Design and Implementation of Transmission-Modulated

DESIGN AND IMPLEMENTATION OF TRANSMISSION-MODULATED

PHOTOCONDUCTIVE DECAY SYSTEM FOR RECOMBINATION LIFETIME

MEASUREMENTS

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Master of Science in Electro-Optics

Emily Clare Erdman

UNIVERSITY OF DAYTON

Dayton, Ohio

December 2016

DESIGN AND IMPLEMENTATION OF TRANSMISSION-MODULATED

PHOTOCONDUCTIVE DECAY SYSTEM FOR RECOMBINATION LIFETIME

MEASUREMENTS

Name: Erdman, Emily Clare

APPROVED BY:

Dr. Jay Mathews Dr. Imad Agha Advisory Committee Chairman Committee Member Assistant Professor Assistant Professor Physics, and Electro-Optics Physics and Electro-Optics and Photonics Affiliate and Photonics

Dr. Partha Banerjee Committee Member Professor Electro-Optics and Photonics, and Electrical and Computer Engineering Chairperson Electro-Optics and Photonics

Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering Professor School of Engineering

ABSTRACT

DESIGN AND IMPLEMENTATION OF TRANSMISSION-MODULATED

PHOTOCONDUCTIVE DECAY SYSTEM FOR RECOMBINATION LIFETIME

MEASUREMENTS

Name: Erdman, Emily Clare University of Dayton

Advisor: Dr. Jay Mathews

Today’s problems in silicon photonics will likely require an integration of CMOS compatible, high quality thin films grown on top of Si. GeSn is one of these thin film contenders and is currently being grown on Si platforms. CMOS devices require planar processing and low defect levels in the crystalline structure. A metric that will allow us to quantify defect densities in GeSn is recombination lifetime. Due to their thin film nature and band structure, measuring recombination lifetime in thin films Ge and GeSn can be difficult using industry standard techniques. Thus, we have developed a novel, contactless method in order to measure carrier lifetime called transmission-modulated photoconductive decay (TMPCD). The TMPCD system was first designed and fabricated and then fully characterized with respect to its optical and RF components. The system was validated by measuring lifetimes in bulk Si and bulk Ge. The recombination lifetimes were measured to be 2.6±0.5 μs and 7.5±0.7 μs for Si and Ge, respectively. These values

iii

were found to agree with the values from the literature that were obtained using alternative measurement techniques. Preliminary results so far do not indicate any usable recombination lifetime measurements for GeSn. However, we believe that fine tuning the

TMPCD system will allow us to obtain recombination lifetime measurements in GeSn.

ACKNOWLEDGEMENTS

I first would like to acknowledge my advisor, Dr. Jay Mathews, for providing me the time, equipment, advice and encouragement necessary to complete this thesis project.

I would also like to express my gratitude towards Dr. Imad Agha, who has helped my project progress due to his teaching and invaluable insight.

I would also like to thank our collaborators at Arizona State University for growing the thin films of Ge and GeSn, specifically Dr. Jose Menendez, Dr. John

Kouvetakis, and Charutha Senaratne.

I would like to express my appreciation to the wonderful and talented undergraduate and graduate students who have helped me on this project. I would like to specifically thank my friends and colleagues Yun Zhao, Joshua Burrow, Gary Sevison,

Zairui Li, David Lombardo, Yining Liu, Vincent Chester, Matthew Mircovich, and Aaron

Svidunovich for your time and talents.

Finally, thank you to the University of Dayton Seed Grant and Graduate Student

Summer Fellowship for additional funding on this project.

TABLE OF CONTENTS

ABSTRACT………………………………………………………………….………...iii

ACKNOWLEDGEMENTS…………………………………………………………….v

LIST OF FIGURES……………………………..……………………………………viii

LIST OF TABLES………………………………………………….…………………..x

CHAPTER 1: BACKGROUND AND MOTIVATION……………….………...... …..1

CHAPTER 2: RECOMBINATION LIFETIME: AN IMPORTANT METRIC FOR THE CHARACTERIZATION OF SEMICONDUCTOR MATERIALS……….……..8

1. Introduction……………………………………………………………………..8 2. Time resolved photoluminescence (TRPL)…………………………………...10 3. Quasi-steady state photoconductivity (QSSPC)……………….....….…...…....11 4. Transient microwave reflection photoconductive decay (µPCD)…………...... 12 5. Resonant coupled photoconductive decay (RCPCD)……………...…...…...... 14 6. Transmission modulated photoconductive decay (TMPCD)……………..…...15

CHAPTER 3: BAND STRUCTURE, ABSORPTION/EMISSION, AND RECOMBINATION…………………………………………………………………..18

1. Band structure……………………………..……………………………....…..18 2. Light-matter interactions: absorption and emission……………………...……19 3. Recombination lifetime……………………………………...………………...21 4. The indirect to direct band gap crossover of GeSn…………………....………27

CHAPTER 4: THEORETICAL AND EXPERIMENTAL CHARACTERIZATION OF TMPCD SYSTEM……...... 29 1. Introduction to TMPCD……………………………………...... …………...... 29 1.1.Mobility………………………….…………………….……………….….30 2. TMPCD experimental set-up and apparatus……………………………….….31 3. Optical and RF discussion……………………………………………………..35 3.1.TMPCD optics…………....………………….…………………………....35 3.1.1. Injection level.....………..………..……………………….…..35

3.1.2. Attenuation optics………………………….…….……………38 3.2.TMPCD RF……………………………………………...... ……………..40 4. Validation of TMPCD with bulk silicon……………………………..………..45 5. TMPCD with bulk germanium………………..………………………..……...46

CHAPTER 5: RESULTS AND DISCUSSION………………………...... ……….…48

1. Part 1: comparison and interpretation of bulk Si photoconductive decay signal with and without CW light source……………………………....…...………..50 2. Part 2: comparison and interpretation of bulk Si photoconductive decay signal over several orders of injection level……………………….…………...….....53 3. Part 3: comparison and interpretation of bulk Ge photoconductive decay signal over maximum and minimum injection levels……………....………………...57

CHAPTER 6: CONCLUSION AND FUTURE WORK……...……………….....…...61

1. Summary……………………………………………..…………………...…...61 2. Short and long term goals…………………………………………....…...…...61

REFERENCES……………………………...... ……………………………………….64

vii

LIST OF FIGURES

Fig. 2.1. RF energy transfer between Tx and Rx coils…………………………………16

Fig. 3.1. Recombination mechanisms: (a) SRH, (b) radiative, and (c) Auger………...23

Fig. 3.2. 푆푒푓푓 versus injection level 휂 as a function of 휎푝푠 Reproduced from reference # 16, with the permission of AIP Publishing……..……..26

Fig. 3.3. Comparison of Sn concentration and tensile strain on Ge band structure From reference # 1.22, with the permission of AIP Publishing………………….….27

Fig. 3.4. Band gap energy of Ge versus Sn concentration ………………..…………..28

Fig. 4.1. Experimental set-up for TMPD, 1st configuration ……….………………….33

Fig. 4.2. Experimental set-up for TMPCD, 2nd configuration ………………….……..33

Fig. 4.3. Power diode voltage versus incident microwave power………….…………..34

Fig. 4.4. Si injection levels at λ=532nm………………………………………………36

Fig. 4.5. Ge injection levels at λ=532 nm……………………………………….…….37

Fig. 4.6. Ge injection levels at λ=1550 nm………………………………..…………..37

Fig. 4.7. GeSn (2% Sn concentration) injection levels at λ=1550 nm………...………38

Fig. 4.8. Attenuation optics…………………………………………………………....39

Fig. 4.9. Transmitting and receiving coil schematic…………………………………..42

Fig. 4.10. Polar plot of emitted radiation strength…………………………………….43

Fig. 4.11. Microwave confinement optimization……………………………………...44

Fig. 4.12. Transmitting and receiving coil configuration tilted at an angle Θ….……..44

Fig. 5.1. Si transient photoconductive decay signal without CW light source………..50

viii

Fig. 5.2. Semi-log plot of exponential decay close-up, Si transient photoconductive decay signal without CW light source……………………………………………...…51

Fig. 5.3. Si transient photoconductive decay signal with CW light source…………...52

Fig. 5.4. Semi-log plot of exponential decay close-up, Si transient photoconductive decay signal with CW light source…………………………………………………….52

Fig. 5.5. Si transient photoconductive decay signal, ND filter 0……………………...53

Fig. 5.6. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 0……………………………………………………………………...54

Fig. 5.7. Si transient photoconductive decay signal, ND filter 1……………………...54

Fig. 5.8. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 1……………………………………………………………………...55

Fig. 5.9. Si transient photoconductive decay signal, ND filter 2……………………...55

Fig. 5.10. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 2……………………………………...... …………………………….56

Fig. 5.11. Ge transient photoconductive decay signal, maximum injection………...... 57

Fig. 5.12. Semi-log plot of exponential decay close-up, Ge transient photoconductive decay, maximum injection…………………………………………..58

Fig. 5.13. Ge transient photoconductive decay signal, minimum injection…………...58

Fig. 5.14. Semi-log plot of exponential decay close-up, Ge transient photoconductive decay, minimum injection……………………………………………………………..59

LIST OF TABLES

Table 1. Measured average power and corresponding pulse energy………………….46

Table 2. Summary of results………………………………………………………...... 49

CHAPTER 1

BACKGROUND AND MOTIVATION

The flourishing of applied optics in the second half of the twentieth century represents a renaissance in and of itself [1]. In the 1950’s, optics was predominantly associated with communication theory; this drew attention to the infrared end of the electromagnetic spectrum, which in turn stimulated the development of infrared materials

[1]. The development of the high-speed digital computer during the mid-1940’s brought with it a need for improvement in the design of much more complicated optical systems

[1]. This would eventually lead to one of the pinnacles of optics research, the invention of the laser. Bell Labs patented this crowning achievement in 1960 [1, 2]. Within a decade laser beams spanned the range from infrared to ultraviolet [1]. The availability of high- power coherent sources led to the discovery of a number of new optical effects and with it, a variety of new devices [1].

In February of 2016, the semiconductor industry acknowledged that Moore’s law is approaching its limit [3]. Chipmakers cannot overcome the heat that is unavoidably generated when more and more transistors are packed into the same small area. Copper wires temporarily kept Moore’s Law going. However, after a short time, it was recognized that copper wires degraded the transmitted signal. The almost exclusive use, for the last one hundred years, of electrical signals to handle and transmit data is now rapidly giving way to more efficient optical techniques [1]. Photonic materials present a

solution to the continued advancement of integrated optoelectronic devices.

The fabrication of truly integrated optoelectronic microchips has dominated research in the semiconductor industry since the last decade of the 20th century. As early as 1993, the possibility of inducing light emission from silicon, an indirect bandgap material in which radiative transitions are unlikely, was starting to be considered in the literature [4]. Limitations that constrain silicon from emitting light efficiently were examined, as well as potential solutions. The postulated solutions that have been since developed include intrinsic and alloy-induced luminescence; radiately active impurities; quantum-confined structures, including zone folding and the recent development in porous silicon; and a hybrid approach, the integration of direct bandgap materials onto silicon [4].

Key advantages of Si-based materials and processing are the high yield and low production cost established in microelectronics, such as in foundry fabrication facilities for integrated silicon circuits [5], as well as true monolithic integration of circuitry and

CMOS technology. Transistors represent one of the pinnacles of modern electronics, and are used extensively in programmable logic, DC-DC converters, automotive electronics, and power electronics [6 ], to name just a few applications. Currently, there are new strained-silicon channel trench-gate power MOSFETs with a 72% improvement in peak transconductance at the cost of only 12% reduction in breakdown voltage when compared to the conventional gate MOSFET [6]. In order to achieve higher quality optoelectronic devices, the continued progression of silicon photonics is vital. Silicon photonics has recently been proposed for a diverse set of applications at mid-infrared wavelengths [7].

While a number of Si waveguide integrated optoelectronic devices have been

demonstrated in this wavelength range, efficient photodetection remains an important and challenging task [7]. Novel 2D Graphene/Silicon heterojuncton photodetectors have been fabricated with considerable responsivitity of 270 mAW-1 [8]. However, though viable heterogeneous photodetectors have been demonstrated [8-12], integration schemes present an inherent difficulty by imposing constraints on material quality and process integration [7]. Extrinsic detectors can alleviate the need for heterogenous integration [7].

Planar waveguide geometric configuration as well as the utilization of dopant-induced trap states within the bandgap of a host material has allowed for the realization of integrated mid-IR silicon photodiodes that offer simple processing, integration, and operation throughout the mid-infrared via appropriate choice of dopant [7]. A silicon- based planar diode with supersaturated gold dopant was demonstrated, with spectral response extending to wavelengths as long as 2,200 nm [13]. Si planar photoconductive detectors using Zn, Se, and Au dopants have also been demonstrated [14-15], as well as room temperature operation of Zn+ implanted Si waveguide photodiodes from 2.2 μm to

2.4 μm [7]. Single-photon detection is also important in CMOS devices, especially over the visible and near-IR range [16]. The development of silicon single-photon avalanche diodes (SPAD) is in progress of achieving high detection efficiency while simultaneously achieving excellent timing jitter over a broad spectral range [16]. Absorption enhancement in silicon has also been used extensively for photovoltaic application in solar cells; third generation Si multi-type layers achieve up to 33% efficiency enhancement in photovoltaics [17]. Besides optical detectors, optical emitters would be a component in integrated optical circuits containing logic, memory, and interconnect functionalities [5]. The progression for silicon-based light-emitting devices is being

motivated particularly for light-emitting diodes (LED’s) and laser applications [5]. Much work has been shown that the issue of inefficient light emission can be overcome from silicon itself due to phonon-mediated light emission [5]. This was realized with the all- silicon Raman laser [18].

Due to the high band gap of Si and its indirect nature, the realization of Si- based active photonic devices, including infrared optical detectors, modulators, and emitters has been limited. Direct-bandgap group IV materials may represent a solution towards the monolithic integration of Si-photonic circuitry and CMOS technology [4]. In particular, germanium/germanium-tin alloys represent a new class of photonic semiconductor materials with tunable band structure for optoelectronics integrated on Si.

Ge has a future in the next generation of optoelectronic devices and they are also attractive candidates for next generation transistors in Si-based microprocessors [19].

Germanium has recently gained attention as a channel material to replace silicon in metal-oxide semiconductor field-effect transistor (MOSFETs). Particularly, Ge is well suited for p-type devices, thanks to its high hole mobility, which is about four times greater than silicon. Ge is also an improvement due to processing related issues, such as dopant solubility and Fermi level pinning in the valence band [20]. GeSn has been predicted to exhibit carrier mobilities exceeding those of both Ge and Si, which makes

GeSn suitable as an alternative channel material in CMOS technology [21]. It has been demonstrated that GeSn thin films can be used to fabricate high quality junctionless depletion-mode operation pMOSFETs on Si substrates [21].

Ge-on-Si devices have already been utilized in order to fabricate novel near-

IR photodiodes and photodetectors [22, 23, 24]. However, a major limitation of Ge1-xSix

alloys is that their bandgaps do not cover the entire telecom range between 1260 and

1670 nm [22]. Another disadvantage is that their inherent mismatch with the underlying

Si platform produces structural and morphological imperfections, which hinder the IR detector performance [22]. Lasing has occurred with monolithic Ge-on-Si [25], but continued improvements of the Ge/Ge-on-Si devices that might eventually lead to practical electrically injected lasers may require a reduction of doping levels in the active region as well as a reduction in tensile strain [26]. However, enhancement of optical absorption and emission in germanium can also be accomplished using Sn-alloying [26,

27]. Increased Sn concentrations in the GeSn alloy are expected to shift the responsivity or near IR photodiodes and photodetectors further into the infrared, overlapping the wavelength range of InGaAs materials [22, 28]. The conjecture of enhanced optical emission has been seen in GeSn waveguides at room temperature [29] and also realized with the low temperature GeSn laser [30]. Another important application for GeSn alloys grown in silicon is photovoltaics. GeSn alloys are the first practical group IV ternary system fully compatible with Si CMOS processing [31]. Not only are they used as active layers for band gap tuning, but they enable structural buffers for the direct integration of dissimilar compounds with Si, making GeSn alloys an extremely versatile IR material

[31]. It has been shown that the ternary alloy SiGeSn alloy can be incorporated as the highly sought ~ 1eV gap material to complement the state-of-the-art Ge/InGaAs/InGaP multijunction solar cells, offering a significant improvement on efficiency and dramatic reductions in the device cost [31]. The Group IV based alloy was utilized to fabricate a four-junction solar cell capable of maximum high efficiency of 47% [32].

Ge and GeSn thin film alloy films are being produced by a number of groups at institutions around the world. Epitaxial growth of single crystal Ge on Si substrates has been an area of interest since the early 1980’s. This growth mechanism can lead to high threading dislocation densities in the Ge films, which is mainly due to the lattice mismatch between Ge and Si. The materials grown at Arizona State University

(ASU) are grown in such a way to minimize the dislocation density. ASU has developed a new method for low-pressure chemical vapor deposition (LPCVD) growth of Ge-on-Si using a custom engineered metal-organic gaseous precursor [19]. Ge is grown directly on

Si(100) substrates via thermal decomposition of digermane Ge2H6 and the purposely- engineered additive digermylmethane (GeH3)2CH2. The deposition is performed in a

UHV-CVD reactor at temperatures of 320-400°C and pressures in the 10-4 Torr range.

This is followed by rapid thermal annealing (RTA) at temperatures of 600-680 °C to reduce the threading dislocation density and improve the crystallinity of the film. This method produces high-quality Ge-on-Si films with atomically flat surfaces. Doping of the films is performed in-situ by addition of diborane B2H6 and trigermyl phosphine

(GeH3)3P for p-type and n-type layers, respectively, producing films with carrier concentrations into the 1019 cm-3 range [19]. These methods were used to synthesize the

Ge films presented within this thesis.

Similarly, the growth of high-quality Ge1-xSnx films (0

thin films is performed in several custom hot-wall UHV-CVD reactors at temperatures of

350-390 °C. Doping of these films is achieved, as in the pure Ge films, by addition of diborane B2H6 and trigermyl phosphine (GeH3)3P for p-type and n-type layers, respectively, producing films with carrier concentrations into the 1019 cm-3 range [19].

These methods were used to synthesize the GeSn films presented within this thesis. In general, it has been found that GeSn alloys have a Ge-like band structure below the indirect to direct band gap crossover, with the expected critical points and a drastic redshift of the interband transitions with increasing Sn content, along with a strong broadening [33]. The compositional dependence of the lowest direct and indirect band gaps in Ge1-xSnx alloys has been determined from room-temperature photoluminescence measurements [34].

CHAPTER 2

RECOMBINATION LIFETIME: AN IMPORTANT METRIC FOR THE

CHARACTERIZATION OF SEMICONDUCTOR MATERIALS

1. Introduction

Knowledge of minority carrier lifetime is of considerable importance in the study of semiconductor and photovoltaic materials [35]. Even though lifetimes are routinely measured in the IC industry, their measurement and measurement interpretation are frequently misunderstood [36]. Both bulk and surface recombination occur simultaneously and their separation is often quite difficult [37]. The measured lifetime is always an effective lifetime, consisting of both bulk and surface components. Whereas

Shockley-Read-Hall (SRH) recombination is controlled by the cleanliness of the material,

Auger recombination is an intrinsic property of the semiconductor [37]. Lifetime is one of few parameters that gives information about the defect densities in semiconductors in the low-density regime. No other technique can detect defect densities as low as 109-1011 cm-3 in a simple, contactless room temperature measurement. In principle, there is no lower limit to the defect density determined by lifetime measurements [36]. The other type of recombination lifetime to consider is called radiative recombination, which plays almost no role in Si except for very high lifetime substrates but is important in direct band gap semiconductors like GaAs [37].

The effective lifetime can be measured by inducing optical or electrical injection; the method used within this thesis, as well as the other methods discussed in this section, utilizes optical injection [37]. Different measurement methods can give widely differing lifetimes for the same material or device. In most cases, the reasons for these discrepancies are fundamental and are not due to a deficiency in the measurement. The difficulty with defining a lifetime is that we are describing a property of carriers within the semiconductor rather than the property of the semiconductor itself [36 ].

A common optical technique is based on the analysis of photoconductance decay transients after a very short light pulse from a laser, flash lamp, light emitting diode

(LED) array or laser diode [38]. The study of the excess conductivity induced in a material by pulsed optical excitation yields information on the optoelectronic properties of the material [39]. These properties indicate performance of devices; for example, decay processes in semiconductors can be used to characterize materials involving lattice defects [39]. In conventional conductivity experiments, the interpretation of results is complicated by the presence of contacts [39]. Thus, a contactless, non-invasive technique is the only viable option for rapid and non-contaminating sample evaluation of carrier lifetime [40]. The effective lifetime is obtained from the slope of the decay curve [38].

There are a number of techniques that are currently in use for contactless measurement of the carrier lifetime in semiconducting and photovoltaic materials [40]. However, there has previously been single diagnostic means available that allows for quick analysis of recombination lifetime applicable to a wide range of materials [41]. The discussion of the methods for recombination lifetime analysis in this section includes their advantages as well as their drawbacks. The techniques discussed are the following: time resolved

photoluminescence, microwave reflection photoconductive decay, quasi-steady state photoconductivity, resonant coupled photoconductive decay, and finally, transmission modulated photoconductive decay, which is the method utilized within this thesis.

2. Time resolved photoluminescence (TRPL)

To obtain insight into the dynamics of recombination processes in a semiconductor, photoluminescence decay is an extensively used experimental technique

[42]. Time-resolved photoluminescence (TRPL) is a common technique used to measure the lifetimes of semiconductors with strong optical emission, such as GaAs and other related compounds [40, 43]. It has also been shown to yield effective lifetimes for certain

PV materials like CdTe [44, 45] and epitaxially grown germanium on silicon [46].

Photoconductive decay senses the conductivity of all excess carriers whereas photoluminescence decay senses only direct electron-hole recombination via photon emission [44]. The diagnostic was developed by Jüri Vilmst and William E. Spicer at

Stanford University in 1964 [43]. The first semiconductor material whose minority carrier radiative lifetime measured with TRPL was p-type gallium arsenide [43]. The apparatus for TRPL includes a photo excitation pulsed laser source, a spectrometer, and a photomultiplier that collects the PL transient intensity for time correlated single photon counting [44, 45]. TRPL is applicable to very low mobility materials (unlike the other photoconductive techniques described later on). The intensity of the photoluminescence was observed to vary linearly with the number of injected carriers over several orders of magnitude, indicating that over a certain range, recombination lifetimes are independent of the excess carrier densities produced by photo excitation [43]. In other words, TRPL is not significantly influenced by mobility variations, unlike the method used in this thesis.

However, the interpretation of the PL curve in order to determine minority carrier lifetime becomes increasingly complicated at higher excitation densities and when the interference recombination velocity (surface recombination velocity) differs from zero

[42]. Auger recombination also increases significantly at high injection, complicating the measurement. The most significant drawback of the TRPL technique is that it is only applicable for semiconductors with strong luminescence; it is very difficult to apply this method to silicon, germanium, and other indirect bandgap materials [40]. TRPL also requires time-correlated single photon detectors, which are very expensive in the infrared.

3. Quasi-steady state photoconductivity (QSSPC)

The simple method for implementing the steady-state photoconductance technique for determining minority carrier lifetime of semiconductor materials was developed by Ronald A. Sinton from Sinton Consulting and Andres Cuevas from the

Department of Engineering at Australian National University; their first publication demonstrating the success of QSSPC appeared in APL in August of 1996 [38]. By means of photoconductance measurements, it is possible to study various mechanisms present in a semiconductor and their characteristic parameters as bulk lifetime, surface recombination, and emitter recombination current in a wide range of injection level conditions [47]. Photoconductance instruments operating at 8-10 MHz are used as apparatus. A coil in a bridge circuit couples to the conductivity of the wafer. A signal proportional to this conductivity is observed on a digital oscilloscope. A light source generated by a flash lamp or LED with a relatively long pulse is used [38, 47]. The steady state condition is maintained as long as the flash lamp/LED source time constant is longer than the effective carrier lifetime [36]. The time-varying photoconductance is

detected by inductive coupling; the excess carrier density is calculated from the photoconductance signal [36]. In this technique, the effective lifetime is determined following every light intensity (similar to a solar cell in action), which allows the measurement of very low lifetimes without fast electronics or short light pulses; the range of lifetimes measured is limited only by signal strength [38, 47]. QSSPC is capable of measuring lifetimes in the ns to ms range [38, 47]. In the case of very low lifetimes, surface recombination transients and minority carrier spreading effects are present that complicate the interpretation of the measurements. QSSPC is aimed at simplifying the determination of very low lifetimes [38]. A further benefit of the QSSP technique is that the data implicitly contains information about the short-circuit current versus open-circuit voltage, an important characteristic in the study of PV materials [38]. The QSSPC technique is designed for and is currently the standard technique used in the wafer silicon community. However, the QSSP does not function for other PV materials [40].

Recombination lifetime measurements on thin films require fast electronics, and a much shorter pulse duration. The QSSPC technique is not sensitive enough for thin films, but sufficient enough for bulk Si wafers.

4. Transient microwave reflection photoconductive decay (µPCD)

The well-known transient microwave-reflection-technique (µPCD) is the silicon industry standard for the contactless measurement of minority-carrier lifetime [40, 48].

Developed in the early 1960’s by S. Deb and B.R. Nag at the Institute of Radio Physics and Electronics, Calcutta, India, [35], this method is used for short minority-carrier lifetime applications. PCD techniques differ from TRPL because PCD senses carriers released from shallow traps as well as the photo-generated electron-hole pairs. The

change in conductivity, which is related to both the excess carrier density the mobility, is given by

∆휎 = 푒휇∆푁 2.1

where ∆푁 is the injection level or excess carrier density, e is the fundamental charge, and μ is the mobility of the carriers. Mobility is a quantity that describes how easily charges can move through a material. At low level injection (∆푁 << po, no), μ stays constant and the conductivity decays at the same rate as the excess carrier density. At high level injection (∆푁 >> po, no) μ is no longer constant and will also decay, but at a different rate than the excess carrier density. The PCD signal picks up both the excess carrier density and mobility variations.

The µPCD apparatus consists of microwaves generated at frequencies from 26.5 to 40 GHz [49, 50], which are directed via a circulator to the sample/waveguide system

[35]. The high frequency combined with the low field strength of the microwave field permits the drift of the charge carriers to be neglected, so that only diffusion, generation, and recombination of charge carriers have to be taken into account [49]; the use of waveguide equipment considerably reduces the geometrical problems inherent to free electromagnetic waves and also reduces perturbations [49]. The reflected microwaves are directed by the circulator to a detector. The guided wave undergoes attenuation because of the presence of the sample. The amount of attenuation suffered due to free carrier absorption is a function of conductivity of the sample. When the latter is modulated by injecting a pulse of minority carriers or by irradiation, the attenuation and hence, the transmitted power changes. The time rate of change of transmitted power on switching off the modulating source, the injected current or the source of light, gives the lifetime of

minority carriers in the sample [35, 39]. Although it has been highly developed, the drawbacks of µPCD are that it has a very low sensitivity and a small dynamic range (low injection level contingent), particularly with low-mobility, short lifetime films, and does not always provide the desired data [40]. The reason being is that the microwave penetration depth is a complicated function of frequency and sample conductivity [50].

However, µPCD is able to measure lifetimes in the ns range [40], which is the range applicable to thin film and many photovoltaic materials.

5. Resonant coupled photoconductive decay (RCPCD)

The Electro-optical Characterization Team at National Renewable Energy

Laboratory (NREL) invented the method of resonant coupled photoconductive decay

(RCPCD) in September of 1997 [40, 48, 50, 51, 52]. It is the primary lifetime tool used by the Measurements and Characterization group at NREL for silicon and other indirect photovoltaic materials [40]. This technique has fewer limitations as compared to microwave reflection. As a pump-probe technique, RCPCD uses an optical pump and microwave frequencies between 400-900 MHz, which penetrate most wafers and common doping levels with several microns thickness [50]. However, the peak response time is over the range of 415-420 MHz [50].

An oscillator provides the bridge circuit with a high frequency voltage signal. The sample to be tested is positioned near the coil such that a variable mutual inductance is created between the sample and the coil. After the dark conductivity or null darkness effects of the sample are negated by balancing the bridge circuit, a pulsed laser or other light source illuminates the sample, which creates a measurable imbalance in the bridge circuit that is indicative of the excess carrier density of the sample under test. The sample

is positioned near the coil such that the illumination of the sample creates a linearly related change in the impedance of the bridge circuit [50, 52]. RCPCD is more sensitive than µPCD yet can only measure a minimum lifetime of 40ns, and depends on the quality factor (Q) of the given RCPCD measurement system [40]. Due to its 40-50ns limit for lifetime measurements, RCPCD cannot measure lifetimes in the shorter lifetime range that are commonly found in compound semiconductor materials and thin film silicon

[40]. RCPCD has a large dynamic range, meaning that its results can range over several magnitude of injection level [40, 50]. The technique has been successful in measuring small-band semiconductors such as InAs and mismatched InGaAs grown on InP substrates [50]. RCPCD gives results on the minority carrier lifetime, as well as information about the ambipolar mobility, the relative diffusion length, the spectral response of the semiconductor, the specific sensitivity of the photoconductor

(semiconductor), and the photoexcitation spectra (PES), which gives the relative absorption coefficient of thin films as well as the absorption coefficient of deep impurity levels [50, 51].

6. Transmission modulated photoconductive decay (TMPCD)

The method described as Transmission Modulated Photoconductive Decay

(TMPCD) was developed by Richard Keith Ahrenkiel and Donald John Dunlavy at

Colorado School of Mines in 2013 [41]. The TMPCD set-up involves two radio frequency coils, operating between approximately 200 MHz and 900 MHz, preferably at or between about 400 MHz and 700 MHz [41]. In principle, contactless excess conductivity measurements can be performed over a relatively large probing frequency range [39]. One coil is used as a transmitter antenna and the second coil as a receiver

antenna. Both coils are mounted in shielded cavities and are shielded from each other.

The photoconducting sample is mounted above the intra-coil shield and acts as a waveguide for radio frequency energy transfer between the transmitting (Tx) coil and the receiving (Rx) coil. This configuration is shown in Figure 2.1.

Thin film

Substrate

Tx coil Rx coil

Fig. 2.1. RF energy transfer between Tx and Rx coils.

The transmitted radio frequency signal is modulated by optically induced photoconductivity in the sample. Using a fast, pulsed light source, the transmitted signal amplitude tracks the photo-induced carriers in real time. The high frequency RF signal at the receiving coil is converted into a transient DC signal that is proportional to the conductivity in the material as function of time. The change in microwave transmission due to photogenerated carrier absorption represents the transient photoconductivity of the sample. This signal is observed and stored, such as on an oscilloscope, and like µPCD, the change in conductivity is modeled by Eq. 2.1. By analyzing the decay time of the transient signal, the carrier recombination lifetime can be measured [41]. The response time (or rise time) is 10ns or less [40, 41]. The recombination lifetime resolution limit is better than in currently known methods, such as RCPCD. It has been shown [40] that

TMPCD has sensitivity equal to or exceeding that of RCPCD and, in addition, has a considerably faster response time [40, 41]. This technique is able to measure carrier

lifetime in non-conventional films that could not be measured with the other techniques in industry; for example, nanocrystalline silicon thin films [40].

CHAPTER 3

BAND STRUCTURE, ABSORPTION/EMISSION, AND RECOMBINATION

1. Band structure

There are two distinct classes of semiconductors: direct and indirect bandgap materials [53]. Direct bandgap materials assume transitions with zero momentum exchange. Conversely for indirect bandgaps, the lowest photon energy that can be absorbed involves a change of momentum. This momentum change is substantial therefore and must come from another source when it cannot be supplied by the incoming photon. In this case, a vibration of the crystalline lattice, or phonon, is utilized to complete the process. These additional constraints serve to lower the emission probability, thereby increasing the radiative lifetime. Since nonradiative lifetimes in thin films are typically fairly low, then the carriers will most likely recombine nonradiatively.

The best-known semiconductor is silicon (Si). Together with germanium (Ge), it is the prototype of a large class of semiconductors with similar crystal structures [54]. The crystal structure of Si and Ge is diamond cubic structure. These tetrahedrally bonded semiconductors form the mainstay of the electronics industry and the cornerstone of modern technology [54]. Also within the family of diamond cubic structures is α –Sn, which is a zero-gap semiconductor also known as “gray” tin [54]. In this crystalline structure, four neighbor atoms surround each atom, forming a tetrahedron.

Si has a large, indirect band gap energy of 1.12eV. It is an inefficient optical emitter with no optical absorption past 1.1 microns (NIR). Ge is an indirect semiconductor with a band gap energy lower than that of Si, equal to 0.66 eV. However, though Ge is indirect bandgap in nature, it is often referred to as a “quasi-direct” band gap material because the small difference between the conduction band minima at the L- and Γ-points results in spillover of charge carriers from the L-valley to the Γ-valley, thereby inducing direct gap optical emission.

Pure Sn has two possible crystal phases: β-Sn (white tin), which has a tetragonal structure, and α-Sn (grey tin), which has the diamond cubic structure. The energy of formation for β-Sn is slightly lower than that for α-Sn, so the typical structure of crystalline Sn at room temperature is tetragonal. However, when Sn is added to the Ge crystal under the right growth conditions, the structure is forced into the diamond cubic configuration. Grey tin is a semimetal [55]. In other words, the bottom of the conduction band and the top of the valence band meet at the Γ-point, so the band gap is zero.

However, if one compares the band structure of Ge and α-Sn, the energy difference between the two bands that form the lowest band gap in Ge is actually negative in the case of α-Sn. The alloy material GeSn has a band structure that is a combination of the individual Ge and α-Sn band structures.

2. Light-matter interactions: absorption and emission

Optical absorption properties of semiconductors are intimately related to the density of states of allowed states in the conduction and valence bands. The calculation of the absorption coefficient α(ω) for direct bandgap materials takes into account the number density of states and 퐸 − 푘⃗ relationships in both the conduction band for electrons (with

effective mass me) and the valence band for holes (with effective mass mh) [53]. The energy different Ecv in the vicinity of the energy gap can be expanded as

ℏ2 퐸 = + 푘2 , 푐푣 푔 2휇 3.1

−1 −1 −1 where 휇 is the effective mass, defined by 휇 = 푚푒 + 푚ℎ [54]. The joint density of states,퐷푗, can be calculated to be [54]

1 3 1 2 2 2 휇 2 [ 2 3] (퐸푐푣 − 퐸푔) 푓표푟 퐸푐푣 > 퐸푔 퐷푗 { 휋 ℏ . 3.2 0 푓표푟 퐸푐푣 < 푔

This calculation takes into consideration the following two conservation laws that rule the optical absorption process [53]:

1. The total energy (electron+hole+photon) must be conserved

2. The total momentum or wavevector must also be conserved

The process of absorption/emission for indirect bandgap semiconductors can occur when the energy of the incoming photon is larger than the indirect bandgap; the wave vector difference between the electrons in the two bands is supplied by the phonon [53,

54]. If the phonon energy and wave vector are denoted by Ep and Q, the energy- and wave vector-conservation conditions in the optical process are represented by the relation

ℏ휔 = 퐸푐푣 ± 퐸푝 and 푘푐 − 푘푣 = ∓푄 , 3.3 where + and – correspond to emission and absorption of a phonon respectively [54].

Processes involving several phonons are in principle also possible but usually with much smaller probabilities [54].

When an electron is excited in the conduction band with energy greater than the gap at the Γ-point so that direct 푘⃗ = 0 transition is possible, it will generally thermalize down very quickly to the indirect band edge, and light emission will only take place at the final 20

recombination step at the lowest bandgap. Since a phonon is also needed in the process of indirect emission, the transitional probability is very low. This makes the materials of Si and Ge poor light emitting systems [53]. Optoelectronic devices, such as lasers and photodetectors, involve the optical transitions of the fundamental absorption edge [54]; therefore, the efficiency of optoelectronic devices is contingent on the band structure of the material that comprises them.

3. Recombination lifetime

Whenever the thermal-equilibrium condition of a semiconductor system is

2 2 disturbed (푝푛 ≠ 푛푖 ), processes exist to restore the system to equilibrium (푝푛 = 푛푖 )

2 2 [56]. These processes are recombination (푝푛 > 푛푖 ) and thermal generation (푝푛 < 푛푖 )

[56].

Lifetimes fall into two primary categories: recombination lifetimes and generation lifetimes. The concept of recombination lifetime 휏푟 holds when excess carriers decay as a result of recombination. Generation lifetime 휏푔 applies when there is a paucity of carriers.

For example, generation occurs in the space-charge region (scr) of a reverse-biased device as the device tries to attain equilibrium [36]. When these recombination and generation events occur in the bulk, they are characterized by 휏푟 and 휏푔. When they occur at the surface, they are characterized by the surface recombination velocity 푠푟 and the surface generation velocity 푠푔 [36].

The bulk recombination rate R depends non-linearly on the deviation of the carrier densities from their equilibrium values [36]. A p-type semiconductor is considered throughout this discussion; therefore, the behavior considered is that of the minority electrons. Confining to linear, quadratic, and third order terms, R can be written as

2 2 2 2 푅 = 퐴(푛 − 푛표) + 퐵(푝푛 − 푝표푛표) + 퐶푝(푝 푛 − 푝표 푛표) + 퐶푛(푝푛 − 푝표푛표 ) , 3.4 where 푛 = 푛표 + ∆푛, 푝 = 푝표 + ∆푝; 푛0, 푝표 are the equilibrium concentrations and ∆푛, ∆푝 are the excess carrier densities. In the absence of trapping (∆푛 = ∆푝), the bulk recombination rate R can be simplified to:

2 2 2 푅 ≈ 퐴(∆푛) + 퐵(푝0 + ∆푛)∆푛 + 퐶푝(푝표 + 2푝표∆푛 + ∆푛 )∆푛 + 퐶푛(푛표 + 2푛표∆푛 +

∆푛2)∆푛 . 3.5

Some terms containing 푛표 have been dropped because 푛표 ≪ 푝표 in a p-type material. The recombination lifetime is defined as

∆푛 1 휏푟 = = 2 2 2 2 . 3.6 푅 퐴+퐵(푝표+∆푛)+퐶푝(푝표 +2푝표∆푛+∆푛 )+퐶푛(푛표 +2푛표∆푛+∆푛 )

Three main recombination mechanism determine the recombination lifetime:

Shockley-Read-Hall (SRH) or multiphonon recombination characterized by 휏푆푅퐻, Auger recombination characterized by 휏퐴푢푔푒푟, and radiative recombination, 휏푟푎푑 [36]. Both radiative and Auger recombination describe the two types of band to band transitions.

During radiative recombination, electron-hole pairs (ehps) recombine directly from band to band with the energy carried away by photons. During Auger recombination, a third carrier, either a free electron or hole, absorbs the recombination energy from band to band transitions [36, 56]. The former is the inverse of direct optical absorption, and the latter is the inverse of impact ionization [56]. Figure 3.1 illustrates both types of band to band (radiative and Auger) transitions and recombination through single level traps

(SRH).

E E Phonon C Photon ET

E V Excited Carrier

(a) (b) (c)

Fig. 3.1. Recombination mechanisms: (a) SRH, (b) radiative, and (c) Auger.

Band-to-band transitions are more probable for direct band gap semiconductors, which are more common among III-V compounds [56]. For this type of transition, the recombination rate,푅푒 is proportional to the product of the electron and hole concentration given by:

푅푒 = 푅푒푐푝푛 . 3.7

The term 푅푒푐 is referred to as the recombination coefficient; it is a function of temperature and contingent on the band structure of the semiconductor. A direct bandgap semiconductor, which has more efficient band to band transitions, has a much larger Rec

(~10-10 cm3/s) than an indirect band gap semiconductor [56]. The radiative lifetime can be written as,

1 휏푟푎푑 = , 3.8 퐵(푝표+푛표+∆푛) where B is the radiative recombination coefficient. The radiative lifetime is inversely proportional to the carrier density because in band to band recombination, both electrons and holes must be present simultaneously [36].

In contrast to radiative transitions, a third carrier absorbs the energy during Auger recombination. Therefore, Auger lifetime is inversely proportional to the carrier density squared; it is given by

1 휏퐴푢푔푒푟 = 2 2 2 2 , 3.9 퐶푝(푝표 +2푝표∆푛+∆푛 )+퐶푛(푛표 +2푛표∆푛+∆푛 ) where 퐶푝 is the Auger recombination coefficient for holes and 퐶푛 for electrons [13].

During SRH recombination, (electron-hole-pairs) EHPs recombine through deep- level impurities or traps. SRH recombination lifetime is characterized by several factors, including density of traps, NT, energy level ET, and capture cross-sections 휎푛 and 휎푝 for electrons and holes respectively [36]. In contrast to band to band transitions (where energy is liberated via a photon or third carrier) SRH recombination lifetime energy dissipates by phonons. SRH lifetime can be described by the following equation

휏푝(푛표+푛1+∆푛)+휏푛(푝표+푝1+∆푝) 휏푆푅퐻 = , 3.10 푝표+푛표+∆푛

퐸푇−퐸𝑖 퐸푇−퐸𝑖 1 1 where 푛1 = 푛푖exp ( ); 푝1 = 푛푖exp (− ); and 휏푝 = ; 휏푛 = . 푘푇 푘푇 휎푝휐푡ℎ푁푡 휎푛휐푡ℎ푁푡

Finally, the overall recombination lifetime 휏푟 is determined according to the relationship

1 휏푟 = −1 −1 −1 . 3.11 휏푆푅퐻 + 휏푟푎푑 +휏퐴푢푔푢푒푟

Eqs. 3.8, 3.9, and 3.10 simplify for both the low-level and high-level injection cases.

Low-level injection holds when the excess minority carrier density is low compared to the equilibrium majority carrier density, ∆푛 ≪ 푝0. Similarly, high-level injection holds when ∆푛 ≫ 푝0. The injection level is important during lifetime measurements [36]. The appropriate expressions for low-level (ll) and for high-level ( hl) injection becomes

푛1 푝1 휏푆푅퐻(푙푙) ≈ 휏푝 + (1 + ) 휏푛 ≈ 휏푛; 휏푆푅퐻(ℎ푙) ≈ 휏푝 + 휏푛 3.12 푝표 푝표

1 1 휏푟푎푑(푙푙) ≈ ; 휏푟푎푑(ℎ푙) ≈ 3.13 퐵푝표 퐵∆푛

1 1 휏퐴푢푔푒푟(푙푙) = 2 ; 휏퐴푢푔푢푒푟(ℎ푙) = 2 . 3.14 퐶푝푝표 (퐶푝+퐶푛)∆푛

The recombination lifetime (as described by equation 3.11) for Si is dependent upon injection level. At high carrier densities (or high doping levels), the lifetime is controlled by Auger recombination due to its characteristic 1/n2 dependence [36]. At low carrier densities, the lifetime is controlled by SRH recombination [36]. Whereas SRH recombination is controlled by the cleanliness of the material, Auger recombination is an intrinsic property of the semiconductor [36]. Radiative recombination plays almost no role in Si. The bulk SHR recombination rate is given by

휎 휎 휐 푁 (푝푛−푛 2) (푝푛−푛 2) 푅 = 푛 푝 푡ℎ 푇 𝑖 = 𝑖 . 3.15 휎푛(푛+푛1)+휎푝(푝+푝1) 휏푝(푛+푛1)+휏푛(푝+푝1)

This leads to the SRH lifetime expression Eq. 3.10. The surface SRH recombination rate is

2 2 휎푛푠휎푝푠휐푡ℎ푁𝑖푡(푝푠푛푠−푛𝑖 ) 푠푛푠푝(푝푠푛푠−푛𝑖 ) 푅푠 = = , 3.16 휎푛푠(푛푠+푛1푠)+휎푝푠(푝푠+푝1푠) 푠푛(푛푠+푛1푠)+푠푝(푝푠+푝1푠) where

푠푛 = 휎푛푠휐푡ℎ푁푖푡; 푠푝 = 휎푝푠휐푡ℎ푁푖푡 , 3.17 where 푝푠 and 푛푠 are the hole and electron densities at the surface; 푁푖푡 is the interface trap density of the material, and 휐푡ℎ is the thermal velocity of the carrier in question. The surface recombination velocity 푠푟 is

푅푠 푠푟 = . 3.18 ∆푛푠

Substituting Eq. 3.16 into Eq. 3.18 yields the following expression for surface recombination velocity:

푠푛푠푝(푝표푠+푛표푠−∆푛푠) 푠푟 = . 3.19 푠푛(푛표푠+푛1푠+∆푛푠)+푠푝(푝표푠+푝1푠+∆푝푠)

The surface recombination velocity for low-level and high-level injection becomes

푠푛푠푝 푠푛푠푝 푠푟(푙푙) = 푛1푠 푝1푠 ≈ 푠푛; 푠푟(ℎ푙) = . 3.20 푠푛( )+푠푝(1+ ) 푠푛+푠푝 푝표푠 푝표푠

SRV is a measure of passivation quality. Surface recombination velocity depends strongly upon both injection level and resistivity. Experimentally in Si, Seff can be as low as 100 cm/sec and as high as 104 cm/sec [57]. Figure 3.3 shows the dependence of effective SRV on injection level at the SiO2/Si interface.

Fig. 3.2. 푆푒푓푓 versus injection level 휂 as a function of 휎푝푠 Reproduced from Ref. # 58, with the permission of AIP Publishing.

Finally, the effective lifetime (휏푒푓푓) of the excess carriers of an indirect semiconductor film be comprised of BOTH bulk (휏푟) and surface (휏푠) recombination components. The relation can be written as

1 1 푠 +푠 = + 1 2 , 3.21 휏푒푓푓 휏푟 푑

where 푠1 and 푠2 are the surface recombination velocities (SRVs) at the top and bottom of the film, and d is the thickness of the film.

4. The indirect to direct band gap crossover of GeSn

The indirect energy band gap in Ge makes it difficult to achieve efficient light emission. Nevertheless, the fact that the tantalizingly small energy separation of 140 meV between indirect (L) and direct (Γ) conduction band valleys in Ge can be overcome; one of the ways utilized to control the Ge band structure is tensile strain [59]. Substituting Sn into the Ge lattice to form the semiconducting GeSn alloy has also been found to result in an effect similar to that observed in Ge under tensile strain [28, 59]. The comparison of the substitution of Sn into the Ge lattice versus the application of tensile strain and its effect on decreasing the energy separation between indirect and direct conduction band valleys in Ge is displayed in Figure 3.3.

Fig. 3.3. Comparison of Sn concentration and tensile strain on Ge band structure Reproduced from Ref. # 26, with the permission of AIP Publishing.

By varying the Sn concentration, it is possible to observe direct band gap emission in Ge. Past the critical Sn concentration (~7%), the minimum of the Γ –point

becomes lower than the L-point, yielding a tunable, direct band gap material [34]. The change in band gap energy as a function of Sn concentration is demonstrated in Figure

3.4. The small Sn concentrations do not alter the optical properties in any measurable way, thus the material is referred to as “quasi-Ge” [60].

Fig. 3.4. Band gap energy of Ge versus Sn concentration.

CHAPTER 4

THEORETICAL AND EXPERIMENTAL CHARACTERIZATION OF TMPCD

SYSTEM

1. Introduction to TMPCD

The TMPCD method works by measuring the change in conductivity of the material as a function of time after a short (nanosecond time scale) pulse from a laser hits the surface of the sample. Light is focused onto the sample where it is absorbed in a process called

“photo-excitation” [53]. In general, when photons are absorbed in a semiconductor material, electron-hole pairs are generated. As a result of the excess energy caused by photo-excitation, electrons jump to permissible excited states. This excited state does not last indefinitely. When these electrons return to their equilibrium, also known as

“recombination”, both radiative and non-radiative process can occur [53]. If a certain density of charges 푁0 are excited with the initial laser pulse, then the number of excited charges (majority and minority) per unit volume (i.e. the excess carrier density) as a function of time 푡 is given by

−푡 ⁄휏 Δ푁(푡) = Δ푁0푒 , 4.1 where 휏 is the recombination lifetime. The change in conductivity of the material due to the minority carriers in a p-type material is related to the excess carrier density of minority electrons (∆푁) by

∆휎 = 푒휇∆푁, 4.2

where 푒 is the fundamental charge and 휇 is the mobility of the carriers, which is a measure of how easily the charges can move through the material. Substituting Eq. 4.1 into Eq. 4.2 yields the relation

−푡 ⁄휏 ∆휎(푡) = 푒휇∆푁0푒 . 4.3

Thus, if the mobility is constant, the conductivity decays at exactly the same rate as the excess carrier density. This means that we can measure the lifetime by measuring the conductivity of the material as a function of time.

1.1. Mobility

Keeping mobility constant is the key assumption in the TMPCD diagnostic that allows us to model the transient photoconductivity as an exponential decay function. At low electric fields, the drift velocity is proportional to the electric field strength and the proportionality constant is defined as the mobility  in cm2/V-s [56]. For nonpolar semiconductors, such as Ge and Si, the presence of acoustic phonons as well as ionized impurities result in carrier scattering that significantly affects the mobility [56]. The mobility from interaction with acoustic phonon of the lattice, l, is governed by the expression:

4 √8휋푞ℏ 퐶푙 1 휇푙 = 2 ∗5/2 3/2 ∝ 5 3 , 4.4 3퐸푑푠 푚푐 (푘푇) ∗ 푚푐 2푇2

where Cl is the average longitudinal elastic constant of the semiconductor, 퐸푑푠 the

∗ displacement of the band edge per unit dilation of the lattice, and 푚푐 the conductivity effective mass [56].

The mobility from ionized impurities i can be described by

2 −1 3 2 3/2 64√휋휀푠 (2푘푇) 12휋휀푠푘푇 푇2 휇푖 = 3 ∗1/2 {푙푛 [1 + ( 1 ) ]} ∝ 1 , 4.5 푁𝑖푞 푚 2 ∗ 푞 푁퐼3 푁퐼푚 2 where Ni is the ionized impurity density. Eq. 4.5 predicts that as impurity concentration increases, mobility decreases. Similarly, Eq. 4.4 describes the relation between mobility and effective mass. As effective mass increases, the mobility decreases. The combined mobility, which includes the two mechanisms above, is given by an effective mobility, or

1 1 −1 휇푒푓푓푒푐푡푖푣푒 = ( + ) . 4.6 휇푙 푢𝑖

To assume 휇푒푓푓푒푐푡푖푣푒 stays constant during the experiment, Ni should kept high. In other words, at low injection level, Ni will be maximized, and 휇푒푓푓푒푐푡푖푣푒 will remain constant.

Since scattering mechanisms control the effective mobility [56], it can also be qualitatively related to the mean free time, 휏푚

푞휏 휇 = 푚 푚∗ . 4.7

For multiple scattering mechanisms, the following relation gives the effective mean free time from the individual mean free times of the scattering events [56]:

1 1 1 = + + ⋯ 4.8 휏푚 휏푚1 휏푚2

2. TMPCD Experimental Set-up and Apparatus

Both Figures 4.1 and 4.2 show the basic parts and operation of the experimental apparatus for the TMPCD measurement. A sample (bulk wafer or wafer with epitaxial thin film) is placed across two microwave coil antennas that are isolated from each other by shielded boxes, with one acting as a transmitter (Tx) and the other as a receiver (Rx).

Microwaves at 500 MHz are produced using a signal generator with a built-in step attenuator, allowing precise control of the RF power output. The generated RF signal is

split, and half the signal is sent to an amplifier to boost the signal. The amplified signal is fed to the transmitting antenna, which produces microwave radiation. Using total internal reflection, microwaves are transmitted transversely through the film/wafer, with a fraction of the incident power arriving at the receiving antenna. The signal from the receiving antenna is fed to a variable gain amplifier to control the power level, and then to the first input on a frequency mixer. The other half of the signal from the power splitter is used as a reference signal and is sent to a set of voltage-controlled phase shifters that can produce a 0-360° phase shift. The phase-shifted signal is fed into a variable gain amplifier to control the power level, and then to the second input on the frequency mixer.

The two phase shifters and variable gain amplifiers were controlled by a voltage sent by an analogue output box; each control voltage was set in LabVIEW. In order to match the power levels of the reference and transmitted signal, the cables carying the microwaves were fed to a power diode converter, which allowed us to read the transmitted power as a voltage reading on a digital mutlimeter. The voltage readings correspond with a power in dbm. The power from dbm can then easily be converted to milliwatts. The graph that displays the power diode voltage as a function of incident power in dbm is given below in

Figure 4.3. By adjusting the phase shift of the reference signal and matching the power levels of the reference and transmitted signal, a DC voltage is produced on the frequency mixer output that is proportional to the intensity of the transmitted signal.

Fig. 4.1. Experimental set-up for TMPD, 1st configuration.

Fig. 4.2. Experimental set-up for TMPCD, 2nd configuration.

Fig. 4.3. Power diode voltage versus incident microwave power.

A pulsed light source was incident on the sample in order to inject charge carriers into the material. Any light pulsed source can be used if it fits the following criteria: 1) photons have energy above band gap and 2) the period between the pulses is at least five lifetimes apart. There are two light sources successfully integrated within the set-up. The first is a Q-switched Nd:YAG laser operating at 532 nm (FWHM = 6 ns, repetition rate =

10 Hz) and the second is a pulsed fiber laser connected to an EDFA operating at 1550 nm

(FWHM=25ns, repetition rate = 10 kHz). The light intensity from the Nd:YAG laser is controlled by a series of attenuation optics and the light intensity from the fiber laser is controlled by setting the amplifier current from 0 to 5 Amps. When the excitation source is off, the DC signal from the frequency mixer is constant and does not change with time.

When the short pulse from the laser is incident on the sample, the light is absorbed, creating free carriers. These photogenerated carriers absorb some of the microwaves that are traveling through the film/wafer, thereby decreasing the microwave power transmitted to the receiving antenna, resulting in a drop of the DC output from the frequency mixer.

Immediately after the laser pulse ends, the photogenerated carriers start to recombine via

various mechanisms, reducing the number of free carriers, which results in an increase in the microwave transmission and DC signal that follows the exponential form of Eq. 4.3, albeit inverted. The signal from the frequency mixer is fed to a DC-coupled amplifier for

DC carrier amplification and then to an oscilloscope to digitize the time-dependent waveform. Finally, the recombination lifetime of the material being measured is extracted by fitting exponential curves to the voltage decay obtained from the oscilloscope.

3. Optical and RF discussion

3.1. TMPCD optics

3.1.1. Injection level

It is necessary to calculate the injection level (i.e. the excess carrier density or the number of charge carriers per unit volume) Δ푛 induced by our laser pulse. Keeping injection level low allows the assumption of constant mobility to hold. Injection level is a function of the laser wavelength 휆, laser pulse energy 퐸푝, laser spot size 푑, and the absorption coefficient of the material at the given wavelength 훼(휆). It was assumed that the laser spot is circular. It was also assumed that the generated carriers are contained in a layer with thickness equal to the absorption length in the material, which is the reciprocal of the absorption coefficient (1/ α). Then the volume that contains the generated carriers is simply the volume of a cylinder

2 휋(푑⁄ ) 휋푑2 푉 = 2 = 훼 4훼 . 4.9

Since each photon creates a charge carrier (i.e. all photons are absorbed), then the number of charges created is equal to the number of photons, so the number of photons 푁 contained in each pulse needed to be calculated. This is just the ratio of the total pulse energy to the energy of a single photon 퐸푝ℎ. The energy of a single photon is

ℎ푐 퐸 = 푝ℎ 휆 , 4.10 where ℎ is Planck’s constant and 푐 is the speed of light. Thus, the number of photons contained in each energy pulse is

퐸 휆퐸 푁 = 푝 = 푝 . 4.11 퐸푝ℎ ℎ푐

The photon density was calculated, which is equivalent to the induced charge carrier density or injection level Δ푛:

휆퐸 푝⁄ 푁 ( ℎ푐) Δ푛 = = 푉 휋푑2 . 4.12 ( ⁄4훼)

Simplifying this result yields

4훼휆퐸 Δ푛 = 푝 휋ℎ푐푑2 . 4.13

Figures 4.4-4.7 show the conditions in order to obtain specific injection levels for

Si and Ge using light of λ=532nm; as well as Ge/GeSn (2% Sn concentration) using light of λ=1550 nm.

Fig. 4.4. Si injection levels at λ=532nm.

Fig. 4.5. Ge injection levels at λ=532 nm.

Fig. 4.6. Ge injection levels at λ=1550 nm.

Fig. 4.7. GeSn (2% Sn concentration) injection levels at λ=1550 nm.

3.1.2. Attenuation optics

The following is a discussion for the optics used in order to control the pulse energy of the light produced by the Nd:YAG laser.

The intensity for a monochromatic propagating wave such as a plane or Gaussian beam after a neutral density filter can be expressed by means of the following:

−푑 퐼 = 퐼0 ∗ 10 , 4.14 where I is the intensity after filtering; I0 is the initial intensity, and d is the order for which the magnitude of the intensity will decrease. Since 퐼~|퐸|2, we can calculate the final intensity incident on the sample by knowing the initial pulse energy and taking into consideration the loss mechanisms of the optical system, specifically the reflectivity of the mirrors that propagate the beam and the loss due to scattering. A schematic of the attenuation optics is shown below in Figure 4.8.

Fig. 4.8. Attenuation optics.

The mirrors are coated for the wavelength of 532 nm with a reflectivity of 0.99. In order to calculate the loss due to reflection, one can use the following relation:

# 표푓 푚푖푟푟표푟푠 (.99) ∗ 퐸푖푛푐푖푑푒푛푡 . 4.15

A beam with an initial pulse energy of 3mJ propagates through a system of attenuation optics. Before the beam splitter, the beam is reflected off four mirrors. Therefore, the total energy propagating through the beam splitter is simply

(.99)4 ∗ 3푚퐽 = 2.88푚퐽.

The beam splits into two beams, one with 4% of the original intensity and the other with

96%. In order to attenuate the signal to keep injection level low, the 4% beam was isolated and reflected off two mirrors. The total loss due to scattering as the beam propagates through the optics was approximated to be 1 mJ. Therefore, the final energy incident on the sample is

(. 99)2(. 04) ∗ (2.88푚퐽 − 1.00푚퐽) = .0737푚퐽~70휇퐽.

70휇퐽 For a wavelength of 532nm and a circular spot size of 1.5cm, the fluence of 1.5푐푚 corresponds with an injection level for Si (Δ푛) of 1e+18 charge carriers.

The condition for low injection level implies that ∆푛 ≪ 푝0 for a semiconductor that is p-doped. For example, since the bulk silicon samples are doped on the order of

1e+14, the injection level of 1e+18 minority charge carriers is considered high injection level (Δ푛 ≫ 푝0). In order to take into consideration the effective lifetime from the data taken at high injection, we need to understand and isolate the mobility effects. However, an easier way than to de-convolute the mobility effects from the signal is to retake data at low injection, and then compare to the data taken at high injection level.

3.2. TMPCD RF

Microwaves have been vastly used for the last 60 years. Although it is possible to probe using any EM radiation sub-band-gap, microwaves are easy to generate and their necessary components for transmission are inexpensive.

The function generator outputs an RF frequency of 500 MHz at a power of -8 dbm. The signal travels to a 50/50 power splitter; half the microwaves act as our reference signal (no modulation, just phase shifted) and the other half are carried through our sample. Mathematically, the split signal can be represented as two sinusoidal waves, out of phase by a factor 휑:

퐹1 = 퐴1sin (휔푡 + 휑) 4.16

퐹2 = 퐴2sin (휔푡) 4.17

퐹1 ∗ 퐹2 = 퐴1퐴2 sin(휔푡 + 휑) sin(휔푡)

1 = 퐴 퐴 [cos(휔푡 + 휑 − 휔푡) − cos(휔푡 + 휑 + 휔푡)] 2 1 2

1 퐹 ∗ 퐹 = 퐴 퐴 [cos(휑) − cos(2휔푡 + 휑)] 1 2 2 1 2 . 4.18

The term cos(휑) is the DC component of the RF signal and the term cos(2휔푡 + 휑) is the

AC component of the RF signal; therefore, since the information about the photoconductivity change travels along the DC carrier, the signal was maximized by phase matching (ie: allowing 휑 = 0) our two split signals before we recombine them in the frequency mixer. Observing the two sinusoidal waveforms on the digital oscilloscope, and adjusting the control voltage to the phase shifters until the reference signal matched the transmitted signal accomplished this.

Radio waves propagate through the wafer by means of transmitting and receiving coils that are designed as helical antennas. The helical antennas are monopole, with an omnidirectional radiation pattern. The microwaves transmitted through the coil antennas are p-polarized; in other words, vertically polarized with respect to the earth.

Since the dimensions of the helix are considerably small (the diameter and pitch) compared to the wavelength of the radiation, the radiation pattern emitted by the antenna is in normal mode. Accordingly, the total radiation ( 휀) from the entire length L of the antenna as a function of angle (휃) at distance d can be written as

60휋 퐿 2휋푥 휀 = 퐼 sin 휃 ∫ 푒−훼푥 sin [휔푡 − (1 − cos 휃)] 푑푥 푑휆 0 0 휆 , 4.19

where 퐼0 is the maximum current, 휆 is the distance corresponding with the wavelength, and α corresponds to attenuation losses [61].

In the common case where the amplitude of the current can be considered constant along the wire (ie: α=0) [61], equation 4.19 becomes

60 휃 휋퐿 휀 = 퐼 cot 푠𝑖푛 (1 − cos 휃) 푑 0 2 휆 . 4.20 41

Figure 4.9 shows a schematic of the transmitting/receiving coil used within the TMPCD experimental set-up and Figure 4.10 shows the radiation pattern emitted from transmitting coil, which models Eq. 4.20.

Fig. 4.9. Transmitting/receiving coil schematic.

Fig. 4.10. Polar plot of emitted radiation strength.

After properly characterizing the microwaves radiating from the transmitting coil and plotting the radiative power as a function of angle, the optimal angle of the antenna coils in reference to the sample for maximum microwave confinement was calculated.

Using Fresnel equations to calculate the amount of EM transmission from the air-silicon interface and assuming symmetry between the transmitting and receiving coil antennas, radiative power optimization was found by taking the product of the normal mode radiation strength and the amount of power able to be transmitted.

Fig. 4.11. Microwave confinement optimization.

The conclusion from Figure 4.11 is that tilting the transmitting and receiving coils at an angle Θ equal to 60° along the perpendicular axis with respect to the thin film/substrate optimizes microwave confinement within the sample being tested; this allows for maximum photoconductivity perturbation. Figure 4.12 displays the configuration of the transmitting and receiving coils when tilted at an angle Θ. However, obtaining results from TMPCD are not contingent on microwave confinement optimization depending on the sample being tested. Microwave confinement optimization will be implemented in the next phase of this project. Excited free carriers

Thin film

Substrate Θ Θ Tx coil Rx coil

Fig. 4.12. Transmitting and receiving coil configuration tilted at an angle Θ.

4. Validation TMPCD with bulk silicon

The TMPCD system was verified with bulk p-type Si wafer with a resistivity of

10-20 Ω*cm. The first variable tested was a CW light source (Pout=500 mW, λ=1555 nm); the Si sample tested was illuminated with this secondary light source while its effect on the transient photoconductivity signal was evaluated. The purpose of shining CW light below band gap was to reduce recombination within deep level traps. This was accomplished while keeping injection level constant. The second variable to test was to observe how the transient photoconductivity signal varied with injection level. This was done by using a series of neutral density filters. The filters used were 0 (full signal), 1

(full signal taken down by a factor of 10) and 2 (full signal taken down by a factor of

100). This was done without the illumination of a CW light source. The Si samples tested came from the same wafer; however, the wafer was broken into different geometric shapes. The Si sample used to test the effect of the CW light source was triangular, whereas the Si sample used to test the effects of mobility variations with injection level was rectangular. However, both shapes were large enough in order to completely cover the transmitting and receiving coils. For every trial, the amount of phase shift between the reference signal and the transmitted (modulated) signal was perturbated in order to obtain the best DC response; likewise, the amount of amplification on the modulated signal was also perturbated in order to obtain the best DC response. A summary of the Si samples (type, resistivity, dopant concentration, and shape), photo-excitation source, fluence, injection level and minority carrier lifetimes measured is displayed in Chapter 5,

Table 2. Included in Chapter 5 is a detailed discussion of the results and conclusions obtained from the measurements.

5. TMPCD with bulk germanium

After verifying the TMPCD diagnostic with Si, the system was then utilized to measure bulk Ge recombination lifetime. The p-type Ge wafer tested was undoped and intact with a diameter of two inches. Since the fiber laser was used as the photoexcitation source, the pulse energy needed to be calculated by measuring the average power at the output of the multimode fiber and dividing the reading by the repetition rate, which was already previously stated to be 10 kHz. Eq. 4.21 was used in order to calculate the pulse energy for different current settings applied to the EDFA. The current for the EDFA was allowed to be range from 0 to 5 amps; the step size chosen was 1. After each successive step, the output power at the end of the fiber was measured and recorded and the corresponding pulse energy was calculated. These results are listed in Table 1:

푃 퐸 = 푃 ∗ 푝푒푟𝑖표푑 = 푎푣푒푟푎푔푒 푝푢푙푠푒 푎푣푒푟푎푔푒 푅푒푝 푅푎푡푒 . 4.21

Table 1. Measured average power and corresponding pulse energy. Current (A) Paverage (mW) Epulse (μJ) 5.00 30 3.0 4.00 23 2.3 3.00 16 1.6 2.00 10 1.0 1.00 4 0.4 0.02 1 0.1

Every current setting applied to the EDFA gave very strong transient photoconductive decay signals on bulk Ge. Since the maximum (5 A) and minimum

(0.02 A) current settings applied correspond with the upper and lower limits of injection level for Ge, these two trials were chosen to be displayed and discussed in detail in

Chapter 5. A summary of the Ge sample (type, resistivity, dopant concentration, and shape), photo-excitation source, fluence, injection level and minority carrier lifetimes

measured is displayed in Chapter 5, Table 2. Included in Chapter 5 is a detailed discussion of the results and conclusions obtained from the measurements.

CHAPTER 5

RESULTS AND DISCUSSION

Below, Table 2 displays the relevant information concerning the measurements taken with the TMPCD system, including details about the sample being tested, photoexcitation source with corresponding injection level information, and effective lifetime measurement obtained from the transient photoconductivity signal. One of the most difficult parts about measuring recombination lifetime is the interpretation of the lifetime measurement once calculated. The following sections, Parts 1-3, offer a detail discussion of each DC photoconductivity signal presented, as well as the conclusions drawn from the effective lifetimes measured.

Table 2. Summary of results. Sample Photoexcitation Source Pulse Energy, Epulse (μJ) Lifetime Spot Size measured (Variable Changed) Injection Level (μs) Bulk Si Nd:YAG 70 μJ 1.8±0.5 p-type 1.5cm μs 10-20 Ω*cm (CW light Source on) ~1*1018 1014 cm-3 Triangular Bulk Si Nd:YAG 70 μJ 2.3±0.5 p-type 1.5cm μs 10-20 Ω*cm (CW light source off) ~1*1018 1014 cm-3 Triangular Bulk Si Nd:YAG 70 μJ 2.4±0.4 p-type 1.5cm μs 10-20 Ω*cm (ND filter 0) ~1*1018 1014 cm-3 Rectangular Bulk Si Nd:YAG 7.0 μJ 3.3±0.3 p-type 1.5cm μs 10-20 Ω*cm (ND filter 1) ~1*1017 1014 cm-3 Rectangular Bulk Si Nd:YAG 0.70 μJ 3.0±0.3 p-type 1.5cm μs 10-20 Ω*cm (ND filter 2) ~1*1016 1014 cm-3 Rectangular Bulk Ge Fiber laser 3.0 μJ 7.0±0.5 p-type 4.45 cm μs >5,000 Ω*cm (Maximum current = ~2*1015 undoped 5.00 A) Circular Bulk Ge Fiber laser 0.1 μJ 8.0±0.3 p-type 4.45 cm μs >5,000 Ω*cm (Minimum current = ~1*1014 undoped 0.02 A) Circular

1. Part 1: comparison and interpretation of bulk Si photoconductive decay signal with and without CW light source

Figure 5.1 shows the entire transient photoconductivity signal of bulk Si with a thickness of 500 μm; Figure 5.2 shows the semi-log plot of the close-up exponential decay portion of the photoconductivity signal. The effective lifetime for each trial was done by finding the line of best fit and taking the inverse of the slope of the semi-log plot.

The R-value displayed on Figure 5.2 indicates the linearity, or how well our data fits the projection that we can model the change in conductivity as one exponential decay function.

18 Δn ~ 10 E = 70 µJ pulse

Fig. 5.1. Si transient photoconductive decay signal without CW light source.

Τ = 2.3 ± 0.5 μs

Fig. 5.2. Semi-log plot of exponential decay close-up, Si transient photoconductive decay signal without CW light source.

The data take above verified that the TMPCD set-up was an appropriate apparatus for taking bulk Si lifetime measurements. The recombination lifetime was expected to vary between 1 and 100 μs; the measured value fell into the lower end of the expected range at 2.3±0.5 μs. At high injection level, the effective lifetime can be expected to be shorter due to fast Auger recombination dominating SRH recombination. However, the dip in the graph that dropped below zero was something that had not been mentioned in the literature with other groups measuring recombination lifetime, with TMPCD or any other appropriate diagnostic. The thought was that other recombination mechanisms other than radiative, Auguer, and SRH were occurring; therefore, the TMPCD model so far had not accounted for it. It was proposed that excited carriers were falling to intermediate band states, or mid level traps, and not from the conduction to the valence band. In order to test this, a CW light source of λ=1550 nm (below band gap of Si) was used with a significant amount of power (Pout=500 mW) in order to make the mid band trap transitions forbidden. Figures 5.3 and 5.4 show the results of this variable change.

18 Δn ~ 10 E = 70 µJ pulse

Fig. 5.3. Si transient photoconductive decay signal with CW light source.

Τ = 1.8 ± 0.5 μs

Fig. 5.4. Semi-log plot of exponential decay close-up, Si transient photoconductive decay signal with CW light source.

It is clear when comparing Figures 5.1 and 5.3 that the tip in the data exists with and without the CW light source. Not only does the dip still exist, it appears to be completely unchanged. There is a slight decrease in the minority carrier lifetime, as well as a decrease in the linearity (R-value) of the semi-log plot in the signal with the CW light

source. However, these changes could simply be due to random error in the apparatus; there is not enough of a change to make any conclusions about the CW light source and its effect on mid band trap recombination.

2. Part 2: comparison and interpretation of bulk Si photoconductive decay signal over several orders of injection level

Measurements obtained via the TMPCD system are sensitive to variations in mobility. The way in which we evaluated how these mobility variations affect the recombination lifetime measurements was to compare data taken at several injection levels. This was done on bulk Si with a thickness of 500 μm. Figures 5.5 and 5.6 show the photoconductivity signal without an ND filter, Figures 5.6 and 5.7 show the photoconductivity signal with an ND filter of 1, and Figures 5.8 and 5.9 show the photoconductivity signal with an ND filter of 2.

18 Δn ~ 10

Epulse= 70 µJ

Fig. 5.5. Si transient photoconductive decay signal, ND filter 0.

Τ = 2.4 ± 0.4 μs

Fig. 5.6. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 0.

17 Δn ~ 10

Epulse= 7.0 µJ

Fig. 5.7. Si transient photoconductive decay signal, ND filter 1.

Τ = 3.3 ± 0.3 μs

Fig. 5.8. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 1.

16 Δn ~ 10 E = 0.70 µJ pulse

Fig. 5.9. Si transient photoconductive decay signal, ND filter 2.

± Τ = 3.3 0.3 μs

Fig. 5.10. Semi-log plot of exponential decay close-up, Si transient photoconductive decay, ND filter 2.

There is an increase in minority carrier lifetime and R-value of the semi-log plot going from an injection level~1018 to 1017. This correlates with findings from other microwave PCD experiments, where injection level is minimized in order to model SRH recombination statistics with an exponential decay function. TMPCD results at low injection levels are less complicated by mobility effect; on the other hand, there also needs to be a sufficiently high excitation density to obtain a measurable photo response signal [1]. Once the pulse energy is on the order of 0.5 μJ , it is suggested in the literature that the pulse energy is no longer sufficient enough to induce a measurable photo response [1], particularly when using an Nd:YAG laser as the photoexcitation source.

This was the case for the injection level~1e+16, where the pulse energy was 0.7 μJ. In exchange for a decrease in injection level, there was a sacrifice in the quality of the photo signal. However, when comparing Parts 1 and 2 to each other, the dip that we tried to isolate and decrease by using a CW light source in Part 1 was still present in the photoconductivity signal in every figure in Part 2, regardless of injection level. Parts 1

and 2 allows us to conclude that the dip is independent of geometric shape since in Part 1, the Si wafer was triangular and in Part 2, the Si wafer was rectangular. The dip was also present, regardless of the phase difference between the reference and modulated signal, as well as the amount of amplification applied to the modulated signal. Therefore, it is not possible to make any conclusion about the dip at this time, and this will be further investigated. The effective recombination lifetime for Si, using the measurements obtained from parts 1 and 2, was calculated to be 2.6 ± 0.5 μs.

3. Part 3: comparison and interpretation of bulk Ge photoconductive decay signal over maximum and minimum injection levels

The bulk Ge photoconductive decay signals for maximum and minimum injection levels are shown below in Figures 5.11-5.14. The bulk Ge wafer has a thickness of 500

μm, the same as the bulk Si wafer tested previously. However, the Ge wafer tested in Part

3 has the geometry of a circle, with a diameter of 2 inches.

15 Δn ~ 10 E = 3.0 µJ pulse

Fig. 5.11. Ge transient photoconductive decay signal, maximum injection.

Τ = 7.0 ± 0.5 μs

Fig. 5.12. Semi-log plot of exponential decay close-up, Ge transient photoconductive decay, maximum injection.

14 Δn ~ 10 Epulse= 0.1 µJ

Fig. 5.13. Ge transient photoconductive decay signal, minimum injection.

Τ = 8.0 ± 0.3 μs

Fig. 5.14. Semi-log plot of exponential decay close-up, Ge transient photoconductive decay, minimum injection.

It has been shown that lifetimes for bulk Ge can range between 30 ns and 500 μs depending on surface passivation state and resistivity and that the carrier lifetime behavior in Ge can be described well by the Shockley-Read-Hall (SRH) model for low and moderately doped samples [62]. The effective recombination lifetime calculated for our bulk Ge sample, 7.5 ±0.7 μs, fall within this range. In regards to the photosignal itself, no dip is noticeable in either the maximum or minimum injection conditions for bulk Ge. The light source used was the 1550nm fiber laser and not the Nd:YAG. It was surmised is that the dip is not due to trap recombination centers in the structure, but rather photoexcitation source related. This theory will be tested in the next phase of our project since both excitation sources can induce free charge carriers in Ge. There was negligible increase in the recombination lifetime when we took data at maximum and minimum injection level. However, the R-value of the semi-log plot as we go from maximum to minimum value injection level increases, which correlates with the model discussed in detail in Chapter 4. We are able to get measurable photo response at the low injection

level for bulk Ge, even when the pulse energy is less than 0.5 μJ. This could potentially be a benefit of the fiber laser versus the Nd:YAG laser as a photoexcitation source.

CHAPTER 6

CONCLUSION AND FUTURE WORK

1. Summary

We have fully characterized and developed a novel, contactless method for measuring effective recombination lifetime including a complete characterization of its optical and RF components. The TMPCD system has shown that it is capable of measuring effective lifetimes of different indirect band gap semiconductor materials in their bulk forms (or wafers), including Si and Ge. The recombination lifetimes were measured to be 2.6±0.5 μs and 7.5±0.7 μs for Si and Ge, respectively. These values were found to agree with the values from the literature that were obtained using alternative measurement techniques. Theoretically, TMPCD is applicable to non-conventional thin film materials; this will be shown with thin film Ge-on-Si and GeSn-on-Si. Effective recombination lifetime measurements obtained by the TMPCD system do not discriminate based on geometric shape; however, the physical size of the sample needs to be large enough in order to transmit enough microwaves for a strong enough photoconductivity perturbation signal.

2. Short and long term goals

Once an effective lifetime system is shown to work, there are a considerable number of changes one can make in order to understand what affects the recombination lifetime of a material. Some of the common things done in the literature is to explore the

dependence of carrier lifetime on surface passivation, resistivity, sample thickness, and type of dopant. Particularly with the test of surface passivation on effective lifetime of

Ge/GeSn alloys, a technique we would use is an iodine/methanol immersion [63, 64]. The short term goals that we hope to specifically accomplish within the next few months of the TMPCD system are making effective lifetime measurements on GeSn alloys with Sn concentrations up to 10%. We also would also like to explore maximizing microwave confinement by physically testing the calculations made for optimal coil angle so that we can obtain a strong enough perturbation signal.

It is important to acknowledge that there are numerous complicating physical effects that mask the true excess carrier recombination lifetime in the TMPCD system; however, these effects should be viewed as a source of additional information, rather than a source of conflict between other measurements [44]. Effective recombination lifetime measurements via PCD systems in particular experience variations in carrier mobility with injection level. One of the ways to further the development and understanding of our TMPCD project would be to do effective recombination lifetime measurements using two different techniques simultaneously. This is one of the long term goals with the

TMPCD project. Particularly, a dual measurements technique involving TMPCD and

TRPL would be ideal. Photoconductivity decay senses the conductivity of all excess carries-both majority and minority carriers; whereas photoluminescence decay senses only direct electron-hole recombination via photon emission [44]. The simultaneous analog data acquisition of TMPCD and TRPL will remove the discrepancy in analyzing effective recombination lifetime, particularly at high injection. This dual-sensor technique has been applied to epitaxial thin film of GaAs and a crystalline wafer of CdTe,

both of which are direct-band gap semiconductors [44]. We hope to utilize this technique to for epitaxial thin films of Ge and GeSn.

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