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

CHARACTERIZATION  OF HIGH-SPEED ELECTRONIC DEVICES  USING ULTRAFAST LASERS  By A n Zeng B. E n g . Tsinghua University, Beijing, C h i n a , 1985 M . A . S c . Institute of Semiconductors, Chinese A c a d e m y of Sciences, 1988 M . S c . University of B r i t i s h C o l u m b i a , Vancouver, Canada, 1992  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF  PH.D.  in T H E FACULTY OF G R A D U A T E STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING  We accept this thesis as conforming to the required standard  T H E UNIVER-SITY OF BRITISH COLUMBIA  M a y , 1996 © A n Zeng, 1996  In  presenting this  degree at the  thesis in  University of  partial  fulfilment  of  the  requirements  British Columbia, I agree that the  for  an advanced  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  department  or  by  his  or  her  representatives.  It  is  by the  understood  that  head of copying  my 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 ( E O S ) . T h e author has built an E O S system w i t h subpicosecond temporal resolution and TeraHertz b a n d w i d t h . Due to the design of the E O S system, signal propagation delay time through an electronic device can be accurately determined i n addition to the input and output waveforms. We performed an experimental study of the measurement errors and invasiveness caused by an external L i T a O a probe used i n the E O S system.  We found that contact (air  gap free) external electro-optic sampling, which has been widely used i n E O S measurement, could lead to more serious measurement errors than previously reported due to probe-tip induced dispersion and reflection. These unwanted effects can be m i n i m i z e d 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 significant 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 i m e of a lattice-matched Alo.48As/In .53Gao.47As M O D F E T are 4.2 ps and 3.2 ps, respectively. 0  In .520  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  11  r  parasitic gate inductance of the integrated structure is about an order of magnitude smaller than that of the wire-bonding structure. W e studied the effects of different gateaccess structures, semiconductor materials, and bias conditions on the performance of M O D F E T s . O u r 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. W e clarified two common misconceptions i n the literature regarding the relationships among the delay times, switching time, and current-gain cutoff frequency of a M O D F E T . T h e signal propagation delay time observed in a M O D F E T switching response and the delay time r  d  small-signal R F measurement cannot be used interchangeably. the two delay times T  PROP  =  T  PROP  -^-r defined i n  However, we find that  and T have similar dependence on drain bias Vd , showing  that they are closely related.  D  s  Further, the 10-90% rise time of the M O D F E T switch-  ing response cannot be directly related to the current-gain cutoff frequency f  t  as has  been suggested. T i m e - d o m a i n 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. T h e results are i n 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.  Finally, 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 1  Introduction  1  1.1  Introduction to Thesis  1  1.1.1  Overview  1  1.1.2  Outline of Chapter  1.2  1.3  1.4 2  xi  .  2  Introduction to Characterization Techniques  2  1.2.1  Conventional A l l - E l e c t r o n i c Methods  2  1.2.2  Ultrafast-Laser-Based Techniques  5  Recent Work on Ultrafast Device Characterization  12  1.3.1  Passive Devices  13  1.3.2  A c t i v e Devices  .  Outline of the Thesis  18 26  Experimental Techniques of Electro-Optic Sampling  29  2.1  Introduction to Chapter  29  2.2  Overall Layout and Design  29  2.3  Optical System  32  2.3.1  32  Laser System  iv  3  4  2.3.2  Electro-Optic Sampler  34  2.3.3  Optical Compensator  39  2.3.4  V i e w i n g Systems  2.3.5  C o m m o n T i m e A x i s for M u l t i p l e Probing Positions  <  44 49  2.4  Noise Reduction and Sensitivity  52  2.5  Resolution and Linearity  55  Measurement Errors and Invasiveness of External E O S Probes  58  3.1  Introduction  58  3.2  Motivation and Background  58  3.3  Experiment  60  3.4  Results and Analysis  61  3.4.1  Risetime and A m p l i t u d e  61  3.4.2  Sensitivity  69  Electro-Optic Characterization of M O D F E T s  72  4.1  Introduction  72  4.2  Lattice-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  4.4  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  S P I C E Modeling  96  4.4.1  97  Motivation v  5  4.4.2  Lumped-Element M o d e l  98  4.4.3  M o d e l i n g Results  108  4.4.4  Analysis  115  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  B  A.0.1  Electro-Optic Effect  135  A.0.2  Electro-Optic Intensity M o d u l a t o r  140  Components Used in the E O S System  146  B.l  146  Items used i n E O S System  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  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  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 i T a O s Externa] Electro-Optic Sampler  37  2.4  Schematic diagram of an external probe tip  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  Ino.52Alo.48As/Ino.53Gao.47As  vii  MODFET  . .  . . .  21  27  2.10 E O S V i e w i n g 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 time resolved E O S measurements  66  3.6  Risetime as a Function of A i r Gap  67  3.7  Sensitivity of E O S as a Function of A i r G a p  69  4.1  Layer Structure of a L M  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  MODFET  .  79  4.5  Dependence of Drain Bias of an  Ino.52Alo.48As/Ino.53Gao.47As  MODFET  .  81  4.6  Gate-Bias Dependence of a  4.7  Characteristics of Nonlinear Switching of a  MODFET  Ino.52Alo.48As/Ino.53Gao.47As  Ino.52Alo.48As/Ino.53Gao.47As  74  MODFET . . . .  Ino.52Alo.4sAs/Ino.53Gao.47As  MODFET 4.8  4.9  Switching Response of a  82  84 Ino.52Alo.48As/Ino.53Gao.47As M O D F E T  with Double-  Gate-Access Structure  86  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 . 2 5 G a o . 7 A s M O D F E T with 0  Single-Gate-Access Structure  5  93  vin  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 4.15 Effects of C  gs  4.16 Effects of C  gd  102  on the Response of M O D F E T s  105  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 L  109  g  on the Response of M O D F E T s  4.19 The Measured and Simulated Responses of a Ino.52Alo.48As/Ino.53Gao.47As MODFET  110  4.20 The Measured and Simulated Responses of a Ino.20Gao.80As/Alo.25Gao.75As MODFET  113  4.21 T h e Measured and Simulated Drain Outputs of a Discrete M O D F E T 4.22 The E O S Measurement of the Gate Input of a Discrete M O D F E T  . .  . . . .  116 118  4.23 Simulations with and without Input Transmission Line  119  A.l  Index Ellipsoid  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 V a n 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 engineering. 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 University G r a d uate Fellowship and St. John's Graduate Fellowship. Finally, 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 C h i n a , I could never have achieved what I have achieved.  xi  Chapter 1  Introduction  1.1 1.1.1  Introduction to Thesis 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 ( E O S ) — 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 characterization techniques, which makes the characterization of these high-speed electronic devices a challenge to research engineers around the world. T h e work described in this thesis is composed of two major topics i n the electro-optic characterization of highspeed 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 , pseudomorphic 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 w i t h coplanar stripline fixtures incorporating photoconductive switches. We also conducted the time-domain simulation of the M O D F E T s monolithically integrated with test fixtures by using a lumped-element  1  2  Chapter 1. Introduction  model incorporating input and output transmission lines. T h e simulations are in excellent agreement with the electro-optic measurements.  1.1.2  Outline of Chapter  T h e 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. B o t h passive devices and active devices are presented with emphasis on active devices. Finally, in Section 1.4, we describe the outline 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 measurement devices—network analyzer and sampling oscilloscope. Section 1.2.2 describes two laser-based techniques — photoconductive sampling and electro-optic sampling. T h e purpose of this section is to provide background knowledge of the high-speed characterization 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. T h e two most widely-used items of equipment are the network analyzer and  3  Chapter 1. Introduction  the sampling oscilloscope, which work i n 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 electronic 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 V  nT  (  and V i (phasors) to each other as follows: n  Sn  S\  n  \ I Vu \ (1.1)  \ V  nr  where V  nr  )  Sn  \ V  ni  J  and V { are reflected and incident voltage phasors. n  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. T h e 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 built-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. Current 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 i n using a N A . T h e 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 . T h e l i m i t e d 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 conventional technique for characterizing high-speed electronic devices. There are two types of sampling oscilloscopes: real-time S O and equivalent-time S O . T h e former is mainly used for nonrecurrent signals which are sampled by an array of relatively-delayed sampling gates. T h e 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. T h e w i d t h of the gate is very narrow compared with that of the signal to be measured. W h e n 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 time 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. T h e time scale of the measurement is determined by the relative delay time, which is why this sampling method is called equivalent-time sampling. T h e resolution of a S O is limited by the width of its sampling gate and the jitter of its delay and trigger circuits. T h e state-of-the-art S O is a superconducting S O 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.  5  Chapter 1. Introduction  1.2.2  Ultrafast-Laser-Based Techniques  From the above discussion it is apparent that the conventional all-electronic characterization methods have some limitations i n characterizing very high-speed devices. T h e bandwidth of some newly developed devices has exceeded that of the conventional techniques.  T w o methods based on ultrafast lasers have been developed with bandwidth  significantly greater than that of conventional methods. T h e y are photoconductive sampling ( P C S ) and electro-optic sampling ( E O S ) . In Section 1.2.2, we describe the common features of time-resolved p u m p / p r o b e measurement using laser-based techniques. T h e n we briefly discuss photoconductive sampling and electro-optic sampling; further details of E O S are given later in Chapter 2 and A p p e n d i x A .  Time-resolved pump/probe experiment In this section, we introduce the basic ideas of p u m p / p r o b e experiments, which are essential to photoconductive sampling and electro-optic sampling. Time-resolved p u m p / p r o b e experiments have been used to measure fast electrical signals as well as physical parameters such as hot carrier relaxation time in semiconductor materials[3] and carrier tunneling time in quantum well materials[4, 5]. T h e experimental setups for these measurements are similar. Here, we only discuss the measurement of fast electrical signals. T h e 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 . T h e laser output is optically split into a p u m p and a probe beam.  T h e pump beam triggers a pulse  generator to provide an ultrafast electrical input to the device under test ( D U T ) . T h e 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. T h e optical delay line has the same function as the electrical delay line i n 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 p u m p / p r o b e delay. A s the optical path is in air, the delay can be simply related to the change i n 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 i n air. T h e factor of 2 comes from the fact that the beam is reflected from the retroreflector and thus travels twice Al. Because the delay time 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 will discuss i n 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 i n F i g . 1.2 (dotted-line box). W h e n 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 time of the electrical  7  Chapter 1. Introduction  optical delay line Al K -  A.  mode-locked laser  probe  P-  pump optoelectronic tannpler  optoelectronic generator  DUT  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 i m e of less than 1 ps while a lowdefect semi-insulating G a A s has a decay time of 40-300 picoseconds. T h e 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. T h e 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 i n 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. T h e structure of the photoconductive switch is slightly different from the one shown in F i g . 1.2 . T h e three-electrode structure allows  8  Chapter 1. Introduction  laser pulse  e l e c t r i c a l pulse  Load  metallic transmission l i n e  photoconductive material !  Figure 1.2: A typical optoelectronic signal generator used in p u m p / p r o b e 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. T h e difference here is that the sampler is biased by the electrical signal on the transmission line instead of a D C supply as i n a pulse generator.  W h e n a probe light-pulse strikes the gate, it creates a very large  carrier density in a very short time at the gate gap and diverts a small part of the signal from the main coplanar stripline electrode to the sampling electrode.  T h e 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. O n l y 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. T h e 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  9  Chapter 1. Introduction  optical delay line  Figure 1.3: A simplified photoconductive sampling system. T h e pulse generator, the D U T , and the sampling gate are connected by stripline. T h e retroreflector can move horizontally to provide relative delay between the pump pulse and the sampling pulse. laser pulses to activate signal generator and sampler. T h e sensitivity and signal-to-noise ratio of photoconductive sampling are extremely good. T h e typical sensitivity is a few [iV/y/Wz,  permitting 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 i n a circuit. Recent development of mobile photoconductive sampling t i p has shown promising progress in solving this problem[8]. Electro-optic sampling to be discussed i n the next subsection provides an excellent way to measure waveforms of electrical signals at several locations of a circuit.  10  Chapter 1. Introduction  optical delay line <—  mode-locked laser  K  1\  ^  V/  pump  X  data acquisition & analysis  z "^Jdetector analyzer DUT 3KL  /  1  V:  eos probe  Figure 1.4: A n electro-optic sampling system uses an electro-optic modulator as its sampler. T h e electro-optic modulator is composed of a polarizer, a compensator, an electro-optic probe, and an analyzer. T h e other parts of the system is similar to those of a P C S system. Electro-Optic Sampling 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. W h e n 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 i g . 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. T h e pulse generator used in E O S is of the same  11  Chapter 1. Introduction  structure as that described in the previous section. T h e electro-optic probe is made of electro-optic crystal, such as LiTaO"3. T h e 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 vicinity of the electrodes. T h e axis of the polarizer is set at 45 degrees with respect to the optical axis of the electro-optic crystal. T h e 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. T h e two components experience different refractive indices because of the birefringence. A s a result, the polarization of the probe beam is changed (modulated) by the fringing electric field. T h e analyzer placed after the electro-optic probe turns this change of polarization into a change of intensity. T h e 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].  T h e 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 A p p e n d i x A . Like in a P C S system, every light pulse generated by an ultrafast laser is split into two by an optical beamsplitter.  T h e pump pulse is directed to the pulse generator  which generates an electrical impulse as input for the D U T . T h e output of the D U T coupled into a output coplanar stripline. T h e probe pulse passes through the sampler, or electro-optic modulator. T h e amplitude 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 i m e as the probe pulse. A s a result, the relatively long electric signal is sampled by the very narrow optical probe pulse. Unlike in a P C S , the sampled signal is carried by light-pulses i n 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  12  Chapter 1. Introduction  pulse and reconstruct the shape of the electric pulse after collecting enough points. T h e temporal resolution of an E O S system is mainly determined by the width of the probe pulse, the transient t i m e 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 t h i n , 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 w i t h 200 fs F W H M (full width at half m a x i m u m ) using an E O S system [11]. T h e sensitivity and signal to noise ratio of electro-optic sampling are reasonably good though not as good as P C S . T h e typical sensitivity is a few m V / \ / H z . Since the electro-optic crystal can be positioned at different locations i n a circuit, it is very flexible i n 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. T h e 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 i n this thesis are made with a custom-made electro-optic sampling system which will be described in detail i n Chapter 2.  1.3  Recent  W o r k  on Ultrafast  Device  Characterization  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 i n this area, but  13  Chapter 1. Introduction  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 including 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 devices 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, radiation 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 mechanisms, 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 i n d 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, G u p t a and co-workers measured the waveforms of a picosecond electric pulse at five propagation distances [16] . T h e picosecond pulse is generated by a low-temperature G a A s photoconductive switch incorporated in a coplanar wave guide. F i g . 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.  T h e pulse width broadens considerably, the amplitude drops dramatically, and  ringing features develop at the tail 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. T h e main features agree very well with those of the experiment. T h e authors concluded that the modal dispersion and radiation loss are the dominant pulseshaping mechanisms for picosecond pulses. A s the conductor loss plays a minor role i n the pulse shaping, the use of superconductor electrodes will 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. T h e results also apply to coplanar striplines.  Pulse F o r m i n g Devices Picosecond electrical pulses are needed in many ultrafast applications, such as S-parameter measurement of ultraf?.st transistors. A l m o s t a l l 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 photoconductivelygenerated electrical impulse is normally of a very fast risetime m a i n l y determined by the optical pulse width and the R C constant of the switch/transmission line structure and a trailing tail determined by the carrier lifetime of the photoconductive substrate. To obtain ultrashort electrical pulses, photoconductive materials w i t h short carrier lifetimes have been used as the substrates of photoconductive switches. Radiation-damaged material 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 processing procedures.  Alternatives to these devices are pulse-forming optoelectronic devices  Chapter 1. Introduction  15  1  n  _  0.8 0) XD  Q. E  0.6 0.4  _  0  X : Gaussian fit  >  -  0.5 mm 1.0 mm  3  —  '  '•  /  \  >  I  0.2  0.0 mm  \ \ 1  /  J 1  '* /  \' '  \  •ii. /••'" *rx •• « '—-~ ,  -0.2  ,  ,  i  3.0 mm -\ ' \ 5.0 mm / v .  , _i—i—L. i  4  r^  \  \  x  i  6  i  (a)  1 i  , ,  8  1 ,  10  12  10  12  time (ps)  0.0 mm  0.5 mm CD  1.0 mm  3 CL  E  CO  5.0 mm  ii -i_i  4  6  i  8  i i_  time (ps) 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. F r o m reference [16] .  16  Chapter 1. Introduction  which are coplanar transmission lines with specially designed impedance-mismatched structures.  T h e 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 i g . 1.6 (a) is a top view of the device.  It is composed  of a coplanar stripline integrated with a photoconductive switch and an impedancemismatched structure. T h e electrodes are deposited on a semi-insulating G a A s substrate. T h e photoconductive switch generates two step-like electrical pulses travelling in the opposite directions along the stripline.  T h e step-like pulse travelling towards the left  is reflected by the impedance-mismatched structure and changes its sign and travelling direction. W h e n the reflected (inverted) step-like pulse superimposes with the step-like pulse travelling toward right, the tails of the step-like pulses cancel and a pulse is formed. T h e width of the pulse is determined by the round-trip time 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 d\ l  T h e best result is obtained with d — 0 \im where unit reflectivity is obtained. Electrooptic sampling was used to measure the electrical pulse at position ' A ' . F i g . 1.6 (b) shows the picosecond electrical pulse generated by the pulse-forming device.  Chapter 1.  Introduction  17  OPTICAL PULSE  PC  V////////S  (a)  T I M P E D A N C E MISMATCH S T R U C T U R E  1  i  10  p. m  1.0  f 3  \  /  3.  S c  /  •5  /  -'  0.5  / /  / /  I  1 r-  '  r*/  \ \ 1-3 PS  (b)  I" 1  \  /  \ \.  V  \  .  _  6  4  10  Time (ps)  Figure 1.6: (a) Top view of a pulse-forming optoelectronic device fabricated on semi-insulating G a A s substrate. T h e separation of the stripline electrodes is 13 fim. T h e 'cf in the impedance-mismatched structure can be varied from 0 (im (short circuited) to 13 (im (impedance matched), (b) Picosecond electrical pulse generated by the pulse-forming optoelectronic device. From Reference [20]  18  Chapter 1. Introduction  (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 ( R T D ) which are active electronic devices. T h e y are of use i n high-speed applications including high-speed oscillators and high-speed pulse generators. R T D - b a s e d 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 quant u m well made of a narrow-bandgap material sandwiched between two wide-bandgap barriers.  T w o heavily-doped layers of the narrow-bandgap material act as electrodes.  F i g . 1.7 shows the conduction band structure where the dashed line represents the lowest energy level in a quantum well. W h e n a voltage is applied, the potential energy of the negative electrode increases, as shown in F i g . 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 condition, the device is said to be at resonance. Further increase in the applied voltage breaks the resonant tunnelling condition and results in a dramatic decrease in current. T h e 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. T h e switching time is 1.7 ps. From reference [24] reaches a valley and then increases again with the applied voltage due to non-resonant mechanisms. F i g . 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. T h e R T D divides the transmission line into two sections: input and output. W h e n 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. T h i s 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 i g . 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 widebandwidth 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 resistors and size of the active area on the bandwidth of a photodiode[26]. F i g . 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 parisitics, the two 7 / i m x 7[im diodes are integrated with load resistors, bypass diodes, and output coplanar waveguides. T h e 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. T h e upper curve in F i g . 1.9 (a) is the response of a discrete 2/zmx 2\im photodiode without a matched resistor. T h e lower two curves are responses of two 7p,mx 7/im integrated photodiodes with and without matched resistors. T h e 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 i g . 1.9 (b) shows the corresponding Fourier transform of the three t i m e resolved measurements. T h e 3 d B 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—  i  0  . . . .  i  5  • .  .  .  i  .  10  .  .  .  r  i  15  i  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 photodiodes. (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 including modulation-doped field-effect transistors ( M O D F E T s ) [ 2 7 , 28], heterojunction bipolar transistors ( H B T s ) [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. T h e modulation-doped field-effect transistor ( M O D F E T ) is also known as a highelectron-mobility transistor ( H E M T ) , a two-dimensional-electron-gas field-effect transistor ( T E G F E T ) , and a selectively-doped heterostructure transistor ( S D H T ) [31] -[32]. In F i g . 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 . T h e M O D F E T is grown on a semi-insulating G a A s substrate and has four layers: the G a A s layer and the very t h i n 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 G a A s is lower than that of A l G a A s as shown in F i g . 1.10 (b), the conduction-band electrons from the n - A l G a A s layer will accumulate in the undoped G a A s layer. Because of the attractive Coulomb force from the ionized dopants in the n - A l G a A s layer, the electrons will remain near the interface and form a 2-dimensional conducting channel between the drain and the source. T h e 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 l G a A s layer. There are two main reasons for the high performance of M O D F E T s . T h e first is that the conducting channel is formed in undoped material. T h e low doping reduces ionized i m p u r i t y scattering, and electrons have a higher mobility than in a conventional G a A s M E S F E T , where the conducting channel is formed in a doped layer. A l t h o u g h the M O D F E T is often operated w i t h the channel velocity saturated, during switching the channel spends time below velocity saturation, and it is  Chapter 1. Introduction  SOURCE  n  23  GATE  DRAIN  n  n-AlGaAs  2 DEG  AlGaAs  GaAs Buffer  GaAs  METAL  - - - - -  El  ;V  AEc  s  VEo L  Ec EF  . . .s  (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]) •  24  Chapter 1. Introduction  in this t i m e that the increased channel m o b i l i t y is significant. T h e high electron m o b i l i t y is also significant i n reducing the parasitic resistances i n series with the source and drain contacts. T h e second reason for the high performance is that i n a M O D F E T the widebandgap layer acts as an insulator between the gate and the channel. T h e 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 . T h e gate control of the channel charge can be very effective w i t h t h i n widebandgap layers, resulting i n very high transconductance.  T h i s is i n contrast w i t h 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 limitations to the gate-to-channel separation possible in M E S F E T s , which l i m i t their scaling to higher frequencies. T h e 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 i n 1980[31]. Several combinations of heterostructure 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 ( G a A s substrate), pseudomorphic A l G a A s / I n G a A s M O D F E T ( G a A s 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].  M o r e 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]. M o s t of the M O D F E T s are fabricated on G a A s or I n P substrates with their conducting channels either in G a A s or I n G a A s . M O D F E T s with I n G a A s conducting channels have demonstrated better performance than those with G a A s conducting channels largely because of the increased confinement of the two-dimensional electron gas. T h e electron m o b i l i t y i n I n G a A s can also be higher than that in GaAs[38]. T h e current gain cut-off frequency f , where the short-circuit current gain goes to t  unity, and the m a x i m u m oscillation frequency /  m 0  x , where the power gain goes to unity,  25  Chapter 1. Introduction  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 w i t h f = 110 G H z a n d f t  max  =  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 w i t h f = 340 t  G H z [39] and f  max  = 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 i m e 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 w i t h 0.85 pm gate length[42].  AlInAs/GalnAs M O D F E T s  with 0.2 fim gate length i n a ring oscillator have demonstrated 5 ps/gate delay t i m e at 77 K (6 ps/gate at room temperature) [43]. T h e 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. T h e 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 electrooptic 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 i n a common-gate configuration, and have a very low current-gain cut-off frequency of 2.5 G H z . T h e switching t i m e and the delay t i m e measured by electro-optic sampling are 5 ps and 9 ps, respectively.  26  Chapter 1. Introduction  l  1  1  1  1  r  Time (5ps/div) Figure 1.11: T h e drain output of the M O D F E T with increasing input signals: A V ^ , 1.9AV^, 2.7 AV , 3 . 6 A K , , and 4AAV , where AV is approximately 0.17V.(From reference g  g  g  [27]) T h e 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 highspeed M O D F E T s , and is shown in F i g . 1.12. W e reported the first electro-optic measurement of a high-speed M O D F E T monolithically integrated w i t h a photoconductive switch and coplanar stripline fixture[46]. F i g . 1.12 shows the electro-optic measurement of the lattice-matched Ino.52Alo.48As/Ino.53Gao.47As M O D F E T , which has a current-gain cut-off frequency f = 78 G H z . T h e lower panel shows four input signals at the gate. T h e upper t  panel shows the corresponding drain output. W e will discuss the experiment and results in more detail in later Chapters.  27  Chapter 1. Introduction  >  10  •  1  15  i  I  1  20  1  25  1  L_  30  Time (ps) Figure 1.12: Switching response for an Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T on InP substrate. T h e 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 i n Chapter 4.  Chapter 1. Introduction  1.4  28  Outline of the Thesis  Chapter 2 describes the electro-optic sampling system. T h e design considerations of our E O S system are described i n detail including overall layout, laser systems, E O S optics, viewing systems, and electronic systems, emphasizing the original aspects of its design. T h e 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 invasiveness caused by an external L i T a O a 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 i n E O S measurement, can lead to measurement errors. However, these errors can be reduced by using a non-contact arrangement with an air gap between the t i p 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 monolithically-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. T h e effects of different gate-access structures, semiconductor materials, and bias conditions on the performance of M O D F E T s are studied. W e also describe a time-domain simulation of the M O D F E T s using a lumped-element model incorporating input and output transmission 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 i n 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, built, and tested a computerautomated electro-optic sampling system with TeraHertz bandwidth.  T h e 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 A p p e n d i x A for readers who are not familiar 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. T h e noise reduction electronics and sensitivity are described in Section 2.4. Finally, in Section 2.5, we describe linearity 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 i g . 2.1 shows a block diagram of the E O S system. It shows more detail than F i g . 1.4 in Chapter 1 and consists of a mode-locked laser, an acousto-optic modulator ( A O M ) , an optical delay line, two viewing microscopes, a probe t i p , 3-D translation stages, optics, and data  29  Chapter 2. Experimental Techniques of Electro-Optic Sampling  mode-locked laser  1  Y  ^  30  optical delay line  probe  1  pump  polarizer  pump focusing & viewing  probe focusing & viewing  analyzer  A  <K"* Data acquisition N * electronics  Y2.  3  V  ^compensator  DUT  probe tip  Translation Stage  Figure 2.1: Block diagram of a complete E O S system built i n our lab. acquisition electronics; the device under test ( D U T ) is also shown. T h e basic structure is similar to the first electro-optic sampling system reported by Valdmanis and coworkers[9]. T h e acousto-optic modulator i n the p u m p beam path is used to modulate (chop) the p u m p beam intensity so that a lock-in amplifier can be used to improve signal-tonoise ratio. This is required because from the discussion i n A p p e n d i x A we can see that to achieve a sensitivity of 1 m V w i t h t y p i c a l half-wave voltages on the order of 3 k V ( L i T a O s ) we must be able to detect the extremely small fractional change i n intensity at  Chapter 2. Experimental Techniques of Electro-Optic Sampling  31  the output analyzer which is less than one part i n 10 . A s a result, the small electro-optic 6  signal is normally buried i n the noise. A lock-in amplifier allows us to detect the electrooptic signal. T h e two focusing/viewing systems are two specially-designed microscopes which are used to align and focus the p u m p and the probe beams at desired positions, and allow precise alignment of the probe t i p w i t h respect to the sample. T h e polarizer, analyzer, compensator, and the probe t i p shown i n F i g . 2.1 form an intensity electrooptic modulator described i n A p p e n d i x A . However, L i T a O s is used as an electro-optic crystal instead of G a A s . This is because the L i T a O s crystal has a much smaller half-wave voltage V (2.7 k V ) compared to G a A s and is transparent for infrared and visible laser n  wavelengths. T h e experimental implementation of the block diagram shown i n F i g . 2.1 is assembled on an optical table. T h e designed layout is original, w i t h most of the optical components mounted directly on an optical table, i n contrast to previous approaches where probe components were mounted on a vertical breadboard which can be moved w i t h a large three-dimensional translation stage to position the probe t i p [47]. In our design, the probe t i p is mounted on a five-degree of freedom miniature translation stage which is fixed on a rack bolted directly to the optical table. T h e five degrees of freedom allow the footprint of the probe tip to be adjusted so that it is parallel to the sample surface. T h i s is required to achieve m a x i m u m sensitivity and to ensure reproducibility on a day-to-day bases. In an experiment the probe t i p does not move once it is aligned to ensure that the alignment of the probe beam i n the probe tip remains the same for all 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 i p . 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 i p , and the focused visible probe  Chapter 2. Experimental Techniques of Electro-Optic Sampling  spot.  There was no viewing system for the p u m p beam.  32  In the present system, two  custom-designed viewing systems equipped w i t h C C D cameras are incorporated. T h e first for the probe views the footprint of the probe t i p , the device features beneath it, and the focused infrared probe beam. The second for the p u m p shows the gap of the photoconductive switch and the focused infrared p u m p beam. T h e design of the viewing systems allow the p u m p 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 p u m p and the probe beams. In addition the system is designed i n such a way that only minor alignment and component change are needed i n order to focus both p u m p and probe beams through one objective lens. This feature is needed i n measurements where p u m p and probe beams need to be overlapped or placed w i t h i n about 200 fj,m of each other. T h e detailed structures of the viewing systems w i l l be presented i n later sections. A detailed diagram of the complete electro-optic sampling system built at U B C can be found i n A p p e n d i x B .  2.3  Optical System  In this section, we discuss the optical aspects of the E O S system.  W e describe the  ultrafast laser system, the electro-optic sampler, and the two custom-designed p u m p and probe viewing systems.  2.3.1  Laser System  T w o lasers, a continuous-wave ( C W ) laser and a mode-locked ( M L ) laser, are used i n the E O S system. T h e C W laser is used to pump the M L laser which produces a t r a i n of ultrafast optical pulses by phase locking, or mode-locking, a large number of longitudinal modes of the laser cavity together [48]. T h e C W laser is a Coherent Innova 310 A r g o n 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 multiline configuration for visible wavelengths from 457.9 n m to 514.5 n m . It is equipped with 'PowerTrack' feature which automatically maintains the o p t i m u m cavity alignment; the m a x i m u m output is 13 W . The M L laser is an all solid state Ti-sapphire laser (Model N J A - 3 ) from Clark Instrumentation Inc. T h e 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 i g . 2.2 shows the schematic of the Ti-sapphire laser which is essentially a linear cavity folded to occupy less space on the table. T h e Argon pump beam is focused at the Ti-sapphire rod through one of the concave mirrors. The optical emission from the gain m e d i u m (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]. T h e 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 oscillation. Consequently, once this less lossy cavity is formed, the laser will stay mode-locked. However, there is no natural mechanism to initiate 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 will disturb the C W operation and initiate pulsing in the cavity. T h e laser operates in the near infrared and is tunable from 700 n m to 990 n m (three mirror sets are needed to cover the whole tuning range; we have used only one set in this work). W h e n pumped by a 5 W A r g o n ion laser, the M o d e l 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. T h e pulse width measured by autocorrelation is 125 fs. We have found that the M o d e l N J A - 3 can take up to 3 hours to warm u p , and then can start pulse operation with no or minor alignment. T h e mode-locked operation is very stable and can last more than 10 hours without interruption.  T h e exact origin of the  long warm-up time is not known at present, but we found the output power of the T i sapphire changes w i t h room temperature. We suspect the Argon-laser p u m p 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. T h e reduction of this time would significantly improve the ease of using the E O S system.  2.3.2  E l e c t r o - O p t i c 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 i p used is not part of the sample or circuit to be measured. It is a separate component. T h e probe tip mentioned in Chapter 1 is an external probe tip. In internal electro-optic sampling, no  Chapter 2. Experimental Techniques of Electro-Optic Sampling  35  external probe tip 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. T h e advantage of this method is that it is noninvasive because the optical beam does not interfere with the electric field in the substrate. However, it can only be used i n samples or circuits fabricated on materials w i t h electrooptic effect, such as G a A s and InP. Samples fabricated on Si or G e substrate cannot be used i n internal electro-optic sampling. In addition, the following extra conditions have to be satisfied to perform internal E O S . T h e 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. T h e wavelength of the probe beam needs to be tuned so that the substrate is transparent for the probe beam. In most cases, the p u m p beam needs to be frequency doubled i n 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 limitations of t h i n n i n g the substrate. Finally, if the substrate is not very uniform, there can be very significant problems with experimental drift. A s described i n A p p e n d i x A , an electro-optic sampler is actually the same as an electro-optic intensity modulator. W e 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 G e . 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 . T h e 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 i n 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 i p , which is polished and shaped as a truncated p y r a m i d structure. A t present these  Chapter 2. Experimental Techniques of Electro-Optic Sampling  36  tips are available commercially from Terametrics[50], T h e external probe t i p is made of a naturally birefringent crystal LiTaOa which is most efficiently used as an transverse modulator. Unlike G a A s described i n A p p e n d i x 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 ellipsoid coincide with its natural principal axes x,y,z when the electric field is parallel to optical axis z. T h e electrically induced indices can be expressed as: n n>  =  x  n  - -^r j,E  0  X  n ni  =  y  ^  3  n  (2.1)  z  3  -Y i3 z r  0  (2-2)  E  n n < -•' n - Y ^E 3  z  r  e  (2.3)  z  where 7*13 and r 3 3 are the electro-optic coefficients; E is the external electric field applied z  in the optical axis z of the L i T a O s c r y s t a 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  =  Si =  8, + ^ ( n r 3  -r—(n - n ) 0  - n r 3  3 3  e  1 3  )£  2  (2.4) (2.5)  ^ 0  where Si is the intrinsic phase retardation caused by the natural birefringence; / is the length of the optical path in L i T a O s crystal. T h e probe t i p 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. T h e optical axis is oriented parallel to one of the rectangular edges of the footprint of the tip. W h e n used to probe the electrical signal on a transmission line, the probe tip is oriented i n 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 i n its o p t i m u m configuration for external electro-optical sampling. T h e optical axis of the L i T a O s crystal is perpendicular both to the propagation direction of the transmission line and to the probe beam. T h e polarization of the polarizer and analyzer is at 45 degrees with respect to the optical axis of the probe t i p . T h e sampler is most sensitive to the electric field parallel to its optical axis. L i T a O s crystal is perpendicular to both the propagation direction of the transmission line and to the probe beam, as shown i n 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 i n L i T a O s and thus is the most sensitive configuration for electro-optic sampling. T h e geometry of the probe t i p is not exactly the same as the schematic shown in F i g . 2.3.  T h e electro-optic crystal L i T a O s is only 20-30 fim thick. It is glued to the  polished end of a fused silica rod. T h e rod is then ground into a p y r a m i d shape as shown in F i g . 2.4 . T h e foot print of the pyramid tip is a 200^mx200/xm square. T h e diameter of the rod is 1.5 m m to 2 m m . This places a l i m i t in how close the pump beam can get to the probe beam i n the experimental setup. T h e smallest separation between the probe  Chapter 2. Experimental Techniques of Electro-Optic Sampling  Input beam  38  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 i p . 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 p u m p / p r o b e distances, a smaller probe tip or a new design of the probe tip would be needed. In F i g . 2.3, the orientations of the polarizer and analyzer are not shown, but from the discussion of intensity modulators i n A p p e n d i x 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 i p . These orientations are required for achieving 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 o p t i m u m operating point. Since it is one of the most important components in an E O S system, we will describe it in detail in next  Chapter 2. Experimental Techniques of Electro-Optic Sampling  39  subsection.  2.3.3  Optical Compensator  The optical compensator used i n 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:  &.(n -n )h e  Oslow  =  0  .  (  _  •>  1  (2.6)  cos[sin cj>) %{nj-n )h l  _ Ofast  e  ,  =  .  (2.7)  cos{sm <p) i  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; 6 i s  ow  and 6f  ast  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 millimeter thickness. For example, the beam separation is less than a micron for a 1 millimeter wave plate w i t h 30 degree incident angle. For a half-wave plate, equations 2.6 and 2.7 can be written as:  Oslow  _  =  (2m +  l)Tr  7 :  T T \  cos(sin~ <p) L  (2-10)  Chapter 2. Experimental Techniques of Electro-Optic Sampling  {n+-n ) 0  (2m + l)7r  (n — n ) cos(sin~ 4>) e  1  0  40  (2.11) (2.12)  where (n -  n )h  e  m—  0  A  where the m the the order of the wave plate.  (2.13)  -0.5  A half-wave plate of 1 m m thickness  working at 800 n m 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). T h e 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. T h e retardation tuning range depends strongly on the order of the wave plate. W e chose to use a multi-order wave plate for its large tuning range. D u r i n g 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. T h i s simple setup can also be used to determine the orientation of the optical axis of a probe t i p i n addition to its intrinsic retardation.  A s described above, the proper  orientation of the optical axis of the probe t i p w i t h respect to the probe beam and transmission line is crucial in achieving m a x i m u m sensitivity of an electro-optic sampling. The details of this measurement technique is describe i n A p p e n d i x C . W e have used this method to measure the retardation tuning range of the compensator used. T h e results are shown in F i g . 2.6. T h e measurements were made with the Ti-sapphire laser at a wavelength of 809 n m . T h e 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. T h e 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  41  Chapter 2. Experimental Techniques of Electro-Optic Sampling  1  1  1  1  1  Rotate about the slow axis 540  Rotate about the fast axis m=ll  450  360  co  o>  <u u  oo CU  270  w  a 0  •rH  CO -  180 m=0  <u  01  H  90  CO ca  ca  A  OH  0 m=ll  -90  -180  10  20  40  30  Incident Angle (degrees) Figure 2.5: T h e calculated phase retardation of an eleventh-order and a zero-order quartz half-wave plates as functions of incident angle of the laser beam. T h e incident angle is defined by the normal of the wave plate and the incident laser beam. n = 1.5459 and n = 1.5375 for laser wavelength 800 n m are used i n the calculation [52]. e  0  Chapter 2. Experimental Techniques of Electro-Optic Sampling  42  I n c i d e n t A n g l e (degree) Figure 2.6: T h e measured phase retardation of the optical compensator as a function of incident angle of the laser beam. T h e incident angle is defined by the normal of the wave plate and the incident laser beam. T h e two curves correspond to the rotations about the slow axis (optical axis) and fast axis of the wave plate. T h e solid lines are the polynomial fits of the experimental data.  Chapter 2. Experimental Techniques of Electro-Optic Sampling  43  270  240 h OJ  <u  tjfl  >H  0)  210 h  o  • f-l -1-1  CO  180  T3  Si td  -!->  0)  150  Kl CO  120 h  800  810  820  830  840  850  Wavelength (nm)  Figure 2.7: T h e measured phase retardation of a multi-order wave plate as a function of h e wavelength of the incident beam. T h e incident angle is set at zero degree for all measurements. T h e 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. T h e retardation decreases almost linearly with increasing wavelength at zero incident angle.  T h e 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. T h e 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 w i d t h of laser pulses used i n an E O S system is t y p i c a l l y 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, w i t h the compensator dispersion, only the center wavelength of the laser pulse is biased at the o p t i m u m operating point when an E O S system is operating at its " m a x i m u m sensitivity". Since the laser pulse w i d t h used i n 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 m a y significantly degrade the performance of the E O S system.  2.3.4  V i e w i n g 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 . T h e typical w i d t h of a coplanar stripline electrode is 50 \im w i t h 5 or 10 pm separation between electrodes. The gap of a photoconductive switch is around 5 \im. T h e focused spot has a typical diameter of 5 to 10 fim. Therefore microscopes are needed i n order to see the focused spots, the electrodes, and the pulse generator. W e 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 i n and be focused through its objective lens. Unlike a normal microscope where the object to be seen is placed beyond the focal plane of the objective lens, our microscope is designed i n such a way that the object to be seen must be placed right i n the focal plane of the objective lens. T h u s , 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 l u m i n a t i o n wavelengths. This allows us to view the sample and the focused spot at the same time. Since the Ti-sapphire laser is operating i n 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. T h e image is shown on a video monitor.  P r o b e V i e w i n g System F i g . 2.8 illustrates the probe viewing microscope which consists of four lenses and two beam splitters. T h e first lens (at the bottom), is a f — 10 m m objective lens w i t h 10 m m 0  working distance. T h e long working distance of the objective makes it possible to fit the probe t i p and other miniature optical components into the space between the objective and the D U T . T h e last lens (at the top), is a f — 75 m m camera lens mounted on a high c  resolution video camera w i t h 4.8 m m x 6.4 m m detecting area. T h e 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 f = 10 m m 0  away from the sample. A s a result, the light collected by the objective lens from the sample is collimated. T h e inserted telescope is used to provide angular magnification for the collimated light reflected from the sample. T h e linear magnification of this four lens system is M =  h  x  Jo  (2.14)  where / i , / , f , and f are focal lengths of the four lenses shown i n F i g . 2.8. B y properly 2  c  0  choosing f\ (100 to 140 m m ) and fi (32 to 50 m m ) according to the sizes of the probe t i p and the transmission line used i n the experiment, we have successfully built a microscope with required resolution and magnification. T h e two beam splitters placed at 45 degrees w i t h respect to the optical axis of the microscope are used to introduce laser beam (IR) and illuminating light (visible), respectively. T h e one used to introduce the laser beam  46  Chapter 2. Experimental Techniques of Electro-Optic Sampling  f  1  1  "Video Monitor  camera lens 50% beamsplitter  Illuminator  telescope lenses f,  probe beam  dlchrolc beamsplitter fo  <=  objective lens  probe tip sample Figure 2.8: Diagram of the custom-designed probe microscope. T h e square i n the video monitor represents the foot print of the probe t i p , the four side blocks represent the four polished sides of the inverted p y r a m i d sampling t i p , 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 i p . A f t e r being reflected at the b o t t o m of probe t i p , the probe beams comes back along a path which is slightly shifted from its incident path due to total internal reflection configuration shown i n Fig.2.8. Most of the probe beam coming back from the probe t i p is reflected from the dichroic beamsplitter and then goes to the analyzer and detector optics (not shown). O n l y 0.2% of the probe beam goes through the dichroic beamsplitter and reaches the camera to form the image of a focused spot. T h e visible light used for illuminating the sample passes through the dichroic beamsplitter w i t h 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 time.  P u m p V i e w i n g System The field of view of the above microscope is about 200 \im x 200 fim. T h i s means that if we use the same objective to focus the p u m p beam, the m a x i m u m separation of the two focused spots (pump and probe) would be l i m i t e d to 200 /xm. However, for most of our applications, the typical separation needed between the probe spot and p u m p 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 p u m p 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 i m i t the m i n i m u m separation of the two focused spots to be i n the order of centimeters instead of millimeters. Most people solve this problem by bringing the p u m p beam at an oblique angle. T h e drawback of this approach is that the p u m p  Chapter 2. Experimental Techniques of Electro-Optic Sampling  48  Figure 2.9: Schematic diagram of the p u m p t i p shown with a probe t i p . T h e diagram is to scale. T h e probe beam shown here is directly reflected from the sample electrode instead of going through a total-internal-reflection configuration. beam will reflect from the sample and will not come back to the microscope, so the pump beam cannot be seen by a p u m p microscope. T h e 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 i p . T h e 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 t i p 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 i p is shown i n F i g . 2.9. Unlike the probe microscope which is mounted on a vertical rack, the p u m p microscope is mounted on a horizontal rack . T h e right-angle prism is used to t u r n horizontal p u m p beam 90 degrees downwards. T h e focal point of the pump t i p is 4.5 m m from the bottom of the prism. T h e p u m p t i p is 5 m m thick and 3.2 m m wide. Because of their miniature sizes, both the p u m p tip and the probe t i p 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 . T h e chromatic aberration of the plano-convex lens results in a slight difference in the focal planes for the illumination 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. T h e resolution of the two microscopes is about 1 micron which is satisfactory for most of our applications. 2.3.5  C o m m o n T i m e A x i s for Multiple P r o b i n g 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 time through a high-speed transistor.  T w o issues are  important in these measurements. F i r s t , 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 i m e axis so that direct comparison of the measurements can be made. Since the probe tip 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. T h e 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. T h e translation stage can move the sample i n 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  2  50  1  Figure 2.10: Schematic diagram of the complete E O S viewing system including two custom-designed microscopes. T h e probe microscope is mounted vertically. T h e pump microscope is mounted horizontally. T h e specially designed p u m p t i p 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.  51  Chapter 2. Experimental Techniques of Electro-Optic Sampling  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 D C 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 L a b V I E W 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 AT — d  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  ^  V  (2,5,  ^  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  w i t h typical errors of ± 0 . 0 5 ps and ± 5 \im respectively.  52  T h e propagation speed on  transmission line can be determined w i t h an error smaller than ± 0 . 0 1 x 10 m / s . 8  2.4  Noise Reduction and Sensitivity  There are three sources of noise i n an E O S system. T h e y are laser noise, shot noise and thermal noise. T h e 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. T h e shot noise is due to the photo-current generated by the probe beams at the detectors and the dark current of detectors. T h e thermal noise is due to the load resistance and detection electronics. B o t h the shot noise and the thermal noise are white noise whose noise spectrum is independent of frequency. T h e dominant noise i n E O S system is laser noise and laser-beam-generated shot noise. Since the signal to be measured is normally very small, i n the range of 1 m V to 1 V , compared w i t h the 2 k V to 10 k V half-wave voltage of the electro-optic sampler (modulator), the depth of modulation is i n the range of 1 0  - 4  to 1 0 . Such a weak signal - 7  is buried i n noise and cannot be used directly as input for the data acquisition system. W e adopted a mixer-based noise reduction system identical to that reported by Chwalek and Dykaar [53]. T h e 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. T h e m a i n 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 w i t h an acoustooptic modulator ( A O M ) at a relatively high-frequency (1.02 M H z i n 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.  53  Experimental Techniques of Electro-Optic Sampling  to data acquisition system < 1 .  Output  Lock-in Amplifier  to calibration  Mixer  20 K H z  1.02 M H z 1.02 M H z  Reffc Input —*—  1.0 M H z  20 K H z  1.0 M H z  Mixer  1.0 M H z  2 way U splitter  3 way splitter  1.02 M H z  Output  Ref  Synthesizer  Differential Amplifier 7H  AOM Driver  7£  _nJ L n J I Photodiodes  Optical Analyzer  1.02 M H z  — AOM  1.02 MHz  Probe Beam  Pump Beam  Figure 2.11: Schematic diagram of the noise-reduction electronics. T h e 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 m i x the 1.02 M H z signal w i t h 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 i n A p p e n d i x 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 i n 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. U n l i k e 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 A p p e n d i x B . The above noise reduction techniques greatly reduce the 1/f  noise i n an E O S system.  The ultimate l i m i t 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. the E O S signal is proportional to the probe beam intensity  Since  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 w i t h y/Ti until 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. B o t h methods improve the signal to noise ratio at the expense of longer data acquisition time. sensitivity of our E O S system, determined by using  /  v  " '" g  The  , is 1-10 m V / v H z , where  V &fnoise  V i  no se  is equivalent rms noise voltage and A /  pass filter of the lock-in amplifier.  n o  ;  s e  is the noise bandwidth set by the low-  Chapter 2. Experimental Techniques of Electro-Optic Sampling  2.5  55  Resolution and Linearity  The temporal resolution of an E O S system is determined by its optical pulse w i d t h , electrical transit time across the sampling spot, optical transit time across the electrooptic crystal and the frequencies of phonon resonances in the electro-optic crystal. T h e width of the optical pulse used i n the present work is normally i n the order of 100 fs. The electrical transit time is the time 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. T h e optical transit time is the time for optical pulse passing through the fringing electric field in the crystal. It depends on the distribution of the electric field i n the electro-optic crystal, and the optical path length i n the crystal. If the effective integration length for the probe beam is 20 /xm, the optical transit time is less than 200 fs. In a well-designed system, the most serious l i m i t a t i o n for temporal resolution i n E O S is the phonon resonance in the electro-optic material i n 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 i m i t the response of linear electro-optic effect to about 300 fs. T h e resolution of our E O S system has reached this fundamental l i m i t 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. T h e 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 i n the 20 fim thick L i T a O s probe. T h e 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. T h e applied 1.02 M H z signal simulates the pumpbeam-created signal i n a p u m p / p r o b e experiment. F i g . 2.13 shows the lock-in amplifier output versus the applied input signal amplitude. T h e 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. T h e full width at half m a x i m u m 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 distribution as the low frequency field. In the next chapter, we will 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: T h e linearity of our E O S system. T h e 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 i T a O a 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.  T h e n , 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. Finally, we discuss the errors caused by the external L i T a O a 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. W h e n a probe t i p is put in contact w i t h 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 i n 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 tip which is 43 for L i T a O s [10]. A s a result, there are reflections at both the front and the back facets of the probe t i p . The front facet is the place where the electrical signal enters the probe tip while the back facet is the place where the electrical signal leaves the probe t i p . T h e probe tip 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 i m i t e d . T h e 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]. T h e authors concluded that a 20 / i m thick L i T a O s probe gave m i n i m u m resonance and best accuracy for measurements on transmission lines w i t h dimensions from 5 to 50 / i m . The effect of probe-tip-induced dispersion on risetime measurements has been studied by putting a d u m m y L i T a O s 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 i n direct contact w i t h the transmission line electrodes and the measurements were performed i n the t i m e domain. The invasiveness of external probes has also been studied i n the frequency domain up to 40 G H z using direct (or internal) electro-optic sampling, where a d u m m y probe was put i n the v i c i n i t y 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 i p and the transmission line has been observed. In this chapter, we report an experimental study of the measurement errors and invasiveness of external L i T a O a probes, extending previous measurements to higher frequencies and lower invasiveness. We show that contact electro-optic sampling can lead to more serious measurement errors than previouly reported. W e also show that noncontact 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 i n this study was a coplanar stripline integrated w i t h a photoconductive switch.  T h e coplanar stripline h a d a 50 /jm electrode w i d t h and 5 pm spacing.  was fabricated on a 400 ^ m thick semi-insulating G a A s substrate.  It  T h e characteristic  impedance of the coplanar stripline was estimated to be approximately 50O. T h e total length of the sample was about 4 m m . T h e photoconductive switch incorporated i n the coplanar stripline was used to generate picosecond step-like pulses. T h e 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 w i t h the electro-optic sampling system described in Chapter 2. T h e experimental arrangement of the sample, probe t i p , and p u m p optics is shown i n F i g . 3.1. T h e probe beam passes through the external probe t i p i n a totalinternal-reflection configuration. T h e probe-sample spacing h can be adjusted by using a translation stage. T h e probe t i p was adjusted using a t i l t stage to be parallel to the sample surface b y reducing the interference fringes on the footprint of the probe to one bright fringe when i n contact.  T h e focused probe-beam spot could be moved around  w i t h i n the footprint of the probe t i p . T h e p u m p beam was focused through a planoconvex lens followed by a right angle prism which turns the p u m p beam by 90°. T h e distance between the p u m p spot and the probe spot can be adjusted and was set at 1.5 m m . T y p i c a l p u m p and probe powers used i n 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 tip and the sample can be adjusted.  3.4 3.4.1  Results and Analysis 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 i p . Referring to Fig.3.1, the data of F i g . 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. T h e measured 10-90% risetimes near the front and the back facets are 1.9 ps and 2.1 ps, respectively.  T h e initial 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 h=0  0.8  CD O)  £  O >  jim  Front Facet Back Facet  0.4 0.2  0.0  16  Time (ps) Figure 3.2: Contact E O S measurements at two probe beam positions in the probe t i p : near the front facet, and near the back facet of the probe t i p . measurements of risetime at varying distances along the transmission line that show no significant difference i n risetime over the same distance. W e attribute the lengthening in risetime to the increased dispersion and attenuation introduced by the L i T a O a probe which functions as a superstrate. O u r results show it is preferable to position the probe beam near the front facet of the probe t i p , i n agreement with the prediction of [61]. T h e feature near 14 ps i n 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 L i T a O a superstrate. The same reflection is not as obvious i n 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 i n the probe t i p : near the front facet, and near the back facet of the probe t i p . is overlapped with the initial peak because of the small separation between probe spot and reflection site. In the following, we will 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. T h e 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 i n the contact configuration near the back facet of the probe t i p . T h e 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 tip. T h e curves have been normalized to 1 at the peaks. the front facet, compared with 18% in the contact measurement. T h e 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 i n the non-contact configuration. The dispersion induced by the external probe can be more clearly seen i n F i g . 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 m a x i m u 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 i n 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 i n 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 i p is i n contact the ringing is still 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 L i T a O a superstrate.  F i n a l l y , we find that the point at which the waveform reaches half of the  m a x i m u m value appears 0.5 ps earlier in the non-contact measurement due to the reduced effective dielectric constant i n non-contact configuration. In other words, the electrical transient travels faster under the probe tip i n the non-contact configuration. To further quantify the probe-tip-induced dispersion, we made a series of measurements at a distance 1.5 m m from the photoconductive switch with varying air gap h. T h e results are shown i n F i g . 3.5 for a variety of air gaps from h = 2.5 /xm just over 100 /xm, as described i n 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. T h e 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. T h e risetime i n i t i a l l y 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, w i t h risetime decreasing from 3.6 ps when i n 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 i r s t , when the t i p is i n contact with the stripline, significant dispersion happens as the signals traverse the region under the t i p . T h i s is supported by F i g . 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 b o t t o m , 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 t i p is moved away from the surface this dispersion under the tip becomes negligible, as can be seen i n 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 i p . 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  Air Gap  30  40  h (\i m)  Figure 3.6: Risetimes of the curves of F i g . 3.5, as a function of air gap h. T h e measurement error is estimated to be ± 0 . 1 ps. explanation is qualitatively consistent with the full-wave simulation of Conn[61]. T h e simulated experimental configuration was similar to ours with the same type of LiTaO"3 probe t i p , but the transmission line used in the simulation was a coplanar waveguide instead of a stripline. T h e simulation results indicate that the reflectivity of the electrical signal at the facets of the probe t i p is frequency dependent.  T h e reflectivity of high-  frequency signals i n the contact configuration is significantly larger than that in noncontact 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 i n non-contact configuration (h=20 /xm) is only 0.4% (99.9%). Contrary to the reflectivity of high-frequency signals, the reflectivities of lowfrequency signals for the two probe configurations are much closer.  For example, the  reflectivity (transmission) of a 20 G H z signal i n the contact configuration is 17.8% (98.4%) while the reflectivity (transmission) of the same frequency signal b u t i n non-contact configuration (h=20 /xm) is about 0.3% (99.9%). In other words, more high-frequency signals (components) are lost (reflected) i n the contact (or small-air-gap) measurement than i n the large-air-gap measurement. T h i s can be more clearly seen i n 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 ) a n d a low-frequency signal (20 G H z ) at the probe facets for two probe configurations: h=0 fxm and h=20 \im. T h e data is obtained from the work b y Conn and coworkers. h/f 0 /xm 20 /xm  20 G H z 98.4% 99.9%  90 G H z 86.6% 99.9%  the relatively large loss of high-frequency components i n the contact configuration due to preferential reflection of high-frequency components at the probe facets. However, the difference i n low and high-frequency reflection appears to be too small to quantitatively explain the data of F i g . 3.6.  Another effect that m a y be important is the frequency  dependence of the strength of the electric field coupled into the t i p for varing heights. Such an effect has been suggested b y W h i t a k e r and Cheng[66].  Full-wave simulation  w i t h 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  Air Gap  69  h (|i m)  Figure 3.7: Sensitivity of non-contact E O S measurements as a function of air gap h. T h e 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]. T h e 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. T h e reduction of sensitivity with air gap will place the ultimate limit 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. T h e E O S signal initially 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 i g . 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. T h e 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 u p to h = 20 / i m . In examining the calculations of Ref.[61] shown i n 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 w i t h 15 / i m center electrode and 10 fxm spacing. T h e data of Ref.[59] shown i n F i g . 3.7 were obtained from non-time-resolved measurements where a low-frequency signal generated by a synthesizer was applied to the coplanar waveguide. T h i s low-frequency signal is often referred t o as the calibration signal since the same method is widely used to calibrate time-resolved E O S measurements. T h e calibration is made by comparing the time-resolved E O S signal to that produced by a calibration signal of known amplitude. This approach i m p l i c i t l y 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.  T h e 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. W e attribute the different dependence on h for large air gaps to the difference in fringing field distributions of high-frequency and lowfrequency 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 i n the substrate and superstrate, but is more concentrating in the substrate. W h i l e for the low-frequency calibration signal, the electric field energy is evenly divided i n the substrate and superstrate. Thus, it extends more above the electrodes than that of high-frequency signal. In other words, the electric field of lowfrequency signal drops less slowly with increasing air gap h than that of high-frequency signal. This difference will introduce a calibration error for non-contact E O S measurement 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 situation, a reasonable compromise between invasiveness and sensitivity, which still 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 FETs.  We also reviewed high-speed characterization of M O D F E T s using ultrafast-  laser-based techniques. MODFETs.  In this chapter, we describe electro-optic characterization of  E x p e r i m e n t a l 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 measurements of the L M M O D F E T s . F i r s t , we describe the fabrication process of the M O D F E T s monolithically integrated with a photoconductive switch/transmission line test fixture. T h e n , we present switching characteristics of the M O D F E T s at different input amplitude 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 simulation of the M O D F E T switching. F i r s t , we briefly describe the motivation of the work. T h e n , we introduce the lumped-element model and methodology used in the simulation. Finally, 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  4.2  Lattice-Matched  4.2.1  Ino.52Alo.48As/Ino.53Gao.47As  73  MODFETs  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 i n detail i n Chapter 2. Before presenting the experimental results, we first describe the fabrication process of the M O D F E T s which are monolithically integrated w i t h 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 i n this chapter were grown and fabricated by D r . M . V a n Hove and D r . W . De Raedt i n Interuniversity Micro-Electronics Center ( I M E C ) i n Belgium[67, 68]. Here we describe the fabrication process they developed.  T h e multilayer structure was grown on a semi-insulating InP substrate by  molecular beam epitaxy ( M B E ) . F i r s t , a 250 n m thick Ino.52Alo.4sAs buffer layer was grown on the I n P substrate, followed by a 20 n m thick narrow-bandgap Ino.53Gao.47As channel layer.  B o t h layers were nominally undoped. T h e nominal I n d i u m content i n  the Ino.52Alo.48As layer and the Ino.53Gao.47As layer are chosen i n such a way that both layers are lattice matched to the I n P substrate.  In other words, the strain i n the epi-  layers is expected to be small, and is due to slight inaccuracy i n 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 1 0  12  cm  - 2  delta-doped Si plane and a 20 n m thick undoped  Ino.52Alo.48As layer. F i n a l l y , a 7 n m thick O h m i c contact layer of Ino.53Gao.47As w i t h Si doping concentration 6 x 1 0  18  cm  - 3  was grown as the cap layer.  T h e 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. D u r i n g this process, G e 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. T h e drain, source and gate electrodes are fabricated on top of the layers. making contact with the two dimensional electron gas ( 2 - D E G ) . T h e 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 transmission lines. T h e sputtered T i W layer was used to improve adhesion to the Ino.52Alo.48As buffer layer.  T h e gate was defined by e-beam lithography i n a bilayer resist scheme  ( P M M A / C o p o l y m e r ) . T h e recess was done by wet etching i n a phosphoric/hydrogenperoxide/water solution. T h e 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 i n 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 .5 Al .48As layer and the two dimensional electron gas 0  2  0  in the channel layer. A f t e r recess etching, a P t / T i / P t / A u gate w i t h a T-shaped cross section was formed. It has a length of 0.35 fim and w i d t h of 100 pm. T h e 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. T h e 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 w i t h two types of gate-access structure have been fabricated. T h e y are double-gate contact and single-gate contact M O D F E T s . T h e mask layouts can be found in A p p e n d i x D . In F i g . 4.2, we show scanning microscope pictures of the two types of devices monolithically integrated w i t h the input and output coplanar striplines. T h e 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 . T h e lower electrode of the input transmission line which is on the left, is made i n contact w i t h the gate through one or two airbridges over the source electrode. T h e drain is connected to the lower electrode of the output transmission line which lies on the right. T h e photoconductive switches are out of the view i n F i g . 4.2. T h e y 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. T h e 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. T h e M O D F E T s are integrated with input and output transmission lines which lie on the left and the right in the photographs, respectively. Photoconductive 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  77  MODFETs  EXCITATION s  s  MODFET G D 2 mm  2 mm  Hi  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 w i t h 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,  V h = —0.7 V . Due to the high gain of the M O D F E T s , they are prone to spurious oscillat  tion. This oscillation could severely affect the electro-optic measurement. The amplitude of the spurious oscillation increases with the D C bias Vd and V . s  gs  To stop the oscillation,  magnetic beads were used in all connecting wires to increase A C loss. T h e 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 i m e window of interest and play no part in the measurement. T h e gate input signal was photoconductively excited at the corner of the L-shaped  Chapter 4. Electro-Optic Characterization of  MODFETs  78  gap, as shown i n F i g . 4.3. T h e amplitude of the input signal can be changed by changing the D C bias across the photoconductive gap. T h e typical laser intensities for the probe beam and the p u m p beam were 10 m W and 3 m W , respectively. T h e laser wavelength was set around 830 n m . T h e input and the output signals of M O D F E T s were measured using a L i T a O s external probe on the input and output striplines, respectively.  The  experimental results are presented i n 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 w i t h 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 i n depletion mode, its gate D C bias was set at 0 Volt. T h e plot shows the voltage at the gate as a function of time. T h e input signal is step-like w i t h a rise time of 2 ps. T h e 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 combination of 0.8 V D C bias and the switching transient, as a function of time. Since the M O D F E T is connected i n common source configuration, it functions as an inverter. W i t h the positive-going gate input, the drain output is negative going w i t h a sharp switching edge followed by a slow decay. T h e 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 i n Ref. [27]. W e attribute the difference to the higher performance of the present device and the integration of the device w i t h 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. T h e upper panel shows the gate input signal; the lower panel shows the drain output signal.  Chapter 4. Electro-Optic Characterization of  MODFETs  80  The time 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. F r o m F i g . 4.4 the delay time from the midpoint of the input transition to the midpoint of the output transition is 8.2 ps. T h e 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. W e estimate the device delay by subtracting from the measured i n p u t / o u t p u t 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 time is significantly smaller than the 6 ps delay time of a similar M O D F E T w i t h 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 time 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. A s 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 i n the upper panel of F i g . 4.4; the D C drain bias V  ds  is changed from 0 to 1 V ; the D C gate bias is set at 0 V . T h e  data in F i g . 4.5 show the deviation AV  ds  from the D C drain biases which are listed on the  right hand side of the plot. W h e n 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 positivegoing gate input signal v i a gate-drain capacitance C d- A s the drain bias Vds increases, g  Chapter 4.  Electro-Optic Characterization of  81  MODFETs  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 various D C drain bias voltages which are listed on the right hand side of the plot. T h e D C gate bias is set at 0 V . the switching amplitude increases until 1 ^ = 1 V but the feedthrough decreases.  The  positive-going feedthrough at around 12 ps becomes negligible for Vd biases larger than s  0.4 V . T h i s is because the feedthrough capacitance C d which represents the effect of g  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 switching characteristics of a single-gate contact M O D F E T . F i g . 4.6 shows the deviation  AVd  s  Chapter 4. Electro-Optic Characterization of  I  J  5  i  i  i  MODFETs  i  10  i  15  i  82  i  i  20  25  i  I  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 V  gs  = 0 V and V  = —0.5 V . T h e sample  gs  used i n 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. Unlike 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 w i t h increasing gate bias V . gs  plitude reduces to less than half of that for V  gs  At V  gs  = —0.5 V , the switching am-  = 0 V . T h e threshold of this M O D F E T is  V h — —0.7 V . W e noticed a large negative-going feedthrough around 10 ps for gate bias t  V  gs  = —0.5 V . T h i s suggest that the feedthrough capacitance C d is also a function of g  Chapter 4. Electro-Optic Characterization of  gate bias V  MODFETs  83  and increases w i t h decreasing V . T h i s seems contradictory to the fact that  gs  gs  w i t h decreasing V  gs  the effective distance between the gate and the drain-side conducting  channel increases, thus causing a decrease i n gate-drain capacitance C - T h e unexpected gd  change of C d w i t h V g  gs  was also observed by Frankel[70]. T h e 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. T h i s dependence of rise t i m e on gate bias is consistent w i t h the fact that the gate-source capacitance decreases w i t h decreasing gate bias V  gs  C  gs  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 singlegate-contact M O D F E T by applying a series of four input signals to the gate. T h e upper panel of F i g . 4.7 shows the four input signals w i t h increasing amplitudes. T h e rise time of the input signal is around 2.0 ps. T h e gate reflection starts around 14 ps. T h e 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 p u m p beam are kept unchanged for all measurements.  T h e gate  input signal is varied by changing the D C bias of the photoconductive switch. T h e four corresponding drain output signals are shown i n the lower panel of F i g . 4.7. T h e drain output starts from 1 V D C bias and switches negatively i n response to the positive-going gate input. In the inset, we plot the drain output amplitude against the gate input amplitude. T h e data are taken at 18 ps and 7 ps i n F i g . 4.7 for the output and the input, respectively. W h e n the gate input is smaller than 60 m V , the output and input have a linear relationship. T h e dashed line i n 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. T h e 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  85  MODFETs  A s mentioned before, the M O D F E T s fabricated at I M E C have two different gateaccess structures: double-gate contact and single-gate contact. So far, all the measurements 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 latticematched 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. T h e 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 transconductance 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 V  ds  starting from the D C drain bias of 1 V . T h e 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 time extracted the same way as described before 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 time and delay time are the shortest ever directly time-resolved in a working three-terminal device[46].  Chapter 4. Electro-Optic Characterization of  86  MODFETs  0.00 ^  -0.05  > Si  -0-10  >  -0.15 15  20 T  25 1  1  30 •  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. T h e upper panel shows a series of negative-going gate inputs, and the lower panel shows the corresponding drain outputs. T h e operating point is V = 0 V and Vd = 1 V . T h e switching time is 4.2 ps and the delay time, estimated as described in the text, is 3.2 ps. gs  s  87  Chapter 4. Electro-Optic Characterization of MODFETs  4.2.3  Analysis  Having made measurements comparing the effects of the gate access structure, we can make the following observations. F i r s t , the switching time w i t h 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 i n A p p e n d i x D.) This m a y be because the R F measurement is l i m i t e d 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 i n 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 i m e through the M O D FET T  prop  on the drain bias, we normalize the curves in F i g . 4.5 for drain bias Vd = s  0.2,0.4,0.6,0.8,1.0 V . Due to the fact that the drain voltage Vd of F i g . 4.5 decreases s  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 normalizing the curve does not significantly affect the results obtained later.)  For easy  comparison, we plot the five normalized curves i n two graphs. T h e top graph of F i g . 4.9 shows three curves near the midpoints of the transitions for three relatively low drain bias Vd = 0.2,0.4,0.6 V ; the bottom graph of F i g . 4.9 shows three curves near the midpoints s  Chapter 4.  Electro-Optic Characterization of  .-j  oI  "12  .  ,  i  13  ,  88  MODFETs  i  ,  14  i  15  ,  i  16  Time (ps) Figure 4.9: Dependence of a M O D F E T propagation delay on D C drain bias Vd - T h e top graph shows the normalized curves of F i g . 4.5 for Vd = 0.2V, 0.4V, 0.6V; T h e bottom graph shows the normalized curves of F i g . 4.5 for V~d = 0.6V, 0.8V, 1.0V. T h e inset shows dependence of a M O D F E T propagation delay on D C drain bias Vds- T h e solid line is the Spline fit of the experimental data. s  s  s  Chapter 4. Electro-Optic Characterization of  89  MODFETs  of the transitions for three relatively high drain bias Vd — 0.6,0.8,1.0 V . B y comparing s  the relative delay of the midpoints of the transitions, we find that the midpoint of the transition appears earlier and earlier w i t h increasing Vd for Vds = 0.2, 0.4, 0.6 V ; while s  the midpoint of the transition appears later and later once Vd exceeds 0.6 V . This depens  dence of the propagation delay time on the drain bias V  ds  can be better seen i n the inset of  Fig.4.9. For small D C bias V , the propagation delay time drops rapidly with increasing ds  Vd . It reaches the lowest value at about Vds = 0.5 V . A f t e r 0.5 V , the propagation delay s  t i m e increases slowly with increasing V - It is interesting to see that a similar depends  dence of delay time r  d  the delay t i m e r  d  = -^j  t  on drain bias Vds has been reported i n Ref.[70, 71] where  was calculated from the bias-dependent current-gain-cutoff frequency  ft estimated from a small-signal R F measurement using a network analyzer. T h e dependence of the delay times on the drain bias can be explained by using the dependence of the electron velocity of I n G a A s on the electric field i n the conducting I n G a A s channel. For small electric field (V  ds  =0.2-0.6 V ) , the electron velocity increases rapidly with the  electric field until it reaches a peak velocity at certain critical electric field (V  ds  = 0.6 V ) .  After this critical electric field (Vd > 0.6 V ) , electron velocity decreases with increasing s  electric field until it reaches a saturation velocity. It should be pointed out that the propagation  delay time  T  prop  through the M O D F E T  extracted from the E O S measurement is different from the delay time T defined i n smalld  signal R F measurements. For historical reasons, both are called "delay times" but their definitions and physical meanings are different. T h e former, the propagation  delay  time  Tprop, is used in time-resolved large-signal or small signal operation and is defined as the t i m e an input signal takes to propagate through the device. Its value can be directly measured by electro-optical sampling or traditionally by ring oscillators.  A l t h o u g h it  can be shown through simulation using a lumped element model that the propagation delay t i m e T  pTOp  is a function of many equivalent circuit parameters, to our knowledge  Chapter 4.  Electro-Optic Characterization of  no analytical expression which relates  90  MODFETs  directly to the circuit parameters has been  T  prop  developed. O n the contrary, the latter, the delay time T , is used i n small-signal operation d  and is denned as:  where f is the current-gain-cutoff frequency of the device. There is an analytical exprest  sion which links the delay time 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 = — tnjt  +  ( C g s +  9m  C 9 d )  [1 + g (R ds  s  + R )} + C (R d  gd  + R)  s  (4.2)  d  9m0  It is clear that delay time r& of the small-signal model is strongly dependent on the transconductance g  m  of the device but is independent of gate inductance L and draing  source capacitance C - Since f is defined as the frequency when the short-circuit current ds  t  gain goes to unity, i t is obvious that Td does not, i n general, describe the behavior of the device w i t h nonzero load impedance.  O n the contrary, i t can be shown through  simulation that the propagation delay time  is a function of L and C  T  g  prop  ds  but not  g , and also strongly depends on the load impedance. Due to these reasons, we cannot m  use the propagation delay time  T  prop  extracted from the E O S measurement and equation  4.1 to determine the small-signal current-gain-cutoff frequency f . However, this does t  not mean that the delay time A s a matter of fact, Td and r  Td  p r o p  and the propagation delay time  T  prop  have many similar characteristics.  are not related.  For example, both  are strongly related to equivalent circuit paramenters, such as C , C d, and channel gs  g  transit time. T h i s can be more clearly seen i n the simulations presented i n Section 4.4. The similar dependence on drain bias for  T  d  and T  prop  as shown i n previous paragraph is  another example. However, the task of finding an analytical expression, if there is one, which links  T  prop  to  Td  and f is beyond the scope of this thesis. To avoid the confusion t  Chapter 4.  Electro-Optic Characterization of  91  MODFETs  between the two delay times, in the following text unless explicitly specified, the words "delay t i m e " are defined as the signal propagation delay t i m e T  prop  through the device  not the delay time Tg of small signal R F measurement.  4.3  Pseudomorphic Ino.20Gao.80As/Alo.25Gao.75As  MODFETs  In the last section, we studied the switching characteristics of lattice-matched Ino.52Al .48As/Ino.53Ga .47As M O D F E T s and the impact of different gate-access structures on 0  0  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 semiconductor materials on the performance of M O D F E T s .  We first describe measurement of  the pseudomorphic device. T h e n , 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 . F i r s t , an undoped G a A s buffer layer was grown on the G a A s substrate, followed by a 13 n m thick narrow-bandgap In .2oGa .8oAs channel layer. U n l i k e the chan0  0  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.  O n top of the Ino.20Gao.80As chan-  nel layer a 5 n m thick undoped Alo.25Gao.75As layer was grown, followed by a 5 x 10 cm  - 2  Si delta-doped plane and a 30 n m thick Si-doped 5 x 1 0  17  cm  - 3  12  Alo.25Gao.75As  layer. F i n a l l y , a 40 n m thick O h m i c contact layer of G a A s w i t h Si doping concentration  Chapter 4.  Electro-Optic Characterization of  92  MODFETs  40 nm n GaAs +  30  nm  nAlo.25Gao.75As  5 nm Alo.25Gao.75As undoped 13 nm I n G a 02  080  Si delta  A s undoped  GaAs undoped  GaAs 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  18  cm"  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. T h e isolation etch was 120 n m deep; the photoconductive switch and interconnection transmission lines were fabricated on the undoped G a A s buffer layer. T h e gate length and w i d t h 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  93  MODFETs  0.2  cn >  0.1  0.0  ui  •o  -0.1  >  5.4 ps 10-90% Risetime  Output -0.2  10  15  20  0.6 V 30  25  Time (ps) 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. T h e 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. T h e operating point is V = 0 V and Vds = 0.0,0.3,0.6 V . T h e switching time for Vd = 0.6 V is 5.4 ps and the delay time, estimated as described i n the text, is 6.0 ps. gs  s  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 . T h i s device has a single-gate-contact structure, so the results can be compared to those shown i n F i g . 4.4 for a lattice-matched device that is otherwise identical. T h e threshold voltage is -0.7 V ; the D C gate bias is set at 0 V . T h e dc drain bias is set at 0.6 V instead of 1 V to avoid spurious oscillations i n this device. T h e 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.  T h e gate reflection  of the input signal starts at approximately 10 ps. T h e corresponding negative-going  Chapter 4.  Electro-Optic Characterization of  MODFETs  94  switching measured on the output transmission line 400 ± 5 \im away f r o m the gate is shown i n the lower panel of F i g . 4.11. T h e 10-90% switching t i m e of the device is 5.4 ps which is comparable to the 5.2 ps switching t i m e for the L M Ino.52Alo.4sAs/Ino.53Gao.47A s M O D F E T . However, the delay t i m e extracted the same way as described i n Section 4.2.2 is 6.0 ps. T h i s delay t i m e is almost twice as large as the 3.3 ps delay t i m e 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 ( F i g . 4.4) and L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T on InP substrate ( F i g . 4.11), we can now t u r n 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 w i t h Cascade electrode layouts fabricated on the same wafers as the devices used i n 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 i m e 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 i n Ref. [27]: 2.2 2TT/  (4.3) (  Similar to the confusion about the two delay times discussed i n the previous section, it appears that equation 4.3 is another common misconception where the current-gaincutoff frequency f  t  filter.  of a transistor is confused w i t h the 3 d B b a n d w i d t h of a low-pass  It can be shown that the 10-90% rise t i m e  r _9o% 10  °f  a  low-pass filter i n response  to a ideal step input is related to its 3 d B b a n d w i d t h f iB by exactly the same relation 3(  Chapter 4.  Electro-Optic Characterization of  MODFETs  95  as equation 4.3 : 2.2 TIO-90% =  77-7—  (4.4)  ^JZdB  where f$ B is the frequency at which the response of the filter drops to half of the value d  at low frequencies. Equation 4.4 is often used to estimate the bandwidth of a step-like signal.  Strictly speaking it can only be used for step-like signals with an exponential  rising edge: i.e. A(\ — e~*).  F r o m the definitions of f and fz B, It is clear that they are t  d  physically different quantities. A s a result, we cannot calculate the current-gain-cutoff frequency f  t  of a M O D F E T (small-signal operation) by using the rise time extracted  from the switching response of a M O D F E T (large-signal operation). To obtain the  f, t  time-domain simulation of the experimental results is needed. This will be described in Section 4.4. W h i l e 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. O n 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 i n delay time. W e have made such bias-dependent measurements of delay time 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 time. 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. T h e observed trends are consistent with a delay time  Chapter 4.  Electro-Optic Characterization of  MODFETs  96  that is dependent on the channel transport properties, as the electron mobility of I n G a A s increases w i t h 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 i n a l l y we would like to emphasize that a full comparison of the switching time measurements w i t h measured f  t  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 highspeed 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]. T h e 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 time-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  4.4.1  MODFETs  97  Motivation  Besides fabrication and characterization of M O D F E T s which we have discussed i n 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 operation 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 . L u m p e d 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 simulating M O D F E T s .  M o n t e 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 i n time domain. Most of the simulations were performed i n the frequency domain. This is m a i n l y 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 i m i t e d 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 describe 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 w i t h 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 time-domain simulation and obtained equivalent-circuit parameters through comparing the simulation w i t h their time domain electro-optic sampling measurements.  The M O D F E T s used i n the electro-optic mea-  surements are discrete devices wire-bonded to test fixtures. A s discussed i n the previous sections, this sample configuration makes it difficult to accurately extract important parameters such as delay time of the M O D F E T s ; i n fact Frankel et al. d i d 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 i n the circuits[41]. In this section, we present the first time-domain simulation of M O D F E T s monolithically integrated w i t h coplanar test fixtures. We used a model of the experimental arrangement which incorporates both input and output transmission lines w i t h the lumped-element model. T h i s significant change allows us to take the gate reflection which is evident i n the electro-optic measurements into consideration. We w i l l show that we have achieved an excellent fit between the modeling and measurement i n risetime, total delay t i m e , and amplitude for reasonable values of model parameters. We will also compare our work w i t h the previous work.  4.4.2  Lumped-Element Model  F i g . 4.12 is the modified lumped-element model used i n the simulation. T h e input and the output transmission lines i n 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 i n 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 w i t h the device.  For  example, the gate inductance L simulates inductance contributed by both gate electrode g  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  Lg  Cgd  Rg  r-"™—/WW  Rd  1"  I input #!SL ff Rin  Ld  AVW— Cds 1  gm  —j— egg rin  99  J n g s  ^  )  =  Ttran  JRds  Tout  Zo  Zo  #OSL  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 i n Ref. [74]. have neglected the parasitic capacitances often associated w i t h the large contact pads used i n R F electrode (cascade layout) contact arrangement, as our device is directly connected to the transmission lines. T h e delay time T  tran  delay i n the conducting channel. T ; and r n  out  models the electron transit  represent the transmission line propagation  delays which are determined by the input and the output electro-optic sampling locations w i t h 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 i n parallel w i t h a input load resistance.  Since the coplanar transmission lines i n 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 # I S L 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 i n the modeling are taken from the electro-optic sampling  Chapter 4. Electro-Optic Characterization of  measurements with some minor changes.  100  MODFETs  A s mentioned i n 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 . W e have removed the gate reflection from the eletro-optic measurements and replaced the removed sections with straight lines. Fig. 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 i n Fig.3.4 i n the range of 0-10 ps. After 10 ps, the input signal is modeled as a constant. T h i s is a slight approximation of the real input signal which decays slowly after the sharp transition. T h e approximation should not have a significant impact on the modeling since it only affects the low-frequency signals. T h e H S P I C E simulator is used i n this work. T h e circuit parameters of the S P I C E model are traditionally generated by  fitting  S-parameter measurements of a network analyzer i n the frequency domain. T h e y 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 V  = 0 V and drain bias Vd = 0.8 V . (The bias condition  gs  s  Table 4.1: T h e 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 V  gs  L  9  Rg  C  g S  60 H  4.0 ft  119.0 f F  Rds  Rd  Ld  169 ft  6.0 ft  70 H  P  P  9m  78.4 mS R  s  3.4 ft  = 0 V and V  ds  Ttran 0.0 ps L  s  1 H P  C  = 0.8 V . Cds  g d  15.5 f F  24.3 f F  Rgs  9.5 ft  is the same as that used in the E O S measurement of F i g . 4.4.) W e start our time-domain simulation by using parameters obtained from the R F measurement.  Chapter 4.  Electro-Optic Characterization of  101  MODFETs  160  l  0  ,  i  10  ,  i  20 Time (ps)  1  1  30  1  1  40  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 w i t h 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  200  B,  w  OS)  >  <  >  B VI  > < -500  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 i n Table 4.1. T h e upper panel shows the simulated and the measured gate input. T h e lower panel shows the simulated and measured drain output. In F i g . 4.14, we show the simulated input and output curves together w i t h E O S measurement at the same bias condition. T h e upper panel shows the gate input signals and their reflections. T h e lower panel shows the drain output signals. T h e dashed lines are simulated curves using R F parameters. of the device.  T h e solid lines are electro-optic  measurement  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 time, amplitude and gate reflection. It seems very likely that some part of the discrepancy can be attributed to device-to-device variability on the wafer. T h e typical variation of the  Chapter 4.  Electro-Optic Characterization of  103  MODFETs  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. T h i s m a y 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 measurement.  It should be pointed out that the channel transit time  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  tran  introduced by the channel transit  delay can no longer be ignored at high frequency as it is at low frequency. Since the total delay time T<£ = ^jchannel transit time r Td = T  tTan  + r  c c  t r a n  of a small-signal R F measurement can be written as a sum of , channel charging time r  c c  and drain delay time ^ [ 8 1 , 70, 72]:  -f Tdd, setting channel transit time to zero will cause an over estimation  of the channel charging time r  c c  and drain delay time Tdd- This may eventually cause an  over estimation of the parasitic parameters which are related to r more clearly seen i n the analytical expression of T  c c  c c  and Tdd- This can be  and Tdd derived i n Ref. [81]: (4.5) (4.6)  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. T h e 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 A p p e n d i x D . In any event, to better model the device, we need to choose another set of  104  Chapter 4. Electro-Optic Characterization of MODFETs  parameters for the S P I C E model. T h e new set of circuit parameters should allow us to produce a smaller delay t i m e , a smaller amplitude, and a slightly faster switching time than what we have obtained with the R F parameters. We performed a series of simulations by varying one parameter at a time and kept all the other parameters unchanged in order find out the role each element plays in determining delay t i m e , switching time, 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. T h e results are summarized in the following. The gate capacitance C  gs  is one of the most important parameters i n the equivalent  circuit. It is closely related to the risetime, delay time, 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 C . gs  The gate input signal used in the simulation is the same as the one  shown i n F i g . 4.13 (a). A smaller C  results i n a faster risetime and a smaller capacitor  gs  related delay time (also referred to as channel charging time T ) as shown in the lower c c  panel of F i g . 4.15. Gate-source capacitance C  also dramatically affects the reflection of  gs  input signal. This is shown in the upper panel of F i g . 4.15.  T h e reflection starts after  14ps and is composed of an initial dip followed by a positive-going step-like signal. A large C  gs  acts like a short for high-frequency components, which results i n the initial dip  in the reflected signal while a small C  acts like an open, which only results in a positive  gs  going step-like reflection. T h i s shows that reflection from the gate actually provides a very sensitive measure of gate capacitance  C. gs  Gate-drain parasitic capacitance C d is another important parameter in the model. g  It is responsible for gate input feedthrough as well as risetime, delay t i m e , and gate reflection. F i g . 4.16 shows the effects of C d on these characteristics. A small C d results g  g  in not only a small feedthrough which is the positive going feature near 15 ps in F i g . 4.16 but also a shorter C d-related delay time (also referred to as parasitic charging time r ) , s  pc  Chapter 4.  Electro-Optic Characterization of  •  T — :  -400  1  ' 10  1  0  '  105  MODFETs  1  r  1  1  20 Time (ps)  Figure 4.15: Effects of gate capacitance C  gs  1  30  1  40  on the response of M O D F E T s .  a shorter switching time and a sharper gate reflection feature. The transconductance g  m  cutoff frequency f  t  affects the drain output amplitude and the current-gain  as well as the gate-drain feedthrough.  the signal propagation delay time through the device.  However, it does not affect  (This is one of the evidences  given i n Section 4.2.3 to support the argument that the propagation delay time is different from the delay time strongly dependent on g .) m  T  pTOp  defined in small-signal R F measurement which is  A M O D F E T with a small transconductance has a much larger  feedthrough than an otherwise the same device w i t h a larger transconductance.  This  effect of transconductance on the feedthrough can be clearly seen i n F i g . 4.17 where all the  Chapter 4. Electro-Optic Characterization of  -400  •  1  0  '  10  106  MODFETs  •  '  20  •  '  30  •  1  40  Time (ps) Figure 4.16: Effects of gate-drain capacitance C d on the response of M O D F E T s . g  other parameters in the simulations are kept the same except for the transconductance. T h e feedthrough signal coupled through C d is actually the same for a l l the simulations g  since C d and related resistors are exactly the same. T h e reason that it is less "visible" g  for the device with a larger transconductance g  m  is because the large gain i n drain current  canceled the relative small feedthrough while for the device with a small transconductance the gain i n drain current is not enough to cancel the feedthrough. A s a result it is more "visible" for the small g  m  device. T h i s effect has been observed i n time-domain electro-  optic sampling measurement where large feedthrough is observed for devices with small transconductance.  Chapter 4. Electro-Optic Characterization of  107  MODFETs  0 g m  -100  =10mS  g = 2 0 mS m  > OT X)  >  <  -200  •300 gm=60 mS  -400 0  20  10  40  30  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 time almost the same way as C  gs  does. A small Cds causes a faster risetime and a smaller delay t i m e  except that the change is slightly less dramatic. However, Cds has very little influence on the gate reflection, in contrast with C - This is perfectly reasonable since Cds is on the gs  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 R  ds  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. T h e gate input resistance R  gs  is the  only intrinsic parameter which has almost no effect on the features discuss above when  Chapter 4.  Electro-Optic Characterization of  it is varied around its R F value 1-10  108  MODFETs  0.  So far, we have only looked at the effects of varying intrinsic parameters on the response of a M O D F E T . N o w , 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 compared with the intrinsic parameters. The extrinsic resistors R  d  and R marginally affect s  the amplitude of the drain output. T h e y have little influence on the risetime and delay time. The gate extrinsic resistor R only slightly affects the risetime of the drain output. g  The three extrinsic inductances L , L , and Ld have almost no effect on the risetime and g  s  amplitude but they affect the delay time. A large source inductance may also contribute to the gate-drain feedthrough signal while a large gate inductance L  g  may result in an  overshoot in drain output. A m o n g all the six extrinsic elements in our model, gate inductance L  is the only element that has significant effect on the reflection of input signal.  g  This is shown i n the upper panel of F i g . 4.18. T h e gate input used i n the simulation is the same as F i g . 4.13 (a). Beside the initial dip and the positive going step observed i n the previous simulation (for C )  with a small gate inductance L  gs  g  = 10 p H , we observed  a positive going feature before the dip for simulation with a larger gate inductance L  g  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 L  g  also delays the arrival of the reflection caused by C  gs  which features a dip  followed by a positive going step. T h e lobe-like feature in the reflection can be used to determine the gate inductance L . g  4.4.3  We w i l l discuss more about this in Subsection 4.4.4.  M o d e l i n g Results  K n o w i n g 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 will present simulation results  Chapter 4. Electro-Optic Characterization of  109  MODFETs  Time (ps) Figure 4.18: Effects of gate inductance L on the response of M O D F E T s . g  for both the L M Ino.52Alo.48As/Ino.53Gao.47As  M O D F E T and P M I n . 2 o G a o . A s / A l o . 2 5 0  80  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 V  gs  = 0 V and drain bias V  ds  = 0.8  V . T h e upper panel shows the measured and simulated gate input signals and their reflections. T h e lower panel shows the measured and simulated response of the drain output. The simulated curves are represented i n dashed lines while the measured ones are in solid lines. T h e input signal used i n the simulation is shown i n 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  T  200 >  '  /  100  tao >  *w  /  /  X  V \  / X •  1  -  i  -  * •• / _  r  /  <  1  i  •  w  110  MODFETs  -  f  /  J  -  0 A Vds (mV)  M e a s u r e m e n t  --- Simulation  -  -100 \\  -200  \  -  0  I  Ii  !.  I  Ii  10  20  1 —  1  30  1  40  Time (ps) Figure 4.19: T h e measured and simulated responses of the Ino.52Alo.4sAs/Ino.53Gao.47A s M O D F E T . T h e dashed lines are the simulated results while the solid lines are the measured ones. T h e lower panel shows the deviation of drain output from the D C bias V  DS  =  0.8 V .  switching. A s a result, a l l the circuit parameters are not bias-dependent. T h e simulated input and output signal correspond to electrical potential at nodes # I S L and # 0 S L of the equivalent circuit, respectively. Table 4.2 shows all the circuit parameters used i n the simulation. T h e input and output transmission line propagation delay  T;  n  +  T  out  =  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. T h e transconductance g  m  is estimated from D C measurement of the device  111  Chapter 4. Electro-Optic Characterization of MODFETs  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 V = 0 V and V = 0.8 V . gs  Rg  R  s  4 ft  10 p H 90 ft  Cgd  40 mS  90 f F  R  Rd  d s  9m  Cg  0.6 ps  s  6 ft  10 p H  ds  3.4 ft  1 pH  3fF  10 f F  Rgs  7"»n "I" Tout  9.5 ft  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.) controlled current source i n the model is controlled by a delayed C  gs  The voltage-  voltage which is  obtained by using a transmission line with a very large impedance (Zo = l O M f t ) and a matched load. T h e propagation delay time of the transmission line is used to model the channel transit time  T  T  R  A  N  .  Those parameters whoes values do not significantly affect the  switching characteristics, such as R  g  R  d  R, s  and R , gs  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 until 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 fitting and the R F fitting 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 i n the E O S and the R F measurements. T h e simulated drain output agrees very well w i t h the E O S measurement. T h e simulation successfully reproduced the correct risetime, total delay t i m e , and drain output amplitude. T h e simulated reflection of the gate input signal is qualitatively i n agreement w i t h 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 i m e - d o m a i n simulation, we also performed frequency-domain simulation using parameters i n Table 4.2. T h e short-circuit current-gain-cutoff frequency f extracted from the simulation is 69 G H z t  which agrees well w i t h the R F measurement f = 63 G H z . E v e n though the simulated t  total delay t i m e agrees perfectly w i t h the measured 3.3 ps delay t i m e , the simulated transit t i m e  T  =  tran  0.6 ps seems to be too small compared w i t h other published values  extracted f r o m R F measurements[73, 81]. T h e average saturation velocity V  3at  calculated  by using a simple formula V t = -^ - and gate length L = 0.35 \im is 5.8 x 10 c m / s a  sa  .  7  g  T h i s value is m u c h larger than the V  sat  = 2.6 x 10 c m / s (V t = 2.7 x 10 c m / s ) 7  sa  7  value extracted from R F measurement i n Ref. [73] (Ref. [81]). However, it is interesting to notice that the saturation velocities extracted f r o m our measurement and the R F measurements of Ref. [73, 81] are a l l consistently larger than the steady-state electron velocity measured i n an Ino.52Alo.48As/Ino.53Gao.47As/Ino.52Alo.4sAs double heterostructure where a V  sat  = 1.8 x 10 c m / s is obtained by time-of-flight measurement [83]. W e 7  speculate that this might caused by velocity overshoot effect i n 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 V — 0 V and drain bias Vd = 0.6V. T h e dashed lines are the simulated gs  s  results while the solid lines are the measured ones. T h e lower panel shows the simulated  Chapter 4. Electro-Optic Characterization of  MODFETs  113  Time (ps) Figure 4.20: T h e measured and simulated responses of the Ino.20Gao.soAs/Alo.25Gao.75A s M O D F E T . T h e solid lines are the simulated results while the dashed lines are the measured ones. and the measured drain output.  T h e upper panel shows the simulated and the mea-  sured gate input signals and their reflections. T h e input signal used i n the simulation is shown i n F i g . 4.13 (b). It is taken from the corresponding E O S measurement but w i t h the gate reflection replaced by a straight line starting from about 9 ps. W e followed the same simulation procedures as those used for the L M Ino.52Alo.4sAs/Ino.53Gao.47As M O D F E T . T h e transmission line propagation delay T{ + r n  out  =  5.7 ps is determined by  the corresponding E O S experiment configuration described i n Section 4.3. T h e transconductance used i n the simulation is 18mS which is much smaller than that used i n the  Chapter 4. Electro-Optic Characterization of  MODFETs  114  previous simulation. There are two reasons for this relatively low g .  F i r s t , i n general,  m  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 . T h e transconductance obtained from  the R F measurement for the P M device is around 4 0 0 m S / m m compared w i t h about 8 0 0 m S / m m for the L M device. Second, due to spurious oscillation i n the circuit we were not able to set the drain bias larger than V  ds  — 0.6V i n our E O S measurement. T h i s 0.6  V drain bias m a y be too small for the M O D F E T to realize its largest transconductance. T h e values of the parasitic resistors R , Rd, R , and R g  s  gs  are kept the same as their R F  values. T h e values of inductors L , L , and R are the same as the previous simulation of g  d  s  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 . T h e other parameters are obtain from the best fitting of the E O S measurement. Table 4.3 lists a l l parameters extracted from the best fit of the E O S measurement.  Table 4.3: T h e 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 V = 0 V and V = 0.6 V . gs  L 10 p H  Rg 2 ft  Cg 70 f F  Rds 110 ft  Rd 8 ft  L 10 p H  9  S  d  9m  Ttran  18 m S 2.2 ps R L 3 ft 1 pH s  s  ds  Cgd 5.0 f F Rgs 8 ft  C 10 f F ds  Tin  ~\~ T ut 0  5.7 ps  We have achieved excellent agreement between the simulation and experiment for the P M Ino.20Gao.80As/Alo.25Gao.75As M O D F E T . T h e simulation of the drain output reproduced the correct risetime, delay time, amplitude and even the small positive-going feedthrough around 12 ps. T h e simulation of the gate input and its reflection is also i n good qualitative agreement w i t h the experiment. T h e channel transit t i m e extracted from the simulation is  T  t r a  n  —  2.2 ps. T h e saturation velocity estimated b y using gate  Chapter 4.  length L  g  Electro-Optic Characterization of  = 0.35 / / m is V  sat  MODFETs  115  = 1.6 x 1 0 c m / s which agrees well w i t h the saturation 7  velocity estimated from R F measurement for the same type of P M device[71] where V  sat  = 2 x 1 0 c m / s was reported. W e performed frequency-domain simulation using 7  parameters listed i n Table 4.3. T h e current gain cutoff frequency extracted f r o m the simulation is 3 6 G H z . U n l i k e the previous simulation for L M device, we do not have R F experimental measurements at exactly the same bias condition ( V  gs  = 0 V , Vds = 0.6 V )  to compare w i t h . T h e current-gain-cutoff frequency extracted f r o m R F measurement at similar bias condition ( V  gs  4.4.4  = 0 V, V  ds  = 1.0 V ) is f — 34 G H z . t  Analysis  In the last section, we presented t i m e - d o m a i n 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 w i t h 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 b y 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. T h e P M Ino.20Gao.80As/Alo.25Ga .75As M O D F E T used i n their E O S measurement had a similar structure to our P M 0  device and had a gate length of 0.35/xm and w i d t h 100/xm. T h e 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. T h e i r discrete device was wire-bonded t o a coplanar test fixture while ours was integrated w i t h the structure w i t h 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 a l l fabricated by the same research group at the Interuniversity Microelectronics Center i n B e l g i u m . T h e model used i n their simulation  Chapter 4.  Electro-Optic Characterization of  0.05  I  . . .  . i . . . .  MODFETs  116  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. T h e gate bias is 0.5 V . T h e discrete M O D F E T was wire-bonded to a coplanar test fixture in the corresponding E O S measurement. A f t e r Ref.[41] as the gate input for their simulation. Table 4.4 lists all 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. T h e extrinsic inductances of their simulation are considerably larger than those of ours, m a i n l y 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  117  MODFETs  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 . T h e D C bias condition for the integrated M O D F E T (this work) is V = 0 V and V = 0.6 V . The D C bias condition for the discrete M O D F E T (Frankel) is V = 0.5 V and V = 1.5 V . gs  ds  gs  L  Rg  9  120 p H  Frankel This Work  10  P  H  Rds  500 ft 110 ft  Frankel This W o r k  ds  Cg  S  12 ft 2 ft  48 f F 70 f F  Rd  Ld  12 ft 8 ft  120 p H 10 p H  9m  15 mS 18 mS R  s  5 ft 3 ft  Ttran  1.5 ps 2.2 ps L  s  80 p H 1 pH  Cgd  10 f F 5.0 f F Rgs  2 ft 8 ft  Cds  1 fF 10 f F  Tin ~\~ T t ou  N/A 5.7 ps  the ringing seen in both their E O S measurement and S P I C E simulation ( F i g . 4.21) to the large inductances contributed by the bonding wires. W e w i 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]. T h e 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 i n F i g . 4.18.  W h i l e 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 . T h i s 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 L  g  is very small.  Through the above comparison, we can clearly seen the advantages of using an integrated structure in characterizing M O D F E T s . The integrated structure not only avoids  Chapter 4.  Electro-Optic Characterization of  0.45 I 0  MODFETs  118  l  I  I  I  z  I  10  20  30  40  50  60  I 70  Figure 4.22: T h e 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. A f t e r Ref. [84] Through the above comparison, we can clearly seen the advantages of using an integrated structure i n characterizing M O D F E T s . T h e integrated structure not only avoids the ringing and input reflection caused by the bonding wires but also provide wider characterization b a n d w i d t h 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 a d d i t i o n , 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 i m e might be slower than the real device switching t i m e .  Chapter 4. Electro-Optic Characterization of  MODFETs  119  200  oo > <  > <  100  h  -100  h  -200 h  Figure 4.23: T h e simulation results of the two different models. T h e solid line is the E O S measurement; the dashed line is the simulation w i t h our model; the dotted line is the simulation w i t h Frankel's model. parameters listed in Table 4.2. T h e results are plotted i n F i g . 4.23 together w i t h the E O S measurement and the simulation with our model using the same parameters. T h e upper panel shows the input signal. T h e dotted-line in the upper panel is the same as the input signal shown i n F i g . 4.13 (a). T h e lower panel shows the output signal. Serious ringing is seen i n the simulation using Frankel's model even though the parasitic inductances Li and L  s  L, g  used i n the simulation are much smaller than those used i n the simulation of  Fig.4.21. T h e 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 i n the model.  Chapter 5  Conclusions and Future W o r k  5.1  Conclusions  To briefly summarize the thesis work, the author designed, built and tested an electrooptic 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 electrooptic sampling using a LiTaC*3 external probe was subsequently performed by using the E O S system. T h e n , the E O S system was used to characterize the switching characteristics of modulation-doped field-effect transistors.  F i n a l l y , time-domain simulation was  performed w i t h a lumped-element model incorporating input and output transmission lines. F r o m 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 w i t h a transmission line/photoconductive switch test fixture. The measured switching t i m e and propagation delay time of a L M Ino.52Alo.4sAs/Ino.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 i n a three-terminal electronic device. • On-wafer integration of coplanar transmission lines w i t h the device under test is a significant improvement over h y b r i d integration involving wire bonds. T h e parasitic gate inductance associated w i t h the integrated structure is approximately one order of magnitude less than that associated with wire bonds, and allowed extension of 121  Chapter 5.  122  Conclusions and Future Work  the electro-optic technique to higher-speed device characterization. • T h e propagation delay time of M O D F E T switching response, T  , and the delay  pTop  time Td = 2 ^ defined i n small-signal R F measurement are physically different quantities. For example, if all other parameters i n the small-signal model are kept but r  equal, Td is a strong function of transconductance g  m  pTop  upon gm. Despite this, the propagation delay time r  pTop  does not depend  and delay time T were d  shown to have similar dependence on drain bias Vd . s  • T h e 10-90% rise time of the M O D F E T switching response cannot be used to calculate the current-gain cutoff frequency f : t  literature. T h e rise time  r _9o% 1 0  a  n  T _9O% ] 0  ^  as suggested i n the  d the propagation delay time r  prop  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. • T h e time-domain simulation with a lumped-element model incorporating input and output transmission agrees well w i t h 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 i n the simulations. Its omission causes severe ringing i n the simulated output waveform, which is an artifact of the incomplete model. • T h e reflection of the input signal by the M O D F E T is very sensitive to the gate inductance L and gate-source capacitance C g  a s  , and can be used t o estimate the  values of these parameters. • Significant inaccuracy occurs i n the electro-optic sampling measurement due to the high-dielectric-constant probe t i p when i n contact w i t h the transmission lines.  Chapter 5.  123  Conclusions and Future Work  This is at variance with previous experimental measurements; we attribute the difference to imperfect contact i n 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 still ensures accurate calibration, occurs for air gaps from 10 to 20 pm. • T h e sensitivity of E O S measurement drops dramatically with increasing probe-tosample distance. T h e measurement sensitivities for time-resolved (high-frequency) signal and calibration (low-frequency) signal drop at the same rate w i t h 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.  • T h e retardation introduced by a compensator made of multi-order wave plate strongly depends on the wavelength of the laser beam, which m a y 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 characterization 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 stateof-the-art high-speed electronic devices. T h e sensitivity l - 1 0 m V / y / H z  is satisfactory for  large-signal switching measurement and is marginal for small-signal measurement. T h e l i m i t a t i o n of using this technique to characterize high-speed electronic devices lies i n  Chapter 5.  Conclusions and Future Work  124  the interconnection between the photoconductive signal generator and the device under test.  E v e n though photoconductive switches (PCSs) are capable of generating pulses  w i t h 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 i n the interconnection transmission line. T h e effects of loss and dispersion on the interconnection transmission line can be reduce by using a shorter transmission lines w i t h a thinner substrate and smaller electrodes.  T h i s change of design for interconnection transmission line is  needed for electro-optic characterization of M O D F E T s w i t h switching times less than 2 ps. However, shorter interconnection transmission line m a y create another problem: reduced measurement time 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 time window needed to measure faster devices should be smaller. If desired, the reflection can be separated from the input signal by using a recently developed technique reported i n reference [85]. The photoconductive switches used i n this work are integrated w i t h the input transmission lines. T h e 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 m m ) 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 i n response to steplike signals w i t h 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 w i t h E O S system, pulses w i t h small F W H M are needed.  However, the  P C S s of our samples are designed to generate step-like pulses. E v e n though i n principle it is possible to generate pulses i n 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 w i t h 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 w i t h 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 w i d t h of the input signal can be adjusted due to the change of dispersion w i t h the length of the transmission line. T h e 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 w i t h a d u m m y 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 d u m m y 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 d u m m y probe.  Besides using step-pulses i n the experiment, pulses w i t h small F W H M should  also be used since they can provide frequency domain information about the invasiveness through Fourier transformation. A n o t h e r way to solve the invasiveness problem is to develop electro-optic probes using materials w i t h small diselectric constant. films w i t h dielectric constant e  T  Polymer  = 3 have been proposed as new materials for electro-  optic probes[86]. Finally, 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 time T  PROP  to the delay t i m e TJ, =  measurement so that the current-gain cutoff frequency f  t  defined i n R F  can be estimated from the  propagation delay t i m e T . A useful idea for attacking this problem m a y be found i n a PROP  related work b y Chor and co-workers on analytical expression of propagation delay t i m e of emitter-coupled gate ( E C L ) [87] where the propagation t i m e 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, " N e w M O D F E T S m a l l Signal C i r c u i t M o d e l Required for Milimeterwave M M I C Design: E x t r a c t i o n and V a l i d a t i o n to 120 G H z , " M T T - S International Microwave Symposium Digest, V o l . 2, pp. 611-614, 1995. [2] H e r m a n n Schumacher and E r i c W . S t r i d , "Electronic Wafer Probing Techniques," i n Measurement of High-Speed Signals in Solid State Devices, edited by R . B . Marcus, A c a d e m i c Press, San Diego, p p . 41-81, 1990. [3] C . L . Tang, F . W . W i s e , 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, p p . 447-455, 1989. [4] F . Sasaki and Y . Masumoto, "Tunneling and Relaxation of Photogenerated Carriers in Semiconductor Q u a n t u m Wells," Phys. R e v . B , V o l . 40, p. 3996, 1989. [5] M . K . Jackson, " O p t i c a l Studies of Semiconductor Heterostructures: Measurements of Tunneling T i m e s , and Studies of Strained Superlattices," P h . D . thesis, California Institute of Technology, Pasadena, California, 1991. [6] D . H . A u s t o n , "Picosecond Optoelectronic Switching and G a t i n g i n S i l i c o n , " , A p p l . Phys. Lett., V o l . 26, p p . 101-103, 1975. [7] D . H . A u s t o n , "Picosecond photoconductivity: High-speed measurements of devices and materials," i n Measurement of High-Speed Signals in Solid State Devices, edited by R . B . Marcus, A c a d e m i c Press, San Diego, p p . 85-133, 1990. [8] H . M . Heiliger, T . Pfeifer, H . G . Roskos, H . K u r z , "Picosecond Electric O n wafer Testing w i t h Freely Positionable Photoconductive Switches," Technical Digest C L E O ' 9 5 , p. 363, 1995. [9] J . A . V a l d m a n i s , G . M o u r o u , and C . W . G a b e l , "Picosecond E l e c t r o - O p t i c Sampling system," A p p l . Phys. Lett., V o l . 41, pp. 211-212, 1982. [10] A m n o n Y a r i v , " O p t i c a l Electronics", Fourth edition, p p . 309-353, Saunders College Publishing, 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 . W h i n n e r y , "Dispersion of picosecond pulses i n coplanar transmission lines," I E E E Trans. Microwave Theory and Tech., V o l . 34, pp. 738-741, 1986. [13] J . F . W h i t a k e r , R . Sobolewski, D . R . Dykaar, T . Y . Hsiang, and G . A . M o u r o u , "Propagation M o d e l for ultrafast signals on superconducting dispersive striplines," I E E E Trans. Microwave Theory Tech. V o l . 36, p p . 277-285, 1988. [14] D . Grischkowsky, I. N . D u l i n g , III, J . C . C h e n , and C . C . C h i , "Electromagnetic Shock Waves F r o m Transmission Lines," Phys. R e v . Lett. V o l . 59, p p . 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, p p . 654-661, 1990. [16] S. G u p t a , J . F . W h i t a k e r , and G . A . M o u r o u , "Subpicosecond pulse propagation on coplanar waveguides: Experiment and simulation," I E E E Microwave and G u i d e d Wave Lett. V o l . 1, p p . 161-163, 1991. [17] M . B . Ketchen, D . Grischkowsky, T . C . C h e n , C - C C h i , I. N . D u l i n g , 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, p p . 751-753, 1986. [18] F . W . S m i t h , S. G u p t a , H . Q . L e , V . D i a d i u k , M . A . Hollis, A . R . Calawa, M . Frankel, D . R . Dykaar, G . A . M o u r o u , and T . Y . Hsiang, "Picosecond GaAs-based Photoconductive Optoelectronic Detectors," A p p l . Phys. Lett., V o l . 54, p p . 890-892, 1989. [19] D . K r o k e l , D . Grischkowsky, and M . B . Ketchen, "Subpicosecond Electrical Pulse Generation Using Photoconductive Switches w i t h Long Carrier Lifetimes," A p p l . Phys. Lett., V o l . 54, p p . 1046-1047, 1989. [20] E . Sano, T . Nagatsuma, T . Shibata, and A . Iwata, "Generation of Picosecond Electrical 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 . B r o w n , C . D . Parker, L . J . Mahoney, J . Y . Y a o , T . G . Anderson, and T . C . M c G i l l , " G r o w t h and Characterization of High-current Density, High-speed I n A s / A l S b Resonant Tunneling Diodes," A p p l . Phys. L e t t . , V o l . 58, p. 275, 1991.  Bibliography  129  [22] E . R . B r o w n , 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 i n 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 . D i a m o n d , 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, p p . 400-402, 1993. [25] R . T s u and L . E s a k i , "Tunneling i n a F i n i t e 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 . R o d w e l l , "108G H z G a l n A s / I n P p-i-n Photodiode w i t h 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 . W h i t a k e r , G . A . M o u r o u , D . H u l i n , A . A n t o n e t t i , M . V a n 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 M o d u l a t i o n Doped F i e l d Effect Transistor," A p p l . Phys. lett., V o l . 61, p p . 1187-1189, 1992. [28] A . Zeng, M . K . Jackson, M . V a n Hove, and W . De Raedt, "Electro-optic Characterization of M o d u l a t i o n - D o p e d Field-Effect Transistors w i t h Monolithically-integrated Test F i x t u r e s . " , Accepted for publication i n the Special Issue of the O p t i c a l and Q u a n t u m Electronics on Optical Probing of Ultrafast Devices and Integrated Circuits, July, 1996. [29] M . Y . Frankel, D . P a v l i d i s , and G . A . M o u r o u , " A study and optoelectronic verification of A l G a A s / G a A s heterojunction bipolar transistor large-signal characteristics," I E E E J . Q u a n t u m Electronics, V o l . 29, p. 2799, 1993. [30] K . E . Meyer, D . R . Dykaar, and G . A . M o u r o u , "Characterization of T E G F E T s and M E S F E T s using electro-optic sampling technique," i n Picosecond Electronics and Optoelectronics, edited by M o u r o u , G . A . , and B l o o m , D . M . and Lee, C . H . , Springer-Verlag, New Y o r k , pp. 54-57, 1985. [31] T . M i n u r a , S. H i y a m i z u , T . Fujii and K . N a n b u , " A N e w Field-Effect Transistor w i t h Selectively Doped G a A s / n - A l G a A s Heterojunction," J p n . J . A p p l . Phys. V o l . 19, p p . L225-L227, 1980. [32] H . M o r k o c and P . M . Solomon, " T h e H E M T : a Superfast Transistor," I E E E Spect r u m , p p . 28-35, February, 1984.  Bibliography  130  [33] Jeffrey Frey and D i m i t r i s E . Ioannou, "Materials and Devices for High-Speed Decices and Optoelectronic A p p l i c a t i o n s , " i n Measurement of High-Speed Signals in Solid State Devices, edited by R . B . Marcus ed., V o l . 28, p p . 1-40, 1990. [34] P. C . Chao, A . J . Tessmer, K . H . G . D u h , P H o , M . Y . K a o , P . M . S m i t h , J . M . B l l i n g a l l , S. M . L i u and A . A . Tabra, " W - b a n d Low-Noise I n A l A s / I n G a A s LatticeM a t c h e d H E M T s , " I E E E Elec. Device Lett, V o l . 11, p p . 59-62, 1990. [35] C . R . Bolognesi, E . J . Caine, and H . Kroemer, "Improved Charge Control and Frequency Performance i n I n A s / A l S b - B a s e d Heterostructure Field-Effect Transistors," I E E E Electron Device Letters, V o l . 15, p p . 16-18, 1994. [36] A . Ozgur, W . K i m , Z . F a n , A . Botchkarev, A . Salvador, S. N . M o h a m m a d , B . Sverdlov and H . M o r k o c , " H i g h transconductance-normally-off G a N M O D F E T s , " Electronics Lett. V o l . 31, p p . 1389-1390, 1995. [37] S. N . M o h a m m a d , A r n e l A . Salvador, and Hadis M o r k o c , "Emerging G a l l i u m N i t r i d e Based Devices," Proceedings of the I E E E , V o l . 83, pp. 1306-1355, 1995. [38] Hadis M o r k o c , "Recent Developments i n high speed heterojunction devices: a tutor i a l , " I E E E International S y m p o s i u m of Circuits and Systems, pp. 2532-2537, 1990. [39] L . D . Nguyen, A . S. B r o w n , M . A . Thompson, and L . M . Jelloian, "50-nm Selfaligned-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 . H o , M . Y . K a o , P. C . Chao, K . H . G . D u h , J . M . B a l l i n g a l l , S. T . A l l e n , A . J . Tessmer, P. M . S m i t h , " E x t r e m e l y High G a i n 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, p p . 325-327, 1991. [41] M . Y . Frankel, J . F . W h i t a k e r , and G . A . M o u r o u , "Optoelectronic Transient Characterization of Ultrafast Devices," I E E E J . of Q u a n t u m Elec. V o l . 28, p p . 2313-2324, 1992. [42] N . C . C i r i l l o , Jr., J . K . A b r o k w a h , 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 M o d u l a t i o n Doped A l G a A s / G a A s F E T s , " Electronic Lett., V o l . 21, p p . 772-773, 1985. [43] U . K . M i s h r a , J . F . Jensen, A . S. B r o w n , M . B . Thonson, L . M . Jelloian and R . S. Beaubien, "Ultra-High-Speed Digital C i r c u i t Performance i n 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, p p . 482-484, 1988.  Bibliography  131  [44] M . M a t l o u b i a n , H . Fetterman, M . K i m , A . O k i , J . C a m o u , S. Moss, and D . S m i t h , "Picosecond Optoelectronic Measurement of S Parameters and O p t i c a 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 i n 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 . V a n Hove, and W . De Raedt, "On-Wafer Characterization of Ino.52Alo.48As/Ino.53Gao.47As M o d u l a t i o n - D o p e d Field-Effect Transistor w i t h 4.2 ps Switching T i m e and 3.2 ps D e l a y " , A p p l . Phys. L e t t . , V o l . 67, p p . 262-263, 1995. [47] J . A . V a l d m a n i s , "Electro-optic measurement techniques for picosecond materials, devices, and integrated circuits," i n Measurement of High-Speed Signals in Solid State Devices, edited by R . B . Marcus, A c a d e m i c Press, San Diego, p p . 136-217, 1990. [48] A m n o n Y a r i v , " O p t i c a l Electronics", Fourth edition, Saunders College P u b l i s h i n g , p. 193, 1991. [49] " A l l Solid State Mode-locked Ti:Sapphire Laser," Product Information M a n u a l , C l a r k 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, USA. [52] Melles G r i o t Catalog, "Optics G u i d e 5," p p . 14-4, 1990. [53] J . M . Chwalek and D . R . Dykaar, " A mixer based electro-optic sampling system for submillivolt signal detection," R e v . Sci. Instrum., V o l . 61, p. 1273, 1990. [54] K . P. Cheung and D . H . A u s t o n , " A Novel Technique for Measuring Far-Infrared Absorption and Dispersion," Infrared Phys. V o l . 26, p p . 23-27, 1986. [55] X . C . Zhang, B . B . H u , J . T . Darrow, and D . H . A u s t o n , "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 . A u s t o n , M . T . Schmidt, P. T h a m , and E . S. Y a n g , " O p t i c a l l y Induced Electromagnetic R a d i a t i o n 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 ElectroO p t i c Probes i n Millimeter-Wave Optoelectronic Characterization," to be publish i n I E E E Trans. Microwave Theory and Techniques, J u l y 1996. [58] T . Nagatsuma, T . Shibata, E . Sano, and A . Iwata, "Subpicosecond sampling using a noncontact electro-optic probe," J . A p p l . P h y s . , V o l . 66, p. 4001, 1989. [59] T . Nagatsuma, T . Shibata, E . Sano, and A . Iwata, "Non-contact electro-optic sampling system i n subpicosecond regime," 1990 I E E E Instrumentation and Measurement Technology Conference, p. 152, 1990. [60] D . C o n n , X . W u , J . Song, and K . Nickerson, " A full wave simulation of disturbances in picosecond signals by electro-optic probing," 1992 I E E E M T T - S Int. Microwave S y m p . Digest, p. 665, 1992. [61] X . W u , D . C o n n , J . Song, and K . Nickerson, "Invasiveness of L i T a O s and G a A s probes i n external E - 0 sampling," I E E E J . Lightwave Tech., V o l . 11, p. 448, 1993. [62] M . Y . Frankel, J . F . W h i t a k e r , G . A . M o u r o u , and J . A . V a l d m a n i s , " E x p e r i m e n t a l characterization of external electrooptic probes," I E E E Microwave G u i d e d Wave Lett., V o l . 1, p. 60, 1991. [63] W . M e r t i n , C . Roths, F . Taenzler, and E . K u b a l e k , "Probe tip invasiveness at i n 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 . V o n Wendorff, G . D a v i d , U . D u r s u m , and D . Jager, " Frequency domain characterization of a G a A s coplanar waveguide up to 40 G H z by electro-optic probing," Conf. P r o c . L E O S ' 92, p. 119, 1992. [65] D . S. Phatak, N . K . Das, and A . P. Defonzo, "Dispersion characteristics of optically 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 . W h i t a k e r , " E l e c t r o - O p t i c - P r o b e System Response: E x p e r i ment and S i m u l a t i o n , " private communication. [67] Y . Baeyens, D . Schreurs, B . Nauwelaers, M . V a n Hove, W . De Raedt and M . V a n Rossum, Proc. o f M I O P ' 9 5 , p. 345, 1995. [68] M . V a n Hove, J . Finders, K . van der Zanden, W . De Raedt and M . V a n Rossum, Y . Baeyens, D . Schreurs, B . Nauwelaers, A . Zeng, M . K . Jackson, "InP-based H E M T Technology for M M I C A p p l i c a t i o n s , " P r o c . 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 . M o r k o c , "Gate Capacitance-Voltage Characteristic of M O D F E T s : Its Effect on Transconductance," I E E E Trans. Electron D e v . V o l . 32, pp. 1675-1684, 1985. M . Y . Frankel, "Ultrafast Device Characterization," P h . D . thesis, University of M i c h i g a n , A n n A r b o r , M i c h i g a n , 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, p p . 879-886. 1988. L . D . Nguyen, P. J . Tasker, D . C . Radulescu, and L . F . E a s t m a n , "Characterization of Ultra-High-Speed Pseudomorphic A l G a A s / I n G a A s (on G a A s ) M O D F E T ' s , " I E E E T r a n . Electron Devices, V o l . 36, p p . 2243-2247, 1989. L . D . Nguyen, L . E . Larson, and Umesh. K . M i s h r a , "Ultra-High-Speed M o d u l a t i o n Doped Field-Effect Transistors: A Tutorial Review," Proceedings of the I E E E , V o l . 80, pp. 494-518, 1992. H . M o r k o c , 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 . D u t t o n , " C i r c u i t simulation models for the high electron mob i l i t y transistor", I E E E Trans. Electron Devices, V o l . 33, p p . 682-691, 1986. P. R o b l i n , S. K a n g , A . Ketterson and H . M o r k o c , " A n a l y s i s of M O D F E T microwave characteristics", I E E E Trans. Electron Devices, V o l . 34, p p . 1919-1928, 1987. M e h r a n Bagheri, " A n improved M O D F E T microwave analysis", I E E E Trans. Electron Devices, V o l . 35, p p . 1147-1149, 1988. D . J . W i d i g e r , 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 m o b i l i t y transistor", I E E E Trans. Electron Devices, V o l . 32, p p . 1092-1102, 1985. Dany Loret, "Two-dimensional numerical model for the high electron m o b i l i t y transistor", Solid State Electron, V o l . 30, p p . 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, p p . 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 - / t m - G a t e 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, p p . 502-504, 1990.  Bibliography  134  [82] P. J . Tasker and B r i a n Hughes, "Importance of Source and D r a i n Resistance to the M a x i m u m f of M i l l i m e t e r - W a v e M O D F E T s , " I E E E Electron Device Lett. V o l . 10, pp. 291-293, 1989. t  [83] N . Shigekawa, T . F u r u t a , and K . A r a i , "Time-of-flight measurement of electron velocity i n 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 . C u r r i e , "Separating Temporally-Overlapped Waveforms w i t h Electro-Optic Sampling," to be published i n the Special Issue of O p t i c a l and Q u a n t u m Electronics on Optical Probing of Ultrafast Devices and Integrated Circuits., July, 1996. [86] H . J . Cheng and J . F . W h i t a k e r , " E l e c t r o - O p t i c Probes: H i g h - P e r m i t t i v i t y Crystals vs. L o w - P e r m i t t i v i t y Polymers," Technical Digest of Ultrafast Electronics and Optoelectronics 1995, p p . 128-130, 1995. [87] E . F . C h o r , A . Brunnschweiler, and P. A s h b u r n , " A Propagation-Delay Expression and its A p p l i c a t i o n to the O p t i m i z a t i o n of Polysilicon E m i t t e r E C L Processes," I E E E Journal of Solid-State C i r c u i t , V o l . 23, p p . 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 i n E O S system was actually an electro-optic modulator. In this appendix, we discuss the electro-optic effect and its application i n E O S system in more detail. T h e 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 w i t h the topic.  A.0.1  Electro-Optic Effect  O p t i c a l materials can be classified into two major groups by means of their optical properties: 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 polarization) of the light. For example, fused silica, S i , 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 K +l 4 + n n  2  t  135  =  1  (A- ) 1  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. n and n are indices of ordinary and extraordinary beams, respectively. 0  e  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; n ,n , x  y  and n are refractive indices for z  optical beams whose electric fields are along the corresponding directions x,y, and z. For an isotropic material,  For a uniaxial anisotropic material, n = n x  y  =  n ',nz — n , where n and n are the refractive indices of what are called the ordinary 0  e  0  e  and extraordinary beams, respectively. F i g . A . l shows an index ellipsoid of a uniaxial crystal i n its principal coordinate system. W e can use the index ellipsoid to determine the refractive indices of an optical beam propagating i n an arbitrary direction i n an anisotropic crystal as follows. F i r s t , we draw a plane perpendicular to the beam direction and passing through the origin of the principal coordinate.  T h e n , we determine the  intersection of this plane w i t h the ellipsoid; this is an ellipse or a circle. T h e 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. T h e intersection of the ellipsoid and this plane is an ellipse w i t h its major and minor radii equal to n  e  and re , respectively. G  This means that a beam propagating i n the y direction w i t h z  polarization w i l l experience a refractive index of n  e  while a beam propagating i n the  same direction but w i t h x polarization w i l l experience a index of n . 0  T h i s method of  determining indices is not l i m i t e d to optical beams along the principal axes. It can also be used for optical beams w i t h arbitrary directions. T h e 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. T h e refractive indices for beams propagating i n a direction parallel to the optical axis are independent of polarization and are equal to n i n uniaxial crystal because the intersection of the xy plane 0  and the ellipsoid is a circle. For light beams propagating i n a direction perpendicular to the optical axis of a uniaxial crystal there are two refractive indices n  0  and n for e  beams w i t h their polarizations perpendicular to and along the optical axis, respectively. Some isotropic materials can be changed into anisotropic materials i n an electric field. For example, G a A s , InP, and ZnTe become anisotropic materials i n the presence of an electric field. In addition, anisotropic material such as L i T a O s can change their degree of anisotropy i n the presence of an electric field. In other words, the refractive indices in these materials change w i t h the external electric field. This change of refractive index w i t h external electric field is called the electro-optic effect.  It only exists i n 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 w i t h diamond structure which has inversion symmetry does not exhibit the electro-optic effect. T h e 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, w i t h 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  , *  2  +  Where (^-^ y  /  +  *  2  +  2  +  ( h ) . " +  2  2  ( h ) .* » =  1  <-> A 2  ( i = 1, • • • 6) are index ellipsoid coefficients due to an arbitrary electric field  ~E(E , E , E ). X  ( h )  i n the index ellipsoid equation:  z  W h e n the external electric field is zero, the above equation reduces to eq.  A.l.  G?)  1  =  4 f > (^) 2  =  4' (^)  =  3  4' (^)  4  =  0  ' ("Os" ' (^)e 0  W h e n an external electric field is applied, the change of the coefficient  =  0  . is related  to the applied field E(E , E , E ) by a 6 x 3 m a t r i x : X  y  z  /  Mi), Mi).  =  \ rn  ri2  r  i 3  r-21  ^"22  r  2 3  »"31  ^32  r  3 3  »~4i  r  r  4 3  r i  r  5  ^ r&\  42  r  r  5 2  r  6 2  /  F  \  •tLrx  (A.3)  Ey  [ E  2  J  5 3  6 3  Where r,j are the electro-optic coefficients, and the 6 x 3 m a t r i x is called the electro-optic tensor. Due to the symmetries of electro-optic crystals, most of the elements of the m a t r i x are zeros and some of the nonzero elements are of the same absolute values. T h i s greatly reduces the complexity of the index ellipsoid equation.  For example, i n any materials  w i t h 43mor23 group symmetry, such as G a A s , InP, C d T e , 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. W e 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 w i t h 43m group symmetry, including InP, In A s , C d T e 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  0  0  0  r i  0  0  0  r  0  ' A  a  (*)  2  (*)  4  Mi)  (A)  A  or:  4 1  0  V  r i 4  / 0  \  0  VE  z  J  /  0 0 0 0 0  \  A  ( i )  /  6  Substituting these zero and nonzero terms of A {j^j.  into equation A . 2 , we obtain the  field-modified index ellipsoid equation: x  2  y  2  ~~2 + ~  n  0  n  0  z^  + ~  + 2 4iE xy r  n  0  z  =  1  where no is the refractive index of G a A s when the external electric field is zero. eliminate the cross t e r m , we rotate the x,y,z  To  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  where n i,n i,n i x  x',y',z';  y  z  140  are indices for beams polarized along corresponding p r i n c i p a l axes  under the assumption n^r^Ex  <C 1 the induced indices can be expressed as: n  n<  =  x  n  3  + Y ^ r  0  E  z  (A.4)  n  3  n> y  =  n  n<  =  n  z  -  0  -^-r E 41  (A.5)  z  (A.6)  0  This means that if an optical beam polarized at 45 degrees w i t h respect to the x' axis travels along the z' direction, the two components of this beam w i t h polarization along x' and y' w i l l experience different refractive indices n > and n i which depend on the applied x  y  field. There w i l l be a phase retardation S between the two orthogonally polarized beams after passing through the crystal. S  —  —(n i — n i)l  =  —n r E l  x  3  where / is the thickness of the crystal; E  0 41  z  y  (A.7)  z  is the external electric field i n the z direction.  A s a result, the linearly polarized beam becomes an elliptically polarized beam after passing through the crystal. T h i s 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 m o d u lator. T h i s section describes the electro-optic intensity modulator i n more detail. F i g . A . 2 shows a t y p i c a l intensity modulator which is composed of an electro-optic crystal, a compensator, and two polarizers (the second polarizer is usually called an analyzer). electro-optic crystal i n this example has the same electro-optic properties  The  (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. T h e crystal is placed between the two orthogonal polarizers w i t h 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 result, 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 crystal, it induces birefringence i n the crystal. Consequently, the e-o crystal w i l l change the linearly polarized beam into an elliptically polarized beam. T h e horizontally-polarized component of the elliptically-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 w i t h the external field, or is modulated by the external  field.  In the following, we derive analytical expressions for an intensity electro-optic m o d ulator. Intensity modulators can be further classified into two types: longitudinal m o d ulator and transverse modulator b y 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; i n a transverse modulator, the optical beam is perpendicular to the electric field. Most of the electro-optic crystals can be used i n 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 i n longitudinal configuration, while LiTaC*3 is most efficient i n 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 i n 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 E i(0) and -£y(0) are i n phase and can be expressed as: x  E i{<S) — Aexp(jut) x  E '(0) y  =  Aexp(jut)  where A is the amplitude of the electric field i n 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: E ,(l)  =  Aexp[j(ut-^l)}  E ,(l)  =  Aexp\j(ut-=^-l)]  x  y  where n > and n < are electrically induced indices given by eq.A.4 and eq.A.5. If we ignore x  y  the compensator for the time being and project the two components E >{1) and E >(l) X  y  onto the polarization axis y of the output polarizer (or analyzer), we can calculate the output intensity I by using the sum of the projections on the y axis. T h e transmission y  0  Appendix A. Principles of Electro-Optic Sampler  143  can be written as: T  8  Y  \ = »-(f)  -KV  (A.8)  =  where K  =  -A-  (A.9)  8 is the phase difference between the E >{1) and E i(l) components and is given b y eq.A.7; X  y  V is the external voltage applied across the crystal [E \ i n eq.A.7). K - is called half-wave Z  voltage and is inversely proportional to the electro-optic coefficient r \. It is the voltage 4  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 = V . v  Vx is often used as a figure of merit for describing a modulator. T h e smaller the halfwave voltage \4j the more sensitive the modulator is. W e can use the data of Ref. [10] to calculate V for G a A s ; the e-o coefficients are given at two wavelength 0.9 and 1.15 T  \xm. T h e corresponding K-'s for A = 0.9 \xm and A = 0.9 / i m are 17.6 k V and 19.8 k V 0  0  showing a significant variation w i t h wavelength. If we let the output polarizer be parallel to the x axis instead of the y axis, and project E I{1) and E >{l) onto the x axis, we can obtain 1% . T h e transmission for this X  y  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 w i t h orthogonal polarizations. 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 w i t h the input beam. However, i n the vicinity of 0 . 5 K , the transmitted beam changes  Appendix A. Principles of Electro-Optic Sampler  144  Applied Voltage V (V ) w  Figure A . 3 : Transmission of an electro-optic modulator w i t h dual beam outputs. T h e 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 w i t h 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 optical 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 i n F i g . A . 2 . T h e 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 S . T h e transmission of the modulator w i t h a compensator 0  can be written as:  EL  (A.ll)  ii  n  (A.12)  where S is the phase retardation introduced by the compensator and should be made 0  equal to | for modulators using naturally isotropic crystals, such as G a A s . For modulators using naturally birefringent crystals, such as LiTaO"3, the crystal itself introduces an intrinsic phase retardation Si which can be determined b y using the natural birefringent indices ra , n and length of the crystal /. T h e retardation of the compensator S i n this Q  e  0  case is set at a value so that the sum of the intrinsic retardation Si and the compensator retardation SQ is equal to | , Si + SQ = \•  Appendix B  Components Used in the EOS System  B.l  Items used in EOS System • Polarizer T h e polarizer is a Melles Griot G l a n - T h o m p s o n p r i s m which made of birefringent material calcite and has an extinction ratio smaller than 1 x 1 0 . Its transmission -5  is larger than 98% i n the wavelength range 650-1100 n m . • analyzer The analyzer is a Melles G r i o t Wollaston prism. It is a cube made of two right angle calcite prisms of orthogonal optical axes. W h e n an optical beam passes through the interface of the two prisms, the ordinary beam and the extraordinary beam i n the first p r i s m become extraordinary and ordinary beam i n the second p r i s m , respectively.  A s a result of refraction at the interface, the input beam is split  into two orthogonally polarized beams. T h e Melles G r i o t Wollaston p r i s m 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 : C i r c u i t diagram of the custom-designed photoreceiver. (The author acknowledges M r . R o d Calinisan for m a k i n g the diagram.)  Appendix B. Components Used in the EOS System  Figure B.2: Complete Diagram of the E O S System  148  Appendix  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 i p , and the orientation of the optical axis of the probe t i p . In this appendix, we describe a simple method we developed for determining phase retardation. F i r s t , we describe how to measure the phase retardation of an anisotropic crystal. T h e n we describe how to use the method to determine the optical axis of a probe t i p . F i g . C l shows the simple experimental setup. It uses a laser, two polarizers and a power meter.  T h e probe tip 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. T h e optical axis of the crystal under test is set at 45 degrees w i t h respect to the polarizer. T h e 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 I  a  and  corresponding to the two analyzer positions.  It is obvious that the linearly polarized laser beam w i l l become elliptically 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 elliptically polarized beam are parallel to the axes of the two analyzer positions described above. words, the I  a  and  In other  are the decomposed intensities of the elliptically 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  Analyzer  Polarizer  Power Meter  Figure C . l : E x p e r i m e n t a l setup for measuring the phase retardation of an anisotropic crystal. T h e analyer can be rotated about the laser beam axis. the retardation S can be calculated from I and /(, by using the following formula: a  ='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 w i t h respect to the polarizer, the formula cannot be used. We have used this setup to measure the tuning range of the phase retardation introduced b y the compensator. The results are plotted i n F i g . 2.6. This method can also be used to determine the orientation of the optical axis of a probe t i p . F i r s t , we set the two polarizers perpendicular to each other. T h e n , we rotate the probe t i p about the axis normal to its foot print. W e 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. B u t 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 i p . 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 i p and the wave plate, the slow axis of the probe t i p 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 tip and the wave plate, the fast axis of the probe t i p is parallel to the optical axis of the wave plate. It should be pointed out that the optical axis of a probe t i p 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 : M a s k Layout for a Single-Gate-Contact M O D F E T w i t h Cascade electrod for R F measurement.  152  Appendix D. MODFET  Mask Layouts  Figure D . 2 : M a s k Layout for a double-Gate-Contact M O D F E T w i t h Cascade electro for R F measurement.  Appendix D. MODFET  Mask Layouts  154  Figure D . 3 : M a s k Layout for a Single-Gate-Contact M O D F E T w i t h coplanar striplines for E O S measurement.  Appendix D. MODFET  Mask Layouts  155  Figure D . 4 : M a s k Layout for a double-Gate-Contact M O D F E T w i t h 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