$SRH-recombination

The generation/recombination process can be assisted by impurities. This is modeled by the Shockley-Read-Hall model (SRH). The recombination/generation rates depend on the deviation of the carrier concentration from the equilibrium value and the scattering rates depend on the doping concentration.

$R_{\text{SRH}}=\frac{pn-n_{\text{i}}^2}{{\tau }_{\text{p}}(n+n_{\text{i}})+{\tau }_{\text{n}}(p+n_{\text{i}})}$

where

${\tau }_{\text{p,n}}(N_{\text{D}}+N_{\text{A}})=\frac{{\tau }_{\text{p0,n0}}}{1+\frac{N_{\text{D}}+N_{\text{A}}}{N_{\text{p,n,ref}}}}$

and $n$ is the electron density, $p$ is the hole density and $n_{\text{i}}$ is the intrinsic density.

$N_{\text{D}}$ and $N_{\text{A}}$ are the donor and acceptor concentrations, respectively.

$N_{\text{n,ref}}$ and $N_{\text{p,ref}}$ are the reference doping concentrations for electrons and holes, respectively.

${\tau }_{\text{n0}}$ and ${\tau }_{\text{p0}}$ are the zero doping scattering times for electrons and holes, respectively.

$SRH-recombination                           optional
 material-name                   character   required
 number-of-parameters            integer     required
 n-N-ref                         double      optional
 n-tau                           double      optional
 p-N-ref                         double      optional
 p-tau                           double      optional
 n-bow-N-ref                     double      optional
 n-bow-tau                       double      optional
 p-bow-N-ref                     double      optional
 p-bow-tau                       double      optional
$end_SRH-recombination                       optional

Explanation of specifiers.

material-name

type:

character

presence:

required

value:

e.g. GaAs

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-N-ref

type:

double

presence:

required

value:

e.g. 7.1e15

unit:

[cm^-3]

The $N_{\text{n,ref}}$ parameter for electrons as specified in the equation above.

n-tau

type:

double

presence:

required

value:

e.g. 4.26e-4

unit:

[s]

The ${\tau }_{\text{n}}$ parameter for electrons as specified in the equation above.

n-bow-N-ref

type:

double

presence:

optional

value:

e.g. 0.0

unit:

[cm^-3]

For ternary alloys there are also bowing parameters possible. n-bow-N-ref = 0.0 means zero bowing, i.e. linear interpolation is used.

n-bow-tau

type:

double

presence:

optional

value:

e.g. 0.0

unit:

[s]

For ternary alloys there are also bowing parameters possible. n-bow-tau = 0.0 means zero bowing, i.e. linear interpolation is used.

p-N-ref

unit:

[cm^-3]

Same as n-N-ref but for holes.

p-tau

unit:

[s]

Same as n-tau but for holes.

p-bow-N-ref

unit:

[cm^-3]

Same as n-bow-N-ref but for holes.

p-bow-tau

unit:

[s]

Same as n-bow-tau but for holes.

Example

!--------------------------------------------!
$SRH-recombination                           !
                                             !
 material-name        = Si                   !
 number-of-parameters = 4                    !
 n-N-ref              = 7.1e15               ! [cm^-3]
 n-tau                = 4.26e-4              ! [s]
 p-N-ref              = 7.1e15               ! [cm^-3]
 p-tau                = 3.95e-4              ! [s]

 material-name        = GaAs                 !
 number-of-parameters = 4                    !
 n-N-ref              = 1.0e19               ! [cm^-3]
 n-tau                = 1.0e-9               ! [s]
 p-N-ref              = 1.0e18               ! [cm^-3]
 p-tau                = 1.0e-9               ! [s]

 material-name        = Al(x)Ga(1-x)As       !
 number-of-parameters = 4                    !
 n-bow-N-ref          = 0.0                  ! [cm^-3]
 n-bow-tau            = 0.0                  ! [s]
 p-bow-N-ref          = 0.0                  ! [cm^-3]
 p-bow-tau            = 0.0                  ! [s]
                                             !
$end_SRH-recombination                       !
!--------------------------------------------!

There is also a keywords section in the input file for $SRH-recombination which you can use to overwrite default material parameters.