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Physical Models
There are now problems remain unspecified in the above Intel’s and Lombardi models. That
is the evaluation of the transverse field and the reduction due to the longitudinal field. We discuss these
issues in the following subsections.
3.1.2.3 Evaluation of Transverse Electric Field
The transverse field is defined as the field component the direction of which is perpendicular to the
current flow, so, mathematically
E × j
E ⊥ = ---------------
(3.20)
j
PISCES-2ET uses this formula to evaluate E ⊥ in the above three mobility models if the parameter
strfld is not specified in model card. Such evaluation is computationally costly and might also
cause numerically instability. Another alternative and simplification is to evaluate the normal field
component based on the geometric proximity to the Si/SiO 2 interface. Thus when strfld is
specified, the following formula is used:
E ⊥ E y e y y int
=
(3.21)
where y is the coordinate in the axis perpendicular to the interface, E y is the transverse field at the
interface (y int
), and L is the characteristic length which has a value of 0.5µ.
3.1.2.4 Watt’s Surface Mobility Model
–( – ) ⁄ L
J. Watt of Stanford proposed a simple approach to modeling the surface mobility in the inversion layer
in silicon near the Si-SiO 2 interface [9]. The inversion layer is assumed to be confined only in the first
grid spacing in the silicon at the direction perpendicular to the interface. Thus the interface is at the top
of the inversion layer whereas the first grid in the silicon lies at the bottom of the inversion layer. The
requirement for the meshing when this model is to apply is that the top grid spacing should be
reasonably large (a couple of hundred angstroms), quite contrary to the conventional thought that the
meshing should be dense at the substrate surface. The carrier mobility in the inversion layer, µ 0,
inv ,
depends on the effective transverse field, E ⊥,
eff , in the inversion layer. The model accuracy has been
verified against the measurement and is in agreement with the universal mobility model requirement
[10]. This model can be invoked by using parameter srfmob in the model card. The effective
transverse field, , is defined and calculated as:
E ⊥,
eff
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 21