Characterization of 4H-SiC MOSFET Interface Trap Charge Density Using a First
Principles Coulomb Scattering Mobility Model and Device Simulation
Siddharth Potbhare, Gary Pennington, Neil Goldsman, James M. McGarrity and Aivars Lelis*
Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742. USA
*
U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783
{potbhare, neil}@glue.umd.edu
1. Introduction:
SiC is material of great interest because it has very large bandgap, and at the same time, has the ability to grow a natural oxide. This
combination can facilitate the design and fabrication of SiC MOSFET devices for extremely high power and high temperature
applications. In fact, it presents the opportunity of extending the micro-electronic revolution to very high power IC’s. However, before
high performance SiC MOSFETs are realized, their performance limitations, due to low surface mobility, must be understand and
overcome. Unusually high interface trap densities currently pose the biggest challenge to SiC device operation. Developing a density
profile for the interface traps and predicting their effect on device operation will help manufacturers to refine their process and
produce better SiC devices. We have developed a physics based device simulator for detailed numerical analysis of 4H SiC
MOSFETs. The core of the simulator is an advanced mobility model that accounts for the effects of surface phonon scattering, surface
roughness scattering and Coulomb scattering of mobile carriers by occupied interface states and fixed oxide charges. We have
developed a first principles, quasi-2D Coulomb scattering mobility model for SiC MOSFETs, that accounts for interface trapped
charges and oxide charges, screening by mobile carriers and temperature dependence. Using this mobility model we have shown that
Coulomb scattering plays a dominant role very close to the interface. A few nanometers away from the interface, Coulomb scattering
is greatly reduced, and other scattering mechanisms control the total low field mobility. We have extracted values for the fixed oxide
charge and the interface trap charge density profile by fitting our simulated IV curves to experimental data. Our simulations show that
interface trap density values are low in the midgap region and very high near the conduction band edge in 4H SiC and that they
severely limit device operation.
2. Interface Trap Density Profile:
Our model for the interface trap density for 4H SiC has a constant
distribution in the midband region and an exponential increase near the
band edge as shown in figure 1. Our analysis indicates the traps are acceptor
like above midgap and donor type below it. The exponential rise in trap
density near the band edges gives a large number of filled acceptor traps
when the MOSFET is given a gate bias. These filled acceptor traps cause
Coulomb scattering of mobile charges in the inversion layer and also cause
a positive shift in the threshold voltage. With increase in temperature, the
number of filled traps decreases. Hence the threshold voltage should
decrease with increase in temperature. Also Coulomb scattering due to these
traps would decrease with increase in temperature giving better mobility
values at higher temperatures.
3. 4H SiC MOSFET Mobility Model:
The extremely high density of occupied interface traps in 4H SiC required
the development of an advanced Coulomb scattering mobility model for the
device simulator. As the effect of Coulomb scattering decreases with distance, the Coulomb mobility was required to have a depthdependence. As the traps are screened by the mobile electrons, it was necessary to put in a screening model for the Coulomb
scattering. In addition to the Coulomb scattering mobility, the bulk mobility, surface phonon mobility and surface roughness mobility
together give the low field mobility. The saturation velocity and parallel component of the electric field give the high field mobility.
The total mobility is a combination of the low field mobility and the high field mobility.
A) Quasi 2D Coulomb Scattering Mobility: To extract the quasi 2D Coulomb mobility, we start with a screened Coulomb potential
as given in (1). The scattering rate is obtained using the Fermi Golden Rule (4). In order to get the 2D matrix element (H2D) for
applying the Fermi Rule, we first take the 3D Fourier Transform of the coulomb potential (2) and then take its 1D inverse transform
(3). The total scattering rate for a N2D(zi) density of scattering charges can be written from the Fermi Golden Rule as (5).
V r  
e2 1 qscr
 e
4 r
 k k 
2
H 3 D  eik r | V  r  | eik r
(1)
(2)

H2D 


 H 2 D  z , zi     E k  E k  
2
(4)
H3D  e
iqz  z  zi 
dqz 

2
2
e2 exp   z  zi  q2 D  qsc

2
q22D  qsc2

N z  
1
 2 D 2 i  k dk    k  k  1  cos   d
  z , zi 
4
k  0
 0

(3)
(5)
The positions of the scattering charge centers are given by zi, while the position (depth) of the mobile carrier is given as z. zi is
positive inside the oxide away from the interface whereas z is positive inside the semiconductor away from the interface. The screened
Coulomb scattering mobility as a function of depth is obtained from this scattering rate. It has an inherent exponential dependence on
the distance between the mobile charge and the scattering charge center (7). The screening factor in the Coulomb potential depends on
the amount of inversion charge present and also on an average depth of the inversion layer (8). Coulomb scattering reduces drastically
over a short distance when there are a lot of mobile carriers present. Our method of dealing with coulomb scattering gives us a
coulomb mobility for a mobile charge at any location inside the semiconductor. This can be directly incorporated in the device
simulator. Our simulations showed that coulomb scattering is the dominant scattering mechanism for mobile charges close to the
interface and at low gate voltages.
1
C

m*e3 N 2 D  zi 
 F  z , zi 
16  2 k BTe

(6)
F  z , zi  
2




exp 2 qsc2  8m*k BTe sin 2 

1  qsc2
q
2
sc
2
 8m*k BTe sin 2 
 z  zi  
2

d
(7)
qsc 
e 2 N inv
 SiC Z avg k BT
(8)
The coulomb scattering mobility model shows that the scattering rate is directly proportional to the density of occupied interface traps
and the fixed charge density at the interface. Hence reducing the interface trap density will reduce coulomb scattering and improve
surface mobility. The coulomb scattering from the interface is an important problem in SiC devices due to the extremely high density
of interface traps at the Si02-SiC interface. The scattering rate decreases with increase in temperature. Hence coulomb mobility will
improve with increase in temperature.
Total Mobility: In addition to the coulomb scattering mechanism described above, the scattering mechanisms included in calculating
the total low field mobility are the surface phonon scattering and surface roughness scattering. The low field mobility is combined
with a high field mobility dependant on the saturation velocity to get the total mobility, and by Matheissen’s rule.
4. Simulation Results:
We want to extract values for the surface roughness parameter, fixed oxide charge and the interface trap density profile inside the
bandgap for 4H SiC MOSFETs. We can extract these values from the simulator by comparing the simulated ID-VGS characteristics at
low VDS to experimental data. Room temperature fits for ID-VGS from the simulator are shown in Figure 2. A fixed oxide charge
density of 1.8e12 cm-2 and the interface state density versus energy (Dit – E) profile shown in Figure 1 has been obtained. The Dit – E
profile seems to agree with a few experimentally measured values reported in literature. The extremely high Dit value close to the
bandgap gives rise to very large occupied interface trap density, which causes a positive shift in the threshold voltage and also lowers
the total mobility at low gate voltages. Figure 3 shows a comparison between the different low field mobilities at two different gate
voltages. It also shows how mobility changes with depth. As can be seen from the Figure 4 the peak of the current density is observed
some distance below the interface, and it moves closer to the interface with increase in gate voltage. Such a detailed picture of the
physics of the MOSFET can be obtained because of an extremely dense mesh generated in the channel of the device. Figure 5 shows
how the device current increases with increase in temperature. As the occupied interface trap density decreases with increase in
temperature, the inversion charge and the mobility increase, resulting in an increase in current.
5. References:
[1]