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This paper proposes a method of modeling the dynamic properties of multi-valley semiconductors. The model is applied to the relevant materials GaN, AlN, and InN, which are now known by the general name of III-nitrides. The method is distinguished by economical use of computational resources without significant loss of accuracy and the possibility of application for both dynamic time-dependent tasks and the fields variable in space. The proposed approach is based on solving a system of differential equations, which are known as relaxation ones, and derived from the Boltzmann kinetic equation in the approximation of relaxation time by the function of distribution over k-space. Unlike the conventional system of equations for the concentration of carriers, their pulse and energy, we have used, instead of the energy relaxation equation, an equation of electronic temperature as a measure of the energy of the chaotic motion only. Relaxation times are defined not as integral values from the static characteristics of the material but the averaging of quantum-mechanic speeds for certain types of scattering is used. Averaging was carried out according to the Maxwellian distribution function in the approximation of electronic temperature, as a result of which various mechanisms of dispersion of carriers are taken into consideration through specific relaxation times. The system of equations includes equations in partial derivatives from time and coordinates, which makes it possible to investigate the pulse properties of the examined materials. In particular, the dynamic effect of the "overshoot" in drift velocity and a spatial "ballistic transport" of carriers. The use of Fourier transforms of pulse dependence of the drift carrier velocity to calculate maximum conductivity frequencies is considered. It has been shown that the limit frequencies are hundreds of gigahertz and, for aluminum nitride, exceed a thousand gigahertz

Fast and stable stationary numerical model of electronic transport in resonant-tunneling diode (RTD) was developed. It was derived from the density functional method, applying assumption about the absence of exchange-correlation term. The model correctly describes interaction between quantum and semi-classical regions of RTD. Self-consistence between space charge and potential can be achieved for all relevant RTD structures. The results of modeling were tested for the model structures of RTDs with barrier layers formed of Al x Ga 1-x As and Al x Ga 1-x N. There is a possibility of efficient visualization of modeling results, such as local density of states, potential and electron concentration in active region.

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