Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Characterization of high-speed electronic devices using ultrafast lasers Zeng, An 1996

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1996-148610.pdf [ 9.16MB ]
Metadata
JSON: 831-1.0065316.json
JSON-LD: 831-1.0065316-ld.json
RDF/XML (Pretty): 831-1.0065316-rdf.xml
RDF/JSON: 831-1.0065316-rdf.json
Turtle: 831-1.0065316-turtle.txt
N-Triples: 831-1.0065316-rdf-ntriples.txt
Original Record: 831-1.0065316-source.json
Full Text
831-1.0065316-fulltext.txt
Citation
831-1.0065316.ris

Full Text

C H A R A C T E R I Z A T I O N O F H I G H - S P E E D E L E C T R O N I C D E V I C E S U S I N G U L T R A F A S T L A S E R S B y A n Zeng B. Eng. Tsinghua University, Bei j ing, Ch ina , 1985 M .A .Sc . Institute of Semiconductors, Chinese Academy of Sciences, 1988 M.Sc. University of Br i t ish Columbia, Vancouver, Canada, 1992 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF PH.D. in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVER-SITY OF BRITISH COLUMBIA May, 1996 © A n Zeng, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract This thesis describes experimental studies on high-speed modulation-doped field-effect transistors ( M O D F E T s ) , using electro-optic sampling (EOS) . The author has built an E O S system with subpicosecond temporal resolution and TeraHertz bandwidth. Due to the design of the E O S system, signal propagation delay t ime through an electronic device can be accurately determined in addition to the input and output waveforms. We performed an experimental study of the measurement errors and invasiveness caused by an external L iTaOa probe used in the E O S system. We found that contact (air gap free) external electro-optic sampling, which has been widely used in E O S measure-ment, could lead to more serious measurement errors than previously reported due to probe-tip induced dispersion and reflection. These unwanted effects can be minimized in the non-contact sampling geometry. B y comparing sensitivities of a time-resolved (high-frequency) signal and a calibration (low-frequency) signal at various air gaps, we show that the common method used for calibrating time-resolved E O S measurement is valid for both contact and small-air-gap non-contact measurements even though the method cannot be used to calibrate large-air-gap E O S measurements. The most signifi-cant result of this thesis is the first electro-optic characterization of ultrafast transistors monolithically integrated with a transmission line/photoconductive switch test fixture. The measured switching time and propagation delay t ime of a lattice-matched In 0.52-Alo.48As/In 0.53Gao.47As M O D F E T are 4.2 ps and 3.2 ps, respectively. These are the shortest switching and delay times ever directly measured in a three-terminal electronic device. We demonstrated that the on wafer integration of coplanar transmission line with the M O D F E T is a significant improvement over previous wire-bonding test fixtures. The r 11 parasitic gate inductance of the integrated structure is about an order of magnitude smaller than that of the wire-bonding structure. We studied the effects of different gate-access structures, semiconductor materials, and bias conditions on the performance of M O D F E T s . Our measurements of propagation delay times of two M O D F E T s made of different semiconductor materials directly confirm that a lattice-matched Ino .52Alo.4sAs/-Ino.53Gao .47As M O D F E T is faster than a pseudomorphic Ino .20Gao . soAs/Alo .25Gao.75As M O D F E T with similar gate-access layout. We clarified two common misconceptions in the literature regarding the relationships among the delay times, switching t ime, and current-gain cutoff frequency of a M O D F E T . The signal propagation delay t ime TPROP observed in a M O D F E T switching response and the delay t ime rd = -^-r defined in small-signal R F measurement cannot be used interchangeably. However, we find that the two delay times TPROP and TD have similar dependence on drain bias Vds, showing that they are closely related. Further, the 10-90% rise t ime of the M O D F E T switch-ing response cannot be directly related to the current-gain cutoff frequency ft as has been suggested. Time-domain simulations of the switching response of M O D F E T s were performed using a lumped-element model incorporating input and output transmission lines. The results are in excellent agreement with the electro-optic measurements, and we show that omission of the input transmission line leads to large oscillatory artifacts in the response. Final ly , equivalent circuit parameters of the M O D F E T s are extracted from the simulations. 111 Table of Contents Abstract ii List of Figures vii Acknowledgement xi 1 Introduction 1 1.1 Introduction to Thesis 1 1.1.1 Overview . 1 1.1.2 Outl ine of Chapter 2 1.2 Introduction to Characterization Techniques 2 1.2.1 Conventional Al l -Electronic Methods 2 1.2.2 Ultrafast-Laser-Based Techniques 5 1.3 Recent Work on Ultrafast Device Characterization 12 1.3.1 Passive Devices 13 1.3.2 Act ive Devices . 18 1.4 Outl ine of the Thesis 26 2 Experimental Techniques of Electro-Optic Sampling 29 2.1 Introduction to Chapter 29 2.2 Overall Layout and Design 29 2.3 Opt ical System 32 2.3.1 Laser System 32 iv 2.3.2 Electro-Opt ic Sampler 34 2.3.3 Opt ical Compensator 39 2.3.4 Viewing Systems < 44 2.3.5 Common T ime Ax is for Mul t ip le Probing Positions 49 2.4 Noise Reduction and Sensit ivity 52 2.5 Resolution and Linearity 55 3 Measurement Errors and Invasiveness of External EOS Probes 58 3.1 Introduction 58 3.2 Motivat ion and Background 58 3.3 Experiment 60 3.4 Results and Analysis 61 3.4.1 Riset ime and Ampl i tude 61 3.4.2 Sensit ivity 69 4 Electro-Optic Characterization of M O D F E T s 72 4.1 Introduction 72 4.2 Latt ice-Matched Ino .52Alo.4sAs / Ino .53Gao.47As M O D F E T s 73 4.2.1 Experiment 73 4.2.2 Results 78 4.2.3 Analysis 87 4.3 Pseudomorphic Ino .20Gao .goAs/Alo .25Gao.75As M O D F E T s 91 4.3.1 Experiment 91 4.3.2 Results 93 4.3.3 Analysis 94 4.4 S P I C E Model ing 96 4.4.1 Motivat ion 97 v 4.4.2 Lumped-Element Model 98 4.4.3 Model ing Results 108 4.4.4 Analysis 115 5 Conclusions and Future Work 121 5.1 Conclusions 121 5.2 Future Work 123 Bibliography 127 Appendices 135 A Principles of Electro-Optic Sampler 135 A.0.1 Electro-Optic Effect 135 A.0.2 Electro-Optic Intensity Modulator 140 B Components Used in the EOS System 146 B . l Items used in E O S System 146 C A Method for Determining Phase Retardation 149 D M O D F E T Mask Layouts 152 vi List of Figures 1.1 Diagram of a typical laser-based sampling system 7 1.2 Diagram of an optoelectronic pulse generator 8 1.3 Diagram of a simplified photoconductive sampling system 9 1.4 Diagram of a simplified electro-optic sampling system 10 1.5 Waveforms of an electrical pulse propagating on a coplanar waveguide . . 15 1.6 Pulse-forming optoelectronic device 17 1.7 Conduction band structure of a R T D 18 1.8 I-V and switching characteristics of a R T D 19 1.9 Electro-optic measurement of ultrafast G a l n P / I n P p-i-n photodiodes . . 21 1.10 Schematic illustration of an A l G a A s / G a A s M O D F E T 22 1.11 Drain output of a M O D F E T with increasing input signals 25 1.12 Large signal switching of an Ino .52Alo.48As/Ino.53Gao.47As M O D F E T . . . 27 2.1 A complete E O S system 30 2.2 Schematic diagram of N J A - 3 Ti-sapphire Laser 33 2.3 L iTaOs Externa] Electro-Optic Sampler 37 2.4 Schematic diagram of an external probe t ip 38 2.5 Calculated Retardation Curves 41 2.6 Measured Retardation Curves 42 2.7 Dispersion of Compensator 43 2.8 Diagram of the probe microscope 46 2.9 Schematic diagram of the pump tip 48 vi i 2.10 E O S Viewing System 50 2.11 Noise Reduction Electronics 53 2.12 Ultrafast electrical pulse measured by E O S 56 2.13 Linearity of an E O S System 57 3.1 Schematic diagram of non-contact E O S measurement 61 3.2 Contact E O S Measurement 62 3.3 Non-contact E O S Measurement 63 3.4 Contact and non-contact E O S Measurement 64 3.5 Non-contact t ime resolved E O S measurements 66 3.6 Riset ime as a Function of A i r Gap 67 3.7 Sensitivity of E O S as a Function of A i r Gap 69 4.1 Layer Structure of a L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T 74 4.2 S E M photographs of M O D F E T s 76 4.3 Layout of a M O D F E T with integrated test fixture 77 4.4 Large-Signal Switching of a L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T . 79 4.5 Dependence of Drain Bias of an Ino .52Alo.48As / Ino .53Gao.47As M O D F E T . 81 4.6 Gate-Bias Dependence of a Ino .52Alo.48As / Ino .53Gao.47As M O D F E T . . . . 82 4.7 Characteristics of Nonlinear Switching of a Ino.52Alo.4sAs / Ino.53Gao.47As M O D F E T 84 4.8 Switching Response of a Ino .52Alo.48As / Ino .53Gao.47As M O D F E T with Double-Gate-Access Structure 86 4.9 Dependence of M O D F E T Delay on D C Drain Bias 88 4.10 Layer Structure of a P M Ino .20Gao.80As /Alo.25Gao.75As M O D F E T . . . . 92 4.11 Switching Response of an Ino.20Gao.80A s /A l 0 . 25Gao .7 5 As M O D F E T with Single-Gate-Access Structure 93 v i n 4.12 Lumped-Element Equivalent Circuit Model for M O D F E T s 99 4.13 Gate input signals for S P I C E simulation of M O D F E T s 101 4.14 S P I C E simulation of a L M Ino .52Alo.48As/Ino.53Gao.47As M O D F E T using R F parameters 102 4.15 Effects of Cgs on the Response of M O D F E T s 105 4.16 Effects of Cgd on the Response of M O D F E T s 106 4.17 Effects of Transconductance on the Response of M O D F E T s 107 4.18 Effects of Lg on the Response of M O D F E T s 109 4.19 The Measured and Simulated Responses of a Ino .52Alo.48As/Ino.53Gao.47As M O D F E T 110 4.20 The Measured and Simulated Responses of a Ino .20Gao .80As/Alo.25Gao.75As M O D F E T 113 4.21 The Measured and Simulated Drain Outputs of a Discrete M O D F E T . . 116 4.22 The E O S Measurement of the Gate Input of a Discrete M O D F E T . . . . 118 4.23 Simulations with and without Input Transmission Line 119 A . l Index El l ipsoid 127 A . 2 Schematic of a longitudinal electro-optic modulator 133 A . 3 Transmission of an electro-optic modulator with dual beam output . . . . 135 B . l Circuit of Photoreceiver 138 B . 2 Complete Diagram of the E O S System 139 C. l Retardation Measurement Setup 141 D . l Mask Layout for a Single-Gate-Contact M O D F E T with Cascade electrodes 143 D.2 Mask Layout for a double-Gate-Contact M O D F E T with Cascade electrodes 144 D.3 Mask Layout for a Single-Gate-Contact M O D F E T with coplanar striplines 145 ix D.4 Mask Layout for a Single-Gate-Contact M O D F E T with coplanar striplines 146 x Acknowledgement I would like to thank my supervisor, Dr. Jackson, for defining the research topics and the opportunity to work in his lab. His patience, support, and knowledgeable guidance made the successful completion of this work possible. I would also like to thank our collaborators Dr. Marleen Van Hove and Dr. Walter De Raedt for fabricating the M O D F E T s used in this project. I am very grateful to Dr. Pulfrey, the graduate chairman of the department of electrical engineering, for his understanding and support during the difficult days of my student life in early 1993. I would also like to thank the technical staff at the department of electrical engi-neering. Their support made the task of setting up the electro-optic sampling system easier. I am grateful to U B C for providing financial support in the form of Universi ty Grad-uate Fellowship and St. John's Graduate Fellowship. Final ly, I would like to thank my parents for their love, support, and high values they placed upon education. Especially, my dad who passed away ten years ago, but without his vision of sending me to the best engineering school in Ch ina , I could never have achieved what I have achieved. x i Chapter 1 Introduction 1.1 Introduction to Thesis 1.1.1 Overview This thesis describes experimental studies on high-speed modulation-doped field-effect transistors ( M O D F E T s ) , using electro-optic sampling (EOS) — an ultrafast laser-based technique. The development of very-high-speed electronic devices has progressed much faster than that of the techniques to characterize their performance. The state-of-the-art M O D F E T s have bandwidth larger than that of the conventional all electronic charac-terization techniques, which makes the characterization of these high-speed electronic devices a challenge to research engineers around the world. The work described in this thesis is composed of two major topics in the electro-optic characterization of high-speed electronic devices: the design and study of an electro-optic sampling system, and the experimental studies on M O D F E T s . The first part, concerning the experimental technique, describes the design of our E O S system and the experimental study of the invasiveness of this technique. In the second part, we describe the electro-optic studies on the switching of lattice-matched Ino.52Alo.48As/Ino.53Gao.47As M O D F E T s , pseudomor-phic Ino.20Gao.80As/Alo.25Gao.75As M O D F E T s . To avoid parasitic effects introduced by bond wires, these devices are monolithically integrated with coplanar stripline fixtures incorporating photoconductive switches. We also conducted the t ime-domain simulation of the M O D F E T s monolithically integrated with test fixtures by using a lumped-element 1 Chapter 1. Introduction 2 model incorporating input and output transmission lines. The simulations are in excellent agreement with the electro-optic measurements. 1.1.2 Outline of Chapter The purpose of Chapter 1 is to describe the motivation and background of the chosen topic and experimental technique. In Section 1.2, we describe both conventional all-electronic techniques and ultrafast laser-based techniques for characterizing high-speed electronic devices; in particular, the advantages of ultrafast-laser-based techniques over conventional all electronic techniques are presented. In Section 1.3, we review recent work on ultrafast device characterization. Both passive devices and active devices are presented with emphasis on active devices. Final ly, in Section 1.4, we describe the outl ine of the thesis. 1.2 Introduction to Characterization Techniques In this section, we introduce measurement techniques used in high-speed electronic device characterization. Section 1.2.1 describes the two most commonly used all-electronic mea-surement devices—network analyzer and sampling oscilloscope. Section 1.2.2 describes two laser-based techniques — photoconductive sampling and electro-optic sampling. The purpose of this section is to provide background knowledge of the high-speed characteri-zation techniques and to show the distinct advantages of the laser-based techniques. 1.2.1 Conventional All-Electronic Methods Conventional characterization techniques used for measurement of high-speed devices are all-electronic techniques, where input and output signals are generated and measured electrically. The two most widely-used items of equipment are the network analyzer and Chapter 1. Introduction 3 the sampling oscilloscope, which work in the frequency domain and the time domain, respectively. Network Analyzer Network analyzers, which operate in the frequency domain, are the most commonly used conventional equipment for characterizing high-speed electronic devices. They measure the scattering parameters (S-parameters) which provide a complete description of an elec-tronic network. Instead of relating voltages and currents at the ports, the S-parameters relate the incident voltage waves to those reflected from the ports. S-parameters relate the reflected and incident voltages VnT and Vni (phasors) to each other as follows: \ Vnr ) ( Sn S\n Sn \ I Vu \ \ Vni J (1.1) where Vnr and Vn{ are reflected and incident voltage phasors. There are two kinds of network analyzers. One is the scalar network analyzer ( S N A ) which measures only the amplitude of the incident and reflected voltage waves. The other is the vector network analyzer ( V N A ) which measures both the amplitude and the phase of the incident and reflected voltage waves. A modern V N A has a bui l t - in microprocessor which provides error correction and various data analysis options. T i m e response of the network under test can be obtained by fast Fourier transformation of the frequency-domain data. Cur-rent state-of-the-art commercial V N A can operate at around 60 G H z , but recently some workers have successfully extended operation to 110 G H z [1]. However, there are some limitations in using a N A . The device under test ( D U T ) can only be tested in small signal operation. Large signal operation, which is normally non-linear, cannot be directly measured by a N A . The l imited bandwidth of N A s can also Chapter 1. Introduction 4 be a problem in characterizing ultrafast electronic devices, where bandwidths as large as several hundreds of G H z have been demonstrated. Sampling Oscilloscope Besides the network analyzer, a sampling oscilloscope (SO) is another widely-used con-ventional technique for characterizing high-speed electronic devices. There are two types of sampling oscilloscopes: real-time SO and equivalent-time SO. The former is mainly used for nonrecurrent signals which are sampled by an array of relatively-delayed sam-pling gates. The latter has better sensitivity and requires that the signal to be measured is recurrent. In an equivalent-time S O , the signal measured is sampled through a very narrow time-gate controlled by a triggering electrical pulse which is synchronized with the signal being measured and can be delayed electrically. The width of the gate is very narrow compared with that of the signal to be measured. When the gate is open, only a very small part of the input signal is sampled. In other words, only the part of the signal which arrives at the gate at the same t ime as the triggering pulses is sampled. B y delaying the triggering pulses with respect to the signal, the whole signal can be sampled one point after another and be reconstructed after sampling a number of delay points. The t ime scale of the measurement is determined by the relative delay t ime, which is why this sampling method is called equivalent-time sampling. The resolution of a SO is l imited by the width of its sampling gate and the j i tter of its delay and trigger circuits. The state-of-the-art SO is a superconducting SO which uses a Josephson sampler and has a bandwidth of 70 GHz[2]. A sampling oscilloscope is normally not equipped with a signal generator, which makes it difficult to use at high-speed since it is difficult to find a fast enough signal generator to generate a synchronized input signal for the device under test. Chapter 1. Introduction 5 1.2.2 Ultrafast-Laser-Based Techniques From the above discussion it is apparent that the conventional all-electronic character-ization methods have some limitations in characterizing very high-speed devices. The bandwidth of some newly developed devices has exceeded that of the conventional tech-niques. Two methods based on ultrafast lasers have been developed with bandwidth significantly greater than that of conventional methods. They are photoconductive sam-pling (PCS) and electro-optic sampling (EOS) . In Section 1.2.2, we describe the common features of time-resolved pump/probe measurement using laser-based techniques. Then we briefly discuss photoconductive sampling and electro-optic sampling; further details of E O S are given later in Chapter 2 and Appendix A . Time-resolved pump/probe experiment In this section, we introduce the basic ideas of pump/probe experiments, which are essen-t ial to photoconductive sampling and electro-optic sampling. Time-resolved pump/probe experiments have been used to measure fast electrical signals as well as physical parame-ters such as hot carrier relaxation t ime in semiconductor materials[3] and carrier tunneling time in quantum well materials[4, 5]. The experimental setups for these measurements are similar. Here, we only discuss the measurement of fast electrical signals. The key part of the laser-based technique is a mode-locked laser which generates subpicosecond optical pulses at a typical repetition rate of 100 M H z . The laser output is optically split into a pump and a probe beam. The pump beam triggers a pulse generator to provide an ultrafast electrical input to the device under test ( D U T ) . The probe beam measures the electrical response of the D U T by one of several sampling techniques. Since both the pump pulse and the probe pulse are split from the same laser pulse, the electrical pulse generated by the pulse generator and the optical probe pulse Chapter 1. Introduction 6 are perfectly synchronized. In F i g . 1.1, such a sampling system is illustrated; it consists of an ultrafast laser, beamsplitter, signal generator, sampler, and optical delay line. Both the generator and sampler are coupled to the D U T with a transmission line. The optical delay line has the same function as the electrical delay line in a sampling oscilloscope. It can delay the probe pulse (in time) with respect to the signal to be measured. B y varying the length of the optical delay line, the response of the D U T can be mapped out as a function of pump/probe delay. A s the optical path is in air, the delay can be simply related to the change in position Al of the delay-line mirrors by the following simple formula where At is the change in delay time; c is the speed of light in air. The factor of 2 comes from the fact that the beam is reflected from the retroreflector and thus travels twice Al. Because the delay t ime At can be very accurately controlled and the optical delay line is intrinsically jitter-free, the measurement bandwidth is determined by the speed of the optoelectronic generator and the sampler which we wi l l discuss in the following subsections. Photoconductive Generation This subsection describes the optoelectronic generation of ultrafast electrical signals. The most common optoelectronic signal generator, often refered to as photoconductive switch or Auston switch [6], is a gap in a D C biased coplanar-stripline that is deposited on a photoconductive material , as illustrated in F i g . 1.2 (dotted-line box). When an optical pulse illuminates the gap, photogenerated currents flow and generate an electrical pulse with very short risetime which is determined by the width of the optical pulse, the dimensions of the gap, and the semiconductor properties. The decay t ime of the electrical Chapter 1. Introduction 7 mode-locked laser A . optical delay line Al K -pump probe P-optoelectronic generator DUT optoelectronic tannpler data acquisition & analysis Load Figure 1.1: Diagram of a typical laser-based sampling system. It consists of five important parts: an ultrafast laser, a pulse generator, a sampler, a stripline, a delay line, and a data acquisition and analysis system. pulse ranges from subpicosecond to a few nanoseconds depending on the photoconductive material and the concentration of defects present. For example, radiation damaged G a A s or low-temperature grown G a A s may have a decay t ime of less than 1 ps while a low-defect semi-insulating G a A s has a decay time of 40-300 picoseconds. The former is often used as an electrical pulse generator as well as a sampler in photoconductive sampling. The latter is often used to generate step-like signals with subpicosecond risetime. The electrical pulses are launched into the transmission line as input signals for the device under test. Photoconductive Sampling In this section, we briefly discuss photoconductive sampling ( P C S ) . A detailed discussion of this topic can be found in [7]. A schematic diagram of a P C S system is illustrated in F i g . 1.3. It is the same as F i g . 1.1 except that the detailed structures of photoconductive switch and the sampler are shown here. The structure of the photoconductive switch is slightly different from the one shown in F i g . 1.2 . The three-electrode structure allows Chapter 1. Introduction 8 l a s e r p u l s e e l e c t r i c a l p u l s e Load m e t a l l i c p h o t o c o n d u c t i v e m a t e r i a l t r a n s m i s s i o n l i n e ! Figure 1.2: A typical optoelectronic signal generator used in pump/probe measurement. bias to be provided to the device under test as well as to the photoconductive switch. The sampler, or sampling gate, is another photoconductive switch which has similar structure to the pulse generator described above. The difference here is that the sampler is biased by the electrical signal on the transmission line instead of a D C supply as in a pulse generator. When a probe light-pulse strikes the gate, it creates a very large carrier density in a very short t ime at the gate gap and diverts a small part of the signal from the main coplanar stripline electrode to the sampling electrode. The time which the carriers can exist in the gap is the width of the sampling gate and is normally chosen to be very small compared to the signal to be measured. Only the part of the output signal which arrives at the gap at the same time as the probe light-pulse is sampled or diverted to the sampling stripline. B y optically delaying the probe pulses, we can sample the output signal one point after another and can reconstruct the shape of the output pulse after collecting enough sampling points, as described above. The resolution of this technique is mainly determined by the carrier life time of the sampling photoconductive switch, which normally is on the order of a picosecond. Comparing with conventional all-electronic methods, P C S improved the resolution by using ultrafast Chapter 1. Introduction 9 optical delay line Figure 1.3: A simplified photoconductive sampling system. The pulse generator, the D U T , and the sampling gate are connected by stripline. The retroreflector can move horizontally to provide relative delay between the pump pulse and the sampling pulse. laser pulses to activate signal generator and sampler. The sensitivity and signal-to-noise ratio of photoconductive sampling are extremely good. The typical sensitivity is a few [iV/y/Wz, permitt ing ultrafast electrical signals of amplitude of approximately one / / V to be measured with realistic acquisition times. One of the disadvantages of photoconductive sampling is the lack of flexibility in terms of sampling locations. Signals on a transmission line can only be sampled at the position the sampling photoconductive switch is built . To characterize an active electronic device, at least two sampling switches are needed at the input and the output side of the D U T , respectively. W i t h this technique, it is very difficult to measure the waveforms of an electrical signal at several different locations in a circuit. Recent development of mobile photoconductive sampling t ip has shown promising progress in solving this problem[8]. Electro-optic sampling to be discussed in the next subsection provides an excellent way to measure waveforms of electrical signals at several locations of a circuit. Chapter 1. Introduction 10 mode-locked laser optical delay line pump DUT 3KL <— K ^ data acquisition 1 \ X V / & analysis z analyzer "^ Jdetector / 1 V: eos probe Figure 1.4: A n electro-optic sampling system uses an electro-optic modulator as its sampler. The electro-optic modulator is composed of a polarizer, a compensator, an electro-optic probe, and an analyzer. The other parts of the system is similar to those of a P C S system. E l e c t r o - O p t i c S a m p l i n g This subsection describes another commonly used laser-based technique — electro-optic sampling[9]. In this technique, an electro-optic crystal is placed into the fringing field of the signal to be measured. When an ultrafast optical pulse passes through the crystal, the field-induced birefringence produced by the signal alters the polarization of the optical pulse. In other words, the amplitude of the electrical signal is recorded in the polarization of the pulse through electro-optic effect. In the following paragraph, we discuss this technique and how to retrieve the signal recorded in the pulse polarization. A schematic diagram of an E O S system is shown in F ig . 1.4 which is similar to the diagram of a P C S system except that the sampler in a P C S system is replaced by an electro-optic modulator ( E O M ) which is composed of a polarizer, a compensator, an electro-optic probe, and an analyzer. The pulse generator used in E O S is of the same Chapter 1. Introduction 11 structure as that described in the previous section. The electro-optic probe is made of electro-optic crystal, such as LiTaO"3. The electric field between the electrodes of the coplanar stripline produces field-induced birefringence in the electro-optic crystal which is put in contact with or in the vicini ty of the electrodes. The axis of the polarizer is set at 45 degrees with respect to the optical axis of the electro-optic crystal. The linearly polarized probe beam can be decomposed into two orthogonal components, one parallel to the optical axis of the crystal, the other perpendicular to the optical axis. The two components experience different refractive indices because of the birefringence. As a result, the polarization of the probe beam is changed (modulated) by the fringing electric field. The analyzer placed after the electro-optic probe turns this change of polarization into a change of intensity. The function of the compensator is to optically bias the system at its most efficient operating points. This optical setup works exactly the same way as an electro-optic modulator[10]. The transmitted light intensity varies as a function of the voltage between the electrodes. A more detailed description of E O S system is given in Chapter 2; principles of E O S are briefly described in Appendix A . Like in a P C S system, every light pulse generated by an ultrafast laser is split into two by an optical beamsplitter. The pump pulse is directed to the pulse generator which generates an electrical impulse as input for the D U T . The output of the D U T coupled into a output coplanar stripline. The probe pulse passes through the sampler, or electro-optic modulator. The ampli tude of the probe pulse coming out of the modulator is modulated by the output signal of the D U T and is proportional to the part of the electric signal which arrives at the modulator at the same t ime as the probe pulse. As a result, the relatively long electric signal is sampled by the very narrow optical probe pulse. Unl ike in a P C S , the sampled signal is carried by light-pulses in E O S rather than electric pulses. Using the same delaying and sampling procedures described before, we can let the narrow optical pulse slowly 'walk' (sample) through the relatively broad electrical Chapter 1. Introduction 12 pulse and reconstruct the shape of the electric pulse after collecting enough points. The temporal resolution of an E O S system is mainly determined by the width of the probe pulse, the transient t ime of the probe pulse through the electro-optic crystal and phonon resonant frequency of electro-optic material . Since the width of a probe pulse can be as narrow as a hundred femtoseconds and the electro-optic crystal can be made very th in , the resolution of an E O S system is even better than that of photoconductive sampling. For example, K e i l and Dykaar have measured electrical pulses with 200 fs F W H M (full width at half maximum) using an E O S system [11]. The sensitivity and signal to noise ratio of electro-optic sampling are reasonably good though not as good as P C S . The typical sensitivity is a few m V / \ / H z . Since the electro-optic crystal can be positioned at different locations in a circuit , it is very flexible in terms of circuit probing if the circuit layout uses coplanar surface electrodes. From the above discussion, we see that laser-based techniques have strong similarities to sampling oscilloscopes. The three conditions for building an ideal sampling oscilloscope can be easily satisfied by using laser-based techniques. The extremely narrow sampling gate, jitter-free optical delay line, and perfectly synchronized signal generation make the laser-based system superior to the conventional electronic techniques. A l l the ultrafast measurements in this thesis are made with a custom-made electro-optic sampling system which wi l l be described in detail in Chapter 2. 1.3 R e c e n t W o r k o n U l t r a f a s t D e v i c e C h a r a c t e r i z a t i o n Ultrafast-laser-based techniques have been used to measure a wide variety of high-speed electronic devices, including both passive and active devices. In this section, we se-lectively introduce recent research works on electro-optic characterization of ultrafast electronic devices. It is not intended to cover all the research works in this area, but Chapter 1. Introduction 13 to provide background information related to the research work to be presented in later chapters. Subsection 1.3.1 describes electro-optic characterization of passive devices in-cluding ultrafast transmission lines and pulse forming devices. Subsecton 1.3.2 describes electro-optic measurement on active devices, such as resonant tunneling diodes, ultrafast photodetectors, and state-of-the-art high-speed transistors. 1.3.1 Passive Devices Transmission Lines Transmission lines are often used as interconnections between high-speed electronic de-vices over short distance. A n ideal transmission line would transmit signals without distortion. However, distortion of high-frequency signals due to dispersion and various losses can be significant in real systems. Theoretical studies of transmission lines have suggested that there are several possible mechanisms responsible for the signal distortion. These mechanisms are conductive loss in the substrate, conductor loss in electrodes, ra-diation or surface wave loss, and modal dispersion caused by the dielectric inhomogeneity at the surface [12, 13, 14, 15]. To verify theoretical simulation based on the above mecha-nisms, it is desirable to compare the calculated waveforms along a transmission line with the measured ones. However, it is very difficult to make this k ind of measurements using conventional all electronic methods. Electro-optic sampling has been demonstrated to be a powerful tool to study transmission lines. To determine the main mechanisms responsible for distortion of high-frequency signals propagating along a transmission line, Gupta and co-workers measured the waveforms of a picosecond electric pulse at five propagation distances [16] . The picosecond pulse is generated by a low-temperature GaAs photoconductive switch incorporated in a coplanar wave guide. F ig . 1.5 (a) shows the waveforms of the pulse at 5 propagation distances. Chapter 1. Introduction 14 Several important features of the pulse change as it propagates along the transmission line. The pulse width broadens considerably, the amplitude drops dramatically, and ringing features develop at the tai l of the pulse. F i g . 1.5 (b) is the simulation of the pulse propagation including three mechanism: modal dispersion, conductor loss, and radiation loss. The main features agree very well with those of the experiment. The authors concluded that the modal dispersion and radiation loss are the dominant pulse-shaping mechanisms for picosecond pulses. A s the conductor loss plays a minor role in the pulse shaping, the use of superconductor electrodes wi l l not reduce pulse distortion. To reduce modal dispersion, a substrate with smaller dielectric constant and smaller size of electrodes are recommended in designing low distortion transmission lines. The results also apply to coplanar striplines. Pulse Forming Devices Picosecond electrical pulses are needed in many ultrafast applications, such as S-para-meter measurement of ultraf?.st transistors. Almost all the picosecond electrical pulses are generated photoconductively, where ultrafast laser pulses are used to activate D C biased photoconductive switches described in the previous section. A photoconductively-generated electrical impulse is normally of a very fast risetime mainly determined by the optical pulse width and the R C constant of the switch/transmission line structure and a trai l ing tai l determined by the carrier lifetime of the photoconductive substrate. To obtain ultrashort electrical pulses, photoconductive materials with short carrier lifetimes have been used as the substrates of photoconductive switches. Radiation-damaged mate-rial and low temperature G a A s are the most commonly-used substrate materials[17, 18]. The disadvantage of these devices is that they are difficult to integrate with the device under test or additional fabrication process steps need to be added to the normal process-ing procedures. Alternatives to these devices are pulse-forming optoelectronic devices Chapter 1. Introduction 15 0) XD Q. E CD 3 CL E CO 1 0.8 0.6 0.4 0.2 0 -0.2 _ n 0.0 mm _ X : Gaussian fit > - 0.5 mm 3 1.0 mm — > ' '• / \ 3.0 mm I \ - \ / \ ' \ 5.0 mm J '* / 1 / v . 1 \ ' ^ \ •ii. /••'" \' rx \ *rx •• « '—-~ , , , i , _i—i—L. i i i 1 i , , 1 , ( a ) 4 6 8 10 12 time (ps) 0.0 mm 0.5 mm 1.0 mm ii 5.0 mm - i _ i i i i_ 4 6 8 time (ps) 10 12 Figure 1.5: Waveforms of an electrical pulse propagating on a coplanar waveguide with 15 \im center electrode and 10 \im slots, (a) is experimental results measured at five different places along the transmission line, (b) is the theoretical simulation including modal dispersion, conductor loss and radiation loss. From reference [16] . Chapter 1. Introduction 16 which are coplanar transmission lines with specially designed impedance-mismatched structures. The advantage of these devices is that they can be easily integrated with device under test without additional fabrication processes. It should be pointed out that the pulse-forming device is not the only way to generate picosecond electrical pulses on semi-insulating substrates. Subpicosecond electrical pulses have also been generated by asymmetric excitation of a charged coplanar transmission line deposited on non-damaged silicon-on-sapphire substrate[19]. Sano and co-workers first reported the generation of picosecond electrical pulses using a pulse-forming device[20]. F ig . 1.6 (a) is a top view of the device. It is composed of a coplanar stripline integrated with a photoconductive switch and an impedance-mismatched structure. The electrodes are deposited on a semi-insulating GaAs substrate. The photoconductive switch generates two step-like electrical pulses travell ing in the opposite directions along the stripline. The step-like pulse travell ing towards the left is reflected by the impedance-mismatched structure and changes its sign and travell ing direction. When the reflected (inverted) step-like pulse superimposes with the step-like pulse travell ing toward right, the tails of the step-like pulses cancel and a pulse is formed. The width of the pulse is determined by the round-trip t ime between the photoconductive switch and the impedance-mismatched structure. Full-wave simulation showed that the reflectivity of the impedance-mismatched structure changes with the gap distance ld\ The best result is obtained with d — 0 \im where unit reflectivity is obtained. Electro-optic sampling was used to measure the electrical pulse at position ' A ' . F ig . 1.6 (b) shows the picosecond electrical pulse generated by the pulse-forming device. Chapter 1. Introduction 17 PC OPTICAL PULSE V////////S T I M P E D A N C E MISMATCH S T R U C T U R E i 1 10 p. m (a) 1.0 3 3. S c •5 0.5 f \ / / \ / - ' \ 1-3 PS / I" / / 1 / I \ 1 r- ' \ / \ . r * / \. _ V (b) 4 6 Time (ps) 10 Figure 1.6: (a) Top view of a pulse-forming optoelectronic device fabricated on semi-insulating G a A s substrate. The separation of the stripline electrodes is 13 fim. The 'cf in the impedance-mismatched structure can be varied from 0 (im (short cir-cuited) to 13 (im (impedance matched), (b) Picosecond electrical pulse generated by the pulse-forming optoelectronic device. From Reference [20] Chapter 1. Introduction 18 (a) (b) Figure 1.7: Conduction band structure of a R T D . (a) at zero bias, (b) at resonant bias. 1.3.2 Active Devices Resonant Tunneling Diode In this subsection, we describe ultrafast characterization of resonant tunneling diodes (RTD) which are active electronic devices. They are of use in high-speed applications including high-speed oscillators and high-speed pulse generators. RTD-based microwave oscillators with operating frequency of 712 G H z have been reported[21, 22]. R T D have also been use to generate step-like impulses with very fast risetime[23, 24]. Resonant tunneling diodes are double-barrier heterostructure devices[25] with a quan-tum well made of a narrow-bandgap material sandwiched between two wide-bandgap barriers. Two heavily-doped layers of the narrow-bandgap material act as electrodes. F ig . 1.7 shows the conduction band structure where the dashed line represents the low-est energy level in a quantum well. When a voltage is applied, the potential energy of the negative electrode increases, as shown in F ig . 1.7 (b). Initially, the current increases with the applied voltage, and reaches a peak when the potential energy of the negative electrode is equal to the energy level in the quantum well. A t this bias condit ion, the device is said to be at resonance. Further increase in the applied voltage breaks the resonant tunnell ing condition and results in a dramatic decrease in current. The current Chapter 1. Introduction 19 Time (psec) Figure 1.8: I-V and switching characteristics of a R T D . (a) I-V characteristics, (b) Switching characteristics measured by electro-optic sampling. The switching t ime is 1.7 ps. From reference [24] reaches a valley and then increases again with the applied voltage due to non-resonant mechanisms. F ig . 1.8 (a) shows the I-V characteristics of a R T D . In reference [24], the device is a coplanar waveguide integrated with an I n A s / A l S b R T D which shunts the center electrode to the ground. The R T D divides the transmission line into two sections: input and output. When the input transmission line, is driven by a sine wave and a dc bias, at the resonant voltage, the R T D switches and launches a step-like signal into the output transmission line. This device is also called a pulse Chapter 1. Introduction 20 forming device. It should be noted that here the pulses are generated electrically not photoconductively as those described in the previous section. Electro-optic sampling was used to measure the switching characteristics. F ig . 1.8 (b) shows the switching of the I n A s / A l S b R T D with a risetime of 1.7 ps. Photodetectors High-speed photodetectors are of interest in optical communication and other wide-bandwidth optoelectronic systems. Photodiodes with 3dB bandwidth over 100 G H z have been reported[26]. Electro-optic sampling has been used to study the effects of load resis-tors and size of the active area on the bandwidth of a photodiode[26]. F ig . 1.9 (a) shows the electro-optic measurement on three G a l n A s / I n P p-i-n photodiodes with different size and loads. To minimize parisit ics, the two 7/ imx 7[im diodes are integrated with load re-sistors, bypass diodes, and output coplanar waveguides. The electro-optic measurement is the same as described above except that here the photodiode is the source of electrical pulses, and the InP substrate is used as electro-optic transducer instead of an external electro-optic probe. The upper curve in F ig . 1.9 (a) is the response of a discrete 2/zmx 2\im photodiode without a matched resistor. The lower two curves are responses of two 7p,mx 7/im integrated photodiodes with and without matched resistors. The measured pulse width are 3.3 ps F W H M , 3.8 ps F W H M , and 4.6 ps F W H M for the above three samples, respectively. F ig . 1.9 (b) shows the corresponding Fourier transform of the three t ime resolved measurements. The 3dB bandwidth of the 7/xmx 7[im photodiodes with and without the matched resistors are 108 G H z and 62 G H z , respectively. Chapter 1. Introduction 21 i— i — i — . — i — r i . . . . i • . . . i . . . . i i 0 5 10 15 20 25 Delay (ps) (a) 5 I—*—'—>—'—i—•—'—>—'—i—i—'—•—>—r Figure 1.9: (a) Electro-optic measurement of response of ultrafast G a l n P / I n P p-i-n pho-todiodes. (b) Corresponding frequency response of the photodiodes obtained by Fourier transform. From reference [26] Chapter 1. Introduction 22 Transistors Electro-optic sampling has also been used in characterizing ultrafast transistors includ-ing modulation-doped field-effect transistors (MODFETs ) [27 , 28], heterojunction bipo-lar transistors (HBTs) [29], and metal-semiconductor field-effect transistors ( M E S F E T s ) j [30]. To provide background knowledge for Chapter 4, we describe the principles of operation and performance of M O D F E T s in the following paragraphs. The modulation-doped field-effect transistor ( M O D F E T ) is also known as a high-electron-mobility transistor ( H E M T ) , a two-dimensional-electron-gas field-effect transis-tor ( T E G F E T ) , and a selectively-doped heterostructure transistor ( S D H T ) [31] -[32]. In F ig . 1.10 (a) we show the structure of a simplified A l G a A s / G a A s M O D F E T . The M O D -F E T is grown on a semi-insulating GaAs substrate and has four layers: the GaAs layer and the very th in A l G a A s layer are undoped; the surface A l G a A s layer is doped n-type. Gate, source, and drain electrodes are fabricated on the surface. Since the conduction-band energy of GaAs is lower than that of A l G a A s as shown in F ig . 1.10 (b), the conduction-band electrons from the n -A lGaAs layer wi l l accumulate in the undoped GaAs layer. Because of the attractive Coulomb force from the ionized dopants in the n -A lGaAs layer, the electrons wi l l remain near the interface and form a 2-dimensional conducting channel between the drain and the source. The density of the electrons in the conducting channel can be controlled by the gate which is a Schottky barrier formed on top of the n -A lGaAs layer. There are two main reasons for the high performance of M O D F E T s . The first is that the conducting channel is formed in undoped material. The low doping reduces ionized impuri ty scattering, and electrons have a higher mobi l i ty than in a conventional GaAs M E S F E T , where the conducting channel is formed in a doped layer. Al though the M O D F E T is often operated with the channel velocity saturated, during switching the channel spends t ime below velocity saturation, and it is Chapter 1. Introduction 23 SOURCE GATE n METAL DRAIN n-AlGaAs n 2 D E G AlGaAs GaAs Buffer GaAs - - - - - ; E l s V AEc VEo L . . . s Ec E F (b) Figure 1.10: (a) Schematic structure of a simplified A l G a A s / G a A s M O D F E T . (b) Energy band diagram of simplified A l G a A s / G a A s M O D F E T . (From reference [33]) • Chapter 1. Introduction 24 in this t ime that the increased channel mobil i ty is significant. The high electron mobil i ty is also significant in reducing the parasitic resistances in series with the source and drain contacts. The second reason for the high performance is that in a M O D F E T the wide-bandgap layer acts as an insulator between the gate and the channel. The final device is much like a M O S F E T , but takes advantage of the more favorable transport properties of G a A s . The gate control of the channel charge can be very effective with th in wide-bandgap layers, resulting in very high transconductance. This is in contrast wi th the M E S F E T , which uses the depletion region formed under the Schottky-barrier gate as the gate-to-channel insulator. Since the size of this depletion layer is determined by the doping level, there are practical l imitations to the gate-to-channel separation possible in M E S F E T s , which l imi t their scaling to higher frequencies. The performance of M O D F E T s has been improved tremendously since the first A l -G a A s / G a A s M O D F E T was reported in 1980[31]. Several combinations of heterostruc-ture material have been used to improve the performance of M O D F E T s . In addition to the lattice-matched A l G a A s / G a A s M O D F E T (GaAs substrate), pseudomorphic A l -G a A s / I n G a A s M O D F E T (GaAs substrate) and both lattice-matched and pseudomorphic I n A l A s / I n G a A s M O D F E T s (InP substrate) have been fabricated[34]. More recently there have been promising preliminary results with I n A s / A l S b (antimonides) [35] and G a N / A l G a N or G a N / A I N (nitrides) M O D F E T s [ 3 6 , 37]. Most of the M O D F E T s are fabricated on G a A s or InP substrates with their conducting channels either in G a A s or InGaAs. M O D F E T s with InGaAs conducting channels have demonstrated better per-formance than those with G a A s conducting channels largely because of the increased confinement of the two-dimensional electron gas. The electron mobil i ty in InGaAs can also be higher than that in GaAs[38]. The current gain cut-off frequency ft, where the short-circuit current gain goes to unity, and the m a x i m u m oscillation frequency / m 0 x , where the power gain goes to unity, Chapter 1. Introduction 25 are two important parameters to characterize small-signal performance of a transistor. A l G a A s / G a A s M O D F E T s have been demonstrated with ft = 110 G H z and fmax = 200 G H z [38] while I n A l A s / I n G a A s M O D F E T s have been demonstrated with ft = 340 G H z [39] and fmax = 455 G H z [40]. Such high frequencies are usually estimated by extrapolating the experimental data of a network analyzer which works up to 60 G H z . Direct measurement of small-signal operation of M O D F E T s up to 100 G H z has been performed by using electro-optic sampling[41]. A delay t ime of 8.5 ps per gate has been measured in a ring oscillator made of A l G a A s / G a A s M O D F E T s with 0.85 pm gate length[42]. A l I n A s / G a l n A s M O D F E T s with 0.2 fim gate length in a ring oscillator have demonstrated 5 ps/gate delay t ime at 77 K (6 ps/gate at room temperature) [43]. The first large-signal measurement on a single pseudomorphic A l G a A s / I n G a A s M O D F E T with 0.35 /xm gate length was reported with 6.2 ps switch-on time measured by electro-optic sampling[27]. F i g . 1.11 shows the response of the M O D F E T for different amplitudes of input signal. The risetime of the negative-going input signal was 2.8 ps, and the fastest switching time of the M O D F E T was 6.2 ps. In previous work[27, 44, 30], the device under test was wire bonded to a test fixture. To avoid parasitic effects introduced by bond wires, and extend these measurements to higher frequencies, it is essential to monolithically integrate the device under test with the test fixture. This approach of on-wafer integrated test fixtures has been applied to electro-optic characterization of I n A s / A l S b resonant tunneling diodes[24], double heterostructure G a l n A s / I n P p-i-n photodiodes[26], and G a A s / A l G a A s M O D F E T s [ 4 5 ] , where the devices of interest were integrated with coplanar waveguide test fixtures. In reference [45], the M O D F E T s have gate lengths of 1.2-1.5 firn, are connected in a common-gate configura-t ion, and have a very low current-gain cut-off frequency of 2.5 G H z . The switching t ime and the delay t ime measured by electro-optic sampling are 5 ps and 9 ps, respectively. Chapter 1. Introduction 26 l 1 1 1 1 r Time (5ps/div) Figure 1.11: The drain output of the M O D F E T with increasing input signals: A V ^ , 1.9AV^, 2.7 AVg, 3 .6AK, , and 4AAVg, where AVg is approximately 0.17V.(From reference [27]) The authors were not able to fully explain the apparent inconsistency between these fast switching times and the low current-gain cut-off frequency. One of the most significant results in this thesis is in the characterization of high-speed M O D F E T s , and is shown in F ig . 1.12. We reported the first electro-optic measure-ment of a high-speed M O D F E T monol i th ical ly integrated with a photoconductive switch and coplanar stripline fixture[46]. F ig . 1.12 shows the electro-optic measurement of the latt ice-matched Ino .52Alo.48As / Ino .53Gao.47As M O D F E T , which has a current-gain cut-off frequency f t = 78 G H z . The lower panel shows four input signals at the gate. The upper panel shows the corresponding drain output. We wil l discuss the experiment and results in more detail in later Chapters. Chapter 1. Introduction 27 > • 1 i I 1 1 1 L _ 1 0 1 5 2 0 2 5 3 0 Time (ps) Figure 1.12: Switching response for an Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T on InP substrate. The lower panel shows a series of increasing gate inputs, and the upper panel shows the corresponding drain outputs. The operating point is V Q S = O V and V D S = I V . Further details of this measurement are given in Chapter 4. Chapter 1. Introduction 28 1.4 Outline of the Thesis Chapter 2 describes the electro-optic sampling system. The design considerations of our E O S system are described in detail including overall layout, laser systems, E O S optics, viewing systems, and electronic systems, emphasizing the original aspects of its design. The resolution and sensitivity of the E O S system are discussed at the end of the chapter. In Chapter 3, we present an experimental study of the measurement errors and inva-siveness caused by an external L iTaOa probe used in electro-optic sampling system. We present electro-optic measurements of step-like signals generated by a photoconductive switch with various probe-tip-to-sample distances (air gaps). We show that contact (air gap free) external electro-optic sampling, which has been widely used in E O S measure-ment, can lead to measurement errors. However, these errors can be reduced by using a non-contact arrangement with an air gap between the t ip and the sample. We also present an experimental study of the sensitivity of electro-optic sampling as a function of air gap. In Chapter 4, we describe electro-optic characterization of ultrafast M O D F E T s mono-lithically-integrated with transmission line/photoconductive switch test fixture. Ex-perimental results and theoretical simulation of both L M Ino.52Alo.48As/Ino.53Gao.47As M O D F E T and P M Ino.20Gao.80As/Alo.25Gao.75As M O D F E T are presented. The effects of different gate-access structures, semiconductor materials, and bias conditions on the performance of M O D F E T s are studied. We also describe a t ime-domain simulation of the M O D F E T s using a lumped-element model incorporating input and output trans-mission lines. Through comparison with a similar work but on discrete M O D F E T s , we demonstrate the advantage of using an integrated test fixture and the importance of incorporating input transmission line in the lumped-element model. Chapter 2 Experimental Techniques of Electro-Optic Sampling 2.1 Introduction to Chapter During the course of the thesis work, the author designed, bui l t , and tested a computer-automated electro-optic sampling system with TeraHertz bandwidth. The details of electro-optic effect are well known, and their application in electro-optic sampling is well-established; see for example Ref. [47]. A brief description of the electro-optic ef-fect and its application in electro-optic sampling is included in Appendix A for readers who are not famil iar with electro-optic effect. In this chapter, we describe the design, hardware, and performance of the electro-optic sampling system built by the author. Section 2.2 describes the layout and design of the electro-optic sampling system. Section 2.3 describes the optical modules of the system including laser system, the electro-optic sampler, optical compensator and the viewing systems. The noise reduction electronics and sensitivity are described in Section 2.4. Final ly, in Section 2.5, we describe l inearity and resolution achieved by our E O S system. 2.2 Overall Layout and Design In this section, we describe the design and overall layout of the E O S system. F ig . 2.1 shows a block diagram of the E O S system. It shows more detail than F ig . 1.4 in Chapter 1 and consists of a mode-locked laser, an acousto-optic modulator ( A O M ) , an optical delay l ine, two viewing microscopes, a probe t ip, 3-D translation stages, optics, and data 29 Chapter 2. Experimental Techniques of Electro-Optic Sampling 30 mode-locked laser ^ probe 1 Y 1 pump optical delay line pump focusing & viewing polarizer A Y2. DUT probe focusing & viewing analyzer c^ompensator probe tip <K"* Data acquisition - 3 V N * electronics Translation Stage Figure 2.1: Block diagram of a complete E O S system built in our lab. acquisition electronics; the device under test ( D U T ) is also shown. The basic structure is similar to the first electro-optic sampling system reported by Valdmanis and coworkers[9]. The acousto-optic modulator in the pump beam path is used to modulate (chop) the pump beam intensity so that a lock-in amplifier can be used to improve signal-to-noise ratio. This is required because from the discussion in Appendix A we can see that to achieve a sensitivity of 1 m V with typical half-wave voltages on the order of 3 k V (LiTaOs) we must be able to detect the extremely small fractional change in intensity at Chapter 2. Experimental Techniques of Electro-Optic Sampling 31 the output analyzer which is less than one part in 10 6 . A s a result, the small electro-optic signal is normally buried in the noise. A lock-in amplifier allows us to detect the electro-optic signal. The two focusing/viewing systems are two specially-designed microscopes which are used to align and focus the pump and the probe beams at desired positions, and allow precise alignment of the probe t ip with respect to the sample. The polarizer, analyzer, compensator, and the probe t ip shown in F i g . 2.1 form an intensity electro-optic modulator described in Appendix A . However, L iTaOs is used as an electro-optic crystal instead of G a A s . This is because the L iTaOs crystal has a much smaller half-wave voltage Vn (2.7 k V ) compared to G a A s and is transparent for infrared and visible laser wavelengths. The experimental implementation of the block diagram shown in F i g . 2.1 is assembled on an optical table. The designed layout is original, wi th most of the optical components mounted directly on an optical table, in contrast to previous approaches where probe components were mounted on a vertical breadboard which can be moved wi th a large three-dimensional translation stage to position the probe t ip [47]. In our design, the probe t ip is mounted on a five-degree of freedom miniature translation stage which is fixed on a rack bolted directly to the optical table. The five degrees of freedom allow the footprint of the probe t ip to be adjusted so that it is parallel to the sample surface. This is required to achieve m a x i m u m sensitivity and to ensure reproducibil i ty on a day-to-day bases. In an experiment the probe t ip does not move once it is aligned to ensure that the alignment of the probe beam in the probe tip remains the same for al l measurements including those at different sampling locations of a circuit. To allow probing at different locations, the D U T which is mounted on a three-dimensional translation stage can be moved relative to the probe t ip . Another original aspect of this E O S system is the design and the incorporation of the two viewing systems. In reference [47], an eye piece was used to view the D U T features, footprint of the probe t ip , and the focused visible probe Chapter 2. Experimental Techniques of Electro-Optic Sampling 32 spot. There was no viewing system for the pump beam. In the present system, two custom-designed viewing systems equipped with C C D cameras are incorporated. The first for the probe views the footprint of the probe t ip , the device features beneath it , and the focused infrared probe beam. The second for the pump shows the gap of the photoconductive switch and the focused infrared pump beam. The design of the viewing systems allow the pump and probe beams to be focused to two locations as close as 1.5 m m through two different lenses. This gives more freedom to separately manipulate the pump and the probe beams. In addition the system is designed in such a way that only minor alignment and component change are needed in order to focus both pump and probe beams through one objective lens. This feature is needed i n measurements where pump and probe beams need to be overlapped or placed within about 200 fj,m of each other. The detailed structures of the viewing systems w i l l be presented in later sections. A detailed diagram of the complete electro-optic sampling system built at U B C can be found in Appendix B . 2.3 Optical System In this section, we discuss the optical aspects of the E O S system. We describe the ultrafast laser system, the electro-optic sampler, and the two custom-designed pump and probe viewing systems. 2.3.1 Laser System Two lasers, a continuous-wave ( C W ) laser and a mode-locked ( M L ) laser, are used in the E O S system. The C W laser is used to pump the M L laser which produces a train of ultrafast optical pulses by phase locking, or mode-locking, a large number of longitudinal modes of the laser cavity together [48]. The C W laser is a Coherent Innova 310 Argon ion Chapter 2. Experimental Techniques of Electro-Optic Sampling 33 Concave Mirrors Figure 2.2: Schematic diagram of N J A - 3 Ti-sapphire laser. laser which operates in a multi l ine configuration for visible wavelengths from 457.9 nm to 514.5 n m . It is equipped with 'PowerTrack' feature which automatically maintains the opt imum cavity alignment; the maximum output is 13 W . The M L laser is an all solid state Ti-sapphire laser (Model N J A - 3 ) from Clark Instru-mentation Inc. The components of the Ti-Sapphire laser kit are mounted directly on an optical table. It was assembled and aligned by the author during the thesis work. F ig . 2.2 shows the schematic of the Ti-sapphire laser which is essentially a linear cavity folded to occupy less space on the table. The Argon pump beam is focused at the Ti-sapphire rod through one of the concave mirrors. The optical emission from the gain medium (Ti-sapphire rod) is collected by the two concave mirrors which form a folded laser cavity together with three plane mirrors. The two prisms are used to compensate dispersion in the cavity and are essential for short pulse generation. The slit is used to tune the operating wavelength by translating in the direction perpendicular to the laser beam. It also helps stablize the laser against the effects of fluctuations in the cavity, which reduces noise. The mode-locking mechanism of the Ti-sapphire laser is the self-focusing effect in Chapter 2. Experimental Techniques of Electro-Optic Sampling 34 the Ti-sapphire rod induced by the intracavity laser pulse[49]. The presence of the weak lens formed in the gain medium by the intracavity pulse creates a cavity that is less lossy for pulsed operation than it is for C W oscil lation. Consequently, once this less lossy cav-ity is formed, the laser wil l stay mode-locked. However, there is no natural mechanism to init iate the pulse needed for the mode-locking operation. In a N J A - 3 Ti-sapphire laser, the mode-locking operation is achieved by moving the prism before the slit out of and then back into the C W lasing path which wil l disturb the C W operation and init iate pulsing in the cavity. The laser operates in the near infrared and is tunable from 700 nm to 990 nm (three mirror sets are needed to cover the whole tuning range; we have used only one set in this work). When pumped by a 5 W Argon ion laser, the Model N J A - 3 can produce about 400 m W average laser power in a train of pulses of 100 M H z repetition rate. The pulse width measured by autocorrelation is 125 fs. We have found that the Model N J A - 3 can take up to 3 hours to warm up, and then can start pulse operation with no or minor alignment. The mode-locked operation is very stable and can last more than 10 hours without interruption. The exact origin of the long warm-up t ime is not known at present, but we found the output power of the T i -sapphire changes with room temperature. We suspect the Argon-laser pump beam may slowly warm-up the enclosed Ti-sapphire cavity. It is also possible that the pointing of the Argon ion laser is not stable during the first three hours of operation. The reduction of this t ime would significantly improve the ease of using the E O S system. 2.3.2 Electro-Optic Sampler Electro-optic sampling can be achieved either by internal electro-optic sampling or by external electro-optic sampling. In external electro-optic sampling, the probe t ip used is not part of the sample or circuit to be measured. It is a separate component. The probe tip mentioned in Chapter 1 is an external probe t ip. In internal electro-optic sampling, no Chapter 2. Experimental Techniques of Electro-Optic Sampling 35 external probe t ip is required and the substrate of the sample is used as the electro-optic material . In this case, the probe beam is focused at the electrode of the D U T from the back of the substrate and the electric field to be measured creates birefringence in the substrate and modulates the probe beam. The advantage of this method is that it is non-invasive because the optical beam does not interfere with the electric field in the substrate. However, it can only be used in samples or circuits fabricated on materials with electro-optic effect, such as G a A s and InP. Samples fabricated on Si or Ge substrate cannot be used in internal electro-optic sampling. In addition, the following extra conditions have to be satisfied to perform internal E O S . The back of the substrate has to be polished to allow access of the laser beam with m i n i m u m scattering loss. The wavelength of the probe beam needs to be tuned so that the substrate is transparent for the probe beam. In most cases, the pump beam needs to be frequency doubled in order to generate carriers in the photoconductive switch. Besides the drawbacks mentioned above, the temporal resolution of internal E O S might be lower than that of external E O S due to the practical l imitations of thinning the substrate. Final ly , if the substrate is not very uniform, there can be very significant problems with experimental drift. A s described in Appendix A , an electro-optic sampler is actually the same as an electro-optic intensity modulator. We have chosen to use external electro-optic sampling because it provides the best temporal resolution and allows measurement of samples with non-electro-optic substrates, such as Si and Ge. F i g . 2.3 is the schematic diagram of an external electro-optic sampler. It is almost the same as the electro-optic modulator of F i g . A . 2 . The only difference is the arrangement of the optical components. Here, the polarizer, electro-optic crystal, compensator and analyzer are not aligned in a straight line as in F i g . A . 2 . However, the operating principles are exactly the same. In this case total internal reflection is used to reflect the probe beam from three facets of the t ip , which is polished and shaped as a truncated pyramid structure. A t present these Chapter 2. Experimental Techniques of Electro-Optic Sampling 36 tips are available commercially from Terametrics[50], The external probe t ip is made of a naturally birefringent crystal L iTaOa which is most efficiently used as an transverse modulator. Unl ike GaAs described in Appendix A , the principal axes of LiTaO"3 do not change when an external electric field is applied to its optical axis. In other words, the principal axes x', y', z' of electrically induced index ell ipsoid coincide with its natural principal axes x,y,z when the electric field is parallel to optical axis z. The electrically induced indices can be expressed as: n 3 nx> = n0 - -^rXj,Ez (2.1) n 3 nyi = n 0 - Y r i 3 E z (2-2) ^ n 3 nz< -•' n e - Yr^Ez (2.3) where 7*13 and r 3 3 are the electro-optic coefficients; Ez is the external electric field applied in the optical axis z of the L iTaOscrysta l . Since r 3 3 is the largest electro-optic coefficient in L i T a 0 3 , to most efficiently use the electro-optic effect the optical beam should be perpendicular to the optical axis z. In this case, the phase retardation S can be written as: S = 8, + ^ ( n 3 r 3 3 - n 3 r 1 3 ) £ 2 (2.4) Si = -r—(n0 - ne) (2.5) ^ 0 where Si is the intrinsic phase retardation caused by the natural birefringence; / is the length of the optical path in L iTaOs crystal. The probe t ip is made of y-cut L i T a 0 3 crystal. This means the optical axis is in the plane of the LiTaO"3 slab and the y axis is perpendicular to the plane. The optical axis is oriented parallel to one of the rect-angular edges of the footprint of the t ip. When used to probe the electrical signal on a transmission l ine, the probe tip is oriented in such a way that the optical axis of the Chapter 2. Experimental Techniques of Electro-Optic Sampling 37 Figure 2.3: A LiTaO"3 external electro-optic sampler in its opt imum configuration for external electro-optical sampling. The optical axis of the LiTaOs crystal is perpendicular both to the propagation direction of the transmission line and to the probe beam. The polarization of the polarizer and analyzer is at 45 degrees with respect to the optical axis of the probe t ip . The sampler is most sensitive to the electric field parallel to its optical axis. L iTaOs crystal is perpendicular to both the propagation direction of the transmission line and to the probe beam, as shown in F i g . 2.3. In this configuration, the transverse electric field between the electrodes is parallel to the optical axis, which most efficiently uses the electro-optic effect in LiTaOs and thus is the most sensitive configuration for electro-optic sampling. The geometry of the probe t ip is not exactly the same as the schematic shown in F i g . 2.3. The electro-optic crystal L iTaOs is only 20-30 fim thick. It is glued to the polished end of a fused silica rod. The rod is then ground into a pyramid shape as shown in F i g . 2.4 . The foot print of the pyramid t ip is a 200^mx200/xm square. The diameter of the rod is 1.5 m m to 2 m m . This places a l imit in how close the pump beam can get to the probe beam in the experimental setup. The smallest separation between the probe Chapter 2. Experimental Techniques of Electro-Optic Sampling 38 Input beam output beam 1.5 mm fused silica support 2 mm 7 60' >| 200 um electro-optic 20~30 um material: UTaO, Figure 2.4: Schematic diagram of a external probe t ip . The dimensions are shown in the diagram, (after Ref [51]) and the pump beam achieved is about 1.5 m m when the beams are focused through two different lenses. To achieve smaller pump/probe distances, a smaller probe t ip or a new In F i g . 2.3, the orientations of the polarizer and analyzer are not shown, but from the discussion of intensity modulators in Appendix A it is obvious that they are very important for the proper operation of the electro-optic sampler (or modulator). In the experiment, the polarizations of the polarizer and analyzer are set at 45 degrees with respect to the optical axis of the probe t ip . These orientations are required for achiev-ing the m a x i m u m sensitivity of the electro-optic sampling system. Another important optical component which affects the sensitivity of the electro-optic sampler is the optical compensator which introduces an adjustable phase retardation to the probe beam so that the electro-optic sampler is biased at the opt imum operating point. Since it is one of the most important components in an E O S system, we wi l l describe it in detail in next design of the probe t ip would be needed. Chapter 2. Experimental Techniques of Electro-Optic Sampling 39 subsection. 2.3.3 Optical Compensator The optical compensator used in our E O S system is a quartz wave plate mounted on a rotation stage which allows the wave plate to be rotated around both its slow axis (optical axis for quartz) and fast axis. It can be shown that the phase retardation 6 and the laser incident angle 6 are related by the following formula: &.(ne-n0)h Oslow = ( . _ 1 •> (2.6) cos[sin lcj>) _ %{nj-ne)h Ofast = , . (2.7) cos{sm i<p) where J> = — (2.8) where the <f) is the refraction angle inside the crystal; is the refractive index of the extraordinary beam at angle <f> with respect to the optical axis; h is the thickness of the wave plate; 6siow and 6fast are the phase retardations when the wave plate is rotated about the slow and the fast axis, respectively. The above equations are derived under the assumption that after passing through the wave plate the separation of the extraordinary beam and ordinary beam is much smaller than the thickness of the the crystal. This is a very good approximation for wave plate of a few mill imeter thickness. For example, the beam separation is less than a micron for a 1 millimeter wave plate with 30 degree incident angle. For a half-wave plate, equations 2.6 and 2.7 can be written as: _ (2m + l ) T r Oslow = 7 : T T \ (2-10) cos(sin~L<p) Chapter 2. Experimental Techniques of Electro-Optic Sampling 40 {n+-n0) (2m + l)7r (ne — n0) cos(sin~14>) (2.11) (2.12) where ( n e - n0)h - 0 . 5 (2.13) m — A where the m the the order of the wave plate. A half-wave plate of 1 m m thickness working at 800 nm is an eleventh-order ( m = l l ) wave plate. F i g . 2.5 shows the calculated retardation as a function of incident angle for an eleventh-order and a zero-order wave plates rotating about its slow axis (solid line) and fast axis (dashed line). The phase retardation increases when the wave plate is rotated about the optical axis (slow axis) but decreases when the wave plate is rotated about the fast axis. The retardation tuning range depends strongly on the order of the wave plate. We chose to use a multi-order wave plate for its large tuning range. During this work, a simple method was developed to measure the phase retardation introduced by an anisotropic plate, using a laser and a power meter, and two polarizers. This simple setup can also be used to determine the orientation of the optical axis of a probe t ip in addition to its intrinsic retardation. As described above, the proper orientation of the optical axis of the probe t ip with respect to the probe beam and transmission line is crucial in achieving maximum sensitivity of an electro-optic sampling. The details of this measurement technique is describe in Appendix C . We have used this method to measure the retardation tuning range of the compensator used. The results are shown in F i g . 2.6. The measurements were made with the Ti-sapphire laser at a wavelength of 809 n m . The open circles and the filled squares in F i g . 2.6 are data corresponding to rotating about the slow and the fast axes of the wave plate, respectively. The retardation tuning range of the compensator is about ± 2 7 0 degrees which are more than enough for the application of electro-optic sampling. It should be pointed out Chapter 2. Experimental Techniques of Electro-Optic Sampling 41 co o> <u u oo CU w a 0 • r H CO-<u 01 CO ca ca A OH 540 450 360 270 180 90 0 -90 -180 1 1 1 1 1 Rotate about the slow axis Rotate about the fast axis m = l l m=0 H m = l l 10 20 30 40 Incident Angle (degrees) Figure 2.5: The calculated phase retardation of an eleventh-order and a zero-order quartz half-wave plates as functions of incident angle of the laser beam. The incident angle is defined by the normal of the wave plate and the incident laser beam. ne = 1.5459 and n 0 = 1.5375 for laser wavelength 800 nm are used in the calculation [52]. Chapter 2. Experimental Techniques of Electro-Optic Sampling 42 I n c i d e n t Angle (degree) Figure 2.6: The measured phase retardation of the optical compensator as a function of incident angle of the laser beam. The incident angle is defined by the normal of the wave plate and the incident laser beam. The two curves correspond to the rotations about the slow axis (optical axis) and fast axis of the wave plate. The solid lines are the polynomial fits of the experimental data. Chapter 2. Experimental Techniques of Electro-Optic Sampling 43 OJ <u >H tjfl 0) o • f-l -1-1 CO T3 Si td -!-> 0) Kl CO 270 240 h 210 h 180 150 120 h 800 810 820 830 Wavelength (nm) 840 850 Figure 2.7: The measured phase retardation of a multi-order wave plate as a function of + he wavelength of the incident beam. The incident angle is set at zero degree for all measurements. The solid line the least-square fit of the experimental data. that the compensator is very sensitive to the wavelength of the laser beam mainly due to the use of the multi-order wave plate in the compensator. For example the phase retardation at zero incident angle is 180 degrees for 827 n m compared to 270 degrees for 808 n m . F i g . 2.7 plots the retardation measured at zero incident angle as a function of laser wavelength. The retardation decreases almost linearly with increasing wavelength at zero incident angle. The slope of the least square fit is about -5 degrees/nm. If a zero-order wave plate is used, the dispersion is expected to be much smaller. The small dispersion of the zero-order plate may help to improve the sensitivity of the E O S system, and would be useful if the tuning range of the compensator is large enough. Chapter 2. Experimental Techniques of Electro-Optic Sampling 44 Since the spectral width of laser pulses used in an E O S system is typical ly i n the order of a few nanometers, the dispersion of the compensator makes it impossible to bias every wavelength of the laser pulse at the m a x i m u m operating point. In other words, wi th the compensator dispersion, only the center wavelength of the laser pulse is biased at the opt imum operating point when an E O S system is operating at its " m a x i m u m sensit ivity". Since the laser pulse width used in the present work is about 125 fs, the -5 degree/nm compensator dispersion does not significantly affect the performance. B u t if shorter pulses or a thicker wave plate were used, the compensator dispersion may significantly degrade the performance of the E O S system. 2.3.4 Viewing Systems In an E O S experiment, it is desirable to know the exact locations of the focused probe and pump spots on the transmission lines connected to the D U T . The typical width of a coplanar stripline electrode is 50 \im wi th 5 or 10 pm separation between electrodes. The gap of a photoconductive switch is around 5 \im. The focused spot has a typical diameter of 5 to 10 fim. Therefore microscopes are needed in order to see the focused spots, the electrodes, and the pulse generator. We designed two microscopes to meet the requirements. Besides the function of a normal microscope, each microscope has a laser access window which allows a laser beam to come in and be focused through its objective lens. Unl ike a normal microscope where the object to be seen is placed beyond the focal plane of the objective lens, our microscope is designed in such a way that the object to be seen must be placed right in the focal plane of the objective lens. Thus, the object to be seen and the laser spot are focused at the same plane, assuming the effective focal length of the objective lens is the same at the laser and the i l luminat ion wavelengths. This allows us to view the sample and the focused spot at the same time. Since the Ti-sapphire laser is operating in the infrared, a C C D camera which can respond to both Chapter 2. Experimental Techniques of Electro-Optic Sampling 45 visible and infrared light is used to view the sample and the focused laser spot. The image is shown on a video monitor. Probe Viewing System F i g . 2.8 illustrates the probe viewing microscope which consists of four lenses and two beam splitters. The first lens (at the bottom), is a f0 — 10 m m objective lens with 10 m m working distance. The long working distance of the objective makes it possible to fit the probe t ip and other miniature optical components into the space between the objective and the D U T . The last lens (at the top), is a fc — 75 m m camera lens mounted on a high resolution video camera with 4.8 m m x 6.4 m m detecting area. The microscope formed by the objective and the camera lens can only provide a linear magnification ^ = 7.5 which is not enough for our application. To increase the magnification, a telescope is inserted between the objective and the camera lens. This is because the objective lens is also used to focus the probe beam and is placed at exactly one focal length f0 = 10 m m away from the sample. A s a result, the light collected by the objective lens from the sample is collimated. The inserted telescope is used to provide angular magnification for the collimated light reflected from the sample. The linear magnification of this four lens system is M = x (2.14) h Jo where / i , / 2 , fc, and f0 are focal lengths of the four lenses shown in F i g . 2.8. B y properly choosing f\ (100 to 140 mm) and fi (32 to 50 mm) according to the sizes of the probe tip and the transmission line used in the experiment, we have successfully built a microscope with required resolution and magnification. The two beam splitters placed at 45 degrees with respect to the optical axis of the microscope are used to introduce laser beam (IR) and i l luminat ing light (visible), respectively. The one used to introduce the laser beam Chapter 2. Experimental Techniques of Electro-Optic Sampling 46 Illuminator f 1 1 "Video Monitor telescope lenses probe beam fo <= probe tip camera lens 50% beamsplitter f, dlchrolc beamsplitter objective lens sample Figure 2.8: Diagram of the custom-designed probe microscope. The square in the video monitor represents the foot print of the probe t ip , the four side blocks represent the four polished sides of the inverted pyramid sampling t ip , the black dot represents the focused probe spot, and the two shaded stripes are the electrodes of the transmission line. Chapter 2. Experimental Techniques of Electro-Optic Sampling 47 is a dichroic beam splitter which has 99.8% reflectivity for the near infrared light, but only 10% for the visible light. It allows the laser beam to be efficiently reflected and focused onto the probe t ip . After being reflected at the bottom of probe t ip , the probe beams comes back along a path which is slightly shifted from its incident path due to total internal reflection configuration shown in Fig.2.8. Most of the probe beam coming back from the probe t ip is reflected from the dichroic beamsplitter and then goes to the analyzer and detector optics (not shown). Only 0.2% of the probe beam goes through the dichroic beamsplitter and reaches the camera to form the image of a focused spot. The visible light used for i l luminat ing the sample passes through the dichroic beamsplitter wi th 90% transmission. In this microscope the sample and probe beam images are focused at the same plane because the objective lens used is corrected for chromatic aberration. So both the sample image and the focused laser spot can be seen on a video monitor at the same t ime. P u m p Viewing System The field of view of the above microscope is about 200 \im x 200 fim. This means that if we use the same objective to focus the pump beam, the m a x i m u m separation of the two focused spots (pump and probe) would be l imited to 200 /xm. However, for most of our applications, the typical separation needed between the probe spot and pump spot is 2 m m to 5 m m , so it is not feasible to focus and view the two beams through one microscope. To solve this problem, another microscope is needed for the pump beam. Unfortunately, we cannot use a microscope which has exactly the same structure as the probe microscope and put the two microscopes side by side because the physical sizes of the lenses w i l l l imi t the m i n i m u m separation of the two focused spots to be in the order of centimeters instead of millimeters. Most people solve this problem by bringing the pump beam at an oblique angle. The drawback of this approach is that the pump Chapter 2. Experimental Techniques of Electro-Optic Sampling 48 Figure 2.9: Schematic diagram of the pump t ip shown with a probe t ip . The diagram is to scale. The probe beam shown here is directly reflected from the sample electrode instead of going through a total-internal-reflection configuration. beam wi l l reflect from the sample and wi l l not come back to the microscope, so the pump beam cannot be seen by a pump microscope. The pump beam must be incident on the sample at a right angle in order for the beam to reflect back from the sample and be seen by a video camera. However, we just mentioned that the two microscopes cannot be mounted vertically side by side since the separation of the two spots would be too large for most applications. To solve the problem, we designed a viewing system with a special pump t ip . The pump viewing system is of the similar structure as the probe viewing system except that the objective lens is replaced by a custom designed pump focusing tip which is a miniature right-angle prism (3.2mm x 3.2mm) and a miniature plano-convex lens (5 m m dia.) glued on a specially designed holder. A schematic diagram of the pump t ip is shown in F i g . 2.9. Unl ike the probe microscope which is mounted on a vertical rack, the pump microscope is mounted on a horizontal rack . The right-angle prism is used to turn horizontal pump beam 90 degrees downwards. The focal point of the pump tip is 4.5 m m from the bottom of the prism. The pump tip is 5 m m thick and 3.2 m m wide. Because of their miniature sizes, both the pump tip and the probe tip can Chapter 2. Experimental Techniques of Electro-Optic Sampling 49 fit into the space between the probe microscope objective and the sample and can move around without interfering with each other since they are at different heights. W i t h this arrangement the pump beam and the probe beam can be focused to two spots as close as 1.5 m m . The chromatic aberration of the plano-convex lens results in a slight difference in the focal planes for the i l lumination visible light and infrared pump beams. However, the difference is small and does not pose a significant problem. Fig.2.10 is a schematic diagram of the complete viewing system including the two custom-designed microscopes. The resolution of the two microscopes is about 1 micron which is satisfactory for most of our applications. 2.3.5 Common Time Axis for Multiple Probing Positions It was mentioned in the previous sections that the E O S system allows measurements at multiple sampling positions along a transmission line. This feature is required in many applications such as the measurements of the signal propagation speed on a transmission line and the propagation delay t ime through a high-speed transistor. Two issues are important in these measurements. First , the optical alignment of both pump and probe beams should be kept unchanged for all sampling locations. Second, it is important that the measurements at different sampling locations share the same t ime axis so that direct comparison of the measurements can be made. Since the probe t ip does not move during the measurements, the alignment of the probe beam is automatically maintained. The alignment of the pump beam can be kept unchanged by using the following sample layout or alignment. The transmission line of the sample under test should be aligned to be parallel to the axis of the horizontal micrometer of the translation stage on which the sample is mounted. The translation stage can move the sample in the direction of the pump beam (horizontal) as well as in the vertical direction. Since the small translation stage holding the pump tip is mounted on the same translation stage as the sample, Chapter 2. Experimental Techniques of Electro-Optic Sampling 50 2 1 Figure 2.10: Schematic diagram of the complete E O S viewing system including two custom-designed microscopes. The probe microscope is mounted vertically. The pump microscope is mounted horizontally. The specially designed pump t ip allows the pump and the probe beams to be brought as close as 1.5 m m and seen through two C C D cameras. Chapter 2. Experimental Techniques of Electro-Optic Sampling 51 moving the sample in the direction of the pump beam (horizontal) does not affect the relative position of the pump beam and the photoconductive switch of the sample. This ensures that the pump beam alignment remains unchanged for all sampling locations. As described in Chapter 1, the time axis of an electro-optic sampling system is relative and is calculated by using the relative delay distance of the delay translation stage. The zero of the time axis (or the starting point of each measurement) is defined by a specific position of the delay translation stage. If every scan (measurement) starts at the same position marked on the delay translation stage, a common time axis is ensured for all the measurements. This is realised in the EOS system by using a computer-control DC motor which drives the translation stage of the optical delay line and can be program to start scan at exactly the same position (error is less than a fraction of a micron) for all the related scans. A LabVIEW program was written to control the motion of the delay translation stage as well as data acquisition of the electro-optic signal. The program controls the whole electro-optic sampling measurement including averaging scans to increase signal to noise ratio, real time display of the measurement data, calibration of the EOS signal, file management, and data analyzing functions. Due to the special pump tip/sample arrangement in our EOS system, the time delay ATd between signals measured at two sampling locations separated by a distance AS" cannot be related to the signal propagation speed v by using a simple formula ATd — Because the pump tip moves with the sample, the pump beam paths for the two measurements at different sampling locations are different. The relationship for the delay time ATd, the speed v and the separation of sampling locations AS is: A ^ - ^ (2,5, V c where the c is the speed of light in air. The second term is due to the AS change in pump beam path. Since the delay time ATd and the distance AS" can be measured accurately, Chapter 2. Experimental Techniques of Electro-Optic Sampling 52 with typical errors of ± 0 . 0 5 ps and ± 5 \im respectively. The propagation speed on transmission line can be determined with an error smaller than ± 0 . 0 1 x 10 8 m/s . 2.4 Noise Reduction and Sensitivity There are three sources of noise i n an E O S system. They are laser noise, shot noise and thermal noise. The laser noise is due to the fluctuation of the laser intensity. It is a flicker noise which drops off at 1/f for increasing frequency. The shot noise is due to the photo-current generated by the probe beams at the detectors and the dark current of detectors. The thermal noise is due to the load resistance and detection electronics. Both the shot noise and the thermal noise are white noise whose noise spectrum is independent of frequency. The dominant noise in E O S system is laser noise and laser-beam-generated shot noise. Since the signal to be measured is normally very small , in the range of 1 m V to 1 V , compared wi th the 2 k V to 10 k V half-wave voltage of the electro-optic sampler (modulator), the depth of modulation is in the range of 1 0 - 4 to 1 0 - 7 . Such a weak signal is buried in noise and cannot be used directly as input for the data acquisition system. We adopted a mixer-based noise reduction system identical to that reported by Chwalek and Dykaar [53]. The system consists of an audio-frequency lock-in amplifier, a synthesizer, two photodiodes, a differential amplifier and two mixers as shown i n F i g . 2.11. The main function of this system is to reduce the 1 / f laser noise and the shot noise generated by the photocurrent i n the detectors by modulating (or chopping) the signal wi th an acousto-optic modulator ( A O M ) at a relatively high-frequency (1.02 M H z in our system) where the 1/f noise is smaller than the white noise floor of the E O S system and by using a lock-in amplifier. However, the audio-frequency lock-in amplifier which is much better than a R F lock-in amplifier only works up to 200 k H z [53]. To solve the problem, a Chapter 2. Experimental Techniques of Electro-Optic Sampling 53 to data acquisition system < 1 Mixer to calibration Lock-in Amplifier . Output Reffc Input — * — 20 K H z 1.02 M H z 1.02 M H z 3 way splitter 20 K H z Mixer 1.0 M H z 1.0 M H z 1.02 M H z 2 way U splitter 1.0 M H z Output Ref Synthesizer Differential Amplifier 7H 7£ _nJ LnJ I Photodiodes A O M Driver Optical Analyzer 1.02 MHz Probe Beam 1.02 M H z — A O M Pump Beam Figure 2.11: Schematic diagram of the noise-reduction electronics. The dashed line box represents a custom-designed photo-receiver system. Chapter 2. Experimental Techniques of Electro-Optic Sampling 54 mixer is used after the differential amplifier to mix the 1.02 M H z signal wi th a 1 M H z reference signal from the synthesizer to 20 k H z at which frequency the audio lock-in amplifier works. A s mentioned in Appendix A , two photodiodes are used to measure the two orthogonally polarized beams split by the analyzer. In response to the modulation signal (or signal to be measured), the intensity of one beam increases, while the other decreases as shown in F i g . A . 3 . The differential amplifier is used to extract and amplify the difference of the two beams which is proportional to the signal to be measured. In addition to the above function, another very important role of the differential amplifier is to reduce the impact of the fluctuation of the laser intensity. Unl ike the signal to be measured, the fluctuation of the laser intensity is a common mode noise which is rejected by the differential amplifier at very high ratio when the two orthogonal beams are very well balanced. The circuit diagram of the custom-designed photo-receiver can be found in Appendix B . The above noise reduction techniques greatly reduce the 1/f noise in an E O S system. The ult imate l imit of the sensitivity of the E O S system is then determined by its white noise level which is dominant by the shot noise generated by the photocurrent. Since the E O S signal is proportional to the probe beam intensity we cannot improve the signal to noise ratio S / N by reducing the probe beam intensity. A s a mater of fact, S / N is proportional to \/Ti because the shot noise voltage is proportional to y/Ii. This mean that the signal to noise ratio S / N increases wi th y/Ti unt i l the photodiodes are saturated by the intense laser beams. The unavoidable shot noise can be reduced by narrowing the bandwidth of the lock-in filter or by averaging over multiple scans. Both methods improve the signal to noise ratio at the expense of longer data acquisition t ime. The sensitivity of our E O S system, determined by using / v " g ' " , is 1-10 m V / v H z , where V &fnoise Vnoise is equivalent rms noise voltage and A / n o ; s e is the noise bandwidth set by the low-pass filter of the lock-in amplifier. Chapter 2. Experimental Techniques of Electro-Optic Sampling 55 2.5 Resolution and Linearity The temporal resolution of an E O S system is determined by its optical pulse width , electrical transit t ime across the sampling spot, optical transit t ime across the electro-optic crystal and the frequencies of phonon resonances in the electro-optic crystal. The width of the optical pulse used in the present work is normally in the order of 100 fs. The electrical transit t ime is the t ime for the electrical signal passing through the focused probe spot, and is less than 50 fs for a focused beam spot of 5 \im diameter. The optical transit t ime is the t ime for optical pulse passing through the fringing electric field in the crystal. It depends on the distribution of the electric field in the electro-optic crystal, and the optical path length in the crystal. If the effective integration length for the probe beam is 20 /xm, the optical transit t ime is less than 200 fs. In a well-designed system, the most serious l imitat ion for temporal resolution in E O S is the phonon resonance in the electro-optic material in the TeraHertz region. For L i T a O a , the resonant frequency of 6.3 T H z , and the 1.1 T H z damping rate of the phonon resonance [47, 54] l imit the response of linear electro-optic effect to about 300 fs. The resolution of our E O S system has reached this fundamental l imit for temporal resolution. F i g . 2.12 is an E O S measurement of a pulse with 0.5 ps F W H M measured 50 \im away from the pulse generator. The measured signal includes contributions from both, a T H z radiation pulse[55, 56] and a step-like pulse generated on the coplanar stripline. The oscillatory features after the pulse are due to multiple reflections of the pulse in the 20 fim thick L iTaOs probe. The linearity of our E O S system was measured by applying a low frequency signal (1.02 M H z ) directly to a transmission line and using an electro-optic probe to sample the voltage on the transmission line. The applied 1.02 M H z signal simulates the pump-beam-created signal in a pump/probe experiment. F i g . 2.13 shows the lock-in amplifier output versus the applied input signal amplitude. The electro-optically measured voltage Chapter 2. Experimental Techniques of Electro-Optic Sampling 56 Time (ps) Figure 2.12: A n ultrafast electrical pulse measured 50 \im away from the pulse generator. The full width at half maximum of the pulse is 0.5 ps. on the transmission line increases linearly with the increasing input signal. This allows us to calibrate the photoconductively generated signal, if we assume the electric field of the high-frequency signal generated by the photoconductive switch has the same distri-bution as the low frequency field. In the next chapter, we wi l l show that this method of calibration can only be used in contact or small air-gap non-contact E O S measurements [57]. Chapter 2. Experimental Techniques of Electro-Optic Sampling 57 Vmput (V) Figure 2.13: The linearity of our E O S system. The lock-in output increases linearly with the low-frequency voltage on a transmission line generated by a function generator. Chapter 3 Measurement Errors and Invasiveness of External EOS Probes 3.1 Introduction In the last chapter, the electro-optic sampling system was described. Before using the E O S system to characterize electronic devices, we need to understand one more key aspect of the experiment—the measurement errors and invasiveness of electro-optic sampling, which is an important issue that was not discussed in the last chapter. In this chapter, we present an experimental study of the measurement errors and invasiveness caused by an external L iTaOa probe used in the electro-optic sampling system. This chapter is organized as follows. In Section 3.2, we describe the motivation and background of this work. Then, we describe the experiment and samples in Section 3.3. In Section 3.4, we present the results of the contact and non-contact electro-optic measurements. Final ly, we discuss the errors caused by the external L iTaOa probe in contact and non-contact measurements. 3.2 Motivation and Background In Chapter 2, we mentioned that the footprint of an e-o probe is normally larger than the size of a transmission line. When a probe t ip is put in contact with a transmission line, which was the case for most of the published E O S measurements, the probe tip acts as a superstrate for the part of the transmission line with which it is in contact. The impedance of this part of the transmission line (under the probe tip) is very different 58 Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 59 from the rest of the transmission line without the superstrate due to the large dielectric constant of the probe t ip which is 43 for L iTaOs [10]. A s a result, there are reflections at both the front and the back facets of the probe t ip . The front facet is the place where the electrical signal enters the probe t ip while the back facet is the place where the electrical signal leaves the probe t ip . The probe t ip also introduces an extra dispersion and loss to the transmission line. W h i l e there are several theoretical simulations on the invasiveness of external e-o probes[58, 59, 60, 61], experimental study on this topic is very l imited. The effects of reflection between the top and the bottom interfaces of a LiTaO"3 crystal on electro-optic measurement of signal amplitude have been studied by Frankel et al [62]. The authors concluded that a 20 / i m thick L iTaOs probe gave m i n i m u m resonance and best accuracy for measurements on transmission lines with dimensions from 5 to 50 / i m . The effect of probe-tip-induced dispersion on risetime measurements has been studied by putt ing a dummy LiTaOs crystal between the electrical signal generator and the probe site[47]. A n 8.3% increase of risetime, from 480 fs to 520 fs, was reported. In both of these studies the LiTaC*3 probes were placed in direct contact wi th the transmission line electrodes and the measurements were performed in the t ime domain. The invasiveness of external probes has also been studied in the frequency domain up to 40 G H z using direct (or internal) electro-optic sampling, where a dummy probe was put in the vic ini ty of the electrodes of a coplanar stripline driven by a microwave synthesizer [63, 64]. A n electric field distortion depending on the air gap between the probe t ip and the transmission line has been observed. In this chapter, we report an experimental study of the measurement errors and invasiveness of external L iTaOa probes, extending previous measurements to higher fre-quencies and lower invasiveness. We show that contact electro-optic sampling can lead to more serious measurement errors than previouly reported. We also show that non-contact electro-optic sampling provides a more accurate measurement of risetime and Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 60 amplitude, at the expense of reduced sensitivity. 3.3 Experiment The sample used in this study was a coplanar stripline integrated with a photoconductive switch. The coplanar stripline had a 50 /jm electrode width and 5 pm spacing. It was fabricated on a 400 ^ m thick semi-insulating G a A s substrate. The characteristic impedance of the coplanar stripline was estimated to be approximately 50O. The total length of the sample was about 4 m m . The photoconductive switch incorporated in the coplanar stripline was used to generate picosecond step-like pulses. The risetime of the electrical transient launched into the stripline by the photoconductive switch was about 2 ps measured at a distance 1.5 m m away from the photoconductive generator. The electro-optic measurements were made with the electro-optic sampling system described in Chapter 2. The experimental arrangement of the sample, probe t ip , and pump optics is shown in F i g . 3.1. The probe beam passes through the external probe t ip in a total-internal-reflection configuration. The probe-sample spacing h can be adjusted by using a translation stage. The probe t ip was adjusted using a t i l t stage to be parallel to the sample surface by reducing the interference fringes on the footprint of the probe to one bright fringe when in contact. The focused probe-beam spot could be moved around within the footprint of the probe t ip . The pump beam was focused through a plano-convex lens followed by a right angle prism which turns the pump beam by 90°. The distance between the pump spot and the probe spot can be adjusted and was set at 1.5 m m . Typica l pump and probe powers used in the experiment were 3.5 m W and 10 m W , respectively. Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 61 Figure 3.1: Schematic of the pump and probe optics of our electro-optic sampling system. The air gap h between the t ip and the sample can be adjusted. 3.4 Results and Analysis 3.4.1 Risetime and Amplitude In F i g . 3.2 we show waveforms measured with two different air gaps, and at two different positions of the probe beam in the sampling t ip . Referring to Fig.3.1, the data of F ig . 3.2 are for two probe beam positions near the front (left) facet of the external probe, and near the back (right) facet of the external probe. In F i g . 3.2 we show the contact measurements (h = 0 /xra) at the two locations. The measured 10-90% risetimes near the front and the back facets are 1.9 ps and 2.1 ps, respectively. The ini t ia l peak (or overshoot) measured near the back facet is 18% smaller than that measured near the front facet. This increased risetime and decreased peak amplitude measured near the back facet is not due to the usual dispersion (modal dispersion and conductor dispersion) and loss (conductor loss, radiation loss and dielectric loss) [13, 65] on the transmission line; we have made Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 62 1.0 0.8 CD O) £ 0.4 O > 0.2 0.0 h=0 j i m Front Facet Back Facet 16 Time (ps) Figure 3.2: Contact E O S measurements at two probe beam positions in the probe t ip: near the front facet, and near the back facet of the probe t ip. measurements of risetime at varying distances along the transmission line that show no significant difference in risetime over the same distance. We attribute the lengthening in risetime to the increased dispersion and attenuation introduced by the LiTaOa probe which functions as a superstrate. Our results show it is preferable to position the probe beam near the front facet of the probe t ip , in agreement with the prediction of [61]. The feature near 14 ps in the curve measured near the front facet is the reflection from the back facet of the probe, due to large impedance mismatch caused by the differing impedances of the transmission lines with and without the LiTaOa superstrate. The same reflection is not as obvious in the measurement near the back facet since the reflection Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 63 Time (ps) Figure 3.3: Non-contact E O S measurements at two probe beam positions in the probe t ip : near the front facet, and near the back facet of the probe t ip . is overlapped with the init ial peak because of the small separation between probe spot and reflection site. In the following, we wil l show that these unwanted probe-induced effects of dispersion, loss, and back-facet reflection can be greatly reduced by performing non-contact E O S measurement. In F i g . 3.3 we show measurements at the same two locations in the external probe but with an air gap h = 10 fim. The 10-90% risetimes measured near the front and the back facets are the same, 1.7 ps, which is about 20% smaller than the 2.1 ps risetime measured in the contact configuration near the back facet of the probe t ip . The peak amplitude measured near the back facet is only 7% smaller than that measured near Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 64 Time (ps) Figure 3.4: Contact and non-contact E O S measurements near the back facet of the probe t ip. The curves have been normalized to 1 at the peaks. the front facet, compared with 18% in the contact measurement. The reflection from the back facet of the probe is also much smaller than that of the contact measurement. These improvements in dispersion, loss, and reflection can be attributed to the reduced effective dielectric constant of the superstrate in the non-contact configuration. The dispersion induced by the external probe can be more clearly seen in F ig . 3.4 where we replot the curves from F i g . 3.2 and F i g . 3.3 measured near the back facet. To allow comparison, both curves have been scaled to have the same maxi mu m value. It is evident that the curve of non-contact measurement has a smaller risetime than that of the contact measurement. We can also see two well-resolved peaks in the non-contact Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 65 measurement while only a peak and a shoulder can be seen in the contact measurement. We attribute the second peak at 12 ps to dispersion of the transmission line [47, 13]. It is interesting to note that when the probe t ip is in contact the ringing is sti l l evident, but much more rapidly damped. We speculate that this may be due to loss experienced by the electrical pulse on the transmission line caused by the presence of the LiTaOa superstrate. F inal ly , we find that the point at which the waveform reaches half of the max imum value appears 0.5 ps earlier in the non-contact measurement due to the reduced effective dielectric constant in non-contact configuration. In other words, the electrical transient travels faster under the probe t ip in the non-contact configuration. To further quantify the probe-tip-induced dispersion, we made a series of measure-ments at a distance 1.5 m m from the photoconductive switch with varying air gap h. The results are shown in F i g . 3.5 for a variety of air gaps from h = 2.5 /xm just over 100 /xm, as described in the figure caption. In the exeriments, longer averaging times were used for the measurements with larger air gaps so that the signal to noise ratio of all curves are about the same. The features appear quite similar, with decreasing amplitude due to the decreased sensitivity with increasing air gap. However, upon closer examination, we find the measured risetime is changing. In F i g . 3.6, we show the 10-90% risetimes extracted from the curves of F i g . 3.5 as a function of air gap from h = 0 to h = 42.5 /xm. The risetime ini t ia l ly decreases with increasing air gap h, and then remains constant (within experimental error) once the air gap exceeds approximately 20 /tm. We performed similar measurements on another sample at a location 3.0 m m from the photoconductive switch, and observed similar results, wi th risetime decreasing from 3.6 ps when in contact to 3.0 ps with h = 20 /xm. Considering the data on dispersion we have presented in F i g . 3.2 to F i g . 3.6, two effects are apparent. F irst , when the t ip is in contact with the stripline, significant dispersion happens as the signals traverse the region under the t ip . This is supported by F ig . 3.2 Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 66 Time (ps) Figure 3.5: Non-contact time-resolved E O S measurements with various air gap distances h. From the top to the bottom, the curves are measured at the following h values: 2.5, 7.5 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 62.5, and 102.5 / i m respectively. where the risetime measured near the back facet is larger than that measured near the front facet. Second, when the tip is moved away from the surface this dispersion under the t ip becomes negligible, as can be seen in F i g . 3.3 where the risetimes measured near the front and the back facets are the same. However, as shown in F i g . 3.6, the measured risetime continues to drop with increasing air gap suggesting a second lengthening effect other than the dispersion under the probe t ip . One contribution to this second effect may be the preferential reflection of high-frequency components at the front probe facet. This Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 67 Ui Q. CD E CD Ui 10 20 30 Air Gap h (\i m) 40 Figure 3.6: Risetimes of the curves of F i g . 3.5, as a function of air gap h. The measure-ment error is estimated to be ± 0 . 1 ps. explanation is qualitatively consistent with the full-wave simulation of Conn[61]. The simulated experimental configuration was similar to ours with the same type of LiTaO"3 probe t ip , but the transmission line used in the simulation was a coplanar waveguide instead of a stripline. The simulation results indicate that the reflectivity of the electrical signal at the facets of the probe t ip is frequency dependent. The reflectivity of high-frequency signals in the contact configuration is significantly larger than that in non-contact configuration. For example, the reflectivity (transmission) of a 90 G H z signal in the contact configuration is 50.1% (86.6%) while the reflectivity (transmission) of Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 68 the same frequency signal but in non-contact configuration (h=20 /xm) is only 0.4% (99.9%). Contrary to the reflectivity of high-frequency signals, the reflectivities of low-frequency signals for the two probe configurations are much closer. For example, the reflectivity (transmission) of a 20 G H z signal in the contact configuration is 17.8% (98.4%) while the reflectivity (transmission) of the same frequency signal but in non-contact configuration (h=20 /xm) is about 0.3% (99.9%). In other words, more high-frequency signals (components) are lost (reflected) in the contact (or small-air-gap) measurement than in the large-air-gap measurement. This can be more clearly seen in Table 3.1 where the transmission co-efficients of the 20 G H z and 90 G H z signals at the probe facets are listed for two probe configurations h=0 /xm and h=20 firn. Table 3.1 clearly demonstrates Table 3.1: Transmission coefficients of a high-frequency signal (90 G H z ) and a low-frequency signal (20 G H z ) at the probe facets for two probe configurations: h=0 fxm and h=20 \im. The data is obtained from the work by Conn and coworkers. h / f 20 G H z 90 G H z 0 /xm 20 /xm 98.4% 99.9% 86.6% 99.9% the relatively large loss of high-frequency components in the contact configuration due to preferential reflection of high-frequency components at the probe facets. However, the difference in low and high-frequency reflection appears to be too small to quantitatively explain the data of F i g . 3.6. Another effect that may be important is the frequency dependence of the strength of the electric field coupled into the t ip for varing heights. Such an effect has been suggested by Whitaker and Cheng[66]. Full-wave simulation wi th our experiment configuration (is needed to quantitatively explain the measurement results. However, this is beyond the scope of this thesis. Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 69 Air Gap h (|i m) Figure 3.7: Sensitivity of non-contact E O S measurements as a function of air gap h. The solid and dashed lines are for time-resolved and calibration signals, respectively. The open circles are the theoretical simulation of Ref. [61]. The triangles are the experimental data of Ref. [59]. The data of [59, 61] has been shifted vertically to coincide at 5 fim to allow easy comparison. 3.4.2 Sensitivity Having discussed the effect of air gap on dispersion and loss, we now examine the change in sensitivity. The reduction of sensitivity with air gap wi l l place the ultimate l imit on how non-invasive the tip can be made. In F i g . 3.7 the solid line shows the peak amplitudes extracted from the data of F i g . 3.5 as a function of air gap h. The E O S signal init ial ly drops dramatically with increasing air gap h, and then less quickly once the air gap exceeds a knee point at approximately 20/xm. In F ig . 3.7 we also plot the experimental Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 70 data and simulation results extracted from references [59, 61], respectively. The data of reference[59] were measured on a coplanar waveguide with 4 / i m electrode width and 13 fxm spacing. There is agreement with our measurement at small air gap values, but the sensitivity continues dropping quickly with increasing air gap showing no sign of a knee point up to h = 20 / i m . In examining the calculations of Ref.[61] shown in F i g . 3.7 , we see there is a knee similar to what we observe. Its appearance at small air gap may be due to the difference between our structure and that simulated in Ref. [61], which was a coplanar waveguide with 15 / i m center electrode and 10 fxm spacing. The data of Ref.[59] shown in F i g . 3.7 were obtained from non-time-resolved mea-surements where a low-frequency signal generated by a synthesizer was applied to the coplanar waveguide. This low-frequency signal is often referred to as the calibration sig-nal since the same method is widely used to calibrate time-resolved E O S measurements. The calibration is made by comparing the time-resolved E O S signal to that produced by a calibration signal of known amplitude. This approach impl ic i t ly assumes that the distributions of the electric fields of the electrical pulse and the calibration signal are the same. To evaluate this assumption, we applied a constant calibration signal to the stripline and measured the variation of the E O S signal with air gap. The results are shown in F i g . 3.7 as a dashed line. In the region from 0 to 35 / x m , the time-resolved and calibration curves overlap almost exactly. This shows that the calibration method used in E O S measurements is valid for contact and small-air-gap non-contact measurements. However, as the air gap exceeds 35 / i m , the time-resolved signal drops more quickly with increasing h than the calibration signal. We attribute the different dependence on h for large air gaps to the difference in fringing field distributions of high-frequency and low-frequency signals. The time-resolved signal contains very high-frequency components. It is well known that for very high-frequency signals in a transmission line the electric field Chapter 3. Measurement Errors and Invasiveness of External EOS Probes 71 energy is no longer evenly divided in the substrate and superstrate, but is more concen-trating in the substrate. W h i l e for the low-frequency calibration signal, the electric field energy is evenly divided in the substrate and superstrate. Thus, it extends more above the electrodes than that of high-frequency signal. In other words, the electric field of low-frequency signal drops less slowly with increasing air gap h than that of high-frequency signal. This difference wi l l introduce a calibration error for non-contact E O S measure-ment with large air gap since the assumption of the same fringing-field distribution for the electrical pulse and the calibration signal is no longer valid. In our experimental sit-uation, a reasonable compromise between invasiveness and sensitivity, which sti l l ensures accurate calibration, occurs for air gaps from 10 to 20 jxm. Chapter 4 Electro-Optic Characterization of M O D F E T s 4.1 Introduction In Chapter 1, we briefly described the structure and the operating principles of M O D -F E T s . We also reviewed high-speed characterization of M O D F E T s using ultrafast-laser-based techniques. In this chapter, we describe electro-optic characterization of M O D F E T s . Experimental results and theoretical simulation of both lattice matched Ino.52Alo.48As/Ino.53Gao.47As M O D F E T s and pseudomorphic Ino.20Gao .goAs/Alo.25Gao.75-A s M O D F E T s are presented. This chapter is organized as follows. In Section 4.2, we present electro-optic measure-ments of the L M M O D F E T s . First , we describe the fabrication process of the M O D F E T s monolithically integrated with a photoconductive switch/transmission line test fixture. Then, we present switching characteristics of the M O D F E T s at different input ampli -tude and bias conditions followed by comparing switching characteristics for M O D F E T s of different gate access structures. In Section 4.3, we describe electro-optic measurements of a P M Ino .20Gao.80As/Alo .25Gao.75As M O D F E T and compare the results with those of the L M M O D F E T described in Section 4.2. In Section 4.4, we present the S P I C E simu-lation of the M O D F E T switching. First , we briefly describe the motivation of the work. Then, we introduce the lumped-element model and methodology used in the simulation. Final ly, we present the simulation results and compare them with the E O S measurements presented in Section 4.2 and Section 4.3. 72 Chapter 4. Electro-Optic Characterization of MODFETs 73 4.2 Lattice-Matched Ino.52Alo.48As/Ino.53Gao.47As M O D F E T s 4.2.1 Experiment In this section, we study switching characteristics of L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T s using electro-optic sampling technique described in detail in Chapter 2. Be-fore presenting the experimental results, we first describe the fabrication process of the M O D F E T s which are monolithically integrated with test fixtures. F i g . 4.1 is the layer structure of the M O D F E T s . A l l the M O D F E T s used in this chapter were grown and fab-ricated by D r . M . Van Hove and Dr . W . De Raedt in Interuniversity Micro-Electronics Center ( I M E C ) in Belgium[67, 68]. Here we describe the fabrication process they de-veloped. The multilayer structure was grown on a semi-insulating InP substrate by molecular beam epitaxy ( M B E ) . First , a 250 n m thick Ino.52Alo.4sAs buffer layer was grown on the InP substrate, followed by a 20 n m thick narrow-bandgap Ino.53Gao.47As channel layer. Both layers were nominally undoped. The nominal Indium content in the Ino.52Alo.48As layer and the Ino.53Gao.47As layer are chosen in such a way that both layers are lattice matched to the InP substrate. In other words, the strain in the epi-layers is expected to be small , and is due to slight inaccuracy in the M B E growth. O n top of the Ino.53Gao.47As channel layer a 6 n m thick undoped Ino.52Alo.4sAs layer was grown, followed by a 5 x 10 1 2 c m - 2 delta-doped Si plane and a 20 n m thick undoped Ino.52Alo.48As layer. F inal ly , a 7 n m thick Ohmic contact layer of Ino.53Gao.47As wi th Si doping concentration 6 x 10 1 8 c m - 3 was grown as the cap layer. The first fabrication step after the epilayer growth was the device isolation which was accomplished by chemically etching mesas down to the undoped Ino .52Alo.4sAs buffer layer. Source and drain areas were then defined and a metal stack of N i / A u G e / N i / A u was evaporated as the electrodes of the source and drain. Following lift-off, the metal stack is alloyed at 280 0 C for one minute. During this process, Ge diffuses into the epilayer Chapter 4. Electro-Optic Characterization of MODFETs 74 G Figure 4.1: Layer structure of a lattice-matched Ino.52Alo.4gAs/Ino.53Gao.47As M O D F E T on InP substrate. The drain, source and gate electrodes are fabricated on top of the layers. making contact with the two dimensional electron gas ( 2 - D E G ) . The next processing step was inter-connection metallization where a metal stack of T i / P t / A u / T i W was deposited on the buffer layer to form the coplanar electrodes of the input and the output transmis-sion lines. The sputtered T i W layer was used to improve adhesion to the Ino.52Alo.48As buffer layer. The gate was defined by e-beam lithography in a bilayer resist scheme ( P M M A / C o p o l y m e r ) . The recess was done by wet etching in a phosphoric/hydrogen-peroxide/water solution. The depth of the recess was chosen to be such that the gate Chapter 4. Electro-Optic Characterization of MODFETs 75 Schottky barrier to be formed at the recessed area would deplete the doped Ino .52Alo.4sAs layer but not the two dimensional electron gas. In other words, the M O D F E T works in depletion-mode or normally-on mode. If an enhancement-mode device or normally-off device is desired, the depth of the recess has to be increased such that the gate Schottky barrier depletes both the doped In 0 .5 2 Al 0 .48As layer and the two dimensional electron gas in the channel layer. After recess etching, a P t / T i / P t / A u gate wi th a T-shaped cross section was formed. It has a length of 0.35 fim and width of 100 pm. The passivation of the device was done by depositing a 200 n m thick silicon nitride layer on the chip; this layer was not deposited over the metallic electrodes. The final step of the fabrication was electroplating of A u for lowering the resistance of the interconnection coplanar electrodes and for forming the airbridges which connect the gate electrode to the input transmission lines. M O D F E T s with two types of gate-access structure have been fabricated. They are double-gate contact and single-gate contact M O D F E T s . The mask layouts can be found in Appendix D . In F i g . 4.2, we show scanning microscope pictures of the two types of devices monolithically integrated with the input and output coplanar striplines. The upper electrode is common for both input and output transmission lines, and is connected to the source electrode of the M O D F E T . The lower electrode of the input transmission line which is on the left, is made in contact with the gate through one or two airbridges over the source electrode. The drain is connected to the lower electrode of the output transmission line which lies on the right. The photoconductive switches are out of the view in F i g . 4.2. They are about 2 m m away from the gate. F i g . 4.3 is a schematic top view of the whole integrated structure. A l l the gaps between coplanar electrodes are 5 / i m , and the coplanar electrode widths are 55 \im on the M O D F E T side of the switches; further from the M O D F E T the three electrode widths are 25, 25, and 55 \im respectively. The three-electrode structure was first reported by Chapter 4. Electro-Optic Characterization of MODFETs 76 Figure 4.2: Scanning electron micrographs of two integrated M O D F E T s with different gate-access structures. The M O D F E T s are integrated with input and output transmis-sion lines which lie on the left and the right in the photographs, respectively. Photocon-ductive switches are incorporated in the transmission lines and are outside the view of the photographs, (a) is a double-gate-contact M O D F E T where the gate is made in contact with the lower left coplanar electrode (input transmission line) through two air bridges over the source, (b) shows a single-gate-contact M O D F E T where the gate is made in contact with the input transmission line through one airbridge over the source. The black and white bars at the bottom of the photographs show the scale; each is 0.1mm. Chapter 4. Electro-Optic Characterization of MODFETs 77 EXCITATION s s MODFET G D Hi 2 mm 2 mm 2 mm 2 mm -H Figure 4.3: Layout of integrated coplanar stripline and M O D F E T (not to scale). The dashed line represents the substrate. The M O D F E T is connected in a common-source configuration, and S, D , and G are the source, drain, and gate contacts, respectively. Frankel [41]. It allows the user to bias the device under test and the photoconductive switch independently. Electro-optic measurement are made with the electro-optic sampling system described in Chapter 2. In most experiments, the M O D F E T s are biased as shown in F i g . 4.3 with the gate and the source shorted. This is because all the M O D F E T s we studied are in depletion-mode (or normally-on device). The threshold of the devices is negative, Vth = —0.7 V . Due to the high gain of the M O D F E T s , they are prone to spurious oscilla-tion. This oscillation could severely affect the electro-optic measurement. The amplitude of the spurious oscillation increases with the D C bias Vds and Vgs. To stop the oscillation, magnetic beads were used in all connecting wires to increase A C loss. The oscillation also strongly depends on the positioning and bending of the connecting wires between the power supplies and the devices under test. A l l the electro-optic measurements were made when the spurious oscillation was suppressed. N o attempt was made to impedance match the connections to the external power supplies because reflections from the these discontinuities fall outside the t ime window of interest and play no part in the measure-ment. The gate input signal was photoconductively excited at the corner of the L-shaped Chapter 4. Electro-Optic Characterization of MODFETs 78 gap, as shown in F i g . 4.3. The amplitude of the input signal can be changed by changing the D C bias across the photoconductive gap. The typical laser intensities for the probe beam and the pump beam were 10 m W and 3 m W , respectively. The laser wavelength was set around 830 n m . The input and the output signals of M O D F E T s were measured using a L iTaOs external probe on the input and output striplines, respectively. The experimental results are presented in the following subsection. 4.2.2 Results In F i g . 4.4, we show the switching response of a L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D -F E T with 0.35 /xm T-shaped gate. It is a single-gate contact M O D F E T , the same as the one shown i n F i g . 4.2 (b). In the upper panel a gate input signal generated by the photoconductive switch is shown. It was measured on the input transmission line 400 ± 5 /xm away from the gate. Since the M O D F E T is in depletion mode, its gate D C bias was set at 0 Volt . The plot shows the voltage at the gate as a function of t ime. The input signal is step-like with a rise t ime of 2 ps. The amplitude of the step is around 100 m V . The feature around and after 15 ps is the gate reflection of the input signal. In the lower panel, we show the corresponding drain output measured on the output transmission line about 200 ± 5 /xm away from the gate; the data show the drain voltage, which is the com-bination of 0.8 V D C bias and the switching transient, as a function of t ime. Since the M O D F E T is connected in common source configuration, it functions as an inverter. W i t h the positive-going gate input, the drain output is negative going with a sharp switching edge followed by a slow decay. The 10-90% switching time is 5.2 ps which is determined by using the amplitude at 18 ps as the switch-on amplitude. This measured switching time is significantly faster than that observed in Ref. [27]. We attribute the difference to the higher performance of the present device and the integration of the device with the test fixture. Chapter 4. Electro-Optic Characterization of MODFETs 79 Figure 4.4: Large-Signal Switching of a L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T with single-gate-access structure. The upper panel shows the gate input signal; the lower panel shows the drain output signal. Chapter 4. Electro-Optic Characterization of MODFETs 80 The t ime axis is common for the gate and the drain signals shown in F i g . 4.4, which enables an absolute determination of the delay through the device. From F i g . 4.4 the delay t ime from the midpoint of the input transition to the midpoint of the output transition is 8.2 ps. The midpoint of the output transition is defined as the point where the amplitude is half of the switch-on amplitude at 18 ps. Since the input signal and the output signal are measured at two different locations separated by 600 fim, the measured 8.2 ps delay is a combination of propagation on the transmission lines and the M O D F E T response. We estimate the device delay by subtracting from the measured input/output delay the propagation delay on the transmission line that would be incurred on a coplanar stripline of equal length, which from the measured propagation velocity, is calculated to be 4.9 ps. This yields a value for the M O D F E T delay of 3.3 ps. This delay t ime is significantly smaller than the 6 ps delay t ime of a similar M O D F E T with 0.2/mi gate length measured in a ring oscillator at room temperature [43]. It should be pointed out that it is difficult to estimate the delay t ime through a device from the E O S measurement of a discrete M O D F E T wire-bonded to a test fixture. This is because the length of the bonding wire is difficult to control, and the effect it has on the gate input signal delay is difficult to measure. As a result, propagation delay due to the bonding wires cannot be determined accurately. We also studied switching characteristics of the M O D F E T at various bias conditions. F i g . 4.5 shows drain response to a step-like gate input at six different drain bias voltages. In the experiment, the gate input is kept the same as the one shown in the upper panel of F i g . 4.4; the D C drain bias Vds is changed from 0 to 1 V ; the D C gate bias is set at 0 V . The data in F i g . 4.5 show the deviation AVds from the D C drain biases which are listed on the right hand side of the plot. When the D C drain bias Vds = 0 V , the drain output is zero except a small positive feature at around 12 ps which is the feedthrough of the positive-going gate input signal v ia gate-drain capacitance Cgd- A s the drain bias Vds increases, Chapter 4. Electro-Optic Characterization of MODFETs 81 V«js (V) T 1 r Time (ps) Figure 4.5: Switching characteristics of a Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T at var-ious D C drain bias voltages which are listed on the right hand side of the plot. The D C gate bias is set at 0 V . the switching amplitude increases unti l 1 ^ = 1 V but the feedthrough decreases. The positive-going feedthrough at around 12 ps becomes negligible for Vds biases larger than 0.4 V . This is because the feedthrough capacitance Cgd which represents the effect of the distributed gate capacitance connected to the drain by the channel, decreases with increasing drain bias due to the increased effective distance between the gate and the drain-side conducting channel[68]. Besides drain bias dependence, we also studied the gate bias dependence of the switch-ing characteristics of a single-gate contact M O D F E T . F i g . 4.6 shows the deviation AVds Chapter 4. Electro-Optic Characterization of MODFETs 82 I J i i i i i i i i i I 5 10 15 20 25 30 Time (ps) Figure 4.6: Switching characteristics of a Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T at two D C gate bias voltages 0 V and -0.5 V . from the D C drain bias of 1 V for two gate bias Vgs = 0 V and Vgs = —0.5 V . The sample used in this measurement is another single-gate-contact M O D F E T on the same chip as the one used for F i g . 4.4 and F i g . 4.5. Unl ike previous measurement here the gate input is a negative-going step-like signal. A s a result, the drain output of the M O D F E T which is also connected as an inverter is a positive-going signal. A s expected, the switching amplitude decreases with increasing gate bias Vgs. A t Vgs = —0.5 V , the switching am-plitude reduces to less than half of that for Vgs = 0 V . The threshold of this M O D F E T is Vth — —0.7 V . We noticed a large negative-going feedthrough around 10 ps for gate bias Vgs = —0.5 V . This suggest that the feedthrough capacitance Cgd is also a function of Chapter 4. Electro-Optic Characterization of MODFETs 83 gate bias Vgs and increases with decreasing Vgs. This seems contradictory to the fact that with decreasing Vgs the effective distance between the gate and the drain-side conducting channel increases, thus causing a decrease in gate-drain capacitance Cgd- The unexpected change of Cgd wi th Vgs was also observed by Frankel[70]. The 10-90% switching times for D C gate bias of 0 V and -0.5 V are 5.2 ps and 4.4 ps, respectively. This dependence of rise t ime on gate bias is consistent with the fact that the gate-source capacitance Cgs decreases wi th decreasing gate bias Vgs due to the increased effective distance between the gate and the source-side conducting channel[69]. In addition to the bias dependence, we also studied nonlinear switching of a single-gate-contact M O D F E T by applying a series of four input signals to the gate. The upper panel of F i g . 4.7 shows the four input signals with increasing amplitudes. The rise t ime of the input signal is around 2.0 ps. The gate reflection starts around 14 ps. The gate bias is again set at 0 V ; the drain bias is 1 V . In the experiment, the intensities of the probe beam and the pump beam are kept unchanged for all measurements. The gate input signal is varied by changing the D C bias of the photoconductive switch. The four corresponding drain output signals are shown in the lower panel of F i g . 4.7. The drain output starts from 1 V D C bias and switches negatively in response to the positive-going gate input. In the inset, we plot the drain output amplitude against the gate input amplitude. The data are taken at 18 ps and 7 ps in F i g . 4.7 for the output and the input, respectively. When the gate input is smaller than 60 m V , the output and input have a linear relationship. The dashed line in the inset is a linear fit of the first a few data including the origin which is at the 1 V D C drain bias. W h e n the input exceeds 60 m V , the drain output slowly departs from the linearity. The solid line is a power fit of the data. Chapter 4. Electro-Optic Characterization of MODFETs Time (ps) Figure 4.7: Nonlinear switching of a L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T . T h upper and the lower panels show the gate input and drain output, respectively. T h inset plots the drain output versus gate input. Chapter 4. Electro-Optic Characterization of MODFETs 85 A s mentioned before, the M O D F E T s fabricated at I M E C have two different gate-access structures: double-gate contact and single-gate contact. So far, all the measure-ments presented are on single-gate contact M O D F E T s . To study the effect of differ-ent gate access structures on the switching characteristics, we studied another lattice-matched M O D F E T on the same wafer as the devices described above. In this case, however, it has a double-gate-contact structure. F i g . 4.8 shows the switching response of the double-gate-contact M O D F E T . In the upper panel a series of four gate input signals is shown, measured on the input stripline 400 ± 5 pm from the gate. The input is a negative-going step-like signal with a risetime of 2 ps followed by a overshoot and a slow decay. The feature at approximately 22 ps is the beginning of the gate reflection. The threshold voltage is -0.7 V , and we used a gate operating point of 0 V ; D C transconduc-tance of the M O D F E T is 300 m S / m m . In the lower panel we show the corresponding drain outputs measured on the output stripline 200 ± 5 fim from the gate; the data show the drain voltage Vds starting from the D C drain bias of 1 V . The 10-90% risetime of the largest drain response is 4.2 ps, which is significantly shorter than the 5.2 ps switching time described above for the single-gate-contact M O D F E T ; the risetimes of the other signals shown are similar. The small kink in the switching edge of the output signal may be due to the slightly different delay times of the two air bridges connecting the input transmission line and the gate electrode of the M O D F E T . We were not able to confirm whether this feature is common to all M O D F E T s with double-gate-access structure due to the lack of working devices. The delay t ime extracted the same way as described be-fore is 3.2 ps, which is comparable to the 3.3 ps switching time of the single gate-contact M O D F E T described above. To our knowledge these measured rise t ime and delay time are the shortest ever directly time-resolved in a working three-terminal device[46]. Chapter 4. Electro-Optic Characterization of MODFETs 86 0.00 ^ -0.05 > Si -0-10 > -0.15 15 20 25 30 T 1 1 • r Time (ps) Figure 4.8: Switching response for a lattice-matched Ino.52Alo.4sAs/Ino.53Gao.47As M O D -F E T with double-gate-access structure. The upper panel shows a series of negative-going gate inputs, and the lower panel shows the corresponding drain outputs. The operating point is Vgs = 0 V and Vds = 1 V . The switching time is 4.2 ps and the delay time, estimated as described in the text, is 3.2 ps. Chapter 4. Electro-Optic Characterization of MODFETs 87 4.2.3 Analysis Having made measurements comparing the effects of the gate access structure, we can make the following observations. First , the switching time with a single gate contact is significantly longer than with a double gate contact even though the device delay times are nearly identical. A s the single-gate-contact and the double-gate-contact M O D F E T s are fabricated on the same chip have the same electrode layout for the source, drain and gate, the only difference for the two M O D F E T s is the gate-access structure. Therefore, we must attribute the difference in switching time to the different gate-access structures of the two M O D F E T s . Network-analyzer measurements made at I M E C comparing M O D F E T s on the same wafer, but with coplanar Cascade electrode layouts show no significant difference between the responses of the two access structures. (The mask layouts of the M O D F E T s with Cascade electrodes and stripline elelctrodes are given in Appendix D.) This may be because the R F measurement is l imited to 26 G H z while the effect of different gate access structures is only evident at higher frequencies. It is also possible that the interconnection electrodes in the electro-optically-tested samples show greater sensitivity to the gate access structure than those with Cascade probe layouts. To study the dependence of the signal propagation delay t ime through the M O D -F E T Tprop on the drain bias, we normalize the curves in F i g . 4.5 for drain bias Vds = 0.2,0.4,0.6,0.8,1.0 V . Due to the fact that the drain voltage Vds of F i g . 4.5 decreases slowly after switching, we choose to normalize the curves to a value of -1 V at 18 ps where the M O D F E T is just switched on. (We have confirmed that this method of nor-malizing the curve does not significantly affect the results obtained later.) For easy comparison, we plot the five normalized curves in two graphs. The top graph of F i g . 4.9 shows three curves near the midpoints of the transitions for three relatively low drain bias Vds = 0.2,0.4,0.6 V ; the bottom graph of F i g . 4.9 shows three curves near the midpoints Chapter 4. Electro-Optic Characterization of MODFETs 88 .-j o I . , i , i , i , i "12 13 14 15 16 Time (ps) Figure 4.9: Dependence of a M O D F E T propagation delay on D C drain bias Vds- The top graph shows the normalized curves of F i g . 4.5 for Vds = 0.2V, 0.4V, 0 .6V; The bottom graph shows the normalized curves of F i g . 4.5 for V~ds = 0.6V, 0.8V, 1.0V. The inset shows dependence of a M O D F E T propagation delay on D C drain bias Vds- The solid line is the Spline fit of the experimental data. Chapter 4. Electro-Optic Characterization of MODFETs 89 of the transitions for three relatively high drain bias Vds — 0.6,0.8,1.0 V . B y comparing the relative delay of the midpoints of the transitions, we find that the midpoint of the transition appears earlier and earlier with increasing Vds for Vds = 0.2, 0.4, 0.6 V ; while the midpoint of the transition appears later and later once Vds exceeds 0.6 V . This depen-dence of the propagation delay t ime on the drain bias Vds can be better seen in the inset of Fig.4.9. For small D C bias Vds, the propagation delay t ime drops rapidly with increasing Vd s . It reaches the lowest value at about Vds = 0.5 V . After 0.5 V , the propagation delay t ime increases slowly with increasing Vds- It is interesting to see that a similar depen-dence of delay t ime rd = -^jt on drain bias Vds has been reported in Ref.[70, 71] where the delay t ime rd was calculated from the bias-dependent current-gain-cutoff frequency ft estimated from a small-signal R F measurement using a network analyzer. The depen-dence of the delay times on the drain bias can be explained by using the dependence of the electron velocity of InGaAs on the electric field in the conducting InGaAs channel. For small electric field (Vds =0.2-0.6 V ) , the electron velocity increases rapidly with the electric field unti l it reaches a peak velocity at certain critical electric field (Vds = 0.6 V ) . After this critical electric field (Vds > 0.6 V ) , electron velocity decreases with increasing electric field unti l it reaches a saturation velocity. It should be pointed out that the propagation delay time Tprop through the M O D F E T extracted from the E O S measurement is different from the delay time Td defined in small-signal R F measurements. For historical reasons, both are called "delay times" but their definitions and physical meanings are different. The former, the propagation delay time Tprop, is used in time-resolved large-signal or small signal operation and is defined as the t ime an input signal takes to propagate through the device. Its value can be directly measured by electro-optical sampling or traditionally by ring oscillators. Al though it can be shown through simulation using a lumped element model that the propagation delay t ime TpTOp is a function of many equivalent circuit parameters, to our knowledge Chapter 4. Electro-Optic Characterization of MODFETs 90 no analytical expression which relates Tprop directly to the circuit parameters has been developed. O n the contrary, the latter, the delay t ime Td, is used in small-signal operation and is denned as: where ft is the current-gain-cutoff frequency of the device. There is an analytical expres-sion which links the delay t ime Td directly to the equivalent circuit paramenters. Based on a small-signal model, Nguyen and co-workers have derived the following formula for submicron M O D F E T s [ 7 2 ] : rd = ^ 7 = — + ( C g s + C 9 d ) [1 + gds(Rs + Rd)} + Cgd(Rs + Rd) (4.2) tnjt 9m 9m0 It is clear that delay t ime r& of the small-signal model is strongly dependent on the transconductance gm of the device but is independent of gate inductance Lg and drain-source capacitance Cds- Since ft is defined as the frequency when the short-circuit current gain goes to unity, it is obvious that Td does not, in general, describe the behavior of the device with nonzero load impedance. On the contrary, it can be shown through simulation that the propagation delay t ime Tprop is a function of Lg and Cds but not gm, and also strongly depends on the load impedance. Due to these reasons, we cannot use the propagation delay t ime Tprop extracted from the E O S measurement and equation 4.1 to determine the small-signal current-gain-cutoff frequency ft. However, this does not mean that the delay t ime Td and the propagation delay t ime Tprop are not related. A s a matter of fact, Td and r p r o p have many similar characteristics. For example, both are strongly related to equivalent circuit paramenters, such as Cgs, Cgd, and channel transit t ime. This can be more clearly seen in the simulations presented in Section 4.4. The similar dependence on drain bias for Td and Tprop as shown in previous paragraph is another example. However, the task of finding an analytical expression, if there is one, which links Tprop to Td and ft is beyond the scope of this thesis. To avoid the confusion Chapter 4. Electro-Optic Characterization of MODFETs 91 between the two delay times, in the following text unless explicit ly specified, the words "delay t ime" are defined as the signal propagation delay t ime Tprop through the device not the delay t ime Tg of small signal R F measurement. 4.3 Pseudomorphic Ino.20Gao.80As /Alo.25Gao.75As M O D F E T s In the last section, we studied the switching characteristics of lattice-matched Ino.52-Al 0.48As/Ino.53Ga 0.47As M O D F E T s and the impact of different gate-access structures on the performance of M O D F E T s . In this section, we study the switching characteristics of pseudomorphic Ino.20Gao.soAs/Alo.25Gao.75As M O D F E T s and the impact of semicon-ductor materials on the performance of M O D F E T s . We first describe measurement of the pseudomorphic device. Then, we compare the results with those of a lattice-matched M O D F E T with the same electrode layout and gate-access structure. 4.3.1 Experiment F i g . 4.10 shows the layer structure of a pseudomorphic Ino.20Gao.80As/Alo.25Gao.75As M O D F E T s . The multilayer structure was grown on a semi-insulating G a A s substrate by M B E at I M E C . First , an undoped G a A s buffer layer was grown on the G a A s substrate, followed by a 13 nm thick narrow-bandgap In 0.2oGa 0.8oAs channel layer. Unl ike the chan-nel layer of the lattice-matched M O D F E T s , the Ino.20Gao.soAs layer is not lattice matched to the G a A s substrate. In other words, there is strain in the epilayers. Since the lattice mismatched Ino.20Gao.soAs layer is below the critical thickness, the lattice mismatch does not cause dislocation in the multilayer structure. On top of the Ino.20Gao.80As chan-nel layer a 5 nm thick undoped Alo.25Gao.75As layer was grown, followed by a 5 x 10 1 2 c m - 2 Si delta-doped plane and a 30 nm thick Si-doped 5 x 10 1 7 c m - 3 Alo.25Gao.75As layer. Final ly , a 40 nm thick Ohmic contact layer of G a A s with Si doping concentration Chapter 4. Electro-Optic Characterization of MODFETs 92 40 nm n +GaAs 30 nm nAlo.25Gao.75As 5 nm Alo.25Gao.75As undoped 13 nm In 0 2 Ga 0 8 0 As undoped GaAs undoped GaAs Si delta Figure 4.10: Layer structure of a pseudomorphic Ino.20Gao.80As/Alo.25Gao.75As M O D F E T on G a A s substrate. The drain, source and gate electrodes are fabricated on top of the layers. 5 x 10 1 8 c m " 3 was grown as the cap layer. The fabrication process was similar to that of the lattice-matched M O D F E T s described above. The masks used here were exactly the same as those used for the lattice-matched devices. The isolation etch was 120 nm deep; the photoconductive switch and interconnection transmission lines were fabricated on the undoped G a A s buffer layer. The gate length and width were 0.35 pm and 100 / /m, respectively. The devices are also in depletion mode or normally-on; the typical gate threshold is -0.7 V . Electro-optic measurements were made with the E O S system described in Chapter 2. Chapter 4. Electro-Optic Characterization of MODFETs 93 cn > ui •o > 0.2 0.1 0.0 -0.1 -0.2 Output 5.4 ps 10-90% Risetime 0.6 V 10 15 20 Time (ps) 25 30 Figure 4.11: Switching response for a pseudomorphic Ino.20Gao.80As/Alo.25Gao.75As M O D -F E T with single-gate-access structure. The upper panel shows a positive-going gate input, and the lower panel shows the corresponding drain output deviation from the drain bias at three different D C drain bias. The operating point is Vgs = 0 V and Vds = 0.0,0.3,0.6 V . The switching time for Vds = 0.6 V is 5.4 ps and the delay t ime, estimated as described in the text, is 6.0 ps. 4.3.2 Results F i g . 4.11 shows the switching response of a pseudomorphic Ino.20Gao.80As/Alo.25Gao.75As M O D F E T . This device has a single-gate-contact structure, so the results can be compared to those shown in F i g . 4.4 for a lattice-matched device that is otherwise identical. The threshold voltage is -0.7 V ; the D C gate bias is set at 0 V . The dc drain bias is set at 0.6 V instead of 1 V to avoid spurious oscillations in this device. The upper panel of F i g . 4.11 shows the positive-going gate input with 2.0 ps risetime, measured on the input transmission line about 300 ± 5 fim away from the gate. The gate reflection of the input signal starts at approximately 10 ps. The corresponding negative-going Chapter 4. Electro-Optic Characterization of MODFETs 94 switching measured on the output transmission line 400 ± 5 \im away from the gate is shown in the lower panel of F i g . 4.11. The 10-90% switching t ime of the device is 5.4 ps which is comparable to the 5.2 ps switching t ime for the L M Ino.52Alo.4sAs/Ino.53Gao.47-A s M O D F E T . However, the delay t ime extracted the same way as described in Section 4.2.2 is 6.0 ps. This delay t ime is almost twice as large as the 3.3 ps delay t ime for the lattice-matched M O D F E T . 4.3.3 Analysis Having made measurements of both P M Ino.20Gao.soAs/Alo.25Gao.75As- M O D F E T on G a A s substrate (Fig. 4.4) and L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T on InP sub-strate (Fig . 4.11), we can now turn our attention to the impact of the semiconductor material on the performance of M O D F E T s . R F measurements of lattice-matched and pseudomorphic M O D F E T s with Cascade electrode layouts fabricated on the same wafers as the devices used in Figs. 4.4 and 4.11 show that the lattice-matched devices have larger ft (63 G H z for L M M O D F E T s and 34 G H z for P M M O D F E T s ) . One might accordingly expect that the switching t ime of the lattice-matched M O D F E T be shorter than that of the pseudomorphic device. However, as shown above the two switching times are very similar which shows that for the devices considered here they are not directly related to the ft as has been suggested in Ref. [27]: 2.2 (4.3) 2TT/( Similar to the confusion about the two delay times discussed in the previous section, it appears that equation 4.3 is another common misconception where the current-gain-cutoff frequency ft of a transistor is confused wi th the 3 d B bandwidth of a low-pass filter. It can be shown that the 10-90% rise t ime r 1 0 _ 9 o % ° f a low-pass filter i n response to a ideal step input is related to its 3 dB bandwidth f3(iB by exactly the same relation Chapter 4. Electro-Optic Characterization of MODFETs 95 as equation 4.3 : 2.2 TIO-90% = 7 7 - 7 — (4.4) ^JZdB where f$dB is the frequency at which the response of the filter drops to half of the value at low frequencies. Equation 4.4 is often used to estimate the bandwidth of a step-like signal. Strict ly speaking it can only be used for step-like signals with an exponential rising edge: i.e. A(\ — e~*). From the definitions of ft and fzdB, It is clear that they are physically different quantities. A s a result, we cannot calculate the current-gain-cutoff frequency ft of a M O D F E T (small-signal operation) by using the rise t ime extracted from the switching response of a M O D F E T (large-signal operation). To obtain the ft, t ime-domain simulation of the experimental results is needed. This wi l l be described in Section 4.4. Whi le the difference in switching times measured with different semiconductor layers is not great, there is a large difference in the observed delay times of the M O D F E T s . It is interesting to note that the delay times of the two M O D F E T s in Figs. 4.4 and 4.8 are comparable even though the switching times are different. On the other hand, the delay times of the two M O D F E T s in Figs. 4.4 and 4.11 differ by nearly a factor of 2 despite the fact that the switching times are nearly the same. One might attribute this difference in delay times to the difference in drain bias: if the dc drain bias of the pseudomorphic device were increased to 1 V , one would expect a change in delay t ime. We have made such bias-dependent measurements of delay t ime in the lattice-matched device. A s shown in Fig.4.9, changing from a drain bias of 0.6 V to 1 V results in an increase of 0.3 ps in delay t ime. Therefore we conclude that the bias dependence is not the origin of the large difference in delay times observed. These results show that the factors that determine the delay times differ from those that determine the switching time. The observed trends are consistent with a delay t ime Chapter 4. Electro-Optic Characterization of MODFETs 96 that is dependent on the channel transport properties, as the electron mobil i ty of InGaAs increases with increasing In content. A comparison of the pseudomorphic device channel (20% Indium) to the lattice-matched channel (53% Indium) would suggest that the gate transit delay be shorter in the lattice-matched devices, which qualitatively agrees with the experimental delay observations. F inal ly we would like to emphasize that a full comparison of the switching time measurements with measured ft and dc results requires a detailed circuit simulation. In addition to the inclusion of appropriate small-signal parameters, it w i l l be essential to incorporate the effect of reflection from the gate input due to the large impedance mismatch. This can be seen from the data shown for the gate input signal, which show that the gate acts very much like a short circuit at the frequencies considered here; such modelling is presented in the following Section. 4.4 S P I C E Modeling In the last two sections, we presented experimental measurements and analysis on high-speed M O D F E T s . To further understand the devices and find out important factors (elements) that may affect their performance as well as obtain parameters which are essential for designing integrated circuits with these devices, we performed theoretical modeling using a widely accepted lumped-element model[73]. The results are presented in this section. This section is organized as the following: in Subsection 4.4.1, we describe the motivation for this work; in Subsection 4.4.2, we introduce the lumped-element model and methodology used in the modeling work; in Subsection 4.4.3, we present the results of both t ime-domain and frequency-domain modeling; finally, in Subsection 4.4.4, we analyze the results and compare them with previous work in this area. Chapter 4. Electro-Optic Characterization of MODFETs 97 4.4.1 Motivation Besides fabrication and characterization of M O D F E T s which we have discussed in the previous sections, theoretical modeling is another important aspect of the research and development of the devices. It not only provides insight into the physics of their oper-ation but also the much-needed circuit element parameters for the design engineers to design integrated circuits with the devices. Even though the structures of M O D F E T s are different from those conventional F E T s , the simulation techniques and tools used for modeling M O D F E T s are nearly the same as those for conventional F E T s . Lumped-element models, which are used for simulating conventional M O S F E T s , are also widely used for modeling M O D F E T s [74, 75, 76]. They have the advantages of being simple, fast and suitable for designing circuits with a large number of transistors. It should be pointed out that the lumped-element model is not the only model used for simulat-ing M O D F E T s . Monte Carlo numerical models based on first principles are also used [77, 78, 79] These models provide much better insight into the device physics. However, the high demand on computing time makes them impractical for circuit design purposes. Even though theoretical simulation of M O D F E T s has been the topic of many recent publications few of them were performed in time domain. Most of the simulations were performed in the frequency domain. This is mainly due to the fact that most of the high-speed measurements which the simulations were compared to were obtained with a network analyzer in the frequency domain. A s pointed out before, the bandwidth of a network analyzer is l imited to about 20-60 G H z while the M O D F E T s normally have a bandwidth larger than 60 G H z . A s a results, the equivalent circuit parameters extracted from these relatively low-frequency measurements might not be able to accurately de-scribe the performance of the M O D F E T s which are capable of operating at much higher frequencies. It is imperative that the simulation be compared with measurements which Chapter 4. Electro-Optic Characterization of MODFETs 98 are conducted over the complete operating frequency range of the M O D F E T s . Frankel and coworkers[41] reported the first t ime-domain simulation and obtained equivalent-circuit parameters through comparing the simulation wi th their t ime domain electro-optic sampling measurements. The M O D F E T s used in the electro-optic mea-surements are discrete devices wire-bonded to test fixtures. A s discussed in the previous sections, this sample configuration makes it difficult to accurately extract important pa-rameters such as delay t ime of the M O D F E T s ; in fact Frankel et al. d id not make absolute delay measurements. In addition, the bonding wires used to connect the M O D F E T s to the test fixtures may degrade the performance of the M O D F E T s and can cause spurious oscillations in the circuits[41]. In this section, we present the first t ime-domain simulation of M O D F E T s monolithically integrated with coplanar test fixtures. We used a model of the experimental arrangement which incorporates both input and output transmission lines with the lumped-element model. This significant change allows us to take the gate reflection which is evident in the electro-optic measurements into consideration. We w i l l show that we have achieved an excellent fit between the modeling and measurement in risetime, total delay t ime, and amplitude for reasonable values of model parameters. We wi l l also compare our work with the previous work. 4.4.2 Lumped-Element Model F i g . 4.12 is the modified lumped-element model used in the simulation. The input and the output transmission lines in F i g . 4.12 simulate the input and output coplanar striplines of the integrated test structure of F i g . 4.2. The elements in the dashed-line box simulate the intrinsic part of the M O D F E T , while the elements outside the box simulate the extrinsic part of the M O D F E T including the test structures integrated wi th the device. For example, the gate inductance Lg simulates inductance contributed by both gate electrode and airbridges which connect input transmission line to the gate of the M O D F E T . We Chapter 4. Electro-Optic Characterization of MODFETs 99 Lg Rg r - " ™ — / W W I input #!SL ff Rin r i n Zo Cgd 1" —j— egg J n g s ^ gm ) = Ttran Cds 1 JRds Rd Ld AVW— Tout #OSL Zo Rout Figure 4.12: Lumped-element circuit for S P I C E simulation of M O D F E T s . It is modified from the model in Ref. [74]. have neglected the parasitic capacitances often associated with the large contact pads used in R F electrode (cascade layout) contact arrangement, as our device is directly connected to the transmission lines. The delay t ime Ttran models the electron transit delay in the conducting channel. T ; n and rout represent the transmission line propagation delays which are determined by the input and the output electro-optic sampling locations with respect to the M O D F E T . The gate input to the M O D F E T is modeled by a current source connected in parallel wi th a input load resistance. Since the coplanar transmission lines in the experiment extend much further from the device than the sampling locations, the model should not artificially introduce reflections from the ends of the input or output transmission lines. Accordingly, the value of the load resistor is chosen to match the impedance of the input transmission line (500), and the output load resistance (50O) is matched to the impedance (50(1) of the output transmission line. Node # ISL of F i g . 4.12 is modeled as the input sampling location while Node # O S L is modeled as the output sampling location. The input signals used in the modeling are taken from the electro-optic sampling Chapter 4. Electro-Optic Characterization of MODFETs 100 measurements with some minor changes. A s mentioned in the previous sections, the electro-optic measurement at the input side of a M O D F E T shows the superposition of the input signal with its reflection from the gate of the M O D F E T . We have removed the gate reflection from the eletro-optic measurements and replaced the removed sections with straight lines. F ig . 4.13 (a) shows the gate input signal used for modeling L M M O D F E T s . It is exactly the same as E O S measurement of the gate input shown in Fig.3.4 in the range of 0-10 ps. After 10 ps, the input signal is modeled as a constant. This is a slight approximation of the real input signal which decays slowly after the sharp transition. The approximation should not have a significant impact on the modeling since it only affects the low-frequency signals. The H S P I C E simulator is used in this work. The circuit parameters of the S P I C E model are traditionally generated by fitting S-parameter measurements of a network analyzer in the frequency domain. They can also be generated by using simulators based on the structure and first principles of the devices. S-parameter measurements have been performed on these devices [67] using a network analyzer in the frequency range of 56 M H z to 26 G H z and circuit parameters were extracted at various bias conditions. Table 4.1 lists equivalent circuit parameters for a L M M O D F E T at gate bias Vgs = 0 V and drain bias Vds = 0.8 V . (The bias condition Table 4.1: The equivalent circuit parameters extracted from a R F measurement of a L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T for bias Vgs = 0 V and Vds = 0.8 V . L 9 60 P H Rg 4.0 ft C g S 119.0 fF 9m 78.4 mS Ttran 0.0 ps C g d 15.5 f F Cds 24.3 f F Rds 169 ft Rd 6.0 ft Ld 70 P H Rs 3.4 ft L s 1 P H Rgs 9.5 ft is the same as that used in the E O S measurement of F i g . 4.4.) We start our time-domain simulation by using parameters obtained from the R F measurement. Chapter 4. Electro-Optic Characterization of MODFETs 101 160 l , i , i 1 1 1 1 0 10 20 30 40 Time (ps) Figure 4.13: Gate input signals used for S P I C E simulation of M O D F E T s . They are taken from E O S measurements but with the gate reflection part (starting at about 10 ps) replaced by constant values, (a) gate input for L M Ino.52Alo.48As/Ino.53Gao.47As M O D F E T s . (b) gate input for P M Ino.20Gao.80As/Alo.25Gao.75As M O D F E T s . Chapter 4. Electro-Optic Characterization of MODFETs 102 > B, w OS) > < 2 0 0 > B VI > < - 5 0 0 Figure 4.14: S P I C E simulation of the L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T using R F parameters in Table 4.1. The upper panel shows the simulated and the measured gate input. The lower panel shows the simulated and measured drain output. In F i g . 4.14, we show the simulated input and output curves together with E O S mea-surement at the same bias condition. The upper panel shows the gate input signals and their reflections. The lower panel shows the drain output signals. The dashed lines are simulated curves using R F parameters. The solid lines are electro-optic measurement of the device. W h i l e the simulation with R F parameters predicts the basic switching function, it fails to model the detailed characteristics such as risetime, delay t ime, am-plitude and gate reflection. It seems very likely that some part of the discrepancy can be attributed to device-to-device variability on the wafer. The typical variation of the Chapter 4. Electro-Optic Characterization of MODFETs 103 parameters between runs is in the range of 20% to 50%. The transconductance of the device used in the R F measurement is 78 mS which is significantly larger than the 40 mS transconductance of the device used in E O S measurement. This may be caused by the nonuniform gate recess obtained by wet etching during the fabrication. The discrepancy between the simulation and its corresponding E O S measurement could be attributed to the fact that the R F parameters are extracted from S-parameter measurement in the frequency range of 56 M H z to 26 G H z while the E O S measurement were performed at a much higher frequency range. The circuit parameters at this higher frequency range might be different from those extracted from the relatively low-frequency R F measure-ment. It should be pointed out that the channel transit t ime T < R A N was set to zero in the R F parameter extraction procedure. This may cause errors in extracting parameters at high frequency because the phase change 2 7 r / r t r a n introduced by the channel transit delay can no longer be ignored at high frequency as it is at low frequency. Since the total delay t ime T<£ = ^j- of a small-signal R F measurement can be written as a sum of channel transit t ime r t r a n , channel charging t ime r c c and drain delay t ime ^ [ 8 1 , 70, 72]: Td = TtTan + r c c -f Tdd, setting channel transit t ime to zero wi l l cause an over estimation of the channel charging t ime r c c and drain delay t ime Tdd- This may eventually cause an over estimation of the parasitic parameters which are related to r c c and Tdd- This can be more clearly seen in the analytical expression of T c c and Tdd derived in Ref. [81]: It could also be attributed to the fact that the sample used in E O S measurement has a different access structure from that used in R F measurement. The mask layouts of the M O D F E T s used in both the R F measurements and E O S measurements are shown in (4.5) (4.6) Appendix D . In any event, to better model the device, we need to choose another set of Chapter 4. Electro-Optic Characterization of MODFETs 104 parameters for the S P I C E model. The new set of circuit parameters should allow us to produce a smaller delay t ime, a smaller amplitude, and a slightly faster switching t ime than what we have obtained with the R F parameters. We performed a series of simulations by varying one parameter at a t ime and kept all the other parameters unchanged in order find out the role each element plays in determining delay t ime, switching t ime, drain amplitude and features such as gate-drain feedthrough and gate reflection of input signal. Each of the parameters in the model is varied around its R F value. The results are summarized in the following. The gate capacitance Cgs is one of the most important parameters in the equivalent circuit. It is closely related to the risetime, delay t ime, current-gain-cutoff frequency as well as gate reflection of input signal. F i g . 4.15 shows the dependence of the mentioned characteristics on Cgs. The gate input signal used in the simulation is the same as the one shown in F i g . 4.13 (a). A smaller Cgs results in a faster risetime and a smaller capacitor related delay t ime (also referred to as channel charging t ime T c c ) as shown in the lower panel of F i g . 4.15. Gate-source capacitance Cgs also dramatically affects the reflection of input signal. This is shown in the upper panel of F i g . 4.15. The reflection starts after 14ps and is composed of an ini t ia l dip followed by a positive-going step-like signal. A large Cgs acts like a short for high-frequency components, which results in the init ial dip in the reflected signal while a small Cgs acts like an open, which only results in a positive going step-like reflection. This shows that reflection from the gate actually provides a very sensitive measure of gate capacitance Cgs. Gate-drain parasitic capacitance Cgd is another important parameter in the model. It is responsible for gate input feedthrough as well as risetime, delay t ime, and gate reflection. F ig . 4.16 shows the effects of Cgd on these characteristics. A small Cgd results in not only a small feedthrough which is the positive going feature near 15 ps in F ig . 4.16 but also a shorter C sd-related delay t ime (also referred to as parasitic charging time r p c ) , Chapter 4. Electro-Optic Characterization of MODFETs 105 T — : • r -400 1 1 ' ' 1 1 1 1 1 0 10 20 30 40 Time (ps) Figure 4.15: Effects of gate capacitance Cgs on the response of M O D F E T s . a shorter switching time and a sharper gate reflection feature. The transconductance gm affects the drain output amplitude and the current-gain cutoff frequency ft as well as the gate-drain feedthrough. However, it does not affect the signal propagation delay t ime through the device. (This is one of the evidences given in Section 4.2.3 to support the argument that the propagation delay t ime TpTOp is different from the delay t ime defined in small-signal R F measurement which is strongly dependent on gm.) A M O D F E T with a small transconductance has a much larger feedthrough than an otherwise the same device with a larger transconductance. This effect of transconductance on the feedthrough can be clearly seen in F i g . 4.17 where all the Chapter 4. Electro-Optic Characterization of MODFETs 106 - 4 0 0 1 • ' • ' • ' • 1 0 10 2 0 3 0 4 0 Time (ps) Figure 4.16: Effects of gate-drain capacitance Cgd on the response of M O D F E T s . other parameters in the simulations are kept the same except for the transconductance. The feedthrough signal coupled through Cgd is actually the same for al l the simulations since Cgd and related resistors are exactly the same. The reason that it is less "visible" for the device with a larger transconductance gm is because the large gain in drain current canceled the relative small feedthrough while for the device with a small transconductance the gain in drain current is not enough to cancel the feedthrough. A s a result it is more "vis ible" for the small gm device. This effect has been observed in t ime-domain electro-optic sampling measurement where large feedthrough is observed for devices with small transconductance. Chapter 4. Electro-Optic Characterization of MODFETs 107 > OT X) > < 0 - 1 0 0 - 2 0 0 •300 - 4 0 0 g m = 1 0 m S gm=20 mS gm=60 mS 0 10 30 40 20 Time (ps) Figure 4.17: Effects of transconductance gm on the response of M O D F E T s . The drain-source capacitance Cds affects the risetime and the delay t ime almost the same way as Cgs does. A small Cds causes a faster risetime and a smaller delay t ime except that the change is slightly less dramatic. However, Cds has very l i tt le influence on the gate reflection, in contrast with Cgs- This is perfectly reasonable since Cds is on the output side of the M O D F E T and is not directly connected to the input transmission line. Another important intrinsic parameter is the drain-source resistor Rds which is connected in parallel with Cds- It affects the amplitude of drain output if its value is comparable with the impedance of the output transmission line. The gate input resistance Rgs is the only intrinsic parameter which has almost no effect on the features discuss above when Chapter 4. Electro-Optic Characterization of MODFETs 108 it is varied around its R F value 1-10 0 . So far, we have only looked at the effects of varying intrinsic parameters on the re-sponse of a M O D F E T . Now, we consider the extrinsic parameters. In the present devices, the extrinsic parameters have much less impact on the performance of a M O D F E T com-pared with the intrinsic parameters. The extrinsic resistors Rd and Rs marginally affect the amplitude of the drain output. They have litt le influence on the risetime and delay time. The gate extrinsic resistor Rg only slightly affects the risetime of the drain output. The three extrinsic inductances Lg, Ls, and Ld have almost no effect on the risetime and amplitude but they affect the delay t ime. A large source inductance may also contribute to the gate-drain feedthrough signal while a large gate inductance Lg may result in an overshoot in drain output. A m o n g all the six extrinsic elements in our model, gate induc-tance Lg is the only element that has significant effect on the reflection of input signal. This is shown in the upper panel of F i g . 4.18. The gate input used in the simulation is the same as F i g . 4.13 (a). Beside the init ial dip and the positive going step observed in the previous simulation (for Cgs) with a small gate inductance Lg = 10 p H , we observed a positive going feature before the dip for simulation with a larger gate inductance Lg at around 16 ps. This lobe-like feature is attributed to the reflection of the input signal by the large gate inductance. Beside causing a noticeable reflection of gate input signal, a large Lg also delays the arrival of the reflection caused by Cgs which features a dip followed by a positive going step. The lobe-like feature in the reflection can be used to determine the gate inductance Lg. We w i l l discuss more about this in Subsection 4.4.4. 4.4.3 Modeling Results Knowing the effects of each element of the equivalent circuit on the response of a M O D -F E T , we are now in the position to simulate the electro-optic measurements of M O D F E T s presented in Section 4.2 and Section 4.3. In this section, we wil l present simulation results Chapter 4. Electro-Optic Characterization of MODFETs 109 Time (ps) Figure 4.18: Effects of gate inductance Lg on the response of M O D F E T s . for both the L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T and P M In 0 .2oGao . 8 0 As/Alo.25-Gao .75As M O D F E T . F i g . 4.19 shows the measured and the simulated response of a L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T for gate bias Vgs = 0 V and drain bias Vds = 0.8 V . The upper panel shows the measured and simulated gate input signals and their reflec-tions. The lower panel shows the measured and simulated response of the drain output. The simulated curves are represented in dashed lines while the measured ones are in solid lines. The input signal used in the simulation is shown in F i g . 4.13 (a). Since the gate input is relatively small , we assume that the signal does not significantly change the bias condition and that the device remains in the vicinity of its quiescent point during the Chapter 4. Electro-Optic Characterization of MODFETs 110 200 T ' i 1 1 i -> • * • • / / -w tao > 100 / _ / f *w / r -< X V / / \ X • J -0 M e a s u r e m e n t A Vds (mV) -100 \ \ --- Simulation --200 - i . i — \ I I ! I I 1 1 1 0 10 20 30 40 Time (ps) Figure 4.19: The measured and simulated responses of the Ino.52Alo.4sAs/Ino.53Gao.47-A s M O D F E T . The dashed lines are the simulated results while the solid lines are the measured ones. The lower panel shows the deviation of drain output from the D C bias VDS = 0.8 V . switching. A s a result, all the circuit parameters are not bias-dependent. The simulated input and output signal correspond to electrical potential at nodes # ISL and # 0 S L of the equivalent circuit , respectively. Table 4.2 shows all the circuit parameters used in the simulation. The input and output transmission line propagation delay T ; n + Tout = 4.9ps is determined by the sep-aration of input and output sampling locations of the E O S measurement described in Section 4.2. The transconductance gm is estimated from D C measurement of the device Chapter 4. Electro-Optic Characterization of MODFETs 111 Table 4.2: The equivalent circuit parameters extracted from an E O S measurement of a L M Ino .52Alo.48As / Ino .53Gao.47As M O D F E T for bias Vgs = 0 V and Vds = 0.8 V . 10 p H Rg 4 ft Cgs 90 fF 9m 40 mS 0.6 ps Cgd 3 f F 10 f F R d s 90 ft Rd 6 ft 10 p H Rs 3.4 ft 1 p H Rgs 9.5 ft 7"»n "I" Tout 4.9 ps at the same bias condition using a curve tracer, (note our curve-tracer measurement of transconductance is smaller than that obtained from R F measurement.) The voltage-controlled current source in the model is controlled by a delayed Cgs voltage which is obtained by using a transmission line with a very large impedance (Zo = l O M f t ) and a matched load. The propagation delay time of the transmission line is used to model the channel transit t ime T T R A N . Those parameters whoes values do not significantly affect the switching characteristics, such as Rg Rd Rs, and Rgs, were kept the same as their R F values. The other parameters in the model are determined by the best fit of the E O S experiment. The values of the equivalent circuit parameters are varied unt i l the best fit to the E O S measurement is obtained while keeping the parameter values physically meaningful and deviations from their R F values as small as possible. It is interesting to notice that except for those parasitic resistors whoes values are kept the same as their R F values the other parasitic parameters extracted from our simulation are consistently smaller than those obtained from R F measurement, in agreement with the argument that the R F parasitic parameters might have been over estimated due to artificially setting T T R A N = 0 in the R F fitting. A s pointed out in the previous section, the difference between parameters extracted from the E O S fitt ing and the R F fitt ing could also be attributed to the following three factors: the device-to-device variability, the inaccuracy caused by the relatively low-frequency range (56 M H z to 26 G H z ) used in the R F measurement, and Chapter 4. Electro-Optic Characterization of MODFETs 112 the different mask layouts of the M O D F E T s used in the E O S and the R F measurements. The simulated drain output agrees very well wi th the E O S measurement. The sim-ulation successfully reproduced the correct risetime, total delay t ime, and drain output amplitude. The simulated reflection of the gate input signal is qualitatively in agreement with the E O S measurement. It correctly predicts the basic features of the reflected input signal which are a dip followed by a step-like signal. Besides the t ime-domain simula-t ion, we also performed frequency-domain simulation using parameters in Table 4.2. The short-circuit current-gain-cutoff frequency ft extracted from the simulation is 69 G H z which agrees well wi th the R F measurement ft = 63 G H z . Even though the simulated total delay t ime agrees perfectly with the measured 3.3 ps delay t ime, the simulated transit t ime Ttran = 0.6 ps seems to be too small compared with other published values extracted from R F measurements[73, 81]. The average saturation velocity V3at calculated by using a simple formula Vsat = -^a- and gate length Lg = 0.35 \im is 5.8 x 10 7 cm/s . This value is much larger than the Vsat = 2.6 x 10 7 cm/s (Vsat = 2.7 x 10 7 cm/s) value extracted from R F measurement in Ref. [73] (Ref. [81]). However, it is interest-ing to notice that the saturation velocities extracted from our measurement and the R F measurements of Ref. [73, 81] are al l consistently larger than the steady-state electron velocity measured in an Ino.52Alo.48As/Ino.53Gao.47As/Ino.52Alo.4sAs double heterostruc-ture where a Vsat = 1.8 x 10 7 cm/s is obtained by time-of-flight measurement [83]. We speculate that this might caused by velocity overshoot effect in these ultrafast devices. Besides the simulation for the L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T , we also performed S P I C E simulation for a P M Ino.20Gao.80As/Alo.25Gao.75As M O D F E T using the same equivalent circuit. F i g . 4.20 shows the simulated and the measured responses for gate bias Vgs — 0 V and drain bias Vds = 0.6V. The dashed lines are the simulated results while the solid lines are the measured ones. The lower panel shows the simulated Chapter 4. Electro-Optic Characterization of MODFETs 113 Time (ps) Figure 4.20: The measured and simulated responses of the Ino.20Gao.soAs/Alo.25Gao.75-A s M O D F E T . The solid lines are the simulated results while the dashed lines are the measured ones. and the measured drain output. The upper panel shows the simulated and the mea-sured gate input signals and their reflections. The input signal used in the simulation is shown in F i g . 4.13 (b). It is taken from the corresponding E O S measurement but with the gate reflection replaced by a straight line starting from about 9 ps. We followed the same simulation procedures as those used for the L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T . The transmission line propagation delay T{n + rout = 5.7 ps is determined by the corresponding E O S experiment configuration described i n Section 4.3. The transcon-ductance used in the simulation is 18mS which is much smaller than that used in the Chapter 4. Electro-Optic Characterization of MODFETs 114 previous simulation. There are two reasons for this relatively low gm. F irst , in general, a P M Ino .20Gao.80As /Alo .25Gao .75As M O D F E T has a lower transconductance than that of a L M Ino.52Alo.48As/Ino.53Gao.47As M O D F E T . The transconductance obtained from the R F measurement for the P M device is around 400mS/mm compared with about 800mS/mm for the L M device. Second, due to spurious oscillation in the circuit we were not able to set the drain bias larger than Vds — 0.6V in our E O S measurement. This 0.6 V drain bias may be too small for the M O D F E T to realize its largest transconductance. The values of the parasitic resistors Rg, Rd, Rs, and Rgs are kept the same as their R F values. The values of inductors Lg, Ld, and Rs are the same as the previous simulation of the L M Ino.52Alo.48As/Ino.53Gao.47As M O D F E T due to the same mask layouts of the two M O D F E T s . The other parameters are obtain from the best f itt ing of the E O S measure-ment. Table 4.3 lists al l parameters extracted from the best fit of the E O S measurement. Table 4.3: The equivalent circuit parameters extracted from an E O S measurement of a P M Ino .20Gao.80As /Alo .25Gao.75As M O D F E T for bias Vgs = 0 V and Vds = 0.6 V . L9 Rg CgS 9m Ttran Cgd Cds 10 p H 2 ft 70 f F 18 mS 2.2 ps 5.0 f F 10 f F Rds Rd Ld Rs Ls Rgs Tin ~\~ T0ut 110 ft 8 ft 10 p H 3 ft 1 p H 8 ft 5.7 ps We have achieved excellent agreement between the simulation and experiment for the P M Ino . 2 0 G a o . 8 0 A s /Alo . 2 5 G a o . 7 5 A s M O D F E T . The simulation of the drain output reproduced the correct risetime, delay t ime, amplitude and even the small positive-going feedthrough around 12 ps. The simulation of the gate input and its reflection is also i n good qualitative agreement w i t h the experiment. The channel transit t ime extracted from the simulation is T t r a n — 2.2 ps. The saturation velocity estimated by using gate Chapter 4. Electro-Optic Characterization of MODFETs 115 length Lg = 0.35 / /m is Vsat = 1.6 x 10 7 cm/s which agrees well wi th the saturation velocity estimated from R F measurement for the same type of P M device[71] where Vsat = 2 x 10 7 cm/s was reported. We performed frequency-domain simulation using parameters listed in Table 4.3. The current gain cutoff frequency extracted from the simulation is 36GHz. Unl ike the previous simulation for L M device, we do not have R F experimental measurements at exactly the same bias condition ( Vgs = 0 V , Vds = 0.6 V ) to compare wi th . The current-gain-cutoff frequency extracted from R F measurement at similar bias condition ( Vgs = 0 V , Vds = 1.0 V ) is ft — 34 G H z . 4.4.4 Analysis In the last section, we presented t ime-domain S P I C E simulation of M O D F E T s using a lumped-element model incorporating input and output transmission lines. B y comparing the simulations to the E O S measurements of M O D F E T s monolithically integrated with coplanar test fixtures, we extracted parameters of the equivalent circuit . To further demonstrate the advantages of the integrated M O D F E T test structure over the discrete wire-bonded one, we compare our work to the similar work by Frankel and co-workers on discrete P M Ino.20Gao.80As/Alo.25Gao.75As devices[41]. F i g . 4.21 shows their simulated and measured drain outputs for two drain bias conditions. The P M Ino.20Gao.80As/Alo.25-Ga 0 .75As M O D F E T used in their E O S measurement had a similar structure to our P M device and had a gate length of 0.35/xm and width 100/xm. The major difference between our E O S sample and theirs is the connection of the M O D F E T and the coplanar test fixture. Their discrete device was wire-bonded to a coplanar test fixture while ours was integrated wi th the structure with an airbridge connecting the input transmission line and gate electrode instead of a bonding wire. It should be pointed out that their discrete M O D F E T s and our integrated ones were al l fabricated by the same research group at the Interuniversity Microelectronics Center in Belgium. The model used in their simulation Chapter 4. Electro-Optic Characterization of MODFETs 116 0.05 I . . . . i . . . . i Time (ps) Figure 4.21: The measured and simulated drain responses of a discrete M O D F E T for two drain bias condition. The gate bias is 0.5 V . The discrete M O D F E T was wire-bonded to a coplanar test fixture in the corresponding E O S measurement. After Ref.[41] as the gate input for their s imulation. Table 4.4 lists al l the parameters used in their simulation together with those of ours for easy comparison. W h i l e most of their intrinsic parameters are comparable to or smaller than those of ours, their extrinsic parameters are consistently considerably larger than those of ours. We attribute the large difference in extrinsic parameters to the different test structures. The extrinsic inductances of their simulation are considerably larger than those of ours, mainly due to the bonding wires used to connect the M O D F E T to the test fixture. Frankel and co-workers attributed Chapter 4. Electro-Optic Characterization of MODFETs 117 Table 4.4: The equivalent circuit parameters extracted from E O S measurements of two P M Ino.20Gao.soAs/Alo.25Gao.75As M O D F E T s . The D C bias condition for the integrated M O D F E T (this work) is Vgs = 0 V and Vds = 0.6 V . The D C bias condition for the discrete M O D F E T (Frankel) is Vgs = 0.5 V and Vds = 1.5 V . L 9 Rg CgS 9m Ttran Cgd Cds Frankel 120 p H 12 ft 48 fF 15 mS 1.5 ps 10 f F 1 f F This Work 10 P H 2 ft 70 f F 18 mS 2.2 ps 5.0 f F 10 fF Rds Rd Ld Rs L s Rgs Tin ~\~ Tout Frankel 500 ft 12 ft 120 p H 5 ft 80 p H 2 ft N / A This Work 110 ft 8 ft 10 p H 3 ft 1 p H 8 ft 5.7 ps the ringing seen in both their E O S measurement and S P I C E simulation (Fig. 4.21) to the large inductances contributed by the bonding wires. We wi l l show later that the ringing in their S P I C E simulation could also be attributed to the model they used. Besides causing the ringing in the E O S measurement, the large gate inductance also causes a reflection of the input signal which is shown in F i g . 4.22 [83]. The positive-going lobe-like feature at around 39 ps is the reflection of the bonding wire. This feature has been predicted by our previous simulation with a large gate inductance shown in F i g . 4.18. Whi le we have not undertake detailed simulations for the device of Ref. [83], we can use F i g . 4.18 to estimate that the parasitic wire bond inductance is about 100 p H . This is about 10 times bigger than that of the integrated structure. Neither the ringing nor the reflection of the gate-inductance are seen in our E O S measurement of the M O D F E T s monolithically integrated with the test fixtures, showing that the contribution of the airbridge to the gate inductance Lg is very small . Through the above comparison, we can clearly seen the advantages of using an inte-grated structure in characterizing M O D F E T s . The integrated structure not only avoids Chapter 4. Electro-Optic Characterization of MODFETs 118 0.45 I l I I I z I I 0 10 2 0 3 0 4 0 5 0 6 0 70 Figure 4.22: The E O S measurement of the gate input to a discrete P M Ino.20Gao.80As/-Alo .25Gao.75As M O D F E T wire-bonded to a test fixture. After Ref. [84] Through the above comparison, we can clearly seen the advantages of using an inte-grated structure in characterizing M O D F E T s . The integrated structure not only avoids the ringing and input reflection caused by the bonding wires but also provide wider char-acterization bandwidth since part of the high-frequency components of the input signal would otherwise be reflected by the bonding wire and would never reach the D U T if a non-integrated structure was used. In addit ion, the large extrinsic parameters caused by the wirebonds may degrade the performance of the D U T . A s a result, the measured switching t ime might be slower than the real device switching t ime. Chapter 4. Electro-Optic Characterization of MODFETs 119 200 oo > < 100 h > < -100 h -200 h Figure 4.23: The simulation results of the two different models. The solid line is the E O S measurement; the dashed line is the simulation with our model; the dotted line is the simulation with Frankel's model. parameters listed in Table 4.2. The results are plotted in F i g . 4.23 together with the E O S measurement and the simulation with our model using the same parameters. The upper panel shows the input signal. The dotted-line in the upper panel is the same as the input signal shown in F i g . 4.13 (a). The lower panel shows the output signal. Serious ringing is seen in the simulation using Frankel's model even though the parasitic inductances Lg, Li and Ls used in the simulation are much smaller than those used in the simulation of Fig.4.21. The result shows that the ringing seen in Frankel's simulation can be attributed to the model they used rather than the large values of parasitic inductors. Due to these Chapter 4. Electro-Optic Characterization of MODFETs 120 facts, we conclude that to correctly simulate the E O S measurement it is imperative that the input transmission line be incorporated in the model. Chapter 5 Conclusions and Future Work 5.1 Conclusions To briefly summarize the thesis work, the author designed, built and tested an electro-optic sampling system with T H z bandwidth suitable for characterizing ultrafast electronic devices. A n experimental study on the measurement errors and the sensitivity of electro-optic sampling using a LiTaC*3 external probe was subsequently performed by using the E O S system. Then, the E O S system was used to characterize the switching character-istics of modulation-doped field-effect transistors. F inal ly , t ime-domain simulation was performed with a lumped-element model incorporating input and output transmission lines. From the work, the following conclusions can be drawn: • The most significant result of this thesis is the first electro-optic characterization of ultrafast transistors monolithically integrated with a transmission line/photocon-ductive switch test fixture. The measured switching t ime and propagation delay t ime of a L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T are 4.2 ps and 3.2 ps, respec-tively. These are the shortest switching and delay times ever directly measured in a three-terminal electronic device. • On-wafer integration of coplanar transmission lines wi th the device under test is a significant improvement over hybrid integration involving wire bonds. The parasitic gate inductance associated with the integrated structure is approximately one order of magnitude less than that associated with wire bonds, and allowed extension of 121 Chapter 5. Conclusions and Future Work 122 the electro-optic technique to higher-speed device characterization. • The propagation delay t ime of M O D F E T switching response, TpTop, and the delay t ime Td = 2 ^ defined in small-signal R F measurement are physically different quantities. For example, if all other parameters in the small-signal model are kept equal, Td is a strong function of transconductance gm but rpTop does not depend upon gm. Despite this, the propagation delay t ime rpTop and delay t ime Td were shown to have similar dependence on drain bias Vds. • The 10-90% rise t ime of the M O D F E T switching response cannot be used to cal-culate the current-gain cutoff frequency ft: T ] 0 _ 9 O % ^ as suggested in the literature. The rise t ime r 1 0 _ 9 o % a n d the propagation delay t ime rprop of the M O D -F E T switching response are determined by different factors. Some M O D F E T s can have the same switching times but different delay times while other M O D F E T s can have the same delay times but different switching times. • The time-domain simulation with a lumped-element model incorporating input and output transmission agrees well wi th the E O S measurement. Equivalent circuit parameters have been extracted from the simulation, and predict cutoff frequencies very close to the measured values. It is imperative to include the input transmission line in the simulations. Its omission causes severe ringing in the simulated output waveform, which is an artifact of the incomplete model. • The reflection of the input signal by the M O D F E T is very sensitive to the gate inductance Lg and gate-source capacitance C a s , and can be used to estimate the values of these parameters. • Significant inaccuracy occurs in the electro-optic sampling measurement due to the high-dielectric-constant probe t ip when in contact with the transmission lines. Chapter 5. Conclusions and Future Work 123 This is at variance with previous experimental measurements; we attribute the difference to imperfect contact in the previous reports. These measurement errors can be reduced by performing noncontact E O S measurement, and experimental signal to noise ratios are achievable to permit routine noncontact measurement. In our experimental situation, a reasonable compromise between invasiveness and sensitivity, which sti l l ensures accurate calibration, occurs for air gaps from 10 to 20 pm. • The sensitivity of E O S measurement drops dramatically with increasing probe-to-sample distance. The measurement sensitivities for time-resolved (high-frequency) signal and calibration (low-frequency) signal drop at the same rate with increasing air gap when the air gap is smaller than a critical distance. This confirms that the common method used for calibrating electro-optic measurement is valid for both contact and small-air-gap non-contact measurements. • The retardation introduced by a compensator made of multi-order wave plate strongly depends on the wavelength of the laser beam, which may significantly degrade the sensitivity of E O S system if a very short laser pulse or thick wave plate is used. 5.2 Future Work The following are some final thoughts regarding the future work of electro-optic character-ization of high-speed electronic devices. It is obvious that the bandwidth of electro-optic sampling which is about 1000 G H z is large enough for characterizing most of the state-of-the-art high-speed electronic devices. The sensitivity l -10mV / y /Hz is satisfactory for large-signal switching measurement and is marginal for small-signal measurement. The l imitat ion of using this technique to characterize high-speed electronic devices lies in Chapter 5. Conclusions and Future Work 124 the interconnection between the photoconductive signal generator and the device under test. Even though photoconductive switches (PCSs) are capable of generating pulses with subpicosecond risetime, much of the high-frequency component is lost before it gets to the device under test ( D U T ) due to the dispersion and loss in the interconnection transmission line. The effects of loss and dispersion on the interconnection transmis-sion line can be reduce by using a shorter transmission lines with a thinner substrate and smaller electrodes. This change of design for interconnection transmission line is needed for electro-optic characterization of M O D F E T s with switching times less than 2 ps. However, shorter interconnection transmission line may create another problem: reduced measurement t ime window due to the reflection of the input signal by the D U T . This is not a problem for the measurement of faster devices because the t ime window needed to measure faster devices should be smaller. If desired, the reflection can be sepa-rated from the input signal by using a recently developed technique reported in reference [85]. The photoconductive switches used in this work are integrated with the input trans-mission lines. The pulse shape generated by the P C S (step-like) and the distance between the P C S and the D U T (about 2 mm) are fixed and difficult to change. These fixed pulse shape and P C S - t o - D U T distance make certain measurements impossible. For example, it is desirable to study the switching characteristics of a M O D F E T in response to step-like signals with different risetimes. This is difficult for the current arrangement since the risetime of the input signal is not adjustable. Further more, to perform S-parameter measurement with E O S system, pulses with small F W H M are needed. However, the P C S s of our samples are designed to generate step-like pulses. Even though in principle it is possible to generate pulses in the current sample by using asymmetric excitation [19], the relatively low gate bias of the M O D F E T cannot be easily reconciled with the large bias voltage required by this technique. These problems may be solved by using an Chapter 5. Conclusions and Future Work 125 improved E O S system which is equipped with mobile photoconductive-switches[8] that allow different types of pulses to be generated and coupled into the D U T . In addition, the distance between the P C S and the D U T can be adjusted continuously. A s a result the risetime or pulse width of the input signal can be adjusted due to the change of dispersion with the length of the transmission line. The mobile P C S s w i l l make the E O S system more complete as a high-speed characterization system since it not only measures the response of the D U T but also provides the input signals for the D U T . Regarding the future work on the invasiveness of electro-optic probes, instead of using one probe and changing its distance to the D U T , a better experimental arrangement is to use two probes with a dummy probe added to the current setup and placed between the P C S and the measurement probe whose distance to the D U T is fixed. In the experiment, the dummy probe is moved up and down to perturb the electric field on the transmission line while the measurement probe measures the invasiveness induced by the dummy probe. Besides using step-pulses in the experiment, pulses wi th small F W H M should also be used since they can provide frequency domain information about the invasiveness through Fourier transformation. Another way to solve the invasiveness problem is to develop electro-optic probes using materials with small diselectric constant. Polymer films with dielectric constant eT = 3 have been proposed as new materials for electro-optic probes[86]. Final ly , to better use the information obtained from the E O S measurement of the switching characteristics of the M O D F E T s , it is desirable to find an analytical expression which relates the propagation delay t ime TPROP to the delay t ime TJ, = defined in R F measurement so that the current-gain cutoff frequency ft can be estimated from the propagation delay t ime TPROP. A useful idea for attacking this problem may be found in a related work by Chor and co-workers on analytical expression of propagation delay t ime of emitter-coupled gate ( E C L ) [87] where the propagation t ime is written as a weighted Chapter 5. Conclusions and Future Work linear combination of the time constants of the circuit. Bibliography [1] P. J . Tasker and J . Braunstein, "New M O D F E T Small Signal Circui t M o d e l Re-quired for Milimeterwave M M I C Design: Extract ion and Val idat ion to 120 G H z , " M T T - S International Microwave Symposium Digest, V o l . 2, pp. 611-614, 1995. [2] Hermann Schumacher and Er ic W . Str id, "Electronic Wafer Probing Techniques," in Measurement of High-Speed Signals in Solid State Devices, edited by R. B . Marcus, Academic Press, San Diego, pp. 41-81, 1990. [3] C . L . Tang, F . W . Wise, M . J . Rosker, and I. A . Walmsley, "Femtosecond Laser Studies of the Relaxation Dynamics of Semiconductors and Large molecules," I B M J . Res. Develop. V o l . 33, pp. 447-455, 1989. [4] F . Sasaki and Y . Masumoto, "Tunneling and Relaxation of Photogenerated Carriers in Semiconductor Quantum Wells ," Phys. Rev. B , V o l . 40, p. 3996, 1989. [5] M . K . Jackson, "Opt ica l Studies of Semiconductor Heterostructures: Measurements of Tunneling Times, and Studies of Strained Superlattices," P h . D . thesis, Cali fornia Institute of Technology, Pasadena, California, 1991. [6] D . H . Auston , "Picosecond Optoelectronic Switching and Gating in S i l icon," , A p p l . Phys. Lett . , V o l . 26, pp. 101-103, 1975. [7] D . H . Auston , "Picosecond photoconductivity: High-speed measurements of devices and materials," in Measurement of High-Speed Signals in Solid State Devices, edited by R. B . Marcus, Academic Press, San Diego, pp. 85-133, 1990. [8] H . M . Heiliger, T . Pfeifer, H . G . Roskos, H . K u r z , "Picosecond Electric On-wafer Testing with Freely Positionable Photoconductive Switches," Technical Digest C L E O ' 9 5 , p. 363, 1995. [9] J . A . Valdmanis , G . Mourou, and C . W . Gabel , "Picosecond Electro-Optic Sampling system," A p p l . Phys. Lett . , V o l . 41, pp. 211-212, 1982. [10] A m n o n Yar iv , "Opt ica l Electronics", Fourth edition, pp. 309-353, Saunders College Publ ishing, 1991. [11] U . D . K e i l , D . R. Dykaar, "Electro-optic sampling and carrier dynamics at zero propagation distance," A p p l . Phys. Lett . , V o l . 61, pp. 1504-1506, 1992. 127 Bibliography 128 [12] G . Hasnain, A . Dienes, and J . R . Whinnery, "Dispersion of picosecond pulses in coplanar transmission lines," I E E E Trans. Microwave Theory and Tech., V o l . 34, pp. 738-741, 1986. [13] J . F . Whitaker , R . Sobolewski, D . R. Dykaar, T . Y . Hsiang, and G . A . Mourou, "Propagation Model for ultrafast signals on superconducting dispersive striplines," I E E E Trans. Microwave Theory Tech. V o l . 36, pp. 277-285, 1988. [14] D . Grischkowsky, I. N . Dul ing , III, J . C . Chen, and C . C . C h i , "Electromagnetic Shock Waves From Transmission Lines," Phys. Rev. Lett . V o l . 59, pp. 1663-1666, 1987. [15] D . S. Phatak, and A . P. Defonzo, "Dispersion characteristics of optically excited coplanar striplines: Pulse propagation," I E E E Trans. Microwave Theory Tech. V o l . 38, pp. 654-661, 1990. [16] S. Gupta , J . F . Whitaker , and G . A . Mourou, "Subpicosecond pulse propagation on coplanar waveguides: Experiment and simulation," I E E E Microwave and Guided Wave Lett . V o l . 1, pp. 161-163, 1991. [17] M . B . Ketchen, D . Grischkowsky, T . C . Chen, C - C C h i , I. N . Dul ing , III, N . J . Halas, J - M Halbout, J . A . K a s h , and G . P. L i , "Generation of Subpicosecond Electrical Pulses on Coplanar Transmission Lines," A p p l . Phys. Lett . , V o l . 48, pp. 751-753, 1986. [18] F . W . Smith , S. Gupta , H . Q . Le, V . Diadiuk, M . A . Holl is , A . R. Calawa, M . Frankel, D . R. Dykaar, G . A . Mourou, and T . Y . Hsiang, "Picosecond GaAs-based Photoconductive Optoelectronic Detectors," A p p l . Phys. Lett . , V o l . 54, pp. 890-892, 1989. [19] D . Kroke l , D . Grischkowsky, and M . B . Ketchen, "Subpicosecond Electrical Pulse Generation Using Photoconductive Switches with Long Carrier Lifetimes," A p p l . Phys. Lett . , V o l . 54, pp. 1046-1047, 1989. [20] E . Sano, T . Nagatsuma, T . Shibata, and A . Iwata, "Generation of Picosecond Elec-tr ical Pulses by a Pulse-forming Optoelectronic Device," A p p l . Phys. Lett . , V o l . 55, pp. 151-152, 1989. [21] J . R. Soderstrom, E . R . Brown, C . D . Parker, L . J . Mahoney, J . Y . Yao, T . G . Anderson, and T . C . M c G i l l , "Growth and Characterization of High-current Density, High-speed I n A s / A l S b Resonant Tunneling Diodes," A p p l . Phys. Lett . , V o l . 58, p. 275, 1991. Bibliography 129 [22] E . R. Brown, J . R. Solderstrom, C . D . Parker, L . J . Mahoney, K . M . Molvar , and T . C . M c G i l l , "Oscillations up to 712 G H z in I n A s / A l S b Resonant-tunneling Diodes," A p p l . Phys. Lett . V o l . 58, p. 2291, 1991. [23] E . Ozbay, S. K . Diamond, and D . M . B l o o m , "Pulse forming and triggering using resonant tunneling diode structures," Electron. Lett . V o l . 26, p. 1046, 1990. [24] E . Ozbay, D . M . B l o o m , D . H . Chow, and J . N . Schulman, "1.7-ps, microwave, integrated-circuit-compatible I n A s / A l S b resonant tunneling diodes," I E E E Electron Device Letters, V o l . 14, pp. 400-402, 1993. [25] R. Tsu and L . Esaki , "Tunneling in a Fini te Superlattice," A p p l . Phys. Lett . V o l . 22, p. 562, 1973. [26] Y i h - G u e i Wey, K i r k S. Giboney, John E . Bowers and M a r k K . W . Rodwel l , "108-G H z G a l n A s / I n P p-i-n Photodiode with integrated bias tees and matched resistors," I E E E Photonics Tech. Lett . , V o l . 5, p. 1310, 1993. [27] M . K . Jackson, M . Y . Frankel, J . F . Whitaker , G . A . Mourou, D . H u l i n , A . Antonet t i , M . Van Hove, W . De Raedt, P. Crozat and H . Hafdallah, "Picosecond Large Signal Switching Characteristics of a Pseudomorphic A l G a A s / I n G a A s Modulat ion Doped Fie ld Effect Transistor," A p p l . Phys. lett., V o l . 61, pp. 1187-1189, 1992. [28] A . Zeng, M . K . Jackson, M . Van Hove, and W . De Raedt, "Electro-optic Characteri-zation of Modulat ion-Doped Field-Effect Transistors wi th Monolithically-integrated Test F ixtures . " , Accepted for publication i n the Special Issue of the Optica l and Quantum Electronics on Optical Probing of Ultrafast Devices and Integrated Cir-cuits, July, 1996. [29] M . Y . Frankel, D . Pavl idis , and G . A . Mourou , " A study and optoelectronic verifica-t ion of A l G a A s / G a A s heterojunction bipolar transistor large-signal characteristics," I E E E J . Quantum Electronics, V o l . 29, p. 2799, 1993. [30] K . E . Meyer, D . R. Dykaar, and G . A . Mourou, "Characterization of T E G F E T s and M E S F E T s using electro-optic sampling technique," in Picosecond Electronics and Optoelectronics, edited by Mourou, G . A . , and B l o o m , D . M . and Lee, C . H . , Springer-Verlag, New York, pp. 54-57, 1985. [31] T . M i n u r a , S. H i y a m i z u , T . Fuj i i and K . Nanbu, " A New Field-Effect Transistor with Selectively Doped G a A s / n - A l G a A s Heterojunction," Jpn. J . A p p l . Phys. V o l . 19, pp. L225-L227, 1980. [32] H . Morkoc and P . M . Solomon, "The H E M T : a Superfast Transistor," I E E E Spec-t r u m , pp. 28-35, February, 1984. Bibliography 130 [33] Jeffrey Frey and Dimitr i s E . Ioannou, "Materials and Devices for High-Speed Decices and Optoelectronic Applicat ions ," in Measurement of High-Speed Signals in Solid State Devices, edited by R. B . Marcus ed., V o l . 28, pp. 1-40, 1990. [34] P. C . Chao, A . J . Tessmer, K . H . G . D u h , P Ho, M . Y . K a o , P. M . Smith , J . M . Bl l inga l l , S. M . L i u and A . A . Tabra, "W-band Low-Noise I n A l A s / I n G a A s Lattice-Matched H E M T s , " I E E E Elec. Device Lett , V o l . 11, pp. 59-62, 1990. [35] C . R. Bolognesi, E . J . Caine, and H . Kroemer, "Improved Charge Control and Fre-quency Performance in InA s/AlSb-Based Heterostructure Field-Effect Transistors," I E E E Electron Device Letters, V o l . 15, pp. 16-18, 1994. [36] A . Ozgur, W . K i m , Z . Fan, A . Botchkarev, A . Salvador, S. N . M o h a m m a d , B . Sverdlov and H . Morkoc , " H i g h transconductance-normally-off G a N M O D F E T s , " Electronics Lett . V o l . 31, pp. 1389-1390, 1995. [37] S. N . M o h a m m a d , A r n e l A . Salvador, and Hadis Morkoc , "Emerging G a l l i u m Nitr ide Based Devices," Proceedings of the I E E E , V o l . 83, pp. 1306-1355, 1995. [38] Hadis Morkoc , "Recent Developments in high speed heterojunction devices: a tuto-r i a l , " I E E E International Symposium of Circuits and Systems, pp. 2532-2537, 1990. [39] L . D . Nguyen, A . S. Brown, M . A . Thompson, and L . M . Jelloian, "50-nm Self-aligned-gate Pseudomorphic A l I n A s / G a l n A s High Electron M o b i l i t y Transistors," I E E E Trans. Electron Devices, V o l . 39, p. 2007, 1992. [40] P. Ho , M . Y . K a o , P. C . Chao, K . H . G . D u h , J . M . Bal l ingal l , S. T . A l l e n , A . J . Tess-mer, P. M . Smith , "Extremely High Gain 0.15-pm gate-length I n A l A s / I n G a A s / I n P H E M T s , " Electronics Lett . , V o l . 27, pp. 325-327, 1991. [41] M . Y . Frankel, J . F . Whitaker , and G . A . Mourou, "Optoelectronic Transient Char-acterization of Ultrafast Devices," I E E E J . of Quantum Elec. V o l . 28, pp. 2313-2324, 1992. [42] N . C . C i r i l l o , Jr. , J . K . Abrokwah, A . M . Fraash and P. J . V o i d , " U l t r a - H i g h Speed R i n g Oscillatiors Based on Self-Aligned-Gate Modulat ion Doped A l G a A s / G a A s F E T s , " Electronic Lett . , V o l . 21, pp. 772-773, 1985. [43] U . K . M i s h r a , J . F . Jensen, A . S. Brown, M . B . Thonson, L . M . Jelloian and R. S. Beaubien, "Ultra-High-Speed Digi ta l Circui t Performance in 0.2 / /m Gate Length A l I n A s / G a l n A s H E M T Technology," I E E E Electronic Device Letters, V o l . 9, pp. 482-484, 1988. Bibliography 131 [44] M . Mat loubian , H . Fetterman, M . K i m , A . O k i , J . Camou, S. Moss, and D . Smith , "Picosecond Optoelectronic Measurement of S Parameters and Optica l Response of an A l G a A s / G a A s H B T , " I E E E Trans. Microwave Theory and Tech., V o l . 38, p. 683, 1990. [45] J . A . Sheridan, B . A . Nechay, D . M . B l o o m , P. M . Solomon and Y . C . Pao, "Direct Measurement of Transit T i m e Effects in M O D F E T s , " IEEE/International Electronic Device Meeting Technical Digest, 1994, PP- 579-582, 1994. [46] A . Zeng, M . K . Jackson, M . Van Hove, and W . De Raedt, "On-Wafer Characteriza-t ion of Ino.52Alo.48As/Ino.53Gao.47As Modulat ion-Doped Field-Effect Transistor with 4.2 ps Switching T i m e and 3.2 ps Delay" , A p p l . Phys. Lett . , V o l . 67, pp. 262-263, 1995. [47] J . A . Valdmanis , "Electro-optic measurement techniques for picosecond materials, devices, and integrated circuits," in Measurement of High-Speed Signals in Solid State Devices, edited by R. B . Marcus, Academic Press, San Diego, pp. 136-217, 1990. [48] A m n o n Yar iv , "Opt ica l Electronics", Fourth edition, Saunders College Publ ishing, p. 193, 1991. [49] " A l l Solid State Mode-locked Ti :Sapphire Laser," Product Information Manual , Clark Instrument Inc., 1991. [50] Terametrics, 1516 Fenway R d , Crofton, M D 21114, U S A . [51] Terametrics documentation 1992, Terametrics, 1516 Fenway R d , Crofton, M D 21114, U S A . [52] Melles Griot Catalog, "Optics Guide 5," pp. 14-4, 1990. [53] J . M . Chwalek and D . R. Dykaar, " A mixer based electro-optic sampling system for submill ivolt signal detection," Rev. Sci . Instrum., V o l . 61, p. 1273, 1990. [54] K . P. Cheung and D . H . Auston , " A Novel Technique for Measuring Far-Infrared Absorption and Dispersion," Infrared Phys. V o l . 26, pp. 23-27, 1986. [55] X . C . Zhang, B . B . H u , J . T . Darrow, and D . H . Auston , "Generation of Femtosecond Electromagnetic Pulses from Semiconductor Surface," A p p l . Phys. Lett . , V o l . 56, p. 1011, 1990. [56] X . C . Zhang, J . T . Darrow, B . B . H u , D . H . Auston , M . T . Schmidt, P. T h a m , and E . S. Yang, "Opt ica l ly Induced Electromagnetic Radiat ion from Semiconductor Surface," A p p l . Phys. Lett . , V o l . 56, p. 2228, 1990. Bibliography 132 [57] A . Zeng, S. Shah, and M . K . Jackson, "Reduced Invasiveness of Non-Contact Electro-Opt ic Probes in Mil l imeter-Wave Optoelectronic Characterization," to be publish in I E E E Trans. Microwave Theory and Techniques, Ju ly 1996. [58] T . Nagatsuma, T . Shibata, E . Sano, and A . Iwata, "Subpicosecond sampling using a noncontact electro-optic probe," J . A p p l . Phys. , V o l . 66, p. 4001, 1989. [59] T . Nagatsuma, T . Shibata, E . Sano, and A . Iwata, "Non-contact electro-optic sam-pling system in subpicosecond regime," 1990 I E E E Instrumentation and Measure-ment Technology Conference, p. 152, 1990. [60] D . Conn, X . W u , J . Song, and K . Nickerson, " A ful l wave simulation of disturbances in picosecond signals by electro-optic probing," 1992 I E E E M T T - S Int. Microwave Symp. Digest, p. 665, 1992. [61] X . W u , D . Conn, J . Song, and K . Nickerson, "Invasiveness of L i T a O s and G a A s probes in external E - 0 sampling," I E E E J . Lightwave Tech., V o l . 11, p. 448, 1993. [62] M . Y . Frankel, J . F . Whitaker , G . A . Mourou, and J . A . Valdmanis , "Experimental characterization of external electrooptic probes," I E E E Microwave Guided Wave Lett . , V o l . 1, p. 60, 1991. [63] W . M e r t i n , C . Roths, F . Taenzler, and E . Kubalek, "Probe t ip invasiveness at in-direct electro-optic sampling of M M I C , " 1993 I E E E M T T - S Int. Microwave Symps. Digest," p. 1351, 1993. [64] W . Von Wendorff, G . D a v i d , U . Dursum, and D . Jager, " Frequency domain char-acterization of a G a A s coplanar waveguide up to 40 G H z by electro-optic probing," Conf. Proc. L E O S ' 92, p. 119, 1992. [65] D . S. Phatak, N . K . Das, and A . P. Defonzo, "Dispersion characteristics of opti-cally excited coplanar striplines: comprehensive full-wave analysis," I E E E Trans. Microwave Theory Tech., V o l . 38, p. 1719, 1990. [66] H . J . Cheng and J . F . Whitaker , "Electro-Optic-Probe System Response: Exper i -ment and Simulat ion," private communication. [67] Y . Baeyens, D . Schreurs, B . Nauwelaers, M . Van Hove, W . De Raedt and M . Van Rossum, Proc. o f M I O P ' 9 5 , p. 345, 1995. [68] M . Van Hove, J . Finders, K . van der Zanden, W . De Raedt and M . Van Rossum, Y . Baeyens, D . Schreurs, B . Nauwelaers, A . Zeng, M . K . Jackson, "InP-based H E M T Technology for M M I C Applicat ions ," Proc. of S O T A P O C S ' 9 5 , Chicago Illinois, Oct.8-13, 1995. Bibliography 133 M . Moloney, F . Ponse, and H . Morkoc , "Gate Capacitance-Voltage Characteristic of M O D F E T s : Its Effect on Transconductance," I E E E Trans. Electron Dev. V o l . 32, pp. 1675-1684, 1985. M . Y . Frankel, "Ultrafast Device Characterization," P h . D . thesis, University of Michigan, A n n A r b o r , Michigan, 1991. N . M o l l , M . R. Hueschen and A . Fischer-Colbrie, "Pulse-doped A l G a A s / I n G a A s pseudomorphic M O D F E T ' s , " I E E E transactions on Electron Devices, V o l . 35, pp. 879-886. 1988. L . D . Nguyen, P. J . Tasker, D . C . Radulescu, and L . F . Eastman, "Characteriza-tion of Ultra-High-Speed Pseudomorphic A l G a A s / I n G a A s (on GaAs) M O D F E T ' s , " I E E E Tran. Electron Devices, V o l . 36, pp. 2243-2247, 1989. L . D . Nguyen, L . E . Larson, and Umesh. K . Mishra , "Ultra-High-Speed Modulat ion-Doped Field-Effect Transistors: A Tutorial Review," Proceedings of the I E E E , V o l . 80, pp. 494-518, 1992. H . Morkoc , G . U n l u , and G . J i , "Principles and Technology of M O D F E T s , " John W i l e y k Sons L t d . , V o l . 2, p. 379, 1991. H . R. Yeager, R . W . Dutton , "Circui t simulation models for the high electron mo-bi l i ty transistor", I E E E Trans. Electron Devices, V o l . 33, pp. 682-691, 1986. P. Robl in , S. K a n g , A . Ketterson and H . Morkoc , "Analysis of M O D F E T microwave characteristics", I E E E Trans. Electron Devices, V o l . 34, pp. 1919-1928, 1987. Mehran Bagheri , " A n improved M O D F E T microwave analysis", I E E E Trans. Elec-tron Devices, V o l . 35, pp. 1147-1149, 1988. D . J . Widiger , I. C . K i z i l y a l l i , K . Hess, J . J . Coleman, "Two-dimensional transient simulation of an idealized high electron mobi l i ty transistor", I E E E Trans. Electron Devices, V o l . 32, pp. 1092-1102, 1985. Dany Loret, "Two-dimensional numerical model for the high electron mobi l i ty tran-sistor", Solid State Electron, V o l . 30, pp. 1197-1203, 1987. V . Ravaioli and D . K . Ferry, " M O D F E T ensemble Monte Carlo model including the quasi-two-dimensional electron gas", I E E E Trans. Electron Devices, V o l . 33, pp. 677-681, 1987. T . E n o k i , K . A r a i , and Y . Ishii, "Delay T i m e Analysis for 0.4- to 0 .5 - / tm -Gate I n A l A s - I n G a A s H E M T s , " I E E E Electron Device Letters, V o l . 11, pp. 502-504, 1990. Bibliography 134 [82] P. J . Tasker and B r i a n Hughes, "Importance of Source and Dra in Resistance to the M a x i m u m ft of Mil l imeter-Wave M O D F E T s , " I E E E Electron Device Lett . V o l . 10, pp. 291-293, 1989. [83] N . Shigekawa, T . Furuta, and K . A r a i , "Time-of-flight measurement of electron velocity in an Ino.52Alo.48As/Ino.53Gao.47As/Ino.52Alo.4sAs double heterostructure", A p p l . Phys. Lett . , V o l . 57, p. 67, 1990. [84] M . K . Jackson, private communication. [85] S. A . Shah, A . Zeng, W . S. Wong, M . K . Jackson, L . Pouliot , A . Lecours and J . F . Curr ie , "Separating Temporally-Overlapped Waveforms with Electro-Optic Sampling," to be published in the Special Issue of Opt ica l and Quantum Electronics on Optical Probing of Ultrafast Devices and Integrated Circuits., July, 1996. [86] H . J . Cheng and J . F . Whitaker , "Electro-Optic Probes: High-Permit t iv i ty Crys-tals vs. Low-Permit t iv i ty Polymers," Technical Digest of Ultrafast Electronics and Optoelectronics 1995, pp. 128-130, 1995. [87] E . F . Chor , A . Brunnschweiler, and P. Ashburn , " A Propagation-Delay Expression and its Appl ica t ion to the Opt imizat ion of Polysil icon Emit ter E C L Processes," I E E E Journal of Solid-State Circui t , V o l . 23, pp. 251-259, 1988. Appendix A Principles of Electro-Optic Sampler In Chapter 1, we briefly described the principles of electro-optic sampling and saw that the optoelectronic sampler used in E O S system was actually an electro-optic modulator. In this appendix, we discuss the electro-optic effect and its application in E O S system in more detail . The details of electro-optic effect are well known, and their application in electro-optic sampling is well-established; see for example Ref. [47]. Here we briefly describe these details for those who is not familiar with the topic. A.0.1 Electro-Optic Effect Optical materials can be classified into two major groups by means of their optical prop-erties: isotropic materials and anisotropic materials. A n isotropic material is a material whose properties, such as the refractive index, do not depend on the direction (or po-larization) of the light. For example, fused silica, Si , and G a A s are isotropic materials. In contrast, the properties of an anisotropic material depend on the polarization of the optical beam. In other words, the refractive index of an anisotropic material depends on the direction of the electric field of the light. For example, K H 2 P O 4 ( K D P ) , quartz, and L i T a 0 3 are anisotropic crystals. In general, the relation between refractive index and polarization of an optical beam can be described concisely by using the index ellipsoid [10]: 4 + 4 + 4 = 1 ( A - 1 ) K nl n2t 135 Appendix A. Principles of Electro-Optic Sampler 136 Figure A . l : Index ellipsoid of a uniaxial birefringent crystal. x,y,z are the principal axes. n0 and n e are indices of ordinary and extraordinary beams, respectively. where x,y, and z are principal axes along which the electric field E and the electric displacement D of the optical beam are parallel; nx,ny, and nz are refractive indices for optical beams whose electric fields are along the corresponding directions x,y, and z. For an isotropic material , For a uniaxial anisotropic material , nx = ny = n0',nz — ne, where n0 and ne are the refractive indices of what are called the ordinary and extraordinary beams, respectively. F i g . A . l shows an index ellipsoid of a uniaxial crystal in its principal coordinate system. We can use the index ellipsoid to determine the refractive indices of an optical beam propagating in an arbitrary direction in an anisotropic crystal as follows. First , we draw a plane perpendicular to the beam direction and passing through the origin of the principal coordinate. Then, we determine the intersection of this plane with the ellipsoid; this is an ellipse or a circle. The dimensions of the major and minor radii of this intersection ellipse are the refractive indices of the Appendix A. Principles of Electro-Optic Sampler 137 beams whose electric fields are parallel to the major and minor axes of the intercept ellipse. For example, to determine the indices of a beam propagating along the y axis, we draw a plane perpendicular to the y axis and passing through the origin. The intersection of the ellipsoid and this plane is an ellipse with its major and minor radii equal to ne and reG, respectively. This means that a beam propagating in the y direction with z polarization w i l l experience a refractive index of ne while a beam propagating in the same direction but with x polarization w i l l experience a index of n0. This method of determining indices is not l imited to optical beams along the principal axes. It can also be used for optical beams wi th arbitrary directions. The property of the dual refractive indices of an anisotropic material is called birefringence. The z axis is often referred to as the optic axis of the crystal. The refractive indices for beams propagating in a direction parallel to the optical axis are independent of polarization and are equal to n0 in uniaxial crystal because the intersection of the xy plane and the ellipsoid is a circle. For light beams propagating in a direction perpendicular to the optical axis of a uniaxial crystal there are two refractive indices n0 and ne for beams with their polarizations perpendicular to and along the optical axis, respectively. Some isotropic materials can be changed into anisotropic materials in an electric field. For example, G a A s , InP, and ZnTe become anisotropic materials in the presence of an electric field. In addition, anisotropic material such as L i T a O s can change their degree of anisotropy in the presence of an electric field. In other words, the refractive indices in these materials change with the external electric field. This change of refractive index with external electric field is called the electro-optic effect. It only exists in crystals without inversion symmetry. For example, G a A s has a zincblende structure which does not have inversion symmetry and is an electro-optic material . W h i l e , Si with diamond structure which has inversion symmetry does not exhibit the electro-optic effect. The index ellipsoid can be used to determine the indices of electro-optic crystals as well . In Appendix A. Principles of Electro-Optic Sampler 138 general, wi th the presence of an external electric field, the ellipsoid of a material changes its shape and orientation, and the x, y, and z axes are no longer the principal axes of the ellipsoid. A s a result, there w i l l be cross terms xy,xz,yz in the index ellipsoid equation: , * 2 + ( h ) / + * 2 + 2 + 2 ( h ) . " + 2 ( h ) . * » = 1 <A-2> Where (^-^ (i = 1, • • • 6) are index ellipsoid coefficients due to an arbitrary electric field ~E(EX, Ey, Ez). W h e n the external electric field is zero, the above equation reduces to eq. A . l . G?)1 = 4f> (^)2 = 4' (^)3 = 4' (^)4 = 0 ' ("Os" 0 ' (^)e = 0 When an external electric field is applied, the change of the coefficient . is related to the applied field E(EX, Ey, Ez) by a 6 x 3 matr ix : / \ rn ri2 r i 3 Mi), Mi). = r-21 "^22 r 2 3 »"31 3^2 r 3 3 »~4i r42 r 4 3 r 5 i r 5 2 r 5 3 / F \ •tLrx Ey [ E 2 J (A.3) ^ r&\ r 6 2 r 6 3 Where r,j are the electro-optic coefficients, and the 6 x 3 matr ix is called the electro-optic tensor. Due to the symmetries of electro-optic crystals, most of the elements of the matr ix are zeros and some of the nonzero elements are of the same absolute values. This greatly reduces the complexity of the index ellipsoid equation. For example, in any materials with 43mor23 group symmetry, such as G a A s , InP, CdTe, and ZnTe, there are only three nonzero elements and all of them are equal r 4 1 = r 5 2 = r 6 3 [10]. In many applications, the external electric field is applied only along one of the axes, for example, the z axis. This further simplifies the field-modified index ellipsoid equation. We use G a A s as an example Appendix A. Principles of Electro-Optic Sampler 139 (the results can be applied to other III-V compound crystals wi th 43m group symmetry, including InP, In A s , CdTe and ZnTe). If an external field is parallel to the optical axis z which can be defined as any of the three cubic axes of G a A s crystal, equation A . 3 is simplified to: ' 0 0 0 0 0 0 A ( * ) 2 a ( * ) Mi) A(A) r 4 i 0 0 r 4 1 V 0 0 0 / 0 0 0 0 0 V Ez r 4 i / \ J or: \ A ( i ) 6 / 0 0 0 0 0 Substituting these zero and nonzero terms of A {j^j. into equation A . 2 , we obtain the field-modified index ellipsoid equation: x2 y2 z^ ~~2 + ~ + ~ + 2r4iEzxy = 1 n0 n0 n0 where no is the refractive index of G a A s when the external electric field is zero. To eliminate the cross term, we rotate the x,y,z coordinate about the z axis by 45 degrees and arrive at the principal axes x', y', z' of the field-modified index ellipsoid. The index ellipsoid i n the new coordinate system is: Appendix A. Principles of Electro-Optic Sampler 140 where nxi,nyi,nzi are indices for beams polarized along corresponding principal axes x',y',z'; under the assumption n^r^Ex <C 1 the induced indices can be expressed as: n 3 nx< = n 0 + Y r ^ E z (A.4) n3 ny> = n0 - -^-r41Ez (A.5) nz< = n0 (A.6) This means that if an optical beam polarized at 45 degrees wi th respect to the x' axis travels along the z' direction, the two components of this beam with polarization along x' and y' w i l l experience different refractive indices nx> and nyi which depend on the applied field. There w i l l be a phase retardation S between the two orthogonally polarized beams after passing through the crystal. S — —(nxi — nyi)l = —n30r41Ezl (A.7) where / is the thickness of the crystal; Ez is the external electric field in the z direction. A s a result, the linearly polarized beam becomes an el l iptically polarized beam after passing through the crystal. This is how an electric field can change the polarization of an optical beam through electro-optic effect as mentioned i n Chapter 1. A.0.2 Electro-Optic Intensity Modulator In Chapter 1, we briefly introduced the structure and principles of an electro-optic modu-lator. This section describes the electro-optic intensity modulator in more detail . F i g . A . 2 shows a typical intensity modulator which is composed of an electro-optic crystal , a com-pensator, and two polarizers (the second polarizer is usually called an analyzer). The electro-optic crystal in this example has the same electro-optic properties (symmetries) Appendix A. Principles of Electro-Optic Sampler 141 as G a A s . W h e n an external electric field is applied along the optic axis (z), the principal coordinates of the index ellipsoid rotate 45 degrees about the z axis and arrive at x', y', and z. The crystal is placed between the two orthogonal polarizers with its optical axis (z) parallel to the input beam direction. If the applied external field is zero, the optical beam w i l l maintain its linear polarization after passing through the e-o crystal. A s a re-sult, there is no light passing through the horizontally polarized analyzer (if we ignore the compensator for the time being). However, when an external field is applied to the crys-ta l , it induces birefringence in the crystal. Consequently, the e-o crystal w i l l change the linearly polarized beam into an ell iptically polarized beam. The horizontally-polarized component of the ell iptically-polarized light passes through the analyzer as output of the modulator. Since the polarization of the beam after passing the crystal changes with the strength of the external field, the intensity of the output beam also changes wi th the external field, or is modulated by the external field. In the following, we derive analytical expressions for an intensity electro-optic mod-ulator. Intensity modulators can be further classified into two types: longitudinal mod-ulator and transverse modulator by the relative directions of the optical beam and the applied electric field. In a longitudinal modulator, the optical beam is parallel to the applied electric field; in a transverse modulator, the optical beam is perpendicular to the electric field. Most of the electro-optic crystals can be used in both longitudinal and transverse configurations. However, only one configuration is most efficient which utilizes the largest electro-optic coefficients. For example, G a A s is most efficient in longitudinal configuration, while LiTaC*3 is most efficient in transverse configuration. F i g . A . 2 is a typical longitudinal intensity modulator where the applied electric field (z) is parallel to the optical beam. We assume the electro-optic crystal is G a A s and the electric field is applied to the z axis. A s described in the last section, the electrically induced principal axes x', y' Appendix A. Principles of Electro-Optic Sampler 142 fast axis slow axis Figure A . 2 : The schematic of a longitudinal electro-optic modulator. are at 45 degrees with respect to the x,y axes. To calculate the response, the linearly polarized input beam must be decomposed into two orthogonal components with equal amplitudes along x' and y' axes. A t the front facet of the electro-optic crystal z — 0, the two components Exi(0) and -£y(0) are in phase and can be expressed as: Exi{<S) — Aexp(jut) Ey'(0) = Aexp(jut) where A is the amplitude of the electric field in the x',y' directions; u> is the frequency of the light. Due to the electrically induced birefringence, the two components are out of phase at the back facet z = / and can be expressed as: Ex,(l) = Aexp[j(ut-^l)} Ey,(l) = Aexp\j(ut-=^-l)] where nx> and ny< are electrically induced indices given by eq.A.4 and eq.A.5. If we ignore the compensator for the t ime being and project the two components EX>{1) and Ey>(l) onto the polarization axis y of the output polarizer (or analyzer), we can calculate the output intensity Iy0 by using the sum of the projections on the y axis. The transmission Appendix A. Principles of Electro-Optic Sampler 143 can be written as: where TY 8 -KV \ = » - ( f ) = (A.8) K = -A- (A.9) 8 is the phase difference between the EX>{1) and Eyi(l) components and is given by eq.A.7; V is the external voltage applied across the crystal [EZ\ in eq.A.7) . K- is called half-wave voltage and is inversely proportional to the electro-optic coefficient r4\. It is the voltage at which the field-induced phase difference 8 is equal to IT and the linear polarization of the input beam is turned 90 degrees after passing through the crystal. A s a result, the output intensity of the modulator is equal to that the input intensity when V = Vv. Vx is often used as a figure of merit for describing a modulator. The smaller the half-wave voltage \4j the more sensitive the modulator is. We can use the data of Ref. [10] to calculate VT for G a A s ; the e-o coefficients are given at two wavelength 0.9 and 1.15 \xm. The corresponding K-'s for A 0 = 0.9 \xm and A 0 = 0.9 / i m are 17.6 k V and 19.8 k V showing a significant variation with wavelength. If we let the output polarizer be parallel to the x axis instead of the y axis, and project EXI{1) and Ey>{l) onto the x axis, we can obtain 1% . The transmission for this beam is given by the following equation: f = <»»(f) = (A.10) In some applications, both IQ and 1% are needed and can be obtained at the same time by using an analyzer which splits the input beam into two beams wi th orthogonal polar-izations. F i g . A . 3 is a plot of transmission versus applied voltage for the two orthogonally polarized output beams IQ and IQ. In general, the output beam does not vary linearly with the input beam. However, in the vic ini ty of 0 . 5 K , the transmitted beam changes Appendix A. Principles of Electro-Optic Sampler 144 Applied Voltage V (Vw) Figure A . 3 : Transmission of an electro-optic modulator with dual beam outputs. The solid line is for the output beam whose polarization is perpendicular to that of the input beam while the the dashed line is for the output beam whose polarization is parallel to that of the input beam. linearly with applied voltage. In addition, the modulation efficiency is also largest at V = 0.5K-. Due to these reasons, a small signal modulator is often biased at this point for efficient and linear modulation. However, this bias is not done electrically by applying a V = 0.5K- voltage across the crystal. Instead, it is done optically by using an opti-cal component called a compensator. A compensator is normally made of birefringent material and can produce a phase difference between two perpendicular axes, the fast and slow axes as shown in F i g . A . 2 . The simplest compensator is a quarter-wave plate which introduces a | retardation between two orthogonally polarized components. Some more complicated compensators allow continuous adjustment of the phase retardation. It should be pointed out that the fast and slow axes of the compensator must be parallel to the electrically induced axes x' and y' for proper phase compensation. Appendix A. Principles of Electro-Optic Sampler 145 Having discussed the function of the compensator, we can now modify eq.A.8 and A . 10 to incorporate the phase retardation introduced by the compensator. Since the fast and the slow axes of the compensator are parallel to the field-induced principal axes x' and y', the total phase retardation is the sum of the phase introduced by the crystal S and that by the compensator S0. The transmission of the modulator wi th a compensator can be written as: where S0 is the phase retardation introduced by the compensator and should be made tors using naturally birefringent crystals, such as LiTaO"3, the crystal itself introduces an intrinsic phase retardation Si which can be determined by using the natural birefringent indices raQ, n e and length of the crystal /. The retardation of the compensator S0 in this case is set at a value so that the sum of the intrinsic retardation Si and the compensator EL ii n (A. l l ) (A.12) equal to | for modulators using naturally isotropic crystals, such as G a A s . For modula-retardation SQ is equal to |, Si + SQ = \• Appendix B Components Used in the EOS System B . l Items used in EOS System • Polarizer The polarizer is a Melles Griot Glan-Thompson prism which made of birefringent material calcite and has an extinction ratio smaller than 1 x 1 0 - 5 . Its transmission is larger than 98% in the wavelength range 650-1100 n m . • analyzer The analyzer is a Melles Griot Wollaston prism. It is a cube made of two right angle calcite prisms of orthogonal optical axes. When an optical beam passes through the interface of the two prisms, the ordinary beam and the extraordinary beam i n the first prism become extraordinary and ordinary beam in the second prism, respectively. A s a result of refraction at the interface, the input beam is split into two orthogonally polarized beams. The Melles Griot Wollaston prism has an extinction ratio smaller than 1 x 1 0 - 5 in the wavelength range 650-1100 n m . The angle between the two output beams is 20 degrees. • custom-designed photoreceiver • complete diagram of the E O S system 146 Appendix B. Components Used in the EOS System 147 Figure B . l : Circui t diagram of the custom-designed photoreceiver. (The author acknowl-edges M r . R o d Calinisan for making the diagram.) Appendix B. Components Used in the EOS System 148 Figure B.2: Complete Diagram of the E O S System A p p e n d i x C A M e t h o d for D e t e r m i n i n g P h a s e R e t a r d a t i o n In the process of setting up our electro-optic sampling system, we needed to know the tuning range of the optical compensator, the intrinsic phase retardation of the probe t ip , and the orientation of the optical axis of the probe t ip . In this appendix, we describe a simple method we developed for determining phase retardation. First , we describe how to measure the phase retardation of an anisotropic crystal. Then we describe how to use the method to determine the optical axis of a probe t ip . F i g . C l shows the simple experimental setup. It uses a laser, two polarizers and a power meter. The probe t ip or compensator under testing is placed between the two polarizers. The polarization or axis of the first polarizer (the one closer to the laser) is set vertically. The optical axis of the crystal under test is set at 45 degrees wi th respect to the polarizer. The second polarizer or analyzer can rotate about its normal axis which is parallel to the incident beam. Its polarization is either set to be parallel or perpendicular to the axis of the first polarizer. The power meter after the analyzer measures the laser powers Ia and corresponding to the two analyzer positions. It is obvious that the linearly polarized laser beam w i l l become el l iptical ly polarized after passing through the crystal under test due to the phase retardation 6 introduced by the crystal. It can be shown that the major and minor axes of the el l iptical ly polarized beam are parallel to the axes of the two analyzer positions described above. In other words, the Ia and are the decomposed intensities of the el l iptically polarized beam along its major or minor axis. A t this experimental configuration, it can be shown that 149 Appendix C. A Method for Determining Phase Retardation 150 Crystal Under Test Polarizer Analyzer Power Meter Figure C . l : Experimental setup for measuring the phase retardation of an anisotropic crystal. The analyer can be rotated about the laser beam axis. the retardation S can be calculated from Ia and /(, by using the following formula: ='trn (ai) It should be pointed out that the above formula can only be used for the above specific experimental configuration. If the optical axis of the crystal under test is not set at 45 degrees with respect to the polarizer, the formula cannot be used. We have used this setup to measure the tuning range of the phase retardation introduced by the compensator. The results are plotted in F i g . 2.6. This method can also be used to determine the orientation of the optical axis of a probe t ip . F irst , we set the two polarizers perpendicular to each other. Then, we rotate the probe t ip about the axis normal to its foot print. We find two axes (angles) which give the m i n i m u m power-meter readings. These two axes are perpendicular to each other are either parallel or perpendicular to the axis of the polarizer. One is the fast axis, the other is the slow axis. But at this point, we don't know which is which. B y inserting a known quartz wave plate into the beam and set the optical axis (slow axis) of the plate at 45 degrees to the polarizer, we can determine which of the two axes is the optical axis of the probe t ip . If the measured total retardation is equal to the sum of the individual Appendix C. A Method for Determining Phase Retardation 151 phase retardation of the probe t ip and the wave plate, the slow axis of the probe t ip is parallel to the optical axis (slow axis) of the wave plate. If the measured total retardation is equal to the difference of the individual phase retardation of the probe t ip and the wave plate, the fast axis of the probe t ip is parallel to the optical axis of the wave plate. It should be pointed out that the optical axis of a probe t ip could be either the slow axis or the fast axis depending one the what type of e-o crystal is used. For L i T a O s crystal, the slow axis is the optical axis. Appendix D M O D F E T M a s k Layouts Figure D . l : Mask Layout for a Single-Gate-Contact M O D F E T wi th Cascade electrod for R F measurement. 152 Appendix D. MODFET Mask Layouts Figure D.2: Mask Layout for a double-Gate-Contact M O D F E T wi th Cascade electro for R F measurement. Appendix D. MODFET Mask Layouts 154 Figure D.3 : Mask Layout for a Single-Gate-Contact M O D F E T wi th coplanar striplines for E O S measurement. Appendix D. MODFET Mask Layouts 155 Figure D.4: Mask Layout for a double-Gate-Contact M O D F E T with coplanar striplines for E O S measurement. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0065316/manifest

Comment

Related Items