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

Physical Models
interface. All the models discussed so far are of local field nature. In next section we will discuss two
non-local models, both developed at University of Texas, Austin.
3.1.2.5 Shin’s Non-local Transverse Field Models
A non-local mobility model is the one in which the mobility is not solely determined by the local
electric field and there are some non-local quantities in the mobility formulation. For example, the
mobility in the inversion layer at the surface of the substrate below the gate oxide may also be affected
by the inversion layer conditions (layer thickness, etc.). In the following, we first provide the model
formulation and then state briefly the requirement on the user input. The first model, invoked by
parameter oldtfld in model card has the following dependence [11]:
µ ( N, T L , E ⊥ , E || )
=
µ 0 ( N, T L , E ⊥ ) E ⊥ – E
--------------------------------- --------------------------------------- dµ 0 0
+
---------
µ 0 E ||
1 + -----------
⎝
⎛ µ 0 E ||
⎠
⎞2 1 + -----------
⎝
⎛ ⎠
⎞2
3 ⁄ 2dE ⊥
v sat
v sat
(3.24)
where the dependence of µ 0 is listed only once. Note that all four parameters, N, T L , E ⊥ , and E || are
functions of space, so are µ and µ 0 . The non-locality is represented by the quantity of E 0 which is
defined as the transverse electric field at the edge (i.e. bottom) of the inversion layer. The inversion
layer edge is in turn determined by the criterion that the inverted carrier concentration starts to drop
below the doping density. The expression for is
µ 0
where
µ 0 ( N, T L , E ⊥ )
=
⎛ ------------------------ 1
3.2 –9
×10 --T p 1 ⁄ 2
+
⎞ – 1
⎝ – 5 ⁄ 2
1150T
z L
⎠
L
(3.25)
3 ⁄ 2
p = 0.09T L + 1.5×10
–8
N f
----------------
n 1 ⁄ 4 T L
(3.26)
0.039T
z
L 1.24×10
= ------------------- + ------------------------------
E ⊥ + E
------------------ 0 ⎛
E ⊥ + E
------------------ 0 ⎞ 1 ⁄ 3
2 ⎝
2
⎠
(3.27)
where n is the inverted carrier density in the inversion layer and in this particular case is the electron
concentration for the n-channel MOSFET, and N f is the fixed interface charge per unit area at the Si/
–5
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 23