Simple-drift-models
For the simple drift-diffusion 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:
- $mobility-model-simba-0
- $mobility-model-simba-1
- $mobility-model-simba-2
- $mobility-model-simba-3
- $mobility-model-simba-4
- $mobility-model-simba-5
- $mobility-model-simba-0e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
- $mobility-model-simba-1e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
- $mobility-model-simba-2e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
- $mobility-model-simba-3e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
- $mobility-model-simba-4e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
- $mobility-model-simba-5e ! with perpendicular E field dependence
(makes only sense in 2D and 3D)
For Si we have two additional models:
-
$mobility-model-lom
! Lombardi
(makes only sense in 2D and 3D)
-
$mobility-model-dar
!
For undoped structures we have a constant mobility model:
-
$mobility-model-constant
! for undoped structures only
- $mobility-model-arora
! phonon
and impurity scattering
- $mobility-model-masetti !
- $mobility-model-minimos !
Three generation/recombination models are implemented:
Shockley-Read-Hall (SRH),
Auger and
direct recombination.
To implement more see the "How to ?" section.
!--------------------------------------------------------------!
$simple-drift-models
optional !
model-number
integer
required !
current-model-numbers
integer_array
required !
mobility-model
character
required !
charge-carriers
character
optional !
SRH-recombination
character
optional !
Auger-recombination
character
optional !
direct-recombination
character
optional !
minimum-density-electrons
double optional
!
minimum-density-holes
double optional
!
$end_simple-drift-models
optional !
!--------------------------------------------------------------!
Syntax:
model-number = 1
Sequential number to label the certain model.
current-model-numbers = 1
Refers to model-number in
$current-models.
mobility-model = mobility-model-simba-0 !
no parallel E field dependence
= mobility-model-simba-1 !
= mobility-model-simba-2 !
= mobility-model-simba-3 !
temperature dependent peak E field
= mobility-model-simba-4 !
= mobility-model-simba-5 !
=
mobility-model-simba-0e !
=
mobility-model-simba-1e !
=
mobility-model-simba-2e !
=
mobility-model-simba-3e !
=
mobility-model-simba-4e !
=
mobility-model-simba-5e !
=
mobility-model-lom !
=
mobility-model-dar !
=
mobility-model-constant ! for undoped structures only
=
mobility-model-arora ! phonon
and impurity scattering
=
mobility-model-masetti ! phonon
and impurity scattering
=
mobility-model-minimos !
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
$mobility-model-simba
$mobility-model-lom or
$mobility-model-dar or
$mobility-model-constant or
$mobility-model-arora
or
$mobility-model-masetti
$mobility-model-minimos
charge-carriers = electrons-and-holes !
(default)
= electrons-only !
= holes-only !
ignore convergence of electron Fermi level EF,n
To speed up the calculations, we allow for a simplified charge carrier
model.
- electrons-only: The current is fully
dominated by electrons.
- holes-only:
The current is fully dominated by holes.
This means that the convergence of the current-Poisson 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 current-poisson-method = blockit
(block-iterative), the Fermi levels for the charge carrier type that is
excluded, is not calculated at all.
SRH-recombination = yes
= no
Shockley-Read-Hall (SRH)
recombination: Flag whether this generation/recombination process has to be used.
Auger-recombination = 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
minimum-density-electrons = 1d-10
! [1/cm^3]
(default value: 1d-10)
minimum-density-holes = 1d-10
! [1/cm^3]
1d-10)
Minimum charge carrier density (lower limit) for both electrons and holes that can
appear in drift-diffusion current equations.
The minimum density might have to be increased in order to obtain
convergence for the drift-diffusion 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 drift-diffusion 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 - 103 cm-3,
the product of 'mu n' in the drift-diffusion 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 drift-diffusion 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 wide-band gap material has a much lower intrinsic density than a low-band
gap material.
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