$mobility-model-minimos

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 ([CaugheyThomas1967]) 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: 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 = 0, equation (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-temp have opposite sign in his PhD thesis.)

Parameter in formula		Description	Input parameter
electrons	holes		electrons	holes
µminn(T0)	µminp(T0)	reference mobility parameter	n-mu-min	p-mu-min
alphamn	alphamp	exponent	n-alpha-mu-min	p-alpha-mu-min
alpham2n	alpham2p	exponent	n-alpha-mu-min2	p-alpha-mu-min2
N0n	N0p	reference impurity parameter	n-n0	p-n0
alphaNn	alphaNp	exponent	n-alpha-n0	p-alpha-n0
Aan	Aap	reference exponent parameter	n-a-a	p-a-a
alphaan	alphaap	exponent	n-alpha-a-a	p-alpha-a-a
µconstn	µconstp	result of $mobility-model-constant
ND	NA	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 !