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Advanced Drift Diffusion
Device Simulator
for
6H and 4H-SiC MOSFETs
MOSFET Device Simulation
MOSFET Device Structure
Semiconductor Equations
Poisson Equation:
 2  

n p N

q

D
 N A

n
   J n  q R  G 
t
Electron current
continuity equation:
q
Hole current
continuity equation:
q
Electron current
equation:
J n  qnn  q(nDn )
Hole current
equation:
J p  qp p   q( pD p )
p
   J p  q R  G 
t
Mobility Models
Oxide
Low field mobility:
Matthiessen's rule
1
 LF

1
B

1
 SP

1
 SR

1
Electron Flow
C
Bulk
LF = Low Field Mobility B = Bulk Mobility
SP = Surface Phonon Mobility
Electron
Surface Phonon
SR = Surface Roughness mobility
Trap
Surface Roughness
Fixed Charge
C = Coulomb Scattering Mobility
High Field Mobility:
High field mobility:
1
Total

1
 LF

1
 vsat 


E
|| 

Screened Coulomb Scattering
Mobility
Screened Coulomb
Potential:

e 2 1 qsc r
V (r ) 
 e
4 r
H 2D
2D Matrix Element:
Fermi’s Golden k k  2  H 2 D  z, zi  2    Ek  Ek 
Rule:

2
2
e 2 exp  z  zi  q2 D  qsc


2
q22d  qsc2


N2 D  zi  
1

k dk   k k  1  cos  d
2

  z, zi 
4
k 0
 0
Scattering Rate:
Screened Coulomb Scattering Mobility:
m*e3 N2 D  zi 

 F  z, zi 
2
C 16  kBTe
1

F  z, zi  
2




exp 2 qsc2  8m*k BTe sin 2 
1  q  q
2
sc
2
sc
2
 8m k BTe sin 
*
2
 z  zi  
2

d
e 2 N inv
qsc 
 SiC Z avg k BT
ID-VGS at Room Temperature
-6
x 10
1e-5
5
1e-7
ID (A)
ID (A)
4
3
2
1
0
-5
0
VGS
5
10
(Volts)
15
1e-10
0
Circles : Simulated Points
Line: Experimental data
5
VGS (Volts)
10
15
Occupied interface trap density
Negatively charged interface traps:
Ec
Qit  qN it  q
 D E  f E dE
it
n
Eneutral
Dit = Interface traps density of states
Dita E   Ditmid  Ditedge
 E  Ec 
exp

 a 
f(E) is the probability density function.
f E  
1
 E  Ec 
1 Nc

1
exp
2 ne
 k BT 
Interface Trap Density of States
14
10
Dit (cm-2eV-1)
1e14
13
Donor
Acceptor
10
12
10
2.5e11
11
10
0
Neutrality Point
1
E (eV)
2
3
Figure . Interface trap density of states for 4H-SiC: Constant
distribution in midgap and an exponential rise near the band edges.
Mobility Variation with Depth
5
5
10
10
4
4
10
Mobility (cm2/Vs)
Mobility (cm2/Vs)
10
3
10
uB
uSP
uSR
uC
uTotal
2
10
2
uB
uSP
uSR
uC
uTotal
10
1
10
0
50
100
150
z (Angstroms)
200
250
VGS = 2V. Less Screening.
Coulomb Mobility dominates
0
50
100
150
z (Angstroms)
200
250
VGS = 14V. Lots of Screening.
Coulomb Mobility effect only very
close
to
interface.
Surface
Roughness mobility dominates
Current Density Variation with Depth
400
VGS = 2V
VGS = 4V
VGS = 6V
VGS = 8V
VGS = 10V
VGS = 12V
VGS = 14V
350
300
Jn (A/cm 2)
250
200
150
100
50
0
0
20
40
60
80
z (Angstroms)
100
120
Peak of the current density is some
distance away from the interface
Nit – VGS and Ninv – VGS at RmT
14
10
Nit & Ninv (cm-2)
12
10
10
10
8
Ninv
10
Nit
6
10
0
5
10
VGS (Volts)
15
Fixed Oxide Charge Density ~ 1.45e12 cm-2
Screened Coulomb Scattering
Mobility
• Coulomb scattering decreases rapidly with
increase in depth inside the semiconductor
• Oxide charges located away from the interface
have less effect on Coulomb scattering
• Screening is directly proportional to the inversion
layer charge density
• Scattering rate is inversely proportional to
electron temperature (energy)
• Scattering rate is directly proportional to the
density of oxide charges and occupied interface
traps
Future Work
• Implement oxide charging - interface trap
charging model in simulator
• Implement a robust surface roughness
mobility model
• High temperature high power simulations
• Modeling of different Power MOSFET
structures
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