The dissertation work proposed a method for modeling and interpreting the high-frequency characteristics of multi-valley semiconductors, in particular, GaN, AlN, and InN. The model is practiced to state-of-the-art, encouraging, and relevant materials GaN, AlN, and InN, which are now recognized under the generic name III-nitrides. The method is noticed by the economical use of computational resources without meaningful loss of accuracy and the feasibil-ity of using both for dynamic tasks over time and variables in the scope of fields.
The introduced approach is based on solving a system of differential equating, which are known as relaxation equations and are obtained from the Boltzmann kinetic equating in the relaxation time approximation by averaging over k-space. In English literature, this method is known as the "method of momentum." Indifference to the traditional system of equations for the concentration of carriers, their momentum, and energy, here, alternately of the energy relaxation equation, the equation for electron temperature is done as a measure of the energy of only chaotic movement. The second meaningful difference is that the relaxation times are not defined as integral values from the static properties of the material, but for averaging the quantum-mechanical scattering rates usually used in the Monte Carlo method for particular types of scattering. The averaging was made over the Maxwell distribution function in the electron temperature approximation, as an outcome of which numerous mechanisms of carrier scattering through their explicit relaxation times are taken into account. Since the system of equations applied includes equations in partial derivatives concerning time and coordinates, it performs it possible to examine the characteristic demonstrations of the impulse properties of the materials under consideration, particularly, the time effect of the “overshoot” of drift velocity and the spatial “ballistic transport” of carriers.
For the first time, the use of the Fourier transform of the impulse dependence of the carrier drifts velocity to calculate the highest frequencies inherent in a semiconductor is recognized. A relationship was found between the contour of the spectral characteristic of the drift velocity and the scattering mechanisms that predominate in a given electric field. The characteristics of III-nitrides in the frequency region in a strong electric field are investigated and correlated with existing methods for predicting cut-off frequencies. It is determined that the limiting frequencies increase with increasing electric field strength and result in hundreds of gigahertz, and for aluminum nitride, it passes one thousand gigahertz. This is due, obviously, to the greatest for him inter-valley distances and, therefore, with a decreased inter-valley scattering. The study of the spatial manifestation of the splash effect gives the possibility of an approximately collisionless, ballistic flight of electrons in a strong field at ranges up to hundredths and tenths of a micrometer.
