$mobility-model-simba

This is one possible model for the mobility parameter µ_n (for electrons) and µ_p (for holes) that is used in the drift-diffusion model. The model is taken from the SIMBA manual (Caughey/Thomas model: [CaugheyThomas1967]).

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

• doping density N_D/N_A

• 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: E_peak

- Model 2: v_saturation

- Model 3: E_peak, v_saturation

- Model 4: v_saturation

- Model 5: E_peak, v_saturation

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: 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 E_p,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 kappa^n,p are temperature dependent then this equation is called Canali model (with µ^p,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 v^p,n_s

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 !

material-name = Si  ! or Al(x)Ga(1-x)As

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-).

The specifiers containing *-bow-* are for alloys, i.e. ternaries. By default, linear interpolation is used if the bowing parameter is zero.

 material-name        = Si
 number-of-parameters = 28

 n-alpha-doping       = 0.73     ! []
 n-N-ref-doping       = 1.072e17 ! [1/cm^3]
 n-mu-min             = 55.2     ! [cm^2/Vs]
 n-mu-doping          = 1374.0   ! [cm^2/Vs]
 n-gamma-temp         = 1.5      ! []
 n-E0-saturation      = 8.0e3    ! [V/cm]
 n-T0-E-saturation    = 300.0    ! [K]
 n-temp-dependence-E  = 0.0      ! [V/Kcm]
 n-alpha-E            = 2.0      ! []
 n-beta-E             = 0.5      ! []
 n-v0-saturation      = 1.03e7   ! [cm/s]
 n-temp-dependence-v  = 0.0      ! [cm/Ks]
 n-kappa-v            = 2.0      ! []
 n-ET-perpendicular   = 64970    ! [V/cm]

 p-alpha-doping       = 0.70     ! []
 p-N-ref-doping       = 1.606e17 ! [1/cm^3]
 p-mu-min             = 49.7     ! [cm^2/Vs]
 p-mu-doping          = 429.67   ! [cm^2/Vs]
 p-gamma-temp         = 2.3      ! []
 p-E0-saturation      = 1.95e4   ! [V/cm]
 p-T0-E-saturation    = 300.0    ! [K]
 p-temp-dependence-E  = 0.0      ! [V/Kcm]
 p-alpha-E            = 1.0      ! []
 p-beta-E             = 1.0      ! []
 p-v0-saturation      = 1.03e7   ! [cm/s]
 p-temp-dependence-v  = 0.0      ! [cm/Ks]
 p-kappa-v            = 1.0      ! []
 p-ET-perpendicular   = 1.87e4   ! [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  = 28
n-bow-alpha-doping    = 0.0  ! [cm2/Vs]
...