CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
Simulation of optically controlled SiC (Silicon Carbide) using analytical modeling of high
frequency response and switching applications
A graduate project submitted in partial fulfillment of the requirements
for the degree of Masters of Science
in Electrical Engineering.
By
Abhishek Bhagat
December 2012
The graduate project of Abhishek Bhagat is approved:
________________________________________________
Dr. Mahmoud Youssef
____________
Date
_________________________________________________
Dr. Matthew Radmanesh
____________
Date
_________________________________________________
____________
Dr. Somnath Chattopadhyay, Chair
Date
California State University, Northridge
ii
ACKNOWLEDGEMENT
I would like to thank my professor Dr.Somnath Chattopadhayay for being my project guide
and advisor. I am grateful to him for his continuous support and invaluable inputs he has
been providing me through the development of the project. This work would not have been
possible without his support and encouragement. I would also like to thank him for
showing me some examples that related to the topic of my project.
I would like to express my gratitude to all those who gave me the possibility to complete
this Project. I want to thank Dr. Mahmoud Youssef and Dr. Matthew Radmanesh for their
stimulating support.
Besides, I would like to thank the Department Chair Prof. Dr. Ali Amini of Electrical and
Computer Engineering for providing me with a good environment and facilities to
complete this project. It gave me an opportunity to participate and learn about the software
MATLAB. In addition, I would like to thank him that he provides me valuable information
as the guidance of my project.
iii
Table of Contents
Signature Page…………………………………………………………………………… ii
Acknowledgement……..………………………….………………………………. …….iii
List of Tables..……………………………………….……………………………...........vi
List of Figures…................................................................................................................vii
Abstract……………………………………………….………………………………….ix
CHAPTER 1 Introduction ………………………………………………………...……...1
CHAPTER 2 SiC (Silicon Carbide Material Properties ……………….………..………..8
2.1 History of SiC material ……………………..…….………….………..8
2.2 Crystal Structure……… ………………………………………............9
2.3 E-k (Energy Band Diagram)………………..………………………..12
2.4 Optical Properties…………...…………………………………..…...13
2.5 Physical Properties of SiC………………………………………….15
2.6 Application and benefits of SiC Electronics………………………...15
2.6.1 High Temperature device operation………………… ………..15
2.6.2 High Power device operation ………………………………….16
2.6.3 Radiation Effect……………………………………………..…17
2.6.4 System Benefits if High Power High Temperature SiC Devices.18
CHAPTER 3 Theory on MESFET……………………………………………………....19
3.1 Physics Of MESFET…………………………………………………..19
3.1.1 Introduction To SiC MESFET…………………………………..19
3.2 Functional Architecture………………………………………………21
iv
CHAPTER 4 Numerical Calculations…………………………………………………25
4.1 Theory on the Model……………………………………………….25
4.2 Switching Characteristics…............................................................. 28
CHAPTER 5 Results and Discussions………………………………………………….30
CHAPTER 6 Conclusion……………………………………………………………….34
References.……………………………………………………………………………..35
Appendix A…………………………………………………………………………….41
Appendix B…………………………………………………………………………….44
v
List of Tables
Table 1: Properties of SiC at 300K…………………………………………………11
Table 2: Comparision of several wide band-gap material to silicon………………..20
Table 3: Range parameter and the corresponding straggle parameter………………26
vi
List of Figures
FIGURE 1: Breakdown voltages for different semiconductors materials……………….2
FIGURE 2: Thermal conductivity for different semiconductors materials………………2
FIGURE 3: Crystal Structure for 3C-SiC and 4C-SiC…………………………………..9
FIGURE 4: Crystal Planes in Sic………………………………………………………..10
FIGURE 5: Micropipes in SiC…………………………………………………………..10
FIGURE 6: SiC,4H Band structure……………………………………………………...12
FIGURE 7: Comparision of square root of apsorption coefficient of different materials as a
function of wavelength and energy at 300 K……………………………………………13
FIGURE 8: Energy Band Diagram of Selected Metals and 4H-Si……………………...14
FIGURE 9: Regular MESFET with no biasing in source and drain…………………….19
FIGURE 10: Photographs of Modern MESFETS……………………………………….20
FIGURE 11: Schematic diagram of SiC MESFET……………………………………...21
FIGURE 12: High-resistivity SiC substrate for sc devices with high break down……...22
FIGURE 13: Structure of MESFET with gate length L and active channel length……..22
FIGURE 14: Device Structure of SiC MESFET………………………………………...23
FIGURE 15: Cross sectional view of a MESFET……………………………………….24
FIGURE 16: Cross section of simulated SiC……………………………………………25
FIGURE 17: Plot of Gate-to-Drain Capacitance (CDS) vs. Drain-to-Source Voltage (VDS) at
different flux density……………………………………………………………………30
FIGURE 18: Plot of Gate-to-Source Capacitance (CGS) vs. Gate-to-Source Voltage (VGS) at
different flux densities…………………………………………………………………..31
Figure 19: Plot of Switching time ( ) vs. Device Gate Length (L) for dark and illumination
condition at different flux densities……………………………………………………..32
vii
Figure 20: Plot of Switching time ( ) vs. Device thickness (A) for dark and illumination
condition at different flux densities…………………………………………………..33
viii
ABSTRACT
SIMULATION OF OPTICALLY CONTROLLED SILICON CARBIDE MESFET USING
ANALYTICAL MODELING (MATLAB SOFTWARE) FOR HIGH FREQUENCY
RESPONSE AND SWITCHING APPLICATIONS.
By
Abhishek Bhagat
Masters of Science in Electrical Engineering
In this project, an analytical modeling of optically controlled Silicon Carbide has been
presented here for an analysis of extrinsic and intrinsic parameters such as, gate
capacitances including both of the gate-source capacitances, gate-drain capacitances and
switching speed under dark and illumination conditions and also the switching frequency
considering different fabrication parameters such as ion dose, ion energy and ion range
parameters, channel length and active channel depth has been incorporated in the model to
understand the better effect of dark intensity and illumination condition to optimize the
fabrication parameter and physical parameters.
ix
CHAPTER 1
INTRODUCTION
Silicon carbide (SiC)-based semiconductor electronic devices and circuits are
presently being developed for use in high-temperature, high-power, and high-radiation
conditions under which conventional semiconductors cannot adequately perform. Silicon
carbide’s ability to function under such extreme conditions is expected to enable
significant improvements to a far-ranging variety of applications and systems. These
range from greatly improved high-voltage switching for energy savings in public electric
power distribution and electric motor drives to more powerful microwave electronics for
radar and communications to sensors and controls for cleaner-burning more fuel-efficient
jet aircraft and automobile engines [1-2].
In the past decade, tremendous progress has been made in the material growth and
processing of wide band-gap semiconductors, particularly SiC and GaN, and high quality
SiC and GaN wafers are now commercially available [3], [4]. Both types of
semiconductors have very wide band-gap (4H–SiC = 3.2 eV and GaN = 3.4 eV) and are
visible blind [3]. Moreover, 4H-SiC has very high breakdown field, outstanding radiation
hardness, and excellent chemical and mechanical rigidity, good thermal conductivity and
as such are excellent candidates for photo detection in high temperature and high
radiation environment conditions [3]. The Figure 1 and 2 shows the breakdown voltage
and thermal conductivity of different semiconductor materials. Due to the wide band-gap
of SiC and GaN, the leakage current can be many orders of magnitude lower than the
leakage current of Si detectors, making SiC and GaN good candidates for high sensitivity
visible blind UV detection. GaN has the advantages of the availability of heterostructures, which allows designing cutoff wavelength in the UV range by using AlGaN
with different Al percentage. It therefore adds great flexibility in detector design and
relieves or eliminates the requirement of optical filters. SiC, however, has much better
material maturity compared to GaN material. Additionally, SiC substrate and epi-growth
technologies have developed to such a level as to allow the fabrication of many different
types of SiC photo detectors with desired features. SiC UV p-i-n photodiodes have
already been fabricated and are commercially available. SiC avalanche photodiodes with
extremely high gain and low excess noise have also been demonstrated [4].
1
Fig 1. Breakdown voltages for different semiconductors materials.
Fig 2. Thermal conductivity for different semiconductors materials.
The 6H-SiC poly-type has a wide band-gap (3 eV), high critical field strength
(300-400 MV/m), high-saturated electron velocity (2.0 x 107 cm/s) and high thermal
conductivity (4.9 W/cm oC). These material properties make semi-insulating 6H-SiC an
attractive semiconductor material for the Photoconductive Semiconductor Switch (PCSS)
application [5].
With the advancements and research in MESFET, optically controlled MESFETs
also referred to as OPFETs have received considerable attention due to the inherent
advantages in the high speed optical switching and high frequency optical
modulation/demodulation applications [6]. Theoretical and experimental observations
have shown that the variations of the DC and dynamic properties in MESFETSs when a
light beam strikes the transistor gate can be accounted for by an appropriate change in the
gate junction equivalent to the built-in voltage [7]. In order to establish the OPFET
device characteristics, a number of theoretical and experimental observations have been
continuously reported [8-9] exploring the illumination effect on the static and dynamic
characteristics of MESFET devices for various biases, optical responses of the MESFET
both at DC and microwave frequencies and large-signal characteristics of the MESFET
under He-Ne illumination source. The optically-controlled MESFET (or OPFET) is of
2
great importance because of its potential as a photo detector and pre-amplifier, rf. switch
and tuner, etc. Different mechanisms which are responsible for the enhanced terminal
properties of the optically-controlled MESFET are:
1. Photo-induced voltage across the Schottky barrier [11], [12],
2. Photo generated carriers below the gate [10], [13], and
3. Photo conductivity effect in the source-gate and drain gate regions and the change in
the gate depletion width [14].
Further, the experimental observation [15] showed a positive voltage across the
depletion region between the n-type channel and the semi-insulating substrate suggesting
that the drain current enhancement is closely related to the channel width modulation of
the device. Considerable interest has been shown in studying and modeling Optically
Controlled Field Effect Transistors (OPFET’s) fabricated with Schottky gate
configuration. These OPFET’s are expected to emerge as promising detectors for use in
integrated optoelectronic circuits.A number of theoretical and experimental investigations
on the effect of illumination on MESFET structures have been reported. Preliminary
investigations reveal that photo response of illuminated MESFET is due to the optically
generated carriers which increase the conductivity of the channel and the photo voltage
developed across the Schottky barrier which affects the applied reverse voltage on the
gate. Simple models have been developed by several workers in order to explain the
results of experimental investigations on the effect of illumination on commercially
available GaAs MESFET’s [16]. The large signal characteristics of an illuminated GaAs
MESFET have been reported. Unfortunately, the models proposed so far are either too
complicated or not adequate to be used for circuit simulation purposes. A simple yet
fairly accurate model which takes into account all the important physical phenomena
involved in an illuminated MESFET need to be considered for this purpose.
GaAs OPFET appears to be an important optical transducer for optical
communication, integrated optics, and optical computer. Studies on GaAs OPFET show
that by controlling the radiation flux density, one can control the threshold voltage, drainsource current, and RF switching parameters of the device. B. B. Pal and S. N.
Chattopadhyay studied the GaAs OPFET Characteristics Considering the Effect of Gate
3
Depletion with Modulation Due to Incident Radiation. It was found that the photovoltaic
effect is important because it develops a forward voltage across the metal-semiconductor
junction which increases with the increase in radiation intensity. This photo voltage
modulates the depletion region width below the gate which, in turn, modulates the
channel width. The photo voltage thus is expected to increase the drain-source current. It
will reduce the threshold voltage in the normally OFF devices and increase in the
normally ON devices. At higher flux density and trap density, the threshold voltage
shows nonlinear effect at lower value of implanted dose which is mainly due to the
recombination term. The device is pinched off at a higher drain-source voltage compared
to the photo generation case only [17].
Some experiments have shown that the FET dc characteristics may alter with
illumination and that FET oscillators may be tuned by varying the intensity of the light
falling on the active region of the device. Also, some authors have recently reported highspeed optical detection with GaAs MESFET’S [18].
There has been considerable work done on the development of silicon based
optoelectronic integrated circuits (OEIC’s) [19]. Mature silicon processing technology,
including micromachining techniques, can be used to fabricate complex optical structures
such as micro optical devices and hybrid optoelectronics. The silicon based OPFET
promises excellent compatibility with current silicon IC technology requiring the same or
similar low-cost and reliable manufacturing techniques of monolithic silicon-based
OEICs. The ion implantation induced defects in a silicon substrate have been
characterized by measuring the bulk generation lifetime of MOS capacitor and
experiments have been conducted to study the dependence of substrate dopant species
(phosphorous and boron) on defect formations. I-V characteristics of ion implanted solar
cell devices at optical illumination have shown the efficiency in the range of 0.01%.
Phosphorous ion implantation not only results in the transition of the crystalline
fullerenes to amorphous material phase, but also produces a significant defect level. An
effective loss of photo-generated carriers due to the ion implantation process induced
defects in the active channel region of OPFET is a major issue of degradation of quantum
efficiency, sensitivity, etc. The channel current obtained from the diffusion and ion
4
implanted OPFET devices are studied and both currents under dark and optical
illumination conditions are compared to realize the process-induced defects as major
problem for optoelectronics device. Use of direct control of microwave semiconductor
devices for optical injection locking, phase shifting, signal distribution and optoelectronic
actuator has the potential to enhance the performance of future space borne phased array
systems and military and commercial aviation. Previously, several authors have
experimentally investigated the effect of light on dc and microwave characteristics of
MESFET. Their investigations show that these changes in the characteristics are due to
photoconductivity and photovoltaic effects. Further, an analytical study, by the authors
taking into consideration material properties of hetro-structures showed that the hetrostructures have a higher sensitivity to optical illumination [20].
The MESFET has been used as an optical detector and control device in microwave
applications by several investigators. Of the many advantages of using the MESFET as
an optical detector, the most notable is compatibility with GaAs MMIC technology. De
Salles has performed a thorough experimental and theoretical characterization on the
MESFET emphasizing the photovoltaic effect, which can be used to increase the drain
current and change the gate capacitance. His analysis is concentrated on the active region
of the device; photocurrent in the substrate is ignored [21]. Darling has developed a
perturbation analysis to account for the photoconductive effect under low level
illumination.
Simons derived analytical expressions for I-V characteristics of different types of
FET configurations under optical illumination on the devices. He also computed
variations in FET small signal parameters such as trans-conductance, channel
conductance with illumination and compared with the commercially available OPFETs
[18].
Several mechanisms have been suggested to explain the photo effects in GaAs
MESFET’s, especially the increase of drain current due to illumination. Graffeuil [22]
suggested that incident photons cause a change in the built-in voltage of the gate junction
and by this mechanism, the drain current increases.
5
Pan suggested that both the photoconductivity effect in the source-gate and the draingate regions and the change of the gate depletion width are responsible for the increase of
the drain current [23].
Edwards measured a positive voltage across the depletion region between the n-type
channel and the semi-insulating substrate and suggested that the drain current increase is
closely related to the channel width modulation by the positive voltage [24]. Analytical
work has been attempted to understand the photo effects on the I-V characteristics and
the device performance of GaAs MESFET’s, but the analyses usually assumed that the
drain current is enhanced either by a photo-induced voltage across the Schottky barrier or
by photo generated carriers below the gate.
Taking into consideration the advantages of high internal impedance which in turn
can simplify impedance matching resulting in efficient power coupling and large
bandwidth, Ahmed Sayed introduced an ultra-wideband power amplifier using a SiC
MESFET that covers the frequency range from 10 MHz to 2.4 GHz [25].
A closed-form analytical model of an ion-implanted Si-MESFET under illumination
condition was first reported by Singh [26]. The paper described that the drain to source
current can be enhanced with increasing radiation flux intensity and decreasing
wavelength. Further, the threshold voltage is found to be reduced under normally OFF
condition and increased under normally ON condition for higher photon flux density and
lower wavelength. This model was further extended by Mishra [27] to investigate the
effect of illumination on an ion-implanted GaAs OPFET. In the later model, the effect of
surface recombination which plays an important role in GaAs MESFET was given due
consideration [27]. When the optical radiation is modulated at the signal frequency, the
incident photon flux in the ion implanted MESFET will generate charge carriers below
the gate depletion region which will also be modulated at the signal frequency. Thus, it is
expected that the I-V characteristics and threshold voltage of the MESFET device will be
affected by the modulating signal. Unfortunately, both models [26, 27] fail to take into
account the following basic factors that shape the device characteristics in the illuminated
condition [28].
6
1. The reflection of the incident radiation from the gate metallization as well as the metalGaAs interface.
2. The forward voltage developed across the Schottky barrier due to photovoltaic effect.
3. The dependence of depletion edge depths on the channel voltage in current calculation.
4. The modulation of the width of the gate depletion region by incident radiation.
The present model takes into account all these factors. An implicit relation
between the gate depletion edge depth and channel voltage has been obtained analytically
from one-dimensional Poisson’s equation subjected to appropriate boundary conditions.
It is observed that the ion implantation causes lattice damage and results in dopant
atoms in both substitutional and interstitial sites. The degree and rate of damage depends
on the substrate and is roughly proportional to the total implanted dose. Both the degree
of damage remaining and the relative number of substitutional or interstitial sites
occupied following ion implantation is significantly influenced by the temperature of the
substrate during implantation or during subsequent annealing, or a combination of the
two. The use of an elevated substrate temperature reduces the lattice disorder.
Consequently, it creates a significant effect on the electrical parameters, which play a
vital role in the performance of' the device. Electrical parameters such as threshold
voltage, drain current, and trans-conductance are changed as the original implant profile
is altered after thermal annealing [28].
7
CHAPTER 2
SiC(Silicon Carbide Material Properties)
2.1 History of SiC Material
Silicon carbide (SiC) was first mentioned by Jons Jacob Berzelius in 1824, and its
formation was confirmed by Eugene and Alfred Cowes in 1885. It does not occur
naturally on earth, although it occurs in meteorites. In 1955, Lely introduced a new
method of growing this material in the laboratory, and the current method used is a
modification of this, now referred to as the modified Lely technique. [29].
This breakthrough led to the formation in 1987, of Cree, Inc, the first commercial
Supplier of SiC. SiC is part of a family of materials which exhibit a one-dimensional
polymorphism called polytypism. The difference among the polytypes is in the
arrangement of layers of Si and C. In SiC, Si and C are bonded tetrahedrally. Over 200
polytypes of SiC are known to exist.The polytypes are divided into three basic
crystallographic categories; cubic (C), hexagonal (H), and rhombohedral (R) . Some of
the common polytypes includes 3C, 2H, 4H, 6H, 8H, 9R, 10H, 14H, 15R, 19R, 20H,
21H, and 24R. With the exception of 2H and 3C, all of the polytypes form onedimensional super lattice structures [30].
Cubic SiC only one possible polytype, and is referred as 3C-SiC or β-SiC. In 3CSiC,
each SiC bi-layer can be oriented into only three possible positions with respect to the
lattice while the tetrahedral bonding is maintained. If these three layers are denoted by A,
B, and C and the stacking sequence is ABCABC.., then the crystallographic structure is
cubic zinc blende. If the stacking of the bi-layers is ABAB…, then the symmetry is
hexagonal and referred to as 2H-SiC. All of the other SiC polytypes are a mixture of the
zinc blende (cubic) and wurtzite (hexagonal). 4H-SiC consists of an equal number of
cubic and hexagonal bonds. 6H-SiC is composed of two-thirds cubic bonds and one-third
hexagonal bonds [30].
SiC occurs in more than 100 different polytype structures. Widely used in RF
8
transistors are the hexagonal 4H and 6H polytypes. Furthermore, the cubic 3C polytype
is of interest because it can be grown on Si substrates. Even though until now the quality
of 3C SiC layers on Si does not satisfy the requirements of RF transistors, this material
combination could offer a low-cost alternative in the future [31].
Silicon carbide substrates are key elements in the development of SiC electronics.
Compared to other wide bandgap semiconductors, the availability of SiC substrates for
homoepitaxy is a big advantage. Because of the phase equilibrium in the SiC material
system (specifically the material sublimes before it melts), the most popular bulk growth
techniques are based on physical vapor transport. Although sublimation techniques are
relatively easy to implement at the high growth temperatures required, these processes
are difficult to control, particularly over large substrate areas [31].
2.2 Crystal Structure
SiC has a structure that depends on the formation of Si and Carbon layers and has more
than 170 polytypes. The polytypes are named based on the crystal structure (Cubic or
hexagonal). For example 3C-SiC is cubic, 2H SiC is hexagonal, and all others are
mixtures of cubic and hexagonal layers. Fig. 3 shows two of these polytypes, 3C and
4H (one hexagonal layer one cubic layer). Depending on the polytype crystal structure,
the band gap varies from 2.2 to 3.3 eV. Drift velocity is 2x107 cm/s [33]. The
breakdown electric field varies from 250 0 to 5000 kV/cm.
Fig. 3. Crystal Structure for 3C-SiC and 4C-SiC
SiC classification also includes a basal type (C plane) and “a” plane (Fig. 4) depending
9
on the
crystal growth and machining. Evidently, C plane SiC indicates a large
micropipes density, causing the breakdown of the devices much earlier than expected. A
micropipe is a defect in SiC.
Fig. 4. Crystal planes in SiC
Fig. 5. Micropipes in SiC
Figure 5 shows the micropipes in Silicon Carbide. In this analysis we have
considered 6H type SiC has been considered in detail for reasons that will be clear in
the next chapter. Now, 6H SiC has a band gap of approximately 3.02eV, which
10
corresponds to an optical absorption of approximately 410nm. In this case, also one will
obtain a large concentration of deep levels, resulting in deep energy states within the
band gap that contribute electrons and holes to the conduction process; 6H SiC can
therefore be switched with a 1.06 µm and or a 532 nm light source using extrinsic
generation of carriers. The location of the trap levels responsible for this is a part of this
research. The optical absorption depth will also be discussed in detail, it ranges over few
cm [35]. In 6H SiC, resistivity values on the order of 1011-1012 Ω-cm can be
obtained. SiC, being an indirect band gap material, has longer carrier lifetimes;
200ns to few microseconds; are expected. Table 1 gives all the basic properties of two
types of SiC [36].
Properties
4H SiC
6H SiC
Band Gap
3.2 eV
3.02 eV
Critical breakdown field
3x106 V/cm
3x106 V/cm
strength
Electron mobility
800 cm2/V-s
200-300
Hole mobility
60 cm2/V-s
cm2/V-s
50 cm2/V-s
Saturation velocity
2x107 cm/s
2x107 cm/s
Thermal conductivity
5 watt/cm°C
5watt/cm°C
Intrinsic carrier concentration
~1x10-8
~1x10-6 cm-
Dielectric constant
cm-39.6
3
9.6
Table 1. Properties of SiC at 300 K
The different polytypes differ, thus ,only the stacking of double layers of Si and C
atoms, however, this affects all electronic and optical properties of the crystal. The band
gaps of liquid helium temperatures of different polytypes range between 2.39 eV for 3CSiC and 3.3 eV for the 2H-SiC polytype. The important polytypes 6H-SiC and 4H-SiC
have bandgaps of liquid helium temperatures of 3.02 eV and 3.27 eV, respectively. All
11
polytypes are extremely hard, very inert and have a high thermal conductivity. Properties
such as the breakdown electric field strength, the saturated drift velocity and impurity
ionization energies are all specific for different polytypes. In the case of 6H-SiC, the
breakdown electric field strength is an order of magnitude higher than Si and saturated
drift velocity of the electrons is even higher than that of GaAs [37].
2.3 E-k (Energy Band Diagram)
Fig. 6. SiC, 4H. Band structure. Important minima of the conduction band and maxima
of the valence band. . 300K; [16]
Eg = 3.23 eV;
EΓ = 5-6.0 eV;
EL ~= 4.0 eV;
EsM ~= 0.1 eV.
Ecr = 0.08 eV;
Eso = 0.007 eV.
Where,
Eg = Energy gap.
EL = Energy at L Valleys.
EM = Energy at M Valleys.
Eso = Energy of spin-orbital splitting in valence band.
Ecr = Energy of crystal field splitting in valence band.
12
Fig. 6 shows the E-k diagram of Silicon Carbide with different energy levels in
valence and conduction band.[38]
2.4. OPTICAL PROPERTIES
The optical properties of silicon carbide crystals have been the subject of a great
deal of research in recent years—both as a source of information about the basic
properties of the material and as a part of potential commercial optoelectronic devices
(such as blue LEDS). Optical absorption measurements give band-gap data for cubic
silicon carbide as 2.2 eV and for the α-form as 2.86 eV at 300 K [38]. In the region of
low absorption coefficients, optical transitions are indirect, whereas direct transitions
predominate for quantum energies above 6 eV. Figure 7 shows the comparision of square
root of apsorption coefficient of different materials as a function of wavelength and
energy at 300 K. The electron affinity is about 4 eV. The electronic bonding in silicon
carbide is considered to be predominantly covalent in nature, but with some ionic
character. In a Raman scattering study of valley-orbit transitions in 6H-silicon carbide,
three electron transitions were observed, one for each of the in equivalent nitrogen donor
sites in the silicon carbide lattice [39]. The donor ionization energy for the three sites had
values of 0.105, 0.140, and 0.143 eV [40]. Silicon carbide is now well established as a
material for optoelectronic devices, in particular for blue LEDS and blue LASER devices.
This market has now become the dominant commercial driver for the development of
silicon carbide wafer technology, and fabricated devices are now entering a variety of
industrial and consumer products. The Figure 8 shows the energy band diagram of
selected metals and 4H-SiC material [41].
Fig. 7. A Comparision of square root of apsorption coefficient of different
materials as a function of wavelength and energy at 300 K.
13
Fig. 8. Energy Band Diagram of Selected Metals and 4H-SiC
2.5 Physical Characteristics of SiC
SiC have many excellent physical properties such as wide bandgap, high
saturation velocity of electrons, high break-down field and high thermal conductivity
[42]. In addition, the limited radiation hardness of Si has accelerated the investigation
of SiC for radiation detector with the improvement of crystal growth technique for
high quality and large size SiC bulk materials [43]. SiC has over 150 polytypes, but
only the 6H– and 4H–SiC polytypes are available commercially in both bulk wafers and
custom epitaxial layers. Between the two polytypes, 4H–SiC is preferred for power devices
primarily because of its high carrier mobility, particularly in -axis direction and its low
dopant ionization energy. In addition, the high electric break-down field of SiC allows for
thinner epitaxial layers to sup-port the high BV in power devices [44]. The effects of
displacement of a pn junction from its corresponding SiGe/Si heterojunction have been
investigated using a simple analytical model. The phenomenon is of interest for
understanding the degradation in the performance of SiGe/Si heterojunction bipolar
transistors when there is boron out diffusion from the base that can produce pn junction
displacement at both the emitter and collector-base junctions [45]. Silicon carbide is a
semiconductor material with interesting properties such as wide band gap and high
breakdown field, the saturation electronic drift velocity and the thermal conductivity.
These factors makes SiC a good candidate for the fabrication of high – power and high –
frequency electronic devices, with lower power losses and smaller size than their Si or
14
GaAs counterparts. It is worth to note that SiC process technology can leverage on many
processes traditionally employed in the Si – based power devices manufacturing. In the
recent years, the availability of large diameter (up to 4’’) SiC substrates from different
suppliers has opened the way for the fabrication of electronic devices with steadily
improving performances. Furthermore, it has been possible the growth of epilayers with a
very low defect density, and with a good control on the doping characteristics.
2.6 Applications and Benefits of SiC Electronics
Two of the most beneficial advantages that SiC-based electronics offer are the area of
high temperature and high-power device operation.
2.6.1
High temperature device operation
The wide bandgap energy and low intrinsic carrier concentration of SiC allow SiC to
maintain semiconductor behavior at much higher temperatures than silicon,which in turn
permits SiC semiconductor device functionality at much higher temperatures than silicon.
Semiconductor electronic devices function in the temperature range when intrinsic
carriers are negligible, so that conductivity is controlled by internationally introduced
dopant impurities. The intrinsic carrier concentration ni is a fundamental perfactor to
well-known equations governing undesired junction reverse-bias leakage currents. As
temperature increases, intrinsic carriers increase exponentially so that undesired leakage
currents grow unacceptably large and eventually at still higher temperatures, the
semiconductor device operation is overcome by uncontrolled conductivity as intrinsic
carriers exceed intentional device dopings.[46] Depending upon specific device design,
the intrinsic carrier concentration of silicon generally confines silicon device operation to
junction temperatures <300°C. SiC’s much smaller intrinsic carrier concentration
theoretically permits device operation at junction temperatures exceeding 800°C. 600°C
SiC device operation has been experimentally demonstrated on a variety of SiC devices .
The ability to place uncooled high-temperature semiconductor electronics directly into
hot environments would enable important benefits to automotive, aerospace, and deepwell drilling industries [33,16]. In the case of automotive and aerospace engines,
improved electronic telemetry and control from high-temperature engine regions are
necessary to more precisely control the combustion process to improve fuel efficiency
15
while reducing polluting emissions. High-temperature capability eliminates performance,
reliability, and weight penalties associated with liquid cooling, fans, thermal shielding,
and longer wire runs needed to realize similar functionality in engines using conventional
silicon semiconductor electronics.
2.6.2
High power device operation
The high breakdown field and high thermal conductivity of SiC coupled with high
operational junction temperatures theoretically permit extremely high-power densities
and efficiencies to be realized in SiC devices. The high breakdown field of SiC relative
to silicon enables the blocking voltage region of a power device to be roughly 10×
thinner and 10× heavier doped, permitting a roughly 100-fold beneficial decrease in
the blocking region resistance at the same voltage rating. SiC’s high breakdown field
and wide energy bandgap enable much faster power switching than is possible in
comparably volt–ampere-rated silicon power-switching devices. The fact that highvoltage operation is achieved with much thinner blocking regions using SiC enables
much faster switching in both unipolar and bipolar power device structures. Therefore,
SiC-based power converters could operate at higher switching frequencies with much
greater efficiency (i.e., less switching energy loss) [44]. Higher switching frequency in
power converters is highly desirable because it permits use of smaller capacitors,
inductors, and transformers, which in turn can greatly reduce overall power converter
size, weight, and cost . While SiC’s smaller on-resistance and faster switching helps
minimize energy loss and heat generation, SiC’s higher thermal conductivity enables
more efficient removal of waste heat energy from the active device. Because heat energy
radiation efficiency increases greatly with increasing temperature difference between the
device and the cooling ambient, SiC’s ability to operate at high junction temperatures
permits much more efficient cooling to take place, so that heat sinks and other devicecooling hardware (i.e., fan cooling, liquid cooling, air conditioning, heat radiators, etc.)
typically needed to keep high-power devices from overheating can be made much smaller
or even eliminated. While the preceding discussion focused on high-power switching for
power conversion, many of the same arguments can be applied to devices used to
generate and amplify RF signals used in radar and communications applications. In
particular, the high breakdown voltage and high thermal conductivity coupled with high
16
carrier saturation velocity allow SiC microwave devices to handle much higher power
densities than their silicon or GaAs RF counterparts, despite SiC’s disadvantage in lowfield carrier mobility [24–26].
The large performance gains made possible by SiC's high-temperature high-power
capabilities offer economically large performance benefits to the aircraft, automotive,
communications, power, and spacecraft industries. The tremendous advantages of SiC
electronics in these specific applications are slowly becoming a reality. SiC's immature
crystal growth and device fabrication technologies are being developed [48].
2.6.3
Radiation Effect
The physical and electronic properties of silicon carbide (SiC) make it an attractive
semiconductor material for high temperature, radiation resistant, and high-powerhandling electronic devices [49]. Previous studies on radiation effects in SiC devices
show that SiC-based neutron and charge particle detectors[50],dosimeters and
spectrometers, have excellent potential for operating in extreme radiation environments.
High-energy particle bombardment, such as by proton, neutron, electron and pion
irradiation, can create vacancies, interstitials, and their associated defects. These radiation
induced defects often produce energy states in the bandgap and therefore can influence
the electrical properties of materials and devices. Diöerent irradiation-induced defects can
be observed if the particle type, energy, fluences are changed, or if the exposure
temperature and material processing diöer [51]. We have previously studied the eöects of
highdose gamma irradiation on 4H-SiC Schottky Barrier Diodes (SBD) and MOS
capacitors and proton irradiation on 4H-SiC Junction Barrier Schottky (JBS) diodes [52].
There was little observed degradation for the SiC SBDs after gamma radiation, but
interestingly, a significant degradation of RS an improvement in reverse characteristics
after proton irradiation of the JBS diodes, potentially compromising their usefulness in
power switching systems operating in extreme environments. Given the closely related
structure of SBD and JBS diodes (a JBS diode is composed of both pn and SBD diodes),
this anomalous diöerence in their radiation response was particularly surprising, and has
not to date been fully understood. In addition, the measured blocking voltages (BV) of
the post proton-irradiated diodes consistently increased by about 200 V compared to the
17
un-irradiated devices, a rare instance when radiation exposure actually improves device
performance [53]. In this paper, we present new results of proton radiation eöects on both
4H-SiC SBDs and MOS capacitors aimed at providing better understand these anomalous
results and to help undustand the unique physics.
2.6.4
System Benefits of High Power High Temperature SiC Devices.
Uncooled operation of high-temperature and high-power SiC electronics would enable
revolutionary improvements to aerospace systems. Replacement of hydraulic controls and
auxiliary power units with distributed “smart” electromechanical controls capable of
harsh ambient operation will enable substantial jet-aircraft weight savings, reduced
maintenance, reduced pollution, higher fuel efficiency, and increased operational
reliability [54]. SiC high-power solid-state switches will also enable large efficiency
gains in electric power management and control. Performance gains from SiC electronics
could enable the public power grid to provide increased consumer electricity demand
without building additional generation plants, and improve power quality and operational
reliability through “smart” power management. More efficient electric motor drives
enabled by SiC will also benefit industrial production systems as well as transportation
systems such as diesel-electric railroad locomotives, electric mass-transit systems,
nuclear-powered ships, and electric automobiles and buses. From the above discussions it
should be apparent that SiC high-power and high-temperature solid state electronics
promise tremendous advantages that could significantly impact transportation systems
and power usage on a global scale. By improving the way in which electricity is
distributed and used, improving electric vehicles so that they become more viable
replacements for internal combustion-engine vehicles, and improving the fuel efficiency
and reducing pollution of the remaining fuel-burning engines and generation plants, SiC
electronics promises the potential to better the daily lives of all citizens of planet Earth.
18
CHAPTER 3
3.1 Physics Of MESFET
3.1.1 Introduction To SiC MESFET:
MESFET stands for metal semiconductor field effect transistor. It is quite similar
to a JFET in construction and terminology. The difference is that instead of using a
MESFET for a gate, a Schottky (metal-semiconductor) junction is used. MESFETs are
usually constructed in compound semiconductor technologies lacking high quality
surface passivation such as GaAs, InP, or SiC, and are faster but more expensive than
silicon-based JFETs or MOSFETs [55-56].
Production MESFETs are operated up to approximately 45 GHz, and are
commonly used for microwave frequency communications and radar. Figure 9 illustrates
the regular MESFET with no biasing in source and drain [59].
Fig 9 Regular MESFET with no biasing in source and drain
SiC is an attractive semiconductor material to overcome limitations of silicon for
high voltage and high power devices. The wide band-gap, high thermal conductivity and
high electron mobility of Sic provide the needed material properties to fabricate high
voltage high power devices. The ability to obtain high performance devices without
significant new investment in cutting-edge fabrication tools is particularly attractive.
Table 2 compares several wide band-gap materials to silicon. Gallium nitride
(GaN) has good mobilities but is limited by low thermal conductivity and unavailability
of GaN substrates [60-61]. Diamond has the highest nobilities, but suffers from a lack of
large area single crystal substrates and non type dopant [61].
19
Properties
4H-
Si
SiC
GaN
Diamond
5.6
1-2
5.45
Thermal
Expansion
(x10-6)/oC
Band-gap (eV)
Carrier Mobility
(cm2/Vs)
Electron
Hole
Dielectric
Constant
2.6
4.24.7
1.12
3.02
3.45
150
1000
125
0
0
2200
1600
600
50
250
11.8
9.7
9
5.7
150
490
130
2000
Thermal
Conductivity
(W/mK)
Table 2 Comparison of several wide band-gap materials to silicon
Fig 10. Photographs of Modern MESFETS
Figure 10 displays pictures of modern MESFETs. SiC has the large band-gap and
high thermal Conductivity necessary for elevated temperature operation, mobilities that
20
enable high-speed switching and low dynamic power loss. Switching speeds above 100
kHz are attainable with dynamic power losses reduced 5-10 times compared to silicon
diodes [65].
3.2 Functional Architecture
The MESFET differs from the common insulated gate FET in that there is no
insulator under the gate over the active switching region. This implies that the MESFET
gate should, in transistor mode, be biased such that one does not have a forward
conducting metal semiconductor diode instead of a reversed biased depletion zone
controlling the underlying channel. While this restriction inhibits certain circuit
possibilities, MESFET analog and digital devices work reasonably well if kept within the
confines of design limits. The most critical aspect of the design is the gate metal extent
over the switching region. Generally the narrower the gate modulated carrier channel the
better the frequency handling abilities, overall [63-67]. Spacing of the source and drain
with respect to the gate, and the lateral extent of the gate are important though somewhat
less critical design parameters. MESFET current handling ability improves as the gate is
elongated laterally, keeping the active region constant, however is limited by phase shift
along the gate due to the transmission line effect. As a result most production MESFETs
use a built up top layer of low resistance metal on the gate, often producing a mushroomlike profile in cross section [68].
The Figure 11 and Figure 12 explain the schematic diagram of SiC MESFET and
high resisitivity SiC substrate for semiconductor devices with high breakdown voltage.
Fig 11. Schematic Diagram of SiC MESFET
21
Fig 12. High-resistivity SiC substrate for sc devices with high break down
The MESFET consists of a conducting channel positioned between a source and
drain contact region. The carrier flow from source to drain is controlled by a Schottky
metal gate. The control of the channel is obtained by varying the depletion layer width
underneath the metal contact which modulates the thickness of the conducting channel
and thereby the current between source and drain [68-70].
Fig 13 Structure of MESFET with gate length, L, and active channel length
Figure 13 shows the structure of MESFET with its internal measurements like gate length
(L), and channel thickness (a). The key advantage of the MESFET is the higher mobility
of the carriers in the channel as compared to the MOSFET. Since the carriers located in
the inversion layer of a MOSFET have a wave function, which extends into the oxide,
their mobility - also referred to as surface mobility - is less than half of the mobility of
bulk material. The MESFET is a majority carrier device and hence the scattering effect is
extremely low resulting in low noise performance. As the depletion region separates the
carriers from the surface their mobility is close to that of bulk material. The higher
mobility leads to a higher current, transconductance and transit frequency of the device.
Figure 14 shows the device structure of SiC MESFET [71-73].
22
Fig 14 Device Structure of SiC MESFET
The turn-on voltage is typically 0.7 V for GaAs Schottky diodes. The threshold
voltage therefore must be lower than this turn-on voltage. As a result it is more difficult
to fabricate circuits containing a large number of enhancement-mode MESFET [74].
The higher transit frequency of the MESFET makes it particularly of interest for
microwave circuits. While the advantage of the MESFET provides a superior microwave
amplifier or circuit, the limitation by the diode turn-on is easily tolerated. Typically
depletion-mode devices are used since they provide a larger current and larger
transconductance and the circuits contain only a few transistors, so that threshold control
is not a limiting factor. The buried channel also yields a better noise performance as
trapping and release of carriers into and from surface states and defects is eliminated
[75].
The use of GaAs rather than silicon MESFETs provides two more significant
advantages: first, the electron mobility at room temperature is more than 5 times larger,
while the peak electron velocity is about twice that of silicon. Second, it is possible to
fabricate semi-insulating (SI) GaAs substrates, which eliminates the problem of
absorbing microwave power in the substrate due to free carrier absorption. The cross
sectional view of MESFET is shown in Figure 15 [76-80].
23
Fig 15 Cross-sectional view of a MESFET
24
CHAPTER 4
Numerical calculations:
4.1 Theory on the Model:
A schematic structure of OPFET device is shown in Figure 14. The transparent
gate is made of indium tin oxide (ITO) material to form a Schottky rectifying contact
with proper antireflection coating and all optical and electrical parameters of this model
are assumed to be the ideal case [85]. Under optically illuminated condition a onedimensional Poisson’s equation can be expressed in the following form
( )
[ (
)
]
(
)
The photogenerated carrier at the steady state derived by the following equation
α
( α )
Where ,
(
)= Impurity concentration with function space and time
G= Optical carrier rate
n= Lifetime of electrons
= Optical absorption coefficient
Fig 16 Cross-section of simulated SiC MESFET.
25
(4.2)
The equivalent circuit parameters such as trans conductance (gm), output
conductance (gd) are taken as bias dependent whereas gate to source capacitance (Cgs) and
gate to drain capacitance (Cgd) are taken as both bias and frequency dependent. The
frequency dependence of parasitic capacitances has been obtained by fitting the results
obtained by simulations with second order polynomial.
In order to fabricate SiC MESFET, the ion implantation process is preferred due
to higher temperature annealing causing impurity diffusion which will assist to activate
the dopant. Therefore, the ion implantation is preferred over the diffusion process, where
low diffusion coefficient is not able to activate the dopant impurities.
D=D0 x e(-EA/k Ta)
(4.3)
Where,
K= Boltzmans constant = 1.38065 X 10-23m2kg/s2
Annealing temperature Ta= 1473 K
Activation energy EA=0.89 eV
Diffusion coefficient D0=6.5x10-11
Dopant
D
Rp
Diffusion
Q implant
Implant
Straggle
coefficient
Diffusion/annea
ion
dose
range
parameter
(cm2/s).
ling time (sec).
(cm-2).
paramete
(cm).
1.3×
45×60=2700
1.6×
r (cm).
SiC
1.2×
3.2×
Table 3 Range Parameter and the corresponding straggle parameter
The information of the range parameter and the corresponding straggle parameter
presented in the above Table 3 had been calculated using SRIM software and this model
was incorporated an annealing time of 45 minutes. The diffusion constant and activation
energy has been obtained from the journal study [84].
26
The derived equation for calculating gate-source capacitance (CGS) is expressed
below,
CGS =
[
√
(
√
√
)) +
( √(
(√
(√
√ )
√
√ )
))] +
√
(
(√
√
√
√ )
√
(4.4)
Where,
N = phib-Vgs-∆-Vop
4.4(a)
R = phib-Vds-Vgs-∆-Vop
4.4(b)
M=
4.4(c)
A1=
4.4(d)
α=
(√ )
√
A2 = erf(
√
A3 = 1 – exp( (
4.4(e)
)–α
√
4.4(f)
) ) – 2α erf(
√
Where,
CGS= Capacitance from Gate to-Source.
q = Electronic charge.
Qion = Implant dose.
Z = Device width.
L= Channel length.
Rp= Implant range parameter.
phib =.Barrier height.
Vgs = Gate to-source.
= Straggle parameter.
Vop = Photo induced voltage.
Φ = Photon flux density.
= Permittivity of semiconductor.
Vds = Drain to-source.
27
)
4.4(g)
Delta= Depth of Fermi level below the Conduction band.
Similarly, we can also derive the gate-drain capacitance for Gallium Nitride ionimplanted MESFET.
CGD =
[
)) +
( √(
√
(
√
(√
√
(√
√ )
√ )
√
√
(
(√
√
√
√ )
√
))] +
(4.5)
Where,
CGD= Capacitance from Gate to-Source.
4.2 Switching Characteristics
The switching time of an OPFET depends on the active layer thickness and active
channel length of the ion implantation process. Switching time
is computed for
different active layer thickness and active channel length expressed by following
equations (4.6) and 4.6(a) [85-86].
√
(
√
)
(
(
)
)
Ndavg is calculated from the following equation
√
(
)
[
(
)
]
Where,
= Switching time.
Vg = Gate voltage
L= Active Channel length
Vop= Photon induced voltage
Ndavg = Average channel doping concentration.
D= Diffusion constant
28
( )
t = Annealing time
Rp = Range parameter.
= Straggle parameter.
Φ = Photon flux density.
Vs= Saturation velocity.
29
CHAPTER 5
Results and Discussions:
The gate capacitance is an important parameter which is responsible for switching speed
performance and frequency response of SiC MESFET device. The gate capacitance has
been mainly contributed by the gate source and gate drain capacitance. The gate source
and gate drain capacitance has been evaluated by physics based analytical model. In
MESFET device fabrication, the ion implantation doping process is preferred compared
to diffusion process, because the diffusion of ion species are extremely small. The post
annealing effect has been incorporated in the model to accurately define the gate
capacitance.
Fig 17. Plot of Gate-to-Drain Capacitance (CDS) vs. Drain-to-Source Voltage (VDS)
at different flux density
The above figure 17 shows the gate-to-drain capacitance versus drain-to-source voltage
for dark condition and different light illumination with light flux density (ϕ) of 5.0x1016
cm2/s, and 10x1017cm2/s respectively at constant gate source voltage. The gate drain
30
capacitance shows a large capacitance value in the order of 3.3pf, 3.1 pf and 2.2 pf for
photo flux density of 10x 1018cm2/s, 5x 1018cm2/s and dark condition respectively at Vds=
5V. As from 5V to 15 V, the gate drain capacitance decreases exponentially for
illumination and dark condition. The gate drain capacitance for three cases becomes
saturated beyond the drain source voltage of 20V. The nature of gate drain capacitance
clearly indicates the influence of drain potential in the space charge, which in turn makes
high value capacitance at low VDS and low capacitance at high VDS. In illumination
condition, the photo generated carrier increases the charge and therefore, the capacitance
for both illumination condition are greater than the dark condition.
Fig 18: Plot of Gate-to-Source Capacitance (CGS) vs. Gate-to-Source Voltage (VGS)
at different flux densities
Above figure 18 shows a plot of gate source voltage for different illumination and dark
condition for constant drain-source voltage for different illumination and dark condition
for constant drain-source voltage Vds. The gate source capacitance Cgs increases from
1.99 pf and 0.8 pf at Vgs =-3V for photo flux density Φ= 1e18cm2/S and Φ= 1e16cm2/S
31
and dark condition respectively. The gate source capacitance increases upto 9.2 pf and 9.1 pf for
illumination and 6 pf for dark condition. The photon assisted charge carrier for photo flux density
of 1x1018 cm2/s and 1x1016 cm2/s. Therefore the gate source capacitance shows higher value
compared to the capacitance in dark condition. The gate source capacitance has been plotted
using the equation 4.4
Fig 19 Plot of Switching time ( ) vs. Device Gate Length (L) at different flux
densities
Above figure 19 displays the plot of switching time versus active channel length for dark
and illumination condition. The switching time exponentially increases from 4.8x10-14
sec to 14x10-14 for active channel length of 1x10-14 to 9x10-14 cm for dark condition.Other
switching time varies from 3x10-14 to 8x10-14 sec and 2.6x10-14 sec to 7.4x10-14 sec for
active channel length of 1x10-14 to 9x10-14 cm respectively. The nature of plot justify the
validity of increment of transit time due to increase of Channel length. This feature of
Switching time shows an excellent proportion of potential application of the device for
high speed optical switch. The plot has been generated by using the equation 4.6
32
Fig 20 Plot of Switching time ( ) vs. Device thickness (A) for dark condition at
different flux densities
Above figure 20 exhibits the plot of switching time versus device thickness for dark and
illumination condition. The maximum switching time is obtained in the order of 3.75x1014
sec for dark condition and of 2.2x10-14 sec to 2x10-14 sec for illumination condition
with photon flux density of of 1x1018 cm2/s to 1x1016 cm2/s for the device channel depth
of 0.5x10-4cm.In both cases, the switching time exponentially drop 1.48x10-14 sec for
dark condition and 0.5x10-14 sec and 0.6x10-14 sec for illumination condition. The plot for
dark and illuminated condition follow the same nature of exponential decay of switching
time with increment of channel depth. The large channel depth contributes the less
generation of the photon assisted carrier and therefore switching time exponentially
decay with increment of channel depth. The above plot has been plotted using the
equation 4.6
33
CHAPTER 6
Conclusion
Analytical modeling based on device physics has been carried out for the
evaluation of intrinsic parameters such as capacitances at dark and illumination
conditions and switching time is obtained for device active layer thickness and active
channel length of SiC MESFET.
The results of those intrinsic parameters such as gate-to-source capacitance and
gate-to-source voltage and switching time indicate the excellent potential of the device
for high frequency amplifier application for space and device communication. This
excellent feature also allows this device to be applied in the field of communication in
high temperature environment.
The present analytical model offers an avenue of accurate optimum device and
fabrication process design as well as establishment of the diffusion process as most
suitable for optoelectronic devices fabrication.
34
REFERENCES
[1] Baliga, B.J., “Power Semiconductor Devices for Variable-Frequency Drives,”
Proceedings of the IEEE 82(8), 1112, 1994.
[2] Baliga, B.J., “Trends in Power Semiconductor Devices,” IEEE Transactions on
Electron Devices 43(10), 1717, 1996.
[3] Elasser, A. and Chow, T.P., “Silicon Carbide Benefits and Advantages for Power
Electronics Circuits and Systems,” Proceedings of the IEEE 90(6), 969, 2002.
[4] Johnson, C.M., “Clear road ahead?” Power Engineer 18(4), 34, 2004.
[5] J.S.Sullivan and J.R. Stanley, “6H-SiC Photoconductive Switches Triggered at Below
Band gap Wavelengths”.
[6] C. Baak, et.al “GaAs MESFET: A high speed optical detector,” Electron Lett., vol 13,
p.139, 1977.
[7] J. Graffeuil, P. Rossel and H.Marinot, Electron Lett.,vol 15.p.439, 1979.
[8] J. L. Gautier, D. Pasquet and P. Pouvil, “Optical effects on the static and dynamic
characteristics of a GaAs MESFET,” IEEE Trans. MTT, vol. Mtt-33, pp.819-822, 1985.
[9] H. Mizuno, “Microwave characteristics of an optically-controlled GaAs MESFET,”
IEEE MTT, vol. MTT-31, pp.596-600, 1983
[10] S. Mishra, V. K. Singh, and B. B. Pal, “Effect of radiation and surface
recombination on the characteristics of an implanted GaAs MESFET,” IEEE Trans.
Electron Devices, vol. 37, pp. 2–10, Jan. 1990.
[11] J. Graffeuil, P. Rossel, and H. Martinot, “Light induced effects in GaAs FET’s,”
Electron. Lett. vol. 15, no. 14, pp. 439–441, July 1979.
[12] R. N. Simon and K. B. Bhasin, “Analysis of optically-controlled
microwave/millimeter wave device structures,” IEEE Trans. Microwave Theory Tech.,
vol. MTT-34, pp. 1349–1355, Dec. 1986.
35
[13] S. N. Mohammad, M. S. Unlu, and H. Morkoc, “Optically-controlled current–
voltage Characteristics of ion-implanted MESFET’s,” Solid-State Electron., vol. 33, no.
12, pp. 1499–1509, 1990.
[14] J. Pan, “GaAs MESFET for high speed optical detection,” in SPIE Int. Tech. Symp.,
San Diego, CA, 1978.
[15] W. D. Edwards, “Two and three terminal gallium arsenide FET optical detectors,”
IEEE Electron Device Lett, vol. EDL-1, pp. 149–150, Aug. 1980.
[16] A. A. De Salles, “Optical control of GaAs MESFET’s,” IEEE Trans. Microwave
Theory Tech., vol. MTT-31, pp. 812-820, 1983.
[17] B.B. Pal and S.N. Chattopadhyay. "GaAs OPFET characteristics considering the
effect of gate depletion width modulation due to incident radiation", IEEE Trans. On
Electron Devices, Vol.ED-39, pp.1021-1027, 1992.
[18] R. N. Simons and K. B. Bhasin, “Analysis of Optically controlled microwave/
millimeter-wave device structures,” IEEE Trans Microwave Theory Tech, vol.34, no.12,
pp.1349-1355, December 1986.
[19] Giovanni Breglio, et.al. “Two silicon optical modulators realizable with a fully
compatible bipolar process,” JOURNAL OF SEMICONDUCTOR TECHNOLOGY
AND SCIENCE, VOL.7, NO.3, SEPTEMBER, 2007 207 IEEE Journal of selected
topics in Quantum Electronics, vol.4, pp. 1003-1010, 1998.
[20] Kei Kanemoto, et. al., “Dependence of ion implantation: Induced defects on
substrate doping,” J. Appl. Phys. 89, pp.3156-3161, 2001.
[21] De Salles, “Al0.3Ga0.7As/GaAs HEMT's under optical illumination”.
[22] J. Graffeuil, P. Rossel, and H. Martinot, “Light-induced effects in GaAs F.E.T.s,”
Electron Lett. vol. 15, no. 14, pp. 439-441, July 1979.
36
[23] J. Pan, “GaAs MESFET for high speed optical detection,” in SPIE Int. Tech. Symp.
(San Diego, CA), 1978.
[24] W. I. Edwards, “Two and three terminal gallium arsenide FET optical detectors,”
IEEE Electron Device Lett, vol. EDL-1, no. 8, pp. 149-150 Aug 1980.
[25] Sayed Ahmed, “Two-Stage Ultra wide-Band 5-W Power Amplifier Using SiC
MESFET”.
[26] V. K. Singh, S. N. Chattopadhyay, and B. B. Pal, Solid-State Electron, vol. 20, p.
707, 1986.
[27] S. Mishra, V. K. Singh, and B. B. Pal, IEEE Trans. Electron Devices, vol. 37, p. 2,
1990.
[28] P. Chakrabarti, Comment on “The effect of surface recombination on the
characteristics of GaAs OPFET,” IEEE Trans. Electron Devices, vol. 38, p. 2578, 1991
[29] Investigation of Extrinsic, Compensated, Semi-Insulating Silicon Carbide
PhotoConductive Switches for Directed Energy Applications. Nunnally, W., et al.
Albuquerque : s.n., 2006. 9th Annual Directed Energy Symposium.
[30] Photoconductive semiconductor switch experiments for pulsed power applications.
Zutavern, F.J. et al. 12, Dec. 1990, Electron Devices, IEEE Transactions on, Vol.
37, pp. 2472-2477.
[31] On the Preparation of V-Doped Semi-Insulating SiC Bulk Crystals. Bickermann, M,
etal. 2, 2002, American Insitute of Physics, Vol. 22.
[32] Deep Levels in silicon carbide: A review. Lebedev, A. A. 2, Feb 1999, American
Institute of Physics, Semiconductors, Vol. 33.
[33] Kraus, John D. Electromagnetics. s.l. : McGraw-Hill, 1984. pp. 56-87. 007035423.
37
[34] Latham, R V. High Vacuum Insulation: Basic Concepts and Tenological Practice.
San Diego : Academic Press, 1995. 0124371752.
[35] Tribo technological aspects of brittle materials grinding. Marinescu, I.D. and
Webster, J. A. Ohio : Society of Manufacturing Engineers, 1993, Proc. of the 5th
International Grinding Conf.
[36] Marinescu, Ioan D., Tonshoff, H. K. and Inasaki, I. Handbook of Ceramic
Grinding and Polishing. Norwich : William Andrew Publishing, 1998. 0815514247.
[37] Silicon carbide photonconductive switch for high-power, linear-mode operations
through sub-band-gap triggering. Kelkar, K S, et al. 9, 2005, Journal of Applied
Physics, Vol. 98.
[38] Processes leading to filaments in optically switched semiconductors. Stout, P.J.
Kushner, M.J. 1993. Proceedings IEEE Pulse Power conference. pp. 808-813.133.
[39] Wall, Dave. Representative. [Email] [prod.] SiC Laser Machining. s.l. : Resonetics,
June 6, 2006.
[39] Tucker, Jeff. Representative. [Email] s.l. : Rohm and Haas, June 6, 2006.
[40] Mittl, Scott, D. Sales Engineer. [Email] [prod.] SiC Grinding. s.l. : Insaco, June 13,
2006.
[41] McNutt, T. R. Ph.D. Process Engineer. [Email] [prod.] SiC Etching. s.l. : Northrop
Grumman, Jan. 31, 2007.
[42]Hannan, Phyllis A. Representative. [Email] [prod.] SiC Laser Machining. s.l. :
LaserUSA, June 6, 2006.
[43] Kelkar, Kapil, Ph. D. Simulations of Contour Etching of 6H-SiC. Unpublished
Computer Simulations using SILVACO. February 2007.
38
[44] Ultrashort-pulse laser machining of dielectric materials. Perry, M. D. et al. 6803,
1999, Vol. 85.
[45] Microstructuering of SiC by laser ablation with pulse duration from ns to fs range.
Kreutz, W. E. et al. 50, s.l. : LAMP 2002, Jan 2003.
[46] Tsai, H and Yukun, H. Femtosecond Laser Contouring of 6H-SiC. MAE Dept.,
University of Missouri-Rolla. s.l. : Unpublished Results from Laser Machining
Experiment, 2007.
[47] Fluid jet polishing of optical surfaces. Fahnle, OW. 28, 1998, Applied Optics, Vol.
37, p. 6771.
[48] Hunter, John. Fluid Jet contouring of SiC. Ottawa, Ontario, Canada :
LightMachinery, July 2007.
[49] High-quality grinding of polycrystalline silicon carbide sphereical surfaces. Yin,
Ling, et al. 2004, WEAR, Vol. 256, pp. 197-207.
[50] High quality grinding of polycrystalline silicon carbide spherical surfaces. Yin, L. et
al. 2004, WEAR, Vol. 256, pp. 197-207.
[51] Ductile-Regime Grinding: A New Techonlogy for Machining Brittle Materials.
Bifano, T.G. 1991, Journal of Engineering for Industry, Vol. 113, pp. 184-189.
[52] Hardness of nanocrystalline diamonds. Tse, J.S. et al. 140102, 2006, Phys. Rev.,
Vol. 73.134
[53] Chemomechanical Polishing of Silicon Carbide. Zhou, L., et al. 6, June 1997, J.
Electrochem. Soc., Vol. 144.
39
[54] Sze, S. M. Physics of Semiconductor Device, 2nd Ed. New York : Wiley, 1981.
[55] Surface Flashover of Insulators. Miller, H. Craig. 5, October 1989, IEEE Trans. on
Electrical Insulation, Vol. 24, pp. 765-786.
[56] C, W. Slayman and L. Figueroa, “Frequency and pulse measurement of a novel high
speed interdigital surface photoconductor (ITJPC),” IEEE Electron Device Lett., vol.
EDL-2, pp. 112-114, May 1981.
[57] W.C. Nunnally, “High-Power Microwave Generation Using Optically Activated
Semiconductor Switches,” IEEE Transactions on Electron Devices, Vol. 37, No.
12, December 1990.
[58] J.R. Mayes, W.J. Carey, and W.C. Nunnally, Experimental Multiple Frequency
Injection Wave Generator,” The Conference Record for the 22“‘
Power Modulator Symposium, 1996.
[59] W.C. Nunnally, Picosecond Optoelectronic Devices, Ed. C.H. Lee, Academic Press,
Inc., New York, 1984.
[60] A. Siegman, Lasers, University Science Books, California,, 1986.
[61] T. Warren and L. Matheus, “Modeling Non-Linear Pulsed Power Components
Behaviors,” 8th IEEE International Pulsed Power Conference, San Diego,
California, 1991.
[62] H. Welker, Z. Naturforsch, Vol. A, No. 7, p. 744, 1952.
[63] S. M. Sze, Semiconductor Devices Physics and Technology, J. Wiley, New York,
1985.
[64] R. F. Pierret, Semiconductor Fundamentals, Addison-Wesley Publishing, New
40
York, 1989.
[65] R. Williams, Modern GaAs Processing Methods, Artech House, Dedham, MA,
1990.
[66] H. C. Casey, “Diffusion in III-V Compound Semiconductors,” Atomic Diffusion in
Semiconductors, D. Shaw, Editor, Plenum, New York, 1973.
[67] S. Y. Chiang, “Properties of Vacancy Defects in GaAs Single Crystals,” J. Appl.
Phys., Vol. 45, p. 2986, 1975.
[68] S. Markram-Ebied, “Nature of EL2: The Main Native Midgap Electron Trap in VPE
and Bulk GaAs,” in Semi-insulating III-V Materials, D. Look, Editor, Shiva Publishing
Ltd., England, 1984.
[69] Y. Nanishi, Jpn. J. Appl. Phys., Vol. 22, 1983.
[70] S. Miyazawa, Appl. Phys. Lett., Vol. 44, 1984.
[71] T. Honda, Jpn. J. Appl. Phys., Vol. 22, 1983.
[72] Christopher Michael Fessler “Improved Contact Design for SiC Photo- Switch used
for High Power Applications”
[73] "photoconductivity." Encyclopædia Britannica. Encyclopædia Britannica Online
Academic
Edition.
Encyclopædia
Britannica,
2011.
Web.
02
Sep.
2011.
<http://www.britannica.com/EBchecked/topic/457776/photoconductivity>.
[74] Photoconductivity. (2011).
In
Encyclopædia
Britannica. Retrieved from
http://www.britannica.com/EBchecked/topic/457776/photoconductivity
[75] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.
41
[76] "photoelectric effect." Encyclopædia Britannica. Encyclopædia Britannica Online
Academic
Edition.
Encyclopædia
Britannica,
2011.
Web.
02
Sep.
2011.
<http://www.britannica.com/EBchecked/topic/457841/photoelectric-effect>.
[77] ” Photoconductivity” http://en.wikipedia.org/wiki/Photoconductivity
[78] High-Power Microwave Generation Using Optically Activated Semiconductor
Switches. Nunnally, W. C. 12, December 1990, IEEE Trans on Elec. Devices, Vol. 37
[80] Toward pulsed power used for photoconductive switches. Loubriel, G. M.,
O'Malley, M. W. and Zutavern, F. J. Arlington, VA : s.n., 1987. Proc. 6th IEEE Int.
Pulsed Power Conference.
[81] R. Anholt, Electrical and Thermal Characterization of MESFETs, HEMTs, and
HBTs, Norwood, MA: Artech House, 1995.
[82] M. Bhatnagar and B.J. Baliga, “Comparison of 6HSiC,3C-SiC, and Si for power
devices”, IEEE Trans. Electron Devices, Vol.40, p.645, 1993.
[83. R.J. Trew, J. Yan, and R.M. Mock, “The potential of diamond and SiC electronic
devices for microwave and millimeter-wave power applications”, Proc. IEEE, Vol.79,
p.598, 1991.
[84] Alok, D. and Baliga, B.J., “High Voltage (450 V) 6H-SiC lateral MESFET
structure”, IEEE Trans. Electronic Letters, Vol.32, No.20, p.1929, 1996.
[85] S.N.Chattopadhyay,N.Motoyama,A.Sharma,S.Sriram,C.B.Overton and P.Pandey in
“Optically controlled Silicon MESFET modeling considering diffusion process”;
[86] S.N.Chattopadyay and B.B.Pal in “The Effects of Annealing on the Switching
Characteristics of an Ion-Implanted Silicon MESFET”, IEEE Trans. On Electron
Devices,Vol. 36 No. 5 May 198
42
APPENDIX – A
Notations and Symbols Used:
Rp: Effective ion Implant Range Parameter
: Implant Straggle Parameter
: SiC Dielectric Constant/Permittivity of SiC
K: Boltzmann constant
q: Electronic charge
T: Absolute temperature at 300K
Z: Device length
L: Channel length
µ: Carrier mobility in SiC
Φb: Metal-Semiconductor Work function difference/Titanium Schottky barrier height
Vbs: Substrate to source voltage
Vgs: Gate-Source voltage
Vds: Drain-Source voltage
Vt: Threshold voltage
Vbi: Build in Voltage of active channel and Substrate junction
Vp: Pinch-off Voltage
N(x,t): Impurity doping concentration of diffused active layer
Na: Substrate doping concentration
Nd: Effective average channel doping concentration
Xdg: Distance from surface to edge of gate depletion region in the channel
Xds: Distance from surface to edge of substrate depletion region in the channel
a: Active layer thickness
Q: Ion Implant Dose
Δ: Depth of Fermi level below the Conduction band
kT/q: Thermal Voltage = 0.0259V at T = 300 K;
t: Annealing time
Cgd: Gate-Drain capacitance
Cgs: Gate-Source capacitance
gm: Transconductance
43
tgs, tgd : time constants
Tt: Total time constant(tgs+tgd)
Ndavg: Average Channel doping concentration
44
APPENDIX – B
MATLAB Codes
MatLab code for Gate-Drain capacitance (Cgd) Vs Drain-Source voltage (Vds) at
different ion doses
clc;
Na=5e15;
sigma=32e-7;
Vbs=0;
phib=0.8;
Vp=0.8117;
eps=8.854e-14;
q=1.60218e-19;
u=900;
Z=1000e-4;
Rp=0.0123e-4;
L=1e-4;
K1 = 1.3806e-23;
45
T1 = 300;
D=6.05e-21;
x = 0.1e-4;
t=7.5e6;
Vds=5:2:40;
ni = 5e-9;
Vgs=-3.5;
alpha=(Rp/(2*sigma))*(sqrt(3.14/2));
delta=0.018;
tn=1e-8;
A3=1-exp(-((Rp/sqrt(2*((sigma*sigma)+(2*D*t))))^2))
((2*alpha*erf(Rp/sqrt(2*((sigma*sigma)+(2*D*t))))));
A1=(alpha*alpha)+A3;
Ndavg=8.0573e17;
S=sqrt((q*Ndavg)/(2*eps));
Qion=1.5e13;
%Impurity flux phi1=0 dark condition
46
-
phi1=0;
deltap1 = (phi1*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
P21= p11 + deltap1;
Vop1 = (0.0259*log(P21/p11));
N1=phib-Vgs-delta-Vop1;
R1=phib+Vds-Vgs-delta-Vop1;
M1=(4*alpha*eps)/(q*Qion*Rp);
x11=(q*Qion*Z*L)/2;
x21=(M1)./(2.*sqrt((M1.*N1)+A1));
x31=sqrt(R1)./(2.*(sqrt(N1)-sqrt(R1)).*(sqrt(N1)-sqrt(R1)));
x41=sqrt(((M1*R1)+A1)./N1);
x51=(M1.*(sqrt(N1)-sqrt(R1))./sqrt((M1.*N1)+A1));
x61=(sqrt((M1.*R1)+A1))./sqrt(N1);
%z71=(1/Qion)*(sqrt((2*Na*eps)/q));
x71=(q*Z*L*tn*phi1*S)./(2*alpha);
47
x81=(2.*(sqrt(N1)-sqrt(R1)))/(sqrt(R1));
x91=(Vds)/(sqrt(R1.*N1));
W1=(x11).*(x21+x31.*(x41-x51-x61-x71.*(x81-x91)))+((3.14*eps*Z)./2);
phi2=5e16;
deltap2 = (phi2*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
Q21= p11 + deltap2;
Vop2 = (0.0259*log(Q21/p11));
N2=phib-Vgs-delta-Vop2;
R2=phib+Vds-Vgs-delta-Vop2;
M1=(4*alpha*eps)/(q*Qion*Rp);
a11=(q*Qion*Z*L)/2;
a21=(M1)./(2.*sqrt((M1.*N2)+A1));
a31=sqrt(R2)./(2.*(sqrt(N2)-sqrt(R2)).*(sqrt(N2)-sqrt(R2)));
a41=sqrt(((M1*R2)+A1)./N2);
a51=(M1.*(sqrt(N2)-sqrt(R2))./sqrt((M1.*N2)+A1));
48
a61=(sqrt((M1.*R2)+A1))./sqrt(N2);
%z71=(1/Qion)*(sqrt((2*Na*eps)/q));
a71=(q*Z*L*tn*phi2*S)./(2*alpha);
a81=(2.*(sqrt(N2)-sqrt(R2)))/(sqrt(R2));
a91=(Vds)/(sqrt(R2.*N2));
W2=(a11).*(a21+a31.*(a41-a51-a61-a71.*(a81-a91)))+((3.14*eps*Z)./2);
phi3=10e17;
deltap3 = (phi3*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
U21= p11 + deltap3;
Vop3 = (0.0259*log(U21/p11));
N3=phib-Vgs-delta-Vop3;
R3=phib+Vds-Vgs-delta-Vop3;
M1=(4*alpha*eps)/(q*Qion*Rp);
b11=(q*Qion*Z*L)/2;
b21=(M1)./(2.*sqrt((M1.*N3)+A1));
49
b31=sqrt(R3)./(2.*(sqrt(N3)-sqrt(R3)).*(sqrt(N3)-sqrt(R3)));
b41=sqrt(((M1*R3)+A1)./N3);
b51=(M1.*(sqrt(N3)-sqrt(R3))./sqrt((M1.*N3)+A1));
b61=(sqrt((M1.*R2)+A1))./sqrt(N2);
%z71=(1/Qion)*(sqrt((2*Na*eps)/q));
b71=(q*Z*L*tn*phi3*S)./(2*alpha);
b81=(2.*(sqrt(N3)-sqrt(R3)))/(sqrt(R3));
b91=(Vds)/(sqrt(R3.*N3));
W3=(b11).*(b21+b31.*(b41-b51-b61-b71.*(b81-a91)))+((3.14*eps*Z)./2);
display(W1);
display(W2);
display(W3);
plot(Vds,W1,Vds,W2,Vds,W3);
xlabel('Drain-to source Voltage Vds(V)');
ylabel('Gate-drain Capacitance Cgd(F)');
50
Matlab code for Gate-to-Source Capacitance (CGS) vs. Gate-to-Source Voltage (VGS)
at different ion doses.
clc;
Na=5e14;
sigma1=20e-7;
%Vbs = 0;
Vds=10;
Vbi=3.1728;
Vp=5.0;
eps=8.55e-13;
q=1.60218e-19;
ni=1.9e-10;
tn=1e-7;
phib=1.24;
u=500;
Z=100e-4;
Rp=40e-7;
51
L=1e-4;
D = 2.3e-21;
t=7.5e6;
Vgs=-2:0.01:1.75;
alpha=(Rp/(2*sqrt((sigma*sigma)+(2*D*t))))*sqrt(3.14/2);
a=exp(((Rp/sqrt(2*((sigma*sigma)+(2*D*t)))))*((Rp/sqrt(2*((sigma*sigma)+(2*D*t)))))
);
b=erf(Rp/sqrt(2*((sigma*sigma)+(2*D*t))));
A3=a-(2*alpha*b);
A1=(alpha*alpha)+A3;
delta=0.018;
x= 0.1e-4;
sigma=(sqrt(sigma1*sigma1))+(2*D*t);
Ndavg=(Q/(sigma*sqrt(2*pi)))*exp(-(Rp/((sigma*1.414)))^2);
Qion=1.5e13;
S=sqrt((q*Ndavg)/(2*eps));
%dark condition phi=0;
52
phi1=1e14;
deltap1 = (phi1*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
P21= p11 + deltap1;
Vop1 = (0.0259*log(P21/p11));
N1=phib-Vgs-delta-Vop1;
R1=phib-Vds-Vgs-delta-Vop1;
M1=(4*alpha*eps)/(q*Qion*Rp);
c11=(q*Qion*Z*L)/2;
c21=(M1)./(2.*sqrt((M1*R1)+A1));
c31=(sqrt(N1))./(2.*(sqrt(N1)-sqrt(R1)).^2);
c41=sqrt(((M1.*N1)+A1)/R1);
c51=(M1.*(sqrt(N1)-sqrt(R1)))./(sqrt((M1*R1)+A1));
c61=sqrt(((M1*R1)+A1)/R1);
c71=(q*Z*L*tn*phi1*S)./(2*alpha);
%c71=(1/Qion)*(sqrt((2*Na*eps)/q))-t71;
53
c81=(2.*(sqrt(N1)-sqrt(R1)))/(sqrt(R1));
c91=(Vds)./(sqrt(R1.*N1));
Y1=(c11).*(c21+(c31.*(c41-c51-c61-c71.*(c81-c91))))+((1.57*eps*Z));
phi1=1e18;
deltap2 = (phi2*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
Q21= p11 + deltap2;
Vop2 = (0.0259*log(Q21/p11));
N2=phib-Vgs-delta-Vop2;
R2=phib-Vds-Vgs-delta-Vop2;
M1=(4*alpha*eps)/(q*Qion*Rp);
b11=(q*Qion*Z*L)/2;
b21=(M1)./(2.*sqrt((M1*R2)+A1));
b31=(sqrt(N2))./(2.*(sqrt(N2)-sqrt(R2)).^2);
b41=sqrt(((M1.*N2)+A1)/R2);
b51=(M1.*(sqrt(N2)-sqrt(R2)))./(sqrt((M1*R2)+A1));
54
b61=sqrt(((M1*R2)+A1)/R2);
b71=(q*Z*L*tn*phi2*S)./(2*alpha);
%b71=(1/Qion)*(sqrt((2*Na*eps)/q))-t71;
b81=(2.*(sqrt(N2)-sqrt(R2)))/(sqrt(R2));
b91=(Vds)./(sqrt(R2.*N2));
Y2=(b11).*(b21+(b31.*(b41-b51-b61-b71.*(b81-b91))))+((1.57*eps*Z));
phi3=1e20;
deltap3 = (phi3*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
R21= p11 + deltap3;
Vop3 = (0.0259*log(R21/p11));
N3=phib-Vgs-delta-Vop3;
R3=phib-Vds-Vgs-delta-Vop3;
M1=(4*alpha*eps)/(q*Qion*Rp);
a11=(q*Qion*Z*L)/2;
a21=(M1)./(2.*sqrt((M1*R3)+A1));
55
a31=(sqrt(N3))./(2.*(sqrt(N3)-sqrt(R3)).^2);
a41=sqrt(((M1.*N3)+A1)/R3);
a51=(M1.*(sqrt(N3)-sqrt(R3)))./(sqrt((M1*R3)+A1));
a61=sqrt(((M1*R3)+A1)/R3);
a71=(q*Z*L*tn*phi1*S)./(2*alpha);
%a71=(1/Qion)*(sqrt((2*Na*eps)/q))-t71;
a81=(2.*(sqrt(N3)-sqrt(R3)))/(sqrt(R3));
a91=(Vds)./(sqrt(R3.*N3));
Y3=(a11).*(a21+(a31.*(a41-a51-a61-a71.*(a81-a91))))+((1.57*eps*Z));
p=plot(Vgs,Y1,Vgs,Y2,Vgs,Y3);
xlabel('Gate to- source Voltage Vgs(V)');
ylabel('Gate to-Capacitance Cgs(F)');
legend('1e14/cm^2','1e16/cm^2','1e18/cm^2','Location','northeast');
Matlab code for Calculating Ndavg to determine switching time against Active layer
thickness (A) and channel length (L)
Na=5e15;
sigma=32e-7;
Vbs=0;
Vgs=3.5;
Vbi=3.178;
56
Vp=0.8117;
epso=8.854e-14;
59
q=1.60218e-19;
u=1000;
Z=600e-4;
Rp=0.0123e-4;
L=10e-4;
D = 6.05e-21;
t=7.5e6;
phi = 3e10;
pi = 3.14;
n11 = sqrt(2*pi);
n21 = sigma*sigma + (2*D*t);
n31 = sqrt(n21);
n41 = n11*n31;
n51 = -Rp/2*n21;
n61= exp(n51);
Ndavrg = (phi/n31)* n61;
display(Ndavrg);
Matlab code for Switching time ( ) vs. Device thickness (A) at different flux
density
clc;
pi=3.14;
%phib = 0.94;
q = 1.6e-19;
L=1e-4;
epselon = 8.854e-14;
sigma = 32e-7;
D = 6.05e-21;
57
phibn =0.8;
Ndavg = 8.0573e17;
Vs= 25e6 ;
Rp = 0.0123e-4;
alpha = 1e-4;
Tn = 1e-7;
ni = 5e-9;
T = 1473;
T1 = 300;
Na = 5e15;
%A = 2e-4:1e-4:10e-4;
A = 2.5e-4:0.5e-4:6.5e-4;
%A = 2.1e-4: 0.2e-4:3.8e-4;
K1 = 1.3806e-23;
Nc = 4.82e15;
x = 0.1e-4;
Vgs = -3.5;
t=7.5e6;
Vg = -3.2;
phi1 = 0;
deltap1 = (phi1*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
P21= p11 + deltap1;
Vop1 = ((K1*T1)/(q))*log(P21/p11);
c0= 0.7-Vop1-Vg;
d0= q*Ndavg;
e0= 2*epselon*c0;
a0= sqrt(e0/d0);
58
f0= A-a0;
g0= L*a0;
h0= Vs*f0;
tau1= g0./h0;
phi2 = 1e16:1e16:9e16;
deltap2 = (phi2*alpha)*exp (-alpha*x);
q11 = (ni*ni)/Na;
Q21= q11 + deltap2;
Vop2 = ((K1*T1)/(q))*log(Q21/q11);
c1= 0.7-Vop2-Vg;
d1= q*Ndavg;
e1= 2*epselon*c1;
a1= sqrt(e1/d1);
f1= A-a1;
g1= L*a1;
h1= Vs*f1;
tau2= g1./h1;
phi3 = 1e18:1e18:9e18;
deltap3 = (phi3*alpha)*exp (-alpha*x);
r11 = (ni*ni)/Na;
R21= q11 + deltap3;
Vop3 = ((K1*T1)/(q))*log(R21/r11);
c2= 0.7-Vop3-Vg;
d2= q*Ndavg;
e2= 2*epselon*c2;
a2= sqrt(e2/d2);
f2= A-a2;
g2= L*a2;
h2= Vs*f2;
tau3= g2./h2;
59
plot(A,tau1,A,tau2,A,tau3);
xlabel('Device thickness A (cm)');
ylabel('Switching time,tau(Sec)');
Matlab code for Switching time ( ) vs. Active Channel length (L) at different flux
density
clc;
pi=3.14;
q = 1.6e-19;
epselon = 8.854e-14;
sigma = 32e-7;
D = 6.05e-21;
phibn =0.8;
Ndavg = 8.0573e17;
Vs= 25e6 ;
Rp = 0.0123e-4;
alpha = 1e-4;
Tn = 1e-7;
ni = 5e-9;
T = 1473;
T1 = 300;
Na = 5e15;
A = 2e-4:0.5e-4:6e-4;
L = 1e-4:1e-4:9e-4;
K1 = 1.3806e-23;
Nc = 4.82e15;
x = 0.1e-4;
Vgs = -3.5;
t=7.5e6;
60
Vg = -3.2;
phi1 = 0
deltap1 = (phi1*alpha)* exp (-alpha*x);
p11 = (ni*ni)/Na;
P21= p11 + deltap1;
Vop1 = ((K1*T1)/(q))*log(P21/p11);
c0= 0.7-Vop1-Vg;
d0= q*Ndavg;
e0= 2*epselon*c0;
a0= sqrt(e0/d0);
f0= A-a0;
g0= L.*a0;
h0= Vs*f0;
tau1= g0./h0;
phi2 = 1e13:1e13:9e13;
deltap2 = (phi2*alpha)*exp (-alpha*x);
q11 = (ni*ni)/Na;
Q21= q11 + deltap2;
Vop2 = ((K1*T1)/(q))*log(Q21/q11);
c1= 0.7-Vop2-Vg;
d1= q*Ndavg;
e1= 2*epselon*c1;
a1= sqrt(e1/d1);
f1= A-a1;
g1= L.*a1;
h1= Vs*f1;
tau2= g1./h1;
phi3 = 1e18:1e18:9e18;
deltap3 = (phi3*alpha)*exp (-alpha*x);
r11 = (ni*ni)/Na;
R21= q11 + deltap3;
Vop3 = ((K1*T1)/(q))*log(R21/r11);
61
c2= 0.7-Vop3-Vg;
d2= q*Ndavg;
e2= 2*epselon*c2;
a2= sqrt(e2/d2);
f2= A-a2;
g2= L.*a2;
h2= Vs*f2;
tau3= g2./h2;
plot(L,tau1,L,tau2,L,tau3);
xlabel('Active Device Length L (cm)');
ylabel('Switching time,tau(Sec)');
62