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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 (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 ND+NA.
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
 alphamn = alpham2n,
 alphamp = alpham2p and
 alphaa = alphaap = 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 !
!-------------------------------------------------------------!

 

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 = 18
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 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.
...