compact nanosecond pulsed power technology with applications to biomedical engineering, biology, and medicine

COMPACT NANOSECOND PULSED POWER TECHNOLOGY WITH APPLICATIONS TO BIOMEDICAL ENGINEERING, BIOLOGY, AND MEDICINE by Xianyue Gu A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL

COMPACT NANOSECOND PULSED POWER TECHNOLOGY

WITH APPLICATIONS TO BIOMEDICAL ENGINEERING, BIOLOGY, AND MEDICINE

by

Xianyue Gu

A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA

In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATERIAL SCIENCE)

August 2006

Copyright 2006 Xianyue Gu

3237721 2007

Copyright 2006 by

Gu, Xianyue

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Dedication

To my parents, my husband, and my unborn children

Acknowledgements

With sincere gratitude, I thank Dr Martin Gundersen for his vision, guidance, support and encouragement; Dr Edward Goo and Dr Chongwu Zhou for serving on

my dissertation committee; Dr Terence G Langdon, Dr Florian B Mansfeld, and

Dr Steven R Nutt for serving on my Ph.D qualifying exam committee; Dr Andrus Kuthi for sharing his knowledge in pulsed power I would like to thank my colleagues, Dr P Thomas Vernier, Dr Chunqi Jiang, Qiong Shui, Yinghua Sun, Tao Tang, Fei Wang, Matthew Behrend, and many other friends for their kindness and help throughout my graduate study at University of Southern California I also thank Song Han, Bo Lei, Wu Jing for their help in the pulsed laser deposition Thanks are also owed to Noreen Tamanaha for her countless work

Table of Contents

Dedication ii Acknowledgements iii

Abstract xi

1 Introduction

1.1 Pulsed Power Technology for Biomedical Applications

1.2 Research Issues in Compact Nanosecond Pulsed Power System

2.2.1 Physical models for simulations

2.2.2 Heat flow equation

3 High Energy Density Capacitor

4.2.2 Modeling of water Blumlein

4.2.3 Fabrication of water Blumlein

4.3 Four-channel Resonant Charging Circuit

4.4 Operation and Conclusion

60

5 Impulse Catheter Devices for Medical Applications

5.1 Impulse Catheter Device Design

5.1.1 Design requirements

5.1.2 Device design

5.2 Materials and Methods

5.3 Evaluation of Impulse Catheters

5.3.1 Load impedance

5.3.2 Electric field distribution

5.3.3 Effect volume

5.4 in vivo Response to Nanopulses Delivered via Impulse Catheter

5.5 Dielectric Dispersion of Biological Load

5.6 Conclusions

77

List of Tables

1.1 Summary of Various Switch Parameters in Pulsed power

Application

6

2.2 Summarized parameters for the impact ionization model 35 2.3 Heat capacitance and thermal conductivity for various materials 38

3.1 Comparison of various methods for BST dielectric layer growth 53 5.1 Measured maximum operation voltages of RF catheters and

microwave cable Measurement was carried out by high voltage pulses

with pulse width of 150ns

81

List of Figures

1.1 Simple inductive storage discharge circuit and voltage and current

waveforms with RL decay

12 1.2 SOS switching circuit schematic and voltage and current waveforms 12

1.3 Simple capacitive storage discharge circuit and output voltage with RC

2.1 Theoretical merits of different semiconductor materials 19

2.5 Electric field dependency of electron and hole impact ionization rate at

T=300 K for GaAs

34

2.6 Electric field dependency of electron and hole impact ionization rate at

T=300 and 400 K for 4H-SiC

34

2.7 Electric field dependency of electron and hole impact ionization rate at

2.9 Cross sectional structure of the Si vertical MOSFET 39 2.10 Predicted hold off voltages for Si vertical MOSFET, GaAs, 4H-SiC,

and GaN vertical JFETs

41

2.11 Predicted electron density in the GaAs vertical JFET at Vds = 300 V

with and without the EL2 defect The x-axis is the distance from the source

toward the drain

42

2.12 Predicted electron mobility in the GaN vertical JFET The x-axis is

the distance from the source toward the drain

43

2.13 Predicted I - V curves for the GaN vertical JFET The dark curves are

results for perfect GaN The gray curves are for GaN with defects

44

2.14 Predicted I-V curve for the 4H-SiC vertical JFET The gray curves are

results for the perfect material The dark curves include the effects of

defects

45

2.15 Predicted hold-off voltage for the 4H-SiC JFET 45 2.16 Hole concentration results from 4H-SiC JFET simulation without

2.17 Comparison of predicted hold-off voltages for the Si, GaAs, SiC, and

GaN devices The plot for the GaN JFET was obtained at Vgs= -25V 48

2.18 Comparison of predicted switching performances of the Si, SiC, GaN

2.19 Predicted effect of gate bias on the hold-off voltage of the GaN JFET 49 2.20 Ratio between temperature rising and current density for GaAs, GaN

and SiC JFET’s

49

3.2 XRD patterns for BST films deposited and annealed at (a) 500˚C,

3.4 Dielectric constant and dissipation factor of the film vs frequency 59

4.2 3.8 inch (5 ns) Blumlein model and simulated output wave form 64

4.3 750 mil Blumlein model and simulated output wave form illustrating

the impact of edge effects at shorter pulse widths

65 4.4 The initial semi-circular outward propagating input wave 66

4.5 The input waveform boundary as the wave propagates through the

4.6 Pulse shape improvement using internal reflections 67 4.7 Picture of fabricated 5-ns and 2-ns Blumlein for 10 ohm cuvette load 68

4.11 4-resonant-channel charging circuit and single resonant channel

4.12 Balancing drain currents in four resonant channels by modifying

ground loop layout on printed circuit board

73

4.13 Charging waveform, 8.5kV peak, 355ns rise time Total peak current

on primary of the transformer is 400 A

74

4.14 Circuit diagram of the lumped element transmission line 75 4.15 Picture of the compact pulsed generator based on a lumped

transmission line and a four-channel resonant charging circuit 75

4.16 Output voltage, 5.5 kV peak and 5.4 ns rise time, and 9.2 ns pulse

5.1 Line impedance as a function of frequency for a commercial RF

ablation catheter transmission line, and input and output pulses showing

distortion of typical line

78

5.3 Impulse catheter models constructed in the CST Microwave Studio®

EM simulator

84

5.4 Process of histogram results from flow cytometric analysis 87 5.5 Frequency dependant load impedances for various catheters 89 5.6 Simulated voltage decay along the center needle of catheter C02 90 5.7 Simulated electric field distribution in RPMI medium pulsed using

5.8 Simulated electric field distribution and fluorescence images of

SKOV-3 ovarian cancer cells pulsed by the flat-cut catheter and catheter C0SKOV-3 with

20 ns, 6 kV, 6 MV/m 150 pulses

93

5.9 Percentages of cells taking YO-PRO-1 staining after pulse exposure

using different catheters

94

5.10 Tumor shrinkage after pulses Left tumor is the control tumor, right

one has been pulsed with 200 pulses repeatedly 95

5.11 Measured load impedances for RPMI and predictions of simulations

that included the second order Debye model of RPMI 99

6.1 Electroporation, electromanipulation, electropermeabilization, and

electroperturbation — overlapping pulsed electric field technologies 103

Abstract

Pulsed power refers to a technology that is suited to drive applications requiring very large power pulses in short bursts Its recent emerging applications in biology demand compact systems with high voltage electric pulses in nanosecond time range The required performance of a pulsed power system is enabled by the combined efforts in its design at three levels: efficient and robust devices at the component level, novel circuits and architecture at the system level, and effective interface techniques to deliver fast pulses at the application level

At the component level we are concerned with the power capability of switches and the energy storage density of capacitors We compare semiconductor materials - Si, GaAs, GaN and SiC - for high voltage, high current, fast FET-type switches, and study the effects of their intrinsic defects on electrical characteristics We present the fabrication of BST film capacitors on silicon substrates by pulsed laser deposition, and investigate their potential application to high voltage, high energy density capacitors

At the system level, a nanosecond pulse generator is developed for electroperturbation of biological cells We model and design a Blumlein PFN (Pulse Forming Network) to deliver nanosecond pulses to a cuvette load The resonant circuit employs four parallel 100 A MOSFET switches and charges the PFN to 8 kV within 350 ns

At the application level, in order to controllably deliver nanosecond electric pulses into tumors, we have designed, fabricated, and tested impulse catheter devices Frequency responds, breakdown voltages and effective volumes of catheters are evaluated With comparison of simulation and experimental results, we further develop dielectric dispersion models for RPMI

This thesis presents a set of strongly interdisciplinary studies based on pulsed power technology and towards biomedical applications Addressed issues include from fundamental materials studies to application engineering designs that are essential to next generation compact pulsed power technology The combined research efforts on these issues enable the further development of pulsed power for biomedical, biophysical, and medicine applications

Chapter 1

Introduction

1.1 Pulsed Power Technology for Biomedical Applications

Pulsed power refers to a technology of accumulating energy over a relatively long period of time and releasing it very quickly thus increasing the instantaneous power Since the late John Chiristopher (Charlie) Martin and his colleagues developed the first modern pulsed power system at the Atomic Weapons Establishment, Aldermaston, U.K., in the 1960s [Martin, 1992], pulsed power has evolved to not only play an important role in defense, including homeland defense, but has evolved

to become an important technology in the biomedical arenas as well [Schamiloglu et al., 2004]

One classical example in biomedical applications of pulsed power technology is electroporation (also termed electropermeabilization) of the cell membrane by applying electric pulses with pulse widths in millisecond-microsecond range and

electric fields of a few kV/cm [Neumann et al., 1982, Weaver, 2000, Zimmerman et al., 2000, Gehl, 2003] The electroporation process transports extracellular ions or molecules into cells, thus allows local drug delivery for cancer therapies, for instance, Electrochemotherapy (ECT) has reached clinical trials [Belehradek et al.,

Vernier et al., 2003], only under certain conditions (pulse width, amplitude) the electric field will perturb organelles within the cell, and an intense electric field will appear within the cell during a time of the order nanoseconds Applying pulses with high voltage (or field), high power, and fast (turning on in nanoseconds) is thus a requirement This in turn requires advanced design of pulse generation, transmission, and coupling to the electrical load, typically cells in culture, or tissue The principal issues encountered include the distortion of nanosecond pulses due to the high frequency characteristics, and the need to retain high field along with high speed Fast rising pulses require advanced switching elements, incorporated into suitable pulse generation architectures Other issues include maintaining reproducible uniformity of the pulse envelope and keeping a compact system size More details in pulsed power technology for studying intracellular effects will be discussed in the section 1.2

At this moment, most pulsed power systems for studying nano-electroperturbation are developed in two research laboratories at University of Southern California and Old Dominion University According to the electrical load applied to, they fall into two categories: 1) pulse generators are used to observe the immediate effect of ultrashort pulse in live cells under a fluorescence microscope [Behrend et al., 2003, Behrend et al., 2004, Kuthi et al., 2004, Kolb et al., 2006] A typical electrical load is

a rectangular conducting channel filled with suspension cells and culture medium on

a microscope slide Walls of the channel act as parallel electrodes with spacing of 25

to 100 µm, which is comparable to the typical size of biological cells Therefore, cells are forced to form a cell array along the channel Also because of the small distance between electrodes, only a few hundred volts are needed to achieve electric fields greater than 1 MV/m (a hypothetical threshold field strength for intracellular effects, the value is highly dependent on cell types.) The design challenges of these pulse generators are miniaturization of system, integration of the pulse generators with the microscope observation stage, and flexibility of pulse parameters; 2) pulse generators are developed to treat million cells in standard electroporation cuvettes to collect statistical cell responses upon electric pulses exposure [Behrend et al., 2003, Schoenbach et al., 2004, Tang et al., 2005] With the 1 – 2 mm electrode separation, cuvette excitation requires high voltages The cuvette with culture presents a low impedance load (typ ~10 ohms), so although the energy is low, the generator must nevertheless be able to deliver high currents as well as high voltages Thus the challenge in designing these generators is to realize a combination of high voltage, high current, and fast rise time For future clinical investigations and applications, the third category of pulse generation will be needed The great difficulty lies in controllably delivery of the consistent, intense, ultrashort electric pulses into tumors,

a complicated “load” that varies in each patient Further more, reduction in the size and the number of components of pulsed power system is essential to make nanoelectropulse therapy actually become a reality [Vernier, 2004]

In addition to biomedical applications, advanced pulsed power technology also provides a powerful method to explore the electrical effects on the subcellular level, hence expand our knowledge about cells [Schoenbach et al., 2004]

1.2 Research Issues in Compact Nanosecond Pulsed Power Technology

To develop advanced ultra-short, high-field pulsed power technology for the biomedical applications of nanoelectropulses, the combined research efforts are required at three levels: efficient and robust devices at the component level, novel circuits and architecture at the system level, and effective interface techniques to deliver nanoelectropulses at the application level

1.2.1 At component level

Now more than ever, the pulsed power field is driven by size, weight, and volume constraints There is an overwhelming need to provide more and more capability in ever smaller and lighter package [Fazio and Kirbie, 2004] At present, the compactness of pulsed power systems is enabled by advanced components with reduced sizes, and key issues lie in the areas of switching and energy storage [Gundersen et al., 2003]

Table 1.1 Summary of Various Switch Parameters in Pulsed power Application

Peak Current (kA)

Switching Speed

Gas-advantages that when operated within specifications will live very long and have reduced house-keeping requirements [Schamiloglu et al., 2004] Table 1.1 summarizes parameters of typical switches used in pulsed power applications

With all the choices, it is necessary to consider switches appropriate for specific applications Biomedical applications are relatively new for pulsed power technology, they usually need switches with fairly broad ranges in switching parameters, for instants, hold-off voltages from a few hundreds volts to tens kilovolts, switching speeds from sub-nanosencond to 10 ns Fast switching speeds support fast rise times

of output pulses, which are essential to bioelectrophysics studies Applying intense electric field is also a key to trigger intracellular effects Thus typically, spark gap and FET-type semiconductor switches appear in pulsed power systems in biomedical applications

At present, the spark gap switch is still not replaceable when a compact pulsed power system is required to generate high voltage (> 10 kV) and high current (> 1 kA) with fast rising (sub-nanosecond) electric pulses for biomedical applications The primary limitation lies in lifetime and repeatability Other shortcomings with spark gaps are related to strong electrode erosion, insulator degradation, high arc inductance, and costly triggering [Winands et al., 2005] Operating gas spark gaps at high pressure can reduce the switching time and obtain the stable switching performance However, this means the large scale of house keeping [Kolb et al., 2005] Using an Air spark

gap with an additional triggering wire can free pulse generators for multi-location experiments, but requiring very careful constructions [Behrend et al., 2003] Small liquid spark gap switches, typically using water as breakdown medium because of its high dielectric constant, have been developed [Deng et al., 2001, Kolb et al., 2003, Xiao et al., 2003] In order to reduce the water recovery time, hence to increase the repetition rate, postbreakdown phenomena and dielectric recovery have been studied [Xiao et al., 2004] The main disadvantage is the water contamination Thus a water circulation system is required at this time

With the increasing demand for compact, portable pulsed power systems and rapid developments of semiconductor technology, solid-state switches are getting more attention in the field previously dominated by gas phase switches The commercial silicon IGBT, in particular, has been finding applications as a replacement module for thyratron switches [Schamiloglu et al., 2004] Undergoing research efforts in solid-state switches are focusing on elevating power handling ability, reducing switching speed of switches, and can be divided into two directions: 1) to push performance limit of silicon-based power switches by adapting advanced materials and device processing techniques, this direction is mainly driven by the semiconductor industry; 2) to develop devices based on advanced semiconductor materials with the higher carrier mobility and wider bandgap than Silicon, a group of academic research are in this direction For more than a decade, GaAs has been considered as an attractive candidate to develop power switches for its optoelectronic

properties and very high electron mobility [Zutavern et al., 1990, Pocha and Druce,

1990, Schoenbach et al., 1989, Hadizad et al., 1992] The latter, the carrier mobility, suggests that this is a great solution for pulsed power – fast rise However, due to possible scattering through intrinsic defects (EL2) or electron-electron collisions, the electron velocity of GaAs saturates as a function of applied electric field, which results in a high forward drop and limits switching performance [Gundersen et al., 2003] Recently, SiC and GaN have attracted interests for their wide bandgaps (> 2 eV), resulting in higher hold-off voltages Significant progress in SiC power devices has been reported by Tan et al (1998) and Khan et al (2002) including the fabrication of UMOSFETs with breakdown voltages of 1400V (10µm drift region) and 5050V (100µm drift region) Nevertheless, although advanced materials hold promise for switching needs in compact nanosecond pulsed power applications, a large scale of research efforts is required to understand and address serious issues in material science, engineering and growth, contacts, doping, and package

In addition, a miniature pseudospark switch may find its potential applications for elevated hold-off voltages and peak currents Pseudosparks are very robust to current reversal and have extended lifetime comparing to spark gaps With optical triggering, the switching time can be reduced within 10 ns [Jiang et al., 2005]

In analyzing what technology is required to produce a compact pulsed power system,

it becomes obvious that energy density of a given system is one of the dominant size

factors The main improvement results from increasing the energy density of storage capacitors The upper limit of the energy density for a given capacitor is given by

Foil and metallized polymer film capacitors have a dominant position as

high-voltage, microsecond-discharge capacitors in pulsed power applications These capacitors have the major advantage of being self-healing, that is, if the film punctures, the nanometer-thick metallization of the film is evaporated in the region

of the breakdown, leaving a “clearing spot” that isolates the breakdown region from the rest part of the capacitor [Ennis et al., 2002] However, foil/film capacitors have low energy density due to small dielectric constants of polymers and large packaging The best commercial high-voltage capacitors achieve an energy density <

1 J/cm3 [WWW, 2002] Ceramic capacitors tend to have very high dielectric constant but relatively low dielectric strength as a result of substantial porosity, which is typical of sintered materials Also their dielectric properties are often temperature and electric field dependent, which limit the operation conditions of capacitors They

can be efficient at low voltages But in order to use them in very high voltage pulsed power, these issues have to be addressed [WWW, 2002]: 1) understanding aging/failure mechanisms, 2) improving dielectric withstand over wide ranges of temperature and electric field, 3) increasing breakdown field By combining high dielectric constant of ceramics and high breakdown strength of polymers, Polymer/ceramic composites may see increasing applications in compact pulsed power systems in the near future

1.2.2 At system level

A comapct nanosecond pulse generator is a useful research tool to explore impact of ultra short electropulses on biological cells, and to further seek applications in biomedical arenas However, commercial generators are rarely available to meet the requirements Large research efforts have focused on developing high voltage, high current, and fast pulse generators There are numerous types of circuits that will provide nanosecond rise time pulses, and they can be categorized as either inductive

or capacitive storage type

Inductive Storage Pulse Generators [Mankowski and kristiansen, 2000]

A basic inductive energy discharge circuit schematic is shown in Fig 1.1 Initially, a

dc current, IL, flows through the inductor, L As switch S1 opens, the current through

decreases rapidly, inducing a voltage across the inductor [Fig 1.1(b)] Near the peak

of V1 , S 2 closes and the load impedance sees the output pulse

(a) (b)

Fig 1.1 (a) Simple inductive storage discharge circuit and (b) voltage and current

waveforms with RL decay [Mankowski and kristiansen, 2000]

Fig 1.2 (a) SOS switching circuit schematic and (b) voltage and current waveforms

[Mankowski and kristiansen, 2000]

Another example of inductive energy storage is that used by semiconductor opening switch (SOS) pulse generators The opening, or recovery, of SOS differs from traditional power diodes in that current interruption occurs in the narrow high-doped regions, not in the long drift region Combined with dense excess plasma in the p-n junction, the SOS can switch high-density currents in nanosecond opening times

A basic circuit schematic of the SOS switching scheme is given in Fig 1.2 Switches

MS 1 and MS 2 are saturable core inductors Initially, MS 1 is open until the core saturates, which closes the switch C then discharges into CP through the SOS, which

is forward biased Eventually, the voltage across CP peaks, at which time MS2 closes The current through the SOS, ISOS , reverses rapidly, eventually opening the SOS The power stored in L from CP the discharge is then diverted to the load

Capacitive Storage Pulse Generators

The basic capacitive energy discharge circuit and typical load voltage curve are shown in Fig 1.3(a) and (b), respectively Arrival of the pulse to the load occurs when the switch, S1, closes Pulse falltime is determined by the RC time constant (for

a resistive load) Ideally, the pulse rise time is zero, however, parasitic inductances from the capacitor, switch, load, and cables increase the rise time [Mankowski and kristiansen, 2000] Detailed circuits review can be found in reference [Mankowski and kristiansen, 2000] and [Roche, web document]

Fig 1.3 (a) Simple capacitive storage discharge circuit and (b) output voltage with

RC decay [Mankowski and kristiansen, 2000]

A pulse forming line (PFL) or transmission line section is usually coupled between the switch and the load for short pulse generation A line is a distributed capacitor, and is charged slowly and the energy is released by means of a switch in a matched load One of the properties of the transmission lines is their ability to produce a constant-voltage output pulse when discharged into a resistive load that matches the line characteristic impedance A widely used line arrangement in compact pulsed power system is the Blumlein transmission line, or the Blumlein because it provides the highest ratio of load voltage to charge voltage possible (VL /V C=1)

In compact fast pulsed power system design, a general research issue is how to improve the system architecture For example, study the geometry-driven issues in PFL Wijetunga et al (2003) discussed the edge effect of the water Blumlein for

short pulse widthes through computational modeling, and optimized the line design based on three dimensional simulations Joler et al (2003) investigated effects of folds on dielectric breakdown and the voltage waveform at the load in a folded Blumlein

As performance of solid-state switches improves, compact nanosecond pulsed power systems are on the road towards fully solid-state systems More components will be integrated into a small space Thus continues attention is required to address following issues such as locally breakdown, ground noise, heat removal, etc

1.2.3 At application level

In medical in vivo applications, a device is needed to deliver electrical energy to the target tissues Typical devices include catheter antennas or antenna arrays transporting single frequency or narrow bandwidth signals in the microwave thermal therapeutic method [Lin, 1999, Sterzer, 2002], and parallel needle electrodes coupled with coaxial cables in the electroporation treatment [Gehl et al., 1999] In nano-electroperturbation method, a key issue is the transmission of pulses without distortion Thus, catheters, the devices delivering nanopulses from pulse generation system to local tumors, requires high breakdown strength to hold peak voltages of kilovolts, broad frequency bandwidth to pass through nanosecond pulses without distortion, and a doctor-friendly interface to in vivo treat tumors with various shapes

The design of such a catheter device is challenging One way is to investigate device performances through in vivo experiments Another more efficient way is to design devices based on electromagnetic simulations In order to obtain valuable results, it

is important to have knowledge of the frequency dependency of the biological load including suspension cells or tissues Many research efforts have been involved to develop circuit models of suspension cells [for example, Schoenbach et al., 2002] and investigate dielectric properties of tissues [for examples, Gabriel et al., 1996a, 1996b, 1996c] However, for cancer therapies, more investigation is needed to develop dielectric dispersion models of cancer tumor tissues

1.3 Thesis Organization

The rest of the thesis is organized into three parts according to the three levels Chapter 2 and chapter 3 describe our work in pulsed power switches and energy storage at component level Chapter 4 presents a compact pulsed power system for biomedical applications at system level Chapter 5 shows design and use of impulse catheter devices at application level Finally, the summary and future work is concluded in Chapter 6

from each of these materials Both perfect material properties and the effects of defects have been included

With increasing demands on the switching and on-state performance of semiconductor switches in fast pulsed power applications, wider band gap materials have been developed as possible replacements for Si For example, GaAs Field-

Effect Transistors (FET’s) have been considered for such applications Although GaAs has a direct bandgap and high electron mobility, its lack of a suitable oxide and its degraded electronic properties under high electric fields (> 4 kV/cm) limit its applications in FET’s Recently, SiC and GaN FET’s have attracted interest for reasons that include their wide band gaps (> 2eV) Two figures of merit,

2)(

πsat

c v E

µis carrier mobility [Chow and Tyagi, 1994] As shown in figure 2.1, for GaN, the

JM and BM values are comparable to those for SiC, and much higher than for Si

and GaAs [Lee, 2002]

1 1 7 16

756 744

278 178

0 100 200 300 400 500 600 700 800

JM

BM

Fig 2.1 Theoretical merits of different semiconductor materials

In addition to promising materials properties, the effect of defects must be considered when evaluating materials for pulsed power applications because they are responsible for device limitations that are not apparent based on analysis of only intrinsic properties In this chapter, we present the results of simulations of the electrical properties of a Si MOSFET and of FET’s based on GaAs, 4H-SiC and Wurtzite GaN We also compare these four materials for pulsed power applications Major defects in these materials are included in the simulations By this means, the influence of defects on the electrical properties can be studied

2.2 Simulation Setup

Device simulations were conducted in a two-dimensional simulator - ATLAS(Silvaco, CA) Parameters of physical models involved in simulations were determined by fitting the ‘literature’ data GaAs, 4H-SiC, and Wurtzite GaN vertical JFETs were simulated with and without defects Device dimensions were kept same

in all vertical JFETs A Si vertical MOSFET was also simulated for the purpose of comparison Si was considered as perfect in simulations

2.2.1 Physical models for the simulations

To obtain realistic results, one must use proper microscopic models as input into the device simulations In our simulations, we have included physical models for the temperature-field-dependent carrier mobility, impact ionization, Shockley-Read-Hall (SRH) recombination and Auger recombination Because of the lack of model parameters in ATLAS for advanced materials, it was necessary to first generate a set of such parameters by fitting experimental data available in the literature [Levinshtein et al., 2001, NSM Archive, Roschke and Schwierz, 2001], or numerical simulation data if no experimental data are available [Kolnik et al., 1995, Bhapkar and Shur, 1997] Each model was programmed in Matlab® and, in conjunction with the collated data, a graphical representation was generated The produced graph displayed the ‘literature’ data and a representation of the fitting equation generated

from the corresponding parameter list This configuration allowed for continuous monitoring of the all the variables and their contribution in the fitting progress A systematic procedure was then made in which the main parameters of the models were fitted, following by successive refinements The result model represents a good fit to the data in the range of interest rather then a unique solution based on

mathematical argument

2.2.1.1 Carrier mobility models

Analytic low field mobility model:

The Caughey−Thomas approximation is used to model the doping- and dependent low field carrier mobilities In this approximation, the following analytic expression is used for the electron and hole mobility:

temperature-δ γ

α β

µ

µ

)()300(1

)300()

300

()

300

min 0

Ncrit

N K

T K

T K

T

+

−+

High field mobility model:

At low electric field, the carrier drift velocity almost linearly increases with the applied electric field according to υ = µE At high electric fields, the drift velocity deviates substantially from linearity The parallel electric field-dependent mobility model we used for Si, 4H-SiC and Wurtzite GaN is given by

E E

Vsat E

E

β β

µ µ

µ

/ 1 0

0])(1[

)(

+

For GaAs, the field-dependent mobility is given by

E E

Ecrit

E Ecrit

E E

Vsat E

γ

γ

µµ

)(1

)()

(b)

(c)

Fig 2.2 Fitted GaAs mobility models, continued (b) Electron drift velocity as a function of electric field at T=300 K (c) Electron mobility as a function of temperature at Nd=1×1016cm-3 To be continued…

(d)

(e)

Fig 2.2 Fitted GaAs mobility models, continued d) Hole low field mobility as a function of doping concentration at T=300K (e) Hole drift velocity as a function of electric field at T=300 K

(a)

(b)

Fig 2.3 Fitted 4H-SiC mobility models (a) Electron low field mobility (// c-axis) as

a function of doping concentration at T=300 K (b) Electron drift velocity (// c-axis)

as a function of electric field at T=300 K To be continued…

(c)

(d)

Fig 2.3 Fitted 4H-SiC mobility models, continued (c) Electron mobility (// c-axis)

as a function of temperature at Nd=1.2×1017 cm-3 Due to the lack of experimental data for electron mobility parallel to the c-axis, the data presented in the plots (a-c) were deducted from electron mobility data perpendicular to the c-axis according to the ratio (µe⊥/µ = 0.8) conclude by Roschke and Schwierz [Roschke and Schwierz, e//2001] (d) Electron low field mobility (⊥ c-axis) as a function of doping concentration at T=300 K To be continued…

(e)

(f)

Fig 2.3 Fitted 4H-SiC mobility models, continued (e) Electron drift velocity (⊥ axis) as a function of electric field at T=300 K (f) Electron mobility (⊥ c-axis) as a function of temperature at Nd=1.2×1017 cm-3 To be continued…