Optical Properties due to Donor Electrons in Semiconductors

Abstract

The free carrier-like absorptions observed at low temperatures have been interpreted, in the previous theory, as due to excitations of donor electrons into the lowest conduction band. This theory is modified by making use of the hydrogen-like wave function for the continuous spectrum of a donor electron. According to the present theory, the maximal value of the absorption coefficient appears at the photon energy of about 2.2 times the donor activation energy. And the qualitative behavior is similar to that by the previous theory. The theory is compared with experiments for n-type GaP and Si, and gives a better agreement with experiments for GaP with respect to the wavelength dependence. The Faraday rotation due to donor electrons is calculated considering the presences of the excited donor states and the lowest conduction band. The result is found to be similar to that due to free carriers with respect to the magnitude and the wavelength dependence, for the photon energy larger than about three times the donor activation energy.