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Techniques for high-speed time-resolved device characterization 1995

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T E C H N I Q U E S F O R H I G H - S P E E D T I M E - R E S O L V E D D E V I C E C H A R A C T E R I Z A T I O N B y Saurin Shah B . A . S c . University of Waterloo, Waterloo, Canada, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Dec. 1995 © Saurin Shah, 1995 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of \\ le-CT/> I C*A &Y^{wt<e/l > The University of British Columbia Vancouver, Canada Date fg D £ £ . ; % DE-6 (2/88) Abstract The objective of this thesis is to address two open issues in time-resolved measurements of electronic devices. The first is the abili ty to perform measurements close to the device under test: we report a new approach to recover temporally-overlapping incident and reflected signals near a device. The technique involves electro-optic measurement at two locations. W i t h suitable time-domain or Fourier-transform processing, the measured waveforms can be decomposed into components propagating towards and away from the device. We show experimental results for coplanar structures. In the second part, we have identified a new feature in measured signals that we can attribute to substrate waves excited photoconductively during electro-optic sampling on coplanar striplines. Measurements at several positions laterally displaced from the center of the transmission line show that this substrate signal is confined to the neighborhood of the electrodes when the substrate is thin. We also show that this feature, which can be an impediment to accurate S-parameter characterization, can be eliminated by delaying it out of the time window of interest. Final ly, the Appendix lists the fabrication steps and process parameters for a lift-off process used to fabricate some of the samples used in this project. 11 Table of Contents Abstract ii List of Figures vi Preface viii Acknowledgment ix 1 Introduction 1 1.1 Introduction to Thesis 1 1.1.1 Overview 1 1.1.2 Summary of Results 2 1.1.3 Outline of Chapter 2 1.2 The Need for High-Speed Measurement Techniques 3 1.3 Coplanar Interconnects 4 1.3.1 Coplanar Waveguide and Coplanar Striplines 4 1.3.2 Surface Waves on Grounded and Ungrounded Dielectrics 7 1.4 Electro-Optic Sampling System 11 1.4.1 The Pump/Probe Technique 11 1.4.2 High-Speed Sampler 14 1.4.3 Photoconductive Generator 15 1.4.4 Performance 18 1.5 Two Open Issues in Time-Resolved Device Characterization 21 i n 1.5.1 Distinguishing Incident and Reflected Signals 21 1.5.2 Photoconductive Exci ta t ion 23 1.6 Outline of Thesis 24 2 Separating Temp orally-Overlapped Incident and Reflected Signals 25 2.1 Introduction to Chapter 25 2.1.1 Background and Motivat ion 25 2.1.2 Summary of Results 26 2.1.3 Outline of Chapter 27 2.2 Time-Domain Approach 27 2.2.1 Theory . . 27 2.2.2 Experimental Verification 31 2.3 Fourier-Transform Approach 36 2.3.1 Theory . 36 2.3.2 Experimental Verification 39 2.4 Experimental Considerations 43 2.5 Conclusions 46 3 Guided Substrate Waves Generated by Photoconductive Excitation 47 3.1 Introduction 47 3.1.1 Background and Motivat ion 47 3.1.2 Summary of Results 49 3.1.3 Outline of Chapter 50 3.2 Experiment 50 3.3 Results 51 3.4 Analysis 55 3.5 Conclusions 60 i v Bibliography A Experimental Device Fabrication List of Figures 1.1 Coplanar waveguide geometry and field distribution 5 1.2 Coplanar stripline geometry and field distribution 8 1.3 Surface waves on a dielectric slab 10 1.4 Surface waves on a grounded dielectric slab 12 1.5 Layout of the electro-optic sampling system 13 1.6 Sampling of electric field on the transmission line 15 1.7 Exci ta t ion of electrical signal . . . 16 1.8 L-shaped photoconductive switch 17 1.9 Step-like waveform generation on L T GaAs 20 1.10 Pulse generation using wire bond 22 2.1 Illustration for separation using time-domain approach 28 2.2 Layout of the open circuit used as D U T 31 2.3 Results for open-circuit device 33 2.4 Comparison between measured signals and reconstructed waveforms from recovered signals 35 2.5 Illustration of recovery of signals using Fourier-transform approach . . . . 37 2.6 Layout of the short circuit used as D U T 40 2.7 Results for short-circuit device 41 2.8 Comparison of Fourier-transform approach and time-domain approach . . 44 3.1 Photoconductively-sampled waveform showing back surface reflection . . 48 3.2 Sampled waveform showing the T H z feature 49 v i 3.3 Layout of coplanar stripline with photoconductive generator 50 3.4 Ar r iva l t ime of the T H z feature on samples wi th different substrate thick- nesses 52 3.5 Measured T H z signals for three substrate thicknesses 54 3.6 Relative delay of the T H z signal for various substrate thicknesses . . . . 57 3.7 Determination of crit ical thickness for the surface-wave-like mode . . . . 59 vn Preface Parts of thesis have been, or wi l l be, published under the following titles: • Chapter 2: — Millimeter-Wave Time-Resolved Measurement Near a Discontinu- ity: Separating Temporally-Overlapped Incident and Reflected Sig- nals, S. A . Shah, A . Zeng, W . S. Wong, M . K . Jackson, L . Pouliot, A . Lecours, and J . F . Currie, Accepted by I E E E Microwave and Guided Wave Letters. To be published in Volume 6, Number 2. — Separating Temp orally-Overlapped Waveforms with Electro-Optic Sampling, S. A . Shah, A . Zeng, W . S. Wong, M . K . Jackson, L . Pouliot, A . Lecours, and J . F . Currie, submitted to Optical and Quantum Electronics, 1 Nov. , 1995. • Chapter 3: — Guided Substrate Waves in Photoconductive Generation, S. A . Shah, A . Zeng, M . K . Jackson, L . Pouliot, A . Lecours, and J . F . Currie, to be submitted to I E E E Microwave and Guided Wave Letters. V l l l Acknowledgment First , I would like to thank my supervisor, Dr . M . K . Jackson, for his patient and knowl- edgeable supervision. I would like to thank my co-worker Andrew Zeng for his help in the lab. I would especially like to thank M a n i Vaidyanathan for great friendship, and reviewing my publi- cations. I would like to thank Benny Tsou for useful discussion about fabrication process and microwave during this project. Some of the samples used in this project were supplied by Dr . J . F . Currie and his co-workers at Department of Engineering Physics, Ecole Polytechnique, Montreal . I am grateful to them for supplying the samples quickly. Samples were also fabricated at the Department of Electrical Engineering and Depart- ment of Physics. I would like to thank Hiroshi Kato and Dr . N . Jaeger for providing me the facility for fabrication and guidance. I would also like to thank Dave for evaporating the metals on the samples and Dr . T . Tiedje for use of the Scanning Electron Microscope. During this research I have been supported by the Natural Sciences and Engineering Research Counci l of Canada ( N S E R C ) . This work was also supported by ( N S E R C ) under the individual research grants and the Networks of Centers of Excellence (Micronet) programs Final ly, I would like to thank my girlfriend, Shanthi, for her patience, concern about my health and providing dinners during long experimental days during this project. i x Chapter 1 In t roduct ion 1.1 In t roduct ion to Thesis 1.1.1 Overview This thesis describes techniques developed for high-speed characterization using time- resolved measurement methods like electro-optic sampling. High-speed active and pas- sive devices are under development in a frequency range where applications of conven- tional measurement equipment is l imited. Thus, alternate measurement techniques like electro-optic sampling are widely used. The work described in this thesis concerns two major open issues in time-resolved measurement methods: the extraction of signals from the measurements performed close to the device under test ( D U T ) and the properties of a T H z signal generated by photoconductive excitation. The first part describes a novel technique developed to separate incident and reflected signals when measurements are performed close to the D U T . This method has implications for characterization of high-speed devices using time-resolved techniques like electro-optic sampling and photo- conductive sampling. The second part describes a study of the properties of a T H z signal generated by the photoconductive switch and elimination of the T H z signal for accurate device characterization. 1 Chapter 1. Introduction 2 1.1.2 Summary of Results One of the major contributions described in this thesis is the development of a technique to separate the incident and reflected signals when measurements are performed close to the D U T . This was accomplished by electro-optic sampling at two different locations on the transmission line close to the D U T . W i t h suitable processing, the signals propagating towards and away from the device can be extracted from the measured waveforms. The theory was experimentally verified by using open-circuit and short-circuit as devices under test integrated with coplanar stripline. This thesis also describes a study of an unanticipated high-frequency feature appear- ing in measured signals; the arrival t ime of this signal was later than that of the signal traveling on the transmission line. We have identified the source of the feature, the pho- toconductive switch, which is capable of generating T H z bandwidth signals. The arrival t ime of the signal compared to that of the leading edge of the step-like signal traveling on the transmission line is related to the substrate thickness. Since the medium in which this T H z signal propagates is the substrate, we have studied the guiding of the signal with on- and off-axis measurements on samples with varying thickness. Measurements show that the T H z signal is guided underneath the transmission line in the substrate when the substrate is thin. Finally, we have effectively eliminated the T H z signal so that it does not interfere with device characterization. 1.1.3 Outline of Chapter The purpose of the Chapter 1 is to provide background information, introduce the topics to be discussed later in the remainder of the thesis and outline the rest of the thesis. Section 1.2 describes the motivation for using the time-resolved technique such as electro- optic sampling to characterize high-speed electronic devices. Section 1.3 describes the Chapter 1. Introduction 3 coplanar transmission lines and surface waves on a dielectric. The electro-optic sampling method is described in Section 1.4. In Section 1.5, two open issues in time-resolved measurement techniques that wi l l be addressed in the remainder of thesis are described. Finally, Section 1.6 describes the organization of the remainder of the thesis. 1.2 The Need for High-Speed Measurement Techniques Currently, high-speed active devices are being developed for analog and digital circuits for applications in fiber-optic systems, and satellite communication. Fiber-optic systems operating at 10 Gb i t / s are in production and systems with a transmission rate of 40 Gbi t / s are in the research and development stage. The demand for other applications operating at high speed is increasing rapidly as well. In order to design systems operating at high speeds and to bui ld test instruments for these systems, active devices such as high-speed bipolar transistors, modulation-doped field-effect transistors ( M O D F E T ) , and heterojunction bipolar transistors ( H B T ) are under development with ft and fmax as high as 340 G H z [1] and 455 G H z [2], respectively. These high-speed devices are integrated on an appropriate substrate by interconnecting them with transmission lines. The tra- ditional microstrip transmission line has high attenuation and dispersion values at these high frequencies. Thus, alternate transmission lines like coplanar stripline and coplanar waveguide are being developed. In order to design circuits operating at high speed, it is essential to understand the operation of active devices and the guiding properties of their interconnections. In order to develop physical understanding of the operation of the electrical devices, it is required to characterize them. Conventional characterization equipment like the network analyzer has a maximum bandwidth of 60 G H z for broadband measurement, and the sampling oscilloscope has a min imum risetime of approximately 5 ps. In addition, the Chapter 1. Introduction 4 network analyzer is only capable of making small-signal quasi-static measurements. Since the conventional electrical measurement methods are l imited in characterization of high- speed devices and interconnects that are under development, alternate optoelectronic methods based on the ultrafast lasers have been developed. Electro-optic sampling [3, 4] and photoconductive sampling [5, 6] are the most popular optoelectronic methods used to characterize high-speed active [7, 8] and passive devices [9, 10, 11]. The electro-optic system used for the development of techniques for time-resolved measurement presented in this thesis is briefly described in Section 1.4. 1.3 Coplanar Interconnects 1.3.1 Coplanar Waveguide and Coplanar Striplines Coplanar interconnects consist of conductors in the same plane, typically on the top surface of a dielectric substrate. The coplanar waveguide ( C P W ) and coplanar stripline (CPS) are two widely-used planar transmission lines in millimeter-wave and microwave circuits. Coplanar transmission lines have an advantage over the microstrip line in that shunt devices can be easily integrated to have the connection with the ground plane on the same side of the dielectric. Coplanar Waveguide The coplanar waveguide was proposed by Wen [12], and consists of a center strip with two ground planes located parallel to the strip placed on the same side of the dielectric surface as shown in F i g . 1.1(a). The electric and magnetic field configurations in the quasi-static l imi t are shown in F ig . 1.1(b). A simple quasi-static analysis for C P W can be carried out as in Ref. [12] using conformal mapping to determine the phase velocity and characteristic impedance for the case when the dielectric substrate thickness is sufficiently large to be Chapter 1. Introduction Figure 1.1: (a) Coplanar waveguide (CPW) geometry, (b) Electric and magnetic field distribution in CPW. (from Ref. [13]) Chapter 1. Introduction 6 considered infinite in the analytical model. It is also assumed that the thicknesses of the strip and ground plane electrodes are negligible. The phase velocity and characteristic impedance are given by r (1.1) _ SOTT K'(k) where c is the velocity of light in free space, K{k) is the complete elliptic integral of the first k ind and K'(k) = K(k'). The effective dielectric constant is given by £ r + 1 . s eefr = —^— • (1-3) Since we assume that eeff is independent of frequency, the group velocity is equal to the phase velocity; this is the quasi-static approximation. The parameters k and k' for ell iptic integral are defined as k' = Vl^¥ (1.4) anc where S and W are the widths of the center electrode and the gap, as shown in 1.1(a). Accurate and simple expressions for the ratio of K/K' are available [13]. K(k) 7T - forO<k< 0.707 (1.7) Chapter 1. Introduction 7 Coplanar Stripline The coplanar stripline (CPS) , which is complementary to the C P W transmission line, consists of two metallic strips running parallel on the same surface of the dielectric slab as shown in F ig . 1.2(a). The electric and magnetic field configurations are shown in F ig . 1.2(b). One can carry out an analysis similar to that used in the C P W case to determine the characteristic impedance and propagation velocity for the quasi-static approximation. Since C P S is complementary to C P W only equation 1.2 needs to be modified from set of equations (1.1)-(1.5). The characteristic impedance of the coplanar stripline is given by 7  12011 KW M 8̂ The velocity is given in this case by the same expression shown in E q . 1.1. 1.3.2 Surface Waves on Grounded and Ungrounded Dielectrics In this Section we examine surface waves on dielectrics, and their importance in coplanar interconnects. It is well known that a dielectric slab and a grounded dielectric slab are capable of guiding propagating electromagnetic energy. The energy is guided in the form of surface wave modes. Since the C P S and C P W are fabricated on a dielectric slab, one would expect that due to discontinuities formed by the connection of transmission lines with active and passive components with different characteristic impedance from the line that surface wave modes could be excited; this has been experimentally verified in Ref. [14]. The radiation of energy from coplanar mode to the surface wave modes can also occur even in the absence of discontinuities when the propagation constant of the coplanar transmission line is comparable to that of the surface wave modes [15, 16, 17, 18]. This leakage of energy causes attenuation of the guided wave on the coplanar lines at higher frequencies. Thus, it is essential to understand the properties of the surface wave Chapter 1. Introduction 8 Figure 1.2: (a) Coplanar stripline (CPS) geometry, (b) Electric and magnetic field distribution in CPS.(from Ref. [13]) Chapter 1. Introduction 9 propagating in the slab with or without metallization to design coplanar interconnects for high-speed operation. In the following two subsections we review the properties of surface waves in these two cases. Surface Waves on a Dielectric Slab On ungrounded dielectric slabs, surface waves have fields that decay exponentially away from the dielectric surface, with most of the field contained in the dielectric or near the surface. The two lowest order transverse electric (TE) and transverse magnetic ( T M ) modes are shown in F ig . 1.3(a) for a dielectric slab of thickness h. They are T E o , T E i , T M o and T M i . The surface wave propagation constants calculated for a GaAs dielectric slab are shown in F i g . 1.3(b) for the two lowest-order T E and T M modes. The y- axis of the F ig . 1.3(b) is plotted with units of normalized propagation constant of the mode; where B is the frequency-dependent propagation constant of mode and ko is the wavenumber related to the wavelength of signal in the free-space, Ao- ko = ^ (1.9) The frequency-dependent normalized propagation constant of a mode, B/ko, is often represented in the form of ^/e^g, where eeff is the effective dielectric constant of the mode. The x-axis is plotted with units of normalized frequency, h / A 0 ; where the wavelength of the signal in the free-space, Ao, is related to the frequency of the signal, / , given by Ao = j - (1.10) It is clear from F i g . 1.3(b) that the two fundamental modes, T E 0 and T M 0 , have no cutoff frequency, and that higher-order modes appear as the frequency of the signal is increased. However, if the signal has constant frequency spectrum then the higher-order slab modes can also appear when the slab thickness is increased. Chapter 1. Introduction 10 Figure 1.3: (a) Dielectric slab of thickness h with the four lowest order surface wave modes that may propagate. F ie ld intensity-is indicated as an excursion along y axis.(After Ref. [14]) (b) Surface wave propagation constants calculated for a GaAs dielectric slab wi th e r = 13. Chapter 1. Introduction 11 Surface Waves on a Grounded Dielectric Slab A grounded dielectric slab is a slab coated with metallic ground plane on one side. Similar to the ungrounded dielectric slab, the grounded dielectric slab can also guide the surface waves; these surface waves are different from those of an uncoated dielectric slab. However, it can be shown that the propagation constants for T E and T M modes of the grounded dielectric slab are same as those of odd T E and even T M modes of the ungrounded dielectric slab with twice the thickness of the coated dielectric slab. The two lowest-order modes of the grounded dielectric slab, T M o and T E l 5 are shown in F ig . 1.4(a). The propagation constants as a function of frequency for a metallized GaAs slab with thickness h are shown in F ig . 1.4(b). It is clear from F ig . 1.4(b) that T M 0 is the only mode that propagates at low frequency. As in the dielectric slab, the higher T E and T M modes of the grounded dielectric can also propagate as the frequency of the signal is increased. 1.4 Electro-Optic Sampling System In this Section we describe the electro-optic sampling system used in the work presented in this thesis. Fu l l details are given in Ref.[19]. 1.4.1 The Pump/Probe Technique The electro-optic sampling system is based on the pump/probe technique for time- resolved measurement of an electrical signal. The source of the pump and probe beams in our setup is a mode-locked Titanium-Sapphire laser which generates 150 fs pulses at a repetition rate of approximately 100 M H z . The laser output is split into two beams, refered to as pump and probe beams, using a beamsplitter as shown in F i g . 1.5. The pump beam is used to excite a fast electrical signal to the input of the device under test Chapter 1. Introduction 12 - -Magnetic Field — Electric Field T M 0 ielectric Slab 3.5 3 2.5 o CO. 1.5 TMfj/f : / / / J / / / / / / ! / i t 1 W i T E 2 I ' j i : / / ' / / / / r t 0.05 0.1 0.15 h/Xc (b) 0.2 0.25 0.3 Figure 1.4: (a) Grounded dielectric slab of thickness h with the two lowest order surface wave modes that may propagate. F ie ld intensity is indicated as an excursion along y axis.(After Ref. [14]) (b) Surface wave propagation constants calculated for a grounded GaAs dielectric slab with e r=13 and thickness h. Chapter 1. Introduction Mode-locked Ti-Sapphire Laser Beam Splitter At = 2L/c L Pump Beam Photoconductive, Generator 1 Probe Beam High-Speed Sampler Delay Line ii Data Acquisition & Analysis mj'PUTjm^sk^^ Figure 1.5: Layout of the electro-optic sampling system Chapter 1. Introduction 14 on the transmission line using a photoconductive generator. The response of the device is measured using the high-speed sampler and the probe beam. The t ime at which the response is sampled is determined by the path lengths traveled by the pump and probe beams from the beamsplitter to the photoconductive generator and sampler, respectively. The function of the delay line is to time-delay the probe beam relative to the electrical signal to be measured. B y varying the relative delay between pump and probe using the delay line, the response can be determined at any desired time. The optical delay-line is made up of two mirrors mounted on a motorized translation stage whose position can be accurately controlled. Since the optical path through the delay line is in air, the delay At is related to the speed of light, c, and change in path length, AL, by Since the pump and probe beams come from the same source at the beamsplitter both are perfectly synchronized, making electro-optic sampling a jitter-free measurement tech- nique. The excitation and measurement bandwidths are determined by the photocon- subsections. 1.4.2 High-Speed Sampler The high-speed sampler must be capable of measuring an electrical signal with a probe pulse. The high-speed sampler used in the electro-optic sampling system is an electro- optic amplitude modulator consisting of a linear polarizer, an electro-optic transducer, a compensator and an analyzer as shown in F ig . 1.6. The propagating electrical signal on the transmission line results in the formation of fringing fields in the semiconductor as well as in the air above the electrodes. As the probe tip is positioned above the electrodes, this fringing field produces a change in the birefringence of the electro-optic At = 2 . c ductive generator and the high-speed sampler which are described in the following two Chapter 1. Introduction 15 Probe Beam A In JL* Polarizer S Fringing Electric Field alyzer Compensator , • _ . . Data Analysis ilectro-Optic Transducer .Transmission Line Figure 1.6: Sampling of electric field on the transmission line using probe beam transducer through the electro-optic effect. The probe beam is polarized linearly before the tip and emerges from the tip with a polarization that is ell iptical . The degree of ell ipticity depends on the electric field in the tip at the instant the probe pulse passes through the t ip , and therefore provides a time-resolved measure of the voltage between the coplanar electrodes [3]. The compensator and analyzer convert this measure of voltage recorded to a change in intensity of the probe beam. The probe beam is detected with photodetectors. The output of the photodetectors are processed using a lockin amplifier and other electronics before being recorded as a voltage on the transmission line as function of delay. The bandwidth of the high-speed sampler is l imited by the lattice vibration frequency of the electro-optic transducer used; it is in excess of 1 T H z for the LiTaOs electro-optic transducer used in our setup. 1.4.3 Photoconductive Generator The photoconductive generator is an essential part of the electro-optic system, and gen- erates an electrical signal on the transmission line when triggered by the pump beam. A gap photoconductive switch integrated with a coplanar stripline and biased wi th a Chapter 1. Introduction 16 Pump Beam .Transmission Line (Metal) 7Z Photoconductive Switch V LLoad Figure 1.7: Exci ta t ion of signal by photoconductive switch controlled by pump beam D C voltage is shown in F ig . 1.7. The photoconductive switch is fabricated on a semi- insulating substrate, and typically has a dark resistance of several megaOhm. Before the pump beam arrives the voltage across the load is close to zero due to the high resistance of the photoconductive switch. The pump beam short-circuits the gap for a short t ime by generating a flow of photoexcited carriers. This generates transient signals on the transmission line which propagate towards the load and towards the D C power supply. The risetime of the signal is determined by the pulsewidth of the pump beam along with the design of the photoconductive switch. The fall t ime is related to the carrier recom- bination lifetime of the material on which the switch is fabricated. One can generate a step-like signal by using a semi-insulating semiconductor with decay time of the order of 40 to 300 ps for semi-insulating GaAs . Photoconductive generators fabricated on photo- conductive material damaged by ion-implantation with carrier lifetime in subpicosecond range is often used to generate pulse-like signals [20]. One can also decrease the carrier lifetime by growing a thin layer of GaAs on semi-insulating GaAs by molecular-beam epitaxy ( M B E ) under highly As-r ich conditions at substantially lower temperature than the conventional ones near 580°C [21]. This low-temperature grown G a A s (LT GaAs) Chapter 1. Introduction 17 Figure 1.8: L-shaped photoconductive switch integrated wi th a coplanar stripline to allow biasing of active devices for characterization. layer has large recombination-center density; as a result the carrier lifetime is reduced to the subpicosecond range. For characterization of active devices, an L-shaped photoconductive switch integrated with a coplanar stripline is often used [7]. A n accurate characterization of active devices such as transistors requires D C operation of the transistor at a bias point similar to that of a working circuit. S-parameter measurements or large-signal measurements are made by applying a stimulus signal on top of the biasing signal. Thus, independent control of the biasing supplies for the transistor and stimulus generator is required. The L-shaped photoconductive switch shown in F ig . 1.8 satisfies this requirement by having a separate D C power supply, Vbias, from the photoconductive switch power supply, V p h , and therefore the stimulus generated by photoconductive excitation in the L-shaped gap is added to the biasing voltage. The process responsible for generation of an electrical signal on the transmission line above is a very simple and widely-accepted view of a complex process. In fact, it is known that a photoconductive switch is capable of generating both guided and freely-propagating electromagnetic radiation with a T H z bandwidth [22]. The radiation coupled into the Chapter 1. Introduction 18 transmission line has been used for generation of electrical signals for high-speed mea- surement techniques such as electro-optic sampling [3] and photoconductive sampling [5] as described earlier in this subsection. In a similar configuration, the freely-propagating radiation generated has been used for free-space T H z transmission measurements [23]. In this case, the radiation is emitted into the substrate in a cone shape perpendicular to the surface and collected by a lens attached to the back side of the substrate. In addition, as describe in Section 1.3.2 above, the substrate can support various propagating modes. In general, these modes can be excited by the photoconductively-generated transient. In fact, we have observed T H z features travelling in the substrate along with the normal electrical signal traveling on the transmission lines; the details can be found in Chapter 3. 1.4.4 Performance In the two previous subsections, it has been claimed that the excitation and measurement bandwidths of the electro-optic sampling system are in excess of 1 T H z . Our standard electro-optic sampling setup restricts the min imum distance between the electro-optic transducer and the pump beam to 1.5 m m , thus attenuating and dispersing the high- bandwidth signal between the excitation and measurement locations. The risetime of the signal that can be measured 1.5 m m away from the photoconductive switch in our standard setup is approximately 2 ps. However, a signal has been measured by Zeng approximately 50 ^ m away from the photoconductive switch having a risetime of about 300 fs and F W H M of 500 fs by modification of the setup [19]; this demonstrates the system capability. The following subsections describe results of step-like waveform generation on an L T GaAs sample and generation of a broad bandwidth pulse by using a wire bond as examples to demonstrate normal performance of our measurement system. Chapter 1. Introduction 19 Step-Like Waveform Generation A n L-shaped photoconductive switch integrated with coplanar strip was fabricated by using the standard lift-off process described in Appendix A . The pattern was defined on the 0.3 /xm thick L T GaAs grown layer on 500 p,m thick semi-insulating GaAs substrate. Figs. 1.9(a) and (b) show top and side views of the sample, respectively. In F i g . 1.9(c) we show a step-like waveform measured approximately 1.5 m m away from the photo- conductive switch. The 10 to 90 percent risetime of the signal is approximately 2 ps. The feature appearing at approximately 17 ps is due to the T H z signal guided by the substrate that wi l l be discussed in Chapter 3. The signal remains at a constant level up to 45 ps. Since the L T GaAs photoconductive layer is expected to contain a^large num- ber of defects, it was expected that the signal generated should be pulse-like; however, a step-like waveform was observed. We can explain the observed result by considering the absorption of the pump beam power as a function of depth in the low-temperature and semi-insulating GaAs layers. The Ti-Sapphire laser in our experiment was operated at a wavelength around 830 nm where the GaAs sample has an absorption length of approxi- mately 1 / im , which is much longer than the 0.3 p,m thickness L T GaAs layer. Thus, we can expect that carriers would be excited in the thin L T GaAs layer wi th subpicosecond carrier lifetime as well as in the semi-insulating layer with long recombination carrier lifetime. A s a result, the generated electrical signal should be the superposition of a fast pulse with short fall-time and a step-like signal with slow decay. The signal plotted in F ig . 1.9(c) exhibits this behavior. We can expect the ratio of amplitudes of the ini t ia l pulse signal and step-like signal to be comparable to the ratio of absorption in the 0.3 /an and the GaAs substrate; the experimentally measured waveform shown in F i g . 1.9(c) is consistent with this. Chapter 1. Introduction 20 Figure 1.9: Step-like waveform generation by excitation of photoconductive switch fab- ricated on 0.3/500 fim LT GaAs/GaAs. (a) Top view of the sample (b) Side view of the sample (c) Time-resolved measurement Chapter 1. Introduction 21 Pulse Shaping using Wire Bond In addition to damaging the semiconductor or growing it at low temperature to reduce the recombination carrier lifetime, the generated step-like waveform can be reshaped to have a pulse-like waveform [24]. F ig . 1.10(a) schematically shows placement of a wire bond close to a photoconductive switch fabricated on a semi-insulating substrate to reshape the step-like waveform generated. The measurement location was selected approximately 1.5 m m away from the photoconductive switch. The measured pulse is shown in F i g 1.10(b). It has a shape similar to a single cycle of a sine wave. The power spectrum of the measured pulse is shown in F i g 1.10(c) obtained by Fourier transformation of the time- domain waveform. The 3dB bandwidth of the measured pulse is in excess of 300 G H z . Thus, by simply using the wire bond as filter one can generate a wideband pulse which could be used to perform S-parameter measurements of devices. 1.5 Two Open Issues in Time-Resolved Device Characterization 1.5.1 Distinguishing Incident and Reflected Signals In order to characterize an electrical device, it is essential to determine the excitation signal to the device and the response of the device. For example, conventional network analyzers used for S-parameter measurements have directional couplers attached to each port to separate the incident signal to the port from the reflected signal. In electro- optic sampling to make measurements of device input and output, the transient voltages are often measured on transmission lines connected to the device. Because electro-optic sampling is insensitive to the direction in which the measured signal is moving, signals propagating towards and away from the device cannot be distinguished if they overlap in time. For example, if a measurement is made at a fixed point on the input transmission line, the waveform wi l l first show the incident signal as it propagates toward the device Chapter 1. Introduction 22 Figure 1.10: Generation of pulse using wire bond (a) Sample layout (b) Time-resolved measurement (c) Power spectrum of the measured signal Chapter 1. Introduction 23 under test ( D U T ) , followed by the reflected signal. If the incident signal duration is greater than the round-trip time from the sampling location to the D U T , the incident and reflected signals wi l l temporally overlap and the two wi l l be indistinguishable. Thus, the electro-optic sampling method lacks any mechanism to separate the incident and reflected signals when measurements are performed close to the D U T . In Chapter 2 we propose and demonstrate a novel technique which allows us to separate the incident signal from the reflected signal. 1.5.2 Photoconductive Excitation In Section 1.4.3 we have stated that the photoconductive switch generates electromag- netic radiation with a T H z bandwidth and that only part of this radiation couples into the transmission line mode. The substrate is capable of supporting modes that can guide this T H z radiation as well. Thus, one would expect the generation of T H z pulses in the sub- strate to accompany the generation of electrical signals propagating on the transmission lines. In fact, there has been a brief description of a feature observed by photoconductive sampling that was attributed to a reflection from the back surface of the substrate [25]. We have also identified a feature appearing after the ini t ia l peak of the step-like signal at approximately 17 ps as shown in F ig . 1.9(c). It is essential to determine the propagation properties of this signal because if the signal is guided by the transmission line as part of the coplanar stripline mode then this wide-bandwidth signal can be used to characterize devices. However, if the signal is not part of the coplanar stripline mode the device may not respond to this wide-bandwidth signal and it wi l l interfere with the device charac- terization. In Chapter 3 we confirm the source of this feature as the photoconductive switch, and identify its propagation properties. In addition, we demonstrate a simple technique to effectively eliminate the feature. Chapter 1. Introduction 24 1.8 Outline of Thesis Chapter 2 addresses the issue of separation of incident and reflected signals from the over- lapping time-resolved signals measured close to a device. The time-domain and Fourier- transform approaches developed to process the measured signals are first described the- oretically with hypothetical examples. Both approaches are then experimentally verified by electro-optic sampling near open-circuit and short-circuit devices. Final ly, Chapter 3 describes a study of a newly identified feature in photoconductive generation. We have confirmed that the photoconductive switch is responsible for gener- ating this feature, and that it is due to a T H z signal traveling to the back surface of the sample before being reflected to the top. In order to study the propagation properties of this T H z signal, samples with different thickness were prepared. The sampling performed on the transmission lines (on-axis) allowed us to look at the signal traveling on the trans- mission line as well as in the substrate. A lateral displacement of the electro-optic probe far away from the transmission line allowed us to sample (off-axis) the signal traveling in the substrate. B y comparing on- and off-axis measurements for samples wi th different thicknesses we have concluded that the T H z signal is confined closer to the coplanar electrodes for th in substrates. Chapter 2 Separating Temporally-Overlapped Incident and Reflected Signals 2.1 Introduction to Chapter 2.1.1 Background and Motivation As described in Chapter 1, electro-optic sampling is insensitive to the direction in which the measured signal is moving, and signals travelling towards and away from the device can not be distinguished if they overlap in time. In order to characterize an electrical device it is necessary to have the incident signal separated from the reflected signal. So it is essential to be able to separate incident and reflected signals when measured close to the device under test ( D U T ) . Several approaches have been used to enable independent determination of the incident and reflected signals. The first, which is simple in princi- ple, involves determining the incident signal on a different test fixture by replacing the D U T with a through line or combinations of open, short, and matched load [26]. This approach relies on being able to generate the same input signal reproducibly with two or more generators, which requires careful control of excitation position and focusing, and cannot be verified during the measurement. The second approach relies on having an in- cident signal duration small enough that the sampling location can be moved sufficiently far from the D U T to prevent temporal overlap. Generation of short incident signals requires reduction of carrier life-time of photoconductor by ion-implantation damage or appropriate choice of the photoconductive material, which may be inconvenient or im- possible, especially when integrated on-wafer. In addition, the short pulses generated 25 Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 26 are inconvenient in studies of large-signal switching, where step-like signals are desirable. Furthermore, locating the signal generator far from the D U T limits excitation bandwidth because transmission lines on the semiconductor substrates are highly attenuating and dispersive at millimeter-wave frequencies [27]. Final ly, it is possible to use an attenua- tor as a directional device [28]; this approach depends on the quality of the broadband attenuator. Even though the electro-optic sampling system has demonstrated excitation and mea- surement bandwidth in excess of 1 T H z [4], the use of the system as time-domain network analyzer for small-signal characterization has been l imited up to 500 G H z due to inabil- i ty to separate incident and reflected waveforms when measured close to the D U T [29]. Thus, a technique is needed to recover temporally-overlapping incident and reflected signals while sti l l allowing their measurement close to the D U T . 2.1.2 Summary of Results To date, no technique has been reported to distinguish temporally-overlapping incident and reflected signals while st i l l allowing their measurement close to the D U T . We pro- pose a novel technique to accomplish separation of temporally-overlapping incident and reflected signals by making measurements at two locations. W i t h suitable processing using either a time-domain approach or a Fourier-transform approach, the measured waveforms can be decomposed into components propagating towards and away from the D U T . We have successfully demonstrated the time-domain approach by separating over- lapping incident and reflected signals using open circuit as D U T . We also have performed error analysis to determine the maximum separation between the two measurement loca- tions required to successfully resolve signals with a 3dB signal bandwidth loss. We have extended the technique for separation of overlapping signals from the time-domain ap- proach to a Fourier transform approach suitable for measured signals that can be Fourier Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 27 transformed. This extended method for separation of signals can be used to account for dispersion and attenuation between the two measurement locations if known. Further- more, we show that the signals can be recovered without any loss of bandwidth for any separation between the two measurement locations. The Fourier-transform approach is demonstrated by separation of incident and reflected signals measured near a short cir- cuit as D U T . Finally, we have compared recovered incident and reflected signals from the measurements on the short circuit sample using both approaches. 2.1.3 Outline of Chapter The time-domain approach which can be applied to any input signal is described in Section 2.2, which also includes a description of the experimental setup, results obtained, and discussion of the results. The technique developed exclusively for signals that can be Fourier transformed is described in Section 2.3. A description of the experimental setup and a discussion of the results are also included in this Section. The factors in the experimental setup that cri t ically affect the success of these approaches are described in Section 2.4. Final ly, conclusions are summarized in Section 2.5. 2.2 Time-Domain Approach 2.2.1 Theory To illustrate the technique involving only time-domain processing, hypothetical step-like signals measured for a D U T which is an open circuit are described below. In Figs. 2.1(a) and (b) we show the signals that would be observed at two positions between the generator and the D U T . F i g . 2.1(a) shows a typical signal 5u(£) measured at location A : the incident step-like signal finc(t) is followed later by a reflected signal fref(t) from the D U T . The curve in F ig . 2.1(b) shows the signal ^B(^) that would be observed at a location B closer Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 28 Time Figure 2.1: (a) and (b) Hypothetical waveforms that would be observed at two locations between the generator and an open-circuit device under test ( D U T ) . The waveform in (b) would be sampled at a location closer to the D U T , and the waveform in (a) further from the D U T . (c) Waveform related to the reflected signal, obtained by subtracting the time-shifted waveform of (a) from the curve of (b) as described in the text. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 29 to the D U T : the incident signal arrives slightly later, and the reflection slightly earlier. These signals can be expressed as 9 Ait) = fmc(t) + fref{t) (2.1) gB(t) = finc(t - r) + fref(t + r ) (2.2) where the time-shift is r = L/v. The length L is the separation between location A and B and v is the propagation velocity on the transmission line. In writ ing equations (2.1)-(2.2) we have assumed that attenuation and dispersion between two measurement locations are negligible over the frequency range of interest. This means that the only difference between the signals measured at the two locations originates in the t ime shift due to propagation delay. If the two sampling locations are close enough, then it is straightforward to recover both incident and reflected signals. For example, to recover the reflected signal fref(t) from the data of F ig . 2.1(b), we can shift the gA(t) in t ime by r so that the incident signal overlaps with the incident signal in the gsif)- Subtracting the time-shifted <7A(̂ ) from the gs(t) gives waveform gdiff(t) shown in F ig . 2.1(c). It is easy to show that for small spatial separation that the curve gdiff(t) of F ig . 2.1(c) is proportional to the derivative of the reflected signal fref(t): 9diff(t) = 9B(t) ~ 9A{t ~ T) = fref(t + T) ~ fref{t ~ T) „ 2rdfref(t) dt Thus, by numerical integration the reflected signal can be recovered. The incident com- ponent finc(t) of the measured signal can be obtained in a similar way by removing the reflected signal during the subtraction process. The reflected and incident signals are Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 30 given by fref(t) W J_ 9B(?) - 9A(t' - T) dt' (2-3) —oo 2r and fincif) ~ J 9A(t' + T) - gB(f) dt' (2.4) — oo 2r We have used a finite difference approximation for the time-derivative. In order to determine the effect of this approximation process on the recovered signals let call hrej(t) the reflected signal recovered; ideally it would be identical to / r e / ( £ ) . The recovered reflected signal href(t) is obtained from One can determine a relationship between the recovered signal href(t) and the true re- flected signal / r e / C O by Fourier-transforming E q . 2.5 followed by simplifications. The resultant relationship in the frequency domain is given by E q . 2.6 shows that the process of recovering signals has a low-pass filtering effect on the recovered signals with a frequency dependence sinciusr). From this, the 3dB bandwidth of the recovery process is 0.22/r. The accuracy of the recovered signals can be increased by decreasing the distance between measurement locations, provided the experimental signal-to-noise ratio is adequate. (2.5) href{u) sin(u>T) (2.6) Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 31 Excitation A B _L — 1 1 • 1 • H ^ • < 55 |Lim 55 L i m 2.5 m m 6 m m Figure 2.2: Layout of coplanar-stripline test-structure wi th open-circuit at the end, and a photoconductive generator. A l l gaps are 5 jiim. 2.2.2 Experimental Verification Experimental Arrangement The open circuit D U T shown in F ig . 2.2 was photolithographically defined on a 425 fxm thick semi-insulating GaAs substrate. The coplanar stripline electrode pattern is one that has been used to allow biasing of active devices [7, 8]; they were patterned by lift-off processing of an electron-beam evaporated bilayer of 10 nm of T i t an ium followed by 200 nm of Gold . Electro-optic measurements were made with 150 fs optical pulses, and an external LiTaOs electro-optic sampling tip with a footprint approximately 220 pm square. Whi le many measurements using external sampling tips have been made with the tip in direct contact wi th the transmission line, it has recently been shown that the impedance mismatch due to the LiTaOs tip can cause significant distortions of the measured results [30, 31]. Therefore, we used the non-contact configuration wi th an air gap between electro-optic transducer and transmission line of approximately 7 fj,m for all measurements. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 32 Results In F ig . 2.3 we show the data measured for the open-circuit sample described above, and the recovered incident and reflected signals. The solid line of F i g . 2.3(a) shows the signal gA(t) measured at location A of F ig . 2.2, which is located 650 jim from the open circuit D U T . The step-like incident signal /,- n c(t) starting at about 5 ps is followed by the reflection fref(t) which starts at approximately 17 ps. The dashed line in F i g . 2.3(a) shows the signal gs(t) measured at location B of F ig . 2.3, which is 50 /xm closer to the open circuit D U T than A . The 3dB bandwidth for the recovery technique for L = 50/xm separation is 500 G H z , which is much larger than the 100 G H z bandwidth of the signal generated. As expected, the incident signal is slightly delayed and the reflected signal is slightly advanced by the change in location. The sampling period was chosen to be 150 fs. In order to aid the numerical processing, the measured waveforms were interpolated by four points between each of the measured data points. The recovery process for the reflection signal described by (2.3) requires that the waveform gA(t) measured at location A to be time-delayed to cancel the incident com- ponent from the measured signal <7B(£). The time-shift, r , was chosen to give the best cancellation. The propagation velocity calculated from this t ime shift compares well wi th the measured velocity. This subtraction process was followed by numerical integration to obtain the signal reflected from the device, which is shown in F ig . 2.3(b) as a dashed line. The incident signal is recovered with a similar procedure, and is shown in F i g . 2.3(b) as a solid line. Discussion As expected, the retrieved incident and reflected signals of F ig . 2.3(b) show features evident in the measured data of F i g . 2.3(a) where both signals overlap. The 10 to 90 Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 33 Figure 2.3: Results for open-circuit device:(a) Waveforms measured at locations A (solid line) and B (dashed line) as shown in Fig. 2.2. (b) Recovered incident (solid line) and reflected (dashed line) signals. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 34 percent risetime of the recovered incident signal is 3.7 ps which is very close to the 3.8 ps risetime of the original incident component in the measured results. In this case, since the risetime and amplitudes of the retrieved signals are very close to the unprocessed measurements the choice of distance between the two locations is satisfactory. It is clear from F ig . 2.3 that the recovered incident and reflected signal are similar to the measured ones. To get a more quantitative measure of similari ty we have compared the measured waveforms with the waveforms reconstructed from the recovered incident and reflected signals. In Figs. 2.4(a) and (b) the solid lines show the total signals at locations A and B obtained by summing the recovered incident and reflected signals. The dashed lines in Figs. 2.4(a) and (b) show the difference between the reconstructed waveforms of F i g . 2.4 and the measured waveforms from F ig . 2.3(a); the difference is very small, showing that the recovered signals are in excellent agreement wi th the measure- ments. The ratio of the rms value of the error waveforms shown with dashed lines in F ig . 2.4 and the rms value of the measured waveforms in F i g . 2.3(a) at locations A and B are 0.012 percent and 0.016 percent, respectively. The above results show that overlapping incident and reflected signals can be re- covered from measured waveforms by processing in the time-domain and the recovered waveforms agree with the measured results. This is the first demonstration of an ap- proach to achieve extraction of step-like signals when measurements are performed close to the device. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 3 5 3 CD O 0.15 0.10 0.05 0.00 0.15 0.10 0.05 0.00 — ' 1 ' 1 1 1 1 1 1 1 • / (a) / (b) / 1 1 . 1 . 1 . 1 0 10 15 20 Time (ps) 25 30 Figure 2.4: Total signals at locations A and B reconstructed from the recovered signals are shown wi th the solid lines in panels (a) and (b), respectively. The difference between the reconstructed signals and the actual measurements are shown as dashed lines in panels (a) and (b), respectively. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 36 2.3 Fourier-Transform Approach 2.3.1 Theory The time-domain approach presented in the previous Section has the advantage that the processing is easily applicable to any incident or reflected signals; the l imitat ion is that the measurement locations must be closely spaced to give adequate measure- ment bandwidth, so that no significant dispersion or attenuation occurs between the two locations. In the following we outline a more general approach that accounts for dis- persion and attenuation, and allows arbitrarily large separation between measurement locations; this approach can only be applied to measured signals that can be Fourier transformed. It is interesting to note that the time-domain microwave simulation tech- niques like Transmission-Line Mat r ix ( T L M ) and finite- difference time-domain ( F D T D ) methods also faces a similar problem when calculations of scattering parameters for a port are required. Thus, numerical processing methods similar to our Fourier-transform approach are used during simulations to calculate the scattering parameters [32]. We outline the Fourier-transform approach by using a hypothetical example to demon- strate that the Fourier-transform approach works remarkably well in the ideal case and to emphasize the usefulness of this approach for S-parameter measurements of a device. To illustrate the technique, suppose that the photoconductive switch generates a pulse as shown in F ig . 2.5(a). A hypothetical reflected pulse from the D U T that is broader and smaller compared to the incident pulse is shown in F ig . 2.5(b). As in the previous Section we assume the signals measured at the two locations A and B have incident and reflected components. The measured signal. 5^(2) at location A as shown in F i g . 2.5(c) with solid line can be expressed as in equation (2.1) of the previous Section. The signal measured at location B is gB(t) = hinc(t) + href(t) Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 37 Freq.(THz) Time(ps) Figure 2.5: Hypothetical example illustrating the technique to separate signals using Fourier-transform approach: (a) Incident signal at location A . (b) Reflected signal from the device under test at location A . (c) Waveforms measured at locations A (solid line) and B (dashed line), where location B is closer to the device, (d) Magnitude spectrum of waveforms measured at location A (solid line) and location B (dashed line), (e) Magnitude spectrum of recovered incident signal (solid line) and reflected signal (dashed line) obtained by method outlined in the text, (f) Recovered incident signal (solid line) and reflected signal (dashed line). Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 38 where the incident and reflected components, hinc(t) and href(t), differ from those mea- sured at location A because of time-delay, dispersion and attenuation. In our hypothet- ical example we have assumed that there is no dispersion and attenuation between two locations. Thus, the dashed line in F ig . 2.5(c) shows the signal gs(t) that would be mea- sured at location B which is a superposition of time-delayed incident and time-advanced reflected signals. The Fourier transform of equations (2.1) and (2.7) shows that where T(u>,L) describes the transmission of a signal traveling on a transmission line of length L; it is given by The complex, frequency-dependent propagation constant 7 describes attenuation and dispersion characteristics of the transmission line; in the following we assume that it is known as a function of frequency as determined by measurements such as those given in Ref. [9]. If the attenuation and dispersion are negligible over the separation L, then T(u>,L) describes a simple phase shift between the two measured signals. This phase shift is equivalent to a time shift of the signal in the time domain. In F i g . 2.5(d) we show the magnitude spectra of the waveforms shown in F ig . 2.5(c) to demonstrate that the Fourier-transform of the measured signals can be significantly different from those of the recovered signals. We can extract incident and reflected signals as a function of frequency from the spectra shown in F ig . 2.5(d) as follows. The incident and reflected signals can be obtained from equations (2.8), and (2.9) as (2.8) (2.9) T(w,L) = e - ^ ) L . (2.10) Finc{u) GA{U)T-\L>,L)-Gb(U) T-i(u,L)-T(u,,L) (2-11) Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 39 and GB(u)-T{u,L) GA(u>) T-^,L)-T(u,L) (2.12) The magnitude spectra of the recovered incident and reflected signals in this hypothetical example are shown in F i g . 2.5(e) with solid and dashed lines, respectively. As expected the magnitude spectra of the recovered signals are Gaussian since the hypothetical mea- sured signals in the time domain are Gaussian. One can obtain the reflection coefficient as a function of a frequency for our hypothetical device just by taking the ratio of the extracted reflected and incident signals. The recovered signals transformed to the t ime domain using the inverse Fourier transform are shown in F i g . 2.5(f). The recovered sig- nals are identical to the incident and reflected signals plotted in F i g . 2.5(a) and (b), which were used to construct the hypothetical measured signals gA(t) and gB(t)- In summary, the approach presented in this Section has advantages compared to the time-domain approach if the measured signals can be Fourier transformed, because it eliminates the finite-difference approximation required in the time-domain approach. This allows signal recovery for arbitrary separation without bandwidth l imitat ion. The above method can be further extended in the case when attenuation and dispersion characteristics of the line are not known by performing measurements at three separate locations instead of two. Details of this are beyond the scope of the present work. 2.3.2 Experimental Verification Experimental Arrangement The short-circuit D U T shown in F ig . 2.6 was photolithographically defined on a 425 pm thick semi-insulating GaAs substrate; the pattern was defined by evaporation of 10nm/200nm thick T i / A u followed by lift-off. During the experiment, we used the non- contact configuration with an air gap between electro-optic transducer and transmission Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 40 Excitation A B J _ — I 1 1 • 1 h4 • i ^ • ! 55 Lim 55 Lim 2.5 mm 6 mm Figure 2.6: Layout of coplanar stripline test-structure with short-circuit device, and a photoconductive generator. A l l gaps are 5 /mi . line of approximately 5 /mi for al l measurements. The other experimental details are identical to those described in Section 2.2.2. Results In F ig . 2.7 we show the data measured for the short-circuit sample described above, and the recovered incident and reflected signals. The solid line of F ig . 2.7(a) shows the signal gA(t) measured at location A of F ig . 2.6, located 600 /mi from the short-circuit D U T . The step-like incident signal finc(t) is followed by a negative-going step-like reflection frefit) starting at approximately 17 ps. The dashed line in F ig . 2.7(a) shows the signal <7B(0 measured at location B , which is 50 fim closer to the short circuit than A . The measured signals gA{t) a n < i <7BOO approach zero at approximately 30 ps. The sampling period was chosen to be 167 fs. For numerical processing, the measured waveforms were interpolated by four points between each of the measured data points. To perform the Fourier transform, we assumed that the measured signals remain at zero after 30 ps. This assumption is not exact but it works nicely for our demonstra- tion. The magnitude spectra of the measured signals at locations A and B are shown in Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 41 Frequency (THz) Time (ps) Figure 2.7: Results for short-circuit device: (a) waveforms measured at locations A (solid line) and B (dashed line) of F ig . 2.6; (b) magnitude spectra of the measured waveforms; (c) magnitude spectra of recovered incident (solid line) and reflected (dashed line) signals; (d) recovered incident (solid line) and reflected (dashed line) waveforms. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 42 F ig . 2.7(b) as solid and dashed lines, respectively. The magnitude spectra look quite sim- ilar as expected from the time-domain signals. However, the second peak in the spectra is slightly shifted towards high-frequency in the dashed line curve corresponding to location B ; this is to be expected since the delay between the positive-going incident signal and the negative-going reflected signal is less in the measured signal. Since the measurement sep- aration of 50 p,m is small, we have assumed that dispersion and attenuation are negligible. The constant propagation velocity v was determined by measurement. The magnitude spectra of the recovered incident and reflected signals are shown in F i g . 2.7(c) as solid and dashed lines, respectively. The magnitude spectra of the recovered signals are quite different; the recovered reflected signal clearly show loss of energy approximately between 10 G H z and 100 G H z . The time-domain recovered waveforms are plotted in F ig . 2.7(d), where the solid line shows the incident signal, and the dashed line the reflection. Discussion The recovered incident signal plotted with solid line in F i g . 2.7(d) shows step-like signal with maximum amplitude close to that seen in the measured signals in F i g . 2.7(a). The features in the recovered incident signal between 10 to 15 ps are similar to the measured signals. It is interesting to note that the reflected signal amplitude is significantly smaller than the incident signal, indicating that reflection from the short circuit is lossy in the frequency range considered here. In general, the recovered signal is a negative-going step-like signal as expected from a short-circuit. The amplitude of both recovered signals at 30 ps are the same with opposite signs to make overall signal zero as assumed. The 10 to 90 percent risetime of the recovered incident signal is 3.9 ps which is similar to those of the measured signals further proving that the Fourier-transform approach is not bandwidth l imited. Here we have demonstrated that it is not necessary to have pulse- like individual incident and reflected signals to use the Fourier- transform approach; the Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 43 approach works equally well with the incident and reflected signals of any shape provided measured signals can be Fourier-transformed. Final ly, we compare the Fourier-transform method demonstrated in this Section to the time-domain approach. The time-domain approach of Section 2.2.1 was used to recover the incident and reflected signals from the data of F ig . 2.7(a) for the short-circuit device; the results are shown as the dashed lines in Figs. 2.8(a) and (b). For comparison, the solid lines in Figs. 2.8(a) and (b) show signals obtained by processing in the frequency domain. The features in the recovered signals using both techniques are quite similar. The discrepancy can be attributed to the slight difference in the propagation velocity used in the two approaches. The non-zero component in the recovered reflected signal at approximately 7 ps can be attributed to the fluctuations in laser power during the measurement, as wi l l be discussed in the following Section. In summary, we have demonstrated that one can recover overlapping signals by pro- cessing in the frequency domain. The recovered waveforms using the Fourier-transform approach are quite similar to the ones obtained by performing calculations in the t ime domain. 2.4 Experimental Considerations There are several experimental factors that play a significant role in determining the suc- cess of the two techniques described in the previous Sections. As described by equations (2.4), (2.3), (2.11), and (2.12) both methods rely on cancelling the incident component to determine the reflected signal and vice versa. Thus, it is essential to have identical con- ditions when signals are measured at two separate locations. The crit ical experimental factor is the drift in the laser power over time. Typica l ly about 6 to 7 signals were aver- aged to obtain the waveforms shown in this Chapter. It took an average of 10 minutes Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 44 Figure 2.8: Comparison of results for short-circuit device: (a) incident signal; (b) reflected signal. In both panels the dashed line shows results obtained by time-domain processing, and the solid line by frequency-domain processing. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 45 to do a single scan, so the laser power and alignment have to be steady for about two hours to have identical measurement conditions. A n y drift in the laser power can show up as features in the recovered signals that are not present in both measured signals. Futhermore, changes in laser alignment or power in general do not have a linear effect on the excited signals that can be easily corrected since the photoconductive switch is a non-linear device with respect to pump power and pump beam location. The second critical factor is the alignment of the LiTaC"3 transducer during change in measurement locations. One cannot move the probe-beam inside the transducer to have change in measurement locations since the measured signal inside the transducer can be location dependent [30, 31]. Thus, it is essential to move either the transducer and the probe beam, or the sample holder and the excitation beam. During this translation it is necessary to have constant air-gap between the transducer and the sample as well as to have identical sampling location for probe-beam on the transmission line. During change in the measurement location, it is also essential to have identical excitation locations since the excitation location has a large effect on the shape and amplitude of the waveform generated. It is clear from equations (2.11)- (2.12) that the accuracy of the results for the Fourier- transform approach depend on the accuracy of the translation stage used during change in measurement locations. In summary, there are several experimental factors that wi l l determine accuracy of the recovered results and success of the above techniques. These weaknesses can be overcome by carefully designing and conducting the experiment. Chapter 2. Separating Temporally-Overlapped Incident and Reflected Signals 46 2.5 Conclusions We have proposed and demonstrated a new technique, based on electo-optic sampling at two different locations, to resolve superimposed incident and reflected signals propagat- ing in opposite directions. If the two locations are close to one another, the incident and reflected signals can be separated unambiguously using simple time-domain processing. To allow high-bandwidth signal recovery, the two sampling locations must be separated by a small distance. We have also extended this approach for signals that can be Fourier transformed, and accounted for dispersion and attenuation between the sampling loca- tions using processing in the frequency domain. This Fourier-transform approach has the advantage that there is no bandwidth l imitat ion for any separation of measurement locations. Final ly, we note that the technique we have described can be applied to any time-resolved sampling technique including photoconductive sampling. Chapter 3 Guided Substrate Waves Generated by Photoconductive Excitation 3.1 Introduction 3.1.1 Background and Motivation As briefly described in Chapter 1, electro-optic and photoconductive sampling employ a photoconductive switch to generate fast electrical signals on the transmission line. The photoconductive switch is also capable of generating T H z bandwidth signals which could propagate in the substrate. The first observation of a feature generated by the photo- conductive switch and attributed to a reflection from the back surface of the substrate was observed by photoconductive sampling on the coplanar transmission line [25]. The dotted line in F i g . 3.1 shows the photoconductively-sampled waveform from Ref. [25]. The feature represented by the first positive-valued peak to the right of the main peak is due to a reflection from the backside of the substrate. The authors of Ref. [25] have observed a direct correlation between the relative arrival t ime of the substrate reflection with respect to the main peak and the substrate thickness. They have completely re- moved the observed back side reflection from the sampled waveforms and also decreased the amplitude of the shoulder by placing a microwave-absorbing material on the back side of the wafer; the waveform showing elimination of the back side reflection is plotted with the solid line in F ig . 3.1. 47 Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 48 a. 2 < 1 ft' 1 - I, : \ ^ «•*% \ ^ — — \ r-v —J i i i 0 25 50 75 100 125 150 TIME (ps) Figure 3.1: Sampled waveform showing the back plane reflection. The dotted line shows a waveform exhibiting a reflection from the back side of the substrate as manifested by the first positive-valued peak to the right of the main peak. The solid line represents the sampled data acquired from a transmission line when a microwave-absorbing material was placed under the GaAs wafer(from Ref. [25]). In Fig. 1.9(c) of Chapter 1 and replotted in Fig. 3.2, we have also seen a feature at approximately 17 ps that cannot be correlated with any physical spacing of the trans- mission line discontinuities. The feature arrives at a sampling location remote from the photoconductive generator at a time later than the signal travelling on the transmission line; we will refer to this feature as the THz signal. In order to identify the path trav- elled by this THz signal we need to perform measurements on similar coplanar structure fabricated on semi-insulating GaAs with various substrate thicknesses. Furthermore, it is essential to determine the propagation properties of this THz signal. If the signal is guided by the transmission line as part of the coplanar stripline mode then this wide- bandwidth signal can be used to characterize devices. However, if the signal is not part of the coplanar stripline mode the device may not respond to this wide-bandwidth signal and it will interfere with device characterization. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 49 20 30 Time (ps) Figure 3.2: Electro-optic measurement showing the T H z feature at approximately 17 ps generated by the photoconductive switch. The sampling was performed on the L T GaAs sample approximately 1.5 m m away from the photoconductive switch. 3.1.2 Summary of Results We show clear observations of a T H z signal generated by the photoconductive switch and measured on the transmission line. The arrival t ime is related to the thickness of the substrate. B y making measurements on the transmission line (on-axis) and far away from the transmission line (off-axis) we are able to clearly show that the T H z feature is due to electromagnetic waves traveling in the substrate. In addition, the electro-optic technique provides a unique probe of the properties of these substrate waves: we find that they are trapped beneath the metallic electrodes in samples with thin substrates. Final ly, we have been able to eliminate this substrate-wave signal by effectively increasing the thickness of the substrate; this delays the signal sufficiently that it arrives outside the time window of interest. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 50 Sampling Figure 3.3: Layout of coplanar stripline with a photoconductive generator (not to scale). A l l gaps are 5 pm, and locations A , B , and C are the excitation positions referred to in the text. 3.1.3 Outline of Chapter In Section 3.2 we describe the experimental arrangement and sample preparation. The electro-optic sampling measurements for samples with different thicknesses are presented in Section 3.3. These results are discussed in Section 3.4. Final ly, in Section 3.5 we have summarized our conclusions. 3.2 Experiment The coplanar stripline (CPS) shown in F ig . 3.3 is photolithographically defined on semi- insulating GaAs substrates of varying thicknesses: 500 and 650 pm. The metallization on 650 pm thick samples are defined by evaporation of 10nm/200nm thick T i / A u followed by lift-off. Exci ta t ion is at one of locations A , B and C; dimensions are shown in F ig . 3.3. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 51 Whi le many measurements using external LiTaG"3 sampling tips have been made with the tip in direct contact with the transmission line, it has recently been shown that the impedance mismatch due to the LiTaO"3 tip can cause significant distortions of the measured results [30,.31]. Therefore, we use a non-contact probing configuration wi th an air gap between electro-optic transducer and transmission line to reduce the distortions of the measured results. In addition to measurements on the axis of the transmission line, we also make measurements with the probe tip laterally displaced from the center by varying distances; we wi l l refer to the two types of measurements as on- and off-axis, respectively. A switch bias of 7.5V was used in all measurements. 3.3 Results Initial measurements of the T H z signal were performed on samples with substrate thick- nesses of 650 /um and 500 /xm. The sampling locations for these on-axis measurements are approximately 1.5 m m away from the photoconductive switch and excitation is at position A of F ig . 3.3. In F ig . 3.4 the solid and dashed lines show signals measured on the 650 and 500 pm thick samples, respectively. We have time-shifted the two signals so that the leading edges coincide to facilitate direct comparison of the relative arrival times of the T H z signals. The arrows in F ig . 3.4 indicate the T H z feature in each mea- surement. It is clear from F ig . 3.4 that the relative arrival t ime of the T H z signal varies with substrate thickness, indicating it travels in the substrate. To further study the properties of the T H z signal, we prepared a new set of samples with a wider range of substrate thicknesses. In addition, in these samples we perform on- and off-axis measurements. In F ig . 3.5(a) the solid line shows the signal measured on-axis for a sample with substrate thickness of 650 p,m. The sampling location for this case is approximately 1.67 m m from the photoconductive switch, and excitation is at Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 52 -5.0 0.0 5.0 10.0 15.0 Time (ps) Figure 3.4: Electro-optic sampling measurements performed approximately 1.5 mm away from the photoconductive switch: the solid and dashed lines show measurements for 650 thick and 500 pm thick samples, respectively. The arrows indicate the THz feature in each waveform. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 53 position A of F ig . 3.3. As expected with the long-lifetime semi-insulating substrate, the generated signal is step-like. However, at approximately 16 ps a new feature is seen with a number of oscillations with a period of approximately 1.5 ps. Bo th the T H z feature and the step signal disappear with zero bias and changes its sign when negative bias voltage is applied to the photoconductive switch verifying that both features are generated by the photoconductive excitation at the switch. Because generation of T H z radiation is related to the separation of charges that occurs after photoconductive excitation, one might expect the oscillatory feature we see to depend upon the direction of the charge separation with respect to the measurement position. We checked this by excitation at the three locations A , B , and C of F ig . 3.3. A t all three positions we observe similar T H z signals, indicating that the orientation responsible for generation of the feature we see is perpendicular to the metal-semiconductor interface. To further characterize the T H z signal, we make measurements off-axis at a distance 350 pm from the center of the transmission lines. W i t h our electrode width of 55 pm we would expect to detect only a small signal from the fringing field of the radiation propagating in the fundamental C P S mode; any observed signal should be related to the evanescent field of any substrate modes that are excited. We have verified that the leakage of field from the transmission lines into the transducer during off-axis probing is small by comparing the electro-optic signals measured on and off-axis when a D C calibration signal is applied to the transmission line. In F i g . 3.5(a) we show the off-axis measurement as a dashed line. The main feature observed in the off-axis curve is an oscillatory feature starting at approximately 16 ps. It is nearly identical in amplitude to the T H z feature observed on-axis. We have performed off-axis measurements at other locations with distances up to 500 pm away from the transmission line and similar off-axis waveforms are observed. To further study the effect of substrate thickness we prepared a sample with 83 Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 54 i 1 1 1 1 1 1———I r • I i I i I i I L 0 5 10 15 20 25 Time (ps) Figure 3.5: Measured signals for three substrate thicknesses, (a) On-axis (solid line) and off-axis (dashed line) measurements for a 650 p,m thick sample, (b) On-axis (solid line) and off-axis (dashed line) measurements for the 83 pm thick sample, (c) On-axis measurements for the 1.3 m m thick sample. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 55 pm substrate thickness by mechanical lapping (grinding) of a 650 pm thick substrate. In F ig . 3.5(b) we show the on- and off-axis measurements as the solid and dashed lines, respectively; sampling and excitation conditions are the same as those used for F i g . 3.5(a). Note that to facilitate comparison of the waveforms for different samples, we have time- shifted the curves of F ig . 3.5(b) so that the leading edge of the on-axis signal coincides with the corresponding waveform of F i g . 3.5(a). The on-axis signal has oscillatory features appearing very soon after the ini t ial peak; in addition, the relative amplitude of these features is significantly greater than in the 650 pm sample. The off-axis measurement shows no obvious evidence of a substrate signal in this case; the origin of the smaller features occurring after approximately 15 ps is not known. Because these T H z signals are problematic in device characterization, it is important to be able to eliminate them from the measurements. In Ref. [25] microwave-absorbing material on the backside of the substrate was used to eliminate the backside reflections. A n alternative approach is demonstrated in F ig . 3.5(c), where the 650 p,m sample being tested is placed on another unpatterned substrate of equal thickness. In this case the sampling location was 1.5 m m from the photoconductive switch. As can be seen in F ig . 3.5(c), only a step-like signal is seen in the time-window shown; the T H z signal actually arrives at approximately 31 ps. We see no evidence of a reflection from the interface between the two substrates, which are simply cleaned and held in mechanical contact. 3.4 A n a l y s i s As seen in the curves of Figs. 3.4 and 3.5, the delay between the leading edge of the step- like and the T H z signals varies significantly with substrate thickness. A simple estimate of the expected delay can be made if we assume the C P S signal travels with a relative Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 56 dielectric constant of (e r + l ) / 2 and the substrate wave travels wi th the relative dielectric constant of the substrate, e r. The substrate wave is assumed to be reflected from the backside, and thus travels a distance that can be simply related to the thickness of the substrate and the position of the sampling location. The delay At is given by where z is the distance from the photoconductive switch to the sampling location, and h is the substrate thickness. In F ig . 3.6 we show the delay A i calculated from E q . 3.1 for £ = 1 . 5 and 1.67 m m as a function of GaAs substrate thickness. We have estimated the relative arrival t ime from the measured waveforms by comparing the delay between the beginning of the step-like, and the T H z signals. The delay estimated for waveforms in F ig . 3.4 are plotted in F ig . 3.6(a) with open circles. F i g . 3.6(a) also includes the delay obtained from the measurement on the 1.3 m m thick GaAs . The delay estimated for on-axis waveforms plotted in Figs. 3.5(a) and (b) for 650 pm and 83 pm thick GaAs substrates are indicated in F ig . 3.6(b). Since it is difficult to determine the beginning of signals the estimated error bars for the delays are also shown in F i g . 3.6. It is clear from Fig . 3.6 that the delay estimated by E q . 3.1 agrees very well wi th the relative arrival times observed, confirming our interpretation of the origin of the signal as reflection from the backside of the substrate. It is interesting to note that the highly-structured T H z signals observed are quite different from those reported in Refs. [23] and [25]. This may be due to the l imited bandwidth for the photoconductive sampling used in Ref. [25]. A direct comparison with the results of Ref. [23] is difficult because of the difference in the direction of ob- servation, and sample geometry. A n explanation for the observed resonance can be found in Ref. [17], where loss on coplanar waveguides ( C P W ) due to coupling between the C P W mode and surface-wave modes was studied. They predicted that for finite Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 57 0.2 0.4 0.6 0.8 1 GaAs substrate thickness (mm) 1.4 0.4 0.6 0.8 1 GaAs substrate thickness (mm) Figure 3.6: Relative delay of the T H z signal calculated from E q . 3.1 for various substrate thicknesses is plotted with the dashed line. The panels (a), and (b) are for distances of 1.5 and 1.67 m m from the photoconductive switch to the sampling location, respectively. The experimental delay from the measured waveforms are plotted with the open circles. The vertical bar through the circle is an error bar for the experimental delay. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 58 ground-electrode widths, resonances would occur in the CPW/surface-wave coupling due to reflections of the surface-wave confined under the electrodes from the outer edges of the ground electrodes. In our situation, such reflections could occur at the outer edges of the two electrodes; the traversal t ime across the 115 pm width of the transmission line by a substrate wave travelling with the dielectric constant of the substrate is approxi- mately 1.4 ps. A recent study of such leakage in coplanar striplines has been reported in Ref. [33]; their study shows no resonances in the C P S mode loss that can be attributed to the resonances seen in the C P W case. However, in using the theoretical studies of surface-wave leakage in the interpretation of our results, it is important to stress the dif- ferences between the calculations and our experiments. The calculations show the effect of surface-wave modes on the propagation of the C P S or C P W modes; the properties of surface wave modes are determined mainly by looking at their influence on the funda- mental coplanar modes. However, in our case we are directly probing the properties of the substrate modes that we have photoconductively excited, even in situations where they may not have great influence on the fundamental C P S mode. A full calculation of the properties of the surface waves has not been reported, and is beyond the scope of the present work; however, we do not feel that the results of Ref. [33] are in contradiction with our interpretation of the resonance in terms of reflections at the outer edges of the electrodes. We further note that this explanation is consistent with the fact that the oscillation period is not significantly affected by the substrate thickness. Another surprising feature of the data shown in F i g . 3.5 is that while the substrate- wave features are very pronounced in the thin sample measured on-axis, no signal is seen off-axis. This means that for the thin sample, the radiation is confined in the vicini ty of the coplanar electrodes. This effective guiding of the surface-wave modes by the metallic electrodes is consistent with the conclusions of Ref. [33], where it was shown that in addition to the C P S mode, a coplanar stripline can also guide a new surface-wave-like Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 59 3.5 2.5 o CO. 1.5 c PS mi ode / / / ' / / / / / / / / / / 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Figure 3.7: Effective dielectric constant for TEo mode of GaAs slab is plotted as a function of h/Xo using the dashed-dot line. The effective dielectric constant of the C P S mode on a GaAs substrate is plotted with the solid line. The crit ical h/Xo where the new surface-wave-like mode wi l l become leaky can be estimated from the point where two curves cross. Chapter 3. Guided Substrate Waves Generated by Photoconductive Excitation 60 mode for th in substrates. The new surface-wave mode has a field distribution similar to that of the TEo mode of the surrounding dielectric. L i n [33] also pointed out that in thick substrates this new mode evolves into a complex leaky mode with power coupling into the TEo mode, similar to what is seen in Ref. [17] for the C P W case. In F ig . 3.7 we show the dispersion curve of the T E 0 mode for the GaAs substrate. We have also plotted the quasi-static effective dielectric constant eeff of the C P S mode on GaAs . According to Ref. [33], a guided surface-wave-like mode can be supported for substrates thinner than a crit ical thickness where the effective dielectric constants of the C P S mode and the TEo mode of the surrounding dielectric slab are equal. From F i g . 3.7 we can estimate that this occurs at /i/Ao=0.1. For our case, where the period of the T H z signal is approximately 1.5 ps, or Ao=450 pm, the crit ical substrate thickness is thus approximately 50 pm. Therefore we expect the substrate waves in the 650 pm sample to be quite leaky, and those in the 83 pm sample to be much closer to being perfectly guided. 3.5 C o n c l u s i o n s We have shown that new features appearing in electro-optic measurement of photo- conductively-generated signals on coplanar striplines can be attributed to substrate waves. The arrival t ime of the T H z feature is related to the thickness of the substrate. Mea- surements on and off the axis of the transmission line show that for thin substrates the substrate waves are effectively guided by the presence of the coplanar stripline electrodes, in agreement wi th recent work by Tsuji et. al. [17] and L i n and coworkers [33]. Bibliography [1] L . D . Nguyen, A . S. Brown, M . A . Thompson, and L . M . Jelloian, "50-nm self- aligned-gate pseudomorphic A l I n A s / G a l n A s high electron mobil i ty transistors," IEEE Transactions on Electron Devices, vol . 39, pp. 2007-2014, September 1992. [2] P. Ho, M . Y . Kao , P. Chao, K . H . Duh , J . M . Bl l inga l l , S. T . A l l e n , A . J . Tessmer, and P. M . Smith, "Extremely high gain 0.15 jum gate-length I n A l A s / I n G a A s / I n P H E M T s , " Electronics Lett., vol. 27, pp. 325-327, February 1991. [3] J . A . Valdmanis, G . Mourou, and C . W . Gabel , "Picosecond electro-optic sampling system," Applied Physics Lett., vol. 41, pp. 211-212, 1982. [4] J . A . Valdmanis, "Electro-optic measurement techniques for picosecond materials, devices, and integrated circuits," in Measurement of High Speed Signals in Solid State Devices (R. B . Marcus, ed.), San Diego: Academic Press, 1990. [5] D . H . Auston, "Picosecond optoelectronic switching and gating in silicon," Applied Physics Lett., vol. 26, pp. 101-103, January 1975. 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Tousley, and T . Y . Hsing, "Picosecond characterization of bent coplanar waveguide," IEEE Microwave and Guided Wave Lett, vol. 1, pp. 231-238, September 1991, 61 Bibliography 62 [11] M . Y . Frankel, R. H . Voelker, and J . N . Hilfiker, "Coplanar transmission lines on thin substrates for high-speed low-loss propagation," IEEE Transactions on Microwave Theory and Techniques, vol . 42, pp. 396-402, March 1994. [12] C. P. Wen, "Coplanar waveguide: A surface strip transmission line suitable for nonreciprocal gyromagnetic device applications," IEEE Transactions on Microwave Theory and Techniques, vol. 17, pp. 1087-1090, December 1969. [13] K . C. Gupta , R. Garg, and I. J . Bah l , Microstrip Lines and Slotlines. New York: Artech House, 1979. [14] E . M . Godshack, "Generation and observation of surface wave on dielectric slabs and coplanar structures," in 1993 IEEE Microwave Theory Tech. Symp. Dig., pp. 923- 926, 1993. [15] D . P. Kasi l ingam and D . B . Rutledge, "Surface-wave losses of coplanar transmission lines," in 1993 IEEE Microwave Theory Tech. Symp. Dig., pp. 113-116, 1983. [16] I . -J . F . M . Riaziat , R. Maj id -Ahy, "Propagation of modes and dispersion charac- teristics of coplanar waveguides," IEEE Transactions on Microwave Theory and Techniques, vol . 38, pp. 245-251, March 1990. [17] M . Tsuji , H . Shigesawa, and A . A . Oliner, "New interesting leakage behavior on coplanar waveguide of finite and infinite widths," IEEE Transactions on Microwave Theory and Techniques, vol. 39, pp. 2130-2137, December 1991. [18] S. Alexandrou, C . - C . Wang, M . Currie, R. Sobolewski, and T . Y . Hsiang, "Loss and dispersion at subterahertz frequencies in coplanar waveguides wi th varying ground- plane widths," in Technologies for Optical Fiber Communications, Proceedings of SPIE, vol . 2149, pp. 108-118, 1994. [19] A . Zeng, Characterization of High-Speed Electronic Devices using Ultrafast Lasers. P h D thesis, University of Br i t i sh Columbia. To be submitted. [20] F . E . Doany, D . Grischkowksy, and C . - C . C h i , "Carrier lifetime versus ion- implantation dose in silicon on sapphire," Applied Physics Lett., vol . 50, pp. 262-263, February 1987. [21] S. Gupta, J . F . Whitaker, and G . A . Mourou, "Ultrafast carrier dynamics in III -V semiconductors grown by molecular-beam epitaxy at very low substrate temper- atures," IEEE Journal of Quantum Electronics, vol. 28, pp. 2464-2472, October 1992. [22] D . H . Auston, K . P. Cheung, and P. R . Smith, "Picosecond photoconducting Hertzian dipoles," Applied Physics Lett., vol . 45, pp. 284-286, August 1984. Bibliography 63 [23] N . Katzenellenbogen and D . Grischkowsky, "Efficient generation of 380 fs pulses of T H z radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface," Applied Physics Lett., vol . 58, pp. 222-224, January 1991. [24] M . Y . Frankel, S. Gupta , J . A . Valdmanis, and G . A . Mourou, "Picosecond pulse formation by transmission line discontinuities," Electronics Lett., vol. 25, pp. 1363— 1364, September 1989. [25] N . G . Paulter, D . N . Sinha, A . J . Gibbs, and W . R. Eisenstadt, "Optoelectronic mea- surements of picosecond electrical pulse propagation in coplanar waveguide trans- mission lines," IEEE Transactions on Microwave Theory and Techniques, vol . 37, pp. 1612-1619, October 1989. [26] M . D . Feuer, S. C. Shunk, P. R . Smith, H . H . Law, and M . C. Nuss, "100 G H z wafer probes based on photoconductive sampling," IEEE Photonics Technology Lett, vol . 5, pp. 361-364, March 1993. [27] H . Cheng and J . F . Whitaker, "300-GHz-bandwidth network analysis using time- domain electrooptic sampling," in 1993 IEEE Microwave Theory Tech. Symp. Dig., pp. 1355-1358, 1993. [28] R. Y . Y u , Y . Konishi , M . Case, M . Kamegawa, and M . Rodwell , " A time-domain millimeter-wave vector network analyzer," IEEE Microwave and Guided Wave Lett, vol. 2, pp. 319-321, August 1992. [29] M . Y . Frankel, "500-GHz characterization of an optoelectronic S-parameter test structure," IEEE Microwave and Guided Wave Lett, vol . 4, pp. 118-120, A p r i l 1994. [30] X . W u , D . Conn, J . Song, and K . Nickerson, "Invasiveness of L iTaOs and GaAs probes in external E - 0 sampling," IEEE J. Lightwave Tech., vol. 11, pp. 448-454, March 1993. [31] A . Zeng, S. A . Shah, and M . K . Jackson, "Reduced invasiveness of non-contact electro-optic probes in millimeter-wave optoelectronic characterization." IEEE Transactions on Microwave Theory and Techniques [in press]. [32] J . Rit ter , V . J . Brankovic, D . V . Krupezevic, and F . Arnd t , " A wide-band S- parameter extraction procedure for arbitrarily shaped, inhomogeneous structures using time domin numerical techniques," in 1995 IEEE Microwave Theory Tech. Symp. Dig., pp. 274-276, 1995. [33] Y . - D . L i n , J . -W. Sheen, and C . - Y . Chang, "Surface-wave leakage properties of copla- nar strips," in 1993 IEEE Microwave Theory Tech. Symp. Dig., pp. 229-231, 1995. Bibliography 64 [34] M. Hatzakis, B. J. Canavello, and J. M. Shaw, "Single-step optical lift-off process," IBM J. Res. Development, vol. 24, pp. 452-460, July 1980. Appendix A Experimental Device Fabrication The coplanar transmission line electrodes were fabricated using a chlorobenzene lift-off process to have overhanging lips on the side-walls of the photoresist [34]. Fabrication of metal electrodes involved the following steps: 1. Clean the substrate with acetone and methanol. Blow dry wi th Nitrogen. 2. Spin on Shipley 1400-27 resist: 5000 rpm for 30 s. 3. Remove edge bead using q-tips and acetone. 4. Soft-bake at 70°C for 20 minutes in oven, cover the sample with petridish. 5. Expose the sample for 20 s with Karl-Suss M J B 3 contact mask aligner operating at 320 n m and with nominal intensity. 6. Place the sample in Chlorobenzene for 12 minutes. 7. Post-bake for 15 min at 70°C. 8. Develope using Shipley MF-319 developer for 6 minutes. 9. Rinse the sample by using deionized (DI) Water. 10. Evaporate 30nm/70nm of C r / A u using E-beam evaporation. 11. Photoresist was dissolved by immersing sample in the acetone. The ultrasonic wasn't normally used to assist lift-off. 65

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