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mobility-model-simba

This is one possible model for the mobility parameter n (for electrons) and p (for holes) that is used in the drift-diffusion model. The model is taken from the SIMBA manual (Caughey/Thomas model: D. Caughey, R. Thomas, Carrier Mobilities in Silicon Empirically Related to Doping and Field, Proc. IEEE 55, 2192 (1967)).

In this model the mobility depends on three quantities and is calculated in this order:

  • doping density                        ND/NA
  • temperature                            T
  • electric field (perpendicular)     E_|_
    -> 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)
    -> mobility-model-simba-0  ! without perpendicular E field dependence
    -> mobility-model-simba-1  ! without perpendicular E field dependence
    -> mobility-model-simba-2  ! without perpendicular E field dependence
    -> mobility-model-simba-3  ! without perpendicular E field dependence
    -> mobility-model-simba-4  ! without perpendicular E field dependence
    -> mobility-model-simba-5  ! without perpendicular E field dependence
    More details: $mobility-models
  • electric field (parallel)              E||
    - Model 0: no parallel electric field dependence
    - Model 1: Epeak
    - Model 2: vsaturation
    - Model 3: Epeak, vsaturation
    - Model 4: vsaturation
    - Model 5: Epeak, vsaturation

There are parameters given in the database for electrons and holes.

 

 

Dependence on...

  • Doping concentration


Parameter in formula Description Input parameter
electrons holes   electrons holes
nmin p,min minimum mobility n-mu-min p-mu-min
Nnref Npref reference doping density n-N-ref-doping  p-N-ref-doping 
nD pD reference mobility n-mu-doping p-mu-doping
alphan alphap parameter for Caughey/Thomas model n-alpha-doping p-alpha-doping
ND NA concentration of ionized donors/acceptors

Note: In nextnano we use the nominal dopant concentration as specified in the input file and not the ionized one.

 

 

  • Temperature


Parameter in formula Description Input parameter
electrons holes   electrons holes
Tn0 Tp0 reference temperature n-T0-E-saturation p-T0-E-saturation
gamman gammap temperature dependence parameter n-gamma-temp p-gamma-temp
T T temperature

 

 

  • Electric field (perpendicular electric field)


Parameter in formula Description Input parameter
electrons holes   electrons holes
EnT EpT parameter n-ET-perpendicular n-ET-perpendicular

 

 

  • Electric field (parallel electric field)

Model 0 (SIMBA):   no dependence on parallel electric field

 

Model 1 (SIMBA):


Parameter in formula Description Input parameter
electrons holes   electrons holes
alphan alphap parameter n-alpha-E p-alpha-E
betan betap parameter n-beta-E p-beta-E

- Temperature dependence of peak electric field Ep,np

      

Parameter in formula Description Input parameter
electrons holes   electrons holes
En0 Ep0 peak electric field n-E0-saturation p-E0-saturation
dnE dpE temperature dependence n-temp-dependence-E n-temp-dependence-E
Tn0 Tp0 reference temperature n-T0-E-saturation n-T0-E-saturation

 

Model 2 (SIMBA):


If the exponents kappan,p are temperature dependent then this equation is called Canali model (with p,n as the low field mobility).

Parameter in formula Description Input parameter
electrons holes   electrons holes
kappan kappap parameter n-kappa-v p-kappa-v

- Temperature dependence of saturation velocity vp,ns

Parameter in formula Description Input parameter
electrons holes   electrons holes
vn0 vp0 saturation velocity n-v0-saturation p-v0-saturation
dnv dpv temperature dependence n-temp-dependence-v n-temp-dependence-v
Tn0 Tp0 reference temperature n-T0-E-saturation n-T0-E-saturation

 

 

Model 3 (SIMBA):

 

 

Model 4 (SIMBA):


 

Model 5 (SIMBA):

 
 

 

 

!-------------------------------------------------------------!
$mobility-model-simba                                optional !
                                                              !
 material-name                       character       required !
 number-of-parameters                integer         required !
                                                              !
 n-alpha-doping                      double          optional !
 n-N-ref-doping                      double          optional !
 n-mu-min                            double          optional !
 n-mu-doping                         double          optional !
 n-gamma-temp                        double          optional !
 n-E0-saturation                     double          optional !
Model 1,3,5
 n-T0-E-saturation                   double          optional !
Model 1,2,3,4,5
 n-temp-dependence-E                 double          optional !
Model 1,3,5
 n-alpha-E                           double          optional !
Model 1,3,5
 n-beta-E                            double          optional !
Model 1,3,5
 n-v0-saturation                     double          optional !
Model 2,3,4,5
 n-temp-dependence-v                 double          optional !
Model 2,3,4,5
 n-kappa-v                           double          optional !
Model 2,3,4,5
 n-ET-perpendicular                  double          optional !
                                                              !
 p-alpha-doping                      double          optional !
 p-N-ref-doping                      double          optional !
 p-mu-min                            double          optional !
 p-mu-doping                         double          optional !
 p-gamma-temp                        double          optional !
 p-E0-saturation                     double          optional !
Model 1,3,5
 p-T0-E-saturation                   double          optional !
Model 1,2,3,4,5
 p-temp-dependence-E                 double          optional !
Model 1,3,5
 p-alpha-E                           double          optional !
Model 1,3,5
 p-beta-E                            double          optional !
Model 1,3,5
 p-v0-saturation                     double          optional !
Model 2,3,4,5
 p-temp-dependence-v                 double          optional !
Model 2,3,4,5
 p-kappa-v                           double          optional !
Model 2,3,4,5
 p-ET-perpendicular                  double          optional !
                                                              !
                                                              !
 n-bow-alpha-doping                  double          optional !
for ternary alloys
 n-bow-N-ref-doping                  double          optional !
for ternary alloys
 n-bow-mu-min                        double          optional !
for ternary alloys
 n-bow-mu-doping                     double          optional !
for ternary alloys
 n-bow-gamma-temp                    double          optional !
for ternary alloys
 n-bow-E0-saturation                 double          optional !
for ternary alloys
 n-bow-T0-E-saturation               double          optional !
for ternary alloys
 n-bow-temp-dependence-E             double          optional !
for ternary alloys
 n-bow-alpha-E                       double          optional !
for ternary alloys
 n-bow-beta-E                        double          optional !
for ternary alloys
                                                              !
 p-bow-alpha-doping                  double          optional !
for ternary alloys
 p-bow-N-ref-doping                  double          optional !
for ternary alloys
 p-bow-mu-min                        double          optional !
for ternary alloys
 p-bow-mu-doping                     double          optional !
for ternary alloys
 p-bow-gamma-temp                    double          optional !
for ternary alloys
 p-bow-E0-saturation                 double          optional !
for ternary alloys
 p-bow-T0-E-saturation               double          optional !
for ternary alloys
 p-bow-temp-dependence-E             double          optional !
for ternary alloys
 p-bow-alpha-E                       double          optional !
for ternary alloys
 p-bow-beta-E                        double          optional !
for ternary alloys
                                                              !
$end_mobility-model-simba                            optional !
!-------------------------------------------------------------!

 

Syntax

material-name        = Si
Name of material to which this set of parameters applies. Name has to be listed in $default-materials.

number-of-parameters = 28
Control parameter if the number of parameters provided is the same as demanded.

The parameters are specified as shown in the tables above. There are two sets, one for electrons (n-) and one for holes (p-). For ternary alloys there are also bowing parameters possible (n-bow-/p-bow-).

material-name        = Si
number-of-parameters = 28
!
n-alpha-doping       = 0.73d0   ! [---]
n-N-ref-doping       = 1.072d17 ! [1/cm^3]
n-mu-min             = 55.2d0   ! [cm^2/Vs]
n-mu-doping          = 1374.0d0 ! [cm^2/Vs]
n-gamma-temp         = 1.5d0    ! [---]
n-E0-saturation      = 8.0d3    ! [V/cm]
n-T0-E-saturation    = 300.0d0  ! [K]
n-temp-dependence-E  = 0d0      ! [V/Kcm]
n-alpha-E            = 2.0d0    ! [---]
n-beta-E             = 0.5d0    ! [---]
n-v0-saturation      = 1.03d7   ! [cm/s]
n-temp-dependence-v  = 0d0      ! [cm/Ks]
n-kappa-v            = 2d0      ! [---]
n-ET-perpendicular   = 64970d0  ! [V/cm]


p-alpha-doping       = 0.70d0   ! [---]
p-N-ref-doping       = 1.606d17 ! [1/cm^3]
p-mu-min             = 49.7d0   ! [cm^2/Vs]
p-mu-doping          = 429.67d0 ! [cm^2/Vs]
p-gamma-temp         = 2.3d0    ! [---]
p-E0-saturation      = 1.95d4   ! [V/cm]
p-T0-E-saturation    = 300d0    ! [K]
p-temp-dependence-E  = 0d0      ! [V/Kcm]
p-alpha-E            = 1.0d0    ! [---]
p-beta-E             = 1.0d0    ! [---]
p-v0-saturation      = 1.03d7   ! [cm/s]
p-temp-dependence-v  = 0d0      ! [cm/Ks]
p-kappa-v            = 1d0      ! [---]
p-ET-perpendicular   = 1.87d4   ! [V/cm]
 

 

See also under section Keywords -> $mobility-model-simba.