$mobility-model-constant¶
The constant mobility model is due to lattice scattering (phonon scattering) and depends only on the temperature. The lattice atoms oscillate about their equilibrium sites at finite temperature leading to a scattering of carriers which results in a temperature dependent mobility \(\mu_{\text{const}}\). \(\mu_{\text{L}}\) is the mobility due to bulk phonon (lattice) scattering. For all semiconductors the temperature dependent lattice mobility is modeled by a power law. 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).
This model is suited for undoped structure.
Note
The \(\gamma\) exponents n-gamma-lattice-temp, p-gamma-lattice-temp have opposite sign in both the PhD thesis of V. Palankovski
and in the MINIMOS documentation compared to the implementation of nextnano³.
In this model the mobility is constant and depends only on the temperature \(T\). The parameters in the database are given for electrons and holes,
\(\mu_{\text{const}}(T)=\mu_{\text{L}}\left(\frac{T}{T_0}\right)^{-\gamma}\),
where \(T_0=300 {~\text K}\).
$mobility-model-constant optional material-name character required number-of-parameters integer required n-mu-lattice-temp double optional n-gamma-lattice-temp double optional p-mu-lattice-temp double optional p-gamma-lattice-temp double optional !------------------------------ ! Bowing parameters for alloys !------------------------------ n-bow-mu-lattice-temp double optional n-bow-gamma-lattice-temp double optional p-bow-mu-lattice-temp double optional p-bow-gamma-lattice-temp double optional $end_mobility-model-constant optional
Explanation of specifiers.
- material-name
- type:
character
- presence:
required
- value:
e.g.
Si
Name of material to which this set of parameters applies. Name has to be listed in $default-materials.
- number-of-parameters
- type:
integer
- presence:
required
- value:
e.g.
4
Control parameter if the number of parameters provided is the same as demanded.
There are two sets of parameters, one for electrons (n) and one for holes (p).
- n-mu-lattice-temp
- type:
double
- presence:
required
- value:
e.g.
1417- unit:
[cm^2/Vs]
\(\mu_{\text{L,n}}\) is the bulk phonon mobility for electrons.
- n-gamma-lattice-temp
- type:
double
- presence:
required
- value:
e.g.
2.5- unit:
[]
\(\gamma_{\text{n}}\) is the exponent of the temperature dependence for electrons.
Bowing parameters
- n-bow-mu-lattice-temp
- type:
double
- presence:
optional
- value:
e.g.
0.0- unit:
[cm^2/Vs]
For ternary alloys there are also bowing parameters possible.
n-bow-mu-lattice-temp = 0.0 means zero bowing, i.e. linear interpolation is used.
- n-bow-gamma-lattice-temp
- type:
double
- presence:
optional
- value:
e.g.
0.0- unit:
[]
Bowing parameters
n-bow-gamma-lattice-temp = 0.0 means zero bowing, i.e. linear interpolation is used.
- p-mu-lattice-temp
- unit:
[cm^2/Vs]
Same as n-mu-lattice-temp but for holes, \(\mu_{\text{L,p}}\).
- p-gamma-lattice-temp
- unit:
[]
Same as n-gamma-lattice-temp but for holes, \(\gamma_{\text{p}}\).
- p-bow-mu-lattice-temp
- unit:
[cm^2/Vs]
Same as n-bow-mu-lattice-temp but for holes.
- p-bow-gamma-lattice-temp
- unit:
[]
Same as n-bow-gamma-lattice-temp but for holes.
Example
!-------------------------------------------- $mobility-model-constant material-name = GaAs number-of-parameters = 4 n-mu-lattice-temp = 8500 ! [cm^2/Vs] PhD thesis V. Palankovski n-gamma-lattice-temp = 2.2 ! [] PhD thesis V. Palankovski but opposite sign compared to MINIMOS p-mu-lattice-temp = 800 ! [cm^2/Vs] PhD thesis V. Palankovski p-gamma-lattice-temp = 0.9 ! [] PhD thesis V. Palankovski but opposite sign compared to MINIMOS material-name = Al(x)Ga(1-x)As number-of-parameters = 4 n-bow-mu-lattice-temp = 0.0 ! [cm^2/Vs] n-bow-gamma-lattice-temp = 0.0 ! [] p-bow-mu-lattice-temp = 0.0 ! [cm^2/Vs] p-bow-gamma-lattice-temp = 0.0 ! [] $end_mobility-model-constant !--------------------------------------------