CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
PHYSICS BASED ANALYTICAL MODELLING OF SILICON CARBIDE (SiC)
MESFET CONSIDERING DIFFERENT ION IMPLANTATION ENERGYWITH HIGH
TEMPERATURE ANNEALING
A graduate project in partial fulfillment of the requirements
For the degree of Master of Science
In Electrical Engineering
By
Karthik Vishwanath Yadavalli
December 2014
The graduate project of Karthik Vishwanath Yadavalli is approved:
____________________________________________________ ______________
Dr. Benjamin Mallard
Date
_____________________________________________________ _____________
Dr. Conner Robert D
Date
_____________________________________________________ _____________
Dr. Somnath Chattopadhyay, Chair
Date
California State University, Northridge
ii
ACKNOWLEDGEMENT
First and foremost I would like to thank my committee chair DR. Somnath
Chatopadhyay for his unlimited cooperation and encouragement in the completion of my
dissertation. His support and guidance are the key points for the completion of my
project. I would also like to thank my committee members Dr. Benjamin Mallard and Dr.
Robert Conner D for their scholarly advice and inspiration in completion of my project
successfully.
Secondly, Iam grateful to the Department of Electrical and Computer Engineering
for giving me this opportunity and providing me the required knowledge in completing
my project.
Finally, I thank my parents for their support, faith and encouragement in the
completion of my project.
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TABLE OF CONTENTS
SIGNATURE PAGE……………………………………………………………………..ii
ACKNOWLEDGEMENT ................................................................................................. iii
LIST OF FIGURES .......................................................................................................... vii
LIST OF TABLES ............................................................................................................. ix
1. INTRODUCTION .......................................................................................................... 1
2. SILICON CARBIDE (SiC) MATERIAL ....................................................................... 4
2.1 History of SiC: .......................................................................................................... 9
2.2 Material defects of SiC: ............................................................................................ 9
2.2.1 Point Defects....................................................................................................... 9
2.2.2 Linear Defects................................................................................................... 10
2.2.3 Planar Defects ................................................................................................... 10
2.2.4 Volume Defects ................................................................................................ 10
2.3 Energy Band Diagram ............................................................................................. 12
2.4 Drift velocity graph for SiC .................................................................................... 17
2.5 Characteristics of SiC and SiC based devices ......................................................... 19
3. ION IMPLANTATION ................................................................................................ 20
3.1 Ion Implantation: ......................................................................................................... 20
3.2 Process of surface modification .............................................................................. 22
3.3 Stopping and Range of Ions in Matter (SRIM) ....................................................... 24
iv
3.4 Annealing ................................................................................................................ 26
3.4.1 Furnace Annealing ............................................................................................ 28
3.4.2 Rapid Thermal Annealing ................................................................................ 28
3.5 Applications ............................................................................................................ 29
3.5.1 Why Ion Implantation is preferred for SiC doping........................................... 29
3.6 Fabrication............................................................................................................... 30
3.7 Ion implantation process induced damage .............................................................. 32
4. MESFET PHYSICS ...................................................................................................... 34
4.1 MESFET ................................................................................................................. 34
4.2 Types of MESFET .................................................................................................. 34
4.2.1
Enhancement MESFET .............................................................................. 35
4.2.2
Depletion MESFET .................................................................................... 35
4.3 structure and characteristics of MESFET ............................................................... 36
4.4 SiC MESFET structure and characteristics ............................................................. 38
4.5 Functional Architecture of MESFET ...................................................................... 40
4.6 Advantages of MESFET ......................................................................................... 41
4.7 Applications of MESFET ........................................................................................ 41
5. THEORY AND MODEL ............................................................................................. 42
5.1 Threshold voltage of SiC MESFET ........................................................................ 42
5.2 I-V Characteristics of Silicon carbide MESFET ..................................................... 45
v
5.3Transconductance of SiC MESFET ..................................................................... 47
6. RESULTS AND DISCUSSIONS ................................................................................. 50
7. CONCLUSION ............................................................................................................. 57
REFERENCES ................................................................................................................. 59
APPENDIX-A................................................................................................................... 67
APPENDIX-B ................................................................................................................... 69
vi
LIST OF FIGURES
Figure 1: Figure showing Silicon Carbide (SiC)wafer ....................................................... 5
Figure 2: The figure shows Moissanite stone ..................................................................... 6
Figure 3: Structure of SiC ................................................................................................... 7
Figure 4: 3D structure of SiC .............................................................................................. 8
Figure 5: Grains of black SiC ............................................................................................. 8
Figure 6: SiC material used in steel making ....................................................................... 9
Figure 7: Figure shows break down voltages for different materials ............................... 12
Figure 8: Energy band diagram of 4H-SiC ....................................................................... 13
Figure 9: 4H-SiC excitonic energy vs. temperature.......................................................... 14
Figure 10: Band gap for 3C, 4H and 6H SiC .................................................................... 15
Figure 11: Intrinsic carrier concentration of 3C, 4H and 6H SiC ..................................... 17
Figure 12: Drift velocity vs. electric field for 4H SiC ...................................................... 18
Figure 13: Flow chart of ion implantation ........................................................................ 21
Figure 14: Direct ion bombardment surface ..................................................................... 22
Figure 15: Distribution before annealing .......................................................................... 23
Figure 16: Gaussian profile after annealing ...................................................................... 27
Figure 17: Rapid thermal annealing system...................................................................... 28
Figure 18: Furnace of rapid thermal annealing system ..................................................... 29
Figure 19: Fabrication process of MESFET ..................................................................... 32
Figure 20: Implanted p+ -n diode structure ....................................................................... 33
Figure 21: Usage ranges in enhancement and depletion mode ......................................... 36
Figure 22: Basic structure of MESFET ............................................................................ 37
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Figure 23: Graph showing I-V characteristics for SiC MESFET ..................................... 38
Figure 24: Basic structure of MESFET ............................................................................ 38
Figure 25: SiC MESFET schematic .................................................................................. 40
Figure 26: High-resistivity SiC substrate .......................................................................... 40
Figure 27: MESFET with gate length „L‟ and active channel length „a‟ .......................... 41
Figure 28: Cross section of Silicon carbide MESFET ...................................................... 42
Figure 29: graph showing I-V characteristics for ion energy 100 keV............................. 50
Figure 30: graph showing I-V characteristics for ion energy 150 keV............................. 51
Figure 31: graph showing I-V characteristics for two ion energies (100 keV and 150 keV)
........................................................................................................................................... 53
Figure 32: graph showing threshold voltage versus ion dose for two ion energies (100
keV and 150 keV) ............................................................................................................. 54
Figure 33: graph showing transconductance versus gate voltage for 150keV.................. 55
viii
LIST OF TABLES
Table 1: SiC polytypes electrical properties ..................................................................... 11
Table 2: SiC polytypic properties ..................................................................................... 19
Table 3: Values extracted from SRIM .............................................................................. 25
Table 4: Comparison between different wide band gap materials .................................... 39
Table 5: showing Rp and σ values for different ion energy .............................................. 49
Table 6: diffusion constant values at different annealing temperature ............................. 49
ix
ABSTRACT
PHYSICS BASED ANALYTICAL MODELLING OF SILICON CARBIDE (SiC)
MESFET CONSIDERING DIFFERENT ION IMPLANTATION ENERGYWITH HIGH
TEMPERATURE ANNEALING
By
Karthik Vishwanath Yadavalli
Master of Science in Electrical Engineering
A Physics based analytical model of ion implanted SiC MESFET has been developed
considering the high temperature annealing effects.
The diffusion of implanted
impurities has been calculated with appropriate activation energy of impurity atoms. The
impurity distribution of impurities has been estimated by incorporating of impurity
diffusion in the bulk during high temperature. The I-V characteristics, threshold voltage
and transconductance have been computed for two ion implantation energies (100KeV
and 150KeV) considering the high temperature annealing. A comparative study on I-V
characteristics for two ion implantation energies has been conducted to understand the
diffusion of impurities during high temperature annealing and its effect on the channel
current. The ion implantation process parameters have been extracted from SRIM. The
threshold voltage was extensively studied to observe the threshold voltage shift for
enhancement and depletion due to ion dose and high temperature annealing.
x
The
transconductance was studied to understand the frequency response in the influence of
high temperature annealing.
xi
1. INTRODUCTION
“Metal semiconductor field effect transistors (MESFET)” which are fabricated from wide
band gap semiconductor material have best performance with microwave power amplifier
applications. “Semiconductor devices came into use for their properties like high power,
high speed, high temperature and radiation hard applications. In addition, these devices
also have properties like wide band gap, high saturated electron velocity and thermal
conductivity [1-4]. Low intrinsic concentration, radiation hardness, low device leakage at
high temperatures is the result of wide band gap”.
High power handling capacity of silicon carbide devices are due to its high
thermal conductivity [5-8]. In a study of 4H-SiC a gate length of 0.5µm was
demonstrated on a conducting SiC substrate which resulted in maximum drain current of
300mA/mm and maximum transconductance of 300mA/mm. “The device had a threshold
frequency of 3.2GHz and maximum frequency of 12.4GHz at drain voltage of 25V and
gate voltage of -4V. The power gain of the device was 25.3dBm with 34.5% power added
efficiency at 2GHz [9-12]”.In a similar study 4H-SiC MESFET was fabricated by ion
implantation without recess gate etching to obtain a lower contact resistance to study the
DC and RF properties for that particular device [13, 14]. The fabricated MESFET
resulted in good RF and DC properties with “maximum oscillation frequency of 34GHz
and cutoff frequency of 9.3GHz. The power gain was 10.1dB and power output was
1.4W for 1mm-gatelength device at 2GHz” [15-17].Usually the MESFET‟s have small
signal characteristics like cutoff frequency of 22GHz and maximum oscillation frequency
of 50GHz [18] and output characteristics are 120W in pulsed operation at 3.1GHz and
80W in clockwise operation. “An output power density of 7.2W/mm was calculated by
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CREE (United States)” [19-22].In July 2006 a study was conducted where MESFET‟s
were fabricated using SiC substrate, “The buffer is p-doped (NA = 5×1015cm-3) and
0.34µm heavy. The channel is n-doped (ND=2.7×1017cm-3 and 1.6×1019cm-3) with
thickness of 0.34µm and 0.33µm respectively” [23]. “The final result of the study, power
density of 7.8W/mm was observed at 3GHz on a wafer for two-finger 400µm gate
periphery SiC MESFET. The PAE for the device was 70% at class AB bias [24-27].The
wide band gap of SiC MESFET makes it possible to use SiC for very high temperature up
to 600oC compared to 150oC for Silicon [28]. SiC devices have low susceptibility to high
radiation doses up to 100 megarad [29]”. “4H-SiC schottky diode had a 5kV breakdown
voltage with edge termination structure [30-32]. 6H and 4H-SiC schottky barrier diodes
had breakdown voltages of 1000V, 1400V and current densities of 100A/cm2, 700
A/cm2” [33, 34]. “The production of high voltage 6H-SiC Schottky diodes and closely
watched, breakdown voltage exceeding 400V have been examined by a few research
gathers” [35]. “Units have been provided with RF yield control thickness of 2.8 W/mm at
1.8 GHz. This power thickness is three times larger than GaAs units with high quality
and lower losses at working temperature [36]. Increased power SiC MESFET units were
adjusted to control yield of 6.8 W and 16 W from a solitary three device chip at a
frequency of 4 GHz” [37]. “Sband 4H-SiC MESFETs for microwave controls have
demonstrated high power densities in the range of 5.6 W/mm and 36% power-added
efficiency (PAE) and CW force of 80 W”. “A study with voltage 6h-Sic MESFET made
with ion implantation process and an asymmetrical source to gate channel structure was
made, which is fit for forward blocking voltage of 450 V with a gate voltage of-20 V
[38]. SiC MESFET‟s are fabricated with more than 60 W of yield power at 450 MHz
2
from single 21.6 mm gate devices(2.9 W/mm) and 27 W of yield power at 3 GHz from
14.4 mm”[39].
“The extreme output power point for the SiC MESFET device operates under
Class A. At a drain bias of V and mA (50%), with the device proportioned for maximum
power, the device had a peak output power of 30.5 dBm (3.37 W/mm) and a 3 dB
compression output power of 30.2 dBm (3.1W/mm)”[40,41]. “The peak efficiency was at
a bias of V and mA (5%), where the device presented 65.7% power added efficiency. The
device had 28.4-dBmoutput power (2.12 W/mm) at the point of peak efficiency, which
was also the 3 dB compression points. At this bias point, the device had 28.8-dBm
maximum output power (2.27W/mm), but efficiency lowered to 61.3% as the device
went into deep compression” [42]. So the power density and the “power aided efficiency”
of SiC were twice as of GaN [43].
In some studies 4H-SiC schottky barrier diodes with breakdown voltages more
than 400V were reported [44]. “6H-and 4H-SiC Schottky block diodes with breakdown
voltages of 1000 V and 1400 V and flow densities 100 A/cm2 also 700 A/cm2
independently were accounted for many research groups”[45,46].
3
2. SILICON CARBIDE (SiC) MATERIAL
Silicon Carbide is a semiconductor with the chemical compounds of silicon and
carbon. As group IV elements i.e. silicon and carbon combined together to form silicon
carbide by covalent bond, since group IV elements only bond by covalent bonding. The
purest form of silicon carbide (SiC) has no color but an industrial graded SiC is brown
down to black depending on the measure of iron impurities added to it. In Silicon carbide
each silicon atom is surrounded by four carbon atoms and vice versa. By this it can be
said that each face of silicon and carbon atom can be seen and are available for bonding.
Comparing the crystal structure of gallium arsenide and silicon carbide, gallium arsenide
has only one crystal structure but silicon carbide has many crystal structures, which is
more than 400 polytypes. The main polytypes of SiC are used for device fabrication 4HSiC, 6H-SiC and 3C-SiC. 4H-SiC polytypes crystal offers high mobility compared to 6HSiC, but 6H-SiC is extremely better material for optoelectronic device compared to 4HSiC and C-SiC. Combining all atoms in a hexagonal pattern is called “Crystallography”
in fact known as hexagonal close packing.
Initially silicon carbide was known as “Carborundum” which exist in nature in
rare condition as a mineral known as moissanite. Powder form of SiC was used in
abundance in1893 as an abrasive. For instance, ceramic plates, car brakes and bullet
proof vests. The electronic use of SiC as LED lights started from 1907. In the recent
years these are used as a high temperature and voltage semiconductor devices. High
4
quality of SiC crystals are formed by a method referred as “LELY”. These SiC crystals
are cut into gems called as “moissanite or synthetic”.
Moissanite is a natural occurring element in less quantity which is partitioned as
certain moissanite and carborundum. Dr. Ferdinand Henri Moissan introduces moissanite
in the year 1893 in Arizona State. He was the one who discovered Silicon Carbide (SiC)
[47]. Below Figure 1 shows the picture of silicon carbide wafer.
Figure 1: Figure showing Silicon Carbide (SiC)wafer
The recent advancements in this technological world, SiC is now used to comply
many purposes. In the recent study it was shown that SiC occurs naturally in outer space
as in meteorites in small quantities [48]. “Murchison known as contrite meteorite which
is related to the ratios of silicon as well as carbon which implements the starting point
from the outside, out of 100 percent SiC grains originate around 99 percent and the else is
5
originated by carbon rich branch stars” [49]. Below Figure 2 shows the picture of
moissanite stone.
Figure 2: The figure shows Moissanite stone
Silicon Carbide (SiC) was determined to use as the best semiconductor device due
to its properties like “high melting point, thermal stability, chemical stability and high
resistance. It has a wider band gap (2.3 eV for 3C-SiC, 2.9 eV for 6H-SiC and 3.3 eV for
4H-SiC)”. “The critical field of SiC is approximately eight to ten times higher that of
later”. This will result in the high voltage SiC devices can be released with much thicker
drift layers and with high doping [50].
The production of silicon carbide manually is done by “Acheson Process”. This
process has a number of steps with a final product of high material quality SiC. The other
procedures are listed below.

“Chemical Vapor Deposition (CVD)”.
6

“Physical Vapor Deposition (PVD)”.

“Liquid Phase Sintering (LPS)”.

“Mechanical Alloying (MA)”.
The union of 2-D effects is important for small device channels. In long channel devices
it is nonlinear with respect to the channel depth. So, a one dimensional structure is used
to describe all the parameters to avoid the above given cases [51]. The Figure 3 below
shows the “structure of Silicon Carbide”.
Figure 3: Structure of SiC
In 1907, the SiC was used in electronic applications and also used as LEDs. SiC is
required in making semiconductor device with high temperature and pressure. The large
crystals of SiC are cut in to small pieces by LELY method. These small crystals are
called Synthetic Moissanite. Figure 4 shows the “3D structure for SiC”.
7
Figure 4: 3D structure of SiC
For making semiconductor devices SiC is used as an enduring applicant. Due to its
various properties it has many uses. SiC is used as abrasive as it is very hard and used in
very high temperatures. Figure 5 shows “grains of black SiC”.
Figure 5: Grains of black SiC
All the doping techniques are not successful with SiC. For example, the ion implantation
with SiC is not a success till late. But with new technologies a lot of development and
improvement have been seen in the growth of SiC and ion implementation techniques
[52].
8
2.1 History of SiC:
Scientists found many methods to process SiC. A bowl of clay and coke were attached to
a lead. They were only able to see few sparks in the lead. Then they placed the lead on a
glass plate. It was SiC which became the first material to cut the glass plate. The
scientists identified this process as Acheson process.
In 1855, a furnace was made for this process and then they discover silicide of carbon
and gave a chemical name as SiC. It is naturally found in meteorites.
Figure 6: SiC material used in steel making
The above Figure 6 shows SiC material for steel making. Many SiC LED‟s, diodes,
FETs are largely produced and many devices are yet to come. In late 1970s silicon
technology was widely used which is equal to wide band gap technology. SiC wafers are
very expensive and delicate. “Their size is less than 4 inch”.
2.2 Material defects of SiC:
2.2.1 Point Defects:
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
“Vacancies”: These vacancies are caused when an atom is removed from an
atomic site.

“Interstitials and self-Interstitials”: These defects are seen when an atom is
triggered in to a non-lattice site.
2.2.2 Linear Defects:

“Dislocations”: They are caused due to the lack of lattice imperfection.
2.2.3 Planar Defects:

“Stacking Faults (SF‟s): They are caused due to the interruption of the original
sequence in the local regime”.

“Low Angle Boundaries (LAB‟s)”: They occur when the crystalline solid consists
of more grains. No long range stress.

“Twins”: As the crystal is cut in the process, the original structure takes a new
shape.

“Inversion Domain Boundaries (IDB‟s)”: They occur when the interstitial atoms
of a bond are inverted with each other.
2.2.4 Volume Defects:

“Inclusion of Different Polytypes: At the time of growth procedure, they occur
during phase transformation” [53,54].
10
Table 1 shows the “SiCpolytypes electrical properties”
Table 1: SiCpolytypes electrical properties
GaN and SiC are almost similar in nature because GaN is grown on SiC
substrates. But taking cost into account it can be grown on silicon and sapphire wafers
too. Due to its wider band gap it provides high breakdown voltages and operates at high
temperatures [55]. Figure 7 shows the “properties of breakdown voltages” for Si, GaAs,
SiC and GaN, where the maximum breakdown voltage is obtained from SiC material.
11
Figure 7: Figure shows break down voltages for different materials
“The implementation of thermal conductivity in Gallium Nitride is 2 times higher than
Gallium Arsenide i.e., GaN= 2*GaAs”. The Motorola's cross hybrid circuit innovation
which is protected in the Gallium Nitride semiconductor property which are depicted
over the formation of new era crossover pick up in the square intensifiers that are utilized
to show prevalent execution in both amplifier and node applications [56].
2.3 Energy Band Diagram
It is a graphical representation of energy bands that are formed by the
combination of molecular orbital in energy. “Due to the mass amounts of different
molecular energies different energy bands are formed and are known as energy bands”
[57]. This energy bands are represented by a graph known as energy band diagram.
12
Figure 8: Energy band diagram of 4H-SiC
The energy band diagram of 4H-SiC is shown in Figure 8. The energy band gap of
3.23eV of 4H-SiC is found in the L-valley at the conduction band minima and valence
band maxima at k ≠ 0 and therefore, semiconductor is found to be indirect bandgap. The
bandgap energy in τ valley differs from 5-6 eV and the bandgap energy gap in L valley is
(EL) is 4 eV. The split off band in the valence band is 0.007 eV. The separation energy
between low and upper conduction bands in M-valleys. The temperature dependent band
gap can be calculated from the following Equation.
“Eg = Eg(0) - 6.5 x 10-4 x T2/(T + 1300)”………………………………. (1)
Where,
Eg is “indirect bandgap of 4H-SiC”
T is the temperature (300 K)
13
The below Figure 9 shows the graphical representation of “excitonic energy gap of
SiCversus temperature”.
Figure 9: 4H-SiC excitonic energy vs. temperature
The following Figure 10shows the energy band diagram for 3C, 4H and 6H SiCmaterials
for different temperatures.
14
Figure 10: Band gap for 3C, 4H and 6H SiC
In Figure 10, the energy gap of 6H-SiC material varies from 3.03eVto 2.8ev for the
temperature range from 700oKto 0oK. Energy gap for 3C-SiC varies from 2.2 eV to 2.38
eV for the temperature range from 780oK to 0oK.
Intrinsic carrier concentration is very important parameter to bring the
indispensible quality of SiC as a wide band gap device. The intrinsic concentration can be
calculated by the following Equation (2)
15
ni = (Nc·Nv)1/2exp(-Eg/(2kBT))………………………….. (2)
Where,
NC =“effective density of states in the conduction band (NC)”and
T = Temperature in K
The effective density of states in the conduction band (NC) can be derived by using the
following Equation (3):
“Nc= 3.25 x 1014 x T3/2(cm-3)”……….. (3)
The effective density of states in the valence band (NV) can be derived by using the
following Equation (4)
NV= 4.8x1015 x T3/2 (cm-3)………….. (4) [58].
The Figure11 shows the “temperature dependence intrinsic concentration of 3C, 4H and
6H SiC”calculated from the Equation (3) and (4).
16
Figure 11: Intrinsic carrier concentration of 3C, 4H and 6H SiC
2.4 Drift velocity graph for SiC:
The below Figure 12 shows the graphical representation of “drift velocity vs. electric
field for 4H-SiC”and no negative differential resistance is observed.
17
Figure 12: Drift velocity vs. electric field for 4H SiC
From the graph, it is observed that the drift velocity increases for increases in electric
field up 5000kV/cm and the value of drift velocity became slight low at high electric
field. The SiC material is still due to reach the maturity of material growth and material
characterization. The drift velocity at high electric field may show low value due to the
defects. In the graph the curve 1 and 2 shows the drift velocity for SiC at temperature of
300 K and curve 3 and 4 for temperature 600 K [59].
.
18
2.5 Characteristics of SiC and SiC based devices:
The large band gap of SiC helps it to use in high temperature without changing its
electrical properties due to which it has high frequency and power applications. The heat
dissolute very quickly as the thermal conductivity is very high in SiC. It has very high
pressure. Sic has “field strength 10 times than Si” and has high drift velocity than Ga As.
Due to these properties SiC is used in extreme environment conditions and can be
operated at high frequencies.The below Table 2 shows the “properties for SiCpolytypes”.
Table 2: SiC polytypic properties
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3. ION IMPLANTATION
3.1 Ion Implantation:
The diffusivities of impurity species are extremely low. The doping process by using the
diffusion process cannot meet the substantial value of diffusion coefficient of impurity
atoms in SiC. Hence, the doping process is preferred by ion implantation followed by
high temperature annealing. When the device dimensions and power supply voltage are
decreased, all the applications of the SiC MESFET becomes attractive and the ion
implantation which helps in making the channel of the device helps to control uniformity
and reproducibility in fabricating the device.
Ion Implantation is the process of producing ions of an element in the special
equipments. It constitutes of an ion source, ion extraction, ion separation magnet, ion
acceleration and a target. Firstly the dopants are induced to ion source. Then the ion
extractor extracts it. The dopants are separated from the dangerous elements through ion
magnet separator and then accelerated to the target element. The impurities are shelled in
to the lattice with dopant ions.
The metals such as B+, Al- and Ga+ are kept at room temperature to make p-type
conductivity use ion implantation process. SiC when kept at room temperature does not
successfully provide p and n type conductivity using above process.
20
These diodes form an area of mono crystals when SiC with initial conductivity is induced
with SiC with different conductivity at high temperature [60]. Figure 13 is the “flow chart
for ion implantation”.
Figure 13: Flow chart of ion implantation
21
3.2 Process of surface modification:
This process takes place “at very low pressure (from 10-4 to 10-5torr) in a vacuum
chamber”. The shelling of ions “(from 1016 to 1017 ions/cm2) perforate interacting” with
the atoms under the surface. The modification takes place when the ions collide with each
other due to which it has different properties. Figure 14 shows the “direct ion
bombardment surface”.
Figure 14: Direct ion bombardment surface
There are many steps used to make ion. Firstly the electronics are removed from
the source. Only desired ions are selected through ion separating magnet and also
separate ions from dangerous particles. The ion acceleration column accurate them. “10200 KeV are the ion energies”. Finally, electromagnetic lens shape the ion stream, check
22
the performance in the scanning and sends it to the station where the ion is implanted
[61]. The doping distribution of ion implanted layer can be defined by
The equation for ion implantation is given by the Equation (5)
“𝑁(𝑥) = 𝑁𝑃 exp
Where𝑁𝑃 =
− 𝑥−𝑅𝑃 2
2 ∆𝑅𝑃2
𝑄
∆𝑅𝑃 2𝜋
− 𝑁𝐵 ” ………………. (5)
…………………. (5a)
The junction depth (𝑥𝑗 ) can be defined as Equation (6)
𝑁
𝑥𝑗 = 𝑅𝑃 ± ∆𝑅𝑃 2ln⁡
( 𝑃 )……………………. (6)
𝑁𝐵
The Figure 15 shows the ion implanted distribution graph before annealing
Figure 15: Distribution before annealing
23
3.3 Stopping and Range of Ions in Matter (SRIM)
Electronic stopping and nuclear stopping:

“Electronic slowing down means slowing down because of the inelastic collisions
between electrons in the medium”.

“The term inelastic is used for the collisions may result in excitations in the
electron cloud, so the collision should not be treated as a classical scattering
process for two charged particles”.

“The kinetic energy of a colliding electron is higher than the ionization energy of
electrons bound to the ion, the inelastic collisions strip electrons from the
recoiling ion”.
In this thesis the values of implant range parameter (RP) and straggle parameter
(σ) have been extracted from SRIM software for different ionization energies for
annealing at high temperature of 19000C. Using nitrogen as dopant. Below Table 3
shows the respective values from SRIM software. Where projected range is RP and
lateral straggling is σ.
24
Table 3: Values extracted from SRIM
25
3.4 Annealing:
The resistivity increases when the ion implantation process is completed in SiC
devices. It increases due to the deep level holes and electrons that obstruct the carriers to
flow freely in the channel [62]. The Equation (7) used for determining the impurity
concentration in annealing technique is as below
“𝑛 𝑥 =
𝑄𝑇
𝜍𝑃2 +2𝐷𝑡
𝑒
2
− 𝑥 −𝑅 𝑃
)
2 𝜍2
𝑃 +2𝐷𝑡
(
2𝜋
− 𝑁𝐵 ”…………………… (7)
Where,
QT= “Ion Dose”
RP= “Implant range parameter”
σp= “Straggle parameter”
D= “Diffusion coefficient of impurity due to annealing
temperature”
t= “Annealing time” and
NB = background concentration
Due to hard annealing temperature of 1800-2000oC, the impurity dopant will be diffused
in the bulk of SiC material and therefore the junction depth will be increased with an
exponential effect in tail-end showing an evidence of impurity diffusion. After annealing
the junction depth can be calculated as below
26
∆𝑅𝑃 =
𝜍 2 + 2𝐷𝑡…………………. (8)
Substituting Equation (8) in Equation (5a), the peak concentration yields as
𝑁𝑃 =
𝑄
𝜍 2 +2𝐷𝑡
2𝜋
…………………….. (9)
So the final junction depth after annealing can be defined as,
𝑄
“𝑥𝑗 = 𝑅𝑃 ±
𝜍 2 + 2𝐷𝑡 2ln⁡
(
𝜍 2 +2𝐷𝑡 2𝜋
𝑁𝐵
)”………………. (10)
Figure 16showsthe comparative plots of “Gaussian profiles for ion implantation”
andpost-annealing. ΔRp shows the straggle parameter of ion implantation process,
whereas the straggle parameter will increase by (2Dt)1/2 and therefore the revised
standard deviation factor of Gaussian profile is increase by ΔRp + (2Dt)1/2.
Figure 16: Gaussian profile after annealing
27
3.4.1 Furnace Annealing:
It is a process to affect the electrical properties of a semiconductor wafer. It
changes the film to film and film to substrate concentration. It is also used in furnace
processing, oxidation and many other independent processes. These furnaces can handle
many wafers at a time. This process takes a lot of time to complete.
3.4.2 Rapid Thermal Annealing:
This process was developed to reduce annealing time and is used to repair
damages in the lattice. “It uses an activation energy of 5eV decreasing the diffusion of
dopant. The dopant has activation energy of 3eV to 4eV”. Due to the difference in
voltage, the repairs in lattice are easier at high temperatures.
Isothermal annealing is a very common type of rapid annealing used to
manufacture tungsten halogen lamps. Figure 17 shows “rapid thermal annealing system”.
Figure 17: Rapid thermal annealing system
Figure 18 shows “furnace of rapid thermal annealing system”.
28
Figure 18: Furnace of rapid thermal annealing system
3.5 Applications:

“Used in the manufacture of aircraft components due to its enormous properties”.

“Used in the manufacture of semiconductor devices”.

“Also used in military equipments, paper industry, glass cutting industry and
chemical processing industry”.

“Used in the manufacture of heavy machinery which is required for underground
usage where there is high temperature and pressure”.
3.5.1 Why Ion Implantation is preferred for SiC doping:

“Provides a very high dosage control”.

“Independent control of impurity distribution and dose”.
29

“Ion implantation is preferred over diffusion based doping because of the
exceptionally slow diffusion rate of impurities in SiC and the preponderance of
interstitial diffusion, rather than substitution diffusion” [63].
3.6 Fabrication
Different masks of fabrication process of a MESFET are as below. There are four
different masks in this process.

“Channel Implantation”

“Source or drain Implantation”

“Contact formation”

“Gate formation” of Schottky
Positive resist masks are used in this process. Fabrication steps are as below

“Firstly, the wafer should be clean”.

“With a cap thickness of 100nm make a deposition using silicon nitride by
reactive sputtering”.

“The silicon ion implantation of device in the channel regions is done with a
maximum energy of 180 keV and ion dose of 5×1012/cm2”.

For the alignment purposes silicon nitride is shallow etched.

Plasma is ash stripped in presence of oxygen.

The patterning of drain and source implant is done by a positive resist with
thickness of 0.8µm.
30

In source and drain regions, the silicon is ionized in single fashion with ion
energy of 200 keV.

The implanted ions are then processed for annealing by thermal annealing which
is rapid. “It has a temperature of 850oC for 2 minutes”.

After annealing the patterning resist contains ohmic formations with a thickness
of 0.8µm.

The semiconductor surface is then etched by CF4.

And the semiconductor surface with the ohmic contacts is etched by SiN.

Lastly the semiconductor surface is wet etched by GaAs surface with a solution of
50% HCL.

Aluminum gets deposited in the gate formation of schottky by electric beam
evaporation known as patterning [64].
The Figure 19 below shows the “process of fabrication” stepwise.
31
Figure 19: Fabrication process of MESFET
3.7 Ion implantation process induced damage

High energetic ions destroy the crystal structure of the target material by using ion
implantation for doping Si.
32

Due to the lattice damage which consists of distribution of frequencies and
distribution of interstitials.

Stable extended defects such as clusters or dislocations are formed due to point
defects which are extremely mobile.

To restore the original crystal lattice, it must be thermally annealed.

As an example the lifetime for minority carriers is reduced to 1 ns for a low dose
(1012 cm-2) boron implant at 100 keV.
Figure 20: Implanted p+ -n diode structure
Figure 20 shows the “implanted p+ -n diode structure”.
33
4. MESFET PHYSICS
4.1 MESFET:
It is expanded as “Metal Epitaxial Semiconductor Field Effect Transistor”. Since,
MESFETs use high frequency amplifier and high performance applications in microwave
domain, they are also known as Field Effect Transistors (FET).
In 1949, the first semiconductor technology for bipolar junction transistor was
invented. MESFET is the first semiconductor which has electronic components.
In 1953, the MESFET‟s technology became important to develop FET in practical
form. This technology was affordable and it was very easy to produce pure form of
semiconductors more in the quantity using this technology. This technology also helped
in the production of layers of oxide.
In 1960, the first MESFET was produced along with semiconductor technology.
With the semiconductor technology other device were also developed like Gallium
Nitride FETs, Gallium Arsenide FETs etc. The first MESFET was developed in 1966
with extra high frequency and microwave performance [65].
4.2 Types of MESFET:
There are two types of MESFETs which are described below:
1. Enhancement (Normally-off) MESFET and
2. Depletion (Normally-on) MESFET
34
4.2.1
Enhancement MESFET:
It is also known as n-channel MESFET where the whole channel with another layer
called depletion and all the device stays in off state. The channel expands more due to
narrow region. Due to this reason there is an ease in the flow of carriers.
4.2.2
Depletion MESFET:
In this n-channel MESFET when the depletion region changes, the Vg also changes. The
non-positive energy stops the carrier flow at a terminal known as Gate and Source. So the
expansion of depletion region takes place. Due to which a reverse biased junction is
formed at the gate and channel terminal which acts like a switch. This switch is called
pinch off. As a result there is high resistance between the source and drain terminal. Due
to SiC material, SiC based MESFET always offers depletion device and enhancement
mode SiC MESFET is extremely hard to fabricate, but recently CREE was successful to
fabricate the enhancement mode SiC based MESFET. Figure 21 shows the usage ranges
in enhancement and depletion MESFET through the varying threshold voltages.
35
Figure 21: Usage ranges in enhancement and depletion mode
By changing the potential applied, the changes in the field occurs which give rise to three
different regions
-
Linear region
-
Saturation region
-
Pinch off region
4.3 structure and characteristics of MESFET:
The Figure 22 below shows the “structure of MESFET”.
36
Figure 22: Basic structure of MESFET
The depletion region forms under schottky contact and is also known as Gate. So,
due to very high modulation in the speed, this device also acts as a switch and a voltage
controller.
“Thus as a result when the operation goes through the current and voltage
characteristics at Vgs at different voltages are shown in the Figure 25 below”.
37
Figure 23: Graph showing I-V characteristics for SiC MESFET
The above Figure 23 shows the plot of drain current Vs drain voltage.
In MESFET, we can apply more drain-source voltage. This mode of operation in
MESFET is known as Breakdown mode [66].
4.4 SiC MESFET structure and characteristics:
The given Figure 24 below shows the “basic structure of MESFET”.
Figure 24: Basic structure of MESFET
38
Due to its high temperature, pressure and voltage SiC can be replaced with silicon
substrate. Due to its fundamental advantages it can be used in the manufacture of the
devices which work in high voltage and high power conditions.
“The below table gives an idea about the physical properties between the Silicon,
4H-Silicon carbide, Gallium Nitride and Diamond.”
The Table 4 below shows that the “diamond lacks in the surface area but has high
thermal conductivity”.
Properties
Si
4H-SiC
GaN
Diamond
(x10-6)/oC
2.6
4.2-4.7
5.6
1-2
Band-gap (eV)
1.12
3.02
3.45
5.45
Carrier Mobility (cm2/Vs)
150
1000
125
Thermal Expansion
2200
Electron
0
0
1600
Hole
600
50
250
Dielectric Constant
11.8
9.7
9
5.7
150
490
130
2000
Thermal Conductivity
(W/mK)
Table 4: Comparison between different wide band gap materials
39
4.5 Functional Architecture of MESFET:
The below Figures 25 show a “graphical idea of the silicon carbide MESFET”. It
consists of source, drain and gate with SiC as high insulating material which is used for
high voltages.
Figure 25: SiC MESFET schematic
The Figure 26 below shows the “high resistivity SiC substrate”.
Figure 26: High-resistivity SiC substrate
The Figure 27 below shows a “SiC MESFET with channel length „a‟ and gate
length „L‟”. MESFETs have many advantages compared to MOSFETs. MESFETs have a
very low noise factor due to low scattering effect. Therefore it is also known as majority
carrier substance. For high frequency and current and large values of transconductance
gm, the important factor is the mobility of electrons in the device [67].
40
Figure 27: MESFET with gate length ‘L’ and active channel length ‘a’
4.6 Advantages of MESFET

“High saturated Electron velocity”.

“Chemically inert”.

“High melting point”.

“Wide energy band gap device”.

“High electrical and thermal conductivity”.
4.7 Applications of MESFET

“Wireless communication”

“Power amplifiers”

“Microwave circuits”
41
5. THEORY AND MODEL
The cross sectional view of silicon carbide MESFET is shown in the Figure 28 below.
The asymmetric gate structure was considered because of avoiding the electric field
crowding to enhance the breakdown voltage.
Figure 28: Cross section of Silicon carbide MESFET
5.1 Threshold voltage of SiC MESFET
In order to develop the analytical model, one dimensional Poisson‟s equation with X
dimension is considered and the Equation (13) presented as
𝜌
ϕ''(x) = - 𝜖 …………………… (13)
42
and the boundary conditions for the equation (13) has been stated as below Equations
(13a), (13b) and (13c)
ϕ'(XDG)=0 ………………….. (13a)
ϕ(0)= VG- ϕB…………………… (13b)
ϕ(XDG)= -Δ+V(y) ………………… (13c)
Where,
ΦB =“metal- semiconductor work function difference”
ϕ(0) =“surface potential”
Δ = “depth of the Fermi level below the conductionband in undepleted region”
V(y) = “voltage at source”
So for the above equations the threshold conditions are given as below Equations (13d)
and (13e)
XDG = XDS= XPM………………… (13d)
Vp= V(y) = 0 ………………….(13e)
So the threshold voltage can be calculated by below Equation (13f)
ϕ(0) = VT - ϕB
………………………. (13f)
The threshold voltage for SiC MESFET is given as below Equation (14)
43
“𝑉𝑇 = ϕB − Δ −
4N A
Q
2E
qN A
q∗Q∗R P
2E
Vbi − VBs +
erf
Rp
2σ
+1−
8N A E
2E
qQ 2
qN A
2N A
2E
Q
qN A
Vbi − VBs
−
q∗Q∗σ
E 2π
R 2p
[exp − 2σ 2 −
Vbi − VBs ]” ………………… (14)
where,
Q: “Implant dose”
VGs: “Gate to source voltage”
E: “dielectric constant”
VDs: “Drain to source voltage”
VBs: “substrate to source voltage”
a: “Active channel layer thickness”
Vbi: “Built-in potential”
Nd: “Doping concentration”
Na: “Substrate concentration”
σ: “Straggle parameter”
∆: “Depth of Fermi level below the conduction band
in the undepleted channel”
Rp: “Implant range parameter”
ϕB:
“Metal-
difference”
44
semiconductor
work
function
5.2 I-V Characteristics of Silicon carbide MESFET
The field dependent mobility for describing a device operation can be incorporated by the
drain current and the gradual channel approximation is used to evaluate the channel
current as
𝑍
“IDs=𝑞 ∗ µ ∗ 𝐿 ∗
𝑉𝐷𝑆
0
𝑄𝑛 𝑉 ∗ 𝑑𝑉 ” ……………………… (11)
Where,
µ: “Electron mobility”
Z: “Device width”
q: “charge of electron”
L: “Device length”
Qn: “Mobile channel charge”
The equation to calculate the channel charge Qn is given as in below equation.
“𝑄𝑛 =
𝑋 𝐷𝐺
𝑋 𝐷𝑠
𝑁(𝑥)𝑋𝑑𝑥” ……………………… (11a)
Where,
XDG= “distance from surface to edge in gate depletion region of the channel”
XDS= “distance from surface to edge in substrate depletion region of the channel”
The current equation for the I-V characteristics are derived with gradual channel
approximation is as below Equation (12)
45
𝑍
“𝐼𝐷𝑠= 𝑞 ∗ 𝑄µ 2𝐿 𝑉𝐷𝑠 1 + 𝛼 −
2∗𝑞∗𝑁𝐴2
3∗𝑄∗𝐸
3
2𝐸
[[𝑄𝑁 ][𝑉𝑏𝑖 − 𝑉𝐵𝑠 + 𝑉𝐷𝑠 ]]2 +
𝐴
𝑉𝐵𝑠
2∗𝑞∗𝑁𝐴2
3∗𝑄∗𝐸
2𝐸
[[𝑄𝑁 ][[𝑉𝑏𝑖 −
𝐴
]]32−𝑄∗𝑞∗𝜍3∗𝐸2𝜋
[𝑎2−2𝛼𝐶1+𝐶12+𝑅(𝑉𝐵𝑠−𝑉𝐷𝑠+ϕB−𝛥)]23+𝑄∗𝑞∗𝜍3∗𝐸2𝜋[𝑎2−2𝛼𝐶1+𝐶12+𝑅 −𝑉𝐺𝑠
+ϕB−𝛥)]23”
…………………………………….. (12)
Where,
“α
=
Rp
2
2σ
π
”………………………………..(12a)
E 2π
"R = qQσ "……………………………….. (12b)
"C1
R
= erf [σ p2]"...................................... (12c)
Nd: “Doping concentration”
Na: “Substrate concentration”
σ: “Straggle parameter”
∆: “Depth of Fermi level below the conduction band in the undepleted channel”
Rp: “Implant range parameter”
ϕB: “Metal- semiconductor work function difference”
Q: “Implant dose”
VGs: “Gate to source voltage”
E: “dielectric constant”
VDs: “Drain to source voltage”
46
VBs: “substrate to source voltage”
a: “Active channel layer thickness”
Vbi: “Built-in potential”
5.3Transconductance of SiC MESFET
The main parameter which determines the quality of a semiconductor for
microwave applications is Transconductance [68]. And it is defined as below Equation
(15)
“gm
=
dI d
”....................................... (15)
d Vgs
When the current equation (2) is differentiated with respect to gate voltage V gs
keeping the drain voltage Vds as constant we obtain Transconductance as in below
Equation (16)
“g m
=
q∗µ∗Z∗Q
4L
∗[
1
ap V1
+
1
V 2 α+1−a p
](VGs − VT )”………….. (16)
Where,
2
𝑞∗𝑄
“𝑉1 = 8𝑁 𝐸” ………………. (16a)
𝐴
“𝑉2 =
2
𝑞∗𝑄 2𝐷𝑡+𝜍
2𝜋𝐸
"………………… (16b)
47
“𝑎𝑝 =
2∗𝑁𝐴
2∗𝐸(𝑉𝑏𝑖 −𝑉𝐵𝑠 +𝑉𝑝 )
𝑞
𝑄𝑁𝐴
"
…………… (16c)
VP= “Pinch off voltage”
VT= “Threshold voltage”
t= “Time”
D= “Diffusion constant”
The diffusion coefficient can be calculated as
−(𝐸𝐴 ×𝑞)
“𝐷 = 𝐷0 exp⁡
(
(𝐾×𝑇)
)”……………………………… ()
Where,
D= “diffusion constant”
EA= “activation energy” = 40meV
T= “annealing temperature” = 2173oK
K= “Boltzmann constant” = 1.38066×10-23 J/K
q= 1.60219×10-19C
D0= 0.69×10-15
The calculation for diffusion coefficient is shown as below
𝐷 = 0.69 × 10
−15 [
𝑒
−(40×10 −3 ×1.6029 ×10 −19 )
]
1.38066 ×10 −23 ×2173
D= 5.5159×10-16
48
Table 5 below shows the RP and σ values for two ionization energies extracted
from SRIM.
Ion energy (keV)
Implant
range
parameter Straggle parameter (σ)
(RP)
100 keV
0.1577×10-4 cm
0.0375×10-4 cm
150 keV
0.2276 ×10-4 cm
0.0486 ×10-4cm
Table 5: showing Rp and σ values for different ion energy
Table 6 shows the values of diffusion coefficient and diffusion constant length at
different annealing temperatures
Temperature 1800oC
1900oC
2000oC
2100oC
2200oC
D
5.5152×10-16
5.5159×10-16
5.6249×10-16
5.6736×10-16
5.7605×10-16
(Dt)1/2
1.99×10-6
2×10-6
2.01×10-6
2.02×10-6
2.03×10-6
Table 6: diffusion constant values at different annealing temperature
The calculation for nc, nv and ni is calculated below
nc= 3.25×1014× (T)3/2
Nc= 3.25×1014× (7200)3/2 = 1.6887×1018
Nv=4.8×1015×(T)3/2 = 2.4942×1019
ni =(Nc·Nv)1/2exp(-Eg/(2kBT))
= (1.6887×1018×2.4942×1019)exp(-(3.23)/(2×1.3807×10-23×7200))= 4.8465×10-9
49
6. RESULTS AND DISCUSSIONS
I-V characteristics, threshold voltage and transconductancehave been developed of an
analytical model of SiCMESFET.
Figure 29: graph showing I-V characteristics for ion energy 100 keV
Figure 29shows a plot of drain-source current versus drain-source voltage for different
gate-source voltage Vgs = 0V, -2V, -6V and -10V afterhigh temperature furnace
annealing of 1900oC and the ion implantation energy of 100KeV. The fabrication
parameters such implant range parameter (Rp) of 0.1577x10-4cm and straggle parameter
(σ1) of 0.0375x10-4cmhave been extracted from SRIM. The diffusion characteristics
50
length of 2.8328x10-6cmhas been calculated from the nitrogen activation energy of
40meV for the temperature of 1900oCand the doping concentration shows a compatible
value to justify the depth of the Fermi level of 0.0190 depicted in the graph. The
maximum drain currents after linear region at the drain-source voltage Vds of 60V show
the range of 5.2A, 5.5A, 6A and 6.5 A for corresponding gate voltage Vgs = 0V, -2V, 6V and -10V respectively.
The drain currents of SiC based MESFET considering
different post implanted parameters show a compatibility with the fabricated device.
Figure 30: graph showing I-V characteristics for ion energy 150 keV
Figure 30 presents a graph of drain-source current versus drain-source voltage for
different gate-source voltage Vgs = 0V, -2V, -6V and -10V for the ion implantation
51
energy of 150KeV followed by high temperature annealing of 1900oC. The implant range
parameter (Rp) of 0.1577x10-4cmand straggle parameter (σ1) of 0.469x10-4cmhave been
extracted from SRIM for implantation energy of 150KeV. The standard deviation of
Gaussian profile presenting the impurity distribution increased due to diffusion
characteristics length of 2.8328x10-6cm, which has been calculated from the nitrogen
activation energy of 40meV for the temperature of 1900oC and the doping concentration
shows a compatible value to justify the depth of the Fermi level of 0.0773 depicted in the
graph. The maximum drain currents after linear region at the drain-source voltage Vds of
120Vwas observed in the range of 8.5A, 8.7A, 9.4A and 9.9 A for corresponding gate
voltage Vgs = 0V, -2V, -6V and -10V respectively. The drain currents of SiC based
MESFET considering different post implanted parameters show a reasonable value of the
fabricated device.
52
Figure 31: graph showing I-V characteristics for two ion energies (100 keV and 150
keV)
Figure 31 displays a comparative plot of drain-source current (Ids) versus drainsource voltage (Vds) for gate-source voltage Vgs = -2V for ion implantation energy of
100KeV and 150KeV followed by high temperature annealing of 1900oC. The implant
range parameters (Rp) of 0.1577x10-4 cm and 0.2276x10-4 cm and straggle parameters
(sigma) of 0.0375x10-4cm and 0.0486x10-4cm have been tabulated from SRIM for
implantation energy of 100KeV and 150KeV.
The comparative study of I-V
characteristics for same ion doses of Q = 3.75x1013 /cm2 shows the maximum current of
6.2A for 150KeV and 4.9A for 100KeV ion implantation energies. The result concludes
that the higher ion implantation energy forms larger junction depth compared to low ion
53
implantation energy, which-in turn increase the active channel depth of MESFET. As a
result, the large drain current is obtained for high ion implantation energy, which obeys
the fabrication process and device physics.
Figure 32: graph showing threshold voltage versus ion dose for two ion energies
(100 keV and 150 keV)
Figure 32 shows the graphical representation of threshold voltage (Vt) versus the
ionization dose (Q) for two ionization energies of 100 keV and 150 keVin SiC MESFET.
The implant range parameter (Rp) for 100 keV and 150 keV extracted from SRIM are
0.1577×10-4 cm and 0.2276×10-4cm respectively. The straggle parameters (σ) for the
same energies are 0.0375×10-4cm and 0.0486×10-4cm respectively. The substrate
54
concentration used to plot this graph is 1×1015cm-3. The diffusion characteristic length for
the high temperature annealing of 1900oC is calculated as 2.8183×10-6cm. The ion doses
varied from 1×1012cm-2to 2.6×1012cm-2 to obtain the threshold voltages ranging from 1.6V to -6.9V and -0.5 to -3.9V for ionization energies of 100keV and 150keV
respectively. SiC MESFET is a depletion mode device so negative values of threshold
voltages confirms it.
Figure 33: graph showing transconductance versus gate voltage for 150keV
Figure 33 shows the sketch of transconductance (gm) versus gate voltage (Vgs) in
SiC MESFET. The implant range parameter (Rp) and straggle parameter (σ) are
0.2276×10-4cm and 0.0486×10-4cm respectively for 150 keV ion energy. The
transconductance is seen increasing with gate voltage from -1.5V to 1.5V. The high
55
values of transconductance conclude the use of this SiC MESFET device at high
frequencies.
56
7. CONCLUSION
A physics based analytical model of ion implanted SiC MESFET has been developed
taking into account of the high temperature annealing effects. The diffusion of nitrogen
implanted ion impurities has been computed by appropriate activation energy of impurity
atoms, which showed that high temperature annealing is required to activate high
percentage of impurities. The impurity distribution of impurities has been calculated by
incorporating (1) the implant range parameters and straggle parameters for 100KeV and
150KeV ion implantation energy from SRIM and (2) diffusion characteristics length due
the impurity diffusion in the bulk during high temperature. The diffusion effect on I-V
characteristics, threshold voltage and transconductance have been significantly observed
for two ion implantation energies of 100KeV and 150KeV considering the high
temperature annealing.
A comparative study on I-V characteristics for two ion
implantation energies and annealing effect shows tremendous effect for process
development of SiC MESFET to optimize the device performance for power aided
efficiency and power density. The shift of threshold voltage was significantly observed
for two ion implantation energies of 100KeV and 150KeV under high temperature
annealing to study the enhancement and depletion MESFET influenced by ion dose and
diffusion of impurities during high temperature annealing. The study of threshold shift by
the influence of fabrication process is important to understand the properties of switching
performance of SiC MESFET. The transconductance under influence of high temperature
57
annealing was evaluated to justify the threshold voltage. The high temperature annealing
effect on transconductance was found to be large value to promote high frequency
response of SiC MESFET device.
58
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66
APPENDIX-A
Notations and Symbols Used:
Rp: Effective ion Implant Range Parameter
σ: Implant Straggle Parameter
ε: 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
67
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
gm: Transconductance
68
APPENDIX-B
Matlab code for Drain current (Ids) versus Drain voltage (Vds) for Ionization
energies of 100keV and 150keV
clc;
clear all;
close all;
% constants
K=1.38066e-23;
q = 1.60219e-19;
Na=1e15;
T=300;
Eg= 3.21;
u=500;
Nc=3.25e14*sqrt(T*T*T)
Nv= 4.8e15*sqrt(T*T*T)
Ni= sqrt(Nc*Nv)*exp(-(Eg*q)/(2*K*T))
Z= 100e-4;
L= 2e-4;
pi= 3.1459;
% annealing time for 2 hours
time= 7200;
Phib = 1.27;
do= 0.69e-15;
Q=3.75e13;
q = 1.602e-19;
Eo= 11.9;
E= Eo*8.854e-14;
T2= 273;
% T1 is annealing temperature
69
T1= 1900+ T2;
% Ea is activation energy
Ea= 40e-3;
diff= do* exp(-(Ea*q)/(K*T1))
% Rp = 0.1577e-4 cm Sigma1 = 0.0375e-4 cm for ion implantation energy
100 KeV
% Rp = 0.2276e-4 cm Sigma1 = 0.0486e-4 cm for ion implantation energy
150 KeV
Rp= [1577e-8 2276e-8];
sigma1= [375e-8 486e-8];
Vbs=0;
Vt= (K*T)/q;
Vds= 0:1:60;
Vgs= -2;
A= (q*Q*u*Z)/(2*L);
x= 0.08e-4
for k =1:2
for i=1:61
sigma= sqrt((sigma1(k)*sigma1(k))+(2*diff*time))
Alpha= Rp(k)/(2* sigma)*sqrt(pi/2);
Nd1= Q/(sigma*sqrt(2*pi))
Nd2= exp(-(((x-Rp(k))/(sigma*sqrt(2)))*((x-Rp(k))/(sigma*sqrt(2)))))
Nd= Nd1*Nd2
Delta= Vt * log (Nc/Nd)
Vbi = Vt*log(Na*Nd/(Ni*Ni));
R= E*sqrt(2*pi)/(q*Q*sigma);
C1= erf(Rp(k)/(sigma*sqrt(2)));
B= Vds(i)*(1+Alpha);
D= (2*q*Na*Na)/(3*Q*E);
F1= (2*E)/(q*Na);
F= sqrt((F1*F1*F1)*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i)));
70
G= D*F;
H1= (2*q*Na*Na)/(3*Q*E);
H2= (2*E)/(q*Na);
H3= sqrt(H2*H2*H2*(Vbi-Vbs)*(Vbi-Vbs)*(Vbi-Vbs));
H= H1*H3;
J1= (q*Q*sigma)/(3*E);
J2= sqrt(2/pi);
J3= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(Vds(i)-Vgs-Phib-Delta)));
J4= sqrt(J3*J3*J3);
J= J1*J2*J4;
M1= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(-Vgs+Phib-Delta)));
M2= sqrt(M1*M1*M1);
M= J1*J2*M2;
Ids(k,i)= A*(B-G+H-J+M);
end
hold on;
plot(Vds,Ids)
end
hold off;
xlabel ('Drain voltage (Vds)')
ylabel ('Drain current (Ids)')
71
Matlab code for Drain current (Ids) versus Drain voltage (Vds) for Ionization energy
of 100keV
clc;
clear all;
close all;
K=1.38066e-23;
u=500;
T=300;
Na=1e15;
Eg= 3.21;
q = 1.60219e-19;
Nc=3.25e14*sqrt(T*T*T)
Nv= 4.8e15*sqrt(T*T*T)
Ni= sqrt(Nc*Nv)*exp(-(Eg*q)/(2*K*T))
Z= 100e-4;
L= 2e-4;
pi= 3.1459;
Phib = 1.27;
Rp=1577e-8;
Q= 3.75e13;
Eo= 11.9;
E= Eo*8.854e-14;
Vbs=0;
time= 7200;
do= 0.69e-15;
Vt= (K*T)/q
T2= 273;
T1= 1900+ T2;
Ea= 40e-3;
72
diff= do* exp(-(Ea*q)/(K*T1))
sigma1= 375e-8;
l= diff*time
y= sqrt(2*diff*time)
x= 0.08e-4
sigma= sqrt((sigma1*sigma1)+(2*diff*time))
Nd1= Q/(sigma*sqrt(2*pi))
Nd2= exp(-(((x-Rp)/(sigma*sqrt(2)))*((x-Rp)/(sigma*sqrt(2)))))
Nd= Nd1*Nd2
Alpha= (Rp/(2* sigma))*sqrt(pi/2);
Vds= 0:1:80;
Vgs= [0 -2 -6 -10];
A= (q*Q*u*Z)/(2*L);
Vbi = Vt*log(Na*Nd/(Ni*Ni))
Delta= Vt * log (Nc/Nd)
R= (E*sqrt(2*pi))/(q*Q*sigma);
C1= erf(Rp/(sigma*sqrt(2)));
for j=1:4
for i=1:81
B= Vds(i)*(1+Alpha);
D= (2*q*Na*Na)/(3*Q*E);
F1= (2*E)/(q*Na);
F= sqrt((F1*F1*F1)*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i)));
G= D*F;
H1= (2*q*Na*Na)/(3*Q*E);
H2= (2*E)/(q*Na);
H3= sqrt(H2*H2*H2*(Vbi-Vbs)*(Vbi-Vbs)*(Vbi-Vbs));
H= H1*H3;
J1= (q*Q*sigma)/(3*E);
73
J2= sqrt(2/pi);
J3= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(Vds(i)-Vgs(j)-PhibDelta)));
J4= sqrt(J3*J3*J3);
J= J1*J2*J4;
M1= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(-Vgs(j)+Phib-Delta)));
M2= sqrt(M1*M1*M1);
M= J1*J2*M2;
Ids(j,i)= A*(B-G+H-J+M);
end
end
plot(Vds,Ids)
xlabel ('Drain voltage (Vds)')
ylabel ('Drain current (Ids)')
hleg1= legend ('Vgs=0V','Vgs=-2V','Vgs=-6','Vgs=-10V')
Matlab code for Drain current (Ids) versus Drain voltage (Vds) for Ionization energy
of 150keV
clc;
clear all;
close all;
K=1.38066e-23;
u=500;
T=300;
Na=1e15;
Eg= 3.21;
q = 1.60219e-19;
Nc=3.25e14*sqrt(T*T*T)
Nv= 4.8e15*sqrt(T*T*T)
Ni= sqrt(Nc*Nv)*exp(-(Eg*q)/(2*K*T))
74
Z= 100e-4;
L= 2e-4;
pi= 3.1459;
Phib = 1.27;
Rp=0.2276e-4;
Q=3.75e13;
Eo= 11.9;
E= Eo*8.854e-14;
Vbs=0;
time= 7200;
do= 0.69e-15;
Vt= (K*T)/q
T2= 273;
T1= 1900+ T2;
Ea= 40e-3;
diff= do* exp(-(Ea*q)/(K*T1))
sigma1= 0.0486e-4;
l= diff*time
i= sqrt(2*diff*time)
sigma= sqrt((sigma1*sigma1)+(2*diff*time))
x= 0.08e-4
Nd1= Q/(sigma*sqrt(2*pi))
Nd2= exp(-(((x-Rp)/(sigma*sqrt(2)))*((x-Rp)/(sigma*sqrt(2)))))
Nd= Nd1*Nd2
Alpha= (Rp/(2* sigma))*sqrt(pi/2);
Vds= 0:1:120;
Vgs= [0 -2 -6 -10];
A= (q*Q*u*Z)/(2*L);
Vbi = Vt*log(Na*Nd/(Ni*Ni))
75
Delta= Vt * log (Nc/Nd)
R= (E*sqrt(2*pi))/(q*Q*sigma);
C1= erf(Rp/(sigma*sqrt(2)));
for j=1:4
for i=1:121
B= Vds(i)*(1+Alpha);
D= (2*q*Na*Na)/(3*Q*E);
F1= (2*E)/(q*Na);
F= sqrt((F1*F1*F1)*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i))*(Vbi-Vbs+Vds(i)));
G= D*F;
H1= (2*q*Na*Na)/(3*Q*E);
H2= (2*E)/(q*Na);
H3= sqrt(H2*H2*H2*(Vbi-Vbs)*(Vbi-Vbs)*(Vbi-Vbs));
H= H1*H3;
J1= (q*Q*sigma)/(3*E);
J2= sqrt(2/pi);
J3= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(Vds(i)-Vgs(j)-PhibDelta)));
J4= sqrt(J3*J3*J3);
J= J1*J2*J4;
M1= ((Alpha*Alpha)-(2*Alpha*C1)+(C1*C1)+(R*(-Vgs(j)+Phib-Delta)));
M2= sqrt(M1*M1*M1);
M= J1*J2*M2;
Ids(j,i)= A*(B-G+H-J+M);
end
end
plot(Vds,Ids)
xlabel ('Drain voltage (Vds)')
ylabel ('Drain current (Ids)')
hleg1= legend ('Vgs=0V','Vgs=-2V','Vgs=-6','Vgs=-10V')
76
Matlab code for threshold voltage (Vt) versus ion dose (Q) for ionization energies of
100keV and 150keV
clc;
clear all;
K=1.38066e-23;
T=300;
Na=1e15;
q = 1.602e-19;
Eo= 11.9;
E= Eo*8.854e-14;
time= 7200;
pie= 3.1459;
Rp= [1577e-8 2276e-8]
sigma1= [375e-8 486e-8]
Eg= 3.21
Vbs=0;
Nc=3.25e14*sqrt(T*T*T)
Nv= 4.8e15*sqrt(T*T*T)
Ni= sqrt(Nc*Nv)*exp(-(Eg*q)/(2*K*T))
Phi =1.27;
VT= (K*T)/q
T2= 273;
T1= 1800+ T2;
Ea= 40e-3;
do= 0.69e-15;
x= 0.08e-4;
for j=1:2
for i=1:25
77
Q=[2e11 3e11 4e11 5e11 6e11 7e11 8e11 9e11 10e11 11e11 12e11 13e11
14e11 15e11 16e11 17e11 18e11 19e11 20e11 21e11 22e11 23e11 24e11 25e11
26e11]
diff= do* exp(-(Ea*q)/(K*T1))
l= diff*time
y= sqrt(2*diff*time)
sigma= sqrt((sigma1(j)*sigma1(j))+(2*diff*time))
Nd1= Q/(sigma*sqrt(2*pi))
Nd2= exp(-(((x-Rp(j))/(sigma*sqrt(2)))*((x-Rp(j))/(sigma*sqrt(2)))))
Nd= Nd1*Nd2
delta = VT*log(Nc/Nd(j))
Vbi = VT*log((Na*Nd(j))/(Ni*Ni))
A= (q*Q(i)*Rp(j))/(2*E);
B1= Rp(j)/(sqrt(2)*sigma);
B= erf(B1);
C1 = (2*Na)/Q(i);
C2=sqrt((2*E*(Vbi-Vbs))/(q*Na));
C=C1*C2;
D = (q*Q(i)*sigma)/(E*sqrt(2*pie));
F1 =((Rp(j)*Rp(j))/(2.0*sigma*sigma))
F= exp(- F1)
G = 2*C;
H1 = (8*Na*E)/(q*(Q(i)*Q(i)));
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H2=Vbi-Vbs;
H=H1*H2;
M= A*(B + 1 - C)
N=D*(F-G+H)
Vt(i,j) = Phi- delta- M- N
end
end
Vt;
plot(Q,Vt)
xlabel ('Ion dose (Q)cm^-^2')
ylabel ('Threshold voltage (Vt)volts')
Matlab code for transconductance (gm) versus gate voltage (Vgs) for Ionization
energy of 150keV
clc;
clear all;
close all;
K=1.3807e-23;
u=500;
T=300;
t=7200;
VT=-1.5;
Na=1e15;
Eg= 3.23;
q = 1.602e-19;
Nc=3.25e14*sqrt(T*T*T)
Nv= 4.8e15*sqrt(T*T*T)
Ni= sqrt(Nc*Nv)*exp(-(Eg*q)/(2*K*T))
Z= 100e-4;
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L= 2e-4;
pi= 3.145;
Phib = 1.27;
Rp=2276e-8;
Q=1e12;
E0= 11.9
E= E0*8.854e-14;
Vbs=0;
time= 7200;
do= 0.69e-15;
Vt= (K*T)/q
T2= 273;
T1= 1800+ T2;
Ea= 40e-3;
diff= do* exp(-(Ea*q)/(K*T1))
sigma1= 486e-8;
l= diff*time
y= sqrt(2*diff*time)
Vds= 30;
Vgs= -1.5:0.5:1.5
x= 0.08e-4;
for i=1:1
for j=1:7
sigma(i)= sqrt((sigma1(i)*sigma1(i))+(2*diff*time))
R= E*sqrt(2*pi)/(q*Q*sigma(i));
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Nd1= Q/(sigma(i)*sqrt(2*pi))
Nd2= exp(-(((x-Rp(i))/(sigma(i)*sqrt(2)))*((xRp(i))/(sigma(i)*sqrt(2)))))
Nd= Nd1*Nd2
Delta= Vt * log (Nc/Nd)
Vbi = Vt*log(Na*Nd/(Ni*Ni))
%Alpha= Rp/(2* sigma)*sqrt(pi/2);
alpha= (Rp(i)*sqrt(pi))/(2*sigma(i)*sqrt(2))
V1= (q*Q*Q)/(8*Na*E)
V21= q*Q*sqrt(sigma(i)*sigma(i)+(2*diff*t));
V22= 1/(sqrt(2*pi*E));
V2=V21*V22
Ap1= (2*Na)/Q;
Ap2= sqrt(((2*E*(Vbi-Vbs+Vds))/(q*Na)));
Ap= Ap1*Ap2
B= (q*u*Z*Q)/(4*L)
D1=1/(V1*Ap)
D2= 1/(V2*(alpha+1-Ap))
D=D1+D2;
F= Vgs(j)-VT;
Gm(i,j)= B*D*F;
end
end
plot(Vgs,Gm)
grid off
xlabel ('Gate voltage (Vgs)Volts')
ylabel('Transconductance (gm)Siemens')
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