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  mobility-model-simba

 

 

 
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mobility-model-simba

This is one possible model for the mobility parameter µn (for electrons) and µp (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
     
  • 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 Units Input parameter
electrons holes     electrons holes
µnmin µp,min minimum mobility [cm^2/Vs] n-mu-min p-mu-min
Nnref Npref reference doping density [1/cm^3] n-N-ref-doping p-N-ref-doping
µnD µpD reference mobility [cm^2/Vs] n-mu-doping p-mu-doping
alphan alphap exponent for Caughey/Thomas model [] n-alpha-doping p-alpha-doping
ND NA concentration of ionized donors/acceptors [1/cm^3]

Note: In nextnano³ we use the nominal dopant concentration as specified in the input file and not the ionized one.

 

 

  • Temperature


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

 

 

  • Electric field (perpendicular electric field)


Parameter in formula Description Units Input parameter
electrons holes     electrons holes
EnT EpT ET normal [V/cm] 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 Units Input parameter
electrons holes     electrons holes
alphan alphap alpha parameter for electric field dependence [] n-alpha-E p-alpha-E
betan betap beta parameter for electric field dependence [] n-beta-E p-beta-E

- Temperature dependence of peak electric field Ep,np

      

Parameter in formula Description Units Input parameter
electrons holes     electrons holes
En0 Ep0 peak electric field E0 [V/cm] n-E0-saturation p-E0-saturation
dnE dpE temperature dependence parameter d of peak electric field [V/Kcm] n-temp-dependence-E n-temp-dependence-E
Tn0 Tp0 reference temperature [K] 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 µp,n as the low field mobility).

Parameter in formula Description Units Input parameter
electrons holes     electrons holes
kappan kappap exponent kappa for electric field dependence [] n-kappa-v p-kappa-v

- Temperature dependence of saturation velocity vp,ns

Parameter in formula Description Units Input parameter
electrons holes     electrons holes
vn0 vp0 saturation velocity v0 [cm/s] n-v0-saturation p-v0-saturation
dnv dpv temperature dependence parameter d of saturation velocity [cm/Ks] n-temp-dependence-v n-temp-dependence-v
Tn0 Tp0 reference temperature [K] 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 !
                                                              !
!++++++++++++++++++++++++++++++++++++
! for binaries, e.g. GaAs
!++++++++++++++++++++++++++++++++++++
 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 !
                                                              !
                                                              !
!++++++++++++++++++++++++++++++++++++
! for ternaries, e.g. Al(x)Ga(1-x)As
!++++++++++++++++++++++++++++++++++++
 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]
 

!++++++++++++++++++++++++++++++++++++
! for ternaries, e.g. Al(x)Ga(1-x)As
!++++++++++++++++++++++++++++++++++++
The specifiers containing "*-bow-*" are for alloys, i.e. ternaries.
By default, linear interpolation is used if the bowing parameter is zero.

material-name         = Al(x)Ga(1-x)As
number-of-parameters  = 4
n-bow-alpha-doping    = 0d0  ! [cm2/Vs]  
Bowing parameters are zero if linear interpolation is used.
...

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