Transcript Slide 1

Modeling, Characterization and Design of
Wide Bandgap MOSFETs for High
Temperature and Power Applications
UMCP: Neil Goldsman
Gary Pennington (Post-Doctoral)*
Siddharth Potbhare (MS-Ph.D)^
ARL: Skip Scozzie
Aivars Lelis (& UMCP Ph.D)
Bruce Geil (& UMCP MS)
Dan Habersat (& Former Merit)
Gabriel Lopez (& Former Merit)
ARO STAS: Barry Mclean & Jim McGarrity
* Partially supported by PEER;
^ Fully supported by PEER
1
Personnel Development: Contribution to
ARL
• Gary Pennington: Finished PhD 2003,
researching SiC for ARL
• Steve Powell: Finished PhD 2003
• Gabriel Lopez: Former MERIT, new ARL
employee
• Aivars Lelis: ARL employee, PhD under
Goldsman (transferring our software to ARL for
use and more development)
• Bruce Geil: ARL employee, MS under Goldsman
(transferring our software to ARL for use and
more development)
2
Outline
•Introduction:
-Benefits of Wide Bandgap Semiconductors
-Difficulties to Overcome
•Atomic Level Analysis of Carrier Transport in 4H & 6H SiC:
-Monte Carlo transport modeling: bulk and surface
• 4H SiC MOSFETS:
-Developing new simulation methods to extract physics
&propose how to improve performance.
-Effects of High Temperatures & High Voltage
-4H MOSFET
-Improved numerical attributes
3
Introduction: Benefits of Wide Bandgap
Semiconductors (SiC)
•
•
•
•
•
Extremely High Temperature Operation
Extremely High Voltage
Extremely High Power
Capable of Growing Oxide => MOSFETs
Potential for High Power and High Temperature
Control Logic
• Power IC’s
• High Temperature IC’s
4
Research Strategy
Device Modeling
Drift-Diffusion
and Compact
Experiment
Material Modeling
Monte Carlo
SiC Device
Research & Design
5
Advanced Drift Diffusion
Device Simulator
for
6H and 4H-SiC MOSFETs
6
Outline




Brief introduction to Silicon Carbide
Mobility Modeling for 4H-SiC MOSFETs
 Coulomb Scattering Mobility Model
Simulations and Extracted Results
Conclusion
7
MOSFET Device Simulation
MOSFET Device Structure
Steady State Semiconductor Equations
Poisson Equation:
 2  
n  p  N


q

D
 N A 
n
Electron current
q
  J n  qR  G  0

t
continuity equation:
p
Hole current
q
   J p  q R  G  0
continuity equation:
t
Electron current
equation:
J n  qnn  q(nDn )
Hole current
equation:
J p  qp p  q( pDp )
8
Mobility Models
Oxide
Low field mobility:
Matthiessen's rule
1
 LF

1
B

1
 SP

1
 SR

1
Electron Flow
C
LF = Low Field Mobility B = Bulk Mobility
Bulk
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:
 HF 
LF
  LF E|| 
1 

 vsat 
9
Why a Coulomb Mobility Model?
 4H-SiC MOSFETs have a high density of interface traps
which fill up during inversion giving rise to a large amount of
charge at the 4H-SiC/Si02 interface.
 This interface trapped charge and fixed charge distributed in
the oxide causes Coulombic scattering of inversion layer
mobile carriers. In fact, Coulomb scattering is the dominant
mobility limiting mechanism in 4H-SiC MOSFETs.
 Coulomb scattering potential is maximum at the interface and
decreases as we move towards the bulk. Also, mobile carriers
in the inversion layer screen the interface charge. Hence,
Coulomb scattering mobility of a mobile carrier is dependent
on its depth and on the amount of screening.
10
Coulomb Scattering Rate
Screened Coulomb Potential:

e 2 1 qsc r
V (r ) 
 e
4 r
Screening Wave Vector:
e 2 N inv
qsc 
 SiC Z avg k BT
Inversion
Charge Density:
Ninv  
z 
z 0
nz dz
z 
Average depth of the Z  z 0 z  n  z   dz
avg
z 
Inversion Layer:
 n  z   dz
z 0
Treating Coulomb scattering as a quasi-2D phenomenon, we take a 1D Inverse
Fourier Transform of the 3D matrix element to extract its dependence on distance
between the mobile carrier and the scattering charge
H 3D  e
3D Matrix Element:
Quasi-2D Matrix
Element:
H 2D

ik r
 ikr
e2
| V r  | e
 


1
q  q sc2
2
3D
2
2

1
e 2 exp  z  zi  q2 D  qsc
iqz z

H 3 D  e dqz 

2π 
2
q22d  qsc2

11
Coulomb Scattering Rate
Quasi-2D Scattering Rate:
Scattering Charge
Distribution

N2 D  zi  
1

k dk   k k  1  cos  d
  z, zi 
4 2 k 0
 0
 Nit  N f  0  zi  0
N 2 D  zi   
zi  0
 N f  zi 
zi
S
Coulomb Scattering Mobility:
m* e 3 N 2 D z i 
1
m* 1


 F z, zi , Te 
2
 C z, zi , Te  e 
16 k BTe


qsc2

F  z , zi , Te    1 
 8m*k BTe
 0
sin 2   qsc2

2


2
Total Coulomb
Mobility at depth z:
D
z
For the results shown in this paper, we have assumed
that the fixed oxide charge is located at the interface.

z=zi=0
Bulk
Electron
Scattering Charge


*


 exp 2 8m k BTe sin 2   qsc2  z  zi  d

2





1
1

C z, Te  zi C z, zi , Te 
12
Comments on the
Coulomb Mobility Model

The model is easy to implement in a drift diffusion device
simulator as it gives local mobility everywhere inside the
device

Coulomb mobility is directly proportional to temperature and
inversely proportional to the density of scattering charge

For a constant scattering charge density, Coulomb mobility
will increase with gate voltage due to increased screening

Coulomb mobility increases rapidly with distance away from
the interface

Effect of oxide charges distributed inside the oxide away from
the interface is less on determining the scattering of inversion
layer charges
13
4H-SiC MOSFET Simulations
and Extracted Results
14
Room Temperature ID-VGS
x 10
5
-6
10
V
DS
-5
VDS=0.25V
=0.25V
T = 300oK
o
T = 300 K
10
I (A)
3
D
D
I (A)
4
10
-6
-7
2
10
1
0
-8
Simulation
Experiment
Simulation
Experiment
0
5
V (Volts)
GS
10
15
10
-9
-5
0
V
GS
5
(Volts)
10
15
15
Interface Trap Density of States
Interface traps Density of States:
Probability of occupation of traps:
 E E

DitA E   Ditmid  Ditedge exp  C
 it 

f n E  
1
 E E
1 NC

1
exp  C
2 n
k
T
B


Occupied Interface Trap Density:
N 
A
it
Ec
A
D
 it E  f n E dE
Eneutral
Dited g e = 9.51013 cm-2eV-1
Ditmid = 4.01011 cm-2eV-1
 it
= 0.0515 eV
Eneutral = 1.63 eV at Room Temperature
16
Ninv and Nit
Owing to the extremely high density of states of the interface traps, the
occupied interface trap density (Nit) is much higher than the inversion charge
density (Ninv) at room temperature.
As fewer mobile charges are available for conduction, the current is less.
10
12
-2
N inv and N it (cm )
10
13
10
10
11
10
N
N
inv
it
o
T = 300 K
10
9
-2
0
2
4
V
GS
6
8
(Volts)
10
12
14 15
17
Coulomb Scattering Mobility
 Coulomb scattering decreases with increasing distance away from the
interface. Hence Coulomb mobility rises with increase in depth.
 With increase in gate voltage, mobile carrier concentration increases
leading to increased screening of trapped charges. Hence, the Coulomb
mobility curves rise more sharply at higher gate voltages.
10
5
T = 300oK
4
2
Coulomb Mobility (cm /Vs)
10
Increasing Screening
10
10
10
3
V = -2V
GS
V = 2V
GS
V = 6V
GS
V = 10V
GS
V = 14V
2
GS
1
0
2
4
6
8
Depth (nm)
10
12
To Bulk
18
Total Low Field Mobility vs. Depth
 The total mobility increases with depth inside the 4H-SiC MOSFET.
 At the surface, the total low field mobility is approximately 25 cm2/Vs at
room temperature.
350
Total Low Field Mobility (cm 2/Vs)
T = 300oK
300
250
200
150
V
V
100
V
V
50
V
Surface Mobility
20 cm2/Vs - 30 cm2/Vs
0
0
2
4
6
8
Depth (nm)
GS
GS
GS
GS
GS
10
= -2V
= 0V
= 2V
= 6V
= 8V
12
To Bulk
19
Effect of Screening
10
4
10
5
VGS = 12V
VGS = 2V
T = 300oK
10
10
3
 SR
2
C
 Total
J
10
10
n
1
0
0
2
4
6
8
Depth (nm)
10
12
VGS = 2V. Less Screening.
Coulomb Mobility dominates
Mobility (cm2/Vs)
2
Current Density (A/cm )
Mobility (cm2/Vs)
2
Current Density (A/cm )
T = 300oK
10
 SR
C
4
 Total
J
10
10
10
n
3
2
1
0
2
4
6
8
Depth (nm)
10
12
VGS = 12V. Lots of Screening.
Coulomb Mobility effect is only very
close
to
interface.
Surface
Roughness mobility dominates
20
Current Density
 Even though the mobile charge concentration is maximum at the interface,
maximum current flows approximately 2nm to 3nm below the interface. This
is due to the large amount of scattering taking place at the interface.
 With increase in gate voltage, the peak of the current density curve shifts
towards the interface indicating that .
450
T = 300oK
Current Density (A/cm2)
400
V = 0V
GS
V = 2V
GS
V = 4V
GS
V = 6V
GS
V = 8V
GS
V = 10V
GS
V = 12V
GS
V = 14V
350
300
250
200
GS
150
100
50
0
0
2
4
6
Depth (nm)
8
10
12
To Bulk
21
Improving the Interface
Reduction in Interface trap density
8
7
x 10
Reduction in surface roughness
-6
1.4
VDS=0.25V
Fit to Experiment
Factor of 10 Reduction
Factor of 100 Reduction
1
I (A)
5
4
0.8
VDS=0.25V
T = 300oK
D
D
-5
1.2
T = 300oK
6
I (A)
x 10
0.6
3
0.4
2
Fit to Experiment
Factor of 10 Reduction
Factor of 100 Reduction
1
0
0
5
V (Volts)
GS
10
15
0.2
0
0
5
V (Volts)
10
15
GS
22
Coulomb Mobility: Key Findings & Remarks
 Room temperature models for different types of mobilities
have been devised and implemented for 4H-SiC MOSFETs,
and good agreement between simulations and experiment
has been achieved.
 A first principles Coulomb Scattering mobility model has
been developed specifically for 4H-SiC MOSFETs
 Interface trap density of states for 4H-SiC MOSFETs has
been estimated
 Coulomb scattering due to interface trapped charge and
surface roughness scattering are the two dominant mobility
degradation mechanisms
 Maximum current flows 2nm – 3nm away from the interface
in 4H-SiC MOSFETs
 Large improvement in current is predicted on reduction of
interface trap densities in 4H-SiC MOSFETs
23
Roughness Mobility for a 4H-SiC
Stepped Surface
24
Surface Morphology
25
•Epitaxial growth of device-quality 4H-SiC is typically achieved by stepflow growth, with the surface offset from the (0001) plane by ~8o towards
the [1120] direction.
•This creates a stepped morphology along the surface, with microsteps
and possibly both macrosteps (facets).
26
•Surface morphology is generated via Monte Carlo methods using
experimental observations.
•Step width distribution indicates meandering, but will use straight steps
for now.
•Random roughness parallel and perpendicular to steps (L, d)
Macrosteps
Syväjärvi et al. J. Crystal Growth. V 236, p297 (2002)
Microsteps (4-2 bunching)
Kimoto et al. J. Appl. Phys. V 81, p3494 (1997)
Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
Number of Bilayers at Microstep
27
•Closer Look at surface morphology:
(4-2) Microsteps + Macrosteps (facets)
(4-2) Microsteps
28
• Meandering of steps is not included at this point. This effect increases
as the distribution of step widths increases.
• Microsteps will meander if step bunching occurs.
(increase in || roughness)
~6nm micostep
~40nm facet
Meandering of microsteps on a facet
29
Roughness Scattering at
4H-SiC/oxide interface
30
•Experiments indicate that the field-effect mobility of 4H-SiC devices
produced by step-flow growth is anisotropic. The mobility perpendicular
to the steps (along [1100]) was found to be significantly lower than that
parallel to the steps (along [1120]).
L. A. Lipkin, M.K. Das, and A. Saxler . ICSCRM (2003)
•Considering these observations, we investigate the role of surface
steps in both the degradation and anisotropy of the surface roughness
mobility in off-axis 4H-SiC.
31
•Band structure anisotropy will be include as a later.
32
•For a random correlation length of 2.2nm and surface field 100kV/cm,can
determine the roughness mobility ratios vs lattice temperature
33
Carrier relaxation rate due to surface roughness
Momentum relaxation rate for carrier with (kx,ky):
1
= e2F2m*
t(kx,ky,F) 2πЋ3
∫ dθ [1-cos(θ)] S(q ,q ) Γ(q ,q )
x
ε(qx,qy)2
y
•
S=power spectrum of roughness
•
Γ=image potential correction, set =1
•
θ = (kxqx + kyqy)
|(kxqx + kyqy)|
•
F=surface field (1X105 V/cm used here)
•
ε=ε(F), screening dielectric function
x
y
2
34
Power Spectrum
Facets + (4-2) microsteps
(4-2) microsteps
•Dynamic screening still needs to be included
35
Mobility with facets and micosteps
36
Mobility without facets
37
Effects of Step Bunching
No bunching
4-2 bunching
Probability
Probability
Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
Random bunching
6
7
8
Number of Bilayers at Microstep
1
2
3
4
5
6
7
8
Number of Bilayers at Microstep
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
Number of Bilayers at Microstep
38
Conclusions
•The presence of the surface steps reduces the mobility of 4H-SiC by a factor
of 5-10.
•With L=2.2nm, mobilities increase approximately linearly with T.
•4H-SiC devices operating at high temperatures should have an enhancement
of the surface roughness mobility when compared to room temperature
operation. Microsteps appear to reduce the anisotropy with increasing
temperature whereas faceting appears to have the opposite effect.
Step bunching significantly degrades the roughness mobility.
39
Key Results for Recent 4H SiC
Technology
• Significant improvement in numerical attributes of simulator:
– Allows for much higher resolution mesh
• Improved physical model for interface state mobility
– Depends on 2D coulomb scattering
• Developing new model for device instability
– Use gate current injected from channel
– Related to oxide charging and interface trap generation
• New Monte Carlo simulations show energy of carriers in channel
– Needed for interface trap generation
– Needed for oxide state occupation
40
Very Recent Publications
1)
G. Pennington, and N. Goldsman, "Empirical Pseudopotential Band Structure of 3C, 4H,
and 6H SiC Using Transferable Semiempirical Si and C Model Potentials,” Phy. Rev. B,
vol 64, pp. 45104-1-10, 2001.
2)
G. Pennington, N. Goldsman, C. Scozzie, J. McGarrit, F.B. Mclean., “Investigation of
Temperature Effects on Electron Transport in SiC using Unique Full Band Monte Carlo
Simulation,” International Semiconductor Device Research Symposium Proceedings, pp.
531-534, 2001.
3)
S. Powell, N. Goldsman, C. Scozzie, A. Lelis, J. McGarrity, “Self-Consistent Surface
Mobility and Interface Charge Modeling in Conjunction with Experiment of 6H-SiC
MOSFETs,” International Semiconductor Device Research Symposium Proceedings, pp.
572-574, 2001.
4)
S. Powell, N. Goldsman, J. McGarrity, J. Bernstein, C. Scozzie, A. Lelis,
“Characterization and Physics-Based Modeling of 6H-SiC MOSFETs”’ Journal of
Applied Physics, V.92, N.7, pp 4053-4061, 2002
5)
S Powell, N. Goldsman, J. McGarrity, A. Lelis, C. Scozzie, F.B McLean., “Interface
Effects on Channel Mobility in SiC MOSFETs,” Semiconductor Interface Specialists
Conference, 2002
6)
G. Pennington, S. Powell, N. Goldsman, J.McGarrity, A. Lelis, C.Scozzie., “Degradation
of Inversion Layer Mobility in 6H-SiC by Interface Charge,” Semiconductor Interface
Specialists Conference, 2002.
41
Very Recent Publications Continued
7) G. Pennington and N. Goldsman, ``Self-Consistent Calculations for n-Type Hexagonal SiC
Inversion Layers,” Journal of Applied Physics, Vol. 95, No. 8, pp. 4223-4234, 2004
8) G. Pennington, N. Goldsman, J. McGarrity, A Lelis and C. Scozzie, ``Comparison of 1120
and 0001 Surface Orientation in 4H SiC Inversion Layers,” Semiconductor Interface
Specialists Conference, 2003.
9) S. Potbhare, N. Goldsman, A. Lelis, “Characterization and Simulation of Novel 4H SiC
MOSFETs”, UMD Research Review Day Poster, March 2004.
10) G. Pennington, N. Goldsman, J. McGarrity, A. Lelis, C. Scozzie, ``(001) Oriented 4H-SiC
Quantized Inversion Layers," International Semiconductor Device Research Symposium,
pp. 338-339, 2003.
11) X. Zhang, N. Goldsman, J.B. Bernstein, J.M. McGarrity, S. Powell, ``Numerical and
Experimental Characterization of 4H-SiC Schottky Diodes,” International
Semiconductor Device Research Symposium, pp. 120-121, 2003.
12) S. K. Powell, N. Goldsman, A. Lelis, J. M. McGarrity and F.B. McLean, High
Temperature Modeling and Characterization of 6H SiC MOSFETs, Journal of Applied
Physics, 2005.
42
Very Recent Publications Continued
13) S. Potbhare, G. Pennington, N. Goldsman, J.M. McGarrity, A. Lelis, “Characterization of 4H SiC
MOSFET Interface Trap Charge Density Using First Principles Coulomb Scattering Mobility
Model and Device Simulation,” Proceedings of the International Conference on Simulation of
Semiconductor Processing and Devices (SISPAD), pp. 95-98, 2005.
14) S. Potbhare, G. Pennington, N. Goldsman, A. Lelis, D. Habersat, F.B. McLean, J.M. McGarrity,
“Using a First Principles Coulomb Scattering Mobility Model for 4H-SiC MOSFET
Simulation,” ICSCRM, 2005 (to appear)
43