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MINIMOS mobility model

More documentation on the MINIMOS mobility model ==> nextnano³ documentation

binary_zb {
 name    = Si                                     # material name, e.g. Si, GaAs, InP, ...

 ...

 mobility_minimos{
   electrons{
     muL300     = 1430                            # bulk phonon mobility for electrons [cm2/Vs] (same as mobility_constant{})
     muLexpT    = -2                              # temperature dependence exponent []           (same as mobility_constant{}
                                                                                      apart from the sign)
     muLImin300 = 80       muLIexpTabove = -0.45  # reference mobility   parameter    [cm2/Vs] and exponent []
                           muLIexpTbelow = -0.15  # [] exponent
     TSwitch    = 200                             # [K] switch between equations at this temperature
     Cref300    = 1.12e17  CrefexpT      = 3.2    # reference impurity   parameter    [cm-3]   and exponent []
     alpha300   = 0.72     alphaexpT     = 0.065  # reference exponent parameter    []         and exponent []
   }
   holes{
     muL300     = 460                             # bulk phonon mobility for holes    [cm2/Vs] (same as mobility_constant{})
     muLexpT    = -2.18                           # temperature dependence exponent []      (same as mobility_constant{}
                                                                                      apart from the sign)
     muLImin300 = 45       muLIexpTabove = -0.45  # reference mobility   parameter    [cm2/Vs] and exponent []
                           muLIexpTbelow = -0.15  # [] exponent
     TSwitch    = 200                             # [K] switch between equations at this temperature
     Cref300    = 2.23e17  CrefexpT      = 3.2    # reference impurity   parameter    [cm-3]   and exponent []
     alpha300   = 0.72     alphaexpT     = 0.065  # reference exponent parameter    []       and exponent []
   }
 }
}

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).

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 accout the reduced mobility due to lattice scattering (i.e. the values in the database under keyword mobility_constant{} are the same as under this keyword apart from the sign of the exponent). 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.

     => (Here we have to insert the equation for the mobility.)

The total concentration of ionized impurities is given by N_D+N_A where N_D and N_A are the concentration of ionized donors or acceptors, respectively.
Note: In nextnano++ we use the nominal dopant concentration as specified in the input file and not the ionized one.
µ_const is the result of mobility_constant{}.

Tswitch = TSwitch = 200 K

For T >= Tswitch: =>    µ_min(T) = muLImin300 (T / T₀)-muLIexpTabove                      (1)

For T <  Tswitch: =>    µ_min(T) = muLImin300 (2/3)^{-muLIexpTabove}  (T / 200 K)-muLIexpTbelow     (2)

By setting
  muLIexpTabove = muLIexpTbelow   and
  alphaexpT     = 0
equation (2) reduces to equation (1) and this model can also be applied to other basic materials.

T₀ = 300 K, T = temperature

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).