$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
!--------------------------------------------