Implementation of spectral broadening by carrier-carrier scattering in quantum well gain-current calculations

The inclusion of spectral broadening due to carrier scattering is an essential element in the calculation of optical gain and radiative recombination spectra of a semiconductor under high injection. We have examined various methods of incorporating this broadening and find that gain and emission spectra obtained by merely broadening the optical transitions do not satisfy the necessary balance which must exist between them. The problem is removed by weighting the spectral contribution by the value of the Fermi functions of the electron and hole at the energies that would be involved in this transition in the absence of spectral broadening. We have also investigated a more exact method which uses separate electron and hole line functions, and is equivalent to broadening the electron and hole quantum states then calculating the newly available transitions, rather than broadening the transitions themselves. Both the latter methods introduce a small amount of optical gain in the bandgap at low injections and we show that this is due to the use of a Lorentzian lineshape which tails off too slowly. We comment on the most appropriate approach to the calculation of gain and emission spectra and gain-current characteristics.