mobility-model-minimos

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The mobility model used in MINIMOS 6 is used to simulate the doping dependent mobility in Si and takes into account the scattering of the carriers by charged impurity ions which leads to a degradation of the carrier mobility (ionized impurity scattering). This model is temperature dependent and takes into account the reduced mobility due to lattice scattering (i.e. the values in the database under keyword $mobility-model-constant are the same as under this keyword). It is a model that combines lattice and impurity scattering.

The formula of Caughey and Thomas (D. Caughey, R. Thomas, Carrier Mobilities in Silicon Empirically Related to Doping and Field, Proc. IEEE 55, 2192 (1967)) is used together with temperature dependent coefficients. This model is well suited for Si.

The total concentration of ionized impurities is given by N_D+N_A.
Note: In nextnano³ we use the nominal dopant concentration as specified in the input file and not the ionized one.

For T >= 200 K: (1)

For T < 200 K: (2)

By setting
alpha_mⁿ =alpha_m2ⁿ,
alpha_m^p =alpha_m2^p and
alpha_aⁿ = alpha_a^p = 0equation (2) reduces to equation (1) and this model can also be applied to other basic materials.

The parameter values used in this model for electrons and holes, respectively, are taken from the PhD thesis of V. Palankovski "Simulation of Heterojunction Bipolar Transistors" (TU Vienna). (Note: The exponents n-gamma-lattice-temp,p-gamma-lattice-temphave opposite sign in his PhD thesis.)

Parameter in formula		Description	Input parameter
electrons	holes		electrons	holes
µ_minⁿ(T₀)	µ_min^p(T₀)	reference mobility parameter	`n-mu-min`	`p-mu-min`
alpha_mⁿ	alpha_m^p	exponent	`n-alpha-mu-min`	`p-alpha-mu-min`
alpha_m2ⁿ	alpha_m2^p	exponent	`n-alpha-mu-min2`	`p-alpha-mu-min2`
N₀ⁿ	N₀^p	reference impurity parameter	`n-n0`	`p-n0`
alpha_Nⁿ	alpha_N^p	exponent	`n-alpha-n0`	`p-alpha-n0`
A_aⁿ	A_a^p	reference exponent parameter	`n-a-a`	`p-a-a`
alpha_aⁿ	alpha_a^p	exponent	`n-alpha-a-a`	`p-alpha-a-a`
µ_constⁿ	µ_const^p	result of `$mobility-model-constant`
N_D	N_A	concentration of ionized donors/acceptors
T	T	lattice temperature
T₀	T₀	temperature (300 K)

!-------------------------------------------------------------! $mobility-model-minimos optional ! ! material-name character required ! number-of-parameters integer required ! ! !++++++++++++++++++++++++++++++++++++ ! for binaries, e.g. GaAs !++++++++++++++++++++++++++++++++++++ n-mu-lattice-temp double optional ! [cm²/Vs] same as$mobility-model-constant n-gamma-lattice-temp double optional ! [] same as$mobility-model-constant (but different sign as in MINIMOS documentation) n-mu-min double optional ! [cm²/Vs] n-alpha-mu-min double optional ! [] n-alpha-mu-min2 double optional ! [] n-n0 double optional ! [cm^-3] n-alpha-n0 double optional ! [] n-a-a double optional ! [] n-alpha-a-a double optional ! [] ! p-mu-lattice-temp double optional ! [cm²/Vs] same as$mobility-model-constant p-gamma-lattice-temp double optional ! [] same as$mobility-model-constant (but different sign as in MINIMOS documentation) p-mu-min double optional ! [cm²/Vs] p-alpha-mu-min double optional ! [] p-alpha-mu-min2 double optional ! [] p-n0 double optional ! [cm^-3] p-alpha-n0 double optional ! [] p-a-a double optional ! [] p-alpha-a-a double optional ! [] ! ! !++++++++++++++++++++++++++++++++++++ ! for ternaries, e.g. Al(x)Ga(1-x)As !++++++++++++++++++++++++++++++++++++ n-bow-mu-lattice-temp double optional ! [cm²/Vs]for alloys n-bow-gamma-lattice-temp double optional ! [] for alloys n-bow-mu-min double optional ! [cm²/Vs]for alloys n-bow-alpha-mu-min double optional ! [] for alloys n-bow-alpha-mu-min2 double optional ! [] for alloys n-bow-n0 double optional ! [cm^-3] for alloys n-bow-alpha-n0 double optional ! [] for alloys n-bow-a-a double optional ! [] for alloys n-bow-alpha-a-a double optional ! [] for alloys ! p-bow-mu-lattice-temp double optional ! [cm²/Vs]for alloys p-bow-gamma-lattice-temp double optional ! [] for alloys p-bow-mu-min double optional ! [cm²/Vs]for alloys p-bow-alpha-mu-min double optional ! [] for alloys p-bow-alpha-mu-min2 double optional ! [] for alloys p-bow-n0 double optional ! [cm^-3] for alloys p-bow-alpha-n0 double optional ! [] for alloys p-bow-a-a double optional ! [] for alloys p-bow-alpha-a-a double optional ! [] for alloys ! $end_mobility-model-minimos 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 = 18Control 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 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-mu-lattice-temp = 0d0 ! [cm²/Vs] Bowing parameters are zero if linear interpolation is used....