MOSFET Device StructureMOSFET Device Structure Semiconductor EquationsSemiconductor Equations

AD NNpnq

2Poisson Equation:

GRqJtnq n Electron current

continuity equation:

GRqJtpq p

Hole current continuity equation:

)( nnn nDqqnJ Electron current equation:

)( ppp pDqqpJ Hole current equation:

MOSFET Device Simulation

Simulation Methodology

Set up the device dimensions, material

properties, temperature, bias voltages, doping

profile, etc.

Discretization of the semiconductor

equations

Initial Guess for , n and p

Iterative Gummel Block Method.

Solve for , n, p

Converged?

Newton’s Method for better accuracy

Current Continuity?

Extract , electron and hole concentrations,

mobility, current density, IV characteristics, etc.

Y

YN

N

Mobility Models

High Field Mobility:

Matthiessen's rule

CSRSPBLF 11111

LF = Low Field Mobility B = Bulk Mobility

SP = Surface Phonon Mobility

SR = Surface Roughness mobility

C = Trapped interface charge mobility

Low field mobility:

1

||1

sat

LF

LFHF

vEHigh field mobility:

Oxide

Bulk

Electron Flow

Electron Surface Phonon

Surface RoughnessTrap

Fixed Charge

min

min0

1

300

n

ref

nn

n n

n

T

ND

T

n

Dn

1

Caughey – Thomas Model for bulk mobility:n

Tn

1 Temperature dependence:

Doping dependence:

32

1

1

E

T

E

n

n

SP

c

acSP m

q

Surface Phonon Mobility:

ac = Surface acoustic phonon relaxation time

E┴ = Perpendicular E. Field

n, n = calculated from phonon scattering equation

SRSR

E

21

Surface Roughness Mobility:

SR = Surface roughness parameter.

Higher the value of SR, smoother is the surface and lesser is the degradation in total mobility

Interface Trap Charge Mobility:

itC

screen_fitneT

NitnfTemp

torscreen_fac

1300

1

Corresponds to effect of coulomb scattering of mobile charged carriers by fixed charge and interface trap charge. The term also accounts for the screening of these charges by electrons at strong inversion.

nf = Fixed oxide charge

ne = Inversion layer electron concentration

screen_fit, screen_factor = fitting parameters for the screening effect

Nit = Occupied interface trap density

temp = Temperature dependence

it = from Coulomb Scattering model

4H SiC 200m x 200m MOSFET: Id-Vgs Simulation Fit at T=27oC

4H SiC 200m x 200m MOSFET: Id-Vds Simulation Fit at T=27oC

Bulk Mobility ….

Parameter 6H SiC 4H SiCn0

in cm2/Vs 500.0 1071.0

nmin in cm2/Vs 0.0 5.0

n 2.4 2.5

Nref 1.1e18 1.9e17

n 0.45 0.40

Bulk mobility at Room Temperature and D ~ 1015 is

4H SiC: ~ 800 cm2/Vs

6H SiC: ~ 400 cm2/Vs

min

min0

1

300

n

ref

nn

n n

n

T

ND

T

Surface Phonon Mobility ….

32

1

1

E

T

E

n

n

SP

132n bulk ac

3 2

2 * 28s

Acac

h vm m Z

12 3

2

2 93 16n

B

q hk qm

Units 6H 4Hm1, m2, m3 - 0.22, 0.90, 1.43 0.29, 0.58, 0.33

m┴ - 0.44 0.41

m║ - 1.43 0.33

mc - 0.35 0.39

m* - 0.44 0.41ZA eV 17.5 15.0

bulk gm/cm3 3.2 3.2

n (cm/s)-1 2.99e-9 2.29e-9

n (V/cm)-2/3K 0.1217 0.1246

Surface Roughness Mobility ….

Parameter 6H 4HSR (V/s) 1e13 5.82e14

4H SR Value is taken from Linewih (2002) paper

SRSR

E

21

Effect of surface roughness is negligible as compared to the effect of interface traps on the total mobility.

CitSR 11

Interface Trap Charge Mobility ….

itC

screen_fitneT

NitnfTemp

torscreen_fac

1300

1

6H 4H

nf 5.4 x 1011 2.2 x 1012

Nit at RmT ~ 2 x 1012 ~3 x 1012

it 1.5 x 1011 1.5 x 1011

screen_fit 1.5 x 1018 1 x 1018

screen_factor 0.8 0.7

Occupied interface trap density (Nit)

Ec

Evititit dEEfEDqqNQ

TkEE

neNc

Ef

B

cexp211

1

a

EEDDED cititit edgemida

expDit = Density of traps per unit energy

f(E) is the probability density function. It is directly proportional to the mobile charge concentration (ne). Hence as MOSFET goes towards stronger inversion, the occupied interface trap density increases.

4H SiC has a higher bandgap than 6H SiC (by 0.2eV). Ditedge value for 4H SiC is obtained by extrapolating the Dit-E curve for 6H SiC by 0.1eV. This gives a very high Ditedge value for 4H SiC because of the exponential relation between Dit and E near the band edge. Hence 4H SiC has much higher interface traps than 6H SiC.

6H 4HDitmid (cm-2eV-1) 1 x 1013 2.19 x 1013

Ditedge (cm-2eV-1) 8 x 1011 8 x 1011

Extrapolation of Dit-E curve for 6H SiC to get Dit-E characteristics for 4H SiC

Dit_edge = 2.15 x 1013 cm-2eV-1

Dit_mid = 6.5 x 1011 cm-2eV-1

Final Dit-E curve for 4H that is used:

Nit vs. position for different Vgs. T=27oC

Occupied interface trap density increases with increase in Vgs. This is because the inversion layer electron concentration increases with increase in Vgs causing more traps to get filled

Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 2 to 4V Vds = 4V

Nit vs. position for different Temperatures

Occupied interface trap density decreases with increase in temperature because trapped electrons can escape by gaining sufficient energy at higher temperatures.

So as the temperature increases, effect of interface trap charge decreases, increasing overall mobility

Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 6V Vds = 1V

Comparing effects of Surface Roughness and Interface traps at different Temperatures

The change in Id values for a tenfold improvement of the surface roughness factor, is very small at all three temperatures. Thus surface roughness does not change the current with change in temperature.

The increase in current with temperature is caused by the reduction of filled interface trap density as temperature increases.

Device: 4H SiC MOSFET W/L: 200 m / 200 m Bias: Vgs = 6V Vds = 0-8V

Future Work…• Better screening model based on Brooks-

Herring ionized impurity scattering model• Surface roughness calculation to get proper

value for SR

• Fitting data at higher temperatures• High power MOSFET simulation• Investigating gate leakage in SiC MOSFETs• Building a Graphical User Interface for the

simulator