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 e ssential element in the calculation of optical gain and radiative reco mbination spectra of a semiconductor under high injection. We have exa mined various methods of incorporating this broadening and find that g ain and emission spectra obtained by merely broadening the optical tra nsitions do not satisfy the necessary balance which must exist between them. The problem is removed by weighting the spectral contribution b y the value of the Fermi functions of the electron and hole at the ene rgies that would be involved in this transition in the absence of spec tral broadening. We have also investigated a more exact method which u ses separate electron and hole line functions, and is equivalent to br oadening the electron and hole quantum states then calculating the new ly available transitions, rather than broadening the transitions thems elves. Both the latter methods introduce a small amount of optical gai n 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 emissi on spectra and gain-current characteristics.