Absorption near band edges in heavily doped GaAs

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Abstract
The optical-absorption coefficient α(ω) in heavily doped n- and p-type GaAs is evaluated for comparison with the observed values of Casey et al. The purpose is to test the theory of electrons in heavily disordered systems derived by Sa-yakanit and the absorption matrix element (ME) which follows from this theory. The present calculation of α(ω) begins with the density of electron states (DOS) and the electron wave functions. The ME is then derived. The screening of the interactions by the carrier electrons depends on the DOS. Since the DOS, ME, screening, and the Fermi energy, which provide the essential input for α(ω), are interdependent they must be evaluated iteratively until consistent. The final α(ω) agrees quite well with experiment. The overall α(ω) is also similar to that calculated by Casey and Stern although very different inputs for α(ω) are used. The α(ω) is found to be very sensitive to the DOS, the ME, and the band-gap shrinkage. The comparison with experiment suggests the present combined model of the DOS and the ME represent heavily doped GaAs well but that the band-gap-shrinkage calculations need further refinement.