Instability in multi-valley semiconductors in external electric and magnetic fields

Abstract

It is theoretically proved that the excited wave in two-valley semiconductors is growing. It is indicated that the directions of external fields play an essential role for the appearance of growing waves in the sample. It is shown that oscillations can occur at certain values of the sample dimensions L ,L ,L x y z Analytical formulas for the frequency of the growing waves are obtained. The interval of variation of the external electric field in a strong magnetic field μH>>c has been determined. The paper takes into account that the time of transition from the lower valley to the upper valley differs from the time of transition from the upper valley to the lower valley. It means τ₁₂≠τ₂₁ In the sample, the total concentration is constant, and therefore, n₀=n_a+n_b=const. The changes in the corresponding concentrations are equal to each other and have n_a'=-n_b'. It is taken into account that at critical values of the electric and magnetic fields and the corresponding concentrations they change as a monochromatic wave. And the change in these quantities differs little from their equilibrium value. For simplicity of mathematical calculations, the external electric and magnetic fields are directed in the same way, i.e. in x direction. Since the current oscillations in one direction (for example, along x) are studied in the experiment, the following equalities were taken into account j_y'=0, j_z'=0. In the vicinity of the critical field at the beginning of the current oscillation in the sample, the current oscillation frequency is ϖ=ϖ₀+iϖ₁, ϖ₁<<ϖ₀. In addition, the magnitude of the critical electric field, at which the current fluctuation changes depending on the magnetic field as follows .