Electronic excitations in a nonparabolic conduction band of ann-type narrow-gap semiconductor

Abstract

Taking full account of nonparabolicity of a conduction-band dispersion, we investigate those electronic excitations in the conduction band of an n-type narrow-gap semiconductor which are coupled with polar phonons. By incorporating the nonparabolic dispersion obtained by a $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method in a complete manner into the random-phase approximation, we calculate the energy dispersion and the energy-loss intensity of two coupled plasmon-phonon modes and a longitudinal optical-phonon mode partially screened by carriers. The results are compared with those of two simplified treatments, namely, one with the spin-orbit splitting neglected and the other assuming a parabolic dispersion of the conduction band with its effective mass modified. This comparison asserts that complete treatment of the nonparabolic dispersion is indispensible to quantitative analysis of the plasmonlike mode at higher carrier concentrations. Simultaneously, it elucidates limitations and shortcomings of the simplified schemes. The complete treatment of the nonparabolicity leads to an excellent agreement with the experiment on the carrier-concentration dependence of an intensity-vanishing point in the infrared-reflection spectrum.