A nonlinear theory of the Gunn effect in GaAs-type semiconductors with negative differential conductivity has been devoleped. The amplitude and the frequency of current oscillations in the second approximation have been found by the method of Bogoliubov-Mitropolski. The dependence of the amplitude of current oscillations on electric field strength has been investigated. The amplitude and frequency of current oscillations on the in here and elsewhere have been calculated in a typical experiment.Subject Index: 341, 356 §1. Introduction Current oscillations in two-valley GaAs-type semiconductors under an external electric field were first investigated by Gunn. 1) The frequency of current oscillations mainly lies in the ultrahigh frequency range (UHF) and differs from that of lowfrequency oscillation. The mechanism of Gunn effect was supposed in Refs. 2)-5). The authors of these works show that, in GaAs and InP the number of carriers with a low energy decreases with increasing electric field strength. Moreover, the electrons transit to the upper valley at L-point or under a low-frequency condition they transit to ionized traps within the band gap. The mobility of electrons in the upper valley at the L-point decreases markedly compared with the mobility of electrons in the lower valley at the Γ -point. When transfer of current carriers is higher than the definite value the conductivity decreases and negative differential conductance (NDC) appears, so thatAt negative NDCs the electric field in the crystal becomes nonhomogeneous and acute regions of the electric field, i.e. domains are created. In this case the theoretical investigations lead to nonlinear solutions of the corresponding equation because of the domains and the amplitude of current oscillation in the crystal depends on the time.Moreover, at σ d < 0 the redistribution of space charge leads to UHF radiation. The small-signal theory (i.e. near the threshold σ d ≈ 0) of this phenomenon has been constructed in Ref. 6). However the dependence of the amplitude of oscillations on time has not yet been investigated theoretically.It should be noted that in Refs. 7)-10) current oscillations due to a negative

Energy radiations depending on linearity of intrinsic semiconductors possessing of two types conductivities have been investigated. It is found that in order to start the radiation, the real part of the impedance must be zero. Frequency of the radiation and the relevance electric field strength, have been calculated analytically. It has been proved that in nano-dimension the radiations take place even though at smaller intense of electric fields

The thermomagnetic waves in conducting medium is theoretically studied. The frequencies of these waves are obtained. The amplitude and conditions of radiation by media are determined in the first approximation.