$direct-recombination

The simplest process for the generation and recombination of electron-hole pairs is the direct process via the emission or absorption of a photon (radiative recombination). This is important for light emitting devices. The local spontaneous emission rate is approximated as

\(R_{\text dir} = C ( n p - n_{\text{i}}^2 )\)

where \(C\) is called the bimolecular recombination coefficient (often abbreviated with the letter \(B\)), \(n\) is the electron density, \(p\) is the hole density and \(n_i\) is the intrinsic density.

This simple equation includes the full spectrum of photons generated by spontaneous band-to-band transition processes. By definition, the radiative recombination rate (= spontaneous electron recombination rate) per unit volume of an electron-hole pair is equivalent to the spontaneous photon generation rate per unit volume, because obviously, each time an electron recombines with a hole radiatively, a photon is emitted.

$direct-recombination                          optional
 material-name                   character     required
 number-of-parameters            integer       required
 C-opt                           double        optional
 bow-C-opt                       double        optional
$end_direct-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. 1

Control parameter if the number of parameters provided is the same as demanded.

C-opt

type:

double

presence:

required

value:

e.g. 7.2e-10

unit:

[cm^3/s]

The parameters are specified as shown in the tables above. The order of magnitude is around \(10^{-10}\) [cm^3/s].

bow-C-opt

type:

double

presence:

optional

value:

e.g. 0.0

unit:

[cm^3/s]

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

Example

!--------------------------------------------!
$direct-recombination                        !
                                             !
 material-name        = GaAs                 !
 number-of-parameters = 1                    !
 C-opt                = 7.2e-10              ! [cm^3/s]
                                             !
 material-name        = GaN                  !
 number-of-parameters = 1                    !
 C-opt                = 2e-10                ! [cm^3/s]
                                             !
 material-name        = Al(x)Ga(1-x)As       !
 number-of-parameters = 1                    !
 bow-C-opt            = 0.0                  ! [cm^3/s]
                                             !
$end_direct-recombination                    !
!--------------------------------------------!

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