$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
\(\tau_{\text{p,n}}\left(N_{\text{D}}+N_{\text{A}}\right)=\frac{\tau_{\text{p0,n0}}}{1+\frac{N_{\text{D}}+N_{\text{A}}}{N_{\text{n,p,ref}}}}\)
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.