PISCES-2ET and Its Application Subsystems - Stanford Technology ...

Physical Models
be used instead with this option. The range of the data for doping concentrations in silicon is from
14
21
N = 1×10
to 1×10 cm – 3 . If the doping concentration falls out of the above range then the closest
boundary value for the mobility is used, otherwise the following interpolation scheme is applied.
µ 0 ( N 2 )–
µ 0 ( N 1 ) N
µ 0 ( N ) = µ 0 ( N 1 ) + ---------------------------------------- log------
(3.3)
log( N 2 ⁄ N 1 ) N 1
where N 2 > N > N 1 . This model is valid for silicon only. Note that if any of the following parameters:
ccsmob, analytic, arora, and user1, is used with or without conmob specified in the model
card, that model takes precedence and the precedency of these models is user1, arora, analytic,
and ccsmob with each preceding one overriding the trailing ones.
3.1.1.3 Analytical Doping Dependent Mobility Model
This model is invoked by parameter analytic in the model card. The formulation for this model
is as follows:
µ 0 ( N,
T L ) = γµ surf ( N,
T L ) + ( 1 – γ )µ bulk ( N,
T L )
(3.4)
where γ is a coefficient with value between 0 and 1 depending on the relative distance from the surface/
interface, µ surf
and µ bulk
are mobilities in the surface layer and bulk, respectively. γ is determined by
an ERFC function as follows:
γ 0.5 erfc y – y int – d
= ⋅ ⎛-------------------------
⎞
(3.5)
⎝ λ ⎠
where the silicon and SiO 2 interface is assumed to be parallel to the x-axis, is the y coordinate of
the interface, d and λ are two parameters: one for offset and the other for the characteristic length.
Their default values are d = 0.06µ and λ = 0.03µ , and both can be accessed by users via parameters
int.off and char.int in mobility card, respectively.
The surface and bulk mobilities have the same form of dependence on N and T L
as follows:
y int
µ ( N,
T L )
T L
d
---------------------- 1 + α( N )
µ α ( N )
=
+ ---------------------- max 1 + α( N )
µ min
(3.6)
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 15