Analytic expression for electronic density of states in random media with weak scattering potential

We evaluate the electronic density of states (DOS) in random media by using the expression from the variational path integral theory. The scattering potential is modeled by a Gaussian function. By imposing the limit of weak scattering, the full spectrum DOS can be approximated by an analytical method. The solution has several features; in the extended states, it is essentially proportional to E. In the localized states, it resembles an exponential tail. However, this tail has less population than that of the compatible Kane DOS. The total energy of the system is lowered by Eα, depending linearly on the density of scatterers. Our results give good description to the photoluminescence spectra of Si:P and the tunneling measurement of GaAs.