Quantum Transport in a Semiconductor Nanolayer Taking into Account the Surface Scattering of Carriers

Interaction of an electromagnetic H-wave with a semiconductor nanolayer

“…where Ĥ0the Hamiltonian of the equilibrium system, µthe chemical potential, k 0the Boltzmann's constant, Tthe temperature. Using (4) and allowing the elastic carrier scattering, the Liouville equation (3) can be reduced to the form (6) by the method similar to the studies [19,20]:…”

“…The found function of distribution allows calculating the density of the current j induced by the electromagnetic wave and the integral conductivity σ a [19,20] by the formulas (12), ( 13):…”

“…Let us note that the problem is solved by the method similar to the studies [19,20]. By solving the equation (6) taking into account the boundary conditions (9), we obtain the following expressions for the functions f…”

“…They substantiate in detail the causes and conditions of occurrence of the quantum dimensional effect. There are studies, whose authors used the various methods taking into account the roughness of the surface for solving the quantum problem on the static conductivity of the metallic film: the method of Green's functions [13][14][15] and direct calculation of the transfer probability of the charge carrier as a result of scattering processes [16][17][18].The studies [19,20] have solved the above-mentioned problem using the boundary conditions of Soffer [21] and examined the cases of a metal and a semiconductor with arbitrary degeneracy. There are some studies dedicated to taking into account the effect of dimensional quantization for solving the problems of interaction of the IR electromagnetic radiation with a superthin metal film [22][23][24][25][26].The authors of these studies have restricted themselves in a case of the smooth surface and have not used the strict mathematical calculation based on the solution of the Liouville's quantum equation.…”

“…The present study has built a theoretical model of the interaction of the electromagnetic radiation with the semiconductor nanolayer. The problem was solved by the method similar to the studies [19,20], which takes into account the surface carrier scattering by the Soffer's boundary conditions imposed on the Liouville's equation.…”