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

Physical Models
µ ( N, T L , E ⊥ , E || ) = r para ( E || )µ 0
( N, T L , E ⊥ )
and the reduction factor is modeled as (refer to [14])
r para
(3.29)
(3.30)
where in silicon β is 1.395 for electrons and 1.215 for holes, and the saturation velocity, v sat , has the
expression in Table 3.9. The parameter β can be changed by the user through two parameters,
b.electrons and b.holes, in the model card.
3.1.3.2 GaAs Mobility Models
µ 0 ( N, T L , E ⊥ )E ||
r para = 1 + ---------------------------------------
⎝
⎛ ⎠
⎞β
v sat
It can be deduced from Eqs. (3.29)-(3.30) that the carrier drift velocity, which is equal to ,
increases monotonically as E || increase and saturates at v sat . However, for electrons in the bulk GaAs
due to the existence of several valleys with different effective mass in the conduction band structure,
the drift velocity reaches a peak as the electric field is increased to a critical value and then the velocity
decreases as the field further increases. This phenomenon, if viewed from the mobility modeling point
of view, amounts to a negative differential mobility (defined as dv ⁄ dE || ). To model this field
dependence for electrons in GaAs, a model proposed first by Thim [15] is used as follows:
– 1 ⁄ β
µE ||
µ ( N, T L , E || )
=
v sat
µ 0 ( N,
T L ) ------- E ||
+ ⎛-----
⎞ 4
E ⎝E 0
⎠
-----------------------------------------------------
E ||
1 + -----
⎝
⎛ ⎠
⎞4
E 0
(3.31)
where E 0
is the critical field and has a default value of 4kV/cm, and v sat = 1.13×10 – 1.2×10 T L . It
can be shown that when E > E 0 Eq. (3.31) leads to a negative differential mobility (NDM). This is the
default field dependent mobility model for electrons in GaAs and the value of E 0
can be altered by the
user through the parameter E0 in the model card.
One problem related to the above formulation is that when applied to the simulation of GaAs
MESFET, the drain output characteristics (current vs. voltage) may exhibit an unrealistic zig-zag
behavior. One possible reason is that the correct mobility model in the bulk may not be suitable to the
carriers in the surface channel. In the program, we provide another mobility model for electrons in
GaAs, in which the carrier velocity approaches the saturation velocity with increased field
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