Simpledriftmodels
For the simple driftdiffusion model one can use several mobility models as
well as several generation/recombination models. So far the following different options
for the
mobility model are implemented:
 $mobilitymodelsimba0
 $mobilitymodelsimba1
 $mobilitymodelsimba2
 $mobilitymodelsimba3
 $mobilitymodelsimba4
 $mobilitymodelsimba5
 $mobilitymodelsimba0e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
 $mobilitymodelsimba1e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
 $mobilitymodelsimba2e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
 $mobilitymodelsimba3e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
 $mobilitymodelsimba4e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
 $mobilitymodelsimba5e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
For Si we have two additional models:

$mobilitymodellom
! Lombardi
(makes only sense in 2D and 3D)

$mobilitymodeldar
! Darwish
(makes only sense in 2D and 3D)
For undoped structures we have a constant mobility model:

$mobilitymodelconstant
! for undoped structures only
Further models are:
 $mobilitymodelarora
! phonon
and impurity scattering
 $mobilitymodelmasetti ! phonon
and impurity scattering
 $mobilitymodelminimos ! phonon
and impurity scattering
Three generation/recombination models are implemented:
ShockleyReadHall (SRH),
Auger and
direct recombination.
To implement more see the "How to ?" section.
!!
$simpledriftmodels
optional !
modelnumber
integer
required !
currentmodelnumbers
integer_array
required !
mobilitymodel
character
required !
chargecarriers
character
optional !
SRHrecombination
character
optional !
Augerrecombination
character
optional !
directrecombination
character
optional !
minimumdensityelectrons
double optional
!
minimumdensityholes
double optional
!
$end_simpledriftmodels
optional !
!!
Syntax:
modelnumber = 1
Sequential number to label the certain model.
currentmodelnumbers = 1
Refers to modelnumber in
$currentmodels .
mobilitymodel = mobilitymodelsimba0 !
no parallel E field dependence
= mobilitymodelsimba1 !
temperature dependent peak E field
= mobilitymodelsimba2 !
temperature dependent saturation velocity
= mobilitymodelsimba3 !
temperature dependent peak E field
= mobilitymodelsimba4 !
temperature dependent saturation velocity
= mobilitymodelsimba5 !
temperature dependent peak E field
=
mobilitymodelsimba0e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodelsimba1e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodelsimba2e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodelsimba3e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodelsimba4e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodelsimba5e ! with perpendicular
E field dependence (makes only sense in 2D and 3D)
=
mobilitymodellom ! Lombardi model,
for Si only
(makes only sense in 2D and 3D)
=
mobilitymodeldar ! Darwish model, for Si only
(makes only sense in 2D and 3D)
=
mobilitymodelconstant ! for undoped structures only
=
mobilitymodelarora ! phonon
and impurity scattering
=
mobilitymodelmasetti ! phonon
and impurity scattering
=
mobilitymodelminimos ! phonon
and impurity scattering
Since it is possible to have more than one mobility model one can specify a
model that has to be declared in the database under keyword
$mobilitymodelsimba or
$mobilitymodellom or
$mobilitymodeldar or
$mobilitymodelconstant or
$mobilitymodelarora
or
$mobilitymodelmasetti
or
$mobilitymodelminimos .
chargecarriers = electronsandholes !
(default)
= electronsonly !
ignore convergence of hole Fermi level E_{F,p}
= holesonly !
ignore convergence of electron Fermi level E_{F,n}
To speed up the calculations, we allow for a simplified charge carrier
model.
 electronsonly : The current is fully
dominated by electrons.
 holesonly :
The current is fully dominated by holes.
This means that the convergence of the currentPoisson equation is already
achieved, if for only one type of charge carrier (electrons or holes) the
Fermi level has been converged.
The Poisson equation (i.e. the electrostatic potential) must have been converged
in any case.
Note: For currentpoissonmethod = blockit
(blockiterative), the Fermi levels for the charge carrier type that is
excluded, is not calculated at all.
SRHrecombination = yes
= no
ShockleyReadHall (SRH)
recombination: Flag whether this generation/recombination process has to be used.
Augerrecombination = yes
= no
Auger recombination: Flag whether this generation/recombination process has to be used.
direct recombination = yes
= no
Direct recombination: Flag whether this generation/recombination process has to be used.
Minimum density
minimumdensityelectrons = 1d10
! [1/cm^3]
(default value: 1d10 )
minimumdensityholes = 1d10
! [1/cm^3]
(default value: 1d10 )
improves condition number of current equation matrix
choose as large as possible, but smaller than
minimum density in converged result
Minimum charge carrier density (lower limit) for both electrons and holes that can
appear in driftdiffusion current equations.
The minimum density might have to be increased in order to obtain
convergence for the driftdiffusion current equations.
The minimum density should be as low as possible.
The minimum density can be chosen as large as
possible but should be smaller than the minimum density in the converged
result.
As the driftdiffusion current is proportional to the charge carrier
density, this eventually also sets the lower limit of the current.
The minimum density is a useful flag for structures where regions are
present that have almost no density (e.g. a barrier, or insulator).
If the density in such an insulator is below 1  10^{3} cm^{3},
the product of 'mu n' in the driftdiffusion current equation varies over
several orders of magnitude.
Consequently, the matrix used in the linear solver is not well conditioned.
Here, the current through these insulating regions is basically zero which has
implications on the convergence behavior of the driftdiffusion current
equations.
Increasing the minimum density will help in these cases.
A useful value for the minimum density of a certain material depends on the
band gap because its intrinsic density also depends on the band gap.
A wideband gap material has a much lower intrinsic density than a lowband
gap material.
