High-Frequency Properties of GaN, AlN and InN in Strong Fields
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Abstract
The article proposed a method for modeling and analyzing the high-frequency properties of multi-valley semiconductors, in particular, GaN, AlN and InN. The model is applied to state-of-the-art, promising and relevant materials GaN, AlN and InN, which are now known under the generic name III-nitrides. The method is distinguished by the economical use of computational resources without significant loss of accuracy and the possibility of using both for dynamic tasks over time and variables in the space of fields.
The proposed approach is based on solving a system of differential equations, which are known as relaxation equations and are derived from the Boltzmann kinetic equation in the relaxation time approximation by averaging over k-space. In English literature, this method is known as the "method of moments." In contrast to the traditional system of equations for the concentration of carriers, their momentum and energy, here, instead of the energy relaxation equation, the equation for electron temperature is used as a measure of the energy of only chaotic motion. The second significant difference is that the relaxation times are not determined as integral values from the static characteristics of the material, but through averaging the quantum-mechanical scattering rates commonly used in the Monte Carlo method for certain types of scattering. The averaging was performed over the Maxwell distribution function in the electron temperature approximation, as a result of which various mechanisms of carrier scattering through their specific relaxation times are taken into account. Since the system of equations used includes equations in partial derivatives with respect to time and coordinates, it makes it possible to investigate the characteristic manifestations of the impulse properties of the materials under consideration, namely, 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 transformation of the impulse dependence of the carrier drift velocity to calculate the maximum frequencies inherent in a semiconductor is considered. A connection was found between the shape of the spectral characteristic of the drift velocity and the scattering mechanisms that prevail in a given electric field. The properties of III-nitrides in the frequency domain in a strong electric field are analyzed and compared with existing methods for estimating cut-off frequencies. It is shown that the limiting frequencies increase with increasing electric field strength and amount to hundreds of gigahertz, and for aluminum nitride it exceeds one thousand gigahertz. This is due, apparently, to the greatest for him inter-valley distances and, accordingly, with a weakened inter-valley scattering. The analysis of the spatial manifestation of the splash effect shows the possibility of an almost collisionless, ballistic flight of electrons in a strong field at distances up to hundredths and tenths of a micrometer.
Ref. 15, fig. 10, tabl. 1.
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