mobility-model-simba

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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: 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 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
µⁿ_min	µ^p_,min	minimum mobility	`[cm^2/Vs]`	`n-mu-min`	`p-mu-min`
Nⁿ_ref	N^p_ref	reference doping density	`[1/cm^3]`	`n-N-ref-doping`	`p-N-ref-doping`
µⁿ_D	µ^p_D	reference mobility	`[cm^2/Vs]`	`n-mu-doping`	`p-mu-doping`
alphaⁿ	alpha^p	exponent for Caughey/Thomas model	`[]`	`n-alpha-doping`	`p-alpha-doping`
N_D	N_A	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	T^p₀	reference temperature	`[K]`	`n-T0-E-saturation`	`p-T0-E-saturation`
gammaⁿ	gamma^p	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
Eⁿ_T	E^p_T	E_T 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	alpha^p	alpha parameter for electric field dependence	`[]`	`n-alpha-E`	`p-alpha-E`
betaⁿ	beta^p	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	E^p₀	peak electric field E₀	`[V/cm]`	`n-E0-saturation`	`p-E0-saturation`
dⁿ_E	d^p_E	temperature dependence parameter d of peak electric field	`[V/Kcm]`	`n-temp-dependence-E`	`n-temp-dependence-E`
Tⁿ₀	T^p₀	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	kappa^p	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	v^p₀	saturation velocity v₀	`[cm/s]`	`n-v0-saturation`	`p-v0-saturation`
dⁿ_v	d^p_v	temperature dependence parameter d of saturation velocity	`[cm/Ks]`	`n-temp-dependence-v`	`n-temp-dependence-v`
Tⁿ₀	T^p₀	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 = SiName of material to which this set of parameters applies. Name has to be listed in $default-materials.

number-of-parameters = 28Control 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.