# Modeling of Sic Power Semiconductor Devices For Switching Converter Applications

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University of South Carolina

### Scholar Commons

Theses and Dissertations

1-1-2013

## Switching Converter Applications

Ruiyun Fu

University of South Carolina

Part of theElectrical and Electronics Commons

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Recommended Citation

Fu, R.(2013).Modeling of Sic Power Semiconductor Devices For Switching Converter Applications.(Doctoral dissertation). Retrieved from

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ODELING OF

I

OWER

EMICONDUCTOR

EVICES FOR

WITCHING

ONVERTER

### A

PPLICATIONS

By

Ruiyun Fu

Bachelor of Science

Huazhong University of Science and Technology, CHINA, 2004

Master of Science

Huazhong University of Science and Technology, CHINA, 2007

Submitted in Partial Fulfillment of the Requirements

For the Degree of Doctor of Philosophy in

Electrical Engineering

College of Engineering and Computing

University of South Carolina

2013

Accepted by:

Enrico Santi, Major Professor

Tangali Sudarshan, Committee Member

Grigory Simin, Committee Member

Jamil Khan, Committee Member

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### ACKNOWLEDGEMENTS

I would like to take this opportunity to express my sincere appreciation and

gratitude to my advisor, Dr. Enrico Santi, for his guidance and support throughout my

doctoral study here in USC. Dr. Santi is a great advisor who really cares about researches,

cares about teaching and cares about his students. With his intelligence and patience, Dr.

Santi always shows a bright way to me when I am wandering in puzzlement. I am really

thankful for him leading me to become a professional researcher. I also want to express

my gratitude to my committee members: Dr. Tangali S. Sudarshan, Dr. Grigory Simin

and Dr. Jamil A. Khan for their valuable feedback.

I would also like to thank all my colleagues in the semiconductor group and

control group for their help, mentorship, and friendship. I cherish the wonderful time that

we worked together. I also would like to express my sincere appreciation to Dr. Grekov

Alexander, Dr. Zhiyang Chen, Kang Peng, Dr. Adam Barkley, Dr. Daniel Martin,

Antonino Riccobono, Isaac I Nam and Jonathan Siegers.

I would like to thank my dear husband, Yucheng Zhang, and my sweet son,

Benjamin Zhang, for their understanding and support during the pursuit of my degree. I

would also like to express my sincere appreciation for years of love and support to my

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### ABSTRACT

Thanks to recent progress in SiC technology, SiC JFETs, MOSFETs and Schottky

diodes are now commercially available from several manufactories such as Cree,

GeneSiC and Infineon. SiC devices hold the promise of faster switching speed compared

to Si devices, which can lead to superior converter performance, because the converter

can operate at higher switching frequencies with acceptable switching losses, so that

passive filter size is reduced. However, the ultimate achievable switching speed is

determined not only by internal semiconductor device physics, but also by circuit

parasitic elements. Therefore, in order to accurately predict switching losses and actual

switching waveforms, including overshoot and ringing, accurate models are needed not

only for the semiconductor devices, but also for the circuit parasitics.

In this dissertation, a new physics-based model accounting for non-uniform

current distribution in JFET region for the power SiC DMOSFET is presented. Finite

element simulation shows that current saturation for typical device geometry is due to

two-dimensional (2-D) carrier distribution effects in JFET region caused by current

spreading from the channel to the JFET region. Based on this phenomenon, a new model

is proposed that represents the non-uniform current distribution in the JFET region using

a non-linear voltage source and a resistance network. Advantages of the proposed model

are that a single set of equations describes operation in both the linear and saturation

regions, and that it provides a more physical description of MOSFET operation. The

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semiconductor device modeling. This model is validated both statically and under

resistive conditions for SiC DMOSFET showing overall good matching with

experimental results and finite element simulations.

This dissertation also presents a simple physics-based power Schottky diode

model which is comprised of a voltage controlled current source, a temperature

dependent drift region resistance and a nonlinear capacitance. A detailed parameter

extraction procedure for this model is also discussed in this work. The developed

procedure includes the extraction of doping concentration, active area and thickness of

drift region, which are needed in the power Schottky diode model. The main advantage is

that the developed procedure does not require any knowledge of device fabrication,

which is usually not available to circuit designers. The only measurements required for

the parameter extraction are a simple static I-V characterization and C-V measurements.

Furthermore, the physics-based SiC Schottky diode model is also temperature dependent

and is generally applicable to SiC Schottky diodes. This procedure is demonstrated for

four different Schottky diodes from two different manufacturers. The parameter

extraction procedure represents an original contribution in the area of characterization of

power semiconductor devices.

In order to capture the parasitic ringing in the very fast switching transients, a

procedure to accurately model circuit parasitics is also presented. A double pulse

test-bench was built to characterize the resistive and inductive switching behavior of the SiC

devices. The parasitic inductances for resistive and inductive switching of SiC devices in

this switching test circuit were modeled and analyzed using a three-dimensional (3-D)

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switching loop parasitic inductances of the PCB layout are extracted and simulated

together with previously developed power SiC device models in Pspice. Simulation

results show good agreement with experimental results under both resistive and inductive

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ACKNOWLEDGEMENTS...iii

ABSTRACT... iv

LIST OF FIGURES ... ix

LIST OF TABLES... xiv

LIST OF SYMBOLS...xv

CHAPTER 1 INTRODUCTION ... 1

1.1 SILICON CARBIDE MATERIAL PROPERTIES FOR POWER ELECTRONICS APPLICATIONS ... 1

1.2 RESEARCH MOTIVATIONS AND OBJECTIVES ... 5

1.3 DIFFICULTIES AND CHALLENGES ... 7

1.4 CONTRIBUTIONS ... 9

1.5 SUMMARY ... 10

CHAPTER 2 POWER SEMICONDUCTOR DEVICES ... 12

2.1 VERTICAL POWER MOSFET ... 12

2.2 POWER SCHOTTKY DIODE ... 18

2.3 SUMMARY ... 22

CHAPTER 3 NEW PHYSICS- BASED SIC POWER DMOSFET MODEL ... 23

3.1 LITERATURE REVIEW OF SICMOSFETMODELING ... 24

3.2 FINITE ELEMENT SIMULATION ... 25

3.3 NOVEL MODEL WITH NON-UNIFORM CURRENT DISTRIBUTION IN THE JFET REGION ... 31

3.4 MODEL VALIDATION ... 39

3.5 DISCUSSION ... 46

3.6 SUMMARY ... 48

CHAPTER 4 PHYSICS-BASED POWER SIC SCHOTTKY DIODE MODEL ... 49

4.1 LITERATURE REVIEW OF SICSCHOTTKY DIODE MODELING ... 50

4.2 SIMPLE PHYSICS- BASED SCHOTTKY DIODE MODEL... 51

4.3 PARAMETER EXTRACTION PROCEDURE ... 53

4.4 VALIDATION OF PARAMETER EXTRACTION PROCEDURE AND DIODE MODEL ... 57

4.5 DISCUSSION ... 65

4.6 SUMMARY ... 66

CHAPTER 5 PARASITICS MODELING FOR FAST SWITCHING BEHAVIOR OF SIC DEVICES ... 68

5.1 INTRODUCTION... 68

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5.3 EFFECTS OF PARASITIC INDUCTANCES ON SWITCHING BEHAVIOR... 72

5.4 EXTRACTION OF PARASITIC INDUCTANCES OF PCBLAYOUT... 74

5.5 MODEL VALIDATION ... 77

5.6 DISCUSSION ... 82

5.7 SUMMARY ... 83

CHAPTER 6 CONCLUSIONS AND FUTURE WORK ... 85

6.1 CONCLUSIONS ... 85

6.2 FUTURE WORK ... 88

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### LIST OF FIGURES

Figure 1.1 Electric field distribution in drift region for SiC ... 3

Figure 1.2 Ideal specific on-resistance of drift regions in 4H-SiC and Silicon. ... 5

Figure 2.1 Power DMOSFET structure ... 13

Figure 2.2 I-V Characteristics of Power DMOSFET ... 15

Figure 2.3 Depletion layer extension of power MOSFET ... 16

Figure 2.4 Inner parasitic capacitances of power MOSFET ... 17

Figure 2.5 Inner capacitances of a 1.2kV power MOSFET in ATLAS simulation ... 18

Figure 2.6 Power Schottky diode structure ... 19

Figure 2.7 Typical forward characteristics of power Schottky diode ... 19

Figure 2.8 Power JBS diode structure... 21

Figure 3.1 Structure of power SiC DMOSFET ... 26

Figure 3.2 I-V characteristic of DMOSFET for VGS=15V obtained from finite element simulation. ... 26

Figure 3.3 Finite element simulation results. Current density two-dimensional distribution along the channel for operation in the linear region, VDS=5V (a) and in the saturation region, VDS=30V (b). ... 27

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Figure 3.5 Finite element simulation results. (a) Current density two-dimensional

distribution and (b) lateral electric field along cutline. ... 30

Figure 3.6 Standard power MOSFET static model structure. ... 32

Figure 3.7 Proposed SiC DMOSFET model structure... 33

Figure 3.8 Model description of JFET region. (a) Specific structure of channel and JFET

region and (b) Circuit representation of JFET region. ... 35

Figure 3.9 Comparison of CGD-V characteristics of experiment, finite-element simulation and PSpice simulation. ... 39

Figure 3.10 Comparison of C-V characteristics obtained experimentally and from

finite-element simulation. ... 40

Figure 3.11 Comparisons of proposed model, Atlas model and standard model forward

characteristics of SiC DMOSFET for VDS = 0 - 7V (a) and for VDS = 0 - 30V (b). ... 41

Figure 3.12 Comparison of experimental and simulated forward characteristic of SiC

DMOSFET. ... 42

Figure 3.13 Model current in accumulation resistors of SiC DMOSFET. ... 42

Figure 3.14 Channel voltage VCH, voltage source VJ2 in JFET region and drain to source voltage VDS at VGS=7V. ... 43 Figure 3.15 Equivalent circuit used for resistive switching simulation using the proposed

model... 44

Figure 3.16 SiC DMOSFET simulated (dashed) and experimental (solid) turn-on

waveforms of resistive switching, (a) Comparison of VDS and IDS and (b)

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Figure 3.17 SiC DMOSFET simulated (dashed) and experimental (solid) turn-off

waveforms of resistive switching, (a) Comparison of VDS and IDS and (b)

Comparison of VGS and IGS. ... 45 Figure 3.18 Time evolution during turn-on of the instantaneous values of nonlinear

capacitance CGDand of the oxide capacitance cOX under resistive switching. ... 45 Figure 3.19 Time evolution during turn-off of the instantaneous values of nonlinear

capacitance CGDand of the oxide capacitance cOX under resistive switching. ... 46 Figure 4.1 (a) Structure of power Schottky diode (b) Simple physics- based Schottky

diode model. ... 51

Figure 4.2 I-V characteristics from 25ºC to 175º for 600V, 50A GeneSiC Schottky diode.

... 54

Figure 4.3 C-V measurement of 600V, 50A GeneSiC Schottky diode. ... 54

Figure 4.4 Comparison of simulated (dashed lines) with experimental (solid lines) static

characteristics of SiC Schottky diodes measured at temperature from 25ºC to

175ºC. ... 59

Figure 4.5 Comparison of simulated (dashed lines) with experimental (solid lines) C-V

characteristics of SiC Schottky diodes measured at frequency f = 1MHz. ... 60 Figure 4.6 Corresponding comparisons of simulated (dashed lines) with experimental

(solid lines) 1/C2-V characteristics of SiC Schottky diodes measured at frequency

f = 1MHz. (a) GeneSiC 1200V, 3A. (b) GeneSiC 1200, 7A. (c) Cree 1200V, 20A. (d) GeneSiC 600V, 50A. ... 61

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Figure 4.8 Simulated (dashed) and experimental (solid) waveforms of inductive

switching for Schottky diode GeneSiC 1200V, 3A. (a) Turn- on; (b) Turn- off. . 63

Figure 4.9 Simulated (dashed) and experimental (solid) waveforms of inductive switching for Schottky diode GeneSiC 1200V, 7A. (a) Turn- on; (b) Turn- off. . 63

Figure 4.10 Simulated (dashed) and experimental (solid) waveforms of inductive switching for Schottky diode Cree 1200V, 20A. (a) Turn- on; (b) Turn- off. ... 64

Figure 4.11 Simulated (dashed) and experimental (solid) waveforms of inductive switching for Schottky diode GeneSiC 600V, 50A. (a) Turn- on; (b) Turn- off. . 64

Figure 5.1 Part of the PCB layout of the double pulse test-bench. ... 71

Figure 5.2 Experimental setup of double pulse test-bench. ... 72

Figure 5.3 Typical inductive switching circuit with main parasitic inductances. ... 73

Figure 5.4 X-Y image of PCB traces of the switching loops in FastHenry. ... 75

Figure 5.5 Extracted resistances in the switching loop. ... 75

Figure 5.6 Extracted inductances in gate-to-source switching loop. ... 76

Figure 5.7 Extracted inductances in drain-to-source switching loop. ... 76

Figure 5.8 Equivalent circuit used for resistive switching circuit. ... 77

Figure 5.9 SiC DMOSFET simulated (dashed) and experimental (solid) turn-on transient of resistive switching. (a) Comparison of VDS and IDS; (b) comparison of VGS and IGS. ... 78

Figure 5.10 SiC DMOSFET simulated (dashed) and experimental (solid) turn-off transient of resistive switching. (a) Comparison of VDS and IDS; (b) comparison of VGS and IGS. ... 79

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Figure 5.12 Bode plot of inductor L1. ... 81 Figure 5.13 SiC DMOSFET simulated (dashed) and experimental (solid) turn-on

transient of inductive switching. (a) Comparison of VDS and IDS; (b) comparison of

VGS and IGS. ... 81 Figure 5.14 SiC DMOSFET simulated (dashed) and experimental (solid) turn-off

transient of inductive switching. (a) Comparison of VDS and IDS; (b) comparison of

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### LIST OF TABLES

Table 1-1 Physical characteristics of Si and 4H- SiC ... 2

Table 4-1 Schottky diode model parameters ... 53

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### LIST OF SYMBOLS

β Constant for saturation velocity

εr Relative dielectric constant

εSiC Dielectric constant of silicon carbide (F/cm)

φb Barrier height between the metal and N-type semiconductor (V)

µ300 Electron mobility at room temperature T=300K (cm2/V·s)

µn, µD Electron mobility (cm2/V·s)

µCH0 Low-field mobility in inversion layer (cm2/V·s)

µD(T) Temperature dependent electron mobility (cm2/V·s)

µn-drift Electron mobility in drift region (cm2/V·s)

µCH Channel mobility (cm2/V-s)

µA Accumulation layer mobility (cm2/V·s)

µJFET JFET region mobility (cm2/V-s)

a Half of width of channel region (cm)

ai Ratio of intercell area to total die area

A Active area (cm2)

A* Effective Richardson constant (A·cm-2·K-2)

CGD Capacitance between gate and drain (F)

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CGS Capacitance between gate and source (F)

COX Oxide capacitance per unit area (F/cm2)

cOX Oxide capacitance (F)

Cr Non-linear capacitance of Schottky diode (F)

EC Critical breakdown electric field (kV/cm)

Emax Maximum electric field (V/cm)

Ek Peak electric field at the end of MOSFET channel (V/cm)

ID Drain current (A)

IDSAT Saturation drain current (A)

IF Forward current of Schottky diode (A)

IF Reverse current of Schottky diode (A)

ISCH Current going through Schottky diode (A)

k Boltzmann’s constant (eV/K)

LD Thickness of drift region (cm)

LCH Length of channel (cm)

LDRIFT Length of drift region (cm)

LJFET Length of JFET region (cm)

LR Distance between adjacent nodes in JFET region (cm)

LD Drain-to-source switching loop parasitic inductance (H)

LDD Parasitic inductance of free-wheeling diode path (H)

LG Gate-to-source switching loop parasitic gate inductance (H)

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n Ideality factor

NDRIFT, ND Doping concentration of drift region (cm-3)

NJFET Doping concentration of JFET region (cm-3)

q Fundamental electronic charge (C)

Rai Accumulation layer resistance (Ω)

RDRIFT Drift region resistance (Ω)

RG Gate resistance (Ω)

RJFET JFET region resistance (Ω)

RJ_net Resistance of JFET region network (Ω)

Ron,sp Specific on-resistance (Ω·cm2)

S1 Slope of I-V curve for Schottky diode

S2 Slope of 1/C2-V curve for Schottky diode

T Absolute temperature (K)

vsat Carrier saturation velocity in silicon carbide (cm/s)

Vbi Built-in voltage in gate source junction (V)

VBR, VB Breakdown voltage (V)

VCH Channel voltage (V)

VCH,SAT Saturation voltage of the channel (V)

VD Voltage applied to Schottky diode (V)

VDR Voltage across Schottky diode (V)

VDS Voltage applied to drain and source (V)

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VGD Voltage applied to gate and drain (V)

Vi Voltage at the node of corresponding i resistor (V)

VJFET Total voltage in JFET region (V)

VR Reverse bias of Schottky diode (V)

VT Threshold voltage (V)

W’ Length of the depletion region under the gate oxide (cm)

WDRIFT Width of drift region (cm)

WDS Width of depletion region between drain and source (cm)

WGS Width of depletion region between gate and source (cm)

WJFET

Depletion layer length of the depletion region under the gate which only begins to grow when VDS=VGS (cm)

Wr Depletion layer thickness of Schottky diode (cm)

x Temperature coefficient of carrier mobility

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1

ILICON

ARBIDE

ATERIAL

ROPERTIES FOR

OWER

LECTRONICS

### A

PPLICATIONS

With the widespread use of medium voltage motor drives, flexible AC

transmission systems (FACTS), high voltage DC (HVDC) systems and hybrid electric

vehicles, the efficiency and reliability of power electronic converters used in these

applications is getting more and more important [ 1 ][ 2 ][ 3 ][ 4 ]. Some of these

applications require large breakdown voltage capability, high power density and high

temperature. Most present commercial power semiconductor devices such as p-i-n

diodes, MOSFETs, IGBTs, GTOs and thyristors are silicon-based devices. The

performance of these Si-based devices is approaching their theoretical limit in high power

applications due to its intrinsic material properties, which make Si-based devices a

limiting factor for high-voltage, high-efficiency and high-temperature applications. For

high blocking voltages, IGBTs and GTOs are commonly used. However, these devices

have relatively slow switching speed. MOSFETs are well-suited for

high-switching-frequency applications up to MHz frequencies, but suffer from relatively high on-state

resistance as the blocking voltage increases, which mean high on-state voltage drop and

high conduction loss. Furthermore, the maximum operating temperature for silicon

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weight. Therefore, there is an urgent need to develop new power electronics devices for

severe thermal environment or reduced cooling, high voltage and high efficiency

systems.

Table 1-1 Physical characteristics of Si and 4H- SiC

Properties Si 4H- SiC

Bandgap, Eg (eV) 1.12 3.26

Relative dielectric constant, εr 11.9 10.1

Critical electric field, EC (kV/cm) 300 2200

Electron mobility, µn (cm2/V·s) 1500 1000

Hole mobility, µh (cm2/V·s) 600 115

Thermal conductivity, (W/cm·K) 1.5 4.9

Saturated electron drift velocity, vsat (×107 cm/s) 1 2

In order to improve the performance of semiconductor devices, alternative

semiconductor materials with better characteristics are being sought. In particular wide

bandgap materials such as Silicon Carbide (SiC) appear particularly promising. Excellent

electrical properties of silicon carbide (SiC) material, such as wider bandgap, higher

thermal conductivity, and higher critical breakdown electric field, make it a very

attractive semiconductor material for power switching devices with capabilities that are

superior to those of devices based on silicon technology [ 1 ]-[ 10 ]. 4H-SiC MOSFET is

one of the most promising candidates for high-speed and low-loss power switching

applications. Table 1-1 compares the physical characteristics of Si and 4H- SiC materials

[ 2 ]. As seen in Table 1-1, the band gap of 4H- SiC (3.26eV) is nearly three times that of

Si. A large bandgap results in lower leakage currents than silicon, in a much higher

operating temperature and higher radiation hardness. The higher critical electric field

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devices with thinner and more highly doped voltage blocking layers and, as a

consequence, a lower on-resistance for a given breakdown voltage is achievable.

Especially for power unipolar devices like MOSFETs and Schottky diodes, specific

on-resistance is mainly determined by a low-doped drift region, which is necessary to block

high voltage.

Figure 1.1 shows electric field distribution in a drift region of thickness LD. Electric field EC is the critical breakdown electric field. The carrier concentration is optimized so that the maximum electric field Emax reaches the critical value EC when the drift region is completely depleted as shown in Figure 1.1.

LD

SiC D qN  

E

Emax

EC=2.2MV/cm

VBR

Figure 1.1 Electric field distribution in drift region for SiC

The breakdown voltage VBR is the integral of the electric field and it is equal to

the triangle area as shown in Figure 1.1 [ 11 ] [ 12 ]. When the maximum electric Emax is equal to the critical breakdown electric field EC, which means that the drift region is blocking the largest possible voltage, this breakdown voltage VBR is given by Equation 1-1.

2

D C BR

L E

V   Equation 1-1

According to Poisson equation, the slope of the electric field curve in Figure 1.1 is

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dielectric constant. Therefore, the maximum electric field EC in the drift region shown in Figure 1.1 is given by:

SiC D D C L qN E

 Equation 1-2

The specific on-resistance of the drift region, which is defined as the ideal specific

on-resistance, is given by

D n D ideal sp on N q L R   ) ( , Equation 1-3

where q is the electron charge and n is the electron mobility. From Equation 1-1 and

Equation 1-2, one can get the following equation for the doping concentration of drift

region.     BR C SiC D V q E N 2 2

 Equation 1-4

Substituting Equation 1-1 and Equation 1-4 into Equation 1-3 gives the ideal

specific on-resistance as Equation 1-5.

3 2 ) ( , 4 C n SiC BR ideal sp on E V R  

 Equation 1-5

Equation 1-5 clearly shows that specific on-resistance of unipolar devices is

inversely proportional to the cube of critical breakdown electric field EC of the semiconductor material. The same equation applies for other semiconductor material

such as Si. Because the critical breakdown electric field of SiC is almost 10 times more

than that of Si, Equation 1-5 shows that the ideal specific on-resistance of SiC can be

almost 1000 times smaller than that of Si. Figure 1.2 shows the comparison of the ideal

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specific on-resistance of SiC device is somewhat less than 1000 times smaller than that of

Si due to the lower electron mobility of SiC with respect to Si.

Figure 1.2 Ideal specific on-resistance of drift regions in 4H-SiC and Silicon.

Furthermore, the high thermal conductivity (4.9 W/cm·K) of SiC semiconductor

material facilitates heat removal and avoids the need for bulky and expensive cooling

systems in most applications. This, in turn, translates into high cost savings in mass

critical applications.

All of the above advantages of SiC material make it an attractive material for high

voltage, high power, high frequency, high temperature, and high efficiency converter

systems.

ESEARCH

OTIVATIONS AND

### O

BJECTIVES

Thanks to recent progress in SiC technology, SiC JFETs, MOSFETs and Schottky

diodes are now commercially available from several companies such as Cree, GeneSiC

and Infineon. Since power devices play important roles in power electronics applications,

in order for the power electronics designers to fully utilize the performance advantages of

power devices, compact power device models are needed in the circuit simulators used in

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Therefore, it is very important to create accurate device models to evaluate the

performance of SiC prototype devices in different applications and guide the switching

converter design process. This dissertation focuses on modeling of SiC power

semiconductor devices such as power MOSFET and Schottky diode for switching

converter applications.

In this dissertation, a new circuit-based SiC DMOSFET model that physically

captures the mechanism of current saturation in power SiC DMOSFET is developed in

PSpice software based on finite element simulation results. A simple SiC Schottky diode

model is proposed together with a specific parameter extraction procedure. In order to

validate the proposed SiC MOSFET and Schottky diode models, a double pulse

test-bench was built to experimentally evaluate the resistive and inductive switching behavior

of the devices. Both models have been verified by comparing simulation results with the

experimental results.

Since both devices operate at a very fast switching transient, it is very important

to capture the parasitic ringing during the switches of the devices. The extraction of

parasitic inductances of the switching circuit is another focus of this dissertation besides

the device models. A simple extraction method of parasitic inductances is developed for

the PCB layout of the double pulse test-bench. The extracted parameters of the

gate-to-source switching loop and drain-to-gate-to-source switching loop of the PCB layout are used in

the simulation circuit of the double pulse test-bench for model validation. Finally, based

on the study of the effect of parasitic inductances in fast switching circuit, the factors that

affect the accuracy of waveform prediction for switching converter are discussed for

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IFFICULTIES AND

### C

HALLENGES

In order to accurately predict the switching behavior of SiC-based power

switching converters, it is necessary to have accurate models for the SiC power devices

and for the parasitic inductances in the switching loops of the converters. However, there

are many challenges related to the development of suitable SiC power device models and

the prediction of high- speed switching behavior.

I

EVICE

### M

ODELS

Due to the development of new power devices with new internal structure and

new SiC semiconductor material, there are many challenges in developing accurate

device models for these new power semiconductor devices. A good device model for

circuit design should ideally satisfy the following basic rules:

1) The model should be able to predict static I-V characteristic with

reasonable accuracy.

2) Since the built-in device parasitic capacitances play an important role in

determining the device dynamic behavior, a good model should include an

accurate model for all these parasitic capacitances.

3) The model should provide accurate device loss predictions during on- state

and off- state.

4) The model should capture temperature-dependent behavior over the entire

temperature operating range of the switching converter applications. In

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5) The model should have as few parameters as needed to accurately capture

device behavior including static characteristics and dynamic

characteristics, and these parameters should be related to the device

structure and fabrication processing (for example active area, oxide

thickness, doping concentration, and the thickness of the device).

Empirical parameters without physical meaning should be avoided as

much as possible.

It is difficult to create a device model to meet all the rules above. In the literature

several device models have been presented for SiC MOSFETs and Schottky diodes. They

can be divided in two major groups: 1) analytical models based on the finite element

solution of drift-diffusion carrier transport in two or three dimensions [ 14 ] - [ 16 ]; and

2) circuit-oriented models which employ equation-based description of device behavior.

Analytical models provide very high accuracy but require long simulation time and

detailed information about device fabrication, while circuit-based models require much

less time for simulation with acceptably accurate results using model parameters that can

be extracted from experimental measurements. An additional advantage of physics-based

circuit-oriented models is that they are compatible with circuit simulators and can be used

to simulate an entire switching converter. New physics-based circuit-oriented SiC

MOSFET and Schottky diode models will be developed in this dissertation.

ARASITIC

OMPONENT

### M

ODELING

The significant advances in power electronics have led to improved performance

of DC-DC converters. New applications of power electronic systems create a demand for

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switching in a practical application, it is necessary to establish high speed switching

techniques. However, there are many challenges that remain to be resolved. In particular,

electromagnetic interference (EMI) issues and switching losses are still serious problems

with high speed switching, due to the influence of the parasitic components of power

electronics circuits, such as the parasitic inductance of both the power devices and printed

circuit board (PCB) traces [ 17 ] - [ 23 ].

Different parasitic parameters affect the device stresses, switching energy losses,

as well as electromagnetic interference (EMI) for very high frequency applications. One

of the major challenges is to predict, with satisfactory accuracy the switching waveforms

of the converter. To achieve this task, precise models of all components of the converter

must be used. In particular, it is important to extract the layout parasitic parameters in

Printed Circuit Board (PCB) and use them in the simulation. The main parasitic

parameters include the switching loop impedances and the device output junction

capacitances. All these parasitic parameters can help better understand the high

switching-speed behavior of these SiC switches.

### C

ONTRIBUTIONS

There are two original contributions in this dissertation.

One is the development of a new physics-based SiC DMOSFET model

accounting for non-uniform current distribution in JFET region based on finite element

simulation results. This model represents the non-uniform current distribution in the

JFET region using a non-linear voltage source and a resistance network. Advantages of

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linear and saturation regions, and that it provides a more physical description of

MOSFET operation.

The other original contribution is the parameter extraction procedure for a simple

physics-based SiC Schottky diode model. The developed procedure for the simple

Schottky diode model includes the extraction of doping concentration, active area and

thickness of drift region. The main advantage is that the developed procedure does not

require any knowledge of device fabrication, which is usually not available to circuit

designers. The only measurements required for the procedure are a set of static I-V

characterization and C-V measurements.

Other contributions of this dissertation include:

1) A double pulse test-bench was built to characterize the resistive and inductive

switching behavior of the SiC devices.

2) The parasitic inductances for resistive and inductive switching of SiC devices

in this switching test circuit were modeled and analyzed using a

three-dimensional (3-D) inductance extraction program FASTHENRY.

3) The gate-to-source switching loop and drain-to-source switching loop

parasitic inductances of the PCB layout are extracted and simulated together

with previously developed power SiC device models in Pspice under both

resistive and inductive switching conditions.

### S

UMMARY

Silicon carbide (SiC) power devices are very promising in high-speed switching

converter applications because of the superior material properties of SiC comparing with

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11

several companies, such as Cree, GeneSiC and SiCED. Modeling of these great devices is

very important for circuit engineers to predict the switching behavior of the SiC-based

converter applications. One focus of the dissertation is modeling of SiC power

semiconductor devices such as power MOSFET and Schottky diode for fast switching

applications. The extraction of parasitic inductances of the switching circuit is another

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12

### POWER SEMICONDUCTOR DEVICES

Power semiconductor devices are semiconductor devices used as a switch in

power electronics. With the fast developments of medium voltage motor drives, flexible

AC transmission systems (FACTS), high voltage DC (HVDC) systems, PV

(photovoltaics) and hybrid electric vehicles, the requirements for power semiconductor

devices include high voltage, high current, high switching speed and high efficiency. So

far there are many kinds of power semiconductor devices commercially in the market,

such as insulated gate bipolar transistor (IGBT), metal oxide semiconductor field effect

transistor (MOSFET), PiN diode, Schottky diode, thyristor and integrated gate

commutated thyristor (IGCT), and so on.

Power semiconductor devices can be divided into two different groups. There are

minority carrier devices such as IGBT, PiN diode and thyristor, and majority carrier

devices such as power MOSFET and Schottky diode which are discussed in this chapter.

ERTICAL

OWER

### MOSFET

Power MOSFET was the first commercially successful unipolar device developed

using silicon material, after resolving the problems related to the metal oxide

semiconductor interface for CMOS technology. The operation of power MOSFET is

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13

under the gate oxide layer [ 12 ]. There are several kinds of vertical power MOSFET

structure so far, including VMOSFET which is named from the V-shaped gate region,

DMOSFET which is named from the planar double-diffusion technology of the gate and

UMOSFET whose channel is vertical because of the U-groove gate structure. Figure 2.1

shows the power DMOSFET structure. The thickness and doping concentration of drift

region determine the blocking capability of the MOSFET. Higher blocking voltage

requires lower doping concentration, which leads to higher on-resistance. Therefore,

there is a trade-off between on-resistance and blocking voltage in power MOSFET

design, as shown in Figure 1.2.

JFET Region

N-Drift Region

P-Base P-Base

P+ N+ N+ P+

Contact SiO2 Contact

Contact N+ Substrate

Gate

Source Source

Drain

Channel

Figure 2.1 Power DMOSFET structure

From the structure shown in Figure 2.1, one can see that there is a parasitic NPN

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off-14

state in all operating modes of the MOSFET otherwise this could lead to device latch-up

and loss of gate control. In order to satisfy this condition, the P-base region is shorted to

the source contact through the P+ region, as shown in Figure 2.1. Besides the parasitic

BJT in the structure, there is a P-N junction connecting the source region to the drain

region, which is called built-in body diode of the MOSFET. This body diode is usually

used as free-wheeling diode in some power electronic applications.

TATIC

### C

HARACTERISTICS

When a positive voltage is applied to the gate-to-source terminal, a conductive

electron channel is formed at the surface of the semiconductor under the gate and

connects the JFET region to N+ region at the source, as shown in Figure 2.1. This

channel provides an electron current flow path between drain and source. The

on-resistance during on-state is determined by the total on-resistance of the current path shown

in the figure, which is comprised of resistances of the N+ substrate, the N- drift region,

the JFET region, the channel resistance, and the N+ region connected to the source and.

Usually one can neglect the resistances in the N+ substrate and the N+ region that is

connected to the source because of the high doping concentrations in these regions. The

on-resistance is a very important parameter of the MOSFET because it determines the

current capability of the device [ 12 ]. It can be extracted from the slope of the I-V

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15 Ron VBR In cr ea si n g V G S Saturation region Linear Region Drain-to-source Voltage D ra in -to -s o u rc e C u rr en t

Figure 2.2 I-V Characteristics of Power DMOSFET

When drain-to-source voltage VDS increases to a certain value, the device goes into the saturation region, where the drain-to-source current IDS saturates as shown in Figure 2.2. In this region device losses are high, since significant voltage and current are

both present at the same time. When the power MOSFET is working as a switch in

switching converter application, it is necessary to avoid the device operating in the

saturation region due to the limitation of high power dissipation of the device.

LOCKING

### C

HARACTERISTICS

Power MOSFET has positive blocking voltage capability. When the

gate-to-source voltage VGS is zero or negative, the device can support a large drain-to-source voltage VDS across the P-base/ N- drift region junction with a little leakage current going through the device (see the green line in Figure 2.2). Actually, during the off-state

operation, the depletion layer (see the black dashed line in Figure 2.1) extends out from

the P-base/ N-drift region junction to support the applied drain-to-source voltage. Figure

2.3 shows the depletion layer extension under off-state operation of power MOSFET for

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16

MOSFET is not only limited by the thickness of the devices and the doping concentration

of N-drift region, but also by the structure inside the devices, such as the P-well spacing.

According to the discussion of advantages of material properties for SiC

compared with Si, SiC has almost 10 times larger critical breakdown electric field than

Si. From Equation 2-1 which is the expression of breakdown voltage of semiconductor

material, one can get almost 100 times higher breakdown voltage VBR for SiC-based device than for Si-based device for the same doping concentration.

D C SiC BR N q E V    2 2

 Equation 2-1

JFET Region

N-Drift Region

P-Base P-Base

P+ N+ N+ P+

Contact SiO2 Contact

Contact N+ Substrate Gate Source Source Drain Channel

Low VDS

High VDS

Figure 2.3 Depletion layer extension of power MOSFET

YNAMIC

### C

HARACTERISTICS

There are three major parasitic capacitances in power MOSFET, which are the

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17

capacitance CDS, as shown in Figure 2.4. It is very important to accurately model the inner parasitic capacitances of power MOSFET in order to accurately capture its dynamic

characteristics, especially the modeling of the gate-to-drain capacitance (CGD), which affects the output switching waveforms due to the “Miller” effect. The dynamic behavior

of power MOSFET is usually dominated by the charging and discharging of the input

capacitance seen from the controlling gate terminal. Because of the Miller effect of

capacitance CGD, the equivalent input capacitance of the MOSFET will be the gate-to-source capacitance CGS in parallel with the amplified value of gate-to-drain capacitance

CGD during the switching transient.

CGS

CDS

CGD

Gate

Source Drain

Figure 2.4 Inner parasitic capacitances of power MOSFET

There are two methods to improve the switching speed of the power MOSFET.

One is reducing the gate resistance RG, the other one is minimizing the parasitic capacitances CGS and CGD. Reducing the gate-to-source capacitance shortens the charging and discharging time of the MOSFET and decreasing the gate-to-drain capacitance CGD reduces the Miller effect, so that the switching time can be faster.

Figure 2.5 shows the inner parasitic capacitances of a 1.2kV power MOSFET in

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18

with increasing drain-to-source voltage. One can see that this Miller capacitance

decreases abruptly at low voltage, which affects the dynamic behavior of the MOSFET

severely during switching time. Therefore, in order to develop an accurate model for

power MOSFET, it is very important to take into account the non-linear gate-to-drain

capacitance CGD.

Figure 2.5 Inner capacitances of a 1.2kV power MOSFET in ATLAS simulation

OWER

CHOTTKY

### D

IODE

Power Schottky diode has a Metal-Semiconductor (MS) junction, as shown in

Figure 2.6. A metal–semiconductor junction is formed between a metal and a

semiconductor, creating a Schottky barrier. Unlike the power P-i-N junction, power

Schottky diode is majority carrier device which does not require a reverse recovery

current to discharge the minority carriers in the depletion region in the device. Therefore,

power Schottky diode is a very fast switching semiconductor device that can be used in

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19

ND

Drift Region

n+ Substrate

Anode

Cathode

LD

Schottky Metal

Contact

Figure 2.6 Power Schottky diode structure

ORWARD

### C

HARACTERISTICS

When a positive voltage is applied to the metal contact with respect to the N-type

semiconductor, the electrons in semiconductor side overcome the Schottky barrier to the

metal side creating the forward conduction current [ 12 ]. The forward current can be

calculated by using the thermionic emission theory.

Figure 2.7 Typical forward characteristics of power Schottky diode

Equation 2-2

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20

EVERSE

### C

HARACTERISTICS

When a negative voltage VR is applied to the metal contact with respect to the N-type semiconductor, a depletion layer will be formed in the semiconductor side to support

the applied voltage. Since the N-type semiconductor holds all the blocking voltage, one

can also use Equation 2-1 to calculate the breakdown voltage of the power Schottky

diode at a certain doping concentration.

The leakage current of Schottky diode under reverse bias is also dominated by the

thermionic current across the Schottky barrier, which can be calculated by Equation 2-3.

From this equation, one can see that the leakage current of Schottky diode is dependent

on temperature. This limits power Schottky diode operation in high temperature

applications.

Equation 2-3

OWER

UNCTION

ARRIER

CHOTTKY

### D

IODE

High performance switching converter applications require minimized conduction

loss and switching loss of power devices. Reducing the on-resistance of the device can

reduce the conduction loss of power Schottky diode, but this means the device has higher

doping concentration in drift region which corresponds to lower blocking voltage.

Therefore, there is a trade-off between on-resistance and blocking voltage in designing

the structure of power Schottky diode. Another way to reduce the conduction loss is to

decrease the Schottky barrier height. However, a lower barrier height will cause higher

leakage current during reverse bias and lower the maximum operating temperature of

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21

The junction barrier Schottky diode (JBS) is a Schottky diode structure with a

P-N junction embedded into its P-N-drift region as shown in Figure 2.7. When a positive

voltage is applied to the metal contact with respect to the N-type semiconductor and this

voltage is not high enough to turn on the embedded P-i-N diode, the forward current just

goes through the Schottky part as seen in Figure 2.8.

ND

Drift Region

n+ Substrate

Anode

Cathode

LD

Schottky Metal

Contact

P+ P+

Figure 2.8 Power JBS diode structure

When a negative voltage is applied to the device, because of the existence of

P-well under the Schottky barrier, a depletion layer will be formed at the P-N junction that

will extend out to the current channel until the channel pinches off. After the channel

pinches off, the Schottky barrier is shielded by the potential formed by the depletion

layer. The further increase in the applied reverse bias is supported by the depletion layer

extending towards the N+ substrate. Once the Schottky barrier is shielded, the leakage

current stays almost constant, except for the little increasing current from the

space-charge generation of the P-N junction, which means that the leakage current is

independent of Schottky barrier height after pinch-off of the depletion layer. Therefore,

the JBS diode can have lower leakage current than conventional Schottky diode with the

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22

JBS structure is not commonly used in Si-based Schottky diode because the

threshold voltage of the embedded P-i-N junction is just 0.7V which can make the diode

operate in minority carrier conductivity modulation (bipolar) mode when the P-N

junction turns on together with the Schottky barrier junction for a higher positive voltage

bias. For SiC Schottky diode with wider bandgap than Si, the threshold voltage of SiC

P-N junction is about 3V, which is higher than the Schottky barrier. Therefore, the Schottky

barrier junction inside the SiC JBS diode, which turns on during forwards conduction

mode, ensures that the P-N junction never turns on during this time.

### S

UMMARY

This chapter briefly discusses the operation of power MOSFET and power

Schottky diode including the static characteristics and dynamic characteristics. Both of

these devices are majority carrier device with no minority carrier modulation during

conduction, which means fast switching speed during turn-off transient. Therefore, power

MOSFET and power Schottky diode can be used in high performance switching

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23

### NEW PHYSICS- BASED SIC POWER DMOSFET MODEL

For switching converter applications at less than 200V, the silicon power

MOSFET has become the device of choice due to its low on-resistance and fast switching

speed. When designed for higher operating voltages, the use of silicon MOSFETs

becomes impractical due to the very high drift region resistance. Excellent electrical

properties of silicon carbide (SiC) material make it a very attractive semiconductor

material for power switching devices with capabilities that are superior to those of

devices based on silicon technology. In particular, 4H-SiC MOSFET is one of the most

promising candidates for high-speed and low-loss power switching applications.

Recently, SiC MOSFETs have become commercially available from Cree Inc.,

including single package and bridge module with voltage rating at 1.2kV. Therefore, it is

necessary to develop accurate models for SiC power devices so that electrical engineers

can evaluate the performance of SiC prototype devices in different applications and guide

the switching converter designs.

In this chapter, a new circuit-based SiC DMOSFET model that physically

captures the mechanism of current saturation in power SiC DMOSFET is developed in

PSpice software based on finite element simulation results. A significant advantage of the

model is that a single set of equations describes operation in both the linear and saturation

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non-24

uniform current distribution in the JFET region that causes current saturation, as shown

by the finite element simulations. Finally, the model is validated by comparing simulated

results with experimental results both under static and dynamic conditions.

ITERATURE

EVIEW OF

I

### M

ODELING

As mentioned above, device models can be divided in two major groups: 1)

analytical models based on the finite element solution of drift-diffusion carrier transport

in two or three dimensions [ 14 ]- [ 16 ]; and 2) circuit-oriented models which employ

equation-based description of device behavior. While extensive research has been done to

develop analytical models for SiC MOSFET [ 24 ]- [ 26 ], there are very few publications

addressing the implementation of circuit-oriented models in simulators such as PSpice

[ 27 ]- [ 28 ].

The physics- based numerical model in [ 24 ], which accounts for incomplete

ionization and the charging and discharging of interface states, is based on the drift-

diffusion equations. This model could reveal the effects of surface phenomena, but it is

quite complex and would require long simulation times. Moreover, the model is not

suitable for implementation in a circuit simulator due to its complexity. The model

presented in [ 28 ] is a simple SPICE behavioral model for SiC power DMOSFETs. The

model is obtained by introducing specific modifications to the conventional level-1 Si

power MOSFET model available in commercial SPICE simulators. The model in [ 27 ] is

based on the latest version of the power MOSFET model utilized in the Hefner IGBT

model [ 29 ], where the parameters of both the Si and SiC MOSFETs can be extracted

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25

models need to extract several fitting factors from device experimental output

characteristics to obtain good matching.

INITE

LEMENT

### S

IMULATION

Typical structure of a power SiC DMOSFET is shown in Figure 3.1. The physical

dimensions and doping concentrations are for a 1.2kV device. It is a vertical device with

a planar gate, the channel has a 1µm length and the drift region has a 10µm thickness.

Applying a positive voltage to the gate larger than the threshold voltage, an inversion

layer is created on top of the p-base region, forming an n-type conducting channel

connecting the source to the JFET region. At the same time, an accumulation layer is

formed under the gate oxide at the top of the JFET region, providing current spreading

for the electron current flowing from the channel into the JFET region. For small values

of drain-source voltage (linear or triode region), the device exhibits an approximately

constant on-state resistance, which is determined by channel and drift region resistances.

Ultimately, at a higher drain-source bias, the current saturates (saturation region). From

standard analysis of power MOSFETs, it is known that there are at least three

mechanisms that can contribute to current saturation in power MOSFET: channel

pinch-off, carrier velocity saturation in high-electric-field regions, and the so-called parasitic

JFET effect, i.e., the fact that the current does not flow uniformly in the JFET region but

is constrained to flow in a narrow JFET channel. According to performed finite element

simulations, carrier velocity saturation at the interface between the channel and the JFET

region is the main reason for current saturation for the SiC DMOSFET structure of Figure

3.1. The JFET effect is also a significant contributing factor. The proposed physics-based

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26

Figure 3.1 Structure of power SiC DMOSFET

Figure 3.2 shows the forward I-V characteristic obtained from finite element

simulation of the device structure of Figure 3.1 using Silvaco ATLAS [ 31 ]. Gate-source

voltage is constant (15V) for all drain-source voltages, ensuring that the device is fully

on. Three values of drain-source voltage are considered: VDS=5V, 15V and 30V. For

VDS=5V the device operates in the linear region, and for VDS=15V, 30V it operates in the saturation region.

Figure 3.2 I-V characteristic of DMOSFET for VGS=15V obtained from finite element simulation.

Figure 3.3 (a-b) shows the current density distribution in a rectangular region

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27

VDS=30V. This region extends for 2µm in the x-direction and for 0.035µm in the y-direction and is identified by the small hatched rectangular region in Figure 3.1. Notice

that the thickness and the shape of the channel are very similar for the two drain-source

voltages and no significant pinch-off is observed even when the device is in deep

saturation (VDS=30V). This shows that channel pinch-off is not a significant contributor to current saturation. The biggest difference between Figure 3.3 (a) and Figure 3.3 (b) is

that for operation in the saturation region a depletion region forms in the JFET region and

the current flows along a narrow vertical path adjacent to the p-base.

(a)

(b)

Figure 3.3 Finite element simulation results. Current density two-dimensional distribution along the channel for operation in the linear region, VDS=5V (a) and in the

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28

Figure 3.4 (a) shows two-dimensional finite element simulation results for the

electric potential in the upper part of the SiC DMOSFET (rectangular dashed region in

Figure 3.1). Figure 3.4 (b) shows the electric potential curve on a cutline along the

channel (cutline: X=7µm-10.5µm, Y=1nm) for the three values of drain-source voltage of

Figure 3.2. Figure 3.5 (a) shows the two-dimensional current transport and Figure 3.5 (b)

shows the lateral (x-axis) electric field component along the same cutline.

From these simulation results one can draw some conclusions on saturation

mechanism in a typical power SiC DMOSFET. Pinch-off of the channel was not

observed under any drain-source bias: even at VDS=30V the channel retains its approximately rectangular shape and does not display channel pinch-off condition.

Additional confirmation of this can be obtained by looking at Figure 3.4 (b), which shows

that the potential drop in the channel does not change much (from 12V to 14V

approximately) as VDS increases from 15V to 30V. This shows that most of the voltage drop across the device in saturation does not occur in the channel, but somewhere else (in

the JFET region). As the drain-source voltage increases, the lateral electric field shown in

Figure 3.5 (b) becomes quite large at the end of the channel, where it reaches its peak

value Ek when current goes to saturation regime. Detailed investigation of carrier transport in the channel region as predicted by the finite element simulations reveals that

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29 (a)

(b)

Figure 3.4 Finite element simulation results. (a) Electric potential two-dimensional distribution for VGS=15V, VDS=15V and (b) electric potential along cutline for three

drain-source voltages.

Traditionally, it is assumed that an accumulation layer is always formed under the

gate oxide in the JFET region and further analysis of current transport in power MOSFET

is based on this assumption. This accumulation layer helps spreading the electron current

coming from the channel uniformly across the undepleted portion of the JFET region. As

a result, the JFET region can be represented as a rectangular piece of semiconductor

material whose width is modulated by change of depletion region width of p-base/n-JFET

junction, with electron current flowing vertically from the JFET accumulation layer under

the gate to the drift region. However, the finite element simulation of Figure 3.5 (a) tells a

different story: the current distribution in the JFET region is highly non-uniform and

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30

layer (see triangular region in Figure 3.5 (a) for VDS = 30V). Notice that the accumulation layer disappears in the JFET region and is replaced by a depletion region (rectangular

region in Figure 3.5 (a)). Notice also that the electric potential increases sharply at the

end of the channel with drain voltage increasing. A significant portion of the voltage drop

is localized in the current spreading region across the depleted portion of the JFET region

(see circled region in Figure 3.4 (a)). So one can divide the JFET region into two parts:

one is the current spreading region across the depleted portion, with electron current

spreading out laterally; the other is the triangular region mentioned before, with electron

current flowing vertically and non-uniformly. Based on this idea, a new circuit-based

model is developed, which physically represents the mechanism of current saturation in

power SiC DMOSFET.

(a)

(b)

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31

The physical treatment of current spreading in DMOSFET proposed by Baliga

considers accumulation and JFET region as two individual regions [ 12 ]. Resistance of

accumulation region is determined by gate voltage only, while resistance of JFET region

is a function of drain-source voltage only. However, based on the performed

finite-element investigation, the resistance of the accumulation region is a strong function of

both VGS and VDS, which is not considered in classical solutions for current transport of power DMOSFET. Moreover, the resistance of JFET region is not only determined by

depletion width of p-base/JFET junction, but also and more predominantly by reduction

of current conduction in the central part of JFET region caused by formation of a

depletion region between adjacent p-base regions (rectangular region in Figure 3.5 (a)).

For large values of gate-source voltage, such as the VGS=15V case, the JFET current channeling effect is significant only for large values of drain-source voltage, such as the

VDS=30V case of Figure 3.5 (a), which are not of great practical interest, since power dissipation is exceedingly large. However, for smaller values of gate-source voltage, this

effect becomes significant at correspondingly lower values of drain-source voltage. For

this reason it is important to capture this effect in order to have an accurate device model.

OVEL

ODEL WITH

ON

UNIFORM

URRENT

### D

ISTRIBUTION IN THE

### R

EGION

The simple standard model of a power MOSFET is a piecewise model using

different equations to describe operation in the linear region and saturation region. The

two equivalent circuits are shown in Figure 3.6. For simplicity device capacitances and

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32

dependent on both gate- source voltage VGS and channel voltage VCH. When VCH ≥

VCH,SAT, the MOSFET operates in the saturation region and ID is a function of VGS only and does not depend on VCH. So there are two different equations for current ID in the standard model, one for the linear region and another one for the saturation region.

Source

-VCH

+

ID (VGS,VCH)

RJFET

RDRIFT

Drain

(a) Linear region

Drain RDRIFT

RJFET

ID (VGS)

-VCH

+ Source

(b) Saturation region

Figure 3.6 Standard power MOSFET static model structure.

For linear region, the drain current ID is given by

2

### 

0 2

2 CH GS T CH CH

OX CH

D V V V V

L Z C

I     Equation 3-1

For saturation region, the drain current ID is

2 , 0

2 CH CHSAT OX CH DSAT V L Z C

I   Equation 3-2

The nonlinear resistors RJFET and RDRIFTare given by

) (

2 JFET JFET JFET

JFET JFET W a Z N q L R       

 Equation 3-3

DRIFT DRIFT drift n DS DRIFT DRIFT W Z N q W L R        

### 

2 Equation 3-4

The structure of the new proposed model is shown in Figure 3.7. It consists of

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33

drift resistance RDRIFT, and capacitances CGS, CDS and nonlinear capacitance CGD. The novelty of this model is in how the JFET region is modeled by VJ2 and RJ_net.

+ -Source Drain Gate CGS CGD CDS -VCH +

ID (VGS,VCH)

-VJ2 + -VJ1 + RJ_net RDRIFT -VJFET + ID

Figure 3.7 Proposed SiC DMOSFET model structure.

Taking into account that SiC MOSFET current saturation is due to a large voltage

drop in JFET region and not to channel pinch- off, it is possible to use only one equation

to describe the channel region forward I-V characteristic. This is the equation

corresponding to linear region of operation in the standard model of Figure 3.6:

2

### 

2

2 CH GS T CH CH

OX CH

D V V V V

L Z C

I     Equation 3-5

Thus, channel region is represented by a voltage-controlled current source and

channel voltage VCH can be determined by subtracting voltage drop in JFET and drift region from total voltage applied to the device:

DRIFT D JFET DS

CH V V I R

V    Equation 3-6

(53)

34 DRIFT DRIFT drift n DS DRIFT DRIFT W Z N q W L R        

### 

2 Equation 3-7

) ( 2 JFET CH bi DRIFT sic

DS V V V

N q

W  

  Equation 3-8

where VJFET is the voltage drop in JFET region.

EGION

### M

ODELING

The proposed method to capture the current saturation in the discussed

DMOSFET is to represent JFET region as two parts: a voltage source and a matrix of

resistors as in Figure 3.7. The specific structure is shown in Figure 3.8. Voltage source

VJ2 represents the voltage drop in the current spreading region and the resistor network allows for a non-uniform current distribution in the JFET region. This approach takes into

account JFET region voltage drop in both lateral and vertical directions, therefore

capturing the two-dimensional nature of current spreading in this region. The top row of

resistors represents the accumulation layer while the remaining matrix resistors represent

the main body of JFET region. The main feature of this approach is that values of the

resistors in the accumulation layer are function of both VGS and VDS. Let us consider a resistor Rai in the top row. Due to the voltage drop on the resistors to its left, the voltage
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