Phonon-assisted optical absorption in germanium

A comprehensive experimental and theoretical study of indirect gap optical absorption in bulk Ge is presented. While this topic has been the subject of intense studies from the early days of semiconductor physics, the resonant aspect of the absorption received very little attention until now. This is a unique property of Ge related to the proximity of the direct and indirect gaps. The absorption coefficient was measured over the entire spectral range between the two gaps for comparison with theory. It is shown that the standard textbook expressions, obtained by assuming intermediate states with constant energy, are in very poor agreement with experiment. A theory first proposed by Hartman [R. L. Hartman, Phys. Rev. 127, 765 (1962)10.1103/PhysRev.127.765], which takes into account the energy dependence of the intermediate states, provides a much better account of the photon-energy dependence of the absorption, but the prediction of the experimental absorption strength requires the incorporation of excitonic effects. The latter, however, have only been considered by Elliott [R. J. Elliott, Phys. Rev. 108, 1384 (1957)10.1103/PhysRev.108.1384] in the limit of constant intermediate state energy. A generalization to the case of energy-dependent intermediate states, consistent with Hartman's theory, is presented here. The basic qualitative difference with the classical Elliott theory is that the excitonic character of the intermediate states affects the computed absorption, generating an additional resonant enhancement that is confirmed by the experimental data. The generalized theory presented here agrees very well with the experimental absorption using independently determined band structure parameters.