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Performance evaluation of S-parameter extraction techniques for time-domain optoelectronic vector network… Ruo, Russell L. 1998

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Performance Evaluation of S-Parameter Extraction Techniques for Time-Domain Optoelectronic Vector Network Analyzers by Russell L. Ruo B.Eng., McMaster University, 1996 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF  M a s t e r of A p p l i e d Science in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Electrical and Computer Engineering) we accept this thesis as conforming to the required standard  The University of British Columbia August 1998 © Russell L. Ruo, 1998  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  &\<?dr\CC\K Qy^S- Co^iyder-  The University of British Columbia Vancouver, Canada •ate  DE-6 (2/88)  Z4r  ku^nst  m%  B^lheer'^  Abstract  The objective of the thesis is to evaluate the performance of two methods recently proposed for scattering parameter (S-parameter) extraction using timedomain optoelectronic vector network analyzers.  Model-based simulations of an  electro-optic sampling experiment for a typical high-speed bipolar transistor were used to investigate the accuracy of the techniques in the presence of experimental non-idealities. In particular, the investigation focused on the effects of finite time window, drift and noise.  The methods use step-like signals and digital filtering  techniques to extract the S-parameters for one of two situations where signals are either temporally overlapped or not. From the simulations, it was determined that the approach for overlapping signals is not feasible. The experimental impairments of drift and noise interfere with the separation of overlapping signals and result in inaccurate S-parameter computation. Fair results may be obtained within a limited range of frequencies for extracting the S-parameters with the approach for nonoverlapping signals. Although feasible, the latter method was not recommended over existing optoelectronic methods which use pulse-like input signals for S-parameter extraction. The digital filtering technique common to both methods was validated by an experimental measurement of signal propagation on a coplanar stripline fabricated on a multilayer S1O2/S1 substrate. The attenuation and effective dielectric constants were measured over a range of frequencies between 20 and 150 GHz. Elecromagnetic ii  simulations of the structure performed by a collaborator were found to be in excellent agreement with the experimental results. The results show high losses and dispersive effects at low frequencies, which are attributed to the conductive substrate used.  iii  Contents  Abstract  ii  Contents  iv  List of Figures  vii  Acknowledgements  x  1 Introduction 1.1  1  Introduction to Thesis  1  1.1.1  Overview  1  1.1.2  Summary of Results  2  1.2  Overview of High-Speed and Broadband Characterization  2  1.3  Optoelectronic Characterization Methods  7  1.3.1  Time-domain Measurement: Pump-probe Technique  7  1.3.2  Time Window  8  1.3.3  Optoelectronic Generation  10  1.3.4  Electro-optic Sampling  12  1.3.5  Photoconductive Sampling  14  1.3.6  Previous Results  16  1.4  Frequency-Domain Characterization with Step-like Signals  20  1.4.1  21  Digital Filtering Techniques  iv  1.5 2  23  1.4.3  S-parameter Measurement: Non-overlapping Signals  26  Outline of Thesis  29 30  2.1  Introduction to Chapter  30  2.2  Methodology  30  2.2.1  Simulation Approach  30  2.2.2  Incorporating Experimental Impairments  38  2.4  2.5  4  S-parameter Measurement: Overlapping Signals  Model-Based Evaluation of Accuracy  2.3  3  1.4.2  Results with Overlapping Signals  42  2.3.1  Time Window  42  2.3.2  Drift  47  2.3.3  Noise  52  Results with Non-Overlapping Signals  57  2.4.1  Time Window  61  2.4.2  Drift  63  2.4.3  Noise  72  Conclusions  77  Propagation on a Coplanar Stripline: Experimental Validation of Digital Filter Technique  79  3.1  Introduction  79  3.2  Experiment  82  3.3  Results and Discussion  84  3.4  Conclusions  89  Conclusions and Future Work  91  4.1  Conclusions  91  4.2  Future Work  92  v  Bibliography  94  vi  List of Figures  1.1  Small-signal characterization and definition of S-parameters  4  1.2  Electronic network analyzer block diagram  6  1.3  Schematic of an optoelectronic time-domain pump/probe measurement system  9  1.4  A photoconductive switch for fast electrical signal generation  11  1.5  Electro-optic sampling transducer  13  1.6  Integrated photoconductive sampler  15  1.7  Electro-optic measurements of a H E M T  17  1.8  Time-domain E O S measurements for propagation on a C P S fabri-  1.9  cated on Silicon on Sapphire  19  Sampling locations for the S-parameter measurements  24  1.10 Separation of incident and reflected signals in the time domain with digital filtering techniques 2.1  28  Simplified schematic of a typical test fixture for an electro-optic sampling experiment  2.2  32  Test network for time-domain simulations of an electro-optic sampling experiment  34  2.3  Input signal for time-domain simulations  36  2.4  Time-domain simulation of an E O S experiment with overlapping signals  37 vii  2.5  Time-domain simulation incorporating linear drift  40  2.6  Time-domain simulation incorporating noise  41  2.7  Overlapping signals: recovered S u with finite time window  43  2.8  Overlapping signals: recovered S21 with finite time window  44  2.9  Overlapping signals: recovered S22 with finite time window  45  2.10  Overlapping signals: recovered S12 with finite time window  46  2.11  Overlapping signals: recovered Sn with drift  48  2.12  Overlapping signals: recovered S21 with drift  49  2.13  Overlapping signals: recovered  with drift  50  2.14  Overlapping signals: recovered S12 with drift  51  2.15  Overlapping signals: recovered Sn in the presence of noise  53  2.16  Overlapping signals: recovered S21 in the presence of noise  54  2.17  Overlapping signals: recovered  in the presence of noise  55  2.18  Overlapping signals: recovered Su  the presence of noise  56  2.19  Time-domain simulation of an E O S experiment with non-overlapping  m  signals  59  2.20  Filtered time-domain data for simulation with non-overlapping signals.  60  2.21  Simulation for non-overlapping signals incorporating time window truncation  62  2.22  Non-overlapping signals: recovered Sn with finite time window. . . .  64  2.23  Non-overlapping signals: recovered 521 with finite time window. . . .  65  2.24  Non-overlapping signals: recovered 522 with finite time window. . . .  66  2.25  Non-overlapping signals: recovered Su with finite time window. . . .  67  2.26  Non-overlapping signals: recovered Sn with drift  68  2.27  Non-overlapping signals: recovered 521 with drift  69  2.28  Non-overlapping signals: recovered 522 with drift  70  2.29  Non-overlapping signals: recovered Su with drift  71  2.30  Non-overlapping signals: recovered Sn  73  viii  m  the presence of noise. . . .  2.31  Non-overlapping signals: recovered S21 in the presence of noise. . . .  74  2.32  Non-overlapping signals: recovered S22  the presence of noise. . . .  75  2.33 Non-overlapping signals: recovered Si 2 in the presence of noise. . . .  76  3.1  Physical layout and structure of a coplanar stripline structure.  80  3.2  Experimental test fixture for propagation measurement  3.3  Electro-optic sampling time-domain measurements of propagation on  m  . . .  83  silicon  85  3.4  Experimentally determined attenuation for a silicon C P S  87  3.5  Experimentally determined effective permittivity for a silicon C P S . .  88  ix  Acknowledgements First, I would like to thank my supervisor, Dr. M . K . Jackson, for giving me the opportunity to work in his lab. For the seemingly endless problems I have approached him with, he has shown great patience and understanding in helping me with them. I would like to thank him for his knowledgeable guidance and for maintaining a sense of optimism for the work. I would like to acknowledge Dr. John Long for performing the calculations used to verify the experimental results in Chapter 3 and also collaborators at Nortel Technology for supplying the samples and models used in the work. In addition, funding from N C E Micronet and financial support from U B C in the form of a University Graduate Fellowship are gratefully acknowledged. I am also very thankful for the support and friendship of the other people in my research group. In particular, Todd Kleckner, Dave Jez, and Rob Coenen who have made the lab at times unusual but always an entertaining and fun place to work in. I am also appreciative for the support and many enlightening discussions with Mahan Movassaghi and Roberto Rosales in the office we shared. I also thank Dr. Jiaming Ziang for his great help and advice with the experiment. In the course of the work both T K and JZ have supplied many ideas and valuable discusions which I am grateful for as well. A very special thanks to my family for their love and support. In particular I would like to thank my parents Tomoki and Misuei for their endless encouragement, my brother and sister, Leslie and Leyo, for their guidance and my grandma for her  x  love. Finally, I am thankful to the Lord for what I have and all the things he has blessed me with. I thank him for my family and friends at West Point Grey Baptist Church and back home at the Taiwanese Justice and Grace Church, all who have been unfailing in their support and guidance during the time I have spent here. In particular I am thankful for Pastor David Morrison, for spiritual guidance and leading me to Christ through baptism. Then you will understand the fear of the Lord, and find the knowledge of God. For the Lord gives wisdom, and from his mouth comes knowledge and understanding. Proverbs 2:5,6  RUSSELL L . RUO  The University of British Columbia August 1998  xi  Chapter 1  Introduction 1.1 1.1.1  Introduction to Thesis Overview  Recent progress in the development of high-frequency electronic devices poses major challenges in device characterization. Optoelectronic techniques are a relatively new alternative, and have been used to allow high-speed and high-bandwidth measurements. Because these approaches are based on time-domain measurement, they are suitable for studying not only the small-signal, or linear response, but also the large-signal switching response. Until recently no techniques were available to perform small-signal frequency-domain characterization using the step-like inputs suitable for switching measurements. Recently, two techniques were proposed that allow such measurements: temporally- overlapped signals can be separated  [1], and  digital filtering can be used to allow Fourier transformation of step-like signals  [2].  It is the goal of the present work to evaluate the performance of these proposed approaches. Specifically, the focus is on quantifying the effects'of experimental non-idealities such as noise, drift and truncation due to inadequate measurement time interval upon the determination of scattering parameters (S-parameters). To do this, simulations were performed using a model of a typical high-speed bipo1  lar transistor. The effects of the various experimental nonidealities were introduced into the modelling, and the errors quantified by comparison with the true frequencydomain characteristics.  This allowed assessment of the type of measurements that  could be expected to give adequate results in realistic experimental situations. To confirm these predictions, measurements were made on a passive device structure, and the results compared to the predictions of an electromagnetic simulator.  1.1.2  Summary of Results  Simulation results showed that it is not feasible to extract S-parameters with steplike signals in the presence of temporal overlap. However, it is possible to obtain reasonable S-parameters with non-overlapping signals. A special case of the latter situation applies to the characterization of propagation on coplanar interconnects. Using these techniques, an experimental measurement of attenuation and dispersion in coplanar strip transmission lines on a SiO"2/Si multilayer substrate was obtained. The attenuation and effective dielectric constant were measured over the range from approximately 20 to 150 G H z . The data show evidence of dispersive effects at lower frequencies attributable to the conductive substrate used. simulations of these structures  Electromagnetic  [3] were found to be in excellent agreement with the  measurements.  1.2  Overview of High-Speed and Broadband Characterization  Techniques for the characterization of high-speed devices can be grouped broadly in terms of the type of information obtained. The most general approach is nonlinear device characterization, which is essential when signal amplitudes are large, and is usually referred to as large-signal characterization. Because of the dependence upon the field of application, there are few standardized nonlinear device measurements:  2  amplifiers are typically characterized by the input power levels at which distortions reach a certain level, while in digital circuits time delays, switching times, etc. are normally of interest.  For some circuits where signal levels are low, knowledge of  device response for small deviations from a fixed operating point, or small-signal characterization, is sufficient. This is the case, for example, in the design of smallsignal amplifiers. Small-signal characterization has also found application in the development of device models. While a number of different types of small-signal characterization could be imagined, there has been widespread agreement upon the use of the standardized test environment shown in Fig. 1.1(a), where the device under test (DUT) has 50 Ohm transmission lines connected to input and output. The most commonly-measured small-signal parameters are S-parameters, which describe the response of a device, or any network, to sinusoidal inputs. This is illustrated in Fig. 1.1(b), which shows the definition of two of the four S-parameters, Su and 52i- In this case it is assumed that the two network ports are connected via 50 Ohm transmission lines or waveguides to 50 Ohm sinusoidal signal sources. In the case illustrated, the signal amplitude propagating towards the port 1 input has complex amplitude A ; the reflected signal from port 1 is defined to be Su transmitted signal from port 2 to be S21 X A.  x  A, and the  The two other S-parameters, 522  and 5i2 are denned in an analogous way, with an input supplied to port 2. These four S-parameters are complex, frequency-dependent quantities which completely describe the small-signal device response. A n important area of current research is the validation of nonlinear device models, such as those developed for high-speed bipolar transistors. In those studies it is essential, for a given device, to characterize both the large- and small-signal response, and it is of interest to be able to do both with a standardized test. Because of device-to-device differences due to manufacturing variations, it is not considered sufficient to measure these parameters on differing devices. The main goal of the present work is to evaluate optoelectronic techniques capable of both large- and  3  Device Under Test  DUT  50 Ohm Transmission Lines  (a)  AxS21 1  AxSn  DUT  1  b b  (b) Figure 1.1: Small-signal characterization:  (a) the device under test (DUT) is nor-  mally embedded in a 50 Ohm transmission-line environment; (b) Definition of scattering parameters (S-parameters).  4  small- signal characterization. Experimental characterization of high-speed devices is based on either freq uency- or time-domain measurement. The most established techniques are frequency domain, and the standard equipment is a network analyzer, which is used to measure the S-parameters. The simplified block diagram of a network analyzer is illustrated in Fig. 1.2.  The network analyzer, indicated by the dashed line in Fig. 1.2, is at-  tached to the device under test (DUT) with 50 Ohm cables or waveguides, depending upon the frequency of operation. The circuitry connected to each port inside the network analyzer consists of three main components: a swept frequency source, a directional coupler, and a detector. The directional coupler ensures that the source output is launched toward the D U T , and that the reflection is coupled to the detector. Signal detection is achieved through one of two means: a narrowband tuned heterodyne detector allows both amplitude and phase measurement, while a less expensive broadband diode allows only amplitude measurement. Depending upon the choice of detection scheme, the instrument is referred to as a scalar network analyzer, which only measures amplitudes, or a vector network analyzer, which measures both amplitude and phase. The majority of device development laboratories use vector network analyzers that operate up to 26 or 40 G H z . Recently, the bandwidth of vector network analyzers has been extended to cover the range to 110 G H z [4]. Time-domain techniques, by contrast, are much less widely used.  Time-  domain electronic methods are based on the use of fast pulse sources and sampling oscilloscopes. These time-domain reflectometry approaches have been used for the characterization of cables and interconnections, but are rarely used in the study of high-speed circuits or devices. One of the reasons for this may be that techniques to de-embed the parasitic effects of cables, connectors, imperfect directional couplers, etc., have not been developed. The optoelectronic techniques that are the subject of the present work operate in a manner that is very similar, in principle, to time-domain electronic methods.  A signal generator is attached to the device  5  Port 1 Swept Signal Sources  Directional Couplers  Detectors  Figure 1.2:  Electronic network analyzer block diagram.  The device under test  (DUT) is attached to the network analyzer, which is denoted by the dashed line, at ports 1 and 2. The components inside the analyzer are described in the text.  6  input by a transmission line, and a high-speed electrical signal is generated that propagates towards the D U T . A high-speed sampler serves to measure the voltage at a particular instant in time, and serves an analogous function to the sampling oscilloscope. However, unlike in the electronic case, optoelectronic samplers do not have to be connected using a transmission line: they can be implemented as probes which are relatively noninvasive, and can be positioned at any location along the input or output transmission line. Further details of the operation of optoelectronic characterization systems will be given in the following section. It is useful to compare and contrast the frequency-domain electronic and the time-domain optoelectronic techniques. First, the frequency-domain techniques are used almost exclusively for small-signal device characterization, and they are quite restricted in nonlinear device characterization. Time-domain techniques, in general, are ideally-suited for nonlinear device characterization. In addition, if experimental sensitivity is sufficiently high, it is possible to use low-amplitude signals and achieve small-signal characterization. In theory, it is possible to use Fourier transformation of time-domain small-signal data to obtain frequency-dependent quantities such as Sparameters. However, substantial errors can occur using this approach; quantitative determination of the magnitudes of these errors is the main subject of this thesis.  1.3 1.3.1  Optoelectronic Characterization Methods Time-domain Measurement: Pump-probe Technique  The high-speed time-domain optoelectronic measurement techniques introduced in the previous section can be implemented in several different ways, but all share a common basis described in this section.  The primary component is an ultrafast  laser, also known as a mode-locked laser, which produces short optical pulses at a relatively low repetition rate. Typical operating parameters are pulse lengths of approximately 100 fs, and repetition rates of around 100 M H z . A schematic of an  7  optoelectronic measurement system is shown in Fig. 1.3. The output of the laser is divided into two beams using a beamplitter; the two are referred to as the pump and the probe beams. The pump beam excites a optoelectronic generator to produce a fast electrical input signal for the device under test ( D U T ) . The device responds to this electrical signal, and reflected and transmitted signals are generated on the two transmission lines. The probe beam synchronously samples the electrical signal through one of two approaches that will be described in subsequent sections. Both approaches are similar, however, in that the arrival of the probe beam stimulates sampling of the voltage by the optoelectronic sampler. The sampler in Fig. 1.3 is shown on the output transmission line, but in general it can be located at a variety of positions along the input or output transmission lines. Most optoelectronic sampling schemes are not sufficiently sensitive to make a measurement with a single probe laser pulse, and averaging for times on the order of a fraction of a second is needed to measure the voltage at a particular pump/probe delay. To allow the electrical signal to be measured as a function of time, the probe beam is passed through an optical delay line which is used to vary the arrival time of the probe beam. The approach described above is known as the pump/probe technique; the ability to characterize high-speed electronic devices depends upon the optoelectronic signal generator and the sampling process, which are described in later sections.  1.3.2  Time Window-  Optoelectronic measurement methods operate in the time-domain, as described in the previous section.  This implies certain features related to measurement over  a finite time interval, as described in the following.  In principle it is possible to  vary the pump/probe delay over very long times. However, it is advantageous in many situations to limit measurements to a small interval, or time window, after the arrival of the pump pulse. The reason for this is that the optoelectronic generator illustrated in Fig. 1.3 cannot be located on the end of the input transmission line,  8  Mode-Locked Laser  Probe Beam  Beam Splitter  Pump Beam  Optical Delay Line  Optoelectronic Sampler Data Acquisition  /  DUT  Optoelectronic Generator Figure 1.3: Schematic of an optoelectronic time-domain pump/probe measurement system.  9  but must be somewhere between the input-side power supply and the D U T . When the pump pulse arrives, signals are generated that propagate both toward the device and towards the power supply. Normally it is very difficult to make a broadband impedance match at the connection of the power supply to the transmission lines, because the frequencies involved in optoelectronic measurement techniques can be in excess of 1,000 G H z . The reflection from this mismatched interface to the power supply arrives at the device input much later than the signal that travels directly from the generator. Therefore it is possible to exclude this spurious effect by limiting the measurement time window. Time-windowing allows parasitic connections to be eliminated from the measurement, but has a significant drawback in some cases. Specifically, if the input signal launched by the optoelectronic generator has a long duration, it may not have returned to its baseline by the end of the measured time window. This is a problem because it introduces truncation errors which can be substantial  [5]. One easy  solution is to increase the lengths of the transmission lines. However, the device under test and the transmission lines are typically integrated on the same semiconductor wafer. Consideration of die size and chip area limit practical transmission line lengths to a few millimeters; with a propagation velocity of approximately 8 ps/mm on such transmission lines, this results in time windows less than 100 ps.  1.3.3  Optoelectronic Generation  The photoconductive generation of fast electrical signals was pioneered and described by Auston [6, 7].  A schematic of a photoconductive switch is shown in  Fig. 1.4. The photoconductive switch is fabricated on a photoconductive substrate, indicated by the outer rectangle in Fig. 1.4.  A n integrated coplanar transmission  line, indicated by the shaded areas in Fig. 1.4, is fabricated on the substrate. The gap has a very high dark resistance and a D C bias is applied across it. Upon illumination by the probe beam, electron-hole pairs are created in the gap. These carriers  10  Photoconductive Switch  Photoconductive Material Substrate Figure 1.4: A photoconductive switch for fast electrical signal generation.  11  move rapidly under the influence of the electric field present in the gap, and generate a fast electrical transient propagating along the transmission line. The rise time of the signal is determined by the optical pulse width and the switch geometry, and is typically on the order of 300 fs. The decay time of the generated signal depends on the same factors, as well as the carrier recombination lifetime. Normally the carrier lifetime is the factor controlling the decay time. For switching measurements, quasi step-like signals are desirable: these have fast rise time and relatively slow decay time. Generators intended to produce such signals are fabricated on semi-insulating gallium arsenide (SI GaAs), where the carrier recombination times are on the order of 40 to 300 ps. For pulse-like signals the generator is fabricated on ion-implanted substrates [8] or low temperature grown gallium arsenide (LT GaAs) [9]. These materials contain many recombination centers which reduce the carrier recombination lifetime; values in the subpicosecond range have been achieved.  1.3.4  Electro-optic Sampling  Electro-optic sampling (EOS) [10] is a probing technique based on use of the electrooptic effect. The key element of this technique is an electro-optic transducer; Fig. 1.5 illustrates a commercially-available transducer.  The transducer shown in Fig. 1.5  is freely positionable, and is placed above the transmission line where the electrical signal is to be sampled. As the propagating electrical signal travels underneath the transducer, the fringing electric field above the transmission line alters the birefringence of the material through the electro-optic effect [11].  The voltage across the  transmission lines can be probed by passing a linearly polarized probe pulse through the transducer: from the output polarization the degree of birefringence can be determined, and by calibration the voltage across the transmission lines ascertained. Differential signal detection and lock-in techniques may be used to improve the measurement sensitivity, which can be on the order of a few m V / \ / H z . The bandwidth of E O S is determined by the speed of the electro-optic effect and the interaction  12  Lineariy Polarized Probe  Elliptically  Transmission Line with Fringing Electric Field Figure 1.5: Electro-optic sampling transducer.  13  time of the optical pulse with the electric field being measured; a bandwidth of 1 T H z has been demonstrated [12].  1.3.5  Photoconductive Sampling  An alternative to electro-optic sampling is known as photoconductive sampling (PCS) [7]. The photoconductive sampler is similar in construction to the photoconductive signal generator described in Section 1.3.3. A schematic of a probe used in P C S is shown in Fig. 1.6. Without illumination, the changing voltage between the upper conductor and the sampling conductor causes a time-varying voltage across the sampling gap. When a probe pulse illuminates the gap, current flows in the same manner discussed earlier with respect to the photoconductive generation process. Here the total charge transferred onto the sampling conductor is proportional to the bias across the gap. If the carrier lifetime is short, the gap will only gate charge onto the sampling conductor for a brief time, and therefore sampling of the voltage can be achieved. The measurement bandwidth is determined by the carrier lifetime in the gap, and is typically on the order of a picosecond in P C S systems. In P C S the signal detector is electronic, measuring the gated charge, as opposed to that in the electro-optic sampling technique described earlier, where the optical polarization is affected. This allows P C S to have a much higher sensitivity than E O S ; sensitivities on the order of a few u-V/y/Rz have been achieved [7].  One of  the disadvantages of P C S using samplers integrated on-wafer is that the voltage can only be measured at the location where the sampling switch is fabricated. This results in less flexible measurement, and occupies substantial chip area. Recent developments have removed this limitation by incorporating the sampling switches on freely-positionable probes. These may be contacted to any sampling point along the transmission lines [13, 14].  14  Data Acquisition Photoconductive Sampling Gap  Signal Source  Transmission Line Figure 1.6: Integrated photoconductive sampler.  15  1.3.6  Previous Results  In the following we outline previously-published results for the optoelectronic characterization of transistors and coplanar transmission lines. All of these results have been obtained with impulse-like input signals, and will serve as a benchmark against which to judge attempts to obtain similar data with step-like inputs. In addition, results for propagation on coplanar transmission lines will be compared directly with measurements made using the techniques evaluated in this thesis; these results are presented in Chapter 3. There have been a number of reports of the determination of S-parameters for active devices, including field effect transistors [15], high electron mobility transistors ( H E M T ) [16] and heterojunction bipolar transistors (HBTs) [17]. A typical result is shown in Fig. 1.7. The transistor used to obtain the results shown in Fig. 1.7 was thinned, diced and wire bonded into a test fixture similar to that shown in Fig. 1.1. The time-domain data for an input to the gate-source and drain output are shown in Fig. 1.7(a). The incident and reflected gate signals are time windowed where the signals reach their baselines as indicated by the arrows. The resulting S-parameters are shown in Fig. 1.7(b), where they are compared to network analyzer measurements taken up to 40 G H z . The results obtained from optoelectronic methods agree with electronic measurements up to 40 G H z , and the E O S results extend to 100 GHz. The results of Frankel et. al. shown in Fig. 1.7 demonstrate a number of issues important in S-parameter characterization of high-speed transistors. The first is the use of wire bonds for test fixturing, which compromises high-frequency characterization because the bond wires play a dominant role in determining the device response at high frequencies.  In principle calibration techniques can be used to  de-embed the bond contribution to the measured results, and allow extraction of the intrinsic transistor response. Such techniques were not used in Ref. [16], likely because of the difficulty of reproducibly fabricating such bonds. The second issue  16  Figure 1.7:  Electro-optic measurements of a H E M T : (a) raw time-domain data  for gate-source input, showing incident, reflected and transmitted signals (from Ref. [18]); (b) resulting S-parameters from E O S (solid lines) and electronic network analyzer (dotted lines), (from Ref. [19])  17  shown in these results relates to the use of impulse-like input signals. Because of the finite length of even an impulse-like signal, and the duration of the device response, the incident and reflected signals will overlap for sampling locations too close to the device input. Therefore, the photoconductive generator and the sampling location must both be located many millimeters from the device input. The techniques which are introduced in the next section and evaluated in Chapter 2 are aimed at overcoming these limitations. In addition, such techniques would solve the apparent incompatibility between the need for impulse-like excitation for S-parameters measurement, and step-like excitation for switching. In the study of coplanar transmission lines, which are used as high-frequency interconnects in high-speed circuits, a wider variety of results have been reported than for active devices. Specifically, coplanar strip (CPS) and coplanar waveguide (CPW) transmission lines have been studied with electrodes made with high temperature superconductors [20], and with metallic electrodes on a variety of substrates including undoped GaAs [12, 21, 22], doped GaAs [23], silicon on sapphire [12, 24], and multilayer SiO^/Si [25]. There is particular current technological interest in the fabrication of such lines on silicon substrates. Because of the difficulty in fabricating semi-insulating Si substrates, such transmission lines are often fabricated on top of a layer of insulator such as SiC>2 or SiN, to decrease substrate losses. The impact of these insulating layers, which can be in excess of 5 fim thick, has not been widely investigated and is discussed later in Chapter 3. A recent optoelectronic result for coplanar waveguides on such substrates was reported by Pfeiffer et. al. [25]. In the present work we have focussed on C P S transmission lines; only one other study of such lines on SiO"2/Si have been reported [26]; based on electronic network analyzer measurements.  A typical result for a coplanar stripline fabricated on a Silicon on  Sapphire (SOS) substrate are shown in Fig. 1.8. The C P S uses ion-implant damaged SOS as the photoconductive material. The influence of the semiconductor film on the propagation measurement is eliminated by etching off the silicon everywhere ex-  18  Figure 1.8: Time-domain E O S measurements for propagation on a C P S fabricated on Silicon on Sapphire: (a) shows typical time domain measurements along a transmission line; (b) shows the measured (dashed) and analytical calculation (solid) for attenuation; (c) shows the measured (dashed) and analytical calculation (solid) for effective permittivity; (from Ref. [12]).  19  cept for a small patch which defines the switch. The figure depicts signal propagation on a C P S fabricated on sapphire with an integrated silicon-on-sapphire photoconductive electrical signal switch generator, and measurements made by electro-optic sampling. The significant features of interest include the broadening of the pulse, the increase in rise time, ringing in the tail, and decrease in amplitude of the pulse. The frequency-dependent propagation factor 7(f) = a(f) + j[3(f), may be calculated by Fourier transformation and manipulation of the time domain data. In this expression  and (3{f) are the attenuation and propagation constants, respec-  tively; from these the effective permittivity, € / / ( / ) i can be calculated. Results for e  attenuation and effective permittivity are shown in Fig. 1.8(b) and (c), respectively. From Fig. 1.8(c) it is apparent that the effective dielectric constant is very close to the value of 5.7 expected from a quasi-transverse-electromagnetic  ( T E M ) analysis,  which suggest the appropriate value is the average of the substrate and air dielectric constants, which are 10.6 and 1, respectively. While SOS technology has attracted substantial research interest, it has had very limited commercial use because of the cost of wafers and the poor thermal conductivity of the sapphire substrate. In Chapter 3 results for C P S lines on the much more widely-used Si substrates will be presented.  1.4  Frequency-Domain Characterization with Step-like Signals  The S-parameter results presented in the previous section were all obtained using optoelectronic measurements with impulse-like input signals. As mentioned earlier, it is desirable to combine the small-signal S-parameter characterization of a device with nonlinear characterization of the same device; it is often desirable to use steplike input signals for nonlinear characterization. Therefore, it is of interest to be able to make S-parameter measurements using step-like input signals. In this section,  20  the theory of an approach proposed by Svensson [2] is presented; the key idea in this approach is the use of digital filtering techniques, which are described first.  1.4.1  Digital Filtering Techniques  As mentioned in Section 1.3.2, practical optoelectronic measurements usually have a measurement time window on the order of 50 to 100 ps, while step-like input signals have durations of the same order. A straightforward application of the conventional fast Fourier transform ( F F T ) cannot, therefore, be used to extract frequency-domain information from the time-domain data, because truncation errors will occur. Therefore, a key element of S-parameter measurement techniques using step-like signals is a method to deal with this problem. There are several methods which may be used to Fourier transform signals which are not time limited [27, 28, 29]. Nicolson  [28]  subtracts a linear ramp from the signal to be transformed, bringing the value to zero at the end of the interval. Samulson [27] takes the derivative of the signal before transformation. The approach of Gans [29] involves subtracting a delayed copy of the signal to be transformed; in the case of a step-like signal which approaches a constant value for long times, this leads to a time-limited signal. A discussion of the limitations of these methods may be found in [2, 30]. While a thorough review of their conclusions is beyond the scope of the present work, all three approaches were found to have limitations that increased in magnitude with shortening of the measurement window. Svensson [2] proposed a generalization of Samulson's approach, and used digital filtering to avoid truncation errors. Digital filtering, or digital signal processing, is a well-developed area that is described in detail in a number of textbooks: Oppenheim [32].  see, for example, Jackson [31] and  In this section only the most important points relevant to the  present work are described. The processing of signals can be achieved in a number of ways; in the present work we use convolution of the experimental data in the time domain with the impulse response of a suitable digital filter. This operation is  21  equivalent to multiplication of the Fourier transform of the experimental data with the digital filter frequency response.  The main requirement influencing the choice  of a suitable filter is that the resulting filtered data be time limited; it can then be Fourier transformed using conventional F F T techniques. The digital filtering operation has two effects. First, it can eliminate the truncation errors discussed earlier, which is the desired effect. However, the resultant spectrum obtained from the F F T of the filtered data is different from the spectrum that would be obtained from the true experimental signal if it were not time limited. While this might appear to be a problem, the algebraic manipulations required to obtain the S-parameters all involve ratios of the spectra. For example, Sn  is  obtained from the ratio of the spectra of the incident and reflected signals arriving at port 1. The impact of the digital filtering, then, cancels in the final calculation of the S-parameters as long as the same digital filter is used in transforming all of the experimental data. As discussed in Ref. [2], to achieve the time limiting function, a high pass filter is chosen. There are a number of possible choices for high-pass digital filters. However, as mentioned above, S-parameters are obtained from the ratios of the various filtered spectra; errors occur if the response of the filter approaches zero, because of the resulting division by zero. A suitable choice of filter, therefore, is a high pass Butterworth filter, because these filters have a maximally fiat frequency response which does not have zero crossings. A n infinite impulse response (IIR) filter was used in Ref. [2] as it is more computationally convenient than a finite impulse response (FIR) filter. The fact that the impulse response is, in theory, infinite in duration is not a practical problem because in a high-pass filter the impulse response rapidly decreases to a negligible value.  While the approach described in Ref. [2]  involved only high pass filtering, in the present work a bandpass filter is used. This has the same time-limiting function of the high pass filter, and in addition results in some noise reduction at high frequencies.  22  1.4.2  S-parameter M e a s u r e m e n t : Overlapping Signals  The general technique used to extract S-parameters with step-like inputs has been described in Ref. [2]; in the present section the main features and equations are described.  This technique is used for measurements sampled close to the device  under test, where incident and reflected signals overlap in time. Signal propagation on the input and output transmission lines can be described by V(f,z) where V(f,z)  =  (1.1)  V(f,0)e-^  z  and V(f, 0) are the Fourier transforms of the voltage waveforms at  positions z = 0 and z, respectively. 7(f) is given by j(f)  The frequency-dependent propagation factor  = a(f) + j@(f), where a(f) and /3(f) are the attenuation and  propagation constants, respectively. The technique is based on signal measurement at a number of different locations. In general, to separate incident and reflected signals which overlap requires measurement at two locations. A typical test fixture, and the sampling locations required for determination of the input reflection coefficient and forward transmission coefficient, are shown Fig. 1.9. Two measurements are taken on the input transmission line at locations A and B, located at ZA and zg, respectively. Sampling location C is on the output transmission line at zc- The device under test is integrated into the transmission line, and is located at ZDUT, as indicated. The signals at the D U T and the three sampling locations can be described by the following, where on the input side the signals consists of a superposition of incident and reflected signals: V(f,z  )  = V (f)  DUT  VA  v(f, z ) = v A  m c  inc  (/)<r  7 ( / ) A  ^-  +  D t , T  V(f, z ) = V (f)e-i^ B-DVT B  z  V  inc  C  = V(f,z ) c  V (f) + v; +  =  (1.2)  ref  y  r e /  e /  (  (/)e+^> ^-^T A  / ) e  +-Y(/)A* _  V (f)e-^ o-ovr out  23  Az  f l  D t  ,  T  (1.3) (1.4) (1.5)  A I I  I  B DUT C I  I  i l l  I I  I  i  1—I—i T O  Photoconductive Switch  111.-  I  r  r  ^Z^^^ZIjZZLj-Z i—i  I I - » — ! I I I I I—I A  Z  _  ;  !  »• I 1 I  I  1  -  ZQUT  Figure 1.9: Sampling locations for the S-parameter measurement with overlapping signals.  The device under test (DUT) is integrated into the transmission line as  indicated; the input signal generator is not shown, but is located to the left of position A . Two sampling locations A and B are required on the input side of the D U T ) , and one measurement is taken on the output side at location C . The positions of the three sampling locations and the D U T are indicated on the lower axis.  24  where A z ; _ j = z; — ZJ; V4, Vg and Vc are the spectra of the signals at the three sampling locations A , B, and C , respectively. The two quantities Vi (f) nc  and  V f(f) re  are the incident and reflected signals on the input transmission line, and V (f) out  is  the output-side signal; these quantities are defined at the D U T input or output planes. Because of the finite time window and the truncation errors introduced by Fourier transformation of the raw data, the quantities VA, VB and VQ are not directly available. However, the filtered waveforms may be Fourier transformed to yield the following three frequency-dependent quantities G  A  = V  H{f)  G  B  = V H(f)  (1.7)  = V H(f)  (1.8)  A  (1.6)  B  G  c  C  where H(f) describes the complex frequency response of the digital filter. Combining the above equations the following expressions for the scattering parameters can be derived: ~Q +lU)&ZA-DUT  =  GAe~ W 1  AzA  A  j4  DC  GBe~^ AzB  _  DUT  e+ 7(/)A2 _ / 2  Be  -  DUT  -2-f(f)Az _  e  Q +~/(f)A.ZB-DUT'  _  Ae  Sn(f)  T  DUT  -2i(f)Az _ B  e  _  DUT  ;i.9)  +2~t(f)Az _ B  e  DUT  and  521 (/)  =  Gc G -iU)&ZA-DUT  -  Ae  e  G  _  -1l(!)&ZA-DUT  g e  e  -i(f)^ _ B  D U T  -1lU)& B-DVT z  (1.10)  e—fU)AzC-DUT  As claimed earlier, these expressions are independent of the filter response, except in the special case H(f)  = 0, which must be avoided.  H(f),  The only other  information required is 7(f), the complex propagation constant on the transmission lines; this quantity would normally be determined by a measurement on a long piece 25  of such a transmission line, using the approach outlined in the following section. Expressions for the other two S-parameters,  >d £12 may be obtained in an  ar  analogous way.  1.4.3  S-parameter Measurement: Non-overlapping Signals  The method presented in this subsection allows for determination of S-parameters when no overlapping of signals occurs.  This is the case when measurements are  made far from the device under test, or when no reflections occur, as in the case of a uniform length of transmission line. Rather than separating the incident and reflected signals in the frequency domain, as was done in the previous section, they are separated in the time domain. This time-domain separation is performed by inspection after the waveform has been digitally filtered for time-limiting. This process is similar to the method used to obtain the H E M T S-parameter  results  from electro-optic measurements presented in Section 1.3.6. In this case only two measurements are required, on the input and output sides of the D U T . We will consider the same test fixture shown in Fig. 1.9, but assume that measurements are performed only at locations A and C . In the present case, it is convenient to describe the signals in the time domain; at locations A and C these signals are given by VA(t) = v (t) inc  + v j(t)  (1.11)  re  and vc{t) = v {t)  (1.12)  out  Unlike in the previous section, here u  8nc  (i), v j(t) re  and v t(t) ou  are the incident,  reflected and output signals, respectively, at the measurement locations. To obtain the S-parameters, the time-domain waveforms for  and vc(t)  are digitally filtered to obtain the following time-domain signals 9A(t) - ginS) + 9rej{t)  26  (1-13)  and 9c{t)  = 9out{t)  (1-14)  from which the portions associated with the input, reflected, and transmitted waveforms, where g  tnc  ( i ) , g ef(t)  and g t{t),  r  ou  respectively, must be determined. To illus-  trate the data processing, in Fig. 1.10 several hypothetical waveforms are shown. Fig. 1.10(a) shows a typical waveform measured at location A : the incident and reflected signals are clearly distinguishable, but because they are step-like they do not return to their baseline within the measurement time window. The digitallyfiltered waveform is shown in Fig. 1.10(b); the intervals associated with incident and reflected signals are indicated. The waveforms for gi (t) nc  and g f{t) re  obtained  from the filtered time-domain data are shown in Figs. 1.10(c) and (d), respectively. The determination of the output-side signal g t(t)  is straightforward, and is not  ou  illustrated here. Having determined r/  JTlc  (£), <7re/(0 and g tip)  as described above, the S-  ou  parameters are given by S (f)  = ^44 -27(/)A^_  n  e  O Y T  (  L  1  5  )  and  521 (/) where Gi (f), nc  G j(f) re  and G t(f) ou  +l(f)Az -DUT  Gout(f)  e  Ginc(f)  e  C  -'l(f)Az _ A  DUT  (1.16)  are the Fourier transforms of the corresponding  time-domain filtered waveforms, and the definitions of the A z ; _ j are the same as in the previous section. In the case of a device where no reflection occurs, the above approach may be further simplified.  This situation only occurs in devices which are perfectly  impedance-matched to the input and output transmission lines, and might appear to be of limited usefulness. However, this situation occurs in the determination, of the propagation constant on a uniform section of transmission line, j(f).  In this  case, the uniform nature of the line means no reflected signal will be generated. In 27  100  100  100  40  Figure 1.10:  50  Time (ps)  60  70  80  90  Illustration of signal processing using hypothetical signals:  100  (a) the  signal measured at location A ; (b) the digitally-filtered waveforms, with the components as indicated; (c) gi (t), nc  signal; (d) g f(t), re  the component of (b) associated with the incident  the component of (b) associated with the reflected signal.  28  that case, the incident and transmitted signals can be determined directly from the filtered time-domain data; the propagation coefficient is given by (1.17)  1.5  Outline of Thesis  The remainder of the thesis is devoted to an examination and validation of the techniques for S-parameter determination using step-like signals presented in Section 1.4.2 and 1.4.3. In Chapter 2 an evaluation of the performance of the methods is presented, based upon simulations representative of realistic experimental situations where noise, drift and finite time windows are accounted for. A n experimental measurement of frequency-dependent propagation on a coplanar strip transmission line fabricated on a multilayer SiO"2/Si substrate is presented in Chapter 3. Conclusions and recommendations for future work are given in Chapter 4.  29  Chapter 2  M o d e l - B a s e d E v a l u a t i o n of Accuracy  2.1  Introduction to Chapter  In this chapter, the S-parameter extraction techniques introduced in Chapter 1 are evaluated for their feasibility and performance under realistic measurement conditions.  The method for evaluating the techniques including the simulation of the  electro-optic sampling experiment is described in Section 2.2.  The results in situ-  ations with and without overlapping signals are presented in Sections 2.3 and 2.4, respectively. Finally in Section 2.5, a summary of conclusions is given.  2.2 2.2.1  Methodology Simulation  Approach  The goal of the present work is a quantitative evaluation of the performance of the techniques described in Chapter 1, under experimental conditions. Specifically, the effects of drift, noise, and finite measurement time window are considered. For an experiment in which these impairments are at their residual level, a controlled  30  experimental study is extremely difficult. Therefore, in the present work, the accuracy of the S-parameter extraction techniques is determined using simulations. To evaluate the accuracy of a measurement technique requires a definition of the device or devices to which it will be applied, and a comprehensive evaluation should be based on consideration of a number of representative devices. The goal of the present work, however, is more focussed, and the evaluation has been limited to measurement of a specific device. Simulations are performed using HSpice, and the device considered is a highspeed heterojunction bipolar transistor fabricated in the Si/SiGe material system. Full details of device fabrication and performance measurements can be found in Ref. [33, 34]. The device emitter size is 0.5 X 10 fim, and simulations are performed with collector currents near that required for peak current-gain cutoff frequency. The compact device model used in the present work was developed by collaborators at Nortel Technology, who extracted model parameters for a Spice Gummel-Poon model from experimental measurements [35]. The test network used is representative of a test fixture used in the actual experiment, as shown by the simplified schematic in Fig. 2.1.  In a typical test  fixture used in our laboratory, the device under test is integrated directly into the coplanar transmission line environment. Bond wire pads located at the ends of the input and output transmission lines allow for connection to power supplies which bias the D U T and photoconductive switch.  The photoconductive switch serves  as a fast electrical signal generator as described earlier; it is located in between the bond wire pads and D U T along the input transmission line. The sketch in Fig. 2.1 is intended to show the relative location of the switch; the exact geometry is somewhat more complicated than shown, to allow D C biasing of the input of the D U T . The lengths of the transmission lines are typically a few millimeters long. For the specific devices used in our laboratory, the transistor is incorporated in a common-emitter configuration.  31  Photoconductive Switch  Device Under Test I Bond Wire Pads  Bond Wire Pads  Figure 2.1: A typical test fixture for an electro-optic sampling experiment. The test fixture consists of a fast photoconductive signal generator switch (PCS), input and output transmission lines and an integrated device under test. Bond wire pads are located at the far ends of the transmission lines on each side of the device under test ( D U T ) . The pads allow for wire bond connections to power supplies for biassing the P C S and D U T . The lengths of transmission lines L , L{ and L are typically a few millimeters long. pcs  32  n  out  A network for calculating the input reflection coefficient Sn and the forward transmission coefficient S21 is shown in Fig. 2.2. The network for calculating the output-side S-parameters,  and Su, is similar, when the input signal source and  sampling locations are reversed.  The input and output coplanar striplines of the  integrated E O S test structure are represented by four transmission line segments, as shown. The two input-side transmission lines, with delays T{ and T& , describe N  S  the propagation from sampling location B to the D U T , and the separation between sampling locations A and B, respectively. Similarly, the two output-side transmission lines, with delays T  OUT  and r ^ , represent propagation between the D U T and en  sampling location C , and the end of the line attached to the wire bonds, respectively. Ideal lossless 50 £1 transmission lines are used: neglecting attenuation and dispersion over these distances is not significant, and is motivated by the lack of good non-ideal transmission line models in HSpice.  In a typical test fixture, the  input and output transmission lines are much longer than the segments between sampling locations and the D U T . Reflections from the transmission line discontinuities at the ends of these lines are not normally of interest, and they appear outside the measurement time window. Therefore, in the simulations the source resistance, R , and output load resistance, R t, are set equal to the characteristic impedance s  ou  of the transmission lines. The input signal source is described by V (t) = ^(l + erf{t/a))e- '  t T  in  (2.1)  which is a convenient analytical expression which closely approximates the step-like signals generated by photoconductive switches fabricated on semi-insulating GaAs; in this expression A, a and r are chosen to fit measured data. For a signal which has propagated a few millimeters along the transmission line, the risetime near the device is on the order of a few picoseconds. Because dispersion is not included in the simulations this is incorporated directly in the generated waveform; a risetime of 3.5 ps is used, which is representative of measured values, as is the decay time 33  Input Signal Source Figure 2.2: Test network for time-domain simulation of an electro-optic sampling experiment when calculating Sn and S21. The input signal source is placed on the input port of the device under test, two measurements are made at the input port, at nodes A and B; one measurement is made at the output port, node C .  34  of 50 ps. The resulting waveform for an amplitude A of 10 mV is shown in shown in Fig. 2.3. The choice of signal amplitude is a significant experimental issue, as an amplitude which is too small will increase noise problems, and one that is too large will cause nonlinear device response and erroneous S-parameter determination. The value of 10 mV shown in Fig. 2.3 was chosen based on simulations with the SiGe transistor under ideal measurement conditions, i.e. in the absence of drift, noise and time-windowing constraints. The input amplitude was increased from very low levels until recovered S-parameters became inconsistent; 10 mV was judged to be the largest input amplitude for which accurate measurements could be expected. To illustrate typical waveforms, the simulated E O S signals where substantial overlap occurs, i.e. for T& = 1 ps, are shown in Fig. 2.4. The transistor is biased to a S  point in the active region of operation, V  o e  = 0.9V and V  ce  = 1.0V; the corresponding  collector current is 2.6 mA. Fig. 2.4(a) and (b) show results when the signal generator is on the base-emitter side of the D U T . The signals at locations A and B are shown in Fig. 2.4(a); a small reflection caused by the mismatch between the base-emitter junction of the D U T and the input transmission line is visible at approximately 25 ps. The corresponding output is shown in Fig. 2.4(b), which shows a larger output swing indicating amplification by the device.  Similar results for the case  of excitation on port 2, i.e. with the generator on the collector-emitter side of the D U T , are shown in Figs. 2.4(c) and (d). In this case, a reflection of the same order of magnitude as the input signal occurs, and the transmitted signal is quite small. As described above, HSpice is used to evaluate typical waveforms that can be expected at the various sampling locations for realistic input signals. The resulting data are sampled with a time step between points typically used in an E O S experiment, which is 0.2 ps. The resulting data are then post-processed using Matlab; a variety of experimental nonidealities are incorporated, as described in the following section; finally, digital filtering is performed, and the expressions given in Section 1.4 are used to determine the four S-parameters. As a basis for com-  35  T i m e (ps)  Figure 2.3: A realistic input signal for time-domain simulations with rise time of 3.5 ps and decay time of 50 ps.  36  Figure 2.4: Time-domain simulation of an E O S experiment with overlapping signals: (a) and (b) shows the simulation results when the signal generator is on the input side of the device under test ( D U T ) ; (a) shows the simulated data for signals measured at a propagation delay of 5 ps (solid line) and 4 ps (dotted line) before the D U T ; (b) is the corresponding waveform simulated at the output side of the D U T ; (c) and (d) are the corresponding simulations when the output port is excited.  37  parison, HSpice frequency-domain simulations are used to determine the "correct" S-parameters; in the case where long time windows are used, and in the absence of noise or drift, the S-parameters calculated using the expressions of Chapter 1 are in agreement with the directly-computed HSpice S-parameters.  2.2.2  Incorporating Experimental Impairments  In the following paragraphs, approaches to incorporate experimental non-idealities or impairments are described; first, the issue of the time window is discussed. As described in Section 1.3.2, a number of effects limit practical time windows for E O S test fixtures to values up to approximately 100 ps. The incorporation of the finite time window in simulations is straightforward, with the HSpice output waveforms being truncated after the time window under consideration. For a device of fixed geometry, i.e. of fixed transmission line lengths, the maximum time window possible depends upon the technique being used for S-parameter extraction. Therefore, it is important to assess correctly the time window for a given geometry: in the case where overlapping signals are acceptable, measurements are best performed near the D U T , while for non-overlapping signals measurement is best performed approximately mid-way between the photoconductive generator and the D U T . The second impairment to be considered is drift, the slow change in experimental sensitivity that is usually attributed to thermal effects such as temperature stability in the laboratory, or in the ultrafast laser system. It is possible to rapidly and repeatedly acquire data over the entire time window, averaging the results; this will reduce the impact of drift. In addition, the drift is not usually monotonic, but after some warmup time drift results in variations in the measurement sensitivity or excitation level around some average value. Therefore an exhaustive study of the impact of drift would require knowledge of the typical drift behavior, both in terms of amplitude and the temporal profile. As such data was not available, and is of limited generality considering the differences in experimental setups, in the present  38  work the evaluation of the impact of drift is based on a "realistic worst case" estimate. This is done by estimating the maximum drift that could be expected over a single scan, and assuming that multiple scan averaging is not used; the results obtained in this way are therefore somewhat conservative.  To include the effects  of drift in the simulations, a linear ramp is applied to one of the simulated waveforms after HSpice calculation. For example, the upper panel of Fig. 2.5 depicts the simulated waveforms in the absence of drift and with linear drift as the solid and dashed lines, respectively.  The linearly-increasing ramp used is illustrated in the  lower panel of the same figure. The noise in the measured signals is also a significant experimental issue, and is therefore included in the calculations.  Noise is incorporated by addition  of normally-distributed white noise to the simulated signals. Experimental studies of the noise level shows that it is primarily determined by shot noise used in the EOS signal detection system; as such, it can be expected to be fairly independent of the signal level.  The noise level is also dependent upon the total acquisition  time, improving as the square root of the total averaging time. In the calculations presented here, a value of approximately 3 m V / v H z is used. The R M S equivalent noise is determined by the equivalent noise bandwidth of the lockin amplifier used in the experiment. The bandwidth for the amplifier is set by the integration time and the slope of the low-pass filter frequency response, normally set to 24 dB/octive. For an integration time of one second per point this translates to an R M S equivalent noise of 0.86 mV, in addition for averaging of five multiple scans this is reduced to 0.43 m V . For a 100 ps time window, the total acquisition time is approximately 30 minutes. Fig. 2.6 shows the typical HSpice data after post-processing to include noise.  39  0.995  5  0.99 o * 0.985  -*—'  |  0.98  '15  ^ 0.975 Q^  0.971-  ^ 0.965 Q  0.96 0.955 h 0.95  0  10  20  30  40  50  60  70  80  90  100  Time (ps)  Figure 2.5: Time-domain simulation incorporating linear drift. The simulated data without drift (solid line) and with drift (dashed line) are shown in the upper panel. The ideal simulated data is post-processed by multiplication with a linearly-increasing ramp (lower panel).  40  12  11 0  i 20  i 40  i 60  i 80  i 100  I 120  Time (ps)  Figure 2.6: Time-domain simulation incorporating noise. The upper panel shows a simulation of a waveform at the input of the device under test (DUT) and the lower panel shows the corresponding output of the D U T . The data is representative of waveforms obtained over a total acquisition time of 30 minutes with a noise level of 3 mV/vtiz. 41  2.3  Results with Overlapping Signals  In this section we present results for extraction of S-parameters in the case where signals overlap in time. The input is measured at propagation delays of r; and t a  s  n  = 4 ps  = 1 ps, corresponding to a physical distances of 500 and 625 fim from the  D U T . The output is measured r  oui  = 5 ps from the D U T ; the length of the output  transmission line end, T d does not affect the results; it was arbitrarily taken to be en  100 ps. The raw time-domain data for the ideal case have been shown in Fig. 2.4.  2.3.1  Time Window  In Figs. 2.7 to 2.10 the S-parameters recovered using two values for the time window are shown; in each figure the solid lines show the true values of the magnitudes and phases as determined by the HSpice frequency-domain simulation. The dashed lines show results for a time window of 100 ps, which is considered to be the maximum value that would ever be integrated in an on-wafer test fixture. The dash-dotted lines show the results for a time window of 40 ps, which corresponds to an experimental SiGe heterojunction bipolar transistor test fixture available in our laboratory. Results for all four S-parameters show a common feature, the discrepancies between extracted S-parameters and the true results shown by solid lines increase at low frequencies.  These low-frequency errors are due to the high-pass filtering  approach used in the present work, and have been described in [5]: in order to timelimit the signals to allow Fourier transformation, the low-frequency components of the measured waveforms are discarded.  In an ideal case without truncation,  this low-frequency attenuation would be the same in all the waveforms, and the recovered S-parameters would be independent of the filter transfer function as claimed earlier.  H(f),  However, even with filtering, finite errors are caused because  the filtered signal has not returned to exactly zero by the end of the measurement interval. These truncation errors are not the same in the various waveforms needed to calculate the S-parameters, and cause the low-frequency errors seen.  42  Figure 2.7:  Calculated magnitude and phase of Su  f° t i r  m e  windows of 100 ps  (dashed), and 40 ps (dash-dot). For comparison, the solid line shows the true value.  43  Frequency (GHz)  Figure 2.8:  Calculated magnitude and phase of S i for time windows of 100 ps 2  (dashed), and 40 ps (dash-dot). For comparison, the solid line shows the true value.  44  Frequency (GHz)  Figure 2.9:  Calculated magnitude and phase of S22 for time windows of 100 ps  (dashed), and 40 ps (dash-dot). For comparison, the solid line shows the true value.  45  0.41  1  1  1  r  ' 100  ' 150  " 200  0.35 -  _20> 0  1  50  1 250  Frequency (GHz)  Figure 2.10:  Calculated magnitude and phase of Sn for time windows of 100 ps  (dashed), and 40 ps (dash-dot). For comparison, the solid line shows the true value.  46  Comparison of results for the 100 ps time window shown in Figs. 2.7 to 2.10 to the true values show that in this case the measurement accuracy is good at all but the lowest frequencies. Results shown in the same figures for 40 ps time window show greater discrepancies: for all four S-parameters, the errors are less than 10% over the range of frequencies shown up to 250 G H z . Accuracy of the phases, however, is worse, particularly at low frequencies where phase inaccuracy would likely be the limiting factor in determining the lower usable bound on the frequencies. From the data shown in the four figures, it can be concluded that acceptable accuracy can be achieved over the range from approximately 25 to 250 G H z .  2.3.2  Drift  Results incorporating linear drift are shown in Figs. 2.11 to 2.14.  In these figures  results for linear drifts of 1% and 5% are shown by the dashed and dash-dotted lines, respectively, and the correct values are shown by the solid lines. A l l results are calculated for a 100 ps time window.  As the calculations for the reflection  coefficients require two measurements from two locations of the port which is being excited, in calculations of input and output reflection coefficients the drift cancels if identical drift is applied to both waveforms. Therefore, in calculations of Sn and 522, drift is only applied to one of the raw time-domain signals. For the forward and reverse transmission coefficients S21 and 5 i , the drift is applied to one of the 2  input-side waveforms; results in which drift is applied only to the output waveform are similar, and are not presented. From the results shown in the four figures, it is apparent that the impact of drift is largest for the reflection coefficients S n and S22• F ° these parameters, there r  are substantial errors in the magnitude and phase over the whole frequency range of interest. The impact of drift increases as the drift grows larger as expected; the specific results shown indicate that experimental control of drift at the 1% level is necessary, and that 5% drift would lead to unacceptable results. This is considered to  47  Frequency (GHz)  Figure 2.11: Calculated magnitude and phase of Su for drifts of 1% (dashed), and 5% (dash-dot). For comparison, the solid line shows the true value.  48  Frequency (GHz)  Figure 2.12: Calculated magnitude and phase of S21 for drifts of 1% (dashed), and 5% (dash-dot). For comparison, the solid line shows the true value.  49  1 r—'  :  1  0.9 V» 0.8 V  x  0.7  • \ \\ \ \ s  \>  s  .  .  I ' ' "  •  3 0.6 -  •  c 0.5 D) CO ^ 0.4 -  -  0.3  -  0.2  -  0.1 -  •  1  •  •  0  50  100  150  200  250  -150 0  1  1  1  50  150  200  250  0  L  1  1  100  Frequency (GHz)  Figure 2.13: Calculated magnitude and phase of S22 f ° drifts of 1% (dashed), and r  5% (dash-dot). For comparison, the solid line shows the true value.  50  0.4  1  1  -  0.35 -  0.3 0.25 -  -  3  0.2  c  0.15 -  -  0.1  -  0.05  -  I  0 -  -0.05 -0.1  0  50  100  150  200  250  100  150  200  250  100  50  Frequency (GHz)  Figure 2.14: Calculated magnitude and phase of S\2 for drifts of 1% (dashed), and 5% (dash-dot). For comparison, the solid line shows the true value.  51  be quite challenging with the present experimental apparatus, and total integration times on the order of 30 minutes. In contrast to the reflection coefficients, the transmission coefficients S21 and Si2 show markedly less impact from drift. The results for the forward transmission coefficient S21 are in a good agreement with the true results.  The error in the  magnitude is less than 5% up to a frequency of 220 GHz for the largest applied drift.  For the phase, the errors are higher and are approximately 10% for the  largest applied drift. The errors appear as small deviations from the true values; the variation of these errors with frequency is not very great, unlike the errors seen in the reflection coefficients discussed above. Similar results are obtained for the reverse transmission coefficient S12. For this parameter, the magnitude recovered is accurate between the frequency range of 50 to 250 G H z with an error of less than 5%.  However, the error of the recovered phase is as high as 10% with a strong  variation with frequency.  2.3.3  Noise  A final test for evaluating the performance and feasibility of the approach for overlapping signals is the extraction of the S-parameters when the simulated data is corrupted by noise as described earlier.  Figs. 2.15 to 2.18 show the recovered S-  parameters when noise is incorporated into the simulation. Results are dependent upon the particular noise sequence used, which is randomly determined; accordingly, the dashed lines show the computed S-parameters for five different noise sequences when the time window is 100 ps. The errors for the computed results were determined for each noise sequence and then the errors were averaged to quantify the average error that occurs for measurements with acquisition times on the order of 30 minutes and the noise level specified earlier. For the input reflection coefficient, significant errors occur in both the recovered magnitude and phase. The error in the phase is substantial and varies strongly  52  Frequency (GHz)  Figure 2.15: Calculated magnitude and phase of 5 n for five different noise sequences (dashed). For comparison, the solid line shows the true value.  53  Frequency (GHz)  Figure 2.16: Calculated magnitude and phase of S21 for five different noise sequences (dashed). For comparison, the solid line shows the true value.  54  0.1 0  200  0  50  100  150  100  150  200  250  F  250  Frequency (GHz)  Figure 2.17: Calculated magnitude and phase of S22 for five different noise sequences (dashed). For comparison, the solid line shows the true value.  55  200 100  ^  ^  ^  ^  CD CD  -100  I  I  I  0  I  I  c3 -200h  I  I I  I  \ \  l  \  l\ II \  I  \ \  -300 \  I  t \  v  - 4 0 0 1  l  » \ \\ I  -500  i  1  50  100  150  200  l»  • • *  250  Frequency (GHz)  Figure 2.18: Calculated magnitude and phase of Si2 for five different noise sequences (dashed). For comparison, the solid line shows the true value.  56  over the entire frequency range shown. This result shows that for a measurement with overlapping signals, control of the noise to a level of less than 3 m V / y l f z is required. The noise may be reduced by increasing the averaging or acquisition time. However, increasing the acquisition time to reduce the noise would also increase the drift which has already been shown to have a large impact on recovering  Su.  The recovery of the forward transmission coefficient, S21, shows less impact of noise. The range of frequencies in which accurate results are obtainable is significantly reduced compared to the results when noise is not incorporated. The error in the recovered magnitude and phase is less than 5% between the frequencies 25 and 80 GHz. Within this frequency range, the variation in the error with frequency is also much smaller than the errors seen in SnThe noise has a large impact on the computed output reflection coefficient 522- From the errors calculated, acceptable results are only obtainable in a very small frequency range between 25 and 60 G H z where the errors are less than 5% for the magnitude and phase. Above 60 G H z , the error is less than 10%, but the variation with frequency is very large making it difficult to ascertain or extrapolate to higher frequencies. Finally, it can be seen that noise has a large impact on the recovery process for the reverse transmission coefficient, 5i2, as well.  The error of the recovered  magnitude and phase varies between 5 and 10% in between the frequency range of 25 to 80 G H z . This parameter is difficult to measure for a transistor because a good device is expected to have a small reverse transmission, which means the transmitted signal has a small amplitude resulting in a poor signal-to-noise ratio.  2.4  Results with Non-Overlapping Signals  In this section the approach for extracting S-parameters without temporal signal overlap is evaluated. In this case, only two sampling locations are required, one on each of the input and output sides, as discussed in Chapter 1. The input waveform 57  was simulated for r;  n  = 20 ps and the output for T  out  = 5 ps, corresponding to  sampling distances of 2.5 mm and 500 jum from input and output location to the D U T respectively. For this case, r = 0 ps because we only consider one input sams  pling location; r ^, the propagation delay between the output sampling location era  and the end of the transmission line, is taken as 100 ps as before. The input propagation delay to the D U T is much longer compared to the approach of Section 2.3 to avoid overlap of the incident and reflection signals.  The simulated waveforms  for the above input and the output locations are shown in Fig. 2.19. Fig. 2.19(a) and (b) shows the simulation for S n and S21, in which the input signal source is placed on the input side of the D U T . The larger input propagation delay results in a reflection that occurs much later in time than the previous simulations. In this case the reflection occurs approximately 40 ps after the beginning of the input signal as seen in Fig. 2.19(a). The output waveform in Fig. 2.19(b) is identical to the previous simulations except for a time shift because no reflections occur in the measurement time window. Fig. 2.19(c) and (d) are the corresponding input and output waveforms when simulating with the signal source on the output side of the DUT. The raw time-domain simulated data is digitally filtered allowing for separation of the portions of the signal that correspond to the incident and reflected signals as described in Chapter 1. The resulting filtered data is shown in Fig. 2.20. Fig. 2.20(a)-(d) show the digitally filtered waveforms corresponding to Fig. 2.19(a)(d).  The results for the case when the input signal source is placed on the input  side of the D U T are shown Fig. 2.20(a) and (b). In Fig. 2.20(a), the portions of the signal associated with the input and reflection signals are separated in the timedomain as indicated.  Fig. 2.20(b) shows the filtered waveform simulated at the  output sampling location. The corresponding filtered data for the simulations used to calculate S22 and S12 are shown in Fig. 2.20(c) and (d). The expressions from Section 1.4.3 are then used to compute the S-parameters using the filtered data. As  58  0  0  Figure 2.19:  50  100  0  50  100  0  Time (ps)  50  100  50  100  Time (ps)  Time-domain simulation of an E O S experiment with non-overlapping  signals: (a) and (b) shows the simulation results when the signal generator is on the input side of the device under test ( D U T ) ; (a) shows the simulated data for a signal measured at a propagation delay of 20 ps before the D U T ; (b) is the corresponding waveform simulated at the output side of the D U T ; (c) and (d) are the corresponding simulations when the output port is excited.  59  | j I  CO  « "5  u  r  Filtered Reflected Signal  M 4  > 1  Filtered Incident Signal  (a) 50  100  Figure 2.20: Filtered time-domain E O S simulation data for non-overlapping signals: (a)-(d) are the filtered waveforms corresponding to panels (a)-(d) of Fig. 2.19. (a) and (b) are the filtered waveforms of a signal that would be simulated on the input and output sampling locations when the input signal source is placed on the input side of the D U T . In (a), the portions of the signal that are associated with the incident and reflected signals are separated as indicated by the arrows; (b) shows the filtered output signal; (c) and (d) are the corresponding filtered waveforms when the input signal source is placed at the output port of the D U T .  60  above, the unfiltered data was post-processed to incorporate finite time windows, drift and noise to assess the accuracy of the non-overlapping signal approach.  2.4.1  Time Window  In the case for non-overlapping signals, a long input transmission line and time window are required.  The long input transmission allows sampling further away  from the device under test so that signals do not overlap, while a long time window is required to sample both the incident and reflection signals. A time window of 100 ps is first studied as before, because it is considered the maximum practical time window possible. For the case of overlapping signals where the sampling location is near the D U T , truncating the data from the end of the scan is not a problem because both the incident and reflected signals appear within the finite time window. However, for non-overlapping signals, a time window truncation cannot be achieved simply by stopping the simulated data at the desired time window. For instance, if the data of Fig. 2.19(a) were to be prematurely truncated at 40 ps, then the information pertaining to the portion of the signal associated with the reflection signal would be lost. It is better to consider a sample with a different geometry and sampling location that would allow both the incident and reflected signal to appear within the reduced time window. This is done for the non-overlapping signal case by using a shorter time window and an input sampling location moved closer to the D U T as shown in Fig. 2.21. In this case the input propagation delay is 12 ps corresponding to a distance of 1.5 mm between input sampling location and D U T as seen in Fig. 2.21(a). The change in sampling location allows both the incident and reflected signal to appear within the finite time window. In Fig. 2.21(a), the reflection now appears 24 ps after the incident signal rather than 40 ps for the larger input propagation delay shown in Fig. 2.19(a). Finally, the data is truncated to a time window of 50 ps, and digitally filtered as shown in Fig. 2.21(b). The separation of the portions of the signal associated with the incident and reflected  61  components  Figure 2.21:  Simulation for non-overlapping signals and finite time window. The  simulated data with the input location moved closer to the D U T , r; shown in (a).  ra  = 12 ps, is  The digitally filtered data is shown in (b), the arrows indicate the  separation of the portions of the signal associated with the incident and reflection signals. 62  are indicated by the arrows. Time-window truncation of the output waveform is more straightforward because no reflections occur so the waveform can simply be truncated from the end of the data. Fig. 2.21 only shows the data with finite time window for the case when the input signal source is placed on the input side of the D U T . Similar results are obtained with the change in the input sampling location when the source is placed on the output side of the D U T and are not shown. The results for the 100 ps and 50 ps time window are shown in Figs. 2.22 to 2.25. In the figures, the results for the 100 ps and 50 ps time windows are indicated by the dashed and dash-dotted lines respectively.  The computed results are then  compared to the true result calculated with the HSpice frequency-domain simulation shown by the solid line. As was seen for the case of overlapping signals, all of the S-parameters show discrepancies between the extracted S-parameters and the true results at low frequencies. The origin of this error was described earlier. The results for the 100 ps time window are in good agreement with the true results calculated directly in HSpice except at very low frequencies. For the 50 ps time window, the errors are less than 10% over the range of frequencies up to 250 G H z for both the magnitudes and phases. From the data shown in the four figures, it can be concluded that acceptable accuracy can be achieved over the range from approximately 25 to 250 G H z with a time window of 50 ps.  2.4.2  Drift  Results incorporating linear drift are shown in Figs. 2.26 to 2.29.  In these figures  results for linear drifts of 5% and 10% are shown with the dashed and dash-dotted lines, respectively, and the correct values are shown by the solid lines.  All of  the results are calculated for a 100 ps time window. For the forward and reverse transmission coefficients S21 and 5i2, the drift is applied only to the input-side waveform; results in which drift is applied only to the output waveform are similar, and are not presented.  63  250  Frequency (GHz)  Figure 2.22:  Calculated magnitude and phase of 5 n for time windows of 100 ps  (dashed), and 50 ps (dash-dot). For comparison, the solid line shows the true value.  64  5 r  1  1  1  1  •I  4.5  4 •\  \  3.5  o I \  CD  c CD  2  '' \ -.' '* N  2.5  /  \  2  1.5 1  f  V — -  0.5 0  t  0  50  i  l  100  l  150  200  250  200  Frequency (GHz)  Figure 2.23:  Calculated magnitude and phase of S21 for time windows of 100 ps  (dashed), and 50 ps (dash-dot). For comparison, the solid line shows the true value.  65  0.3 • 0.2 • 0.1 • 0  I  0  1  1  50  100  .  1  1  150  200  250  Frequency (GHz)  Figure 2.24:  Calculated magnitude and phase of 522 for time windows of 100 ps  (dashed), and 50 ps (dash-dot). For comparison, the solid line shows the true value.  66  Figure 2.25: Calculated magnitude and phase of S12 for time windows of 100 ps (dashed), and 50 ps (dash-dot). For comparison, the solid line shows the true value.  67  11  1  r  1  0.1 h QI  0  I  I  I  •  I  50  100  150  200  250  Frequency (GHz)  Figure 2.26: Calculated magnitude and phase of Sn for drifts of 5% (dashed), and 10% (dash-dot). For comparison, the solid line shows the true value.  68  Frequency (GHz)  Figure 2.27: Calculated magnitude and phase of S21 for drifts of 5% (dashed), and 10% (dash-dot). For comparison, the solid line shows the true value.  69  0.3 • 0.2 • 0.1 )l  0  i  i  i  i  1  50  100  150  200  250  Frequency (GHz)  Figure 2.28: Calculated magnitude and phase of S22 f ° drifts of 5% (dashed), and r  10% (dash-dot). For comparison, the solid line shows the true value.  70  Frequency (GHz)  Figure 2.29: Calculated magnitude and phase of £12 for drifts of 5% (dashed), and 10% (dash-dot). For comparison, the solid line shows the true value.  71  The results show that the drift does not cause a large error for any of the Sparameters as seen in the figures. Specifically, the error in the recovered magnitudes for all four parameters over frequencies between 25 and 250 G H z is between 5-10% for the largest applied linear drift of 10%. The error in the recovered phase for each parameter is negligible over the same frequencies. Also of note is that the variation in the error over this frequency range is small, that is, the error is nearly the same for all frequencies. In contrast to the case for overlapping signals, the results here show that the level of control over the experimental drift may be relaxed.  Reasonable  results are expected for a level of drift between 5 and 10% which may be possible with the present experiment. Also of note is the comparison between the reflection coefficients 5 n and 522 in Fig. 2.26 and 2.28. The errors were about the same for both coefficients despite the difference in the magnitudes of the two coefficients. The input reflection, 5 n , is normally small for a transistor because the device is normally used to transmit an input signal with gain. Likewise, the output reflection coefficient is normally large as the transistor does not usually have unilateral design, that is the transistor is designed to have gain for the forward transmitted signal and not for the reverse transmitted signal.  2.4.3  Noise  The results for the S-parameters when noise is incorporated into the simulation are shown in Fig. 2.30 to  2.33.  As before, results are dependent upon the particular  noise sequence used and therefore results for five different noise sequences are shown as indicated by the dashed lines. The true results are represented by the solid lines. As for the previous case, the average of the errors for the five noise sequences was found and used to quantify the accuracy of the results. The results for parameter 5 n shown in Fig. 2.30 for the non-overlapping case are better than the case for overlapping signals shown in Fig. 2.15.  72  For both the  200 r 100 r-  /  cn CD  Q"  \  100  co |  s/  -200\  Q_ -3001-4001 -500  1  50  100  150  200  *  250  Frequency (GHz)  Figure 2.30: Calculated magnitude and phase of Sn for five different noise sequences (dashed). For comparison, the solid line shows the true value.  73  Figure 2.31: Calculated magnitude and phase of S21 for five different noise sequences (dashed). For comparison, the solid line shows the true value.  74  250  200  100  150  250  Frequency (GHz)  Figure 2.32: Calculated magnitude and phase of S22 for five different noise sequences (dashed). For comparison, the solid line shows the true value.  75  — i —  2 0 0  -r  » »n  1  f  1 0 0  *  1  f /  0  D) CD  J §  1 0 0  - 2 0 0  - 3 0 0  - 4 0 0  - 5 0 0  5 0  1 0 0  1 5 0  2 0 0  2 5 0  Frequency (GHz)  Figure 2.33: Calculated magnitude and phase of Su for five different noise sequences (dashed). For comparison, the solid line shows the true value.  76  magnitude and phase, the error is less than 10% between 15 and 80 G H z , and the variation of error with frequency is smaller than in the case for overlapping signals. For the forward transmission coefficient, S21, the recovered magnitudes and phases are in excellent agreement with the true result over a large bandwidth as seen in Fig. 2.31. The error in the magnitude is less than 5% up to approximately 115 G H z and increases to 10% above 120 G H z , with very little deviation versus frequency. The recovered phase shows errors of less than 5% up to a frequency of 50 G H z and than gradually increases to 10% above 100 G H z . The lower frequency limit for reliable results is approximately 15 GHz for both the magnitude and phase. The results for the output reflection coefficient, S22, shown in Fig. 2.32, show fair agreement with the true result over a large bandwidth. The errors in the magnitude and phase are less than 5% between 15 and 130 G H z increasing above 10% at 150 G H z . This is a significant improvement over the results obtained for the case of of overlapping signals shown in Fig. 2.32. The results for the non-overlapping case show much less variation with frequency and significantly smaller errors. The most significant impact of noise is seen in the results for the reverse transmission coefficient, 5 , shown in Fig. 2.33. The errors for the magnitude and 12  phase are in excess of 10% over the entire frequency band shown in the figure. The rippling or deviation over the whole frequency range is large. As mentioned before, the noise is problematic for recovering Su  because the reverse transmitted signal  is small for a good transistor, in this case 1.5 mV for a 10 mV input, resulting in poor signal-to-noise ratio. It may be possible to decrease the noise by increasing the integration time for the non-overlapping signals case, because it was shown that drift does not cause large errors even for linear drift as high as 10%.  2.5  Conclusions  Simulation results show that for realistic experimental situations, accurate extraction of S-parameters is problematic for the case where temporally-overlapping signals 77  are measured. The greatest difficulties are posed in extraction of the reflection coefficients Su and S22 in the presence of drift and noise. Results for the transmission coefficients, £21 and 512, show much less drift-induced error. The noise does not cause a significant problem for recovering S21 but has a severe effect on the extraction of S12. Control of drift at the 1% level is required, which is presently considered to be quite demanding in practical experimental situations. Noise reduction to the 1 mV/y/Kz  level is required for accurate S-parameter extraction. Time-windowing  at the 40 ps level was found to introduce tolerable errors, and does not appear to be a significant issue in this case. Overall, S-parameter measurement in the presence of temporally-overlapping signals would appear to be difficult with current optoelectronic measurement systems. In contrast to the above, the accurate extraction of S-parameters under realistic experimental conditions for the case of non-overlapping signals is possible. It is concluded that for this case, the drift does not pose a large problem for levels which can be experimentally controlled, i.e. at or below 10%.  In the presence of  noise, the only difficult parameter to extract is the reverse transmission coefficient S12. The remaining parameters can be accurately recovered over a large frequency range. Improvement of the sensitivity to the same level mentioned above is required to accurately extract all four parameters. Also, a time-window of 50 ps was shown to be sufficient for accurately recovering the S-parameters as the truncation errors were not significant. In conclusion, S-parameter measurement for non-overlapping signals is viable with current optoelectronic measurement systems.  78  Chapter 3  Propagation on a Coplanar Stripline:  Experimental  V a l i d a t i o n of D i g i t a l F i l t e r Technique 3.1  Introduction  In this chapter, experimental results are presented for signal propagation on coplanar striplines (CPS) fabricated on a heavily-doped silicon substrate with a thick silicon dioxide layer. The experimental results serve to demonstrate the signal processing technique for the case of non-overlapping signals presented in the previous chapter. In addition to validating the technique, the study of propagation on silicon substrates is motivated by technological interest in its use as a substrate for high-speed and microwave circuits [36, 37]. The coplanar stripline consists of two coplanar conductors on the surface of a substrate, as illustrated in Fig. 3.1. The coplanar stripline on a multilayer SiO^/Si  79  Aluminum Silicon Dioxide  Silicon Buffer  Doped Silicon Substrate  (a)  Silicon Dioxide  Aluminum  w sw Figure 3.1:  (b)  Physical layout and structure of coplanar stripline (CPS) fabricated  on a silicon substrate and silicon dioxide layer: (a) cross section of the structure consisting of aluminum conductors, Si02, and semiconductor buffer and substrate layers; (b) top view. 80  substrate is of interest used as a high-frequency transmission line. In this structure a thick oxide layer is often used to locate the conductors as far as possible from the substrate in an attempt to minimize the impact of substrate losses, which are problematic because of the difficulty in manufacturing a high-resistivity silicon substrate. These types of metal-insulator-semiconductor (MIS) structures are more complex than typical coplanar striplines fabricated on a uniform semiconductor substrate, and allow a number of guided wave modes to propagate.  Three types of modes  are possible: a quasi-transverse electric magnetic (quasi-TEM) mode, a skin-effect mode and slow-wave mode [38]. The mode depends on the substrate conductivity and permittivity, structure dimensions and the frequency. The propagation mode is quasi-TEM if the substrate has a high resistivity. At the other extreme, if the substrate has a high conductivity due to heavy doping, then the substrate acts as a lossy conductor and the mode of propagation is known as the skin effect mode. For substrate conductivities in between these two extremes a slow-wave mode of propagation is possible. This mode is of particular interest because it exhibits increased phase velocities at low frequencies and may find application in microwave delay lines.  A very qualitative explanation for the increase in phase velocity is  attributed to the separate storage of electric and magnetic fields. Because the electric fields do not penetrate far into the lossy semiconductor substrate, the electric fields are confined in the insulator while the magnetic field penetrates deep into the substrate as if it was unaffected by the lossy semiconductor. This results in an increased line capacitance and relatively unchanged line inductance leading to the change in phase velocity. However, due to the lossy substrate this structure suffers from high losses. Coplanar structures, specifically coplanar waveguides have been studied theoretically using mode matching methods [39, 40], finite-difference timedomain method [26], method of lines [41] and quasi-TEM analysis [42,43,44,45]. Fewer experimental results are available: coplanar waveguide ( C P W ) MIS structures results have been published for low frequency network analyzer measurements  81  [36, 37, 43, 26], and high-frequency electro-optic measurements  [25]. One result  has been published for coplanar stripline (CPS) MIS silicon structures [26]; network analyzer measurements were taken up to 40 G H z for an unbalanced coplanar MIS stripline on weakly-doped substrates with a thin oxide layer. This is in contrast to the results that will be presented here for a heavily doped, thick film MIS coplanar stripline for frequencies up to 150 G H z .  3.2  Experiment  The coplanar stripline is fabricated on a silicon substrate with a process [33, 34] used for the fabrication of high-speed silicon-germanium/silicon heterojunction bipolar transistors. The physical structure was shown in Fig. 3.1, it consists of aluminum metallization that is of order 1  in thickness, a silicon dioxide layer approximately  5 /fm thick, a silicon buffer layer and a 0.01 Cl • cm highly doped silicon substrate layer approximately 800 /im thick. The metal conductors of equal 65 /J,m width, and the spacing between them is 5 jwn. In order to launch photoconductively-generated step-like signals onto the CPS, the structure is wire bonded to a photoconductive signal generator as shown in Fig. 3.2(a). The signal generator is similar to the one described in Chapter 1, consisting of a C P S structure with 1.2 fim thick gold conductors photolithographically defined on a 635 /im thick semi-insulating GaAs substrate.  The conductor  width and spacing is 50 /tm and 5 /J,m respectively for the C P S and the photoconductive switch gap is 5 fxm wide. The two structures are positioned closely together on a sample holder which is fabricated to compensate for the different substrate thickness as shown in Fig. 3.2(b). They are then held in place by wax, and wire bonded.  Using this approach, sufficiently fast rise time signals can be launched  despite the bandwidth-limiting effects of the wire bonds. When performing the experiment the sample is connected as shown in Fig. 3.2(a) with a D C power supply biasing the photoconductive switch. For these experiments the D C bias is set to 4.0  82  Wire Bonds  Photoconductive Switch  (a)  Wire Bonds GaAs  Si0 /Si 2  Sample Holder (b) Figure 3.2: Experimental test fixture with GaAs photoconductive signal generator wire bonded to the C P S fabricated on silicon: (a) top view, showing how samples are positioned close together and then wire bonded; (b) side view, showing how the test fixture is fabricated to account for the slight difference between the substrate thicknesses. 83  V . A mode-locked solid state Titanium Sapphire laser which produces 80 fs pulses at a repetition rate of 100 M H z and wavelength of 832 nm is used as the ultrafast optical source for these experiments. Measurements are taken at several positions along the transmission line on the silicon side of the wire bonds. The measurements are obtained by electro-optic sampling using an external LiTaO"3 sampling tip with a 220 u-m square footprint; further details of the experimental system can be found in [46]. Measurements are made with the sampling tip in a non-contact configuration because it has been shown that the LiTaOa tip can perturb the signals if placed in contact with the sample [47, 48]. The tip is placed approximately 5 pm above the transmission line for each sampling position. Calibration of the measurements is achieved by applying a low-frequency calibration signal of known voltage to the silicon C P S structure; this is repeated at each sampling location along the transmission line to compensate for variations of the tip-sample distance with measurement position.  3.3  Results and Discussion  Experimental time-domain results are shown in Fig. 3.3. The launched electrical step-like signal was measured approximately 250 pm from the interface between the signal generator structure and the C P S on silicon.  This position is taken as the  origin with position z = 0.0 mm; two other measurements are taken at z = 0.575 and z = 1.0 mm from this location. Comparison of the three curves shown Fig. 3.3 shows a number of effects. Most obvious are the effects of attenuation and dispersion, evidenced by the decreasing amplitude and increasing rise time with propagation distance. Quantitatively, the 10-90 % rise time is 3.3 ps at 0.0 mm, increasing to 3.9 and 4.5 ps at locations 0.575 and 1.0 mm, respectively, and the corresponding peak amplitudes are 254, 221 and 206 m V . Using E q . 1.17 from Chapter 1, the frequency-dependent propagation factor was calculated, and the attenuation and effective permittivities determined. Re84  Figure 3.3:  Electro-optic sampling time-domain measurements of propagation on  silicon. Three separate measurements are made. The first position, considered the origin, is located 250 /im away from the gap-between the signal generator and the C P S on silicon. The two remaining sampling locations were 0.575 mm and 1.0 mm from the origin.  85  suits are presented in Figs. 3.4 and 3.5, as labeled. In each figure, the experimental results (solid lines) are compared to theoretical results from electromagnetic simulations (squares) performed elsewhere [3]. As discussed in Chapter 2, low-frequency errors can be quite large using the present approach; accordingly, experimental results are not shown below 20 G H z . Similarly, structure similar to that seen in Chapter 2 is seen in the experimental results above 150 G H z , and suggests that is an appropriate upper bound for the frequency over which experimental data is accurate. The electromagnetic simulations [3] shown in Figs. 3.4 and 3.5 were performed for the same dimensions as the experimental samples. The simulations were performed for a substrate resistivity of 0.01 Q • cm, the measured substrate conductivity. The attenuation shows excellent agreement between measured and modelled data at frequencies below 50 G H z . Above 50 G H z , the measured attenuation is overestimated by the modelled results. The discrepancy is attributed to slight inaccuracy in the estimated substrate conductivity. The attenuation at 150 G H z is relatively high: a loss of 0.9 N p / m m , or 78 d B / c m , is much higher than comparable structures on semi-insulating GaAs, where values on the order of 0.2 N p / m m for similar structures are typical [22]. Excellent agreement between experimental and modelled effective permittivities is seen over nearly the entire range from 20 to 150 GHz.  Beyond 100 G H z , the effective permittivity is nearly constant at approxi-  mately 6.2.  The rise in effective permittivity at lower frequencies, below 80 G H z ,  is consistent with similar effects seen in previous measurements and calculations for coplanar waveguides fabricated on multilayer silicon dioxide / silicon substrates. In comparison to the electromagnetic simulations, it is clear that the results shows either a skin effect or slow wave effect at low frequencies because of the rise in effective permittivity. This feature probably is more likely to be attributed to the skin effect because of the very high doping level of the substrate and the very high losses observed experimentally. A slow-wave effect typically results in a larger change in  86  1.2  lr  Q|  20  1  1  40  60  1  1  80 100 Frequency (GHz)  1  120  ;  1  140  1  Figure 3.4: Attenuation data: E O S measurements (solid line), electromagnetic simulations (squares), (from Ref. [3]).  87  Figure 3.5: Effective permittivity data: E O S measurements (solid line) and from electromagnetic simulations (squares), (from Ref. [3]).  88  effective permittivity with frequency in the low frequency regime than seen in the experimental result. From the results, it is clear that the highly-doped structure is not suitable for high-speed interconnect on silicon integrated chips. From previous theoretical calculations [41] for coplanar waveguides on similar substrates, it was shown that an inhomogeneous doping profile reduces the losses and thick insulators improve the dispersion characteristics over a large frequency range. The use of an inhomogeneous doping profile restricted to areas under the metal conductors reduces the portion of the emerging tangential electric field in contact with the doped portion of the lossy substrate, reducing the total losses compared to a homogenously doped substrate.  In addition, calculations showed that thick film insulator struc-  tures exhibit less dispersive slow-wave effects over a larger band of frequencies than similar thin insulator structures. The excellent agreement between experimental and modelled results for propagation of coplanar striplines on lossy multilayer silicon dioxide/silicon substrates shows that frequency domain characterization is possible with step-like input signals. The results therefore validate the digital filtering signal processing technique used in the S-parameter extraction methods. In comparison to similar electronic measurements [26], the results here significantly extend the bandwidth for characterization of MIS coplanar striplines on silicon. Although reasonable frequency domain characterization is possible with step-like signals, the bandwidth of the measurement, approximately 150 GHz, is significantly less than those obtained optoelectronically with pulse-like signals. Optoelectronic methods using pulse-like signals have been used for characterization of coplanar transmission lines for frequencies up to 500 GHz or greater including MIS coplanar waveguides on silicon  3.4  [25].  Conclusions  The experimental study of propagation on metal-insulator-semiconductor  (MIS)  coplanar striplines fabricated on silicon verified and validated the digital filter sig89  nal processing technique used in the S-parameter extraction methods evaluated in Chapter 2. The experimental results presented are the first for heavily doped silicon MIS coplanar stripline structures. Excellent agreement between measurements and calculations from an electromagnetic simulation was achieved. The results show that frequency-domain characterization with step-like signals is possible so long as signals do not overlap. However, the techniques are more difficult to use than impulse measurements using optoelectronic methods.  90  Chapter 4  Conclusions and Future W o r k 4.1  Conclusions  To briefly summarize the work, two methods for extracting S-parameters in the time-domain using step-like signals were evaluated for their performance under realistic experimental conditions through simulation of an electro-optic sampling experiment of a high-speed transistor.  The first method allows determination of the  S-parameters for situations in which signals overlap. In contrast to this, the second method is applicable for non-overlapping signals. In addition to the model-based evaluation of the two approaches, an experimental validation of the digital filtering techniques common to both methods was shown by measuring the propagation of signals on a coplanar stripline fabricated on a multilayer SiO"2/Si substrate. The experiment is a special case of the approach for non-overlapping signals.  Several  conclusions were drawn from the work described above. First, it was concluded that accurate extraction of S-parameters for measurements with overlapping signals is not feasible. The primary reasons for this are that the experimental impairments of drift and noise significantly affect the extraction of incident and reflected signals during the algebraic manipulations in the frequency domain. This results in inaccurate S-parameter calculations.  91  Second, the simulations showed that for non-overlapping signals, the Sparameters can be extracted reliably over a reasonable bandwidth with the exception of the reverse transmission coefficient, S i 2 . For non-overlapping signals, the drift does not play a large role in comparison to the overlapping case because it does not affect the separation process which occurs in the time domain rather than in the frequency domain. The noise for the non-overlapping case only causes significant problems in the extraction of S i because of the small-signal levels involved; a further 2  improvement in noise sensitivity should allow extraction of all four parameters. The experimental confirmation of propagation on C P S fabricated on the multilayer silicon substrate validates the digital filtering technique used in both of the methods evaluated.  The experimental results showed dispersive or skin effects at  low frequencies and high losses which were attributed to the conductive substrate used. From the experimental and simulation results, it is apparent that using steplike signals is more difficult for small-signal frequency domain characterization. This is attributed to the limited bandwidth of the signal in comparison to impulse-like signals used in other methods. Therefore, it is concluded that impulse-like measurements are more practical for obtaining reliable frequency-domain characterization with optoelectronic methods.  4.2  Future Work  The conclusions drawn from the work suggested that impulse-like measurements were more practical for small-signal characterization.  This implies that a device  cannot be characterized in the frequency- and time- domain simultaneously using step-like input signals and optoelectronic techniques.  The last statement brings  us precisely "full circle" to the beginning of the thesis in which we try to resolve this issue of using a standardized test fixture for simultaneous small-signal and large-signal characterization by using the methods proposed by Svensson [2].  The  work of this thesis showed that the methods do not work for practical situations.  92  An alternative to this requires a change in the experimental setup.  One change  which might be more practical is the use of freely positionable photoconductive probes [13, 14] for launching high-speed signals onto the input transmission lines of the device. The use of probes avoids the problem of having a fixed test fixture with only one type of signal generator, this allows the interchange of step- and pulse-like generators by interchanging different probes. Doing measurements in this manner allows small-signal and large-signal device characterization  on the same  device. Alternatively, nonlinear characterization with impulse-like signals could be pursued. While these signals do not closely resemble those used in switching circuits, they may provide data for nonlinear device modelling. In addition to the work on small-signal characterization of active devices, it may be of interest to study further the propagation characteristics of high-speed signals on coplanar striplines fabricated on multilayer S i 0 2 / S i substrates. 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