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A model for the calculation of the absorption and emission spectra for GaAs at carrier concentrations in excess of 1×1018 cm−3 is described. This model utilizes a Gaussian fit to Halperin-Lax band tails for the concentration-dependent density of states and also includes an energy-dependent matrix element. The calculated absorption and emission spectra are compared to previous experimental results. All results are for 297 K. For p-type GaAs, the agreement is very good. The concentration dependence of the effective energy gap is obtained and can be expressed as Eg (eV) =1.424−1.6×10−8 p (cm−3)1/3. The concentration-dependent thermal equilibrium electron-hole density product n0p0 and the radiative lifetime τr are calculated for p-type GaAs. The value of n0p0 increases from the low-concentration value of 3.2×1012 cm−6 to 1.2×1013 cm−6 at p=1.6×1019 cm−3. This value of n0p0, together with the thermal generation rate obtained from the experimental absorption coefficient, gives τr as 0.37 nsec at p=1.6×1019 cm−3.
Casey et al. (Sun,) studied this question.