The frequency-dependent relaxation time of free carriers in InP

Abstract

At frequencies higher than 200–300 cm−1 in InP, the classical Drude theory fails to predict the observed wavelength dependence of the absorption coefficient and hence the optical conductivity to which it is proportional. In this paper, the optical conductivity is calculated for InP at 300 °K as a function of frequency and carrier concentration by use of a quantum extension of the Boltzmann transport equation which reduces to the quasiclassical Boltzmann equation in the limit of low frequencies and elastic scattering mechanisms. The conductivity is expressed in terms of a frequency-dependent relaxation time which reduces to a constant in the far infrared. It is given as a function of carrier concentration over the spectral region from 218 to 2180 cm−1 for carrier concentrations from 4.69×1015 to 2.13×1018 cm−3, and used to calculate the reflectivity spectrum over the same range of frequencies and concentrations. The low-frequency limit is used to estimate the dc mobility as a function of concentration, and the effect of compensation on mobility is calculated for the purest materials. Comparison with experimental results is given.