

980 nm VCSEL

234567

Mode spacing (nm)

(b)

Oxide-aperture diameter (µm)

(a)

Fig. 6-10. Measured cold cavity emission wavelengths [107] (a) for the LP01, LP11, and LP21 modes;

and (b) measured mode spacing between the fundamental mode LP01 and second order mode LP11 as

a function oxide-aperture diameter for 980 nm VCSELs.

88 Chapter 6 Temperature-Stable 980 nm VCSELs

temperatures for currents above ~4 mA, where thermal effects introduced by Joule

heating lead to a reduced f−3dB at a given current. The f−3dB is nearly constant at

~18 GHz at 85 °C for currents larger than 3.7 mA, and larger than 18 GHz at lower

temperatures. A nearly temperature-independent high bit-rate over a large current

range is possible. For example, 38 Gb/s error-free transmission is achieved at cur-

rents above 3.7 mA without a change in the bias current or in the voltage modulation

conditions from 25 to 85 °C. The extracted relaxation resonance frequency fr shows

a similar change trend versus the temperature as f−3dB, as shown in Fig. 6-13(b),

in which a reverse point at 4.5 mA, where fr at 25 °C starts to exceed the value at

85 °C, can be seen clearly. For large bias current (> 5 mA), the fr is higher at room

temperature than at higher temperatures. This is different with low current, but still

reasonable. The differential gain increases with increasing active region temperature

until it reach a maximum value at around 360 K (~87 °C) then starts to decrease

with further temperature increases due to the –15 nm QW gain-to-etalon wavelength

offset design. The active region temperature depends on the ambient temperature,

and increases with the bias current. At an ambient temperature of 25 °C, a bias

current of 5 mA leads to an active region temperature of 82.1 °C (355.25 K), close

to the maximum differential gain value. For a higher ambient temperature of 85 °C

the same bias current results in a much higher active region temperature of 142.1 °C

0 3 6 9 12 15 18 21 24

-24

-16

-8

Frequency (GHz)

0 3 6 9 12 15 18 21 24

-24

-16

-8

Frequency (GHz)

-16

-8

0 3 6 9 12 15 18 21 24

-24

Frequency (GHz)

0 3 6 9 12 15 18 21 24

-24

-16

-8

Frequency (GHz)

Modulation response (dB)

25 °C 45 °C

65 °C 85 °C

(a) (b)

(d)(c)

1 mA

2 mA

3 mA

5 mA

1 mA

2 mA

3 mA

5 mA

1 mA

2 mA

3 mA

5 mA

1 mA

2 mA

3 mA

5 mA

Fig. 6-11. Magnitude of the small signal modulation response S21 for bias currents of 1, 2, 3, 5 mA

and corresponding fittings at 25 °C (a), 45 °C (b), 65 °C (c), and 85 °C (b) for the ~4 µm oxide-aper-

ture diameter VCSEL.

6.2 Small-Signal Modulation Analysis 89

(415.25 K), leading to a lower differential gain compared to the value at 25 °C. There-

fore, at large bias currents higher relaxation resonance frequencies can be reached at

room temperature than at higher temperatures.

For applications in optical data communications, it is of much interest to obtain

high modulation bandwidths at small operating currents to reduce the energy con-

sumption. The D-factor describes how fast the relaxation resonance frequency fr

increases with increasing bias current above the threshold current. A large D-factor

implies the VCSEL can reach a large fr at low bias currents. The D-factor can be

obtained from the linear dependence of the relaxation resonance frequency versus

the square root of current above threshold at low currents, where the increase of the

active region temperature due to the self-heating is small. The modulation current

efficiency factor MCEF specifies the increase of f−3dB, which can be obtained by the

linear dependence of f−3dB on the square root of current above threshold at low cur-

rents. The extracted relaxation resonance frequencies fr versus the square root of the

bias current minus the threshold current and the corresponding linear fittings for the

0 5 10 15 20 25 30

-15

-12

-9

-6

-3

25 °C

45 °C

65 °C

85 °C

Modulation response (dB)

Frequency (GHz)

4.0 mA

(a)

0 5 10 15 20 25 30

-15

-12

-9

-6

-3

Modulation response (dB)

Frequency (GHz)

5.4 mA

(b)

~4 µm oxide-aperature Ø~4 µm oxide-aperature Ø

25 °C

45 °C

65 °C

85 °C

Fig. 6-12. Magnitude of the small signal modulation response S21 and corresponding fittings at bias

currents of 4 mA (a) and 5.4 mA (b) at 25, 45, 65, and 85 °C for the ~4 µm oxide-aperture diameter

VCSEL.

0123456789

Current (mA)

(b)

0123456789

Current (mA)

(a)

~4 µm oxide-aperature Ø ~4 µm oxide-aperature Ø

−3 dB bandwidth (GHz)

Resonance frequency (GHz)

25 °C

45 °C

65 °C

85 °C

25 °C

45 °C

65 °C

85 °C

Fig. 6-13. f–3dB (a) and fr (b) extracted from small-signal modulation response measurements at dif-

ferent bias currents for the ~4 µm oxide-aperture diameter 980 nm VCSEL at 25, 45, 65 and 85 °C.

90 Chapter 6 Temperature-Stable 980 nm VCSELs

980 nm VCSELs are shown in Fig. 6-14(b). These curves are different from what

is typically observed, since the D-factor is larger at 85 °C compared to the value at

25 °C. High-speed and energy-efficient operation from room temperature to 85 °C

can be achieved due to the stable and large D-factor. The extracted f–3dB versus the

square root of the bias current minus threshold current and the corresponding linear

fittings are shown in Fig. 6-14(a), showing the MCEF data is similar to the D-factor

data, but with higher values.

6.3 Highly Temperature-Stable VCSELs

The data transmission measurements are carried out at various bit rates and heat-

sink temperatures. To demonstrate the VCSELs are highly temperature-stable, data

transmission tests are performed at a fixed bit rate, bias, and modulation conditions.

Figure 6-15(a) shows that the error-free data transmissions at 35 Gb/s at 25 up to

85 °C are achieved at the same bias and modulation conditions by using a ~3 µm

oxide-aperture diameter VCSEL. The CW bias currents used for these measurements

are all 2.7 mA, and the modulation conditions with a peak-to-peak amplitude of

470 mV are used over the entire measured temperature range. With a little increase

of bias current to 2.9 mA, 38 Gb/s error-free data transmissions at 25 up to 85 °C

at the same bias and modulation conditions are realized using the same VCSEL, as

shown in Fig. 6-15(b).

In Fig. 6-16, 38 Gb/s error-free data transmission at 25 up to 85 °C are shown

by using a slightly larger oxide-aperture diameter (~3.5 µm) VCSEL without any

changes in bias and modulation conditions. The CW bias current is 3.5 mA, which is

0.0 0.5 1.0 1.5 2.0 2.5 3.0

(a)

−3 dB bandwidth (GHz)

sqrt(I-Ith) (sqrt(mA))

0.0 0.5 1.0 1.5 2.0 2.5 3.0

(b)

Resonance frequency (GHz)

sqrt(I-Ith) (sqrt(mA))

25 °C

45 °C

65 °C

85 °C

~4 µm oxide-aperature Ø ~4 µm oxide-aperature Ø

( )

I I

−

( )

3dB

MCEF

I I

−

25 °C

45 °C

65 °C

85 °C

Fig. 6-14. –3 dB bandwidth (a) and relaxation resonance frequency (b) versus the square root of the

bias current minus the threshold current for the ~4 µm oxide-aperture diameter VCSEL at 25, 45, 65

and 85 °C.

6.3 Highly Temperature-Stable VCSELs 91

a little higher than the bias current used for the same bit-rate operation of the smaller

oxide-aperture diameter (~3 µm) VCSEL, and the modulation conditions with a

peak-to-peak amplitude of 470 mV are used over the entire temperature range. For a

~4 µm oxide-aperture diameter VCSEL, the error-free operation at 35 Gb/s at 25, 45,

65, and 85 °C are shown in Fig. 6-17(a). The bias current used for these four measure-

ments is 3.2 mA. Also the error-free operation at 38 Gb/s at 25, 45, 65, and 85 °C

by using a bias current of 5.4 mA and a modulation condition with a peak-to-peak

amplitude of 380 mV, are shown in Fig. 6-17(b). It is found that up to the temperature

of 65 °C no penalty of received optical power occurs. Figures 6-15, 6-16 and 6-17

show that very temperature-stable data transmission can be achieved by using small

oxide-aperture VCSELs (with oxide-aperture diameters of 3 − 4 µm). Even smaller

oxide VCSELs, for example ~2.5 µm oxide-aperture diameter VCSELs, are also not

beneficial for temperature-stable data transmission tests due to their small optical

output power, large differential resistance, and large thermal resistance (high active

region temperature).

45 °C

65 °C 85 °C

25 °C

~3.5 µm aperture

PBRS: 27-1

38 Gb/s

Received optical power (dBm)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

25 °C

45 °C

65 °C

85 °C

3.5 mA

-log(BER)

Fig. 6-16. Bit error ratio versus received optical power for an ~3.5 µm oxide-aperture diameter 980 nm

VCSEL operating at 38 Gb/s at 25, 45, 65 and 85 °C, respectively, and eye diagrams at the correspond-

ing temperatures and modulation conditions.

-9 -8 -7 -6 -5 -4 -3 -2

2.7 mA

35 Gb/s

-log(BER)

~3 µm aperture

PBRS: 27-1

25 °C

45 °C

65 °C

85 °C

Received optical power (dBm)

-8 -7 -6 -5 -4 -3 -2 -1

38 Gb/s

-log(BER)

2.9 mA

PBRS: 27-1

~3 µm aperture

25 °C

45 °C

65 °C

85 °C

Received optical power (dBm)

(a) (b)

45 °C

65 °C

85 °C

25 °C

45 °C

65 °C

85 °C

25 °C

Vpp: 470 mV Vpp: 470 mV

Fig. 6-15. Bit error ratio versus received optical power for a ~3 µm oxide-aperture diameter 980 nm

VCSEL operating at 35 Gb/s (a) and 38 Gb/s (b) at 25, 45, 65 and 85 °C, respectively, and eye diagrams

at the corresponding temperatures and modulation conditions.

92 Chapter 6 Temperature-Stable 980 nm VCSELs

Figure 6-18 shows the BER versus received optical power for a ~4 µm oxide-aperture

diameter VCSEL operating at 38 Gb/s at the bias currents yielding the maximum

energy-efficiency at different temperatures. The corresponding eye diagrams are

shown in Fig. 6-19(a). The error-free operation at 38 Gb/s is achieved with low HBR

values of 197, 179, 177, and 177 fJ/bit at 25, 45, 65, and 85 °C, respectively. The cor-

responding EDR values are 231, 211, 207, and 203 fJ/bit, respectively. The CW bias

current used at 25 °C for the BER measurements is 3.78 mA (at a corresponding

voltage of 2.33 V), and the CW bias current is 3.6 mA for the BER measurements at

-7 -6 -5 -4 -3 -2 -1 0

-log(BER)

38 Gb/s

3.78 mA

HBR=197fJ/bit

~4 µm aperture diameter

25 °C

Received optical power (dBm)

-9 -8 -7 -6 -5 -4 -3 -2 -1

-log(BER)

3.6mA

HBR=179fJ/bit

-9 -8 -7 -6 -5 -4 -3 -2 -1

-log(BER)

3.6mA

HBR=177fJ/bit

-8 -7 -6 -5 -4 -3 -2 -1

-log(BER)

3.6mA

HBR=177fJ/bit

Received optical power (dBm)

Received optical power (dBm) Received optical power (dBm)

45 °C

65 °C 85 °C

38 Gb/s

38 Gb/s 38 Gb/s

~4 µm aperture diameter

(a) (b)

Fig. 6-18. BER versus received optical power for the ~4 µm oxide-aperture diameter 980 nm VCSEL

operating at 38 Gb/s at the bias currents that yield the maximum energy efficiency at 25 °C (a), 45 °C

(b), 65 °C (c), and 85 °C (d).

-8 -7 -6 -5 -4 -3 -2

3.2 mA

-log(BER)

35 Gb/s

~4 µm aperture

PBRS: 2

-1

25 °C

45 °C

65 °C

85 °C

Received optical power (dBm) -9 -8 -7 -6 -5 -4 -3 -2 -1 0

~4 µm aperture

PBRS: 2

7-1

38 Gb/s

-log(BER)

Received optical power (dBm)

25 °C

45 °C

65 °C

85 °C

5.4 mA

25 °C

45 °C

65 °C

85 °C

(a) (b)

45 °C

65 °C

85 °C

25 °C

Fig. 6-17. Bit error ratio versus received optical power for a ~4 µm oxide-aperture diameter 980 nm

VCSEL at 35 Gb/s (a) and 38 Gb/s (b) at 25, 45, 65 and 85 °C, respectively, and eye diagrams at the

corresponding temperatures and modulation conditions.

6.4 Summary 93

45, 65, and 85 °C with voltages of 2.23, 2.19 and 2.14 V, respectively. Both the HBR

and EDR values are highly temperature-stable, as show in Fig. 6-19(b). Besides these

highly temperature-stable static properties and high-speed modulation properties,

the modulation bandwidth, data transmission bit rate, and energy dissipation also

show high temperature stability, which are all beneficial for the use of these VCSELs

in optical interconnect applications.

6.4 Summary

In this Chapter the experimental results of the highly temperature-stable 980 nm

VCSELs are presented. Systematic characterizations including static measure-

ments, small-signal analysis, and data transmission experiments are carried out.

The error-free data transmissions at bit rates of 38 Gb/s at 25, 45, 65, and 85 °C are

demonstrated without any change of the operating point or the modulation conditions.

The VCSELs demonstrate very temperature-insensitive static and dynamic charac-

teristics. The superior results are attributed to the employment of InGaAs QWs and

GaAsP barrier layers, and the −15 nm gain-to-etalon wavelength offset.

20 40 60 80

120

150

180

210

240 EDR

HBR

EDR, HBR (fJ/bit)

Temperature (°C)

980 nm VCSEL

38 Gb/s

25 °C 45 °C

65 °C 85 °C

270 (b)(a)

Fig. 6-19. Eye diagrams for the ~4 µm oxide-aperture diameter 980 nm VCSEL operating at 38 Gb/s

at the bias currents yielding the maximum energy-efficiency at 25, 45, 65, and 85 °C (a), and the mini-

mum electrical energy-to-data ratio EDR and heat-to-bit rate ratio HBR change with temperature (b).

Chapter 7

Energy-Efficient High Bit-Rate VCSELs

The increasing demand for optical communication can only be met by the realization

of ever more energy-efficient emitters with increased bandwidth and thus higher

information capacity via faster modulation capabilities. Exascale supercomputers

will require billions of optical interconnects and are predicted to require high-speed

interconnects operating at least at 25 Gb/s before 2020 [28, 140], thus the VCSELs

within the optical interconnect (OI) systems and links must operate at high bit-rates

with a low energy consumption. A maximum energy dissipation of ~100 fJ/bit is

predicted for VCSELs used for OIs by circa 2015 [56]. The experimental results

of energy efficient high bit-rate 980 nm VCSELs will be presented in this Chapter.

Section 7.1 shows the oxide-aperture diameter-dependent static characteristics.

The oxide-aperture diameter-dependent small-signal modulation analysis at room

temperature and high temperature will be presented in Section 7.2 and 7.3. The

energy efficient high bit-rate results at room temperature and at high temperature

are presented in this Chapter as well.

7.1 Static Characteristics

In this section, detailed static results at 25 and 85 °C for VCSELs with oxide-

aperture diameters ranging from ~2.5 to 7 µm are given. The continuous wave (CW)

figures-of-merit are extracted and the change of these parameters with changing

oxide-aperture diameter is discussed. It is demonstrated that the –15 nm quantum

well gain-to-etalon wavelength offset allows the VCSELs to operate well at room

temperature and also at high temperatures up to 85 °C.

7.1 Static Characteristics 95

7.1.1 Static LIV Characteristics

Static LIV measurement results at room temperature (25 °C) and at high temperature

(85 °C) for the 980 nm VCSELs with oxide-aperture diameters ranging from ~2.5 to

7 µm are shown in Fig. 7-1. The LIV curves are similar at room temperature and high

temperature. The significant difference is that the output power at 85 °C is lower. The

threshold currents and rollover currents are also changed with changing temperature.

The extracted parameters at room temperature for VCSELs with oxide-aperture

diameter ranging from ~2.5 to ~7 µm are shown in Fig. 7-2. The threshold current Ith

increases with increasing oxide-aperture diameter, and is 0.38, 0.33, 0.33, 0.40, 0.54,

and 0.77 mA for ~2.5, 3, 4, 5, 6, and 7 µm oxide-aperture diameter VCSELs, respec-

tively. The smallest Ith of 0.33 mA is achieved with oxide-aperture diameters of ~3

and 4 µm. The smaller (< 3 µm) oxide-aperture diameter VCSELs have higher Ith at

25 °C due to several opposing interacting parameters including modal gain, cavity

losses, gain-to-etalon wavelength offset, and other factors. As the oxide-aperture

25 °C

0 4 8 12 16 20

Optical power (mW)

Current (mA)

Voltage (V)

2.5 µm

3 µm

3.5 µm

4 µm

5 µm

6 µm

7 µm

85 °C

0 3 6 9 12 15

Optical power (mW)

Current (mA)

Voltage (V)

2.5 µm

3 µm

3.5 µm

4 µm

5 µm

6 µm

7 µm

(a) (b)

Fig. 7-1. Measured CW L-I-V characteristics for the 980 nm VCSELs with oxide-aperture diameters

ranging from ~2.5 to ~7 µm at 25 °C (a) and 85 °C (b).

2345678

0.1

0.3

0.5

0.7

0.9

1.1

Oxide aperature Ø

(a)

2345678

0.7

1.4

2.1

2.8

3.5

Oxide aperature Ø

2345678

1.4

1.6

1.8

2.0

Oxide aperature Ø 2345678

0.0

0.4

0.8

1.2

1.6

Oxide aperature Ø

Ith (mA)

Pth (mW)

Jth (KA/cm2)

Uth (V)

(b) (c) (d)

2345678

20 (e)

Oxide aperature Ø

Irollover (mA)

2345678

0.0

2.5

5.0

7.5 (f)

Pmax (mW)

Oxide aperature Ø 2345678

40 (g)

DQEmax (%)

Oxide aperature Ø Oxide aperature Ø

2345678

24 (h)

WPEmax (%)

25 °C 25 °C 25 °C 25 °C

Fig. 7-2. Threshold current Ith (a), threshold current density Jth (b), threshold voltage Uth (c), threshold

electrical power Pth (d), rollover current Irollover (e), maximum output power Pmax (f), maximum differ-

ential quantum efficiency DQEmax (g), and maximum wall-plug efficiency WPEmax (h) versus oxide

aperture diameter for ~2.5 to ~7 µm 980 nm VCSELs at 25 °C.

96 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

diameters increase beyond ~4 µm there is a noticeable increase in the threshold

current as a function of the oxide-aperture diameter, because the lasing area of the

VCSEL is increasing with the aperture diameter and a larger current is required to

achieve the lasing threshold, even as the scattering and other optical losses become

less significant. For VCSELs with small oxide-aperture diameters (from ~2.5 to

4 µm), the quite stable low threshold current Ith is beneficial for the energy efficient

operation. The threshold electrical power Pth has the similar change with Ith. The

rollover current and maximum output power nearly linearly increase with increas-

ing oxide-aperture diameter. The maximum optical output power is 1.22 mW for

the ~2.5 µm oxide-aperture diameter VCSEL with a rollover current of 5.21 mA,

and increases to 5.42 mW with a rollover at 16.01 mA for the ~7 µm oxide-aperture

diameter VCSEL. The maximum differential quantum efficiency DQEmax is 23.58 %

for the ~2.5 µm oxide-aperture diameter VCSEL, and increase to 28.45 % for the

~3 µm oxide-aperture diameter VCSEL. The DQEmax reaches a value of 32.32 % at

the oxide-aperture diameter of ~7 µm. The maximum WPEmax has a similar trend as

the differential quantum efficiency. The WPEmax is 12.13 % for the ~2.5 µm oxide-

aperture diameter VCSEL, and increases to 15.53 % for the ~3 µm oxide-aperture

diameter VCSEL. The WPEmax remains about constant for apertures from ~3 to

0.8 2.4 1.6 1.2

Ith (mA)

rollover

(mA)

2345678

0.2

0.4

0.6

2345678

0.8

1.6

2345678

1.3

1.4

1.5

2345678

0.0

0.4

0.8

Pth (mW)

Jth (KA/cm2)

Uth (V)

(a) (b) (c) (d)

2345678

16 (e)

2345678

0.0

2.5

5.0 (f)

max

(mW)

2345678

35 (g)

DQE

max

(%)

2345678

24 (h)

WPE

max

(%)

Oxide aperature Ø Oxide aperature Ø Oxide aperature Ø Oxide aperature Ø

85 °C 85 °C 85 °C 85 °C

Fig. 7-3. Ith (a), Jth (b), Uth (c), Pth (d), Irollover (e), Pmax (f), DQEmax (g), and WPEmax (h) versus oxide aper-

ture diameter for ~2.5 to 7 µm 980 nm VCSELs at 85 °C.

0 5 10 15 20

100

300

500

700

25 °C

(Ω)

Current (mA) 0 5 10 15

100

300

500

700 85 °C

Current (mA)

(Ω)

2.5 µm

3 µm

3.5 µm

4 µm

5 µm

6 µm

7 µm

2.5 µm

3 µm

3.5 µm

4 µm

5 µm

6 µm

7 µm

(b)(a)

Fig. 7-4. Differential resistance (Rd) versus current for the 980 nm VCSELs with oxide-aperture diam-

eters ranging from ~2.5 to ~7 µm at 25 °C (a) and 85 °C (b).

7.1 Static Characteristics 97

~5 µm, then increases to 19.33 % for the ~7 µm VCSEL. Thus the small aperture

VCSELs (~2.5 to 5 µm) have small Ith, and small Pth, which are both beneficial for the

energy efficient operation. However, the output power of the small aperture VCSELs

is small, resulting in small WPEmax and DQEmax values. For larger oxide-aperture

diameter VCSELs (larger than ~5 µm), the WPEmax and DQEmax are larger, but also

have large Ith and Pth values, which will increase the energy consumption.

The extracted parameters at 85 °C for VCSELs with oxide-aperture diameters

ranging from ~2.5 to 7 µm are shown in Fig. 7-3. The Ith increase with increasing

the oxide aperture, which is 0.25, 0.23, 0.26, 0.35, 0.46, and 0.62 mA for the ~2.5, 3,

4, 5, 6, and 7 µm oxide-aperture diameter VCSELs, respectively. Ith is lower than at

25 °C for all devices of a given size. The changing of Ith and Pth with the aperture

diameter corresponds to the behavior at room temperature. These two parameters are

nearly constant for the small oxide-aperture diameters (~2.5 to 4 µm) but increase

for the larger oxide-aperture diameter VCSELs. The Irollover and Pmax increase linearly

as the oxide-aperture diameter increases. The Pmax is 0.85 mW for the ~2.5 µm

oxide-aperture diameter VCSEL with Irollover of 4.2 mA, and increases to 3.45 mW at

12.4 mA for the ~7 µm oxide-aperture diameter VCSEL, respectively. The DQEmax

is 20.6 % for the ~2.5 µm aperture VCSEL, and increases to 23.6 % for the ~3 µm

aperture VCSEL. The DQEmax remains quite stable until ~5 µm when it increases to

28.6 % at ~7 µm. The WPEmax and DQEmax behave similarly. As at 25 °C, the small

oxide-aperture diameter VCSELs (~3 to 5 µm) have small I

and P

values quite high

WPEmax and DQEmax values. The smallest VCSELs (~2.5 µm) have small Ith and Pth,

but the Popt is very small, as are the WPEmax and the DQEmax, which limit the VCSELs’

high-speed operation at 85 °C. From a static analysis, it is found that VCSELs with

oxide-aperture diameters between ~3 and ~4 µm are best suited for energy-efficient

and high bit-rate operation at 85 °C. Differential resistance (Rd) versus current for

2345678

-40

-30

-20

-10

dIrollover (%)

2345678

-40

-35

-30

-25

dPmax (%)

2345678

-24

-16

-8

dDQEmax (%)

2345678

-20

dWPEmax (%)

2345678

-40

-30

-20

-10

2345678

-45

-30

-15

2345678

-20

-15

-10

-5

2345678

-45

-30

-15

dPth (%)

dUth (%)

dJth (%)

dIth (%)

(a) (b) (c) (d)

(e) (f) (g) (h)

Oxide aperature Ø Oxide aperature Ø Oxide aperature Ø Oxide aperature Ø

Fig. 7-5. Relative change of Ith (dIth) (a), relative change of Jth (dJth) (b), relative change of Uth (dUth) (c),

relative change of Pth (dPth) (d), relative change of Pmax (dPmax) (f), relative change of Irollover (dIrollover) (e),

relative change of WPE

max

(dWPE

max

) (h), and relative change of DQE

max

(dDQE

max

) (g) with a tempera-

ture increase from 25 to 85 °C for VCSELs with oxide-aperture diameters ranging from ~2.5 to ~7 µm.

98 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

the VCSELs with oxide-aperture diameter from ~2.5 to 7 µm at 25 and 85 °C are

shown in Fig. 7-4. Small oxide-aperture diameter VCSELs have larger differential

resistance R

, which is not favorable for matching the input impedance of the VCSEL

to the 50 Ω impedance of a standard radio frequency transmission line. The differ-

ential resistance Rd decreases with increasing oxide-aperture diameter.

The relative change of Ith (dIth = ((Ith (85 °C) − Ith (25 °C)) / Ith (25 °C)) ∙ 100 %) for

~3, 4, 5, 6, and 7 µm oxide-aperture diameter VCSELs is shown in Fig. 7-5(a). The

Pth (Fig. 7-5(d)) follows the trend of Ith. The Ith and Pth are temperature-stable for all

VCSELs, due to around –15 nm QWs gain-to-etalon wavelength offset at room tem-

perature [141]. For VCSELs with a smaller gain-etalon wavelength offset [142], the

Pth increase with increasing temperature and the relative change is as high as 30 %

to 60 % for VCSELs with oxide-aperture diameter from ~2.5 to 7 µm. The VCSELs

with smaller oxide-aperture diameters generally have the smallest relative change

with a temperature increase. For the structure in this work, the Pth decreases with a

temperature increase with a relative change of only between –42 % to –27 %. In this

case, the ~5 µm oxide-aperture diameter VCSEL has the smallest relative change.

-40

974 976 978 980 982 984

-40

0.4 mA

Relative intensity (dB)

25 °C

45 °C

65 °C

85 °C

Wavelen

(

)

-40

972 974 976 978 980 982 984

-40

1mA

25 °C

~4 µm oxide-aperture Ø

3mA

Relative intensity (dB)

5mA

7mA

Wavelen

(

)

(a) (b)

~4 µm oxide-aperture Ø

Fig. 7-6. Measured emission spectra (a) at 0.4 mA at different heat-sink temperatures and (b) at 25 °C

at different bias currents for the ~4 µm oxide-aperture diameter 980 nm VCSEL.

0 8 16 24

978

982

986

Wavelength (nm)

Dissipated electrical power (mW)

25 °C

(a)

∆λ/∆P

diss

0.2915 nm/mW

20 40 60 80

978

980

982

Wavelength (nm)

Temperature (°C)

0.4 mA

(b)

∆λ/∆T=

0.06226 nm/K

Fig. 7-7. Measured emission wavelength (fundamental mode) versus (a) dissipated electrical power and

(b) heat-sink temperature for the ~4 µm oxide-aperture diameter 980 nm VCSEL.

7.1 Static Characteristics 99

7.1.2 Spectral Characteristics

Measurements of emission spectra are carried out for the ~4 µm oxide-aperture

diameter VCSEL at different bias currents and different temperatures. The measured

CW emission spectra at a fixed forward bias current of 0.4 mA as a function of heat-

sink temperature from 25 to 85 °C are shown in Fig. 7-6(a), and the measured CW

emission spectra at 25 °C as a function bias current from 1 to 7 mA are shown in

Fig. 7-6(b). The cavity etalon resonance wavelength shift rate versus the dissipated

power Δλ/ΔPdiss, and versus heat-sink temperature Δλ/ΔT are 0.292 nm/mW and

0.062 nm/K, respectively, giving a thermal resistance Rth = ΔT/ΔPdiss [100] of 4.68 K/

mW for the ~4 µm oxide-aperture diameter VCSEL.

Optical spectral measurements following the same evaluation procedure are

performed for different oxide-aperture diameter VCSELs. The cavity resonance

wavelengths change with the dissipated power for VCSELs with oxide-aperture

diameter ranging from ~2.5 to ~7 µm are shown in Fig. 7-8(a). The cavity resonance

wavelengths shift faster for small oxide-aperture diameter VCSELs than larger ones,

as shown in Fig. 7-9(a). The cavity resonance wavelength changes with heat sink

20 30 40 50 60 70 80 90

975

978

981

984

987

Wavelength (nm)

Heatsink Temperature (°C)

0.4mA

(b)

980 nm VCSEL

0 5 10 15 20 25 30

976

978

980

982

984

986

Wavelength (nm)

Dissipated electrical power (mW)

25 °C

2.5 µm

3 µm

4 µm

5 µm

6 µm

7 µm

5 µm

6 µm

7 µm

2.5 µm

3 µm

4 µm

980 nm VCSEL

(a)

Fig. 7-8. Measured emission wavelength as a function of the dissipated power and (b) measured emis-

sion wavelength as a function of heat-sink temperature for 980 nm VCSELs.

2 3 4 5 6 7 8

Oxide aperture diameter (µm)

Rth (K/mW)

0.1

0.2

0.3

0.4

0.05

0.06

0.07

0.08

Δλ/ΔPdiss (nm/mW)

Δλ/ΔT (nm/K)

(a)

2345678

Oxide aperture diameter (µm)

6(b)

Fig. 7-9. Measured shift rate of cavity resonance wavelength with dissipated electrical power and with

heat sink temperature (a), and the calculated thermal resistance (b) for 980 nm VCSELs.

100 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

temperature are shown in Fig. 7-8(b). The lines are nearly parallel, which means

the cavity resonance wavelength shift rates with heat sink temperature are nearly

independent of oxide-aperture diameter. The thermal resistances are calculated by

using the data in Fig. 7-9(a), and the results are shown in Fig. 7-9(b). The smaller

oxide-aperture diameter VCSELs have a large thermal resistance compared with

larger VCSELs, which matches well with the thermal model [26, 143] and the simula-

tion results shown in Chapter 2.

The heat flow inside the VCSEL can be approximated as a disk heat source on an

isotropic, semi-infinite substrate. This model gives a simple relation for the thermal

resistance [26, 143], by assuming the heat flow from a circular area with diameter

Da (equal to the oxide-aperture diameter) into a half-space filled with medium of

thermal conductivity λTh (in W/cm·K):

1 1

Th a

≈ ⋅

(K/mW) (7.1)

Figure 7-10 is a plot of the thermal resistance as a function of inverse oxide-aperture

diameter using the measured data in Fig. 7-9(b). Using the data in Fig. 7-10 and

Equation (7.1) the thermal conductivity λTh can be obtained from the slope of the

linear fitting of the data, which is ~0.41 W/cm·K. This value is comparable to the

published values of other groups [73, 144]. Various methods have been tried to in-

crease the thermal conductivity. Thermal conductivity can be increased from 0.41 to

0.53 W/cm·K by using 2 µm of Cu-plating on the VCSEL [144]. Thermal resistance

can be reduced by another factor of 2 by using a Au-plated heat spreading layer

[145]. Oxide-free lithographic VCSELs have also been that thermal resistance can

be further reduced [146].

The active region temperature T

active

change with increasing operating bias current

can be estimated for the linear LI region using Tactive = Tambient + Rth × (I × V − Pout)

[100], as shown in Fig. 7-11. The active region temperature is much higher than

Tambient, and small oxide-aperture diameter VCSELs suffer higher Tactive for the same

bias current compared with larger VCSELs due to their larger thermal resistance Rth.

Fig. 7-10. Measured thermal resistance as a func-

tion of inverse oxide-aperture diameter (1/Da) for

980 nm VCSELs.

Thermal resistance (K/mW)

0.10 0.20 0.30 0.40

Reversed Aperture Ø (1/µm)

7.2 Room Temperature Energy Efficiency 101

7.2 Room Temperature Energy Efficiency

In this section, detailed small-signal analyses for different oxide-aperture diameter

VCSELs at room temperature are performed to obtain the –3 dB bandwidths f−3dB,

which indicate the achievable bit rate information, and the D-factor and MCEF,

which indicate the ability of the VCSEL to obtain high modulation bandwidths at

small operating currents (as required for energy efficiency). Then the data transmis-

sion results at room temperature are shown, including the maximum achievable

error-free bit rates and the minimum dissipated energy.

7.2.1 Small-Signal Analysis at Room Temperature

The –3 dB modulation bandwidth f–3dB versus the bias current for VCSELs with

oxide-aperture diameters from ~3 to 7 µm are shown in Fig. 7-12(a). The maximum

f–3dB at room temperature is 20.9, 21.4, 21.5, 21.3, and 18.9 GHz for ~3, 4, 5, 6, and

7 µm oxide-aperture diameter VCSELs, respectively. The maximum f–3dB reaches

similar values of 21 GHz for VCSELs with oxide-aperture diameters from ~3 to

6 µm, and starts to decrease with further increases of the oxide-aperture diameter.

At the same bias current, the f–3dB is higher for the smaller oxide-aperture diameter

VCSELs compared to larger VCSELs. In addition, the smaller oxide-aperture diam-

eter VCSELs need a smaller current to achieve a certain f–3dB. The f–3dB versus the

consumed electrical power Pel for VCSELs with oxide-aperture diameters of from ~3

to ~7 µm are shown in Fig. 7-12(b), showing the influence of oxide-aperture diameter

on the potential energy consumption of the data transmission. The change of f–3dB

with Pel is similar to the change with current due to a nearly linear dependence of

0 2 4 6 8 10 12 14 16

100

120

140

0 2 4 6 8 10 12 14

100

120

140

160

180

200

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Tambient=25 °C Tambient=85 °C

(a) (b)

Current (mA) Current (mA)

Active region temperature (°C)

Aperture Ø

Fig. 7-11. Active region temperature Tactive change with bias current for 980 nm VCSELs with oxide-

aperture diameters ranging from ~3 to 7 µm at ambient temperatures of 25 °C (a) and 85 °C (b).

102 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

the bias voltage with current. The f–3dB increase with increasing Pel until reaching a

saturation point (the maximum f–3dB), and a further increase of Pel does not lead to an

increase of f–3dB. To achieve a certain f–3dB, smaller oxide-aperture diameter VCSELs

need a lower Pel compared to larger VCSELs.

Fig. 7-13 shows the f–3dB versus the current density. It is known that VCSELs

biased at higher current densities tend to have a reduced device lifetime [147], while

small oxide-aperture diameter VCSELs are generally more reliable [147]. Slightly

higher current density is needed for smaller VCSELs to reach the same f

–3dB

compared

to larger VCSELs. The lifetime of VCSELs should be nearly aperture-independent

because the smaller oxide-aperture diameter VCSELs are more capable of handling

larger current densities. Overall, smaller oxide-aperture diameter VCSELs need

smaller current, smaller electrical power, and slightly larger current density than

larger VCSELs to achieve the same bandwidth.

A larger D-factor and a correspondingly larger MCEF mean a faster increase of fr

and f–3dB with the current. These factors indicate the ability of the VCSEL to obtain

high modulation bandwidths at small operating currents. The extracted f–3dB at room

temperature versus the square root of bias current minus the threshold current and

0 3 6 9 12 15

Current (mA)

–3dB bandwidth (GHz)

0 10 20 30 40

Electrical power (mW)

3 µm

4 µm

5 µm

6 µm

7 µm

(b)(a)

25 °C25 °C

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-12. –3 dB modulation bandwidth f–3dB versus current (a) and versus electrical power (b) at 25 °C

for 980 nm VCSELs with oxide-aperture diameters ranging from ~3 to 7 µm.

Fig. 7-13. –3 dB modulation bandwidth

versus current density at 25 °C for

980 nm VCSELs with oxide-aperture

diameters ranging from ~3 to 7 µm.

–3dB bandwidth (GHz)

0 10 20 30 40 50 60 70 80

Current density (kA/cm2)

25 °C

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

7.2 Room Temperature Energy Efficiency 103

the corresponding linear fittings for VCSELs with oxide-aperture diameters ranging

from ~3 to ~7 µm are shown in Fig. 7-14(a), in which the MCEF decreases with in-

creasing oxide-aperture diameter. The extracted f

versus the quantify the square root

of bias current minus the threshold current and the corresponding linear fittings are

shown in Fig. 7-14(b). From the slope, it is found that smaller oxide-aperture diameter

VCSELs have larger D-factors, and a faster increase of the resonance relaxation fre-

quency with current. The D-factor is 9.1, 7.3, 5.9, 4.8, 3.9 GHz/(mA1/2) for ~3, 4, 5, 6,

and 7 µm oxide-aperture diameter VCSELs, respectively. Thus, at room temperature

smaller oxide-aperture diameter VCSELs should achieve higher energy efficiency

due to their higher MCEFs and D-factors compared to larger VCSELs.

7.2.2 High Bit-Rate Data Transmission

The small-signal measurement results show that the VCSELs can achieve high

bit-rate error-free transmission at room temperature, and the maximum achiev-

able transmission bit-rate should be different for different oxide-aperture diameter

VCSELs. The results of bit error ratio (BER) measurements for maximum achievable

transmission bit-rates at room temperature and the corresponding eye diagrams are

shown in Fig. 7-15. Error-free data transmission is achieved at 42 Gb/s for VCSELs

with oxide-aperture diameters smaller than 7 µm, and at 40 Gb/s for the ~7 µm

oxide-aperture diameter VCSEL, using a standard non-return-to-zero (NRZ) modu-

lation scheme with a pseudorandom binary sequence (PRBS) of word-length of 27–1

bits. This result matches well the small-signal results, where a similar maximum

01234

Resonance frequency (GHz)

(I-Ith)1/2 (mA1/2)

(b)

1 2 3 4

–3dB bandwidth (GHz)

(I-Ith)1/2 (mA1/2)

(a)

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

25 °C

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-14. –3 dB modulation bandwidth (a) and relaxation resonance frequency (b) versus the square

root of bias current minus the threshold current at 25 °C for 980 nm VCSELs with oxide-aperture di-

ameters ranging from ~3 to 7 µm.

104 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

f–3dB can be reached for VCSELs with oxide-aperture diameters smaller than ~7 µm,

and smaller maximum f–3dB can be reached for the ~7 µm oxide-aperture diameter

VCSEL.

7.2.3 Energy-Efficient Data Transmission

The dissipated heat-to-bit rate ratio (HBR) is commonly used to compare the energy

dissipation of different VCSEL designs for applications in energy-efficient optical

interconnects. The devices are measured at operation currents that require the

minimum energy per bit, which means the VCSELs operate at the lowest currents

where still error-free data transmission is observed. Error-free data transmission

at 35, 38, and 42 Gb/s with low energy dissipations of 145, 147, and 217 fJ/bit are

achieved using the ~3 µm oxide-aperture diameter VCSEL, as shown in Fig. 7-16,

with the corresponding eye diagrams. Each of these are the record energy efficiency

result at the measured bit rate for 980 nm VCSELs [54, 86, 148, 149]. The same

measurements are performed for slightly larger oxide-aperture diameter VCSELs.

Error-free 35, 38, and 42 Gb/s data transmission with low heat dissipations of 161,

181, 228 fJ/bit are achieved by using the ~3.5 µm oxide-aperture diameter VCSEL,

and 175, 197, and 296 fJ/bit are needed for a ~4 µm oxide-aperture diameter VCSEL.

These entire three small oxide-aperture diameter (~3 to 4 µm) VCSELs can achieve

high-speed data transmission with a low energy dissipation.

The small-signal analysis and BER measurement results show the energy dissipa-

tion change with the oxide-aperture diameter. To show this influence numerically,

error-free data transmission at certain bit rates are performed using ~3, 3.5, and 4 µm

-6 -5 -4 -3 -2 -1 0 1 2

-log(BER)

Received Optical Power (dBm)

3.5 µm @ 42 Gb/s

4 µm @ 42 Gb/s

6 µm @ 42 Gb/s

7 µm @ 40 Gb/s

25 °C

3.5µm 42Gb/s 4 µm 42 Gb/s

6 µm 42 Gb/s 7 µm 40 Gb/s

Fig. 7-15. Bit error ratio versus received optical power for a ~3.5, 4, 6, and 7 µm oxide-aperture diam-

eter 980 nm VCSELs at 42 and 40 Gb/s at 25 °C, respectively, across 5 m of MMF with a PRBS word

length of 27–1 and a NRZ modulation scheme, and eye diagrams at the corresponding points of error-

free data transmission.

7.2 Room Temperature Energy Efficiency 105

oxide-aperture diameter VCSELs. In Fig. 7-18(a), 35 Gb/s error-free data transmis-

sion at room temperature is shown. The CW bias current for the BER measurements

is 2.7, 3.0, and 3.3 mA for ~3, 3.5, and 4 µm oxide-aperture diameter VCSELs, with

the voltage of 2.31, 2.30, and 2.18 V, respectively. The ~3 µm oxide-aperture diam-

eter VCSEL needs a lower bias current and electrical power, which matches with the

conclusion obtained from our small-signal analysis. Low HBR values of only 145,

161, and 175 fJ/bit are required for 35 Gb/s error-free data transmission at 25 °C using

VCSELs with oxide aperture diameters of ~3, 3.5, and 4 µm. The corresponding EDR

values are 178, 197, and 206 fJ/bit, respectively, as shown in Fig. 7-18(b). Higher HBR

and EDR values are needed for larger oxide-aperture diameter VCSELs compared

with smaller VCSELs. The same data transmission experiments are performed at

higher bit rates of 38 and 42 Gb/s using ~3, 3.5, and 4 µm oxide-aperture diameter

VCSELs. The BER results are shown in Fig. 7-19. For 38 Gb/s error-free data trans-

mission, the CW bias current for ~3, 3.5, and 4 µm oxide-aperture diameter VCSELs

is 2.9, 3.5, and 3.78 mA with the voltage of 2.35, 2.38, and 2.32 V, respectively. Heat

25 °C

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

42 Gb/s

35 Gb/s

HBR:145fJ/bit

38 Gb/s

HBR:147fJ/bit

HBR:217fJ/bit

-log(BER)

Received optical power (dBm)

~3 µm oxide aperture diameter

42 Gb/s

35 Gb/s

38 Gb/s

42 Gb/s

Fig. 7-16. Bit error ratio (BER) versus received optical power for the ~3 µm oxide-aperture diame-

ter 980 nm VCSEL operating at 35, 38 and 42 Gb/s at 25 °C, respectively, and the corresponding eye

diagrams.

35 Gb/s

38 Gb/s

42 Gb/s

-8 -7 -6 -5 -4 -3 -2 -1 0

35 Gb/s

-log(BER)

Received optical power (dBm)

HBR:175 fJ/bit

38 Gb/s

HBR: 197 fJ/bit

42 Gb/s

HBR: 296 fJ/bit

25 °C

~4 µm oxide aperture Ø

-9 -7 -5 -3 -1 1 3

HBR:181 fJ/bit

HBR:228 fJ/bit

42 Gb/s

38 Gb/s

35 Gb/s

HBR:161 fJ/bit

25 °C

-log(BER)

Received optical power (dBm)

~3.5 µm oxide aperture Ø

42 Gb/s

35 Gb/s

38 Gb/s

(a)

(b)

Fig. 7-17. Bit error ratio (BER) versus received optical power for ~3.5 µm (a) and ~4 µm (b) oxide-

aperture diameters 980 nm VCSELs operating at 35, 38, and 42 Gb/s at 25 °C, respectively, and the

corresponding eye diagrams.

106 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

dissipation HBR of 147, 181, and 197 fJ/bit are required for 38 Gb/s error-free data

transmission, and the corresponding EDR values are 180, 220, and 231 fJ/bit, respec-

tively. For 42 Gb/s error-free data transmission, the CW bias current for ~3, ~3.5, and

~4 µm oxide-aperture diameter VCSELs is 4.1, 4.4, and 5.5 mA, respectively, with

HBR values of 217, 228, and 296 fJ/bit, respectively. For all the bit rates investigated

here, VCSELs with small oxide-apertures between ~3 to ~4 µm achieve error-free

data transmission with a low energy dissipation. Furthermore, the ~3 µm oxide-

aperture diameter VCSEL requires a lower bias current, lower electrical power, lower

HBR, and lower EDR to achieve the same error-free data transmission as for the ~3.5

and ~4 µm oxide-aperture diameter VCSELs. This proves that small oxide-aperture

diameter VCSELs are more energy-efficient than larger oxide-aperture diameter

VCSELs. This behavior has also previously been observed for 850 nm VCSELs. In

[142, 150], it is been demonstrated that VCSELs with small oxide-aperture diameters

of from ~3 to ~4 µm are more energy-efficient than VCSELs with larger oxide-

aperture diameters of 5 µm or larger when operating at room temperature. But the

different part is that 850 nm VCSELs with larger oxide-aperture diameter (5 µm)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

35 Gb/s

-log(BER)

3 µm

HBR:145 fJ/bit

3.5 µm

HBR:161 fJ/bit

4 µm

HBR:175 fJ/bit

Received optical power (dBm)

4 µm

3 µm

3.5 µm

3.0 3.5 4.0

120

160

200

240

35 Gb/s

25 °C

EDR

HBR

EDR, HBR (fJ/bit)

Oxide Aperture Diameter (µm)

25 °C (a) (b)

Fig. 7-18. Bit error ratio (BER) versus received optical power (a) in a back-to-back configuration for

~3, 3.5, and 4 µm oxide-aperture diameter 980 nm VCSELs at 35 Gb/s at 25 °C, and the corresponding

eye diagrams. Plotted EDR and HBR values versus the oxide-aperture diameter (b).

-8 -7 -6 -5 -4 -3 -2 -1 0 1

38 Gb/s

-log(BER)

HBR:147 fJ/bit

HBR:197 fJ/bit

HBR:181 fJ/bit

Received optical power (dBm)

25 °C 3.5 µm

4 µm

3 µm 4 µm

3 µm

3.5 µm

-6 -5 -4 -3 -2 -1 0 1 2

-log(BER)

42 Gb/s

HBR:217fJ/bit

HBR:228fJ/bit

HBR:296fJ/bit

Received optical power (dBm)

25 °C

3.5 µm

4 µm

3 µm

4 µm

3 µm

3.5 µm

(a) (b)

Fig. 7-19. Bit error ratio (BER) versus received optical power in a back-to-back configuration for ~3,

~3.5, and ~4 µm 980 nm VCSELs at 25 °C at 38 Gb/s (a), and at 42 Gb/s (b), and the corresponding

eye diagrams at the point of error-free operation.

7.3 High Temperature Energy Efficiency 107

achieve larger maximum f–3dB values as compared to VCSELs with smaller-oxide

aperture diameter (3 µm) [142]. However, the structure used in this work shows that

the 3 and 5 µm oxide-aperture diameter VCSELs achieve the same maximum f–3dB at

room temperature. At 85 °C, larger oxide-aperture diameter (5 µm) VCSEL achieve

smaller maximum f–3dB values as compared to VCSELs with smaller oxide-aperture

diameters (3 µm), which is the opposite with the 850 nm VCSELs results showed

in [142]. The modulation response of optimized oxide-aperture diameters for high

maximum f–3dB can be different for different structure designs. Due to different

damping and parasitic level, the small oxide-aperture (3 µm) VCSELs can reach the

same, smaller, or larger maximum f–3dB. However, due to a larger D-factor, small

oxide-aperture diameter VCSELs usually show better energy efficiency.

7.3 High Temperature Energy Efficiency

It is very important to achieve high energy efficiency and high bit-rate operation at

high temperatures due to the high operation temperature in commercial applications.

This section focuses on high temperature operation (85 °C) of high bit-rate 980 nm

VCSELs. The VCSEL epitaxial structure is designed to have improved temperature

stability by introducing an around –15 nm gain-to-etalon wavelength offset [98,

141]. With this offset, the VCSELs display much improved static and dynamic per-

formance (including the maximum bit rate at the high temperature of ~85 °C, and

the energy efficiency of VCSELs) at the high temperatures of 85 °C simultaneously

compared to VCSELs with a smaller gain-to-etalon wavelength offset.

7.3.1 Small-Signal Analysis at High Temperature

The same small-signal measurements and evaluation presented in section 7.2.1 are

performed at temperatures of 45, 65, and 85 °C. The f–3dB results versus the bias

current at 45 °C are shown in Fig. 7-20(b), showing a comparable behavior as at 25 °C.

The difference is that the maximum f–3dB only stays at high values for VCSELs with

oxide-aperture diameters of between ~3 to ~5 µm, and starts to decrease for ~6 µm

and larger oxide-aperture diameter VCSELs. At room temperature, the maximum

f–3dB stays at high values for VCSELs with oxide-aperture diameters smaller than

7 µm. The maximum –3 dB bandwidth is 21.3, 21.6, 20.6, 19.2, and 17.8 GHz for

~3, 4, 5, 6, and 7 µm oxide-aperture diameter VCSELs at 45 °C, respectively. The

extracted relaxation resonance frequencies fr versus the quantity the square root of

108 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

the current above the threshold current and the corresponding linear fittings to this

data are shown in Fig. 7-20(a). This data also shows a similar trend of variation with

current as at 25 °C. The D-factor is 9.5, 8.0, 6.1, 5.3, and 4.5 GHz/(mA1/2) for ~3, 4, 5,

6, and 7 µm oxide-aperture diameter VCSELs, respectively. The maximum f

slightly

decreases with increasing oxide-aperture diameter at 45 °C, while at room tempera-

ture the maximum fr reach similar values for VCSELs with oxide-aperture diameter

ranging from ~3 to ~7 µm. The f–3dB change with the current density is very similar to

the result at room temperature as well, as shown in Fig. 7-20(c). The change of f–3dB at

65 °C with the current and current density are similar to the results at 45 °C, where

the only difference is a smaller maximum value. The extracted relaxation resonance

frequencies fr versus the square root of the current above the threshold current are

shown in Fig. 7-21(a). The D-factor is 10.4, 8.5, 6.3, 5.6, and 4.6 GHz/(mA1/2) for ~3,

4, 5, 6, and 7 µm oxide-aperture diameter VCSELs, respectively, which are higher

than the results at 25 and 45 °C. The maximum fr value is 16.7, 16.1, 14.7, 14.1, and

13.2 GHz for ~3, 4, 5, 6, and 7 µm oxide-aperture diameter VCSELs, respectively,

which decreases with increasing oxide-aperture diameter. This is different from the

01234

0 3 6 9 12 15

Current (mA) 0 10 20 30 40 50 60 70

45 °C45 °C45 °C

fr (GHz)

f-3dB (GHz)

(I-Ith)1/2 (mA1/2)Current density (kA/cm2)

(b)(a) (c)

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-20. Relaxation resonance frequency fr (a) at 45 °C versus the square root of the current above

the threshold current for 980 nm VCSELs with oxide-aperture diameters ranging from ~3 to 7 µm.

The dots show the measurement data and the straight lines indicate the linear fittings used for obtain-

ing the D-factors. Also shown is the –3 dB modulation bandwidth f–3dB versus the current (b), and as

a function of the current density (c).

01234

0 2 4 6 8 10 12 14

0 10 20 30 40 50 60 70

65 °C65 °C

fr (GHz)

f-3dB (GHz)

(b)(a) (c)

Current (mA)(I-Ith)1/2 (mA1/2)Current density (kA/cm2)

65 °C

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-21. Relaxation resonance frequency fr (a) at 65 °C versus the square-root of the current above

the threshold current for 980 nm VCSELs with oxide aperture diameters ranging from ~3 to 7 µm.

The dots show the measurement data and the straight lines indicate the linear fittings used for obtain-

ing the D-factors. Also shown is the –3 dB modulation bandwidth f–3dB versus the current (b), and as

a function of the current density (c).

7.3 High Temperature Energy Efficiency 109

result at 25 °C, where the maximum fr, (i.e. the saturation values of fr for a given

oxide-aperture diameter) for the 3, 4, and 5 µm oxide-aperture diameter VCSELs

are almost equal.

Fig. 7-22(a) shows the extracted f–3dB for the VCSELs against current at 85 °C.

The small oxide-aperture diameter VCSELs need smaller bias currents to achieve a

certain f–3dB compared to the larger oxide-aperture diameter VCSELs. Furthermore,

the small oxide-aperture diameter VCSELs can achieve slightly higher maximum

f–3dB than large oxide-aperture diameter VCSELs. Thus the small oxide-aperture

VCSELs are able to operate at higher bit rates, which will be proved later via data

transmission experiments. The –3 dB bandwidth f–3dB versus the electrical power

for the VCSELs with oxide-aperture diameters of from ~3 to ~7 µm are shown in

Fig. 7-22(b). The f–3dB increase with increasing the electrical power at small values

until they reach the saturation, then a further increase in electrical power does not

lead to an increase of f–3dB. VCSELs with smaller oxide-aperture diameters achieve

larger f–3dB at a given electrical power compared to VCSELs with large apertures.

In addition, VCSELs with smaller oxide-aperture diameters need lower electrical

power to achieve a given f–3dB compared to larger VCSELs. Fig. 7-22(c) shows the

0 2 4 6 8 10 12 14

0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Current (mA)

f-3dB (GHz)

Electrical power (mW) Current density (kA/cm2)

(b)(a) (c)

85 °C85 °C85 °C

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-22. –3 dB modulation bandwidth f–3dB versus current (a), electrical power (b), and current density

01234

–3dB bandwidth (GHz)

Resonance frequency (GHz)

(I-I

)

1/2

(mA

1/2

) (I-I

)

1/2

(mA

1/2

)

(a) (b) 85 °C85 °C

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

3 µm

4 µm

5 µm

6 µm

7 µm

Aperture Ø

Fig. 7-23. –3 dB bandwidth f–3dB (a) and relaxation resonance frequency fr (b) at 85 °C versus the square-

root of the current above the threshold current for 980 nm VCSELs with oxide-aperture diameters

ranging from ~3 to 7 µm. The dots show the measurement data and the straight lines indicate the lin-

ear fittings used for obtaining the MCEF and D-factors.

110 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

f–3dB versus the current density at 85 °C. Smaller oxide-aperture diameter VCSELs

need lower currents, lower electrical powers, and nearly the same current density to

reach the same bandwidth at 85 °C compare with larger VCSELs.

Figure 7-23 shows the f–3dB and the fr versus the quantity the square root of the

current above the threshold current at 85 °C for the VCSELs with oxide-aperture

diameters ranging from ~3 to ~7 µm. The MCEF and D-factor decrease with increas-

ing oxide-aperture diameter, which are 14.97 and 10.7 GHz/(mA)1/2 for the ~3 µm

oxide-aperture diameter VCSEL and 7.0 and 4.7 GHz/(mA)1/2 for the ~7 µm oxide-

aperture diameter VCSEL, respectively. The small oxide-aperture diameter VCSELs

have larger MCEF and D-factors and thus a faster increase of f–3dB and fr with the bias

current and larger values of MCEF and D-factors at a given forward bias current. In

combination with the f

–3dB

evaluation, it should be noted that the small oxide-aperture

VCSELs (from ~3 to ~4 µm) have larger MCEF and D-factors and achieve slightly

higher bit rates at the same current compared to the large oxide-aperture VCSELs

(larger than 4 µm). This means small oxide-aperture VCSELs (from ~3 to ~4 µm) in

this work will be beneficial for the high-speed and energy-efficient operation at high

temperatures such as at 85 °C.

Figure 7-24(a) shows the f–3dB as a function of temperature at certain bias cur-

rents for a ~3 µm oxide-aperture diameter VCSEL, in order to study the effect of

temperature on the f–3dB. For small bias currents, the f–3dB increase with increasing

the heat sink temperature, due to an around –15 nm QW gain-to-etalon wavelength

offset, which leads to an increased differential gain with increasing the active region

temperature. The D-factor has the same change trend with the differential gain as

for the f–3dB. The differential gain reaches a maximum value at around 87 °C then

starts to reduce slowly. The active region temperature can be much higher than the

heat-sink temperature. When the current is low, the active region temperature is

lower than 87 °C. The differential gain increases with the current until it reaches

20 30 40 50 60 70 80 90

~3 µm aperture Ø

1 mA

2 mA

3 mA

4 mA

Temperature (°C)

(a)

20 30 40 50 60 70 80 90

Temperature (°C)

(b)

–3dB bandwidth (GHz)

1 mA

2 mA

3 mA

4 mA

~4 µm aperture Ø

Fig. 7-24. –3 dB modulation bandwidth f–3dB change with temperature at certain currents for ~3 µm (a)

and ~4 µm (b) oxide-aperture diameter 980 nm VCSELs.

7.3 High Temperature Energy Efficiency 111

its maximum value. The increasing differential gain leads to a larger fr, and thus a

larger –3 dB bandwidth f–3dB can be reached before reaching thermal limitation. For

a large bias current, the f–3dB decreases with increasing the temperature due to the

high active region temperature. The f–3dB shows the high temperature-stability over

the entire current range. Larger oxide-aperture diameter (~4 µm) VCSELs show a

similar change trend as shown in Fig. 7-24(b).

Fig. 7-25(a) shows the maximum f–3dB versus oxide-aperture diameter at 25, 45, 65,

and 85 °C. At room temperature, VCSELs with oxide-aperture diameters ranging

from ~3 to~6 µm can reach a similar high f–3dB. At a higher temperature of 45 °C,

the small oxide-aperture (~3 to ~4 µm) VCSELs can reach a slightly higher f–3dB,

and then f–3dB starts to decrease as the aperture diameter increases. For even higher

temperatures of 65 and 85 °C, the maximum f–3dB starts to decrease with the ~4 µm

oxide-aperture diameter VCSEL. Large aperture VCSELs have smaller maximum

bandwidths over all of the temperature range. The results predicted from the modula-

tion theory match the measured results, where the MCEF and D-factor decrease with

increasing oxide-aperture diameter, as shown in Fig. 7-25(b) and 7-25(c).

7.3.2 High Bit-Rate Data Transmission

Due to the optimized active region and mirror design, process flow, and optimized

gain-mode offset, the 980 nm VCSELs can achieve high bit-rate also at high tempera-

tures besides at room temperature. The eye diagrams for the ~3.5 µm oxide-aperture

diameter VCSEL operated at 20, 30, and 42 Gb/s at room temperature and operated

at 35, 36, and 38 Gb/s at 85 °C are shown in Fig. 7-26. At room temperature, clear

open eyes can be achieved from 20 to 42 Gb/s. Open eyes at 38 Gb/s with a signal to

noise ratio (S/N) of 3.08 is achieved for the temperature of 85 °C. With increasing

34567

Oxide-aperture diameter (µm)

(f-3dB)max (GHz)

34567

MCEF (GHz/(mA)1/2)

34567

D-factor (GHz/(mA)1/2)

Oxide-aperture diameter (µm) Oxide-aperture diameter (µm)

25 °C

45 °C

65 °C

85 °C

25 °C

45 °C

65 °C

85 °C

25 °C

45 °C

65 °C

85 °C

(a) (b) (c)

Fig. 7-25. Maximum –3 dB bandwidth f–3dB (a), MCEF (b), and D-factor (c) versus oxide-aperture di-

ameter at 25, 45, 65, and 85 °C for 980 nm VCSELs with oxide-aperture diameters ranging from ~3

to ~7 µm.

112 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

bit-rate, the eye openings are getting smaller and the S/N value decreases. The BER

measurement results of this maximum achievable transmission bit-rate, which are

42 Gb/s at room temperature and 38 Gb/s at 85 °C, are shown in Fig. 7-26.

The BER results of maximum achievable error-free transmission bit-rate at the

maximum temperature for the ~4 µm oxide-aperture diameter VCSEL are shown

in Fig. 7-27. Error-free data transmission at 42 Gb/s is achieved at room temperature,

while 40 and 38 Gb/s is achieved at 75 and 85 °C, respectively.

Eye diagrams at 24, 32, 38, and 42 Gb/s at 25 °C using the ~6 µm oxide-aperture

diameter VCSEL are shown in Fig. 7-28. Clear open eyes can be obtained up to

42 Gb/s (with a signal-to-noise ratio of 3.14). At 45 and 65 °C, clear open eyes at

40 Gb/s are obtained with S/N ratios of 2.78 and 2.86, respectively. At 85 °C, clear

open eyes at 31 and 35 Gb/s are achieved. The BER measurement results of these

corresponding clear open eyes at room temperature are shown in Fig. 7-29(a). Error-

free data transmission at 24, 32, 38, and 42 Gb/s can be achieved at 25 °C using the

~6 µm oxide-aperture diameter VCSEL. As shown in Fig. 7-29(b), error-free data

transmission at 31 and 35 Gb/s can be achieved at 85 °C. The maximum achievable

25°C

20Gb/s

30Gb/s

42Gb/s

S/N:4.49

S/N:4.17

S/N:3.19

85°C

35Gb/s

36Gb/s

38Gb/s

S/N:3.48

S/N:3.44

S/N:3.08

Received Optical Power (dBm)

-log(BER)

~3.5 µm aperture diameter

980 nm VCSEL

-6 -5 -4 -3 -2 -1 0 1

42 Gb/s@25 °C

38 Gb/s@85 °C

Fig. 7-26. Bit error ratio (BER) versus received optical power operating at 42 and 38 Gb/s at 25 and

85 °C, and eye diagrams at 20, 30, and 42 Gb/s at 25°C, and at 35, 36, and 38 Gb/s at 85 °C for a ~3.5 µm

oxide aperture diameter VCSEL.

Fig. 7-27. Bit error ratio (BER) ver-

sus received optical power for a

~4 µm oxide-aperture diameter

980 nm VCSEL operating at 42, 40,

and 38 Gb/s at 25, 75, and 85 °C, re-

spectively, and the corresponding

eye diagrams.

-7 -6 -5 -4 -3 -2 -1 0 1

38 Gb/s@85 °C

40 Gb/s@75 °C

42 Gb/s@25 °C

-log(BER)

Received optical power (dBm)

~4 µm aperture Ø

980 nm VCSEL

38 Gb/s 85 °C

40 Gb/s 75 °C

42 Gb/s 25 °C

7.3 High Temperature Energy Efficiency 113

bit rate at the highest preset temperature is 42, 36 and 35 Gb/s at 25, 75, and 85 °C,

respectively. For the large oxide-aperture diameter VCSELs (~6 µm), the maximum

achievable speed at high temperature (75 and 85 °C) slightly decreases compared to

the smaller oxide-aperture diameter (from ~3 to ~4 µm) VCSELs.

Figure 7-30 shows the BER results for the maximum achievable transmission

bit rate at 85 °C using the VCSELs with oxide-aperture diameters ranging from ~3

to ~5 µm [34]. 38 Gb/s error-free data transmission for VCSELs smaller than 5 µm

is achieved, and only 35 Gb/s can be achieved for ~5 µm oxide-aperture diameter

VCSELs, which is 3 Gb/s lower than for the VCSELs with smaller oxide-aperture

diameters. These data transmission results match well with the predictions from

the small-signal analysis, where the maximum −3 dB bandwidth is predicted to be

a stable high value for VCSELs with small oxide-aperture diameters (smaller than

5 µm), and start to decrease for ~5 µm and larger oxide-aperture diameter VCSELs.

For the smaller VCSELs (with an oxide-aperture diameter smaller than 5 µm), the

maximum achievable bit rate only has a 4 Gb/s (9.5 %) change, decreasing from 42

to 38 Gb/s when the temperature increases from 25 to 85 °C, thus showing highly

temperature-stable modulation.

25 °C 25 °C 25 °C 25 °C24 Gb/s 32 Gb/s 38 Gb/s 42 Gb/s

S/N: 4.94 S/N: 4.53 S/N: 3.23 S/N: 3.14

45 °C 65 °C 85 °C 85 °C40 Gb/s 40 Gb/s 31 Gb/s 35 Gb/s

S/N: 2.78 S/N: 2.86 S/N: 1.63 S/N: 1.46

Fig. 7-28. Eye diagrams for the ~6 µm oxide-aperture diameter 980 nm VCSEL operating at 24, 32, 38

and 42 Gb/s at 25 °C, 40 Gb/s at 45 °C, 40 Gb/s at 65 °C, and 31 and 35 Gb/s at 85 °C.

-8 -6 -4 -2 0 2

-log(BER)

Received optical power (dBm)

-6 -5 -4 -3 -2 -1 0 1 2

-log(BER)

Received optical power (dBm)

-10 -8 -6 -4 -2 0 2

-log(BER)

Received optical power (dBm)

24 Gb/s

32 Gb/s

38 Gb/s

42 Gb/s

25 °C

42 Gb/s

@25 °C

36 Gb/s

@75 °C

35 Gb/s

@85 °C

31 Gb/s

35 Gb/s

85 °C

(a) (b) (c)

Fig. 7-29. Bit error ratio (BER) versus received optical power for the ~6 µm oxide-aperture diameter

980 nm VCSEL operating at 24, 32, 38 and 42 Gb/s at 25 °C (a), and operating at 31, and 35 Gb/s at

85 °C (b), and at the maximum achievable bit rate at different temperatures (c).

114 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

7.3.3 Energy-efficient data transmission

Highly temperature-stable static performance (threshold current, threshold electrical

power, differential quantum efficiency, and more) and highly temperature-stable

high bit-rate modulation performance (maximum achievable modulation bandwidth,

D-factor, and MCEF) provide the possibility of energy-efficient operation at high

temperature as at room temperature. 35 and 38 Gb/s error-free data transmissions at

85 °C are achieved with low energy dissipation of only 139 [34], and 177 fJ/bit with

the ~3 µm oxide-aperture diameter VCSEL, as shown in Fig. 7-31. These are the

lowest values for VCSELs operating at 85 °C at any wavelength [49, 54] at the corre-

sponding bit-rate. Figure 7-32 shows that the slightly larger VCSELs (~3.5 and 4 µm

oxide-aperture diameter) operate at 35 and 38 Gb/s at 85 °C. Also the low power

dissipation of only 140 and 177 fJ/bit are needed by using ~3.5 µm oxide-aperture

diameter VCSEL for 35 and 38 Gb/s error-free data transmission, respectively, while

159 and 177 fJ/bit are needed by using a ~4 µm oxide-aperture diameter VCSEL.

20 fJ/bit more power dissipation per bit is needed for 35 Gb/s error-free data trans-

mission by increasing the oxide-aperture diameters of the VCSELs from ~3 µm to

4 µm. All of the small VCSELs with an oxide-aperture diameter between ~3 and

4 µm are investigated and can achieve a high bit-rate data transmission with a low

energy dissipation at the high temperatures.

Error-free data transmission at certain bit rates at 85 °C are performed using ~3,

3.5, and 4 µm oxide-aperture diameter VCSELs to show how the oxide-aperture di-

ameter impacts the power dissipation. Error-free 35 Gb/s data transmission at 85 °C

using ~3, 3.5, and 4 µm oxide-aperture diameter VCSELs are shown in Fig. 7-33(a).

The CW bias current for 35 Gb/s error-free data transmission is 2.7, 2.8, and 3.2 mA

3 µm 3.5µm

4µm 5µm

38Gb/s 38Gb/s

38Gb/s 35Gb/s

3 µm @ 38 Gb/s

3.5 µm @ 38 Gb/s

4 µm @ 38 Gb/s

5 µm @ 35 Gb/s

85 °C

-log(BER)

Received Optical Power (dBm)

-8 -7 -6 -5 -4 -3 -2 -1 0

Fig. 7-30. Bit error ratio versus received optical power in a BTB configuration for ~3, 3.5, 4, and 5 µm

oxide-aperture diameter 980 nm VCSELs at 38 and 35 Gb/s at 85 °C, respectively, and eye diagrams

at the corresponding points of error-free data transmission.

7.3 High Temperature Energy Efficiency 115

where a low energy dissipation of only 139, 140, and 159 fJ/bit are needed for ~3, 3.5,

and 4 µm oxide-aperture diameter VCSELs, respectively. Smaller oxide-aperture

diameter VCSELs need lower operating bias currents and have lower energy dissipa-

tion than larger oxide-aperture diameter VCSELs, as is predicted from small signal

analysis. The same data transmission experiments are performed at the higher bit

rates of 38 Gb/s and the results are shown in Fig. 7-33(b). The CW bias current for

38 Gb/s error-free data transmission is 3.4, 3.5, and 3.6 mA and low energy dissipa-

tion of 177, 177, and 177 fJ/bit for ~3, 3.5, and 4 µm oxide-aperture diameter VCSELs,

respectively. For 38 Gb/s error-free data transmission, VCSELs with oxide-aperture

diameters from ~3 to 4 µm have the same power dissipation. This is because the bias

current needs to be slightly larger than the minimum current needed to reach the

given bandwidth due to the low output power for the ~3 µm oxide-aperture diameter

VCSEL. Small oxide-aperture diameter VCSELs display low bias currents, low

electrical power, and low energy dissipation to achieve high bit-rate error-free data

-9 -8 -7 -6 -5 -4 -3 -2 -1

35 Gb/s

-log(BER)

Received optical power(dBm)

38 Gb/s

HBR: 159 fJ/bit

HBR: 177 fJ/bit

~4 µm aperture Ø

85 °C

-8 -7 -6 -5 -4 -3 -2 -1 0

35Gb/s

-log(BER)

Received optical power(dBm)

38 Gb/s

HBR: 140 fJ/bit

HBR: 177fJ/bit

~3.5 µm aperture Ø

85 °C

(a) (b)

Fig. 7-32. Bit error ratio versus received optical power for 980 nm VCSELs with oxide-aperture diam-

eters of ~3.5 µm and 4.0 µm operating at 35 and 38 Gb/s at 85 °C, and eye diagrams at the correspond-

ing bit rates and modulation conditions.

Fig. 7-31. Bit error ratio versus received optical

power for 980 nm VCSELs with oxide-aperture

diameters of ~3 µm operating at 35 and 38 Gb/s

at 85 °C, and eye diagrams at the corresponding

bit rates and modulation conditions.

-9 -8 -7 -6 -5 -4 -3 -2 -1

35 Gb/s

85 °C

-log(BER)

Received optical power(dBm)

HBR: 177 fJ/bit

38 Gb/s

HBR: 139 fJ/bit

~3 µm aperture Ø

116 Chapter 7 Energy-Efficient High Bit-Rate VCSELs

transmission, which proves the small oxide-aperture diameter (from ~3 to ~4 µm)

VCSELs are very energy-efficient, suitable for high bit-rate, energy-efficient optical

interconnect applications.

7.4 Summary

For the first time it is experimentally demonstrated that 980 nm VCSELs can achieve

temperature-stable, energy-efficient, and high bit-rate operation concurrently. Error-

free data transmission at 42 and 38 Gb/s are achieved at 25 and 85 °C, respectively.

Record low 139 and 177 fJ/bit for 35 and 38 Gb/s error-free transmission at 85 °C

are achieved with a ~3 µm oxide-aperture diameter VCSEL, which are the most

energy-efficient VCSELs operating at 85 °C at any wavelength. At room temperature,

only 145, 147, and 217 fJ/bit energy dissipation are needed for 35, 38 and 42 Gb/s

error-free transmission. These are the record low energy dissipations for any 980 nm

VCSELs. These VCSELs also demonstrate very temperature-insensitive static and

dynamic properties. 38 Gb/s error-free transmission can be achieved at 25, 45, 65,

and 85 °C without any change of the operating point or the modulation conditions

using ~3.5 and 4 µm oxide-aperture diameter VCSELs. The 980 nm VCSELs with

oxide-aperture diameters from ~3 to 4 µm have a small threshold current, large mode

spacing, large D-factor, are very energy efficient, are very temperature-stable, and

are capable of operating at high bit-rates. Such VCSELs are especially well suited

for optical interconnects in high performance computers.

-9 -8 -7 -6 -5 -4 -3 -2

35 Gb/s

-log(BER)

HBR: 139 fJ/bit

HBR: 140 fJ/bit

HBR: 159 fJ/bit

Received optical power (dBm)

3 µm

3.5 µm

4 µm

85 °C

4 µm

3 µm

3.5 µm

-9 -8 -7 -6 -5 -4 -3 -2 -1

38 Gb/s

-log(BER)

HBR:177 fJ/bit

HBR: 177 fJ/bit

85 °C

3 µm

3.5 µm

4 µm

Received optical power (dBm)

4 µm

3 µm

3.5 µm

(a) (b)

Fig. 7-33. Bit error ratio versus received optical power in a back-to-back configuration for a ~3, ~3.5,

and 4 µm 980 nm VCSELs at 35 Gb/s in (a) and at 38 Gb/s in (b), both at 85 °C, and the corresponding

eye diagrams at the point of error-free operation.

117

Chapter 8

Conclusions and Outlook

In this Chapter the main contributions and conclusions of this dissertation are

summarized along with an outlook for future research in the area of vertical-cavity

surface-emitting lasers (VCSELs).

8.1 Conclusions

The work presented in this dissertation is centered around one key problem, how to

achieve high bit-rate performance with 980 nm GaAs-based oxide-confined VCSELs

at room temperature and at high temperatures while simultaneously operating with

minimal energy dissipation. These VCSEL performance attributes are a main re-

quirement for the use of VCSELs as light sources in future short-reach (hundreds of

meters across multimode optical fiber) to on-chip (centimeters or shorter distances

across waveguides) optical interconnect applications. In order to achieve these

requirements concurrently, VCSELs are developed to be capable of high bit-rates

at low forward bias currents at room temperature and at high temperatures (up to

about 85 °C). This involves the consideration of all aspects of the devices including

the epitaxial design, device geometry and device fabrication, and device character-

ization. This work experimentally demonstrates for the first time that high bit-rate,

temperature-stable, and energy-efficient operation can be achieved concurrently. The

key contributions and conclusions of this dissertation are:

1. Optimized 4.2 nm-thick compressive-strained In0.21Ga0.79As QWs are used in the

active region to improve high bit-rate performance.

Tensile strained GaAs0.88P0.12 barrier layers which can partially compensate strain

are used to improve performance at high temperature.

3. An around –15 nm QW gain-to-etalon wavelength offset is used to improve tem-

perature stability. The influence of the QW gain-to-etalon wavelength offset on

the static performance and the high-speed modulation performance is simulated

and experimentally studied.

118 Chapter 8 Conclusions and Outlook

4. Linearly graded, modulation-doped DBRs, multiple-oxide layers, thick BCB

under the bond pad, and a double mesa structure with an optimized geometry

are used to improve the parasitic cutoff frequency.

5. Photon lifetime is adjusted during the device processing by etching the topmost

DBR layer to change the power reflectance as seen by photons propagating up

toward the top DBR. This DBR reflectivity tuning increases the output power

and increases the −3 dB modulation bandwidth.

Temperature-dependent and oxide-aperture diameter-dependent impedance

characteristics are investigated. The small oxide-aperture diameter VCSELs are

not limited by parasitics at temperatures from 25 to 85 °C. The larger capaci-

tance of larger oxide-aperture VCSELs restricts the VCSELs’ parasitic cutoff

frequency and limits the −3 dB modulation bandwidth.

7. The relative intensity noise is investigated at different bias currents at room tem-

perature for different oxide-aperture diameter VCSELs. The studied VCSELs

can satisfy the requirements of bandwidth and RIN for the 32 GFC Fibre

Channel standard.

8. Systematic characterization including temperature-dependent and oxide-aper-

ture diameter-dependent static measurements, small-signal analysis, and data

transmission experiments are presented. Important parameters, for example

−3 dB modulation bandwidth, D-factor, resonance frequency, parasitic cutoff

frequency are extracted.

9. Different from what is typically observed, the threshold current, threshold

electrical power, D-factor, MCEF, and –3 dB modulation bandwidth (at low bias

current) are larger at 85 °C compared to their values at 25 °C for the 980 nm

VCSELs, which results from the QW gain-to-etalon wavelength offset.

10. The maximum −3 dB modulation bandwidth can reach high values of 21 GHz

for VCSELs at room temperature with oxide-aperture diameters from 3 to 6 µm,

and the bandwidth starts to decrease with further increase of the oxide-aperture

diameter at room temperature.

11.

The maximum −3 dB modulation bandwidth can reach high values of 19 GHz for

VCSELs at 85 °C with oxide-aperture diameters from 3 to 4 µm, and starts to de-

crease with further increase of the oxide-aperture diameter at room temperature.

12. Both at room temperature and high temperature, the smaller oxide-aperture

diameter (3 to 4 µm) VCSELs need a smaller bias current and smaller electrical

power to achieve a certain −3 dB modulation bandwidth.

8.2 Outlook 119

13. The VCSELs demonstrate very temperature insensitive static and dynamic char-

acteristics. Error-free data transmission at a bit rate of 38 Gb/s is achieved at 25,

45, 65, and 85 °C, without any change of the operating point or the modulation

conditions.

14. The VCSELs demonstrate that high bit rates can be reached at room temperature

and at high temperature. Error-free data transmission at 42 and 38 Gb/s are

achieved at 25 and 85 °C, respectively.

15. A record low energy dissipation of 139 and 177 fJ/bit for 35 and 38 Gb/s error-

free transmission at 85 °C is achieved with a 3 µm oxide-aperture diameter

VCSEL. These VCSELs are the most energy efficient VCSELs operating at 85 °C

at any wavelength to date.

16.

At room temperature, only 145, 147, and 217 fJ/bit of energy dissipation is needed

for 35, 38 and 42 Gb/s error-free transmission. These are record low energy dis-

sipations for 980 nm VCSELs.

To conclude and summarize, 3 to 4 µm oxide-aperture diameter 980 nm VCSELs

studied in this work have a small threshold current, large mode spacing, large

D-factor, are very energy-efficient, are very temperature-stable, and are capable

of operating at high bit-rates, compared to larger oxide-aperture diameters. Such

VCSELs are especially well suited for optical interconnects in high performance

computers.

8.2 Outlook

Based on fabrication and characterization methodologies the work has proven that

with one 980 nm VCSEL design it is possible to achieve high bit-rate, temperature-

stable, and energy-efficient operation concurrently. Nevertheless, there is still room

for further improvement. Following is listed some key points of potential improve-

ments based on the results of this dissertation.

1. Reduce the 1.5λ-thick optical cavity to a 0.5λ-thick optical cavity to further

increase the photon density and reduce the mode volume.

2. Change the Al0.12Ga0.9As/Al0.9Ga0.1As bottom DBR to a binary GaAs/AlAs DBR

to improve the thermal conductivity and reduce the effective cavity length to

improve the thermal performance and high bit-rate modulation performance.

3. Improve the VCSEL’s doping profile to further lower the resistance and absorp-

tion, by for example lowering the doping levels of the grading layer when the

aluminum-arsenide composition increases from a low value to high values to

lower free carrier absorption.

120 Chapter 8 Conclusions and Outlook

Use undoped substrates and remove the bottom contact layer beneath the contact

GSG pads to further reduce the pad capacitance.

5. Add deep oxide layers in addition to the two oxide-aperture layers to further

lower the mesa capacitance.

6. Reduce the size of the top mesa for large oxide-aperture diameter VCSELs to

reduce mesa capacitance.

7. Reduce the number of top DBR pairs from 24 pairs to 20 pairs to increase the

output power and lower the photon lifetime.

8. Use different QW barrier material besides GaAs and GaAsP, for example,

Al0.35Ga0.65As to improve the differential gain.

9. Use QDs as the active region media to improve temperature stability.

10. Use higher strained InGaAs QWs for longer wavelength VCSELs, like 1060 nm

VCSEL to improve the differential gain.

11. Use a tunnel junction for longer wavelength (1060 nm) VCSELs to further lower

resistance and absorption and increase the modulation bandwidth.

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Appendix A 133

Appendix A

High Bit-Rate VCSEL Process Flow

I. Sample preparation

1. Cleave a VCSEL 76.2 mm-diameter epitaxial wafer into quarters

II. Top-metal deposition

1. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

2. Dehydration bake: hot plate 120°C, 5 min

3. Spin negative photoresist MaN-1420: 3000 rpm, 30 s, and edge bead removal

4. Post-bake: hot plate 100 °C, 2 min, wait ≥ 10 min

5. Expose: 60 s (6 mW/cm2), wait ≥ 5 min

6. Develop: MaD 533S, 50 s; Stop water one (20 s), stop water two (30 s), DI rinse

and N2 dry

7. O2 plasma descum: 150 W, 3 min

8. Dip: HCl (37 %): H2O = 1 : 4 (15 mL/ 60 mL), 15 s; N2 dry

9. Deposit metal: E-beam evaporation system

a. Ti: 20 nm @ 0.5 Å/s

b. Pt: 50 nm @ 0.5 Å/s

c. Au: 300 nm @ 1 Å/s

10. Lift-off: N-Methyl-2-pyrrolidinone (NMP) (Microposit Stripper 1165), hot plate

75 °C, 50 min, water to remove NMP, and N2 dry

III. Mesa one etch

1. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

2. Dehydration bake: hot plate 120 °C, 5 min

3. Spin HMDS: 2000 rpm, 30 s

4. Bake: hot plate 90 °C, 3 min

5. Spin positive photoresist AZ MIR 701: 1000/ 3000 rpm, 2/ 40 s, and edge bead

removal

6. Bake: hot plate 90°C, 2 min, wait ≥ 10 min

7. Expose: 35 s, wait ≥ 5 min

134 Appendix A

8. Develop: AZ 726 MIF, 40 s; Stop water one (20 s), stop water two (30 s), DI rinse

and N2 dry

9. O2 plasma descum: 150 W, 3 min

10. Etch: ICP-RIE, sample with oil on AlOx Chuck, Cl2 @ 2.5 sccm, BCl3 @ 12.5

sccm, Reactor Pressure: 0.33 Pa, RF-Generator: 30 W, Source: 500 W, in-situ

etch depth control with Nanomess

11. Clean: Acetone/ Isopropanol solvent clean to remove oil

12. Photoresist etch mask removal: NMP, hot plate 75 °C, 50 min, water to remove

NMP, and N2 dry

13. O2 plasma descum: 600 W, 5 min

IV. Oxidation

1. Calibrate oxidation time with dummy samples

2. Remove native oxide: AZ MIF 726, 5 min, Stop water one (20 s), stop water two

(30 S), DI rinse and N2 dry, immediately to furnace

3. Oxidize: furnace 420 °C, N2 flow: 0.8 Liter/min, H2O flow: 0.8 Liter/min, Pres-

sure: 50 mbar, with in-situ control

V Mesa two etch

1. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

2. Spin positive photoresist AZ 4562: 4000 rpm, 30 s, and edge bead removal, wait

5 min

3. Bake: hot plate 100 °C, 7 min, wait ≥10 min

4. Expose: 150 s, wait ≥ 10 min

5. Develop: AZ 351B: H2O= (1 : 4), 140 s; Stop water one (10 s), stop water two

(5 s), DI rinse and N2 dry

6. O2 plasma descum: 150 W, 3 min

7. Etch: ICP-RIE, sample with oil on AlOx Chuck, Cl2 @ 2.5 sccm, BCl3 @

12.5 sccm, Reactor Pressure: 0.33 Pa, RF-Generator: 30 W, Source: 500 W,

in-situ etch depth control with Nanomess

8. Clean: Acetone/ Isopropanol solvent clean to remove oil

9. Photoresist removal: NMP, hot plate 75 °C, 50 min, water to remove NMP, and

N2 dry

10. O2 plasma descum: 600 W, 5 min

VI. Bottom-metal deposition

Appendix A 135

1. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

2. Dehydration bake: hot plate 120 °C, 5 min, wait 1 min

3. Spin negative photoresist MaN-490: 700/ 2500 rpm, 5 /40 s, and edge bead

removal

4. Postbake: hot plate 100 °C, 14 min, wait ≥ 20 min

5. Expose: 150 s (6 mW/cm2), wait ≥ 20 min

6. Develop: MaD 532S, 8 min; Stop water one (20 S), stop water two (20 S), DI

rinse and N2 dry

7. O2 plasma descum: 150 W, 3 min

8. Dip: HCl (37 %): H2O = 1 : 4 (15 mL/ 60 mL), 15 s; N2 dry

9. Deposit metal: Vecco evaporation system

a. Ni: 20 nm

b. Au/Ge: 88/12 nm

c. Au: 300 nm

10. Lift-off: NMP, hot plate 75 °C, 50 min, water to remove NMP, and N2 dry

11. Annealing: RTA, 380 °C, 60 s

VII. BCB Planarization

1. Warmup BCB at least 1 hour

2. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

3. Dry: 4000 rpm, 90 s

4. Spin adhesion promotor AP3000: 3000 rpm, 20 s

5. Spin photo BCB 4026–46: 700/ 3000 rpm, 10/ 40 s, edge bead removal, wait

1 min

6. Bake: hot plate 80 °C, 90 s

7. Expose: 50 s (CP mode without UV filter)

8. Develop: DS3000, 35 °C, 10 min

9. Develop: DS3000, RT, 90 s

10. Cure BCB: N2 flow, 500-600 mbar

11. BCB etch: O2 @ 13.75 sccm, CF4 @ 11.25 sccm, Reactor Pressure: 20 Pa, RF-

Generator: 50 W

VIII. GSG Pad metal deposition

1. Solvent clean: Acetone (5 min @ RT), Isopropanol (5 min @ RT) clean and N2

dry

2. Dehydration bake: hot plate 120 °C, 5 min

136 Appendix A

3. Spin negative photoresist MaN-1440: 3000 rpm, 30 s, and edge bead removal

4. Post-bake: hot plate 90 °C, 5 min, wait ≥ 5 min

5. Expose: 24 s (6 mW/cm2), wait ≥ 5 min

6. Develop: MaD 533S, 90 s; Stop water one (20 S), stop water two (20 S), DI rinse

and N2 dry

7. O2 plasma descum: 150 W, 3 min

8. Dip: HCl (37 %): H2O = 1 : 4 (15 mL/ 60 mL), 15 s; N2 dry

9. Deposit metal: E-beam evaporation system

a. Cr: 50 nm @ 0.5 Å/s

b. Pt: 50 nm @ 0.5 Å/s

c. Au: 300 nm @ 1 Å/s

10. Lift-off: NMP, hot plate 75 °C, 50 min, water to remove NMP, and N2 dry

Appendix B 137

Appendix B

Abbreviations

BCB bisbenzo-cyclobutene

BER bit error ratio

BTB back-to-back

CW continuous wave

DBR distributed Bragg reflector

EDR electrical energy-to-data ratio

EEL edge-emitting laser

ESA electrical spectrum analyzer

GSG ground-signal-ground

HBR dissipated heat-to-bit rate ratio

ICP-RIE inductively coupled plasma reactive ion etching

LIV light output power-current-voltage

MBE molecular beam epitaxy

MCEF modulation current efficiency factor

MOCVD metal-organic chemical vapor deposition

NMP N-Methyl-2-pyrrolidinone

NRZ non-return-to-zero

QW quantum well

OSA optical spectrum analyzer

PECVD plasma-enhanced chemical vapor deposition

PRBS pseudorandom binary sequence

PD photodetector

RF radio frequency

RIE reactive ion etching

RIN relative intensity noise

RTA rapid thermal annealing

SEM scanning electron microscope (or microscopy)

SMF single mode fiber

SMSR side-mode-suppression ratio

S/N signal-to-noise ratio

MMF multimode fiber

VCSEL vertical-cavity surface-emitting laser

VNA vector network analyzer

138 Appendix C

Appendix C

Symbols

αi internal loss (cm–1)

Rt top-mirror power reflectance (unitless)

Rb bottom-mirror power reflectance (unitless)

Leff effective resonator length (nm)

L cavity length (nm)

Γ optical confinement factor (unitless)

g gain (cm–1)

gth threshold gain (cm–1)

g0 gain coefficient (cm–1)

ε gain compression factor (unitless)

N carrier density (cm–3)

Ntr transparency carrier density (cm–3)

Np photon density (cm–3)

q electron charge (C)

τ carrier lifetime (s)

τp photon lifetime (s)

ηd differential quantum efficiency (W/A)

ηi current injection efficiency (unitless)

V volume of active region (cm3)

Vp mode volume (cm3)

vg group velocity of the lasing mode (cm–1)

H(f) transfer function (dB)

fR relaxation resonance frequency (GHz)

γ damping factor (s-1)

f−3dB −3 dB modulation bandwidth (GHz)

fP parasitic cut-off frequency (GHz)

I bias current (mA)

Ith threshold current (mA)

Jth threshold current density (Acm–2)

V bias voltage (Volts)

Pth threshold electrical power (mW)

Pel input CW electrical power (mW)

Rth thermal resistance (K/mW)

Acknowledgments 139

Acknowledgments

First of all, I would like to express my sincere gratitude to my advisor Prof. Dr.

Dieter Bimberg for his continuous support of my PhD study and research, and for

his patience, guidance, motivation, enthusiasm, and encouragement along the way.

Prof. Bimberg showed me the importance of both optimism and courage to grasp

opportunities by taking risks and challenges, and what I learned from Prof. Bimberg

is priceless to my future. His guidance helped me throughout the entire duration of

my research. I could not have imagined having a better advisor and mentor. I am very

grateful to Prof. Dr. Gadi Eisenstein for reviewing my dissertation. Many thanks to

Prof. Dr. Michael Lehmann for taking on the chair of the dissertation committee.

I would like to give my warmest thanks to my colleagues, Philip Wolf, Philip

Moser, and Gunter Larisch, who patiently guided me off to a smooth start from the

very first day. Nothing in this thesis could have been done without their great efforts.

I would also like to thank all of my former and current colleagues in Prof. Bimberg’s

group. I have been honored getting to know you wonderful people.

I am very grateful to Prof. Dr. James A. Lott for all of his patient help, valuable

advice, and interesting discussions on physics, philosophy, and life. As one of the

world’s famous professors and pioneering scientists on the topic of VCSELs, Prof.

Lott always likes to help young scientists, and I will forever value his encouragement,

his desire for me to always do my best work, his constant assurance that I am able to

go well beyond what I though I was capable of, his extensive review of manuscripts,

his help with English, and his intense, and highly nontrivial lectures and lessons on

VCSELs. I really have learned a lot from Prof. Lott, especially about his professional

way of doing things in all aspects.

I would also like to thank all the people of the Center of Nanophotonics, for

sharing the equipment, for keeping such a nice laboratory, and for all of the much-

appreciated assistance. I give my special thanks to Stefan Bock.

I want to thank all my Chinese friends in Berlin for their continuous help and

companionship. I must express my special gratitude to Xingwei An, Nan Zhu, and Ye

Zhu for teaching me to cook Chinese food, and for helping me to survive and enjoy

my life in Berlin. Many thanks to my neighbors, Quan Liu, Xiaobei Ma, and Juan

Liu. We have been like a family all the time.

I give my gratitude to the China Scholarship Council (CSC) for financial support.

Last and foremost, to my family, thank you for always being with me and for

supporting me. I love you all.

Berlin, 30 May 2015

Hui Li

140 List of Publications

List of Publications

[1] H. Li, P. Wolf, P. Moser, G. Larisch, J. A. Lott, and D. Bimberg, “Temperature-

Stable, Energy-Efficient and High-Speed Oxide-Confined 980 nm VCSELs for Optical

Interconnects,” IEEE J. Sel. Top. Quant. Electron. vol. 21, no. 6, pp. 1700409–1–9, Nov./

Dec. 2015.

[2] H. Li, P. Wolf, P. Moser, G. Larisch, A. Mutig, J. A. Lott, and D. Bimberg, “Impact

of the quantum well gain-to-cavity etalon wavelength offset on the high temperature

performance of high bit-rate 980 nm VCSELs,” IEEE J. Quantum Electron., vol. 50, no.

8, 613–621, Aug. 2014.

[3] H. Li, P. Wolf, P. Moser, G. Larisch, J. A. Lott, and D. Bimberg, “Temperature-Stable

980 nm VCSELs for 35 Gb/s Operation at 85 °C with 139 fJ/bit Dissipated Heat,” IEEE

Photon. Technol. Lett., vol. 26, no. 23, pp. 2349–2352, Dec. 2014.

[4] H. Li, J. A. Lott, P. Wolf, P. Moser, G. Larisch, and D. Bimberg, “Temperature-

Dependent Impedance Characteristics of Temperature-Stable High-Speed 980 nm

VCSELs,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 832–835, Apr. 2015.

[5] H. Li, P. Wolf, P. Moser, G. Larisch, A. Mutig, J. A. Lott, and D. Bimberg, “Energy-

efficient and temperature-stable oxide-confined 980 nm VCSELs operating error-free at

38 Gbit/s at 85 °C,” Electron. Lett., vol. 27, no. 8, pp. 103–105, Jan. 2014.

[6]

Hui Li, Philip Moser, Philip Wolf, Gunter Larisch, Leszek Frasunkiewicz, Maciej Dems,

Tomasz Czyszanowski, James A. Lott, and Dieter Bimberg, “Energy efficiency, bit rate,

and modal properties of 980 nm VCSELs for very-short-reach optical interconnects,”

in proc. SPIE 9001 on Vertical-Cavity Surface-Emitting Lasers XVIII, Feb. 2014, pp.

900110B–90010B–8.

[7] H. Li, P. Wolf, P. Moser, G. Larisch, J. A. Lott, and D. Bimberg, “Temperature-

Stable Energy-Efficient High-Bit-Rate Oxide-Confined 980 nm VCSELs for Optical

Interconnects,” in proc. Asia Communications and Photonics Conference (ACP), Nov.

2014, pp. ATh1A. 5.

[8] H. Li, P. Wolf, P. Moser, G. Larisch, J. A. Lott, and D. Bimberg, “Vertical-cavity

surface-emitting lasers for optical interconnects,” SPIE Newsroom Optoelectronics &

Communications, pp. 1–3, Nov. 2014. DOI: 10.1117/2.1201411.005689

[9] D. Bimberg, H. Li, P. Moser, P. Wolf, G. Larisch, and J. A. Lott, “VCSELs for computer

interconnects,” in proc. IEEE Photonics Conference (IPC), Oct. 2014, ME1.2, pp. 89–90.

[10] P. Wolf, H. Li, P. Moser, G. Larisch, J. A. Lott, and D. Bimberg, “Extraction and

analysis of high-frequency response and impedance of 980 nm VCSELs as a function

of temperature and oxide aperture diameter,” in proc. SPIE 9381 on Vertical-Cavity

List of Publications 141

Surface-Emitting Lasers XIX, Feb. 2015, pp. 9381-9381-15.

[11]

H. Li, P. Moser, P. Wolf, G. Larisch, J. A. Lott, and D. Bimberg, “Energy efficient 850 nm

VCSELs for Multimode Fiber Based Optical Interconnects,” in proc. International

Nano-Optoelectronics Workshop (iNOW), Aug. 2013, pp. B60–B61.

[12] P. Wolf, P. Moser, G. Larisch, H. Li, J. A. Lott and D. Bimberg, “Energy efficient 40

Gbit/s transmission with 850 nm VCSELs at 108 fJ/bit dissipated heat,” Electron. Lett.,

vol. 49, no. 10, pp. 666−667, May 2013.

[13] P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, and D. Bimberg, “85-fJ Dissipated

Energy Per Bit at 30 Gb/s Across 500-m Multimode Fiber Using 850 nm VCSELs,”

IEEE Photon. Technol. Lett., vol. 25, no. 16, p. 1638−1294, Aug. 2013.

[14] P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, and D. Bimberg, “56

fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gb/s,”

Electron. Lett., vol. 48, no. 20, pp. 1292−1294, Sep. 2012.

[15] P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, and D. Bimberg, “Error-free 46 Gb/s

operation of oxide-confined 980 nm VCSELs at 85 °C,” Electron. Lett., vol. 50, no. 19,

pp. 1369−1371, Sep. 2014.

[16] Dieter Bimberg, Dejan Arsenijević, Gunter Larisch, Hui Li, James A. Lott, Philip

Moser, Holger Schmeckebier, Philip Wolf, “Green nanophotonics for future datacom

and Ethernet networks,” in proc. SPIE9134 on Semiconductor Lasers and Laser

Dynamics VI, May 2014, pp. 913402–913402.

[17] P. Moser, P. Wolf, G. Larisch, H. Li, J. A. Lott, and D. Bimberg, “Energy Efficient

850 nm VCSELs for Error-free 30 Gb/s Operation across 500 m of Multimode Optical

Fiber with 85 fJ of Dissipated Energy per Bit,” in proc. IEEE Optical Interconnects

Conference 2013, May 2013, pp. 13–14.

[18] Philip Moser, Gunter Larisch, Philip Wolf, Hui Li, James A. Lott, and Dieter Bimberg,

“Green photonics for data and computer communication,” in proc. IEEE Photonics

Society Summer Topical Meeting Series 2013, Jul. 2013, pp. 5–6.

[19] Philip Wolf, Philip Moser, Gunter Larisch, Hui Li, James A. Lott, and Dieter Bimberg,

“119 fJ of Dissipated Energy per Bit for Error-free 40 Gbit/s Transmission Across 50 m of

Multimode Optical Fiber Using Energy Efficient 850 nm VCSELs,” in proc. Conference

on Lasers and Electro-Optics (CLEO), Jun. 2013, pp. CTu3L.

[20] Philip Moser, Philip Wolf, Gunter Larisch, Hui Li, James A. Lott, and Dieter Bimberg,

“Energy-efficient oxide-confined high-speed VCSELs for optical interconnects,” in

proc. SPIE 9001 on Vertical-Cavity Surface-Emitting Lasers XVIII, Feb. 2014, pp.

9001103–900103.

[21] Philip Wolf, Philip Moser, Gunter Larisch, Werner Hofmann, Hui Li, James A. Lott,

Chien-Yao Lu, Shun L. Chuang, Dieter Bimberg, “Energy-efficient and temperature-

stable high-speed VCSELs for optical interconnects,” in proc. 15th International

142 List of Publications

Conference on Transparent Optical Networks (ICTON), Jun. 2013, pp. 1–5.

[22] Dieter Bimberg, Gunter Larisch, Philip Moser, Philip Wolf, Hui Li, and James A. Lott,

“Energy-efficient, temperature stable, high data rate VCSELs for optical interconnects,”

in proc. 16th International Conference on Transparent Optical Networks (ICTON), Jul.

2014, pp. 6–10.

[23]

Philip Moser, James A. Lott, Philip Wolf, Gunter Larisch, Hui Li, Nikolay N. Ledentsov,

and Dieter Bimberg, “Impact of the aperture diameter on the energy efficiency of

oxide-confined 850 nm high speed VCSELs,” in proc. SPIE 8639 on Vertical-Cavity

Surface-Emitting Lasers XVIII, Mar. 2013, pp. 86390V–86390V.

[24] Philip Moser, James A. Lott, Philip Wolf, Gunter Larisch, Hui Li, and Dieter Bimberg,

“Temperature-stable oxide-confined 980 nm VCSELs operating error-free at 46 Gb/s

and 85°C,” in proc. IEEE International Semiconductor Laser Conference (ISLC), Sep.

2014, TA7, pp. 76–77.

[25] Werner Hofmann, Philip Moser, Philip Wolf, Gunter Larisch, Hui Li, Wei Li, James

A. Lott, Dieter Bimberg, “VCSELs for exascale computing, computer farms, and green

photonics,” in proc. SPIE 8552 on Semiconductor Lasers and Applications V, Nov. 2012,

pp. 855205–855205.