The frequency of current fluctuations in two-valley semiconductors in an external electric and strong magnetic (𝛍𝐇 > 𝒄) fields

Abstract

Boltzmann's kinetic equations have not been used to date to study nonequilibrium phenomena in semiconductors, and therefore, to obtain analytical expressions for the oscillation frequency inside the semiconductor and the critical external electric field, it is of theoretical interest. In this theoretical work, the frequency of oscillations occurring inside a two-valley semiconductor of the GaAs type in an external constant electric field and in an external strong magnetic field (𝜇Н ≫ с, μ-mobility of charge carriers, H-magnetic field strength, cspeed of light) is calculated. It has been proved that the critical values of the external electric field fully correspond to the values of the electric field, which were obtained by the Gunn experiment. It is proved that unstable waves are excited in GaAs if the crystal dimensions are 𝐿𝑦 > 4𝐿𝑧 and 𝐿𝑥 ≪ 𝐿𝑦. Analytical expressions are obtained by theoretical calculation for an external constant magnetic field, when unstable oscillations are excited inside the sample. It is proved that the growth rate of the excited waves is much less than the wave propagation frequency𝛾 ≪ 𝜔0. Numerical comparisons of theoretical expressions for the frequency of oscillations are carried out using the data of the Gunn experiment 𝜔0~107 ÷ 109 Hz.