Document [original]

Growth and Characterization

cubic AlGaN/GaN based Devices

Dem Department Physik

der Universit¨at Paderborn

zur Erlangung des akademischen Grades eines

Doktors der Naturwissenschaften

vorgelegte

Dissertation

von

Stefan Potthast

Paderborn, November 2006

Abstract

Cubic GaN and AlGaN layers are grown by radio frequency plasma assisted molecular

beam epitaxy on freestanding 3C-SiC (001) substrates. Detailed analysis of the substrate

quality reveal a direct dependence of the roughness of the 3C-SiC on the dislocation den-

sity. Additionally a strong influence of the substrate quality on the quality of cubic GaN

layers is found. GaN, AlGaN and AlN buffer layers grown at different temperatures are

used to improve the structural properties of the c-GaN buffer. Best values are obtained

for AlN buffers deposited at TSubs = 720◦C. Furthermore, the growth temperature of

the buffer itself is varied. Optimized results are found for TSubs = 720◦Cgrown under a

Ga coverage of one monolayer. On top of the GaN buffer, AlGaN films (0 < x < 0.74)

are grown using Ga coverages of one monolayer and much greater than one monolayer.

A linear dependence between the Al metal flux and the Al mole fraction is measured.

Investigation of the growth front using reflection high energy electron diffraction as a

probe, show a predominant two-dimensional growth mode. With increasing Al mole

fraction, a change in the resistivity of the AlGaN layer is observed due to the gettering

of oxygen by aluminum and the variation of the oxygen ionization energy as a function of

the Al content. Schottky diodes are fabricated on GaN and AlGaN using nickel as con-

tact material. A strong deviation of the current voltage characterisitics from thermionic

emission theory is found, measuring anormal high leakage current, caused by the pres-

ence of oxygen donors near the surface. It is investigated, that thermal annealing in air

reduces the reverse current by three orders of magnitude. AlGaN/GaN are used to fabri-

cate heterojunction field effect transistor structures. Analysis of the capacitance-voltage

characteristics at T=150 K revealed clear evidence for the existence of a two-dimensional

electron gas, and a sheet carrier concentration of about 1.6x1012cm−2is measured at the

interface in good agreement with the numerical simulation. The source-drain current

source-drain voltage characteristics measured at 155 K exhibit a clear field effect of

source-drain current induced by the gate voltage. A strong influence of the conductive

buffer on the source-drain current source-drain voltage characteristics is observed. Ne-

glecting this influence, a clear evidence for the current transport via a two-dimensional

electron gas is found.

List of Figures

2.1 The zincblende structure of cubic GaN. . . . . . . . . . . . . . . . . . . . 2

2.2 Heteroepitaxy: a) separated layers b)strained c)relaxed with incorpora-

tionofdefects. ................................ 3

2.3 Critical thickness of c−AlxGa1−xNon c-GaN as function of the Al mole

fractionxonGaN. .............................. 4

2.4 Schematic drawing of the materials research diffractometer system. . . . 7

2.5 Schematic drawing of the Photoluminescence spectroscopy system. . . . . 9

2.6 Schematic drawing of the I-V measurement setup. . . . . . . . . . . . . . 10

2.7 Schematic drawing of the C-V measurement setup. . . . . . . . . . . . . 11

2.8 Schematic drawing of the temperature dependence of carrier mobility for

bulk material (solid line) and a two-dimensional electron gas (2DEG)

(dashedline). ................................. 12

2.9 Schematic drawing of the contact arrangement and the current flow during

a four-point probe measurement. . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Schematic drawing of the structure of the investigated c-GaN layers. . . . 16

3.2 Measured RHEED intensity during the initial growth of c-GaN. The

RHEED intensity after opening the N shutter yields the amount of excess

Gaonthec-GaNsurface. .......................... 17

3.3 Terrace width of a c-GaN film. . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 RMS roughness on a 5x5µm2scan range as function of the FWHM of the

X-ray rocking curve for φ= 0◦(triangles) and φ= 90◦(squares) of the

freestanding 3C-SiC substrates. . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 The FWHM of the X-ray rocking curve of c-GaN as function of the SiC

RMS roughness on a 5x5µm2scan range for φ= 0◦(triangles) and φ= 90◦

(squares). ................................... 20

3.6 The RMS roughness of c-GaN as function of the SiC RMS roughness on

a 5x5µm2scanrange.............................. 21

3.7 The FWHM of the X-ray rocking curve of c-GaN as function of the buffer

type....................................... 22

3.8 The RMS roughness (circles) and the amount of hexagonal phase inclusion

(squares) of c-GaN as function of the buffer type. . . . . . . . . . . . . . 23

3.9 The FWHM of the X-ray rocking curve of c-GaN as function of substrate

temperature................................... 24

iii

List of Figures

3.10 The RMS roughness (circles) and the amount of hexagonal phase inclusion

(squares) of c-GaN as function of the substrate temperature. . . . . . . . 25

3.11 Measured RHEED intensity during the initial growth of c−Al0.25Ga0.75N.

The RHEED intensity after opening the N shutter yields the amount of

excess Ga on the c-GaN surface. After opening the Al shutter the excess

of Ga increases and RHEED oscillations are observed indicating a two-

dimensional growth mode with a rate of 177nm/h. . . . . . . . . . . . . . 26

3.12 Relation between the Al mole fraction x of all AlxGa1−xNand the flux

ratio of Al to the total metal flux in the vapor phase for films grown

under 1ML and >>1ML Ga coverage. The mole fraction was determined

byHRXRD................................... 27

3.13 AlxGa1−xNgrowth rate derived by RHEED oscillation and optical mea-

surements for Al mole fraction between x=0 and x=0.74 at a constant

nitrogen flux of FN= 2.2∗1014cm−2s−1. The data reveal a constant

growth rate for all AlxGa1-xN alloys independent on the Al flux. . . . . . 28

3.14 RMS roughness on a 5x5µm2area for AlxGa1−xNalloys with an Al mole

fraction between x=0 and x=0.74 grown under the coverage of 1ML (cir-

cles) and >>1ML (triangles) at 720◦C. The lines are a guide for the

eyes. ...................................... 29

3.15 Reciprocal Space Map arround the (-1-13) reflex of an Al0.25Ga0.75Nfilm. 30

3.16 Strain status of Al0.25Ga0.75Nfilms as function of the layer thickness. . . 30

3.17 Unintentional doping level of AlxGa1−xNfilms as function of the Al con-

tent x before (circles) and after (squares) change of the purifier. . . . . . 31

3.18 Photograph of the investigated AlGaN/GaN samples. . . . . . . . . . . . 32

3.19 Equivalent current circle of the investigated AlGaN/GaN samples. . . . . 33

3.20 Relative conductance and carrier concentration as function of the Al mole

fractionx.................................... 34

4.1 Schematic drawing of the energy bands of a metal and a semiconductor

beforecontact. ................................ 37

4.2 Schematic drawing of the energy bands of a metal and a semiconductor

incontact.................................... 37

4.3 Schematic draw of the carrier distribution, the electric field strength and

the potential (from upside to downside). . . . . . . . . . . . . . . . . . . 40

4.4 Comparison of the IV curve of a real Ni/c-GaN Schottky diode (GNJ1204)

(open circles) and an ideal diode using the Schotty-Mott equation (solid

line)....................................... 41

4.5 Arrangement of the metal contact used for the c-GaN Schottky diodes

(left side) and the equivalent circuit (right side). . . . . . . . . . . . . . . 42

4.6 Sketch of the circuit for a real Schottky diode under forward bias. . . . . 43

4.7 Comparision of the measured IV curve (full circles), without the limitation

by the serial resistance (open circles) and the Schottky-Mott equation

(solid line) in forward direction for GNJ1204. . . . . . . . . . . . . . . . 44

4.8 Sketch of the circuit for a real Schottky diode under reverse bias. . . . . 45

List of Figures

4.9 Comparison of the measured I-V curve (full circles), eliminating the in-

fluence of RS(open circles) and the calculation using the Schottky-Mott

equation (solid line) in reverse direction for GNJ1204. . . . . . . . . . . . 46

4.10 IV curves in forward direction measured at different temperatures of

300K (open circles), 150K (full circles) and 50K (open squares) of sample

GNJ1204. ................................... 47

4.11 IV curves in reverse direction measured at different temperatures of 300K

(open circles), 150K (full circles) and 50K (open squares) of GaN film

(GNJ1204). .................................. 48

4.12 IV curves in reverse direction measured at different temperatures of 300K

(open circles), 150K (full circles) and 50K (open squares) of a GaN/Al0.35Ga0.65N/GaN

heterostructure (GANS1352). . . . . . . . . . . . . . . . . . . . . . . . . 48

4.13 Temperature dependence of the Schottky barrier height calculated from

the built-in voltage at different temperatures between 5K and 300K of

a Ni/GaN (open squares)(GNJ1204) and a Pd/GaN/AlGaN/GaN (full

circles) (GANS1352) Schottky diode. . . . . . . . . . . . . . . . . . . . . 49

4.14 Schematic sketch of the Thin Surface Barrier (TSB) model. . . . . . . . . 51

4.15 Schematic sketch of the formation of the current plateau in the forward

direction of a Schottky diode. . . . . . . . . . . . . . . . . . . . . . . . . 52

4.16 Carrier concentration profile of a Pd/c-GaN/c-AlGaN/c-GaN Schottky

diode (GANS1352) measured at temperatures between 175K and 350K. . 53

4.17 Room temperature current voltage characteristics of a Ni/c-GaN Schottky

diode (GNS1285) before annealing (open circles) and after annealing in

air at 200C(fullcircles)............................ 54

4.18 Breakdown voltage of Ni/c-GaN Schottky diode before annealing (GNJ1204)

(open circles) and after annealing in air at 200C(GNS1285) (full circles). 55

4.19 Breakdown voltages vs net donor concentration of Schottky diodes on

c-GaN and c-AlGaN (full symbols) and h-GaN (open symbols). . . . . . 56

5.1 Experimental setup for the investigation of the photoconductivity: a)

sample structure b) contact arrangement. . . . . . . . . . . . . . . . . . . 58

5.2 IV curves of the Schottky contacts on a 750nm c-GaN measured (GNS1382)

atT=300K................................... 59

5.3 IV curve of the Ni Schottky contacts (2)-(3) on a 750nm c-GaN (GNS1382)

measuredatT=300K. ............................ 60

5.4 Comparison of the IV curve measured in the darkness (open circles) and

under illumination (full squares) of the structure (GNS1382) excited with

P=4.5mW at λ= 325nm. .......................... 61

5.5 Effective photo current of the MSM structure measured at T=300K. . . . 62

6.1 Schematic drawing of a AlGaN/GaN based HEMT device. . . . . . . . . 64

6.2 Steps in the construction of the band diagram for a doped AlGaN and

GaNheterojunction. ............................. 65

List of Figures

6.3 Band diagram of a AlGaN/GaN based HEMT device calculated with the

1D Poisson program for a temperature of 175K. . . . . . . . . . . . . . . 66

6.4 Sheet carrier concentration of the 2DEG and the residual carrier concen-

tration of the AlGaN barrier as function of the Al mole fraction x for a

temperatureof300K.............................. 67

6.5 Sheet carrier concentration of the 2DEG and residual carrier concentra-

tion of the AlGaN barrier as a function of the AlGaN donor concentration

for a temperature of 300K. . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.6 Sheet carrier concentration of the 2DEG and the residual carrier concen-

tration of the AlGaN barrier as a function of the AlGaN barrier thickness

for a temperature of 300K. . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.7 Photoluminescence spectra of different structures measured at T=2K. a)

pure GaN-layer, b) Al0.2Ga0.8N/GaN heterostructure, c) pure Al0.2Ga0.8N

layer....................................... 70

6.8 Photoluminescence spectra of AlxGa1−xN/GaN heterostructures with Al

mole fractions of 0.25, 0.30 and 0.35 measured at T=2K. . . . . . . . . . 72

6.9 Photoluminescence spectra of Al0.35Ga0.65N/GaN heterostructures with

different background doping concentrations of ND= 1∗1017cm−3(GANS1384)

(open circles) and ND= 1 ∗1018cm−3(GNP1429) (full circles) measured

atT=2K. ................................... 72

6.10 Principle of the change in the band bending at the heterointerface due to

the change in the c-GaN background doping . . . . . . . . . . . . . . . . 73

6.11 PL spectra of a Al0.35Ga0.65N/GaN heterostructure (GANS1384) mea-

sured at different temperatures between 2K and 300K. . . . . . . . . . . 74

6.12 The peak position of the X, DAP1, DAP2 and the 2DEG correlated tran-

sition for temperatures between 2K and 300K for a Al0.35Ga0.65N/GaN

heterostructure (GANS1384). . . . . . . . . . . . . . . . . . . . . . . . . 75

6.13 The normalized PL intensity of the X, DAP and the 2DEG correlated

transition for excitation power between 0.2Wcm−2and 20Wcm−2of a

Al0.35Ga0.65N/GaN heterostructure (GANS1384). . . . . . . . . . . . . . 76

6.14 The peak position energy of the 2DEG related transition for excitation

power between 0.2Wcm−2and 20Wcm−2for GANS1384 . . . . . . . . . 77

6.15 The peak position energy of the 2DEG related transition for applied volt-

ages between -1.5V and +1.5V for GANS1228 . . . . . . . . . . . . . . . 78

6.16 Schematic drawing of the AlGaN/GaN heterostructure. . . . . . . . . . . 79

6.17 Current-Voltage characteristic of Al0.35Ga0.65N/GaN heterostructures with

different GaN cap layer thickness of 5nm (GANS1356)(triangles), 10nm

(GANS1357)(squares) and 20nm (GANS1352)(circles). . . . . . . . . . . 80

6.18 Influence of the RMS roughness on the electrical behaviour of heterostruc-

tures with different cap layer thicknesses. . . . . . . . . . . . . . . . . . . 80

6.19 Capacity-Voltage characteristics of the Al0.35Ga0.65N/GaN heterostruc-

ture (GANS1352) at temperatures of 300K, 175K and 150K. . . . . . . . 81

List of Figures

6.20 Carrier concentration profile of the Al0.35Ga0.65N/GaN heterostructure

(GANS1352) at temperatures of 300K (circles), 175K (squares) and 150K

(triangles).................................... 82

6.21 Experimental (full circles) and simulated (dotted line) carrier concen-

tration vs. the distance from the surface. The experimental data were

calculated from a CV measurement done at 150 K. . . . . . . . . . . . . 83

6.22 Structure and photograph of the AlGaN/GaN heterostructure which is

used for the Hall-effect analysis. . . . . . . . . . . . . . . . . . . . . . . . 84

6.23 Electron concentration and mobility of a Al0.35Ga0.65N/GaN heterostruc-

ture for various temperatures between 10K and 300K. . . . . . . . . . . . 85

6.24 Electron mobility limited by acoustic phonon scattering for various tem-

peratures between 1K and 300K. . . . . . . . . . . . . . . . . . . . . . . 87

6.25 Electron mobility limited by impurity scattering for a temperature of

T=10K. .................................... 88

6.26 Electron mobility limited by dislocation scattering for various carrier den-

sities in the channel in the range of N2D= 1012cm−2to N2D= 1013cm−2. 89

6.27 Electron mobility limited by roughness scattering for various carrier den-

sities in the channel in the range of N2D= 1012cm−2to N2D= 1013cm−291

6.28 Electron mobility limited by different scattering mechanism for various

carrier densities in the channel in the range of N2D= 1012cm−2to N2D=

1013cm−2and the comparison to experimental result . . . . . . . . . . . . 91

6.29 Arrangement of the source, drain and gate contact for our FET structures

with a gate length of 6µm and a gate width of 100µm using Ref. [73]. . . 92

6.30 The different masks used for the fabrication of our FETs. a)Mesa struc-

ture b)Source and Drain contacts c)Gate contact. . . . . . . . . . . . . . 93

6.31 a)A schematic sketch of the FET structure and the Mesa arrangement

realized on GANS1416, b)An optical micrograph with the contacts and

an enlargement of the gate region (GANS1416). . . . . . . . . . . . . . . 94

6.32 Source-gate I-V curve of FET structure B-1 realized on GANS1416 mea-

sured at a temperature of T=155K. . . . . . . . . . . . . . . . . . . . . . 95

6.33 Source-drain I-V curve of FET structure B-1 realized on GANS1416 mea-

sured at a temperature of T=155K. . . . . . . . . . . . . . . . . . . . . . 96

6.34 Current circuit used for the investigation of the field effect at our FET

structure. ................................... 96

6.35 Source-drain I-V curve of FET structure B-1 for different gate voltages be-

tween -0.25V and +1V realized on GANS1416 measured at a temperature

ofT=155K. .................................. 97

6.36 Calculated banddiagrams of the FET structure for VG=+0.5V and VG=-

0.25V. ..................................... 97

6.37 Source-drain I-V curve of FET structure B-1 for different gate voltages

between +0.25V and +1V without the influence of the buffer conductivity

realized on GANS1416 measured at a temperature of T=155K. . . . . . . 98

vii

List of abbrevations

2DEG Two-Dimensional Electrongas

AFM Atomic Force Microscopy

AlGaN cubic AlxGa1−xN

BEP Beam Equivalent Pressure

C-V Capacitance Voltage

cw Continious Wave

DAP Donor Acceptor Pair

ECV Electrochemical Capacitance Voltage

EL Electroluminescence

FET Field Effect Transistor

FWHM Full Width at Half Maximum

GaN cubic GaN

HEMT High Electron Mobility Transistor

HFET Heterojunction Field Effect Transistor

HRXRD High Resolution X-Ray Diffraction

I-V Current Voltage

MBE Molecular Beam Epitaxy

MESA (span. ) table, freestanding structures on one substrate

MODFET Modulation Doped Field Effect Transistor

MSM Metal-Semiconductor-Metal Structure

PAMBE Plasma-assisted Molecular Beam Epitaxy

PL Photoluminescence

rf Radio Frequency

RHEED Reflection High Energy Electron Diffraction

RIE Reactive Ion Etching

RSM Reciprocal Space Map

SD Schottky Diode

TFE Thermionic Field Emission

TSB Thin Surface Barrier

UHV Ultra High Vacuum

UV Ultraviolet

XExciton

viii

List of symbols

a, b deformation potentials (eV)

a0lattice constant ˚

A contact area cm2

b burgers vector ˚

relative dielectric permittivity

0vacuum dielectric permittivity

E energy (eV)

EAacceptor energy (eV)

ECconduction band energy (eV)

EDdonor energy (eV)

EFFermi energy (eV)

Egband gap energy (eV)

EVvalence band energy (eV)

flattice mismatch

FAl Al metal flux (cm−2s−1)

FGa Ga metal flux (cm−2s−1)

hccritical thickness (nm)

I current (mA)

J current density (Acm−2)

L channel width (nm)

µcarrier mobility (cm2(V s)−1)

m∗

eeffective electron mass

m∗

heffective hole mass

n free electron concentration (cm−3)

NAacceptor concentration (cm−3)

NDdonor concentration (cm−3)

NCconduction band density of states (cm−3)

N2D2DEG concentration (cm−2)

ρresistivity (Ωcm)

RHHall constant (cm3(As)−1)

νPoisson ratio

V voltage (V)

T temperature (K)

Contents

1 Introduction 1

2 Fundamentals 2

2.1 Physical properties of cubic III-Nitrides . . . . . . . . . . . . . . . . . . . 2

2.2 Growth and structuring techniques . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Molecular beam epitaxy . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Photolithography........................... 6

2.3 Characterization techniques . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 X-rayDiffraction ........................... 6

2.3.2 Luminescence spectroscopy . . . . . . . . . . . . . . . . . . . . . . 8

2.3.3 Electrical measurements . . . . . . . . . . . . . . . . . . . . . . . 10

3 Growth of GaN and AlGaN 16

3.1 GrowthofGaN ................................ 16

3.2 GrowthofAlGaN............................... 25

3.3 Electrical properties of GaN and AlGaN . . . . . . . . . . . . . . . . . . 30

4 GaN and AlGaN Schottky diodes 36

4.1 Thermionic Emission Theory . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Thin Surface Barrier Model . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3 Breakdown Voltages of Schottky Diodes . . . . . . . . . . . . . . . . . . 55

5 Photoconductivity in GaN based Schottky diodes 58

6 AlGaN/GaN based field effect transistors 63

6.1 Structure and band diagram . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.2 Opticalproperties............................... 70

6.3 Electricalproperties ............................. 78

6.3.1 I-V and C-V analysis . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.3.2 Hall effect analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3.3 Theoretical description of carrier scattering . . . . . . . . . . . . . 85

6.3.4 Fabrication and electrical characterization of HFET structures . . 92

7 Conclusion 99

1 Introduction

A main point of modern research in physics is the reduction of dimensionality in op-

toelectronic and electronic devices, like quantum wells, quantum dots or high electron

mobility transistors, which allow a more faster and efficient way of data transfer in elec-

tro optical communication systems.

AlGaN/GaN heterojunction field effect transistors (HFETs) are presently of outstanding

interest for electronic devices, in particular, for high power and high frequency amplifiers.

This is motivated by the potential commercial and military field application, namely,

in the area of communication systems, radar, wireless stations, high temperature elec-

tronics and high power solid state switching [1][2]. The Group III-nitrides crystallize in

the stable wurtzite structure or in the metastable zincblende structure. An important

difference between these material modifications is the presence of strong internal electric

fields in hexagonal (wurtzite) III-nitrides grown along the polar c-axis, while these build-

in fields are absent in cubic (zincblende) III-nitrides. Since polarization fields can limit

the performance of HEMTs some attention has been focused recently on the growth of

wurtzite structures with nonpolar orientations e.g., growth along a, m or R directions

[3][4][5] and also on cubic nitrides [6][7]. The cubic III-nitride polytype is metastable

and can only be grown successfully in a narrow window of process conditions [[8] and

references therein]. The realization of devices based on cubic nitrides has also been

limited due to the difficulty to grow phase pure cubic nitrides with smooth interfaces,

low defect density, high resistivity and the lack of appropriate substrates. The most

promising candidate nowadays is 3C-SiC having a cubic crystal symmetry with a lattice

mismatch between 0.7% (AlN) and 3.5% (GaN). This low lattice mismatch is connected

with a high chemical inertness and a high thermal stability and conductivity. On the

other hand due to the conductance of the substrates the devices show poor electrical

characteristics.

The work will describe the growth and characterization of device structures based on

cubic nitrides. They base on AlGaN/GaN layers grown by plasma-assisted molecular

beam epitaxy on freestanding 3C-SiC (001). Chapter 3 will give an introduction in the

optimization of the growth of GaN and AlGaN and the influence of the substrate quality

and growth parameters on the crystal quality. In chapter 4 the properties of Schottky

diodes, which will be used as gate contacts in field effect transistors, will be described.

In chapter 5 some results about photoconductivity in our Schottky diodes, will be pre-

sented, which demonstrates the suitability of c-GaN for the realization of solarblind

photodectors. Chapter 6 deals with the main issue of the thesis. Here the theory, the

optical and electrical properties of AlGaN/GaN heterostructures will be described. At

the end of chapter 6 the device operation of a AlGaN/GaN heterojunction field effect

transistor structure will be demonstrated. All the results are summarized in chapter 7.

2 Fundamentals

2.1 Physical properties of cubic III-Nitrides

The basic issue of this work is the epitaxial growth of cubic AlN and GaN and their

ternary alloys on freestanding 3C-SiC (001) and carbonized Si (001) substrates. This

section will give an introduction in the physical properties of cubic group-III nitrides.

The crystallographic structure of the cubic group III-nitrides, which is drawn in Fig. 2.1

Figure 2.1: The zincblende structure of cubic GaN.

is based on a face centered unit cell with a base of two atoms. In case of stoichiometric

growth conditions the metal is incorporated on the (0,0,0) lattice point, and the nitro-

gen is placed on the (1

4,1

4) lattice site. In the direction of the basic vectors the crystal

consists of two altering layers which content only metal or nitrogen. The structure is

very similar to that of diamond and the bond shows a strong covalent nature due to the

comparable covalence radius of each element. This results in a high chemical inertness

and thermodynamical stability. In addition a high isotropy of other parameters, like

conductivity or refractive index is found. The table 2.1 gives a short overview of the

physical properties of GaN and AlN. The parameter of the ternary alloys are calculated

by the linear interpolation of the binary compounds.

2.1 Physical properties of cubic III-Nitrides

Parameter AlN GaN References

Lattice constant(˚

A) 4,38 4,52 [9][10]

Band gap(direct)(eV) 5,14 3,24 [11]

effective conduction band mass

(me

m0) 0,19 0,15 [11]

effective hole mass

(mhh

m0) 1,20 0,80 [11]

(mlh

m0)0,33 0,18 [11]

Deformation potential (eV)

ac-6,8 -2,77 [12][13]

b-1,5 -2,67 [13][14]

Elastic coefficients (GPa)

c11 304 296 [13]

c12 152 154 [13]

Table 2.1: Overview of the physical parameters of cubic AlN and GaN.

The paremeter, which are given in the table, are used for the calculation of the critical

thickness as well as for the determination of the band diagram (see chapter 6) and for

the modeling of the carrier mobility (also chapter 6).

During growth of different layers with different lattice constants one can distinguish

three types of growth modes of the top layer. The schematic principle is shown in Fig.

2.2. In the case of a lattice matched top layer, the film is deposited on the substrate

Figure 2.2: Heteroepitaxy: a) separated layers b)strained c)relaxed with incorporation

of defects.

with out any changes in the unit cells. In the case of a layer with a lattice constant

larger than that of the substrate, the in-plane lattice constant is reduced, whereas the

constant in the growth direction is enlarged, due to the constant volume of the unit

cell. If the layer has a smaller constant, the changes in the in-plane and perpendicular

lattice constant are switched in comparision to the first case. The change in the lattice

constants during heteroepitaxy creates energy which is stored as elastic energy in the

crystal. On the other hand the total energy of the crystal can be minimized by the

2 Fundamentals

incorporation of defectcs. For that at a certain thickness (critical thickness) it is better

for the crystal to incorporate defects in order to minimize its energy. The value for the

critical thickness can be calculated from the equality of the elastic and defect energy,

which ends in an implicite equation for the critical thickness after Matthwes et al. [15].

Figure 2.3: Critical thickness of c−AlxGa1−xNon c-GaN as function of the Al mole

fraction x on GaN.

hc=b

2πf ∗(1 −νcos2α)

(1 + ν)cosλ ∗(lnhc

b+ 1) (2.1)

in which b is the length of the Burgers vector, ν=c12

c12+c11 the Poisson ratio and f=

alayer−asubstrate

alayer the lattice mismatch. αand λare the angles which describe the geometry

of the defects. This equation is modified by Sherwin et al. [16] for a group-III nitride/

3C-SiC system:

hc=alayer(1 −ν/4)

4√2π(1 + ν)f∗(ln √2hc

asubstrate

+ 1) (2.2)

This equation can be transferred to the cubic AlGaN/GaN system, if the following things

are regarded:

hc=aGaN (1 −ν/4)

4√2π(1 + ν)f∗(ln√2hc

aGaN

+ 1) (2.3)

2.2 Growth and structuring techniques

with f=aGaN −aAlGaN

aGaN

and ν=c12

c12 +c11

using c11 =x∗c11,AlN + (1 −x)∗c11,GaN

c12 =x∗c12,AlN + (1 −x)∗c12,GaN

in which f is the lattice mismatch between GaN and AlGaN and νis the Poisson ratio

derived from the elastic constants c11 and c12 of the AlGaN. With the variation of the

Al mole fraction x, we can determine the critical thickness of AlGaN layers on GaN as

function of x. The results of the calculation are plotted in Fig. 2.3. The plot illustrates

the decrease of the critical thickness from ∞for pure GaN to a value of 1.3nm for pure

AlN on GaN.

The knowledge and the manipulation of the critical thickness has a direct influence on

the strain status of epitaxial layers, which influences the defect density and the positions

of the conduction and valence bands. Especially in low-dimensional device structures

this changes can have a lot of effects on their performance, for example on the density

of a two-dimensional electron gas (2DEG) in an AlGaN/GaN heterostructure.

2.2 Growth and structuring techniques

2.2.1 Molecular beam epitaxy

All the samples presented in this work are based on the epitaxial growth of thin semicon-

ductor layer by Molecular Beam Epitaxy (MBE)[17]. MBE allows the growth of crys-

talline films on mono crystalline substrates, based on the evaporation of solid and liquid

materials out of so called Knudsen-cells in ultra-high vacuum (UHV, p<10−10mbar).

Gases are dissociated with plasma sources or they are cracked on the substrate surface.

Under these conditions a molecular beam, which can be interrupted by metallic shut-

ters, hits the substrate and condensates on the surface. This method allows growth

rates in the order of a few hundred nm/h. The quantity of the evaporated material can

be controlled by the temperature of the source, because the atomic flux of a source is

direct proportional to its temperature. The flux of the atoms is measured with an ioni-

sation gauge (Bayard- Alpert). With the knowledge of the atomic fluxes of the different

materials the composition of ternary compounds can be controlled by the temperatures

of the cells. The control of the temperature of the source is done by a thermocouple,

which is mounted below the bottom of the crucibile and connected with a temperature

controller. In order to incorporate as less impurities as possible, high purity (99.9999%)

source materials are used.

In this work a commercial Riber 32 MBE system is used. Details and a schematic draw

can be found in Ref. [18]. The chamber is equipped with Knudsen cells for Al, Ga, In,

and Si. For the Nitrogen a plasma source from Oxford Applied Research model HD25

was bought.

2 Fundamentals

During growth a liquid nitrogen reduces the amount of impurities by one order of mag-

nitude within the growth chamber .

The growth is monitored in situ by reflection of high energy electron diffraction (RHEED).

This method uses a high energetically electron beam (10-20kV acceleration voltage),

which hits the surface with an angle of 1◦−3◦. The electrons are diffracted at the atoms

of the surface, after the reflection they can be monitored on a fluorescence screen. The

RHEED pattern gives some information about the conditions on the surface. The main

point during the growth of cubic group-III nitrides is the control of the stoichiometry.

This can be checked by the change in the surface reconstructions from a c(2x2) to a

(2x2), and the control of the intensity of the main streak [39].

2.2.2 Photolithography

Photolithography is the most used commercial technique to create lateral structures in

semiconductor technology [20],[21],[22]. The principle of the photolithography bases on

the transfer of lateral structures of a metal (NiCr) mask to the surface of a semiconduc-

tor.

In order to guarantee a perfect transfer the sample surface has to be cleaned from dust

and organic contamination. Therefore the samples are rinsed in Aceton, Propanol and DI

water for 5min. The surface oxide is removed using Buffer oxide etching (Ammonuim-

fluoride, Flouride acid and DI water). Then the samples are rinsed in DI water and

dried with nitrogen. After the cleaning procedure the surface is covered with an UV

light sensitive photo resist(AR-P 3510). The resist has to be dried by thermal annealing

for 30min at a temperature of 93◦. After that the sample is put under the metal mask

and exposed to UV light for 20s. Following by developing and fixing of the structure

for 20s using a mix of developer:DI water=1:1. The exposed resist is removed by aceton

and the structure is seen. Now the sample can be used for further steps, for example

etching or evaporation of metal contacts or dielectric films.

2.3 Characterization techniques

2.3.1 X-ray Diffraction

Due to the use of a short wavelength, high resolution X-ray diffraction (HRXRD) is a

very powerful technique for the investigation of structural properties on an atomic scale

[23]. In this work, a Phillips XPert materials research diffractometer was used with a

copper anode emitting the Kα1radiation with a wavelength of λ= 1.54˚

A. The tube

is equipped with a line focus and a hybrid monochromator, which guarantees a beam

divergence of 47arcsec. The monochromator consists of a graded parabolic mirror in

connection with a (220) channel cut Germanium crystal. The mirror parallelizes the

beam and the Germanium crystal removes the Kα2line. The samples are mounted

onto a Euler cradle which allows the independent changes of angle of incidence ω, the

2.3 Characterization techniques

diffraction angle 2Θ, the rotation around the surface normal φand the incident axis

Ψ, as well as a linear motion in the three directions x, y, and z. The measurements

were performed in double axis configuration using a 1

16 ◦slit in front of the detector

resulting in a resolution of 1.8arcmin, as well as in the triple axis mode with a second

(220) Germanium crystal in front of the detector with a resolution of 0.084arcmin. A

schematic drawing of the diffractometer can be seen in Fig. 2.4. For a single crystal the

Figure 2.4: Schematic drawing of the materials research diffractometer system.

diffraction of X-Rays can be described by the Bragg condition:

λ= 2dhklsin(Θ) (2.4)

The triplet (hkl) denotes the Miller indices, and dhkl the spacing of the lattice planes.

For a cubic crystal symmetry and a given lattice constant a0the spacing dhkl is given by

dhkl =a0

√h2+k2+l2(2.5)

Three different types of scans were performed to investigate the properties of the layers.

•ω−2Θ-scan

This kind of scan allows measurements where the angular rotation speed of the

detector is twice as that of the incident angle. In case of scanning symmetrical

lattice points, this is equal to reflection from lattice planes parallel to the sample

surface. We get information with respect to vertically aligned properties, like the

composition of ternary alloys.

•ω-scan

The so called rocking curve is a scan with the detector angle in a fixed position,

2 Fundamentals

while only the angle of incidence is changed. From the width of the reflex perpen-

dicular to the surface the density of defects can be evaluated.

•Reciprocal Space Map (RSM)

The combination of both types of scans gives a two-dimensional distribution of

the intensity. In case of scanning around an asymmetric lattice point, information

about the strain status of the layers are observed.

2.3.2 Luminescence spectroscopy

In general, luminescence refers to the emission of visible radiation. In the present con-

text, this will also include the emission of near UV and IR light. The luminescence is

caused by the radiative recombination of excess carriers. In common use, different types

of luminescence are distinguished with respect to the kind of carrier excitation:

•Photoluminescence (PL)

excitation of carriers by means of light irradiation

•Cathodoluminescence (CL)

cathode rays (electrons) as a source of carrier excitation

•Electroluminescence (EL)

carrier injection through an externally applied electric field

In general luminescence allows the observation of the optical properties [24],[25],[26]. In

bulk semiconductors different kind of optical transitions are present. In films of high

purity, i. e. intrinsic semiconductors band to band (e, h) and free exciton (X) transitions

are typically dominating.

Band to band transitions are described by the difference of the conduction and the va-

lence band edge:

E= ¯hω =EC−EV+¯h2k2

2(1

m∗

) (2.6)

in which EC, EVare the energy of the conduction and valence band, and m∗

e, m∗

hare the

effective masses.

The excitons are formed through Coulomb interaction between an electron and a hole.

The intensity and width of the excitonic transition gives a quick estimate of the relative

sample quality. The physics of excitons is described by a model similar to the hydrogen

atom:

E= ¯hω =EC−EV−13,6eV

m02

m∗

)−1(2.7)

in which represents the dielectric constant of the semiconductor.

In semiconductors with a high impurity concentration (defects or doping), these impu-

rity levels offer a further possibility for radiative recombination. These levels, typically

2.3 Characterization techniques

separated from the conduction (valence) band by their ionization energy, are calculated

in a similar way to the excitons:

ED=13,6eV

m02

m∗

and EA=13,6eV

m02

m∗

(2.8)

for the donor states EDand analog for the acceptor states EA. The total transition

energy is then given by:

E= ¯hω =Eg−(ED+EA) + 1

2kBT(2.9)

The factor 1

2kBTbases on the thermal distribution of the carriers.

For an excact determination of the transition energy, the Coulomb interaction of the

ionized donors and acceptors has to be taken into account. In that case equation 2.9

has to be extended by a term which describes the Coulomb interaction. The transition

energy is then determined by the following relation [18]:

E= ¯hω =Eg−(ED+EA) + 1

2kBT+e2

4πR (2.10)

The last term in the equation describes the Coulomb interaction of the donors and ac-

ceptors. In this term R is the distance of the impurities calculated with R=1

√NI,

where NIis the density of the impurities. Therefore from the transition energy the dop-

ing density can be estimated. In contradiction to the bulk materials, low dimensional

layers show further transitions, but the nature and behaviour will be discussed later.

A schematic sketch of the PL system used in this work is given in Fig. 2.5. A cw

Figure 2.5: Schematic drawing of the Photoluminescence spectroscopy system.

HeCd laser from the company Kimmon is used as the coherent light source emitting

a wavelength of λ= 325nm ≡3.81eV . The line is singled out from the plasma lines

by a Fabry-Perot interference filter. The output power after the filter is about 5mW,

2 Fundamentals

with the possibility to variate the power by four orders of magnitude by using neutral

density filters. The light is then focussed onto a spot with a diameter of 100µm, yield-

ing a power density of 20Wcm−2. The luminescent light is collected with an exit lens

and dispersed in a Spex 270M monochromator by a 1200 line grating and 270mm focal

length. The detection system consists of a photomultiplier tube and a photon counting

system (Hamamatsu C3866 photocounting unit + Hewlett-Packard HP 53131A Univer-

sal counter), controlled by a personal computer (PC). The spectral resolution of the

system is δλ = 0.2nm ≡1.5meV at λ= 400nm ≡3.1eV .

The samples were mounted into a customer-designed liquid Helium bath-flow cryostat

that allows measurements at temperatures between 2 and 350K. A Lake Shore 300 Auto

tuning temperature controller with an AlGaAs temperature diode and a heating tran-

sistor are used to adjust the sample temperature during measurement. In addition the

system is equipped with the possibility to apply an electric field on the mounted sample.

2.3.3 Electrical measurements

In the field of device research, electrical characterization is the most important tech-

nique for the investigation of device performance. A general introduction in the electric

properties of semiconductor can be found in [27],[28]. Details of electrical measurements

will be given in the chapters 4-6.

The most common analyzing methods are current-voltage characteristics (I-V), capacitance-

Figure 2.6: Schematic drawing of the I-V measurement setup.

voltage characteristics (C-V) and Hall-effect analysis. A detailed description of these

methods can be found in [29].

The I-V measurements are done with a four tip prober from S¨uss Microtec. An optical

microscope is used for positioning the probe onto the contact with a resolution less than

10µm. The probes consist of tungstencarbide having a diameter of 7µm. The Fig. 2.6

illustrates the arrangement and the principle of operation for the I-V setup.

2.3 Characterization techniques

A Hewlett-Packard HP6632 was used as voltage source applying an electric field in the

range of -9V. . +9V. The current is measured with a multimeter model HP34401, also

from Hewlett-Packard, for a current >2mA, whereas for a current <2mA a Keithley

Picoamperemeter is connected to the current circuit. The applying of the voltage and

the readout of the current is controlled by a PC using a self written Pascal program. The

program allows the variation of the step width in the applied voltage, the time difference

between applying the voltage and the readout of the current. A limiting of voltage and

current is also avaiable. Voltages below -20V or above +20V are applied manually using

an Electroautomatik EA 6056 voltage source.

A further method for the investigation of electrical properties is the C-V analysis. The

method allows the determination of a carrier concentration profile vs. the depth by mea-

suring the capacitance vs. voltage. A detailed description can be found in [35] and will

also be discussed later.

For the determination of the CV characteristics a setup, which is described in Fig. 2.7,

is used. The HP6632 is also used as the voltage source for CV measurements. The

Figure 2.7: Schematic drawing of the C-V measurement setup.

capacitance is measured by a Boonton 72B capacitance bridge (1MHz, VAC=100mV).

The capacitance is put out as a DC voltage signal, which is proportional to the capaci-

tance. From the voltage, the knowledge of the measurement range and the contact size,

a Pascal based computer program is able to calculate the capacitance in units of pF.

A real diode normally consists of a superposition of a ideal diode and a resistance. If

the resistance is small enough, it has to be take into account for the calculation of the

capacity. Therefore a so-called Q-factor is defined as:

Q=RL

(2.11)

with

XC=1

ωC (2.12)

in which XCis the capacitive reactance and RLis the ohmic part of the resistance. For a

measuring frequency of 1MHz, which is used for the Boonton 72B, and a capacitance of

2 Fundamentals

100pF, XCis equal to 10kΩ. With the known ohmic resistance the Q-factor is determined

and the real capacity is calculated using the relation:

Creal =Q2

Q2+ 1Cmess (2.13)

The system contains a phase-sensitive detector, which allows the precise measurement

of capacitance down to a Q-factor of 1, if the leakage resistance is higher than the serial

resistance, which is the case in all the samples.

Hall-effect measurements allow the determination of the carrier concentrations in semi-

conductors, as well as the carrier type. Additionally the mobility can be measured.

Details are given in Ref. [29]. The Hall voltage UHgiven by

UH=−1

d(2.14)

where n carriers of charge e flow with an external current I under the influence of

Figure 2.8: Schematic drawing of the temperature dependence of carrier mobility for

bulk material (solid line) and a two-dimensional electron gas (2DEG) (dashed

line).

a magnetic field B through a semiconductor layer of thickness d. Defining the Hall

constant RHthe equation can be written as:

RH=UHd

IB (2.15)

2.3 Characterization techniques

Conventionally a negative sign of RHmeans n-type and a positive sign means p-type

conductivity. For the measurements a magnetic field of 0.8T is used. For the determi-

nation of the carrier mobility µ, the knowledge of the resistivity of the film is essential.

The resistivity ρis calculated by:

ρ=πd

2ln2

If(2.16)

in which the formfactor f describes the ratio of the resistance parallel to the edges of the

sample. Then the mobility µis given by:

µ=RH

ρ(2.17)

From the variation of the mobility with temperature, one can distinguish between elec-

trons in the bulk and electrons located in the channel of a heterojunction field effect

transistor (HFET) structure. Figure 2.8 depicts the differences in a semilogarithimic

scale. For a carrier with a mobility in three dimensions µshows an increasing value with

increasing temperature up to 100K due to the reduction of ionized impurity scattering.

After reaching a maximum at T=100K, the values decreases with increasing tempera-

ture, because of the influence of phonon scattering, which is the dominant mechanism for

temperature above 100K. In the case of a spatial separation of carriers and their ionized

impurities a different temperature dependence is observed. At lower temperatures there

is no freeze out of carriers at the impurities and impurity scattering do not occur due

to the spatial separation. This results in a further increase of the carrier mobility with

deceasing temperature.

For that reason and in addition also for the investigation of temperature dependent mea-

surement of the IV and CV curves, the samples are mounted in Cryovac flow cryostat

model 3-06-4251C. The system allows a temperature variation in the range from 5K

to 350K, controlled by cryovac temperature controller model MK4, equipped with two

AlGaAs temperature diodes, one directly mounted on the sample holder, the other in

the cryostat.

The four-point probe technique is one of the most common methods for measuring the

semiconductor resistivity [30].Two probes carry the current and the other two probes are

used for voltage sensing. A schematic drawing of the contact arrangement and the way

of current flow is given in Fig. 2.9. The probes are generally arranged in-line with equal

probe spacing. The use of four probes has an important advantage over two probes.

Although the two current-carrying probes still have contact and spreading resistance

associated with them, that is not true for the two voltage probes because the voltage

is measured either with a potentiometer which draws no current at all or with a high

impedance voltmeter which draws very little current. The contact resistance and the

spreading resistance are negligible in either case because the voltage drops across them

are negligibly small due to the very small current that flows through them. Under the

assumption of a infinite sample and that the current I flows between contact 1 and 4 the

electric field E1(r) around contact 1 in a distance r is given by:

E1(r) = ρ·j(r) = ρ·2I

4πr2(2.18)

2 Fundamentals

Figure 2.9: Schematic drawing of the contact arrangement and the current flow during

a four-point probe measurement.

in which j is the current density and ρthe resistivity. If the probes are arranged in the

same distance s, the potential φ1, which is generated by the contact 1 between probe 2

and 3, is equal to:

φ1=

E1dr =ρ·I

4πs (2.19)

On the other hand, the contact 4 generates also a electric potential between probe 2 and

3. The potentials φ1and φ2are equal. Therefore the voltage U2,3between probe 2 and

3 is given by the sum of both:

U2,3=φ1+φ2=ρ·I

2πs (2.20)

So the resistivity ρof an infinite sample is equal to:

ρ= 2πs ·U2,3

I(2.21)

For real samples with a finite lateral extension and a finite thickness equation 2. has

to be modified. Therefore three correction factors F1,F2and F3have to be take into

account. The factor F1considers the finite thickness t [32]. If t < s

2the factor is given

by:

F1=t/s

2 ln(2) (2.22)

2.3 Characterization techniques

The finite lateral extension of the samples is compensated by the factor F2. In case of

radial symmetric samples with a diameter d the correction factor is calculated by [?] [33]

F2=ln(2)

ln(2) + ln{[(d/s)2+ 3]/[(d/s)2−3]}(2.23)

The position of the probes in relation to the edges of the sample influences also the

determination of the resistivity. This is take into account by the factor F3[34]. If the

contacts are located at the distance l1perpendicular to one edge, F31 is given by

F31 =1

1 + 1

1+2l1/s −1

2+2l1/s −1

4+2l1/s +1

5+2l1/s

(2.24)

For the second edge of the sample with a parallel arrangement we have to consider a

second correction:

F32 =1

1 + 2

√1+(2l2/s)2−1

√1+(l2/s)2

(2.25)

Both factors have to be used two times, because the contacts are arranged perpendicular

and parallel to two edges. Therefore the resistivity is given by:

ρ=F1F2F2

31F2

32 ·2πsU2,3

I(2.26)

3 Growth of GaN and AlGaN

3.1 Growth of GaN

The growth of phase-pure cubic GaN with a low defect density (<109cm−2) and a

smooth surface is the basic feature for the realization of high quality electronic devices.

The optimum conditions for the epitaxial growth of c-GaN are mainly determined by

two parameters, the surface stoichiometry and the substrate temperature [8]. Both pa-

rameters are interrelated; therefore an in-situ control of both substrate temperature and

surface stoichiometry is highly desirable. This has been achieved by monitoring the MBE

growth process by RHEED. The study of the surface reconstruction behaviour was one

of the key issues in understanding the c-III nitride growth. First principle calculations

by Neugebauer et. al. [36] showed that all energetically favored surface modifications

of the nonpolar (001) c-GaN surface are Ga-stabilized and therefore optimum growth

conditions were expected under slightly Ga-rich conditions.

The c-GaN films, which are schematically drawn in Fig. 3.1 are grown on freestanding

Figure 3.1: Schematic drawing of the structure of the investigated c-GaN layers.

3C-SiC (001) substrates backcoated with silicon for efficient radiative heating. Prior to

growth, the substrates are subjected to an Al deoxidation process at TSubs = 800◦Cusing

an Al beam equivalent pressure of 8.2∗10−8mbar [37] in order to remove native oxide.

3.1 Growth of GaN

Then an AlxGa1−xNbuffer is deposited, having an Al mole fraction between x=0 and

x=1 and a thickness ranging from 8nm to 30nm. The temperature for the deposition

of the buffer varies from TBuffer = 600◦Cto TBuffer = 850◦C. Following this step, a

200nm-3000nm thick GaN layer is grown at temperatures ranging from TSubs = 720◦C

to TSubs = 850◦C. During the growth of all these films, the nitrogen plasma conditions

were kept constant at 260W rf power and 0.4sccm nitrogen flow equal to an active ni-

trogen flux of FN= 2.2∗1014cm−2s−1. The growth was continously monitored in situ

by RHEED at 16kV energy and an incidence angle of 1.3◦. The intensity of the main

streak and other regions of interest along the [-110] azimuth of c-GaN (001) are recorded

using a digital RHEED analysis system. The arrival rate of the group-III atoms was

determined by measuring the beam equivalent pressures (BEP) prior to growth, using a

nude ionization gauge placed at the substrate position. The impinging flux Fimp

iof the

i species (in cm−2s−1), is given by [38]:

Fimp

i=Ci

√mikBTi

(3.1)

where Piis the measured BEP, miis the atomic mass, and Tiis the vapor temperature,

Figure 3.2: Measured RHEED intensity during the initial growth of c-GaN. The RHEED

intensity after opening the N shutter yields the amount of excess Ga on the

c-GaN surface.

which is taken to be approximately equal to the corresponding effusion cell absolute

3 Growth of GaN and AlGaN

temperature. The constant Cireflects the ionization gauge sensitivity factors for gallium

as well as geometrical factors related to placing the ion gauge in the exact position of

the substrate.

The Ga coverage of c-GaN was obtained by measuring the intensity of the reflected

electron beam ((0,0)-streak RHEED intensity) [39]. During growth interruption the

adsorption and desorption of gallium on a c-GaN (001) surface was measured employing

the intensity of a reflected high energy electron beam (RHEED intensity) as a probe.

After opening the Ga shutter we observed a decrease of the RHEED intensity to a

saturation value, which was related to the impinging Ga flux. Using the known value of

the Ga-flux and the transient time of the RHEED intensity we were able to estimate the

amount of adsorbed gallium. After closing the Ga shutter the RHEED intensity reached

the starting value indicating a total desorption of excess Ga. A similar procedure was

used to measure the Ga coverage during c-GaN growth. Figure 3.2 shows the RHEED

intensity measured after opening the N shutter with the Ga flux on. From the decrease

of the RHEED intensity after the nitrogen shutter was opened we were able to measure

the Ga-coverage during growth with an accuracy of 0.1ML. The stoichiometric growth

of c-GaN without Ga coverage was realized, if after opening the N shutter no drop in the

RHEED intensity (dotted line) was observed, whereas c-GaN growth with 1ML coverage

was defined by a certain drop in the intensity (solid line). The total impinging Ga flux

for the growth of GaN is given by:

Fimp

Ga,1ML(GaN) = Fimp

Ga,0ML(GaN) + F1ML,cov

Ga =Finc

Ga (GaN)

sGa

+F1ML,cov

Ga (GaN) (3.2)

where Fimp

Ga,1ML was the impinging Ga flux for Ga growth with 1ML coverage, Fimp

Ga,0ML

was the corresponding flux for stoichiometric growth, F1ML,cov

Ga was the Ga flux necessary

for the coverage of 1 ML, and Finc

Ga was the incorporated Ga flux and sGa the sticking

coefficient, respectively. The difference in the Ga flux necessary for 1ML coverage and

0ML coverage is about 25% of Fimp

Ga,1ML. This recipe is used as the standard process for

the growth of the samples which a described in this work.

The RHEED is also used to determine the properties of the GaN surface during growth,

i. e. the terrace width. This parameter will have a strong influence on the mobility of

carriers in a 2DEG. Therefore we measure RHEED linescans parallel to the shadow edge.

From Lent at al. [40] it was known that the lineshape of these scans can be approximated

by a Voigt function. A Voigt function is the superposition of a Gauss and a Lorentz

function. And from the theory the terrace width Λ is given by:

Λ = C∗π

FWHMGauss

(3.3)

Fig. 3.3 depicts the result of this calculation. For a GaN film grown at 720◦Ca constant

terrace width of about 3.5nm is observed for GaN for thicknesses up to 480nm. The

most important parameters for the investigation of the quality of the c-GaN are the

dislocation density, given by the FWHM of the X-ray rocking curve [18], the phase

purity and the surface roughness. These parameters influence the device performance of

3.1 Growth of GaN

Figure 3.3: Terrace width of a c-GaN film.

Figure 3.4: RMS roughness on a 5x5µm2scan range as function of the FWHM of the

X-ray rocking curve for φ= 0◦(triangles) and φ= 90◦(squares) of the

freestanding 3C-SiC substrates.

3 Growth of GaN and AlGaN

c-AlGaN/GaN based FETs by scattering of carriers and therefore reducing mo-

bility. In order to check how these paramters can be influenced by the substrate quality

or by the growth process, the structural properties of the substrate as well as that of

the GaN growth process were studied.

The 3C-SiC substrate can influence the quality of the c-GaN buffer in two ways, first by

the amount of dislocation density generated and second by the surface RMS roughness.

Therefore we determine the FWHM of the rocking curve and the RMS roughness on a

5x5µm2scan range of our substrate and check their dependency on each other. The

Fig. 3.4 depicts the results of these measurements. The FWHM of the rocking curve

is plotted as function of the RMS roughness FWHM for a substrate angle of φ= 0◦

(triangles) and φ= 90◦(square). The angle φrepresents the angle between the incident

X-ray beam and the (110) direction of the crystal. The dashed and the solid line are a

guide for the eye. An increase of the FWHM with increasing RMS roughness is observed

for both substrate orientation angles. At a half width of the rocking curve of 5arcmin,

the RMS roughness is typically in the order of 1.5nm, whereas with an increase of the

width up to 20arcmin the roughness is approximately 10nm. The increase in rough-

ness with increasing dislocation density is caused by the fact that the typical defects

in 3C-SiC are so called twinning domains [41]. These twinning domains originate from

Figure 3.5: The FWHM of the X-ray rocking curve of c-GaN as function of the SiC

RMS roughness on a 5x5µm2scan range for φ= 0◦(triangles) and φ= 90◦

(squares).

the growth process of the SiC and the incorporation of stacking faults [42]. These do-

3.1 Growth of GaN

mains causes then a groove in the substrate surface, such that the measured roughness

increases with increasing groove number. The dependence between the defect density

and the roughness allows one to investigate the properties of GaN only as function of

surface roughness.

Figure Fig. 3.5 shows the influence of the substrate roughness on the structural prop-

Figure 3.6: The RMS roughness of c-GaN as function of the SiC RMS roughness on a

5x5µm2scan range.

erties of cubic GaN. The rocking curve half width of the c-GaN with a thickness of

t=600nm is plotted as function of the substrate roughness. The measurements of the

rocking curve are performed in the substrate orientation of φ= 0◦(triangles) and φ= 90◦

(squares). For both orientation an increase of the GaN half width with increasing rough-

ness of the substrate is observed. The increase originates from the increasing number

of twinning domains, which causes several grooves in the substrate surface. During the

initial growth of the GaN buffer, these grooves act as nucleus for the incorporation of

threading dislocations in the GaN. Thus with increasing number of grooves the defect

density of the c-GaN increases.

A further parameter, which has to be investigated, is the influence of the substrate

roughness on the roughness of the GaN film. The results are depicted in Fig. 3.6. The

plot shows the RMS roughness of 600nm thick c-GaN films on a 5x5µm2scan range ver-

sus the RMS of the 3C-SiC substrate. An increase of the GaN roughness with increasing

substrate RMS is revealed. The values range from 6.7nm for the GaN on a 1.5nm rough

3 Growth of GaN and AlGaN

SiC substrate to 17nm for GaN on SiC with a RMS of 8.6nm. The solid line is a guide

for the eye. from this observed dependence, it can be surmise, that grooves present in

the SiC surface transferred to the GaN layer, thereby, contributing to surface roughness

as well. The standard values for the delivered substrates are 3.5arcmin for the rocking

curve half width and a RMS roughness of 1nm, which gives the best results for the

growth of GaN.

Following the investigation of the substrate properties the influence of the GaN growth

Figure 3.7: The FWHM of the X-ray rocking curve of c-GaN as function of the buffer

type.

process itself on the structural properties of GaN is studied. The initial point of this

investigation is to study the influence of the buffer type on the quality of the GaN.

Therefore a series of 600nm thick GaN films was grown at TSubs = 720◦Con top of a

GaN, Al0.1Ga0.9Nand AlN buffer with a thickness of 8nm and at TSubs = 720◦C. The

results of these experiments are shown in Fig. 3.7 and 3.8. Figure 3.7 depicts the influ-

ence of the buffer type on the rocking curve half width of our GaN layers. The FWHM

is nearly constant at a value of 29arcmin, and therefore independent on the buffer type.

This effect is caused by lattice mismatch between the different epitaxial layers. In case

of a GaN buffer the buffer relaxes after a few nm due to the lattice mismatch between

the SiC and GaN. The mismatch causes then the incorporation of dislocations. For a

Al0.1Ga0.9Nbuffer the situation is not that different to the GaN buffer, because of the

low Al content. Therefore the relaxation process is the same and the incorporation of

3.1 Growth of GaN

dislocations also. If we look to the AlN buffer, it was found that this buffer is strained

on the SiC, due to the small lattice mismatch of 0.7%. But if we continue the growth

of GaN, the layer relaxes on the AlN, due to the mismatch of AlN to GaN, which is

comparable to that of SiC to GaN. In the end, the relaxation process is shifted from the

SiC/GaN interface to the AlN/GaN interface.

As described previously, the roughness and the phase purity of the GaN are also im-

Figure 3.8: The RMS roughness (circles) and the amount of hexagonal phase inclusion

(squares) of c-GaN as function of the buffer type.

portant for device performance. Figure 3.8 shows the values for the phase purity and

roughness for the different buffer types. We observe a clear reduction of the GaN rough-

ness (circles) with increasing amount of Al in the buffer layer. For the GaN a RMS

roughness of 19.9nm was measured on a 5x5µm2scan range and for the AlN buffer a

value of 7.8nm. The result indicates, that the Al may act as a surfactant. The amount of

hexagonal inclusions (squares)are also plotted in the figure, they decrease from 1.5% for

the GaN buffer to 0.5% for the AlN buffer. If both dependences are compared, one can

see, that the roughness of the buffer may influence the amount of hexagonal inclusions

in the layer. A higher roughness (or differences in height) forces the formation of (111)

planes in the cubic phase, which then act as a nucleus for the hexagonal (001) planes.

On these (111) planes the growth of h-GaN is favoured, due to its higher thermodynamic

stability and growth rate.

3 Growth of GaN and AlGaN

The second point of discussion is the influence of the growth temperature on the struc-

Figure 3.9: The FWHM of the X-ray rocking curve of c-GaN as function of substrate

temperature.

tural properties of c-GaN. Figure 3.9 shows the rocking curve half width of 600nm thick

c-GaN films grown on a GaN buffer as function of growth temperature in the range

from TSubs = 720◦Cto TSubs = 810◦C. In this range a decrease of the half width from

31arcmin to 26arcmin by increasing the substrate temperature from TSubs = 720◦Cto

TSubs = 810◦Cis observed. The decrease of the FWHM of the GaN is caused by the

higher surface mobility of the Ga and N atoms on the surface at higher temperatures.

The higher mobility of the atoms allows a more perfect arrangement in the crystal lat-

tice. Therefore we have less dislocation in the crystal and the width of the rocking curve

decreases.

In Fig. 3.10 the results for the influence of the temperature on the roughness and on

the phase purity is depicted. The data reveal an increase of the roughness (circles) from

12nm on a 5x5µm2scan range for TSubs = 720◦Cto 22nm for TSubs = 810◦C. The in-

crease of the roughness originates from the same reason like the decrease of FWHM. The

higher mobility at higher growth temperatures causes the formation of structures on the

surface, which are mainly confined by (111) planes. As mentioned above, these planes

are also responsible for the formation of hexagonal inclusions and a look on the phase

purity (squares) shows an increase of hexagonal phase with increasing temperature. The

data show 0.5% for a temperature of TSubs = 720◦Cand 4.3% for TSubs = 750◦C. This

3.2 Growth of AlGaN

Figure 3.10: The RMS roughness (circles) and the amount of hexagonal phase inclusion

(squares) of c-GaN as function of the substrate temperature.

is a further hint for a correlation between surface roughness and phase purity.

In summary a GaN buffer grown at TSubs = 720◦Cwas choosen together with the deposi-

tion of the GaN bulk also at TSubs = 720◦C. This set of parameter is a good compromise

between disclocation density, surface roughness and phase purity and is used for all fur-

ther experiments.

3.2 Growth of AlGaN

On top of the GaN cubic AlxGa1−xNfilms, about 50nm to 600nm thick, are grown at

a temperature of TSubs = 720◦C. Two series of AlxGa1−xNepilayers were realized, one

with a coverage of 1 monolayer (ML) Ga on the growing surface, a second one having

a Ga coverage >>1ML. After the determination of the fluxes Fimp

Ga,0ML and F1ML,cov

Ga by

the experiment described above (see chapter 3.1), the impinging Al and Ga fluxes for

the growth of a c−AlxGa1−xNalloy with 1 ML coverage were easily adjusted using the

3 Growth of GaN and AlGaN

relations:

Fimp

Al (AlGaN) = xFinc

Ga (GaN)

sAl

and (3.4)

Fimp

Ga,1ML(AlGaN) = (1 −x)Finc

Ga (GaN)

sGa

+F1ML,cov

Ga (3.5)

In the next step the procedure was transferred to the growth of c−AlxGa1−xNfilms.

Figure 3.11 shows the variation in the RHEED intensity during the initial growth of a

Figure 3.11: Measured RHEED intensity during the initial growth of c−Al0.25Ga0.75N.

The RHEED intensity after opening the N shutter yields the amount of

excess Ga on the c-GaN surface. After opening the Al shutter the excess

of Ga increases and RHEED oscillations are observed indicating a two-

dimensional growth mode with a rate of 177nm/h.

c−Al0.25Ga0.75Nlayer. When the nitrogen shutter was opened with Ga on, an increase

of the RHEED intensity was observed, indicating a Ga coverage of about 0.15ML due

to the reduced Ga flux in comparison to the pure GaN growth. When the Al shutter

was opened the intensity dropped down revealing an increase in the surface coverage to

1ML. The increase of the coverage is given by the additional metal flux and contains an

exchange process in which the Ga incorporation in the layer is depleted by the Al due

to the higher bond energy of Al-N of EAlN =2.88eV [43] in comparision to Ga-N with

3.2 Growth of AlGaN

EGaN =2.24eV [43]. Further clearly, weakly damped RHEED oscillations were observed,

indicating a two-dimensional Al0.25Ga0.75Ngrowth mode at substrate temperatures of

720◦Cwith a growth rate of 177nm/h. The surface diffusion length of aluminium is

smaller than that of gallium, therefore one would expect RHEED oscillations with the

growth of GaN rather then with AlGaN. However, our experiments show the opposite

behavior. The reason for that is not clear, it may be due to a kind of surfactant effect

of Ga on the (001) surface, similar to what has been reported for In on hexagonal GaN

[44].

The relation between the flux ratio of the Al flux to the total metal flux and the Al

Figure 3.12: Relation between the Al mole fraction x of all AlxGa1−xNand the flux ratio

of Al to the total metal flux in the vapor phase for films grown under 1ML

and >>1ML Ga coverage. The mole fraction was determined by HRXRD.

mole fraction x of the epilayer is drawn in Fig. 3.12. It was found that the Al content

x was nearly linear proportional to the Al mole ratio of the vapor phase for the samples

grown with 1ML and >>1ML Ga coverage. The linear increase indicate, that the Al

was preferently incorporated. For the films deposited with 1ML coverage a 1:1 relation

between the flux ratio and the Al content was observed, whereas for the Ga coverage

much greater than 1ML the slope was >1 due to the higher amount of Aluminum in

relation to the total metal flux.

In case of InyGa1−yNgrowth, the growth rate depends on the In flux [45]. In order to

verify similar behaviour during the growth of AlxGa1−xN, the growth rate of AlxGa1−xN

alloys was determined in a wide range of the Al mole fraction x. The data are summa-

3 Growth of GaN and AlGaN

Figure 3.13: AlxGa1−xNgrowth rate derived by RHEED oscillation and optical measure-

ments for Al mole fraction between x=0 and x=0.74 at a constant nitrogen

flux of FN= 2.2∗1014cm−2s−1. The data reveal a constant growth rate for

all AlxGa1-xN alloys independent on the Al flux.

rized in Fig. 3.13. The growth rate shows no markable change with varying Al mole

fraction between x=0 and x=0.74. The observed variations are within the experimental

error. So in contradiction to the InyGa1−yNgrowth the Ga adlayer does not influence

the nitrogen flow to the growing surface. The presence of a surfactant effect of Ga during

the growth of AlxGa1−xNis very useful for the optimization of the surface morphology.

The influence of the Al flux (i. e. the Al mole fraction) on the roughness of c-AlxGa1−xN

layers is depicted in Fig. 3.14. The RMS-roughness measured on a 5x5µm2area was

constant with a value of 5nm over the whole Al range, if the films were grown under a

Ga coverage of 1ML (circles). With increasing coverage (>>1ML) a strong dependence

of the RMS roughness on the Al content was observed (triangles). The values increased

from 2.5nm (GaN) to 22.5nm (Al0.44Ga0.56N) due to the formation of Ga droplets on

the surface. The presence of droplets is investigated by optical microscopy.

The strain status is a further parameter, which influences the dislocation density. With

increasing relaxation in the layer, the defect density increases (s ee chapter 2.1). The Fig.

3.15 shows a reciprocal space map (RSM) arround the (-1-13) reflex. In the RSM the

reflex of the GaN buffer is observed at qk=−1.97˚

A−1and q⊥= 4.16˚

A−1as well as the

Al0.25Ga0.75Nfilm with qk=−1.97˚

A−1and q⊥= 4.23˚

A−1. The position of the AlGaN

3.2 Growth of AlGaN

Figure 3.14: RMS roughness on a 5x5µm2area for AlxGa1−xNalloys with an Al mole

fraction between x=0 and x=0.74 grown under the coverage of 1ML (circles)

and >>1ML (triangles) at 720◦C. The lines are a guide for the eyes.

reflex relative to the GaN reflex indicates, that the AlGaN is pseudomorphic strained on

the GaN (see chapter 2.1). This is confirmed by the observation that the relaxed AlN is

located at qk=−2.03˚

A−1and q⊥= 4.30˚

A−1. The strain status as function of the film

thickness for c-Al0.25Ga0.75Nlayers is plotted in Fig. 3.16. The plot shows, that only

for a thickness of 20nm the AlGaN layer is totally strained. With increasing thickness

from 50nm to 450nm the strain is reduced from 0.8 to 0.3. The data are fitted using a

1/d dependence of the strain status on the thickness (dashed line). It is an interesting

observation, that the films are still partially strained, because after Sherwin et al. is the

critical thickness for an Al mole fraction of x=0.25 in the range of t=10nm [16]. The

reason for deviation from theory is the high dislocation density. The high density forces

the partial reduction of the strain energy at the dislocation lines, and therefore the layer

relaxes at higher thickness than predicted by the model. But Sherwin et al. take only

the screw dislocation into account. If other types of defect will also included in the

calculation, the critical thickness will increase.

3 Growth of GaN and AlGaN

Figure 3.15: Reciprocal Space Map arround the (-1-13) reflex of an Al0.25Ga0.75Nfilm.

Figure 3.16: Strain status of Al0.25Ga0.75Nfilms as function of the layer thickness.

3.3 Electrical properties of GaN and AlGaN

A further important parameter are the electrical properties of our GaN and AlGaN

layers, especially the unintentional doping level and the resistivity. The doping of the

GaN and AlGaN determines for example the band diagram of the heterostructure and

3.3 Electrical properties of GaN and AlGaN

Figure 3.17: Unintentional doping level of AlxGa1−xNfilms as function of the Al content

x before (circles) and after (squares) change of the purifier.

therefore the density of the 2DEG (see chapter 6.1). On the other hand the resistivity,

which includes the doping concentration, determines the suitability of a film as insulation

layer in order to prevent parallel conductivity to the 2DEG.

In order to measure the background doping concentration some samples with a Al mole

fraction between x=0 and x=0.48 are analyzed by electrochemical CV (ECV) [35]. The

results of the measurements are depicted in Fig. 3.17. Two series of samples have

been grown, one before changing the purifier and one series after changing the purifier.

Before the change of the purifier in our nitrogen gas line (circles) the unintentional

doping concentration of the c-GaN is about ND= 2 ∗1018cm−3and increases to ND=

1.4∗1020cm−3for an Al0.48Ga0.52Nlayer. The increase of the concentration is caused by

the high affinity of Al to oxygen. The aluminum forces the incorporation of oxygen into

the AlGaN film. Oxygen acts as a shallow donor in the group-III nitrides if it occupies a

N site, which is then responsible for the unintentional n-type doping. After changing the

purifier (squares), which prevents oxygen contamination of the nitrogen gas, the doping

of the GaN is reduced by two orders of magnitude down to ND= 1 ∗1017cm−3and for

the Al0.48Ga0.52Ndown to ND= 2 ∗1018cm−3,respectively. Fitting the experimental

data with a power function, it was found that 1 Al atom getters 1.4 O atoms. These

concentrations are used for the calculation of the band diagrams in chapter 6.1.

The investigation of the resistivity of the AlGaN films are performed by a four point

probe measurement [30](see also chapter 2.3.3). Due to the conducting nature of the

substrate it is not suitable to perform Hall-effect measurements. The In contacts on the

3 Growth of GaN and AlGaN

Figure 3.18: Photograph of the investigated AlGaN/GaN samples.

semiconductor surface are realized by microsoldering. The contacts have a diameter of

500µm and a distance of 1mm. A photograph of the sample with the contacts is shown

in Fig. 3.18. The Fig. 3.19 illustrates the current circuit, used for the measurements.

The total resistance Rtot is given by the three times the resistance between the inner

probes R2,3and the serial resistance RSof the outer probes:

Rtot =RS+ 3R2,3(3.6)

The resistance RSis measured by the resistance of the In/AlGaN interface RIn/AlGaN ,

the resistance of the AlGaN layer RAlGaN , the resistance of the GaN/AlGaN interface

RGaN/AlGaN , the resistance of the GaN RGaN , the resistance of the GaN/SiC interface

RGaN/SiC and the resistance of the 3C-SiC substrate RSiC:

RS=RIn/AlGaN +RAlGaN +RGaN/AlGaN +RGaN +RGaN/SiC+RSiC =RAlGaN +RRest (3.7)

In RRest all the resistances without RAlGaN are summarized. The resistance of the

contacts as well as the interface resistances can be neglegted. RSis dominated by

RAlGaN , because if RAlGaN << RRest, the current flow is located in the AlGaN layer, and

if RAlGaN >> RRest, the AlGaN prevents the current flow into the substrate. Therefore

RAlGaN is calculated from:

RAlGaN =Rtot −R2,3−RRest (3.8)

RRest can not be directly determined, but all the samples are grown on GaN/SiC layer

with comparable values for RRest, so it is set constant, and changes in the total resistance

3.3 Electrical properties of GaN and AlGaN

Figure 3.19: Equivalent current circle of the investigated AlGaN/GaN samples.

are caused by a change of RAlGaN . From the calculated values for RSof the AlGaN films,

the resistivity is calculated using:

ρS(x) = RSdc

ttot

(3.9)

where dcis the diameter of the contacts and ttot the total thickness of the sample in-

cluding the substrate. For the determination of the resistivity the geometrical correction

factors are taken into account [32]. The resistivity is then normalized to the resistivity

of GaN and the ratio σ(AlGaN)

σ(GaN)is plotted as a function of the Al content in Fig. 3.20 in

a semilogarithmic scale. The lines are a guide for the eye. The plot shows an increase

of the conductance by a factor of 3, if the Al content is increased up to x=0.4. With a

further increase of the Al mole fraction, the relative conductance decreases to a value of

0.08 for a pure AlN layer.

In order to find an explanation for this behavior, some rough calculations were done.

The conductance σis given by:

σ=neµ (3.10)

where n is the carrier concentration and µthe carrier mobility. The concentration is

determined by:

n=rNCND

2exp(−EC−EF

2kBT) = rNCND

2exp(−ED

2kBT) (3.11)

where NCis the effective density of states in the conduction band and EDthe ionization

energy of the donor. NCis given by:

NC= 2(2πm∗

ekBT

h2)3/2(3.12)

3 Growth of GaN and AlGaN

m∗

eis the effective electron mass given as function of the Al content [46]:

m∗

e= 0.15 + 0.15x(3.13)

Knowing from Fig. 3.17, that the donor concentration increases with increasing Al

content due to the incorporation of oxygen, the donor concentration as function of the

Al mole fraction is approximated by:

ND(x)∝cx + 1 (3.14)

From Ref. [47] the activation energy of the Si donor shows a strong dependence on the

Al content. The binding energy varies from 20meV for GaN to 320meV for AlN and is

linearly interpolated by

Eact(x) = 0.02 + 0.3x[eV ] (3.15)

Under the assumption that our residual donor behaves similar and using Equation 3.14

for the activation energy the carrier concentration can be approximated by:

n(x)∝p(cx + 1)(0.15 + 0.15x)exp(−(0.02 + 0.3x)

2kBT) (3.16)

The results of the calculation are depicted in the 3.20 and given by the curves. The

Figure 3.20: Relative conductance and carrier concentration as function of the Al mole

fraction x.

values are also normalized to GaN. The curves represent different values for the constant

c of 1, 10 and 100. The coefficient c takes into account the different affinity of O to Ga

3.3 Electrical properties of GaN and AlGaN

and Al and is c=ND,AlN

ND,GaN . For example if c=100, the carrier concentration increases

up to an mole fraction of 0.2, then the concentration starts to decrease again. Two

points have to be taken in consideration. First, the residual donor will be with great

probability O and the binding energy of O as a function of the Al content is unknown

up to now. This may change Equation 3.14. The affinity of Al to O is quite different

to the affiniity of Ga to O, this may change the value of c. Therefore the calculations

have been performed for three different values of c, ranging from 1 to 100. In addition

the mobility µalso enters the conductivity and the variation of µis also unknown up

to now. Nevertheless, with this simple model that with increasing Al content the depth

of the donor binding energy increases and that Al has a higher affinity to O than Ga

the tendency observed in Fig. 3.20 can well be explained. The not avaiable values for

the mobility complicates the calculation of absolute values for the conductance of the

AlGaN films, but our rough approximation describes the tendency in a good way.

4 GaN and AlGaN Schottky diodes

In this chapter the theory and physics of Schottky diodes based on cubic GaN and

AlxGa1−xNfilms will be described. Schottky diodes are the key elements for the re-

alization of c-GaN based electronic devices such as high power high electron mobility

transistors, high power metal semiconductor field effect transistors and UV photodectors.

A short introduction in the general principle of the Schottky diode with the character-

istic barrrier and the current-voltage (IV) behaviour will be given below.

In principle a metal-semiconductor structure can be designed in two ways: the first is the

configuration as a Schottky contact in which the electron affinity of the semiconductor

and the metal work function form a barrier and a depletion zone at the metal semicon-

ductor interface, thus that termionic emission dominates the current flow. And second,

in special cases, depending on the material parameter of the metal and the doping of

the semiconductor, the depletion layer is so thin, that tunneling through the barrier

dominates the current flow, leading to an ohmic behaviour.

4.1 Thermionic Emission Theory

The physics of a Schottky diode can very well be described by the thermionic emission

theory. Due to the condition of thermal equilibrium (constant Fermi level) a potential

barrier is formed at the metal-semiconductor interface. This barrier causes the formation

of the depletion zone [28]. In case of Schottky diodes, the height and shape of the

potential barrier can be influenced by an external magnetic or electric field. The barrier

is normally located at or near the interface of a two-layer system like in pn-junctions or

heterojunctions.

Figure 4.1 shows the energy band diagram of a separated metal and semiconductor.

The work function of the metal is defined as:

WA=qφM(4.1)

which is the energy, electrons need, to escape from the Fermi level to the vacuum level.

In the semiconductor the work function is defined similar as WS=qφS. But with respect

to the fact that in this case the Fermi level is located in a forbidden band, it is more

useful to define a so called electron affinity qχS. It is the difference between the vacuum

level E0and the conduction band edge EC:

qχS=E0−EC(4.2)

4.1 Thermionic Emission Theory

Figure 4.1: Schematic drawing of the energy bands of a metal and a semiconductor before

contact.

The electron affinity for cubic GaN can be calculated from the known value for hexagonal

GaN with qχS=4.11eV [48]. Using the approximation that E0-EVis the same for both

materials, we get for c-GaN qχS=4.31eV, because Eg,c−GaN =Eg,h−GaN -0.2eV [49]. For

the calculation the assumption of an n-type doped semiconductor is used and that the

work funktion of the metal is larger than that of the semiconductor. Connecting both

Figure 4.2: Schematic drawing of the energy bands of a metal and a semiconductor in

contact.

4 GaN and AlGaN Schottky diodes

materials, like plotted in Fig. 4.2, the formation of a potential barrier at the metal-

semiconductor interface is observed. The height of the barrier is the difference between

the metal work function and the electron affinity of the semiconductor:

qφB=q(φM−χS) (4.3)

We see also the relation between the built-in voltage Vbi and the barrier height:

qφB=qVbi + (EC−EF) (4.4)

The Joyce-dixon approximation [50] is used to determine the difference of ECand EF:

EF−EC=kBT[ln(n

) + 1

√8

] (4.5)

in which n is the background carrier concentration and NCthe effective density of states,

which is given by

NC= 2(m∗

ekBT

2π¯h2)3/2(4.6)

With an effective electron mass of m∗

e= 0.15m0we get for the effective density of states

NC= 1.7∗1018cm−3. This results in a difference of EF−EC=0.05eV using equation

(4.5) and a background concentration of c-GaN n=1 ∗1017cm−3.

The connecting of the metal and the semiconductor takes the Fermi levels in thermal

equlibrium and causes a transport of carriers until the vacuum level becomes continuous

at the interface. In the semiconductor a positive charge is present, whereas the metal

will have a negative charge in order to guarantee electrical neutrality. The result of

the charge transport is the formation of the band bending. In order to describe the

transport of carriers under an external bias the thermionic emission theory by Bethe

[51] is used. This theory is derived from the assumptions that the barrier height is

much larger than kBT, thermal equilibrium is established at the plane that determines

emission and the existence of a net current flow does not affect this equilibrium. The

current density JS→Mfrom the semiconductor to the metal is given by the concentration

of electrons with energies sufficient to overcome the potential barrier and transversing

in the z direction:

JS→M=Z∞

EF+φB

qvzN(E)F(E)dE (4.7)

where EF+φBis the minimum energy required for thermionic emission into the metal,

vzis the carrier velocity in the direction of transport and N(E) and F(E) are the density

of states and the distribution function, respectively. If we postulate that all the energy

of electrons in the conduction band is kinetic energy and Vbi is the built-in potential for

zero bias we get for the current density:

JS→M=A∗T2exp(−qφB

kBT)exp(qVext

kBT) (4.8)

where

A∗=4πqm∗k2

h3(4.9)

4.1 Thermionic Emission Theory

is the effective Richardson constant for thermionic emission, neglecting diffusion and Vext

the external applied voltage. For free electrons the Richardson constant is 120A2cm−2K−2.

Since the barrier height for electrons moving from the metal into the semiconductor re-

mains the same, the current flowing into the semiconductor is thus unaffected by the

applied voltage. Therefore it must be equal to the current flowing from the semicon-

ductor into the metal when thermal equilibrium prevails (i. e. when Vext=0). The

corresponding current density is obtained from equation (4.08) by setting Vext=0,

JM→S=−A∗T2exp(−qφB

kBT) (4.10)

The total current density is given by the sum of equations (4.08) and (4.10):

Jn= [A∗T2exp(−qφB

kBT)][exp(qVext

kBT)−1] = JS[exp(qVext

kBT)−1] (4.11)

where JSis called the saturation current density. The equation is similar to the trans-

port equation for pn junctions and also known as Schottky-Mott-Model. However, the

expression for the saturation current density is quite different.

If the height of the Schottky barrier is known, the width, the capacitance of the de-

pletion layer and the built-in voltage can be calculated. In Fig. 4.3 the distribution of

the ionized donors, the electric field and the electric potential is plotted. In case of a

homogeneous doped semiconductor (first picture) using the assumption that we have an

abrupt metal-semiconductor interface and no free carriers within the depletion zone, the

following distribution of carriers is established:

ρ(z) = qND: 0 < z < w

0 : z > w (4.12)

We get the bending of the potential by integrating the one-dimensional Poisson equation:

d2V

dz2=−ρ

0

(4.13)

V(z) = qND

0

(z−w)2V(∞) = 0 (4.14)

where is the dielectric constant of the semiconductor, 0the dielectric constant for the

vacuum, NDthe donor concentration and w is the width of the depletion zone. The

built-in voltage Vbi can be determined by the potential difference between the left and

right side of the depletion zone

Vbi =V(0) −V(w) = eND

20

w2(4.15)

where the width of the depletion zone is equal to

w=r20

eND

Vbi (4.16)

4 GaN and AlGaN Schottky diodes

Figure 4.3: Schematic draw of the carrier distribution, the electric field strength and the

potential (from upside to downside).

and in case of an externally applied field

w=r20

eND

(Vbi −Vext) (4.17)

The area near the edge of the depletion zone is conductive, but the zone itself is depleted

and therefore an insulator. Therefore the structure is similar to a plate condensator,

which includes a dielectric material with the width w and the dielectric constant of

the material and the area A given by the size of the contact. The capacitance of the

structure is then

C=0A

w=As0eND

2(Vbi −Vext)(4.18)

With the variation of the external voltage, the width of the depletion zone is changed, e.

g. we have a charge transfer into the shallow impurities. If the capacitance is measured

as the function of external voltage we get information about the concentration of shallow

4.1 Thermionic Emission Theory

impurities in the semiconductor. If equation (4.18) is written in the differential form,

like d(1/C2)

dVext |w=−2

A20eND(w)Vext |w(4.19)

equal to

ND(w) = −2

A20d(1/C2)

dVext eVext

and w=0A

C(4.20)

we are able to design a carrier concentration profile in connection with the width w of

the depletion zone which is equal to the distance from the semiconductor surface.

For the investigation of the Schottky characteristics of c-GaN and c-AlGaN, samples

Figure 4.4: Comparison of the IV curve of a real Ni/c-GaN Schottky diode (GNJ1204)

(open circles) and an ideal diode using the Schotty-Mott equation (solid line).

with the following structures are used: the GaN Schottky diodes consist of a 800nm-

1000nm thick c-GaN layer deposited on 3C-SiC substrate at a temperature of 720◦C.

The AlGaN diodes are grown on top of a c-GaN buffer with a thickness of 800nm with

an AlGaN film thickness between 40nm and 100nm and an Al mole fraction varied

between x=0.15 and x=0.35. The samples are cut into pieces of 5x5mm2. Then Ni/In

or Pd/In Schottky contacts with a thickness of 50nm/150nm are produced by thermal

evaporation. The geometry of the contacts is defined by contact lithography having a

diameter of 300µm. The ohmic contact is realized by pure In using the micro soldering

technique. Details for the choice of the contact material and the thickness are given in

4 GaN and AlGaN Schottky diodes

[52][53].

Figure 4.4 shows the semilogarithmic room temperature I-V curve of one of our Ni/c-

GaN Schottky diodes (GNJ1204), which is measured in the voltage range between -5V

and +3V(open circles). A clear nonlinear behaviour is observed, the current density in

forward direction is about 160Acm−2at a voltage of 3V; whereas in reverse direction

the current density is about 1.5Acm−2at a voltage of -5V. The solid line in the figure

represents the current density across the Schottky diode, calculated by the model of

Schottky and Mott, that assumes the current flow is dominated by thermionic emission.

In the Schottky-Mott equation a saturation current density of JS= 7.6∗10−11Acm−2

is used. The saturation current density is calculated by using equation (4.11). We

clearly observe a strong deviation between the theory and the experimental results.

In forward direction the experimental values follow the theoretical prediction up to

a voltage of 0.5V, for higher voltage the current flow is orders of magnitude less than

given by the Schottky-Mott equation. In reverse direction also a discrepancy is observed.

The measured current is ten orders of magnitude higher than the calculated saturation

current of JS= 7.6∗10−11Acm−2and in addition we see an exponential increase of the

current density as function of the applied voltage instead of a constant reverse current.

In order to find an explanation for these deviations, at first one has to look on the sample

structure and how it can influence the electrical properties.

The schematic sketch of the contact arrangement, which is used for our c-GaN Schottky

Figure 4.5: Arrangement of the metal contact used for the c-GaN Schottky diodes (left

side) and the equivalent circuit (right side).

diodes is drawn in the left side of Fig. 4.5, as well as the equivalent circuit in the right

side of the figure. The Schottky (Ni) contact and the ohmic (In) contact are deposited

with a distance of 3mm on the GaN film. This arrangement is known as coplanar contact

arrangement and offers some advantages in the electrical characterization especially in

case of different types of substrates [52]. The right side of the figure illustrates the flow

4.1 Thermionic Emission Theory

of the current through the device. Starting with the Nickel contact the current has to

pass the metal semiconductor interface, which is characterized by a transition resistance

RNi−GaN and the Schottky diode. After this the current can flow by the GaN layer RGaN

as well as through the 3C-SiC substrate RSiC and in the end it has to pass a second

metal semiconductor interface, that of the ohmic (In) contact, which is characterized

by a transition resistance RIn−GaN . At last one has to take into account that the GaN

posses a lot of defects, which cause current transport, so that the diode itself has to

be described by a diode in parallel arrangement with a leakage resistance RL, which

represents the influence of defects. All the resistances, which are not parallel to the

diode can be summed as the series resistance RS:

RS=RNi−GaN + ( 1

RGaN

RSiC

)−1+RIn−GaN (4.21)

Using the assumption, that RSiC >> RGaN , we get for the serial resistance

RS=RNi−GaN +RGaN +RIn−GaN (4.22)

The circuit of our Schottky diode can now drastically simplified: It consists only of the

Figure 4.6: Sketch of the circuit for a real Schottky diode under forward bias.

ideal diode itself in parallel arrangement with the leakage resistance RLand in serial

arrangement with the serial resistance RS, like it is drawn in Fig. 4.6. If a forward bias

is applied to the structure, the current passes the serial resistance and flows through

the diode, because its internal resistance can be neglected in comparison to the leakage

4 GaN and AlGaN Schottky diodes

resistance. The voltage Vext, which is measured, is the voltage over the serial resistance

RSplus the voltage over the ideal diode Vdiode:

Vext =JARS+Vdiode or Vdiode =Vext −JARS(4.23)

Using the thermionic emission theory [51] we assume that the current flow is dominated

by thermionic emission of carriers over the Schottky barrier, taking into account that

the barrier height is much larger than the thermal energy of the carriers, the current

density in forward direction is given by

J=JSexp(qVext

nkBT) (4.24)

The deviation from the ideal behaviour, due to recombination within the depletion zone

or the dependence of the barrier height on the voltage is described by the ideality factor

n. The serial resistance affects the I-V curve for voltages above Vbi [54]. First the forward

direction will be discussed. Figure 4.7 shows the measured I-V curve (full circles) for

Figure 4.7: Comparision of the measured IV curve (full circles), without the limitation

by the serial resistance (open circles) and the Schottky-Mott equation (solid

line) in forward direction for GNJ1204.

sample GNJ1204 in a linear scale for voltages between 0V and +3V. A linear increase

of the current density is observed as function of the forward bias for voltages above

Vbi=0.7V. Using Ref. [54] one can evaluate a series resistance of RS=21Ω. With this

4.1 Thermionic Emission Theory

value the voltage over the diode Vdiode can be calculated using equation (4.22). The result

of the calculation are plotted in the figure as open symbols. An exponential increase of

the current density as function of the voltage is observed for voltages above Vbi=0.7eV,

which is in good agreement with the prediction of the thermionic emission theory (solid

line).

Neglecting the influence of the serial resistance equation (4.24)can be used in order to

calculate the saturation current density as well as the ideality factor n. For JSwe get

JS= 1 ∗10−5Acm−2and for n=2.3. In comparision to h-GaN based Schottky diodes

values of JS= 1 ∗10−8Acm−2and for n=1.05, respectively are published in Ref. [55].

From that observation we conclude, that in our structures some mechanisms exist, which

reduce extremely the performance of our diodes. In summary we think, that the forward

current at room temperature is dominated by thermionic emission and can be described

by thermionic emission theory.

However, if we focus on the reverse direction of the I-V charcteristics the behaviour is

totally different. Using the same arrangement as in Fig. 4.6, only adapted for the reverse

direction (see Fig. 4.8), the following is happened The current flows through the serial

Figure 4.8: Sketch of the circuit for a real Schottky diode under reverse bias.

resistance and then parallel through the diode as well as through the leakage resistance.

The total current density is then given by

J=JS+Vext

ARL

(4.25)

The reverse current density is given by JS= 1∗10−5Acm−2determined from the forward

current characteristics. With the approximation that JS<< J, the leakage current

4 GaN and AlGaN Schottky diodes

density JLcan be determined by

RL=JLA

V(4.26)

So the leakage resistance is the inverse slope of the reverse I-V characteristic for volt-

ages, which full fill the condition eV >> kBT[54]. This condition is fullfilled for voltages

larger than 0.3V at room temperature. Figure 4.9 illustrates the comparison of the mea-

sured (full circles), the fitted (open circles) and the theoretical (solid line) saturation

current density in reverse direction between -5V and 0V at room temperature. The

Figure 4.9: Comparison of the measured I-V curve (full circles), eliminating the influence

of RS(open circles) and the calculation using the Schottky-Mott equation

(solid line) in reverse direction for GNJ1204.

inverse slope of the measured I-V curve reveals two things. First, that the magnitude

of the reverse current is generally larger than the current density given by the fit and

the thermionic emission model. Additionally, a nearly exponential increase of the re-

verse current is observed with increasing reverse voltage. Similar effects have also been

measured with Schottky diodes on h-GaN [56] [57] [58]. They are explained by strong

contribution of tunneling currents to the reverse current [59].

To identify the mechanism responsible for the large leakage current, we measured the IV

curves of c-GaN and c-AlGaN Schottky diodes at temperatures between 50K and 300K.

In Fig. 4.10 the results of the I-V measurements of a c-GaN Schottky diode are plotted

in a double logarithmic scale in the voltage range of 0.01V to 1.5V for sample GNJ1204.

4.1 Thermionic Emission Theory

Figure 4.10: IV curves in forward direction measured at different temperatures of

300K (open circles), 150K (full circles) and 50K (open squares) of sam-

ple GNJ1204.

With increasing temperature an increase of the forward current density at a constant

voltage is observed. The decrease of the serial resistance is due to an increase of the

ionisation of impurities. We also see an increase of the current density with increasing

voltage at a fixed temperature. The curvature is quite different for different temperature

for voltages less than Vext=0.7V. If one looks on the I-V curve measured at T=50K, the

formation of a current plateau, which means a nearly constant current density, in the

voltage range of 0.3V to 0.6V is observed. This was also found in h-GaN based Schot-

tky diodes [60]. The plateau cannot be explained by thermionic emission. The current

plateau still exists at a temperature of 150K, but it disappears at a temperature of 300K.

A pronounced deviation from thermionic emission transport across the barrier is evi-

dent from the reverse bias characteristics, which is plotted in Fig. 4.11 for temperatures

of 50K (open squares), 150K (full circles) and 300K (open circles), respectively, for the

sample GNJ1204. The magnitude of the reverse current density, plotted in a semilog-

arithmic scale in the voltage range from -5V to 0V shows a reduction of less than one

order by decreasing the temperature from 300K to 50K. It is nearly independent on

temperature and more than eight orders of magnitude higher than predicted by the

thermionic emission model, especially at low temperatures. Further the current density

shows a dependence on the reverse bias voltage and increases exponentially with increas-

ing voltage.

4 GaN and AlGaN Schottky diodes

Figure 4.11: IV curves in reverse direction measured at different temperatures of 300K

(open circles), 150K (full circles) and 50K (open squares) of GaN film

(GNJ1204).

Figure 4.12: IV curves in reverse direction measured at different temperatures of

300K (open circles), 150K (full circles) and 50K (open squares) of a

GaN/Al0.35Ga0.65N/GaN heterostructure (GANS1352).

4.1 Thermionic Emission Theory

Similar effects were also observed in Pd/GaN/AlGaN/GaN based Schottky

diodes. The Fig. 4.12 shows the reverse I-V characteristic of an GaN/AlGaN/GaN

heterostructure with a GaN cap layer of 20nm and an AlGaN thickness of 40nm and an

Al content of x=0.35 in the voltage range between -5V to 0V for different temperatures

of 50K (open squares), 150K (full circles) and 300K (open circles). Here the current den-

sity for a fixed bias voltage is really independent on the temperature in the measured

range, and further, that in comparision to GaN based diodes the current density for the

GaN/AlGaN/GaN diodes is now one order of magnitude higher.

A further deviation from the thermionic emission theory is observed by the determina-

Figure 4.13: Temperature dependence of the Schottky barrier height calculated from

the built-in voltage at different temperatures between 5K and 300K of a

Ni/GaN (open squares)(GNJ1204) and a Pd/GaN/AlGaN/GaN (full cir-

cles) (GANS1352) Schottky diode.

tion of the Schottky barrier height using equation 4.4 and 4.5 at various temperatures.

The barrier height qφBis calculated from the measured built-in voltage Vbi using

qφB=qVbi −kBT[ln n

√8

] (4.27)

Figure 4.13 illustrates the Schottky barrier height for a Ni/GaN (open squares) and

Pd/GaN/AlGaN/GaN (full circles) Schottky diode in the temperature range from 5K

to 350K as Arrhenius plot. The Schottky barrier height of the Ni/GaN diode increases

4 GaN and AlGaN Schottky diodes

from 0.87eV at 350K to 2.14eV at 50K and in case of the Pd/GaN/AlGaN/GaN from

0.65eV at 350K to 2.05eV at 5K.

In case of the AlGaAs/GaAs system the changes in the barrier height can not be ex-

plained by thermionic emission, it is caused of the pinning of the Fermi level due to the

presence of ionizied defects near the semiconductor metal interface [61][62]. In this case,

the temperature change of the barrier would reflects the temperature motion of the de-

fect relative to the appropriate band edge,i. e. their ionization energy. The Fermi level is

pinned at an occupied localized defect state, whose wavefunction is mainly of a bonding

type. Thermal ionization of such a state involves the release of free carriers. The change

in concentration of free carrier induces the temperature dependence of the barrier height

[63]. In other words from the Arrhenius plot in Fig. 4.13 we can estimate the ionization

energy of these defects. We get for the Ni/GaN diode a value of EA= 51meV . In the

Pd/AlGaN/GaN diode the same ionization process occures, because it can be fitted to

a value of EA= 56meV . These results indicate that in the case of GaN and AlGaN

the same type of defects are present near the semiconductor surface. The experimental

value fits very well to the ionization energy of oxygen in GaN [49].

4.2 Thin Surface Barrier Model

For the hexagonal group-III nitrides a simple model is developed by Hasegawa et. al [60].

The so called Thin Surface Barrier (TSB) model postulates a high densitity of un-

intentional defect donors near the semiconductor surface (in agreement with the Al-

GaAs/GaAs system) which reduces the width of the barrier (in contrast to the Al-

GaAs/GaAs) in such a way that the tunneling probability for electrons through the

barrier is increased. If we look to the temperature dependence of the barrier height in

the hexagonal nitrides, an opposite behaviour is found in comparison to the GaAs and

c-GaN systems, here a decrease of the barrier height with decreasing temperature is

observed, caused by the Schottky effect. Both models use the same reason in order to

explain the anomalous current transport by thermionic field induced electron tunneling.

But only the model of Hasegawa can explain the current flow and the formation of the

current plateau in the forward direction. The model is characterized by the presence

of donor states within a thin layer at the surface below the Schottky barrier, having a

thickness d, a density NSD and an effective barrier height φB. The current through the

region with the surface states is dominated by thermionic field emission (TFE).

Figure 4.14 shows the influence of the TSB regions on the band diagram of our Schottky

diodes. For a quantitative description, we assume, that lateral extension of each region

is much larger than the value of d, so that the one-dimensional treatment of the current

transport is possible using the band diagram in Fig. 4.14. It is formed on a surface of

an n-type semiconductor with a bulk doping of ND. In Fig. 4.14, the potential at the

boundary x=D is defined as φD. If V0is defined as the bias voltage at which φ0=φD

4.2 Thin Surface Barrier Model

Figure 4.14: Schematic sketch of the Thin Surface Barrier (TSB) model.

holds, then V0and φ0are given by the following equations:

V0=φB−eNDS

20

D2−Vn(4.28)

in which Vnis given by

Vn=kBTlog(NC

) (4.29)

If Vext < V0the height qφ0is given by

φ0=eND

20

(1 −ND

NDS

)(r20

eND

(V0−Vext) + D2−D)2+Vext +Vn(4.30)

and if Vext > V0the height qφ0is given by

φ0=Vext +Vn(4.31)

Following similar steps by Padvani and Stratton [64] one can calculate currents by the

TFE/TE process. The value of φ0is an important parameter for the thermionic field

emission and determines the amount of current caused by tunneling. The energy position

of the maximum of the tunneling current is then

φm−φ0

φB−φ0

cosh2(E00/kBT)(4.32)

where E00 =¯h

2qND

m∗0is the so called tunneling Parameter. So the density of sur-

face donors and the background carrier concentration determines the amount of current

4 GaN and AlGaN Schottky diodes

caused by thermionic emission or by tunneling through the TSB regions as function of

the external voltage. This dependence is responsible for the formation of the current

plateau in forward direction as shown in Fig. 4.15. If the thickness of the TSB regions

Figure 4.15: Schematic sketch of the formation of the current plateau in the forward

direction of a Schottky diode.

becomes small (a few nm), V0becomes large and at low temperatures three different

ranges in the I-V characteristics occur:

•The first region given by Vext > V0is determined by localization of the depletion

zone within the TSB region, and the thermionic field emission process through the

TSB is direct proportional to the external voltage.

•In the second region, given by V0< Vext < VDin which VDis the voltage when

φD=φm, meaning that the energy maximum of the TFE is equal to the minimum

of the parabola. So we have TFE process through the barrier, but the current

dependence on the voltage is compensated by the decrease of the voltage in the

bulk, which ends in the formation of the plateau.

•In region three, for voltage above VDthe TFE enters the bulk material and the

TFE decreases, because the influence of the barrier thickness disappears.

The relevant donor like defects may be nitrogen vacancies [60], other possible candidates

are oxygen impurities, their density is expected to be high in AlGaN films due to the

increased affinity of Al to O, which is supported by the fact, that the leakage current

in the AlGaN/GaN Schottky diodes is even higher than that of GaN based diodes (see

4.2 Thin Surface Barrier Model

Fig. 4.19).

A very useful method to determine the carrier type and concentration of the defects

Figure 4.16: Carrier concentration profile of a Pd/c-GaN/c-AlGaN/c-GaN Schottky

diode (GANS1352) measured at temperatures between 175K and 350K.

is the measurement of the Hall effect. But in our case it is not possible due to the

conducting nature of the 3C-SiC substrate. The second is, the carrier concentration is

needed near the semiconductor surface and not in the bulk material. In our case the

best way is to use the Schottky diode itself as a probe and measure C-V. This allows

us to measure a concentration profile as from the surface using equation (4.19). In Fig.

4.16 a calculated concentration profile is plotted in a semilogarithmic scale versus dis-

tance from the surface of a Pd/c-GaN/c-AlGaN/c-GaN Schottky diode (GANS1352) for

temperatures between 175K and 350K. The plot shows an exponential decrease of the

carrier concentration from n= 3 ∗1018cm−3at a depth of 20nm to n= 1 ∗1018cm−3at

60nm, which means a very high concentration of donors near the semiconductor surface.

In order to determine the amount of donor states near the surface, we extrapolate the

concentration profile exponential to a depth of 10nm, which is a reasonable value for the

thickness of the TSB. For a temperature of 350K a concentration of n= 5.6∗1018cm−3

is calculated. This value decreases with decreasing temperature, for T=200K it is only

n= 4.1∗1017cm−3. The reduction in the donor concentration is caused by the freeze-

out of the carriers at their impurities. However, we have shown, that c-GaN and c-

AlGaN/GaN based Schottky diodes suffer from abnormal large leakage current under

reverse bias, which strongly degrade gate control characteristics and increase power con-

sumption. This anormalous high current is caused by a high density of surface donor

states with a density of ND−NA= 4.2∗1019cm−3at room temperature. A promising

4 GaN and AlGaN Schottky diodes

Figure 4.17: Room temperature current voltage characteristics of a Ni/c-GaN Schottky

diode (GNS1285) before annealing (open circles) and after annealing in air

at 200C(full circles).

canditate for the donor states is oxygen owning an activation energy of 51meV, which

is in good aggrement with the values given in the literature [49].

For an improvement of the performance of our Schottky devices the density of surface

donors have to be reduced. In our case there are two possibilities for the reduction. First

the reduction of the oxygen background during growth. This can be achieved by the

use of high purity nitrogen or mounting chemical purifiers in front of the plasma source.

The second possibility is a post growth process. One promising process is the thermal

annealing of the structure in air. This is done for a Ni/c-GaN Schottky diode on a hot

plate located on a lab bench in open room air for 10min at 200C. The Fig. 4.17 shows

the I-V curves before and after the annealing. In the figure the IV characteristics of

the Ni/c-GaN Schottky diode before (open circles) and after (full circles)annealing are

plotted in a semilogarithmic scale as function of the bias voltage in the range from -5V

to 5V measured at T=300K. In the as grown characteristics the typical I-V behaviour

of our Schottky diodes is observed. If we now focus on the I-V curve after the annealing

step we see a dramatic change. In the forward direction, the current density reveals a

weak change, the serial resistance increases from 230Ω to 310Ω. On the other hand, the

barrier height increases from 0.6eV to 1.2eV using equation 4.27. Further observations

could be seen in the reverse direction. If the current density before and after the an-

4.3 Breakdown Voltages of Schottky Diodes

nealing step is compared, a decrease of the current density by two orders of magnitude

is measured, however the exponential increase with increasing voltage still exists. The

results show that the density of surface donors can be reduced by the annealing due

to the reduction of the current, but they are still present and dominating the reverse

current. These donor like defects maybe compensated by Ga4Ni3;Ni3Nand Ni4N

clusters which are formed during the annealing at the Ni-GaN interface [65].

4.3 Breakdown Voltages of Schottky Diodes

A very important parameter in the field of device performance is the size of the break-

down voltage. The breakdown voltage VBD is defined by the reverse voltage at which

the avalanche breakdown of the carriers occurs. The result is a very high current in

reverse direction, which destroys the diode. It would be an interesting point if thermal

annealing can influence the density of surface donor states and the breakdown voltage.

In Fig. 4.18 the I-V curves of an as grown (GNJ1204) and an annealed (GNS1285) Ni/c-

Figure 4.18: Breakdown voltage of Ni/c-GaN Schottky diode before annealing

(GNJ1204) (open circles) and after annealing in air at 200C(GNS1285)

(full circles).

GaN diode are plotted in a semilogarithmic scale for voltages between -90V and +10V.

For both devices the breakdown is observed, due to the huge increase of the current

density in reverse direction. In case of the as grown sample the breakdown occurs at

4 GaN and AlGaN Schottky diodes

VBD=-9V. For the annealed sample a saturation of the current density is measured at

about 150Acm−2and the breakdown occurs at a voltage of -80V, which is nearly one

order of magnitude higher than for the as grown sample.

Figure 4.19: Breakdown voltages vs net donor concentration of Schottky diodes on c-

GaN and c-AlGaN (full symbols) and h-GaN (open symbols).

Figure 4.19 shows the breakdown voltages VBD of Schottky diodes on c-GaN and

c-AlGaN plotted versus the net donor concentration of the semiconductor (full symbols).

The donor density (ND−NA) is measured either by CV or ECV. Also included in the

figure are experimental data obtained from h-GaN [67][68]. The lines in Fig. 4.19 are

calculated using a model for the relation between VBD and the net donor concentration

[66]. Using this model the breakdown voltage VBD is given by

VBD[V] = 3.5∗1010(cm1.5

V)∗ND[cm−3]−0.5(4.33)

Our experimental data clearly follow the trend of increasing VBD with decreasing donor

concentration. However, all experimental values of VBD are one-third smaller than the

calculated values. We suggest that the TSB leads to premature breakdown. Our in-

terpretation is supported by experimental data obtained with c-AlGaN/GaN Schottky

4.3 Breakdown Voltages of Schottky Diodes

diodes (full squares) where an even larger difference between experimental and calcu-

lated data is observed. We suppose that this difference is to a high oxygen concentration

in the TSB region. In case of the annealed sample the breakdown voltage of 80V fits

very well to the prediction by the theoretical calculation. We believe that the effect of

compensation of the donors prevent the premature breakdown.

5 Photoconductivity in GaN based

Schottky diodes

In order to investigate the suitability of c-GaN for photodetector applications, a 750nm

thick c-GaN layer is deposited directly on freestanding 3C-SiC at a substrate tempera-

ture of Tsubs = 720◦C(GNS1382). A schematic sketch of the sample structure is given

Figure 5.1: Experimental setup for the investigation of the photoconductivity: a) sample

structure b) contact arrangement.

in Fig. 5.1a.

The sample is cut into a piece of 5x10mm2and the electrical contacts were formed.

Firstly the Schottky contacts are generated. They are structured by photolithography

using a hole mask with a diameter of 1mm. Then the Ni was deposited by thermal evap-

oration under UHV conditions using a thickness of t=12nm. The thickness is selected

in that way that due to the optical absorption coefficient of Ni (α= 9.489 ∗107m−1),the

thickness guarantees a high transmittivity (about 32%) as well as the high mechanical

inertness and electrical conductivity. The ohmic contact for the test of the Schottky

diodes are made of In pads with a size of 1x5mm2which are realized by soldering tech-

nique at the edges of the sample (see also Fig. 5.1b).

Before the sample is exposed with light in order to exhibit the generation of a photon

induced current, it has to be proved that the contacts for the MSM show Schottky char-

acteristics, so the sample is firstly mounted into the IV measurement setup. Both Ni

contacts are connected to the positive potential and the In pads are connected to the

negative potential. The Fig. 5.2 depicts the result of the measurement taken at room

temperature for a voltage between -5 and +5V. The current density is plotted vs. the

bias voltage in a linear scale. A clear rectifying characteristics under reverse bias was

Figure 5.2: IV curves of the Schottky contacts on a 750nm c-GaN measured (GNS1382)

at T=300K.

observed having a current of 4Acm−2at a voltage of -5V for both contacts, whereas in

forward direction the current reaches a value of 66Acm−2for contact 3 and 40Acm−2

for contact 2 at a forward voltage of +5V. The differences in the forward characteristics

have their origin in the additional series resistance (longer distance Ni(2)-In(4) contact

than Ni(3)-In(4)) for the second diode. Additional a clear Schottky barrier of 0.5V is

measured in both cases by the built-in voltage.

In the next step the IV characteristics between both Ni contacts is measured in order to

investigate the dark current behaviour of the structure in the voltage range between -5V

and +5V. So it was able to measure the reverse current of one of the Schottky diodes

in every direction due to the symmetric arrangement. In Fig. 5.3 the IV curve between

both Ni contacts (2)-(3) is plotted versus the bias voltage in the range of -5V to +5V.

The curvature of the IV curve is symmetric. In the case of positive potential the current

increases up to 4Acm−2at a voltage of +5V and on the other side we have -3Acm−2

at a negative potential of -5V. The measured current density fits very well to results

of the reverse current of the Schottky diodes obtained from Fig. 5.2. So the principle

operation of the structure is given due to the Schottky characteristics of the Ni contacts

and the symmetry in their IV curve.

In order to investigate the properties of c-GaN as photodetector material, the sample

has to be irradiated with light. The influence on the electrical properties of the c-GaN

can be investigated using two different methods. This can be realized in to ways. The

5 Photoconductivity in GaN based Schottky diodes

Figure 5.3: IV curve of the Ni Schottky contacts (2)-(3) on a 750nm c-GaN (GNS1382)

measured at T=300K.

current can be measured as a function of the wavelength for a fixed bias voltage or as a

function of the bias voltage for a fixed wavelength, which is the so-called photoresponse.

The second possibility is easier to realize, because this can investigated using the PL

setup. The measurement has to be done in the darkness and then repeated under the

irradiation of light using a excitation energy which is above the bandgap of GaN in

order to guarantee photon absorption. The effective photo current is calulated as the

difference of the light and the dark IV curves.

The Fig. 5.4 illustrates the results of the two measurements. Here the current density

is plotted as function of the bias voltage between -5 and +5V in a linear scale. The open

circles represent the values for the measurement in the darkness, and the full squares

show the values for the analysis under light illumination. Again a symmetric behaviour

is observed in both cases for the IV curves and in case of irradiation the current is much

higher than under dark conditions, caused by a reduction of the serial resistance under

illumination. The change in the serial resistance is due to the influence of the photoin-

duced current. The serial resistance RSis determined by the resistivity of the c-GaN.

From equation 3.10 it is known, that the resistivity is proportional to the free carrier

concentration n. So a decrease of RSwill lead to an increase of n, which are generated

by the absorption of the laser light. At +4V the dark current is about 4Acm−2and

under illumination about 6Acm−2. In contradiction to the theory of Schottky diodes

the dark current of the structure is much higher (see chapter 4.1). Normally it is given

Figure 5.4: Comparison of the IV curve measured in the darkness (open circles) and

under illumination (full squares) of the structure (GNS1382) excited with

P=4.5mW at λ= 325nm.

by the reverse saturation current of a Schottky diode:

IS=A?

nT2exp(−eΦbn

kBT) (5.1)

For the given structure it should be in the order of 10−10Acm−2which is a deviation

of eleven orders of magnitude lower than the experimental data. The strong deviation

origins from the presence of defects in the structure which results in a high leakage

current. Details of this mechanism and how it can be controlled are given in chapter 4.2.

For a more quantitative analysis of the photo current the results of both measurements

are subtracted and plotted in a semilogarithmic scale in Fig. 5.5. The effective photo

current shows also a symmetric behaviour as function of the bias voltage. An interesting

point is the saturation effect at a current of 2Acm−2. This saturation starts at a bias

voltage of about 1.4V and it is limited due to the power of the light source. A further

increase of the bias does not increase the photocurrent. This value is not comparable to

the built-in potential of 0.5V. The further increase of the current at bias voltages above

the built-in potential seems to be caused by the generation of electron-hole pairs in the

metal contacts.

From the measured current and the known excitation power, a very rough calculation

of the efficiency of the diode could be done.

The current of 2Acm−2is equal to a carrier flow of 1.3∗1016s−1and the excitation power

5 Photoconductivity in GaN based Schottky diodes

Figure 5.5: Effective photo current of the MSM structure measured at T=300K.

of 4.5mW from which 80% are coupled into the semiconductor due to the difference in

the refractive indices are equal to 7.4∗1015s−1of photons. Assuming that each photon

generates one elctron-hole pair and both carrier types have the same amount on the

photocurrent, the efficiency is nearly 100%. Thus the saturation of the photocurrent

can be explained by the excitation of all carriers.

6 AlGaN/GaN based field effect

transistors

6.1 Structure and band diagram

Transistor structures are the most important devices in modern computer and telecom-

munication systems. Typical bipolar transistors (npn) were used since their develope-

ment in 1947 by Bardeen et. al. . This transistors use the 3-dimensional mobility of

both carrier types (electrons and holes) for the operation. Therefore their operation

speed is limited by the carrier type, which has the lower mobility. Today they are more

and more replaced by field effect (FET) transistors like a metal-insulator-semiconductor

FET (MISFET) or metal-oxide-semiconductor FET (MOSFET). One of the advantage

of the FETs is firstly, that they are unipolar devices. They use only one type of carrier

for current transport, especially electrons due to their higher mobility. At second their

current channel can easily be controlled by a gate bias and their realization is easier. In

the channel a 3DEG or 2DEG is located. A disadvantage is that the operation speed

suffers from the scattering of the electrons at surface defects of the semiconductor or at

their ionzed donor states. An improvent of the FETs are the modulation doped FET

(MODFET) or heterojunction field effect transistor (HFET), also called high electron

mobility FET (HFET or HEMT). These structures use in genaral the mobility of a

2DEG, but it is shifted from the surface to the interface of a heterojunction, which

prevents the scattering at the surface defects. But the most important feature is, that

modulation doping allows the spatial separation of carriers and impurities, so that im-

purity scattering do not occur(see chapter 2.3.3). This results in much higher operation

speed in comparison to all other transistors.

The basic feature of a HFET consists of a simple AlGaN/GaN heterostructure, in which

the 2DEG is located at the AlGaN/GaN interface. In order to get a high performance

of the device the two materials have to join perfectly in an ideal heterostructure. It is

quiet difficult to realize this, but heterostructures offer the opportunity to manipulate

their behaviour of carriers through bandgap engineering [71].

In general it means to control the band offsets of both materials at the heterointerface.

In case of group-III nitrides the band offsets can be changed by the variation of the Al

mole fraction in the AlGaN barrier. The total bandgap of AlxGa1−xNis given by the

linear interpolation of the c-GaN and c-AlN gap [72]:

Eg,AlGaN = (3.2+1.85x)[eV ] (6.1)

The band offsets of the conduction and valence band are calculated using an empirical

equation which sets 65% of the total bandgap discontinuity to the conduction band and

6 AlGaN/GaN based field effect transistors

35% to the valence band [50].

The operation of an HFET depends mainly on free carrier transport parallel to the

heterojunction. The obvious way of introducing carriers, used in classical devices, is to

dope the regions where the electrons or holes are desired. Unfortunately, charged donors

or acceptors are left behind when electrons or holes are released, and scatter the carriers

through their Coulomb interaction (ionized impurity scattering). The solution for the

appearing problem is the remote or modulation doping, where the doping is grown in

one region but the carriers subsequently migrate to another. In connection with the

conduction band discontinuity two things occur: First the electrons from the modula-

tion doped layer are trapped into a roughly triangular potential well, and prevents the

electric field from returning the electrons to their donors. The dimension of the well

is typically less than 10nm, and the levels for motion along the growth direction are

quantized in a way similar to those in a square well. With propriate doping only the

lowest level is occupied and all electrons are free in motion parallel to the interface. This

is the two-dimensional electron gas and the basis for the majority of electronic devices in

heterostructures. The separation of carriers and impurites allows higher mobility due to

the reduction of scattering mechanism. For device operation the density of a 2DEG can

be controlled, as in a MOSFET, applying a gate voltage by a Schottky contact. Adding

ohmic source and drain contacts completes the FET. This is called a modulation doped

FET (MODFET) or HEMT.

A simple structure for a high-speed device based on c-AlGaN/GaN is shown in Fig.

Figure 6.1: Schematic drawing of a AlGaN/GaN based HEMT device.

6.1. The structure is typically grown on freestanding 3C-SiC at a substrate temper-

ature of T=720◦C. A GaN buffer layer reduces the defect density and prevents the

drift of carriers to the conducting substrate [73]. The thickness is typically in the order

of 600nm-1000nm. The heterointerface is formed by depositing an AlGaN film with a

thickness of 20nm-40nm on top of the GaN. The thickness of the barrier is choosen in

6.1 Structure and band diagram

that way, that the residual doping level prevents parallel conductivity in the barrier.

The Al mole fraction is varied between x=0.2 and 0.5 to study the dependence of the

behaviour of the 2DEG on the shallow doping concentration and the depth of the po-

tential well. The structure is capped by an GaN layer with a thickness between 0nm

and 20nm in order to guarantee the formation of a Schottky barrier on the low doped

GaN. No intentional doping is used in our structures. The unintentional doping levels

are n= 1 ∗1017cm−3for the GaN and n= 2 ∗1018cm−3for the AlxGa1−xN(see chapter

3.3). The gate contact is realized by thermal evaporation of Ni (see also chapter 4) and

the source and drain consists of pure In (chapter 4)[6].

Considering a junction between n+-AlGaN (material A) and n-GaN (material B), the

Figure 6.2: Steps in the construction of the band diagram for a doped AlGaN and GaN

heterojunction.

Fig. 6.2 illustrates the principle for sketching the band diagram. An accurate treatment

requires a self-consistent solution of Poisson equation for the electrostatic potential and

Schr¨odinger equation for the wave function and the quantized states, with the Fermi-

Dirac distribution describing the occupation of the levels.

•Starting with flat bands in each material, with the band in their natural alignment

and the Fermi levels set by the doping on each side. This gives the position of the

Fermi level far from the junction. To cancel out the effect of the discontinuities

6 AlGaN/GaN based field effect transistors

temporarily, we draw lines on side A at ¯

C=EA

C−∆ECand ¯

V=EA

V+ ∆EV.

Note that ¯

C−¯

V=EB

C−EB

V, so that the effective band gap is the same on both

sides.

•The next step is the alignment of the Fermi levels. The difference far from the

junction is set by any applied voltage. We assume that there is a positive bias V

applied to side B, so that EA

F−EB

F=eV .

•Next one has to join ¯

Cto EB

Cand ¯

Vto EB

V, with parallel curves due to the

electrostatic potential, for a qualitative picture a S-shape curve whose curvature

is set by the sign of the charge density is useful.

•At last EA

Con side A as a line at ¯

C+ ∆ECand EA

Vat ¯

V−∆EVis restored,

including the discontinuities in ECand EVat the junction.

The recipe creates a very rough picture for the band diagram of an heterojunction. For

detailed and quantitative analysis it is necessary to solve the Poisson and Schr¨odinger

equation in a self consistent way.

The numerical solution of both equations are generated by a commercial reliable com-

Figure 6.3: Band diagram of a AlGaN/GaN based HEMT device calculated with the 1D

Poisson program for a temperature of 175K.

puter program called 1D-Poisson [74], which regards a set of material parameter like

band gap energy, band offset, effective masses, doping,.... This program calculates the

band diagram as well as the distribution of electrons and holes, the wave function and

6.1 Structure and band diagram

also the energy level of the quantized states in the channel. Fig. 6.3 illustrates the

result near the AlGaN/GaN interface calculated for the structure in Fig. 6.1 using a

temperature of T=150K. This temperature of 150K is choosed in order to compare the

calculation with experimental data. For the calculation the thicknesses given in the

figure and the material constants given in chapter 2.1 are used. For the doping levels

a value of 1 ∗1017cm−3for the GaN and 2 ∗1018cm−3for the AlGaN is assumed (see

chapter 3.3). The Fermi level (grey line) is set to zero as a definition, the black solid line

represents the curvature of the conduction band around the AlGaN/GaN interface in the

depth of 60nm from the surface. A spike with a height of 300meV above EFis formed

on the AlGaN side. The channel at the GaN side is created by decreasing the band edge

110meV below the Fermi level for a depth between 60nm and 66nm. The band edge

increases again above the Fermi level with a distance of a few meV for depths above

66nm. The distribution of the carrier concentration (dashed line) shows the opposite

behaviour. Whenever the band edge increases, the carrier concentration decreases. The

most remarkable point is the strong increase of the concentration at the position of the

channel up to 1 ∗1019cm−3.

The possibility to calculate the properties of the heterostructures allows to design and

optimize the structure prior to growth. The following diagrams illustrate the dependence

of the 2DEG density and the parallel conductivity in the AlGaN barrier on the barrier

height, doping concentration of the barrier and barrier thickness. For an optimized de-

sign the conductivity of the 2DEG is much higher than that of the AlGaN layer.

The Fig. 6.4 shows the calculated sheet carrier concentration of the 2DEG (circles) and

Figure 6.4: Sheet carrier concentration of the 2DEG and the residual carrier concen-

tration of the AlGaN barrier as function of the Al mole fraction x for a

temperature of 300K.

6 AlGaN/GaN based field effect transistors

the residual sheet carrier concentration (squares) of the AlGaN barrier as function of the

Al mole fraction x for a temperature of 300K. The barrier thickness is set to a value of

t=20nm and the donor concentration in the AlGaN barrier is fixed at ND= 1∗1019cm−3.

This value is above the typical background doping concentration of the AlGaN and sim-

plifies the influence of the Al mole fraction on the carrier concentration (see chapter

3.3). For the GaN a constant background doping of ND= 1 ∗1017cm−3is used. The

Al mole fraction x is varied between 0 and 1. In case of x=0, we have a GaN/GaN

structure, which can not form a 2DEG channel. For a AlN/GaN heterostructure the

quantum confinement in the channel is so strong, that the energy of the ground state

is above the Fermi level and therefore it is not occupied with carriers. If an Al content

of x=0.1 is used, a flat channel with a sheet carrier density of n2DEG = 1.5∗1012cm−2

is formed, whereas the concentration in the barrier reaches nearly the same value with

NAlGaN = 1.4∗1012cm−2. With increasing Al mole fraction the depth of the channel

becomes deeper, and therefore the number of electrons in the channel increases linearly

up to n2DEG = 6 ∗1012cm−2for an Al content of x=0.9. On the other hand the residual

concentration in the barrier is nearly independent on the Al content. A possible reason

is the prevention of carrier diffusion into the channel due to the increasing electric field.

A further parameter which has a strong influence on the parallel conductivity in the

Figure 6.5: Sheet carrier concentration of the 2DEG and residual carrier concentration

of the AlGaN barrier as a function of the AlGaN donor concentration for a

temperature of 300K.

barrier, is the doping concentration of the barrier itself. Figure 6.5 shows the depen-

dence of the carrier concentration in the channel (circles) and the barrier (squares)

for a AlGaN doping level between 1018cm−3and 1020cm−3. The other parameters are

6.1 Structure and band diagram

set constant with x=0.3 for the Al content and t=40nm for the thickness of the bar-

rier. In this case the density of the 2DEG increases from n2DEG = 1.5∗1012cm−2to

n2DEG = 4.3∗1012cm−2, but with a slope<1. This is due to the maximum filling of the

channel with carriers. It can be confirmed by the observation that the residual carrier

concentration in the barrier increases more rapidly.

At last we want to study the influence of the variation of the barrier thickness on

Figure 6.6: Sheet carrier concentration of the 2DEG and the residual carrier concentra-

tion of the AlGaN barrier as a function of the AlGaN barrier thickness for a

temperature of 300K.

the parallel conductivity. The results are depicted in Fig. 6.6. For the calculation

an AlGaN barrier with a mole fraction of x=0.3 and a doping of ND= 1 ∗1019cm−3

is used. The density of the 2DEG is independent on the barrier thickness and only

determined by the complete filling of the channel, which is influenced by the Al con-

tent. However, the carrier concetration increases linear from NAlGaN = 3.6∗1011cm−2

to NAlGaN = 1.6∗1013cm−2if the thickness is varied from 10nm to 100nm. The carrier

concentration in the barrier is determined by the difference between the doping concen-

tration and the number of carriers which diffuse into the channnel. Therefore at high

thicknesses of the barrier the amount of diffused carriers is neglectable and the sheet

carrier concentration is direct proportional to the thickness. Above a thickness of 50nm

the carrier concentration in the barrier is significatly higher than in the channel.

In summary the optimal AlGaN/GaN heterostructure consists of an Al0.3Ga0.7Nlayer

with a thickness of tAlGaN =20nm a doping of ND,AlGaN = 2 ∗1018cm−3.

6 AlGaN/GaN based field effect transistors

6.2 Optical properties

Photoluminescence (PL) spectroscopy is a nondestroying and very sensitive methode

to investigate the optical properties of semiconductor heterostructures. It offers the

possibility to vary the temperature as well as the excitation intensity. Furthermore it

can be used as a depth sensitive probe if the sample structure changes.

Due to the high absorption coefficient of α= 1.07 ∗107m−1for the cubic group-III

nitrides the penetration depth of our HeCd laser is about 300nm. If the thicknesses of

the different layers are carefully adjusted, one can investigate the spatial origin of the

optical transitions by performing PL measurements on different structures.

Therefore three different structures are grown and measured by PL at a temperature

Figure 6.7: Photoluminescence spectra of different structures measured at T=2K. a)

pure GaN-layer, b) Al0.2Ga0.8N/GaN heterostructure, c) pure Al0.2Ga0.8N

layer.

of T=2K with an excitation power of 20Wcm−2. Figure 6.7 shows the structures of the

samples on the left side. On the right side the corresponding PL spectra are plotted. The

luminescence of the DAP is normalized to one and the spectra are linearly shifted for

a better overview. Figure 6.7a exhibits schematically the penetration of the laser beam

into a 1000nm thick unintentionally doped c-GaN layer. The corresponding PL spectrum

shows the typical transitions of c-GaN [75]. The bound exciton transition at an energy

of EX= 3.268eV and the donor acceptor pair recombination at EDAP = 3.134eV are

clearly observed. In Fig. 6.7b the PL spectrum of an Al0.2Ga0.8N/GaN heterostructure

6.2 Optical properties

with an AlGaN layer thickness of 100nm is shown. An important note is, that the

AlGaN thickness is below the penetration depth of the laser. Therefore the two bulk c-

GaN related transtions X and DAP are observed. However no AlGaN related transition

is observed, which should be at EAlGaN = 3.570eV . In this spectrum an additional peak

at an energy of E=3.247eV is found. This belong neither to the bulk GaN comparing

to Fig. 6.7a, nor to the AlGaN bulk material as shown in Fig. 6.7c. In Fig. 6.7c the

excitation of an Al0.2Ga0.8Nlayer with a thickness of 700nm (>>penetration depth)

is drawn. The corresponding PL spectrum shows only a transition with an energy of

E=3.552eV. Taking into account that Eg,AlGaN =3.2+1.85*x[eV] [72], the energy of the

transition fits very well to the band gap of Al0.2Ga0.8N. In conclusion, an additional

transition measured at 3.247eV that belongs to a 2DEG located at the interface between

AlGaN and GaN.

In order to investigate the nature of the transition and to see if it could really origin from

a 2DEG, the band diagram of the measured AlGaN/GaN heterostructure was calculated.

The structure is similar to that drawn in Fig. 6.1. In detail two quantized states in the

channel are formed, but only the first sub band is below the energy of the Fermi level.

For the second one the energy is above the Fermi edge,and therefore unoccupied. The

localization energy of the first subband is about 51meV, so that the transition energies of

two possible transitions can be calculated as follows: For the optical transiton from the

2DEG state to the valence band E2DEG =Eg,GaN +Eloc=3.302eV+0.051eV=3.353eV,

and from the 2DEG state to the acceptor level its about E2DEG =Eg,GaN −EA+

Eloc=3.302eV-0.110eV+0.051eV=3.243eV. These are the maximum and the minimum

energy for the transition energy of the 2DEG. So the measured value of E2DEG = 3.247eV

fits well to the calculated data. Transitions within this energy range are allowed. From

the AlGaAs/GaAs system it is well known, that the so called H-band transition are not

vertically in the k-space [76].

To confirm the attribution to the emission of an 2DEG, the dependence of the 2DEG on

different parameters was investigated, like the depth of the channel (by the Al content

x) or the background doping in the GaN, as well as the dependence on the temperature,

excitation power or an electric field.

Figure 6.8 illustrates the influence of the Al content x of the barrier on the transition

energy of the 2DEG measured at a temperature of T=2K with an excitation power of

20Wcm−2. The intensity of the excitonic transition is normalized to one and the spectra

are shifted for a better overview. The excitonic transition of c-GaN was observed at

an energy of EX= 3.268eV for each structure, as well as the donor-acceptor related

transition located at EDAP =3.134eV. This confirms the constant background doping in

the GaN layer and excludes the influence of this parameter on the transition energy of

the 2DEG. If the Al mole fraction is varied from x=0.25 (squares)(GANS1228), where

the 2DEG transition is observed at an energy of E2DEG=3.258eV, to x=0.30 (open

circles)(GANS1239) the energy shifts downwards to E2DEG=3.228eV. The shift of the

2DEG transition is 30meV, whereas the change in the band gap of AlGaN is about

92meV. The same behaviour is found for the increase of the Al content up to x=0.35

(full circles)(GANS1384). Here the transition energy changes

6 AlGaN/GaN based field effect transistors

Figure 6.8: Photoluminescence spectra of AlxGa1−xN/GaN heterostructures with Al

mole fractions of 0.25, 0.30 and 0.35 measured at T=2K.

Figure 6.9: Photoluminescence spectra of Al0.35Ga0.65N/GaN heterostructures with dif-

ferent background doping concentrations of ND= 1∗1017cm−3(GANS1384)

(open circles) and ND= 1 ∗1018cm−3(GNP1429) (full circles) measured at

T=2K.

6.2 Optical properties

down to E2DEG=3.200eV. The discrepancy occurs due to the quantum confine-

ment of the electrons in the channel. If the depth of the channel is increased by 92meV,

which should reduce the transition energy of the 2DEG in the same range, the ground

state energy of the subband increases due to the increasing confinement. In summary

the effective energy shift is smaller than the band edge variation. It is quite difficult to

find a quantitative model for the dependence due to the indirect nature of the transition,

and therefore it will not discussed here.

One of the important parameters is the background doping of c-GaN buffer. With run-

ning time the efficiency of the chemical purifiers degradates and the background doping

increases due to the increasing contamination with oxygen (see chapter 4.2). Figure

6.9 shows the photoluminescence of two samples consisting of an Al0.35Ga0.65N/GaN

heterostructure. The excitonic transition from the c-GaN buffer at E=3.268eV can be

as well observed as the donator acceptor pair recombination at 3.132eV for the low

doped sample GANS1384 (open circles) and E=3.157eV for the higher doped GNP1429

(full circles). From the structural similarity of both samples one can conclude, that the

measured shift of the DAP transition is due to the change in the background doping

level. This shift is equal to a change in the unintentionally doping concentration from

n= 1017cm−3(GANS1384)(open circles) to 1018cm−3(GNP1429)(full circles). The ef-

fect of this higher doping level on the transition energies of the H-band (2DEG) is a shift

to lower energies. For the low doped sample the transition is located at E2DEG=3.204eV

whereas for the higher doped one a energy of E2DEG=3.178eV is measured. The shift

of the 2DEG transition due to the change of the band bending at the AlGaN/GaN het-

erointerface. Figure 6.10 illustrates the principle. For a low doping level the difference

Figure 6.10: Principle of the change in the band bending at the heterointerface due to

the change in the c-GaN background doping

between the conduction band ECand the Fermi level EFis relatively huge. This results

6 AlGaN/GaN based field effect transistors

in a strong bending of the GaN conduction band at the interface and in a high ground

state energy of the 2DEG level as shown in the left side of Fig. 6.10. If the doping level

increases, the distance between ECand EFdecreases. This leads to a reduction in the

bending of the conduction band of GaN and a wider potential well with a lower ground

state energy. This reduces in total the transition energy of the 2DEG.

Next the temperature and intensity dependence of the 2DEG transition is studied. The

Figure 6.11: PL spectra of a Al0.35Ga0.65N/GaN heterostructure (GANS1384) measured

at different temperatures between 2K and 300K.

variation of temperature allows the determination of the activation energies of the levels

which cause the transitions. For the analysis the temperature is varied between 2K and

300K using an excitation power of P=20Wcm−2. Figure 6.11 shows the PL spectra of

aAl0.35Ga0.65N/GaN heterostructure (GANS1384) measured at different temperatures

between 2K and 300K. The excitonic transition is normalized to one and the spectra

6.2 Optical properties

are shifted linearly for a better overview. The dotted line represent the measurement

done at T=2K. Here one can clearly observe two DAP and X transitions as well as the

2DEG related one. The DAP1 transition is located at an energy of 3.076eV and the

DAP2 at 3.127eV. With increasing temperature a suppression of the DAP2 is observed

at a temperature of 80K due to the thermalization of the level, the DAP1 transition

with the lower energy indicating a higher ionization energy shows the thermalization at

temperatures of 200K. Additionally a suppression of the DAP2 and 2DEG intensity is

found in comparision to the X transition, which is a hint for a thermalisation of these

levels. But the reduction in intensity of the DAP2 and 2DEG continious. At room

temperature only the X transition of GaN is observed.

The energy positions of the exciton, donor-acceptor-pair recombination and the 2DEG

transition of a Al0.35Ga0.65N/GaN heterostructure (GANS1384) are depicted in Fig.

6.12 for temperatures between 2K and 300K. The solid line describes the behaviour of

Figure 6.12: The peak position of the X, DAP1, DAP2 and the 2DEG correlated tran-

sition for temperatures between 2K and 300K for a Al0.35Ga0.65N/GaN

heterostructure (GANS1384).

the band gap energy as function of temperature using the equation of Varshni et al. [77]

Eg(T) = Eg(0) −αT2

T+β(6.2)

where Eg(0)=3.302eV , α= 6.697∗10−4eV K−1and β=600K. The dashed line is the gap

energy minus the exciton binding energy of 19meV [18]. The behaviour of the DAP2

6 AlGaN/GaN based field effect transistors

recombination is given by the difference of the gap energy and total activation energy

of the donor and the acceptor. For the donor a value of 55meV (O2) [49] and for the

acceptor 110meV [18] was used. A temperature dependence of 0.5kT is added. The

DAP1 transition is described by a donor activation energy of 20meV [18] and a acceptor

energy of 210meV. The excitonic transition (full squares) shows a temperature indepen-

dent transition energy up to 120K due to a strong localisation, may be related to an

impurity. At values above 120K the position follows very well the gap like behaviour.

In contradiction to the band gap energy, the 2DEG transition (open squares) shows no

shift in the observed temperature range. This is influenced by two effects which act in a

contradictional way. On the one hand the energy is lowered by the lowering of the GaN

band gap and on the other hand the transition energy is increased due to the change of

the Fermi level and the occupation of higher states with increasing temperature. The two

DAP transition, which were observed in the spectra show both a bandgap-like behaviour.

They have their origin in the incorporation of oxygen (DAP2) and carbon (DAP1). The

presence of the carbon related transition is may caused by memory effect of carbon. An

Figure 6.13: The normalized PL intensity of the X, DAP and the 2DEG correlated

transition for excitation power between 0.2Wcm−2and 20Wcm−2of a

Al0.35Ga0.65N/GaN heterostructure (GANS1384).

additional hint for the existence of a 2DEG is the shift of the transition energy using dif-

ferent excitation power [76]. In Fig. 6.13 different PL spectra are plotted in the energy

6.2 Optical properties

range from 3.15eV to 3.3eV for the Al0.35Ga0.65N/GaN heterostructure GANS1384. The

excitation power of the laser is varied between 0.2Wcm−2and 20Wcm−2by inserting

UV-neutral density filters into the excitation beam. The temperature is set to T=2K.

The spectra are normalized to one and they are linearly shifted for a better overview.

With increasing excitation power the 2DEG transition shows a clear blue shift, whereas

the energy of the X transition is independent on the power. Fig. 6.14 depicts the energy

Figure 6.14: The peak position energy of the 2DEG related transition for excitation

power between 0.2Wcm−2and 20Wcm−2for GANS1384

position of the 2DEG transition vs. the excitation power in the range from 0.2Wcm−2

to 20Wcm−2. A logarithmic increase of the peak position with increasing excitation

power from a value of 3.197eV at a power of 0.2Wcm−2to 3.207eV at 20Wcm−2is

observed. A logarithimic fit reveals a shift of 3.3meV/decade. This effect is attributed

to the recombination of electrons trapped in the potential notch next to the interface

caused by the band-bending with free holes in the valence band at some distance away

from the heterointerface. The power dependence of the emission energy is explained

as a result of photoexcited carrier screening of the built-in heterointerface field. This

screening drives the band structure flat band and causes a blue-shift of the emission

energy, which is proportional to the logarithm of the excitation power [76].

A direct experimental proof of this assignment to an H-band like transition is obtained

by applying a weak electric field parallel to the growth direction. Such experiments were

performed by applying an electric field parallel to the growth direction via a semitrans-

parent Ni-Schottky contact at a temperature of T=2K. On top of a Al0.27Ga0.73N/GaN

heterostructure (GANS1228) layer a Ni contact with a thickness of 4.5nm is deposited,

6 AlGaN/GaN based field effect transistors

Figure 6.15: The peak position energy of the 2DEG related transition for applied voltages

between -1.5V and +1.5V for GANS1228

using a contact size of 4x4mm2. The thickness allows, that 70% of the laser light are

coupled into the layer and 70% of generated luminescence is transmitted. In comparision

to an ungated structure we loose 70% ∗70% = 50% of intensity. The contact size allows

the lateral adjustment of the laser beam on the sample surface on a useful position.

The Fig. 6.15 shows the energy position of the 2DEG as function of the applied electric

field. The solid line in the figure is a guide for the eye. A clear blue shift in the energy

position of 4 meV is observed by changing the bias voltage from -1.5V to 1.5V. The shift

of the transition energy can be explained by the variation of the band structure due to

different applied external voltages. The shape and the depth of the potential well will

change, which results in a shift of the quantization energy of the 2DEG.

6.3 Electrical properties

The determination of the electrical properties is the main issue in the investigation of

electronic devices. This chapter will focus on the electrical properties of our AlGaN/GaN

heterostructures grown on free-standing 3C-SiC and on carbonized Si wafer. A scematic

sketch of the samples, which were characterized, is drawn in Fig. 6.16. On top of a

3C-SiC layer a 1000nm thick c-GaN layer is deposited, followed by c−Al0.35Ga0.65N

layer with a thickness of 40nm. The structure is capped by GaN film using different

thicknesses ranging from 0nm to 20nm. For the whole structure no intentional doping is

used, resulting in a doping level of the GaN of about n=1 ∗1017cm−3and of the AlGaN

n=2 ∗1018cm−3, respectively. In order to apply an electric field, pure In is used as the

6.3 Electrical properties

Figure 6.16: Schematic drawing of the AlGaN/GaN heterostructure.

ohmic contact on top of the SiC layer, fixed by micro soldering. The Schottky contact

is realized by Ni/In contact with a diameter of 300µm, consisting of a 50nm thick Ni

layer and a 150nm thick In film.

A tip prober from S¨uss Microtech, Model PM5 is used for contacting the samples in

order to perform I-V and C-V analysis at room temperature.

6.3.1 I-V and C-V analysis

Figure 6.17 shows the I-V curves for the Al0.35Ga0.65N/GaN heterostructures with dif-

ferent cap layer thickness of 5nm (GANS1356)(triangles), 10nm (GANS1357)(squares)

and 20nm (GANS1352)(circles). The samples are grown on carbonized Si substrates

[79]. The measurements are performed at room temperature in the voltage range from

-3V to +3V. Only for the sample GANS1352 with the cap thickness of 20nm we observe

a nonlinear I-V curve. The curve indicates a barrier height of 1eV, which is nearly 0.3eV

higher in comparison with pure GaN on freestanding SiC. This may be related to the

higher band gap of the AlGaN layer, which forms a higher barrier. The samples with the

thinner GaN cap layer reveal a linear dependence between the voltage and the current.

This dependence can be explained by the surface RMS roughness. In Fig. 6.18 a

scematic sketch of the interface region between the AlGaN and the GaN cap layer and

the Pd Schottky contact is drawn. If the cap layer thickness is larger than the surface

roughness, the highly doped AlGaN is fully covered by the GaN and the Pd covers the

whole GaN surface. This results in a nonlinear I-V curve, comparable to the results on

thick GaN (see chapter 4). But if the cap layer thickness is below the RMS roughness,

there are still some areas of AlGaN, which are not covered by GaN, and for that the

Pd is deposited directly on the AlGaN. The doping concentration of the AlGaN favours

6 AlGaN/GaN based field effect transistors

Figure 6.17: Current-Voltage characteristic of Al0.35Ga0.65N/GaN heterostructures with

different GaN cap layer thickness of 5nm (GANS1356)(triangles), 10nm

(GANS1357)(squares) and 20nm (GANS1352)(circles).

Figure 6.18: Influence of the RMS roughness on the electrical behaviour of heterostruc-

tures with different cap layer thicknesses.

6.3 Electrical properties

the formation of a Schottky contact with a very thin barrier, which can be tunneled at

nearly 0V, comparable to an ohmic contact. In case of this series of samples the doping

in the AlGaN may slightly higher than in the case of the AlGaN/GaN Schottky diodes

described in chapter 4.1. So the semiconductor is maybe degenrated, when the doping

concentration is above the effective density of states. The AlGaN/GaN Schottky diodes

are directly grown after the renewing of the nitrogen purifiers, whereas the structures

with the cap layers are realized nearly one year later, equal to a degradation in the

purifier efficiency.

A very simple method to investigate the doping concentration as function of the dis-

Figure 6.19: Capacity-Voltage characteristics of the Al0.35Ga0.65N/GaN heterostructure

(GANS1352) at temperatures of 300K, 175K and 150K.

tance from surface of Schottky diodes is the measurement of the capacitance voltage

(C-V) dependence. In Fig. 6.19 the C-V characteristics of GANS1352 is plotted for

different temperatures of 300K (circles), 175K (squares) and 150K (triangles). For the

measurement at 300K the curve shows a three-dimensional dependence on the voltage,

i. e. a parabolic shape with a decrease in the capacitance from 230pF at 0V to 90pF at

-5V. For the lower temperature of 175K the behaviour changes dramatically. The ca-

pacitance decreases to 120pF at 0V and the slope is smaller than for room temperature.

If the temperature is decreased again to a value of 150K, the change continues. Between

a bias voltage 0V and -1V the capacitance is nearly constant at 95pF. Below -1V the

capacitance decreases again with a linear curve shape to a value of 55pF at a voltage

of -5V. The change in the slope of the capacitance at this temperature is a hint for a

6 AlGaN/GaN based field effect transistors

change in the carrier concentration at a certain distance from the surface [78]. In order

to investigate the carrier profile, the following assumptions are used:

The consideration of the depletion zone as a condensator with the size of the contact

area and the distance as the depletion width allows the determination of the doping level

versus the depth from the surface using the following relations:

The noncompensated impurity concentration can be calculated from:

ND−NA=−2

eA2d(1/C2)

(6.3)

were A is the area of the contact and the dielectric constant of the semiconductor. The

distance from the surface is derived by:

x=A

C(6.4)

where x is equal to the distance from the surface. From semiconductor theory it is known

with respect to charge neutrality condition, that the width of the depletion zones in the

different doped layer are inverse proportional to the doping level. So the total depletion

zone is nearly equal to depletion zone in the semiconductor. Using both equations the

Figure 6.20: Carrier concentration profile of the Al0.35Ga0.65N/GaN heterostructure

(GANS1352) at temperatures of 300K (circles), 175K (squares) and 150K

(triangles).

noncompensated donor profil is calculated and plotted in Fig. 6.20 for temperatures

between 300K and 150K. As one can see in the figure, the concentration profile at room

6.3 Electrical properties

temperature (circles) is nearly a constant value between 2.4∗1018cm−3and 8∗1017cm−3

for a distance from the surface between 20nm and 60nm. The increase of the concentra-

tion in direction to the surface is may due to the presence of surface donor states in the

AlGaN layer (see also chapter 4.2). At lower temperature of 175K (squares) the total

concentration decreases to 1.4∗1018cm−3due to the freeze out of free carriers at the

impurities in the bulk layer of AlGaN and GaN. If the temperature is lowered again to

150K (triangles) a dramatical change in the profile occurs. The profile shows a maxi-

mum concentration of 4.8∗1018cm−3at a distance from the surface of 60nm, whereas

the concentration in the other regions between 65nm and 90nm is about 8 ∗1017cm−3

and also for a depth less than 57nm. The shift in the position of the maximum of the

carrier concentration for 175K and 150K is caused by influence of the leakage resistance

on the capacitance measurement (see chapter 2.3.3). In Fig. 6.21 the comparison of

Figure 6.21: Experimental (full circles) and simulated (dotted line) carrier concentration

vs. the distance from the surface. The experimental data were calculated

from a CV measurement done at 150 K.

the simulated carrier profile (dashed line) in terms of the sheet carrier concentration

of the sample with the experimental data (circles) from Fig. 6.20 for a temperature of

150K is plotted. The simulated profile shows a maximum sheet carrier concentration of

3.5∗1012cm−2at a depth of 60nm which is correlated at the position of the AlGaN/GaN

interface and the formation of a two dimensional electron gas. The experimental data,

which we got from Fig. 6.20, reveal a sheet carrier concentration of 1.6∗1012cm−2. The

value of the concentration is estimated from the width of the electron distribution and

the peak electron concentration.

6 AlGaN/GaN based field effect transistors

6.3.2 Hall effect analysis

Figure 6.22: Structure and photograph of the AlGaN/GaN heterostructure which is used

for the Hall-effect analysis.

Due to the conducting nature of the freestanding 3C-SiC substrates it is not

possible to perform Hall-effect measurements on these sample, because the parallel con-

ductivity in the substrate is in the same order of magnitude than the conductivity of the

2DEG. In order to avoid this problem, some carbonized Si wafers from the University

of Ilmenau were used for the growth. They consist of a 395µm thick semiinsulating Si

wafer with a 3nm thick 3C-SiC layer on top of it [79]. On this substrate a AlGaN/GaN

heterostructure with a GaN buffer thickness of 1000nm is deposited followed by a 20nm

thick Al0.35Ga0.65Nfilm and capped with a GaN layer of 20nm. For Hall-effect analysis

the sample is cleaved into a piece of 5x5mm2and In metal is used as the ohmic con-

tact realized by microsoldering in van-der-Pauw geometry. A schematic drawing of the

structure and a photograph of the sample is shown in Fig. 6.22. The sample is mounted

into the cryostat and Hall effect measurements are performed in the temperature range

from 10K to 300K. The results of the analysis are plotted in Fig. 6.23. The left side

of Figure 6.23 shows the electron concentration of the Al0.35Ga0.65N/GaN (GANS1416)

heterostructure as function of the temperature in the range from 10K to 300K measured

for the total sample thickness of 1040nm. On the one hand the dependence of the car-

rier concentration looks like that for a bulk layer, because we observed a decrease from

n=1 ∗1019cm−3at room temperature to n=1 ∗1017cm−3at 10K. A detailed analysis

of the experimental data show, that the calculated concentration is above the effective

density of states NC= 9.6∗1017cm−3. So semiconductor is degenerated and has no tem-

perature dependence of the carrier concentration. With respect to this contradiction,

the free carrier concentration is the sum of carriers in the thin 3C-SiC layer, the GaN

buffer, the AlGaN and the 2DEG at room temperature. With decreasing temperature

the 3D related carriers freeze out and at a temperature of 10K only the carriers of the

2DEG can be observed. The measured concentration of n=1 ∗1017cm−3at T=10K for a

6.3 Electrical properties

Figure 6.23: Electron concentration and mobility of a Al0.35Ga0.65N/GaN heterostruc-

ture for various temperatures between 10K and 300K.

thickness of 1040nm can be converted to a carrier concentration of N2D= 1 ∗1013cm−2

in the 2DEG channel using N2D=n3D∗L, in with L is the width of the channel.

The evidence for the 2DEG in the structure is confirmed by the calculation of the mobil-

ity as function of temperature, like it is plotted in the right side of Fig. 6.23. A very low

mobility in the order of µ= 1cm2(V s)−1is observed for temperatures above 50K. If the

temperature is decreased, an increase of the mobility up to µ= 70cm2(V s)−1is found.

This temperature dependence is typical for a 2DEG system in which a spatial separation

between impurities and carriers is present, but nevertheless the value is rather low.

6.3.3 Theoretical description of carrier scattering

In order to find an explanation for the result, the influence of scattering on the motion

of carriers in a two-dimensional channel has to be discussed. The most reasonable

scattering mechanism in the group-III nitrides are acoustic phonon scattering, impurity

scattering, dislocation and interface roughness scattering [80], [81].

The mobility µof carriers in a semiconductor is calculated as

µ=e

m∗τtot (6.5)

where m∗is the effective mass of the electrons and τtot represents the total momentum

relaxation time, given by:

τtot

=X1

τi

(Matthiessen rule) (6.6)

6 AlGaN/GaN based field effect transistors

where τiare the relaxation times for the different processes, which can occur in a semi-

conductor. In contrast to a bulk semiconductor the scattering processes in 2DEG system

are quite different. The relaxation time in this case is the superposition of the relaxation

due to optical and acoustical phonon scattering and impurity scattering, which strongly

depend on the temperature, as well as scattering by alloy disorder (proportional to the

carrier density) and dislocation and interface roughness scattering. The relaxation time

τiis given by

τi=¯h

2π|< ki|Hi|kf>|2δ(ki−kf)(6.7)

where Hidescribes the Hamiltionian for the scattering process. From equation (4.42) one

can see, that the process with the smallest relaxation time dominates the total relaxation

time and the mobility. If an adequate description is found for the Hamiltonian of each

scattering process, one can calculate the mobility limited by each process.

The first scattering mechanism is the influence of acoustic phonons on the mobility.

Phonons can be described by a periodic pertubation of the semiconductor lattice. This

is done in an approximation of a harmonic oszillator, the Hamiltonian is given by:

|Hap|=|aceAl

V|ZBloch function dr3(6.8)

in which acis the deformation potential of the conduction band and Althe amplitude

of the harmonic oscillator which is equal to the change in the position of the conduction

band relative to the unperturbated crystal, and which is influenced by the absorption

or emission of a accoustic phonon. Alis given by

Al= ( N¯h

2Mωl

)0.5(emission) and Al= ((N+ 1)¯h

2Mωl

)0.5(absorption) (6.9)

describing the emission and absorption of a phonon. Due to the fact, that a crystal

consists of many oscillators the number N can be approximated by the average number

of phonons at a certain temperature T with respect to the Planck statistics. After

some transformations of the equation we can calculate the relaxation time of accoustic

phonons:

τap

=3a2

c(m∗kBT)3/2

2√2π¯h4c11

(6.10)

The equation shows that the mobility depends only on the temperature and is indepen-

dent on the sheet carrier concentration of the 2DEG. The Fig. 6.24 shows the mobility

limited by acoustic phonon scattering as function of the temperature in the range from

1K to 300K. As one can see in the figure, the mobility is limited by phonon scattering

to µ= 4 ∗106cm2(V s)−1at room temperature and exhibits a strong increase by orders

of magnitude to µ= 6 ∗108cm2(V s)−1at T=10K.

The next parameter, which can have an influence on the carrier mobility, is the scat-

tering at ionized impurities. Especially in the case of our GaN, which has a relativly

high impurity level of ND= 1 ∗1017cm−3, a strong influence is expected. Assuming a

6.3 Electrical properties

Figure 6.24: Electron mobility limited by acoustic phonon scattering for various temper-

atures between 1K and 300K.

high degenerated electron gas and a constant background density Nii of impurities the

relaxation time τii is given by:

τii

=Niim∗

2π¯h3k3

(e2

2) (6.11)

where kF=√2πN2D. Details of the calculation are presented in Ref. [71]. The re-

sults are plotted in Fig. 6.25 for impurity densities between Nii = 7 ∗1016cm−3

and Nii = 7 ∗1017cm−3at a temperature of T=10K. We see, that the mobility in-

creases proportional to N3/2

2Dfor a constant impurity level. In case of our typical back-

ground of Nii = 1 ∗1017cm−3the mobility increases from µ= 4 ∗104cm2(V s)−1for

N2D= 1 ∗1012cm−2to µ= 1 ∗106cm2(V s)−1for N2D= 1 ∗1013cm−2. These values are

three orders of magnitudes higher than the experimental data. So it is clear, that the

mobility in our case is not limited by scattering at ionized impurities.

A further parameter, which can be important in our heterostructures, is the dislocation

density. Due to the high misfit between the substrate and the layer, the typical dislo-

cation density in 3C-SiC/GaN is about 1 ∗109cm−2(calculated from the FHWM of the

rocking curve). The basic idea for calculation is the screening of a perfect 2DEG by an

additional electrostatic potential, which refers to the dislocations. The dislocations can

be modeled by a line of charge, like described in Ref. [82]. The Hamiltionian HDis can

6 AlGaN/GaN based field effect transistors

Figure 6.25: Electron mobility limited by impurity scattering for a temperature of

T=10K.

be calulated and the relaxation time τDis is equal to [83]:

τDis

=¯h32a2

NDism∗e4f2

16πk4

1.84kF

qsc −0.25 (6.12)

where NDis is the dislocation density, f is the fraction of filled states in the charged

dislocation. It can be extracted from the minimization of the free energy per disloca-

tion line in the case of 60 dislocations after Weimann et al. [84] and depends on the

concentration of carriers in the channel. In our case a value of f=0.84 is a resonable

approximation, which leads to a carrier concentration of n= 1019cm−3in the channel.

a0refers to the in plane lattice parameter of GaN and describes the minimal spacing of

two charged lines. kFis the Fermi vektor given by √2πN2D, where N2Dis the sheet

carrier concentration. qSC is the screening length, which is determined from 2

a∗

B, where

a∗

B= 1.18 ∗10−9mis the effective Bohr radius. The results are plotted in Fig. 6.26,

which shows the electron mobility of a 2DEG as function of the sheet carrier density

for dislocation densities between 109cm−2and 1011cm−2. The mobility increases with

the carrier density at a constant dislocation density by a factor of 7, when the carrier

density increases from N2D= 1 ∗1012cm−2to N2D= 1 ∗1013cm−2. The curve shows a

dependence which is roughly proportional to N3/2

2D. For a dislocation density of 1010cm−2

we expect a mobility between 104and 7 ∗104cm2(V s)−1for a carrier density between

1012cm−2and 1013cm−2. If the dislocation density is reduced by one order of magnitude,

6.3 Electrical properties

Figure 6.26: Electron mobility limited by dislocation scattering for various carrier den-

sities in the channel in the range of N2D= 1012cm−2to N2D= 1013cm−2.

the mobility increases by a factor of 10 due to the inverse proportional dependence in

equation 4.48. The range between a dislocation of 109cm−2and 1010cm−2represents the

values, which are state of the art for cubic GaN on freestanding 3C-SiC (lower density)

and on carbonized Si (higher density). If the results are compared with hexagonal based

structures it was found, that in the cubic regime the theoretical mobility at the same

defect density is one order of magnitude higher than in the h-based samples due to lower

effective masses and higher coherence length. Therefore, scattering at dislocations is also

not the limiting parameter for mobility in our heterostructures. At the end the influence

of the interface roughness is discussed. The roughness can be described by randomized

position variation of the walls of a squared infinite quantum well. This results in a trans-

formation of the coordinates for the well in z-direction and in an additional potential in

the Schr¨odinger equation. The additional potential refers to intersubband and also to

intrasubband transitions, which will be only consider in these calculations. In the end

the relaxation time for roughness scattering is determined by [85]:

τRMS

=2φ3Λ2E1

¯hL4D2I(ΛkF,kF

qsc

) (6.13)

Λ is the coherence length of the interface fluctuations and can be approximated by

half of the terrace width of GaN (experimentally measured by quantitative RHEED

analysis, see chapter 3.1), the value is about Λ=2.5nm. E1is the energy of the first

6 AlGaN/GaN based field effect transistors

subband. The length L represents the width of well, in our case about 5nm. The factor

D describes the interface roughness, approximated by the surface roughness measured

by AFM. I(ΛkF,kF

qsc ) is an integral, which represents the influence of the roughness in

combination with the coherence length and depends also on the Fermi vektor kF. This

integral can be expressed by the following equation:

I(ΛkF,kF

qsc

) = 1

2πZ(1 −cosΘ

(1 + qsc

2kFsinΘ

2)2exp(−Λ2k2

Fsin2Θ

2)dΘ (6.14)

This integral is numerically calculated for different kF, representing a sheet carrier con-

centration between 1012cm−2and 1013cm−2and fitted by a polynom of the fifth order.

The value of the integral is given by:

I(ΛkF,kF

qsc

) = 0.102 + 9.34 ∗10−14N2D−2.79 ∗10−26N2

2D(6.15)

+4.06 ∗10−39N3

2D−2.95 ∗10−52N4

2D+ 8.54 ∗10−66N5

The mobility is calculated for carrier densities between 1012cm−2and 1013cm−2and for

interface roughnesses ranging from 1nm to 8nm. The value of 8nm is a reasonable value

for GaN grown on carbonized Si on a 100x100µm2scan range. The scan range is com-

parable to the free path length of the scattered electrons. The results are plotted in

Fig. 6.27. The plot shows that the mobility is nearly independent of the carrier density

and only influenced by the RMS roughness. If the roughness is reduced by one order

of magnitude, the mobility increases by a factor of 100 due to the squared dependence.

For example at a RMS roughness of 8nm (standard samples) the mobility will be expect

in the range of 80cm2(V s)−1and for the best value (3nm) we get 600cm2(V s)−1.

After the investigation of the different scattering mechanism and their influence on the

mobility in the channel it is very helpful for future work to compare them. The compar-

ison of impurity, dislocation and roughness scattering together with the experimental

data (GANS1416) shows clearly, like depicted in Fig. 6.28, that impurities and disloca-

tions are not the limiting parameter for mobility in our heterostructures. The scattering

mechanism, which causes the lowest values for the mobility, is the interface roughness.

The results are in the range of80cm2(V s)−1, and two orders of magnitude lower, than

for dislocations or impurities. In comparison with the experimental data of GANS1416,

an excellent agreement is observed, if the measured RMS roughness of 8.5nm is take

into account. In addition we get the information, that the RMS roughness has to be

reduced below 1nm in order to reach the mobility limit due to dislocation scattering for

a dislocation density of 1010cm−2.

6.3 Electrical properties

Figure 6.27: Electron mobility limited by roughness scattering for various carrier densi-

ties in the channel in the range of N2D= 1012cm−2to N2D= 1013cm−2

Figure 6.28: Electron mobility limited by different scattering mechanism for various

carrier densities in the channel in the range of N2D= 1012cm−2to

N2D= 1013cm−2and the comparison to experimental result

6 AlGaN/GaN based field effect transistors

6.3.4 Fabrication and electrical characterization of HFET structures

Figure 6.29: Arrangement of the source, drain and gate contact for our FET structures

with a gate length of 6µm and a gate width of 100µm using Ref. [73].

Nevertheless some FETs were fabricated on Mesa structures and measure them

at T=155K. Therefore the structural arrangement for the FET contacts was choosed

using Ref. [73]. The structure, which is drawn in Fig. 6.29, consists of a source contact

with a size of 70µmx100µm and a drain contact with a size of 170µmx100µm. The sep-

aration of both contacts is 18µm. The gate contact is placed in the center of the source

and drain contact with a gate length of 6µm and a gate width of 100µm. Additionaly

the source is connected with a finger structure, with a finger length of 380µm, a width

of 30µm and a separation of 15µm. The finger structure is completed by second finger

structure connected with a further contact, having the same dimensions. The finger

structure allows the determination of the insulation resistance of the structure as well

as the insulation between different structures.

For the fabrication of the FET structures three steps are necessary. Therefore three types

of masks are needed. Figure 6.30 illustrates the different masks. Figure 6.30a shows the

Mesa structures in an arrangement of 3x3 Mesa. The size of one is 575µmx865µm with

a separation of two different structures of 40µm. The Mesa are 50µm wider than the

source-drain contact mask, in order to ensure that the source-drain contact structure

fits to the Mesa, even if the etching step produces flat edges between the Mesa and the

groove. The 3x3 arrangement guarantees, that the mask fits to our 5x5mm2samples,

which is normally used in our photolithography process. The mask is completed with

a description for each column (A, B, C) and each row (1, 2, 3) in order to identify the

FET on the sample. In Fig. 6.30b a picture of the mask for the source-drain contacts is

drawn. They are also arranged in 3x3 structures together with the finger structure for

the resistivity measurements. The Fig. 6.30c shows the mask for the gate contacts. All

three masks are transfered by optical lithography to a glass substrate, which is covered

with a 120nm thick Ni layer and with 2.3µm of a positive photo resist (AR-P3510).

6.3 Electrical properties

Figure 6.30: The different masks used for the fabrication of our FETs. a)Mesa structure

b)Source and Drain contacts c)Gate contact.

Optical lithography means in this case that the model of the masks is converted to a

bitmap data file and then projected onto the glass with a conventional beamer. Then

the resist is exposed by the light of the beamer. After fixing the resist with a conven-

tional developer, the Ni layer is etched for t=60s at room temperature using a solution

of 500g Ammoniumcernitrat, 87.5ml ethanioc acid and 2.5l DI water. At the end it is

rinsed in DI water and dried with pure nitrogen. This home-made mask is used for the

fabrication of the FET structures.

For the fabrication of the FET structures an AlGaN/GaN heterostructure grown on

carbonized Si substrate is used. A sketch of the structure and the Mesa arrangement is

given in Fig. 6.31a. The FET bases on the sample GANS1416. On top of a carbonized

Si substrate a 980nm thick, unintentional doped GaN buffer is deposited at a substrate

temperature of 720◦C. After that an AlGaN layer with a Al mole fraction of x=0.3 and a

thickness of 20nm is grown using the same temperature without intentional doping. The

sample is capped with a 20nm thick GaN layer. The Mesa structure is realized using

reactive ion etching (RIE) technique [86]. The sample is etched in an Ar:SiCl4=1:1 gas

mix using a flow of 74sccm for both gases. The rf power is 1.4kW and the background

pressure is about p=2.5∗10−2mbar. The temperature of the sample is about T=20◦C.

The etching rate for the GaN and AlGaN is about 1nm/min and the etched depth is

50nm. This guarantees, that the 2DEG of each structure is separated from the others.

In the next step the source and drain contact are deposited by thermal evaporation us-

ing In as contact material. The thickness of the In is about 200nm, in order to prevent

the structure of mechanical damage and to guarantee a small contact resistance. At

last the gate contact is realized by thermal evaporation using Ni as Schottky contact

material with a thickness of 50nm. Nine structures are fabricated on the sample in an

6 AlGaN/GaN based field effect transistors

Figure 6.31: a)A schematic sketch of the FET structure and the Mesa arrangement re-

alized on GANS1416, b)An optical micrograph with the contacts and an

enlargement of the gate region (GANS1416).

arrangement of 3x3.

Figure 6.31b shows an optical micrograph of the whole MESA structure with the con-

tact arrangement and an enlargement of the gate region. The MESA with a size

575µmx865µm can clearly be seen. The separation of the MESA is about 40µm. The

enlargement of the photo shows the gate region. The gate with a width of 100µm and a

length of 6µm is also observed. The channel length (the separation between source and

drain) is about 18µm.

Before the feature of the FET is characterized, the sample is cooled down to a tem-

perature of T=155K. This temperature guarantees on the one hand that the parallel

conductivity in the GaN buffer is reduced by some orders of magnitude in order to en-

sure, that the conductance of the 2DEG is maybe the dominant contribution. On the

other hand it allows the use of our tip prober in a modified setup. Therefore a box with

a brass block was designed, which is cooled down with liquid nitrogen and on which the

sample is mounted. The temperature is controlled by a thermocouple. The box posses

some slits for the positioning of the tips and it is closed with a glass plate in order to

look to the sample. The box is rinsed with nitrogen gas to prevent the humidity of the

air from the sample and the tips.

After the sample preparation the measurements are performed in the same way as at

room temperature. Before the field effect is investigated the source-gate and the source-

drain I-V curves are checked. In Fig. 6.32 the source-gate I-V curve of the FET structure

B-1 fabricated on GANS1416 is plotted in a linear scale for voltages between -4V and

+4V. The curve is measured at a temperature of T=155K. A clear Schottky behaviour

for this gate contact was observed. One can see a linear increase of the current up to

0.35mA as function of the forward bias for voltages above Vbi=1.7V. This value of Vbi is

6.3 Electrical properties

Figure 6.32: Source-gate I-V curve of FET structure B-1 realized on GANS1416 mea-

sured at a temperature of T=155K.

nearly a factor of 2 higher than on conventional Ni/c-GaN Schottky diodes and maybe

correlated to a high background doping of ND= 1018cm−2(compare GANS1429). The

serial resistance of the structure is about 6052Ω which is one order of magnitude higher

than for the conventional samples. This can maybe explained by the dominance of the

contact resistance on the serial resistance, because for these structures the contact area

is reduced by a factor of 5. In reverse direction we found a nearly constant reverse cur-

rent of -0.02mA for voltages down to -3.5V. At voltages below -3.5V a clear breakdown

is observed by the increase of the current from -0.02mA to -0.2mA at a voltage of -4V.

This fast breakdown occurs due to the high backround doping (compare Fig. 4.20).

In the Fig. 6.33 the source-drain I-V curve of FET structure B-1 measured at a tem-

perature of T=155K is depicted in a linear scale using a gate voltage of VG=0V. The

current is measured at voltages between 0V and +7V. A linear increase of the current

up to 2.7mA is observed for voltages up to 7V. The slope of the curve reveals a se-

ries resistance of RS= 2560Ω. This is quite high in comparison to our other Schottky

diodes, but it is due to the partial freeze out of carriers and to the strong reduction of

the contact area by one order of magnitude. Nevertheless the contacts can be used for

the measurements.

Figure 6.34 shows a sketch of the current circuit used for the measurement of the source-

drain current at different gate voltages. The source contact is set to negative potential

for the source-drain measurement as well as for the control of the gate voltage, so the

6 AlGaN/GaN based field effect transistors

Figure 6.33: Source-drain I-V curve of FET structure B-1 realized on GANS1416 mea-

sured at a temperature of T=155K.

Figure 6.34: Current circuit used for the investigation of the field effect at our FET

structure.

gate and drain contacts are set to positive potential, which can be independently con-

trolled from each other. Then gate voltages between -0.25V and +1V were applied and

the source-drain voltage source-drain current characteristics are measured as a function

of the gate voltage. The results of these measurements are depicted in Fig. 6.35. The

source-drain voltage is varied in a range between 0V and +7V. For all the I-V curves the

linear increase of the current is observed with increasing voltage. The results are compa-

rable to those measured on h-AlGaN/GaN FETs without a seminsulating buffer [87]. In

addition the plot shows, that the slope of the source-drain current varies as function of

the source-gate voltage. With increasing gate voltage from +0.25V and further to 0.75V

and 1V the slope also increases caused by the field-effect of the gate. This is the first

6.3 Electrical properties

Figure 6.35: Source-drain I-V curve of FET structure B-1 for different gate voltages

between -0.25V and +1V realized on GANS1416 measured at a temperature

of T=155K.

hint of a field-effect operation in c-AlGaN/GaN based FET structures. Nevertheless,

there are two differences to conventional FETs. The first one is, that no saturation in

the source-drain current is observed, which we believe, is due to a non-neglegtable part

of the current caused by parallel conductivity in the GaN buffer.

In order to investigate the influence of the buffer conductivity, the banddiagrams were

Figure 6.36: Calculated banddiagrams of the FET structure for VG=+0.5V and VG=-

0.25V.

calculated for gate voltages of +0.5V and -0.25V. The results are plotted in Fig. 6.36.

6 AlGaN/GaN based field effect transistors

A more detailed description of the band edge curvate is given in Fig. 6.3. The calcu-

lation of the band diagrams for the applied gate voltages shows, that at VG=-0.25V a

2DEG ground state does not exsist. In this case the current transport is only realized

by the GaN buffer. For a gate voltage of 0.5V the exsistence of a 2DEG ground state is

investigated and therefore a parallel conducting of the current via the GaN buffer and

the 2DEG is measured.

Therefore the source-drain current-source-drain voltage curve for a gate voltage of -0.25V

is substracted from each other and then plotted again as function of the gate voltage.

The results are shown in Fig. 6.37. Neglecting the influence of the GaN buffer, we can

observe a clear field-effect behaviour of our FET structure. An additional feature is, that

Figure 6.37: Source-drain I-V curve of FET structure B-1 for different gate voltages

between +0.25V and +1V without the influence of the buffer conductivity

realized on GANS1416 measured at a temperature of T=155K.

a saturation of the drain current occurs at voltages above 3V, which is a clear evidence

for the current transport via a 2DEG. At this voltage the channel reaches the maximum

filling level with carriers and an increase of voltage cannot increase the current. The

saturation current increases as function of the gate voltage due to the increasing depth

of the 2DEG channel. If we compare the saturation voltage of 3V and the saturated

drain current of 0.38mA (VG=+0.25V) to 0.70mA (VG=+1.00V) with data of hexagonal

based AlGaN/GaN FETs [88], we find that the values are in the same range. Here a

saturation voltage of 3V and a drain current in the order of 1mA is typical, if the gate

voltage is varied in the same range.

7 Conclusion

Phase-pure cubic GaN films on freestanding 3C-SiC (001) substrates were grown by

rf plasma-assisted molecular beam epitaxy. AFM investigations showed that the RMS

roughness directly depend on the defect density of the samples, due to the formation of

grooves on the surface by the domain defects. Best values were obtained for wafers with

a rocking curve half width of 4.5arcmin, which had a RMS roughness of 1.8nm. It was

demostrated, that the properties of the substrate directly influenced the quality of the

GaN buffer.

Using the best substrates, 600nm thick c-GaN films with a rocking curve width of 20ar-

cmin and a RMS of 5.2nm could be realized. For these parameters the influence of the

buffer type as well as the growth temperature were investigated. It was found, that

a 8nm thick c-AlN buffer, deposited at TSubs = 720◦Crevealed the smoothest surface.

With the variation of the growth temperature one can show, that the rocking curve half

width decreased with increasing temperature, on the other hand the RMS roughness

increased. Both were caused by the increasing surface mobility of the Ga at higher

temperatures. For a growth temperature of TSubs = 720◦C, a rocking curve width of

20arcmin and a RMS of 5.2nm was obtained. The phase purity of the c-GaN was better

than 99.5%.

On top of the optimized c-GaN, cubic-AlxGa1−xNfilms (0 < x < 0.74) were deposited.

Measurements of the RHEED intensity were employed in order to obtain well defined

metal-rich growth conditions. The Al content of our layers was directly proportional to

the Al flux while the roughness of the layers was strongly depending on the excess Ga-

coverage during growth. Lowest values of the RMS roughness which was independent

of the Al content x were obtained with a 1ML coverage. Pronounced oscillations of the

RHEED intensity which were observed after growth interruptions indicate predominant

two-dimensional growth of our c-AlxGa1−xNfilms. It was found, that the background

doping of the AlGaN increased with increasing Al content, due to the high affinity of

oxygen to Al. The level increased from ND= 1∗1017cm−3for GaN to ND= 2∗1018cm−3

for a Al0.45Ga0.55Nlayer. The conductivity of our AlGaN films increased by a factor of

3 at x=0.45 in comparison to GaN and then decreased by one order of magnitude for

c-AlN, caused by the increasing activation energy of the oxygen impurity.

The c-GaN and c-AlGaN films were used to realize Schottky diodes by the deposition

of Ni as contact material. Temperature dependent I-V measurements showed a strong

deviation between the classical thermionic emssion theory and the current flow in our

structures. The high leakage current, which was observed, originated in the presence of

surface donor states with a concentration of NSD = 2 ∗1019cm−3at room temperature.

Temperature dependent C-V analysis revealed a ionization energy between 14meV and

23meV. It was demonstrated that the surface donors can be influenced by thermal an-

7 Conclusion

nealing. Using a temperature of 200◦Cfor 10min the leakage current was reduced by

three orders of magnitude and the breakdown voltage increased by one order from -9V

to -80V. The breakdown voltage directly depend on the background concentration of the

films.

Therefore cubic AlxGa1−xN/GaN heterostructures were fabricated by MBE on 3C-SiC

(001) substrates. An additional luminescence band at 3.250eV was observed at low tem-

perature which was attributed to a 2DEG transition. The position of the luminescence

was influenced by the Al content and the background doping of the AlGaN barrier. In-

tensity dependent and voltage dependent PL measurements showed characteristic shifts

of this transition of 3.3meV/decade and 1.3meV/V, respectively, due to the change in

the carrier confinement by varying the laser excitation power or the external bias voltage.

These shifts are quantitatively verified by a self consistent solution of the Schr¨odinger

and Poisson equation. C-V measurements at T=150K reveal a clear evidence for the

existence of a 2DEG, and a sheet carrier concentration of about 1.6∗1012cm−2is mea-

sured at the interface in good agreement with the numerical simulation. Temperature

dependent Hall-effect analysis revealed a carrier mobility of 100cm2(V s)−1at 5K for

the 2DEG. The influence of different scattering mechanisms like phonon, impurity, dis-

location or roughness scattering was investigated. It was found, that the mobility of

the 2DEG was limited by scattering at the interface roughness. Then c-AlGaN/GaN

based HFET structures were fabricated. The MESA structures were realized by RIE

technique. The source and drain contacts were made from pure In, for the gate contact

Ni was used. The samples were prepaired for device operation. The presence of the field

effect operation was demonstrated at a temperature of 155K.

100

Bibliography

[1] L. Shen, R. Coffie, D. Bultari, S. J. Heikman, A. Chakraborthy, A. Chini, S. Keller,

S. P. DenBaars and U. K. Mishra, IEEE Elec. Div. Lett. 25, 7 (2004)

[2] S. Rajan, P. Waltereit, C. Poblenz, S. J. Heikman, D. S. Green, S. P. DenBaars

and U. K. Mishra, IEEE Elec. Div. Lett. 25, 247 (2004)

[3] M. D. Craven, P. Waltereit, F. Wu, J. S. Speck, and S. P. DenBaars,

Jpn. J. Appl. Phys. 42 L235 (2003)

[4] P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner,

M. Reiche, and K. H. Ploog, Nature (London) 406, 3850 (2000)

[5] H. M. Ng, Appl. Phys. Lett. 80, 4369 (2002)

[6] S. Potthast, J. Sch¨ormann, J. Fernandez, D. J. As, K. Lischka, H. Nagasawa and

M. Abe, phys. stat. sol. (c), 3, No 6, 2091 (2006)

[7] J. Sch¨ormann, S. Potthast, D.J. As, and K. Lischka, Appl. Phys. Lett. (accepted)

[8] D. J. As, in Optoelectronic Properties of Semiconductors and Superlattices, series

editor M. O. Manasreh, (Taylor and Francis Books, Inc. , New York, 2003),

Vol. 19 chapter 9, pp. 323-450

[9] I. Petrov, E. Mojab, R. C. Powell and J. E. Greene, Appl. Phys. Lett. 60, 2491

(1992)

[10] T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham and J. Scanlon,

Appl. Phys. Lett. 59, 944 (1991)

[11] S. K. Pugh, D. J. Dugdale, S. Brand and R. A. Abram, Semicond. Sci. Techn. 14

(1), 23 (1999)

[12] C. G. van de Walle and J. Neugebauer, Appl. Phys. Lett. 70 (19), 2577 (1997)

[13] K. Kim, W. R. L. Lambrecht and B. Segall, Phys. Rev. B53 (24), 16310 (1996)

[14] S. H. Park and S. L. Chuang, J. Appl. Lett. 87 (1), 353 (2000)

[15] J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974)

Bibliography

[16] M. E. Sherwin and T. J. Drummond, J. Appl. Phys. 69, 8423 (1991)

[17] M. A. Herrmann and H. Sitter Molecular Beam Epitaxy: Fundamentals and cur-

rent status, Springer Verlag, Berlin 1989

[18] B. Sch¨ottker Molecular Beam Epitaxie and Characterization of doped and undoped

cubic GaN Layers, Ph.D. thesis, Shaker Verlag Aachen 1999

[19] J. Sch¨ormann, S. Potthast, M. Schnietz, S. F. Li, D. J. As and K. Lischka,

phys. stat. sol. (c), No 6, 1604 (2006)

[20] H. Beneking Halbleitertechnologie, Teubner Verlag Stuttgart (1991)

[21] Brodie, J. J. Murray Semiconductor Microfabrication, New York 1982

[22] W. M. Moreau Semiconductor Lithography, Principles, Practices and Materials,

New York (1993)

[23] B. E. Warren, X-ray diffraction, Dover, New York 1968

[24] L. Pavesi, M. Guzzi, J. Appl. Phys. , 75, 4779 (1994)

[25] P.Y. Yu, M. Cardona, Fundamentals of Semiconductors, Springer Verlag, Berlin,

Heidelberg 1996

[26] C.F. Klingshirn Semiconductor Optics, Springer Verlag, Berlin Heidelberg 1995

[27] E. F. Schubert, Doping in III-V Semiconductors, University Press, Cambrigde

1993

[28] S. M. Sze Physics of Semiconductor devices, John Wiley and Sons, New York 1981

[29] D. C. Look Electrical Characterization of GaAs Materials and Devices, John Wiley

and Sons, New York 1989

[30] D. K. Schroder Semiconductor Material and Device Characterzation, Wiley Inter-

science, 1998

[31] R. A. Bowling and G. B. Larrabee, Surface Characterization, Anal. Chem. 55

133R-156R, (1983)

[32] R. A. Bowling and G. B. Larrabee, Surface Characterization, Anal. Chem. 57

130R-175R, (1985)

[33] G. E. McGuire Surface Characterization, Anal. Chem. 59 294R-308R, (1987)

[34] R. E. Honig, Surface and Thin Film Analysis of Semiconductor Materials, Thin

Solid Films 31, 89 (1976)

[35] T. Wolff, M. Rapp and T. Rotter phys. stat. sol. (c) 1, No. 10, 2417 (2004)

Bibliography

[36] J. Neugebauer, Z. Zywietz, M. Scheffler, J. E. Northrup and C. G. van der Walle,

Phys. Rev. Lett. 80, 3097 (1998)

[37] S. Potthast, J. Sch¨ormann, E. Tschumak, D. J. As and K. Lischka,

Jour. Appl. Phys. submitted

[38] D. L. Smith, Thin Film Deposition (McGraw-Hill, New York, 1995)

[39] J. Sch¨ormann, S. Potthast, M. Schnietz, S. F. Li, D. J. As and K. Lischka,

phys. stat. sol. (c), 3, 1604 (2006)

[40] C. S. Lent and P. I. Cohen, Phys. Rev. B 33 (12), 8329 (1986)

[41] H. Nagasawa, T. Kawahara and K. Yagi, Mater. Sci. Forum 389-393 (2002)

[42] H. Nagasawa, K. Yagi, T. Kawahara and N. Hatta, Mater. Sci. Forum 433-4

(2002)

[43] W. A. Harrison, Electronic Structure and the Properties of Solids (Dover, New

York, 1980)

[44] J. Neugebauer, T. Zywietz, M. Scheffler, J. E. Northrup, H. Chen and R. M. Feen-

stra, Phys. Rev. Lett. 90, 056101 (2003)

[45] C. Adelmann, R. Langer, G. Feuillet and B. Daudin Appl. Phys. Lett. 75, (22),

3518 (1999)

[46] J. H. Edgar, S. Strite, I. Akasaki, H. Amano and C. Wetzel Galluim Nitride and

related Semiconductors, INSEPC 1999

[47] M. Stutzmann, O. Ambacher, A. Cros, M. S. Brandt, H. Angerer, R. Dimitrov,

N. Reinacher, T. Metzger, R. H¨opler, D. Brunner, F. Freudenberg, R. Handschuh

and Ch. Deger, Mat. Sci. Eng. 50, 212 (1997)

[48] A. C. Smitz, A. T. Ping, M. Asif Khan, Q. Chen, J. W. Yang and I. Adesida,

Semicond. Sci. Technol. 11, 10,1464 (1996)

[49] J. H. Edgar Properties of Group III Nitrides, INSPEC, Short Run Press Ltd. Ex-

eter (1994)

[50] J. Singh, Physics of Semiconductors, Mc Graw Hill, (1997)

[51] H. A. Bethe, Theory of the boundary layer of crystal rectifiers, MIT Ra-

diat. Lab. Rep. 43-12 (1942)

[52] J. Fernandez, Growth and Characterization of c-GaN based Schottky diodes, Mas-

ter thesis (2005)

[53] D. J. As, S. Potthast, J. Fernandez, J. Sch¨ormann and K. Lischka,

Appl. Phys. Lett. 88 152112 (2006)

iii

Bibliography

[54] J. H. Werner, Appl. Phys. A47, 291 (1988)

[55] S. N. Mohammad, J. Apl. Phys. 97, 063703 (2005)

[56] V. Adivarahan, G. Simin, J. W. Yang, A. Lunev, M. A. Kahn, N. Pala, M. Shur

and R. Gaska Appl. Phys. Lett. 77, 862 (2000)

[57] J. D. Guo, M. S. Feng, R. J. Guo, F. M. Pan and C. Y. Chang,

Appl. Phys. Lett. 67, 2657 (1995)

[58] A. C. Schmitz, A. T. Ping, M. A. Kahn, Q. Chen, J. W. Yang and I. Adesia

J. Electron. Mater. 27, 255 (1998)

[59] D. K. Schroder Semiconductor Material and Device Characterization, Wiley, New

York 1990

[60] H. Hasegawa and S. Oyama, J. Vac. Sci. Technol. B 20, 1647 (2002)

[61] J. M. Langer and P. Revva, Mat. Sci. Forum 83-87, 1545 (1992)

[62] J. M. Langer, Jpn. J. Appl. Phy. 32, Suppl. 32-1, 83 (1993)

[63] P. Revva, J. M. Langer, M. Missous and A. R. Peaker J. Appl. Phys 74 (1), 416

(1993)

[64] F. A. Padovani and R. Stratton, Solid-State Electron. 9, 695 (1966)

[65] J. D. Guo, F. M. Pan, M. S. Feng, R. J. Guo, P. F. Chou and C. Y. Chang,

J. Appl. Phys. 80, 1623 (1996)

[66] K. Matocha, T. P. Chow and R. J. Gutmann, Mater. Sci. Forum 383-393, 1531

(2002)

[67] J. J. Bandic, P. M. Bridger, E. C. Piquette and T. C. McGill, Appl. Phys. Lett. 74,

1266 (1999)

[68] G. T. Dang, A. P. Zhang, M. M. Mshewa, F. Ren, J. I. Chyi, C. M. Lee, C. C. Guo,

G. C. Chi, J. Han, S. N. G. Chu, R. G. Wilson, X. A. Cao and S. J. Pearton,

J. Vac. Sci. Technol. A 18, 1135 (2000)

[69] Y. -Z. Chiou, Y. K. Su, S. -J. Chang and C. -H. Chen, IEE Proc. Optoelectron. ,

Vol. 150, No. 2, (2003)

[70] C. K. Wang, S. J. Chang, Y. K. Su, Y. Z. Chiou, C. S. Chang, T. K. Lin, H. L. Liu

and J. J. Tang, Semicond. Sci. Technol. 20, 485-489, (2005)

[71] J. H. Davies The Physics of Low Dimensional Semiconductors, Cambridge Uni-

versity Press, 1997

[72] A. Nakadaira and H. Tanaka, Appl. Phys. Lett. 70 (20), 2720 (1997)

Bibliography

[73] S. M¨uller, K. K¨ohler, R. Kiefer, R. Quay, M. Baeumler and L. Kirste,

phys. stat. sol. (c),2, No 7, 2639 (2005)

[74] I. H. Tan, G. Snider and E. L. Hu, J. Appl. Phys. 68, 4071 (1990)

[75] D. J. As, F. Schmilgus, C. Wang, B. Sch¨ottker, D. Schikora and K. Lischka,

Appl. Phys. Lett. 70, 1311 (1997)

[76] Y. R. Yuan, M. A. A. Pudensi, G. A. Vawter and J. L. Merz, J. Appl. Phys. 58,

397 (1985)

[77] G. Ramirez-Flores, H. Navarro-Contreras, A. Lastras-Martinez, R. C. Powell and

J. E. Greene, Phys. Rev. B 50, 8433 (1994)

[78] S. R. Kurtz, A. A. Allerman, D. D. Koleske, A. G. Baca, R. D. Briggs,

J. Appl. Phys. 95 4 (2004)

[79] V. Cimalla, Th. Stauden, G. Eichhorn, J. Petzold; Mat. Sci. Eng. B61-62, 553-558

(1999)

[80] L. Hsu and W. Walukiewcz, Phys. Rev. B 56, No 3, 1520 (1997)

[81] X. Han, D. Li, H. Yuan, X. Sun, X. Liu, X. Wang, Q. Zhu and Z. Wang,

phys. stat. sol. (b) 241, No 13, 3000 (2004)

[82] F. A. Ponce, MRS Bull. 22, 51 (1997)

[83] D. Jena, A. Gossard and U. K. Mishra, Appl. Phys. Lett. 76 (13), 1707 (2000)

[84] N. G. Weimann, L. F. Eastman, D. Doppalapudi, H. M. Ng and T. D. Moustakas

J. Appl. Phys. 83, 7, 3656 (1998)

[85] V. V. Mitin, V. A. Kochelap and M. A. Stroscio in Quantum Heterostructures-

Microelectronics and Optoelectronics, p.249 Cambridge University Press (1999)

[86] M. Panfilova Reactive Ion Etching and Photoenhanced Wet Chemical Etching of

cubic group-III Nitrides Masterthesis (2006)

[87] C. Poblenz, P. Waltereit, S. Rajan, S. Heikman, U. K. Mishra and J. S. Speck,

Jour. Vac. Sci Technol. B 22 (3), 1145 (2004)

[88] D. Kikuta, J. P. Ao and Y. Ohno, Sol. Stat. Elec. 50, 316 (2006)

Bibliography

List of samples

Sample Subs. TGaN (◦C)tGaN (nm)TAlGaN (◦C)tAlGaN (nm) x

GNSJ951 SiC 720 628

GNSJ953 SiC 750 623

GNSJ954 SiC 780 643

GNSJ955 SiC 810 607

GNS982 SiC 720 595

GNSK987 SiC 720 580

GNSK988 SiC 720 560

GANJ998 SiC 720 354 720 300 0.22

GANJ1000 SiC 720 400 720 360 0.22

GANJ1001 SiC 720 400 720 440 0.22

GANJ1005 SiC 720 420 720 160 0.22

GANJ1006 SiC 720 390 720 90 0.22

GANJ1007 SiC 720 400 720 50 0.22

GANS1034 SiC 720 720 0.18

GANS1052 SiC 720 270 720 300 0.25

GANS1074 SiC 720 240 720 480 0.52

GNSC1108 SiC 720 70 720 540 0.20

GNS1183 SiC 720 780

GNJ1204 SiC 720 850

GANS1211 SiC 720 520 720 540 0.25

GANS1228 SiC 720 900 720 90 0.25

GANS1239 SiC 720 900 720 90 0.30

GNS1285 SiC 720 850

GANS1352 Si 720 800 720 40 0.35

GANS1356 Si 720 800 720 40 0.35

GANS1357 Si 720 800 720 40 0.35

GNS1382 SiC 720 755

GANS1384 SiC 720 750 720 20 0.35

AGN1397 SiC 675 675 0.33

AGN1398 SiC 700 700 0.44

AGN1403 SiC 725 725 0.57

GANS1416 Si 720 980 720 20 0.30

List of samples

Sample Subs. TGaN (◦C)tGaN (nm)TAlGaN (◦C)tAlGaN (nm) x

725 0.14

AGN1426 SiC 700 700 0.25

0.38

0.67

GNP1429 SiC 720 740 720 20 0.35

0.18

AGN1436 SiC 700 700 0.32

0.52

AGN1437 SiC 700 700 0.80

AGN1441 SiC 735 735 0.74

AGN1445 Si 690 690 0.44

AGN1447 SiC 640 640 0.48

AGN1448 SiC 700 700 0.54

AGN1449 Si 700 700 0.54

AGN1452 SiC 725 725 0.54

AGN1455 SiC 720 720 0.63

AGN1459 SiC 745 745 0.82

AGN1463 SiC 750 750 0.65

vii

Bibliography

Acknowledgements

This is the last chapter of my thesis, which I have to write down, and believe me,

it will be the most difficult. This Ph. D. thesis would have been much harder to do and

to finish without the help, support, contributions and encouragement of many people,

who I have to mentioned here.

First I have to thank Prof. Dr. D. J. As, who offered me this interesting, fascinating

work, which contains the field of basic research and device physics, as well as entailed

engineering. Without his support it would not be possible to solve the problem he gave

me (cite: The goal is a HEMT device!). I will not forget to thank Prof. K. Lischka and

Dr. D. Schikora for sharing their own experiences, knowledge and readiness to engage

in sometimes rather longish discissions (especially on friday!).

The next I have to mentioned are my dear colleagues of the last years. At first I have to

name my earlier Diplom student and office partner J. Sch¨ormann. I thank him for every-

thing (this includes: correcting my thesis, growing samples for my thesis, the sweets,

the after-work beers...)!

In addition I would like to thank my other fellow Ph. D. students C. Arens and S. Preuss

for the physical and technical discussions made many things clearer to myself (especially

Ohms law!). I will not forget our Postdoc Dr. A. Pawlis, who shows me that life contin-

ious after finishing of the Ph. D. thesis.

And I have also to named the Diplom students M. Schnietz, C. Peitzmeyer and D. M¨ugge,

they are not present anymore, but I would thank them also for the discussions and the

social events.

And last but not least, here comes the special section for our ladies! I did not forget

them, my favoured Bachelor student M. Panfilova, my favoured Master student J. Fer-

nandez and my favoured Ph. D. student E. Tschumak. I thank them for showing me

and the rest of the group that women exist, who study physics and for the sucessful and

unsucessful discussions we had, for the cakes, apples and icecream...

I will thank all of you for the last years and the friendly atmosphere in the group- I will

definitely miss everybody!

Of course I am also grateful for the (not only technical) help of our optoelectronics staff,

I. Zimmermann, S. Igges and B. Vollmer.

At the end I would like to thank my parents for more than thirty years of endless

patience, help and support.

viii

Publication list

D. J. As, U. K¨ohler, S. Potthast, A. Khartchenko, and K. Lischka, V. Potin and

D. Gerthsen Cathodoluminescence, high-resolution x-ray diffraction and transmission-

electron-microscopy investigations of cubic AlGaN/GaN quantum wells, phys. stat. sol. (c)

0, no. 1, 253-257 (2002)

O. C. Noriega, J. R. Leite, E. A. Meneses, J. A. N. T. Soares, S. C. P. Rodrigues,

L. M. R. Scolfaro, G. M. Sipahi, U. K¨ohler, D. J. As, S. Potthast, A. Khartchenko and

K. Lischka Photoluminescence and photoreflectance characterization of cubic GaN/AlxGa1-

xN quantum wells, phys. stat. sol. (c) 0, no. 1, 528 (2002)

U. K¨ohler, D. J. As, S. Potthast, A. Khartchenko, K. Lischka, O. C. Noriega,

D. G. Pachenco-Salazar, A. Tabata, S. C. P. Rodrigues, L. M. R. Scolfaro, G. M. Siphari,

J. R. Leite Optical charachterization of cubic AlGaN/GaN quantum wells, phys. stat. sol. (a)

192 (1), 129 (2002)

D. J. As, S. Potthast, U. K¨ohler, A. Khartchenko and K. Lischka Cathodolumines-

cence of MBE-grown cubic AlGaN/GaN multi-quantum wells on GaAs (001) substrates

MRS Symp. Proc. Vol. 743 L5.4 (2003)

J. R. L. Fernandez, F. Cerdeira, E. A. Meneses, M. J. S. P. Brasil, J. A. N. T. Soares,

A. M. Santos, O. C. Noriega, J. R. Leite, D. J. As, U. K¨ohler, S. Potthast, and

D. G. Pacheco Salazar Optical and x-ray studies on the incorporation of carbon as a

dopant in cubic GaN, Phys. Rev. B 68, 155204 (2003)

D. J. As, D. G. Pacheco Salazar, S. Potthast and K. Lischka Carbon doping of cubic

GaN under gallium-rich growth conditions, phys. stat. sol. (c) 0, no. 7, 2537-2540 (2003)

D. J. As, D. G. Pacheco-Salazar, S. Potthast, K. Lischka Electrical and optical prop-

erties of carbon doped cubic GaN epilayers grown under extreme Ga excess,

MRS Symp. Proc. Vol. 798, Y8.2 (2004)

R. Goldhahn, C. Buchheim, V. Lebedev, V. Cimalla, O. Ambacher, C. Cobet, M. Rakel,

N. Esser, U. Rossow, D. Fuhrmann, A. Hangleiter, S. Potthast, and D. J. As Dielectric

function and critical points of the band structure for hexagonal and cubic GaN and AlN,

BESSY (Berliner Elektronenspeicherring-Gesellschaft fr Synchrotronstrahlung m.b.H.)

Annual Report 2005, ed. K. Godehusen, p. 206

Bibliography

D. J. As, S. Potthast, J. Fernandez, K. Lischka, H. Nagasawa, M. Abe Cubic GaN/AlGaN

Schottky-barrier devices on 3C-SiC substrates, Microelectronic Engineering 83 (2006) 34-

D. J. As, S. Potthast, J. Fernandez, J. Sch¨ormann, and K. Lischka Ni Schottky diodes

on cubic GaN, Appl. Phys. Lett. 88, 1521112 (2006)

S. Potthast, J. Sch¨ormann, J. Fernandez, D. J. As, K. Lischka, H. Nagasawa, M. Abe

Two-dimensional electron gas in cubic AlxGa1-xN/GaN heterostructures, phys. stat. sol. (c)

3,No. 6, (2006) 2091

J. Sch¨ormann, S. Potthast, M. Schnietz, S. F. Li, D. J. As, and K. Lischka Growth

of ternary and quaternary cubic III-nitrides on 3C-SiC substrates, phys. stat. sol. (c) 3,

No. 6 (2006) 1604

D. J. As, S. Potthast, J. Fernandez, K. Lischka, H. Nagasawa, M. Abe Mechanism

of current leakage in Ni Schottky diodes on cubic GaN and AlxGa1-xN epilayers, MRS

Symp. Proc. Vol. 892, 283 FF 13.4.1 (2006)

D. J. As, S. Potthast, J. Sch¨ormann, S. F. Li, K. Lischka, H. Nagasawa, M. Abe

Molecular beam epitaxy of cubic group III-Nitrides on free-standing 3C-SiC substrates,

Mat. Sci. Forum Vol. 527-529, 1489 (2006)

M. Abe, H. Nagasawa, S. Potthast, J. Fernandez, J. Sch¨ormann, D. J. As, and K. Lis-

chka Cubic GaN/AlGaN HEMTs von 3C-SiC substrate for normally-off operation, IEICE

Trans. Electron. Vol.E89-C, No. 7, 1057 (2006)

J. Sch¨ormann, S. Potthast, D. J. As, and K. Lischka Near UV emission from non-

polar cubic AlxGa1-xN/GaN Quantum Wells, Appl. Phys. Lett. 2006 (accepted)

S. Potthast, E. Tschumak, J. Sch¨ormann, D. J. As, and K. Lischka Growth and Prop-

erties of nonpolar cubic AlxGa1−xNfilms, Jour. Appl. Phys. (submitted)