Terahertz Multilayer Thickness Measurements: Comparison of Optoelectronic Time and Frequency Domain Systems [original]

Vol.:(0123456789)

https://doi.org/10.1007/s10762-021-00831-5

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Terahertz Multilayer Thickness Measurements: Comparison

ofOptoelectronic Time andFrequency Domain Systems

LarsLiebermeister1 · SimonNellen1 · RobertB.Kohlhaas1 ·

SebastianLauck1· MilanDeumer1 · SteffenBreuer1 · MartinSchell1,2·

BjörnGlobisch1,2

Received: 22 June 2021 / Accepted: 3 November 2021

Abstract

We compare a state-of-the-art terahertz (THz) time domain spectroscopy (TDS) sys-

tem and a novel optoelectronic frequency domain spectroscopy (FDS) system with

respect to their performance in layer thickness measurements. We use equal sample

sets, THz optics, and data evaluation methods for both spectrometers. On single-

layer and multi-layer dielectric samples, we found a standard deviation of thickness

measurements below 0.2 µm for TDS and below 0.5µm for FDS. This factor of

approx. two between the accuracy of both systems reproduces well for all samples.

Although the TDS system achieves higher accuracy, FDS systems can be a com-

petitive alternative for two reasons. First, the architecture of an FDS system is essen-

tially simpler, and thus the price can be much lower compared to TDS. Second, an

accuracy below 1µm is sufficient for many real-world applications. Thus, this work

may be a starting point for a comprehensive cross comparison of different terahertz

systems developed for specific industrial applications.

1 Introduction

Terahertz (THz) spectroscopy is an interesting sensing technology for many appli-

cations in material and structural analysis, compound identification, and testing

[1, 2]. The measurement is non-contact and non-destructive, can easily handle air-

material interfaces, and uses non-ionizing radiation. One of the key applications for

THz spectroscopy is the thickness measurements of paint and coating layers. Until

today, time domain spectroscopy (TDS) is almost exclusively used for this kind of

* Lars Liebermeister

[email protected]er.de

1 Fraunhofer Institute forTelecommunications, Heinrich Hertz Institute, Einsteinufer 37,

10587Berlin, Germany

2 Institut Für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, EW 5-1,

10623Berlin, Germany

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applications, as these systems are mature and commercially available. In addition,

THz TDS offers high acquisition speed and high THz bandwidth. The latter ena-

bles thickness measurements of sub-mm dielectric layers [3–5] and the detection of

defects in polymers, foams, and other non-conductive materials [6].

In contrast, frequency domain spectroscopy (FDS), which is based on the gen-

eration and coherent detection of continuous wave (cw) THz radiation, hitherto is

barely used for non-destructive testing (NDT) [7, 8]. The inherently low measure-

ment rate of most scientific FDS implementations and all commercial FDS prod-

ucts makes NDT with cw THz radiation highly inefficient. However, it was shown

already in 2014 that THz FDS can be used for multilayer thickness measurements

[9]. We have recently demonstrated a THz FDS system that allows acquisition rates

of 200 Hz, which is comparable to the speed of most commercial TDS systems.

With this FDS system, a PET film with a thickness of 23µm could be measured with

an accuracy better than 2%, which corresponds to an uncertainty below 0.5µm. This

demonstrates that FDS can compete with TDS for accurate thickness measurements

on thin dielectric layers [10]. Thereby, the main advantage of FDS compared to TDS

is the simplicity of its system architecture. FDS systems are all-fiber coupled, and

they do not require femtosecond optical pulses, moving optics, or complex phase

locking electronics. This is why many industrial applications may benefit from using

frequency domain spectroscopy instead of TDS. To date, there is no detailed com-

parison between the two methods in terms of measurement accuracy, measurement

time, and reproducibility.

In this paper, we present the first direct comparison of a state-of-the-art TDS and

optoelectronic FDS system for layer thickness measurements in reflection geometry.

Both TDS and FDS measurements were performed on the same samples, namely

PET films with thicknesses between 23 and 350 µm, a Si wafer with a thickness

of 350µm, and a ceramic coated with spray paint on both sides. Based on this, we

compare the ability of the two systems to achieve the same results in consecutive

measurements. Thereby, we analyze the effects of instrument noise, dynamic range,

and bandwidth of the respective system on thickness determination. As the central

figure of merit, we investigated the standard deviation of consecutive measurements

at the same position on the sample. We found that the standard deviation of both

TDS and FDS is always lower than 2%.

This paper is organized as follows: In Section2 we describe in detail the TDS

and FDS system used for the comparison. Section3 explains the experimental setup,

data evaluation, and thickness determination. The measurement results are presented

and discussed in Section4 before we summarize our results in Section5.

2 TDS andFDS System

The TDS measurements in this comparison were done with a commercial state-of-

the-art system, the TeraFlash pro system from TOPTICA Photonics AG [3]. A func-

tional diagram of its optical components is shown in Fig.1a. The system uses a fem-

tosecond fiber laser centered at 1560nm, which generates pulses with a duration of

100fs at a repetition rate of 100MHz. A voice-coil driven-optical delay allows for

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time-domain sampling with update rates up to 100Hz. An additional optical delay

line in the receiver arm of the spectrometer allows for compensating a wide range of

THz free space path lengths. Fiber-coupled InGaAs-based photoconductive modules

are used as emitter (Tx) and receiver (Rx), respectively. The photoconductive mate-

rial of the receiver is rhodium-doped InGaAs (InGaAs:Rh) [11, 12]. The Tx uses

iron-doped InGaAs (InGaAs:Fe) [13]. In this configuration, the spectral maximum

of the system is centered at 1THz, and the peak dynamic range reaches 70dB in

single shot (66ms measurement time) and exceeds 95dB for 1000 averages (see

Fig.2a). The total available bandwidth is more than 6THz and the spectral resolu-

tion can be as low as 1GHz. All measurements presented here were acquired with a

scan range of 70ps, corresponding to a spectral resolution of 14GHz.

FDS measurements were performed with a recently published optoelectronic

continuous-wave terahertz spectrometer [10]. The working principle of this sys-

tem is based on frequency-modulated continuous-wave (FMCW), which is an

Fig. 1 Schematics of the two optoelectronic THz spectrometers used in this paper. (a) The TDS system

compromises a pulsed fiber laser (fs-laser), a fast (voice-coil delay) and a slow (path length compensa-

tion) free-space optical delay, photoconductive emitter (Tx) and receiver (Rx), and a real-time control-

ler to drive the voice-coil and acquire the data. All components are fiber-coupled. (b) The FDS system

compromises a fixed-frequency (cw-laser) and a swept laser (Swept cw-laser), an erbium-doped fiber

amplifier (EDFA), a PIN-photodiode emitter (Tx), and a photoconductive receiver (Rx) as well as a

data acquisition unit (DAQ). The Tx- and Rx paths are indicated with yellow- and green-shaded arrows,

respectively. The different path length in the Tx and Rx arm of the spectrometer are a prerequisite for the

optoelectronic FMCW technique [10]

Fig. 2 Comparison of typical spectra recorded with the TDS (a) and FDS (b) systems. The dynamic

range is plotted against frequency. Both records use 1min of averaging. In contrast to the measurements

on the sample, these signals are recorded in a transmission setup consisting of two off-axis parabolic mir-

rors, which is filled with air of ambient humidity

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established technique used in purely electronic THz systems [14]. A schematic dia-

gram of the optoelectronic THz FDS system is shown in Fig. 1b. The spectrom-

eter uses two fiber-coupled, continuous-wave semiconductor lasers emitting in the

c-band (1530–1565nm). The frequency of one of these lasers is swept periodically,

while the emission frequency of the second laser stays fixed. The laser outputs are

spatially overlapped in a 3dB coupler, which generates an optical beat note. This

beat note is amplified by an EDFA before being converted into THz radiation via

photomixing in a waveguide-integrated PIN photodiode [15, 16]. The same beat sig-

nal is also used to drive the coherent detection in the photoconductive Rx [15]. Tx

and Rx are based on commercially available, fiber-coupled modules from TOPTICA

Photonics AG. Further details on the THz FDS system can be found in the litera-

ture [10]. The most significant and fundamental difference of this FDS system com-

pared to common setups with coherent detection of cw THz signals is the method

employed to obtain the phase. When no phase modulation is used, fringe-detection

or Hilbert-transform [17] are common methods to extract the phase information.

Alternatively, active phase modulation by a free-space optical delay line [18], a fiber

stretcher [19], or an optical phase modulator [20, 21] can be employed, which allows

for amplitude and phase determination with a quadrature lock-in detector. The FDS

system used here bases on an optoelectronic adaption of the FMCW technique [10],

which results in passive phase modulation. The tunable cw-laser is frequency swept

with more than 500THz/sec. In combination with a path length imbalance of 20cm

between the emitter and the receiver arm (indicated by shaded arrows), an inter-

mediate frequency of 500kHz is generated in the photomixing receiver, which can

be directly used for coherent detection with a software-based lock-in amplifier. This

quadrature lock-in detection allows to detect amplitude and phase as a function of

frequency. Note that this FDS system neither requires optomechanics nor free space

optics nor electro-optic phase modulation. The THz amplitude spectrum acquired

with the FDS system is depicted in Fig.2b. The spectral maximum is centered at

100GHz with a peak dynamic range exceeding 90dB for 4000averages. In a single

shot measurement, which is acquired in 14ms, the dynamic range measures 60dB

with a 2THz bandwidth. With averaging, the peak dynamic range and bandwidth

can reach 117dB and 4THz, respectively [10]. Figure2 compares the THz spectra

acquired with the TDS and the FDS system for a measurement time around 60s.

3 THz‑Setup andMeasurement Procedure

This section covers the experimental setup, the set of samples, the data preparation,

and the algorithm for thickness determination.

3.1 Experimental Setup

All measurements were carried out in reflection geometry, which is the most

industrially relevant setup. It requires only single-side access to the sample under

test, and reflection measurements can be performed independent of the substrate.

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A schematic diagram and photograph of the THz reflection head used for TDS

and FDS measurements are depicted in Fig.3. Since the mechanical dimensions

and beam profile of pulsed and cw emitter and receiver modules are almost identi-

cal, the same THz optical beam path is used for both systems. A 90° off-axis par-

abolic mirror with 2inch focal length collimates the THz beam of the emitter and

another 90°off-axis parabolic mirror with 4inch focal length focuses the beam

on the sample surface under an angle of 8°. The reflected THz beam is collected

and focused on the detector by an equal configuration of mirrors. The diameter

of all parabolic mirrors measures 1inch, which allows for constructing a compa-

rably compact reflection head. The resulting measurement spot is about 1mm in

diameter and the THz-beam is s-polarized with respect to the plane of incidence.

The beam path is oriented upwards (see Fig.3), which allows for placing the sam-

ples reproducibly in the THz focus. In order to suppress THz absorption from

water vapor, the reflection head is encapsulated (housing in Fig.3) and purged

with nitrogen (see photograph in Fig. 3)). Between background, reference, and

sample measurement, the alignment of the reflection head was kept unchanged.

The placement of the sample in the THz-beam path as well as the alignment

is a common cause of variations of the measurement result. This effect can even

dominate the uncertainty of thickness measurements in industrial applications.

However, these variations are mainly related to the geometry of the samples,

the sample holder, the design of the THz optics, and environmental conditions.

Therefore, it is not an effect caused by the THz system used. In our comparison,

we tried to minimize the influence of positioning errors and sample inhomogene-

ity by focusing our analysis on the reproducibility of consecutive measurements

taken on the same position on the sample.

Fig. 3 Schematic and photo-

graph of the reflection head used

for non-contact layer thickness

measurements. The reflection

head was identical for TDS and

FDS measurements. The diam-

eter of the parabolic mirrors

measures 1”. In this view, THz

transmitters and receivers and

their respective beam paths are

arranged one behind the other.

Both beam paths hit the sample

at the same spot and under an

angle of 8°. Tx and Rx have a

distance of 5mm. The housing

is purged with nitrogen to avoid

detrimental effects from water

vapor absorption

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