The problem of the conductivity of a thin conductive nanolayer is solved taking into account the quantum theory of transport processes. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. The constant-energy surface has the form of an ellipsoid of revolution with the main axis parallel to the layer plane. Analytical expressions are obtained for the conductivity tensor components as a function of dimensionless thickness, chemical potential, ellipticity parameter, and surface roughness parameters. The conductivity analysis for the limiting cases of a degenerate and non-degenerate electron gas are conducted. The results are compared with known experimental data for a silicon layer.
The interaction of electromagnetic H-waves with the thin metal film subject to the shape of the ellipsoidal Fermi surface and a constant mean free path of electrons for various angles of incidence of the electromagnetic waves of theta and different from each other of the coefficients of specularity of q1 and q2 in the reflection of electrons from surfaces of the film is calculated. The metal film is enclosed between two media with permittivity ε1 and ε2. The behavior of reflection coefficients R, passage T and absorption A from the effective mass of conduction electrons is analyzed.
Построена теоретическая модель электропроводности полупроводникового нанослоя в переменном электрическом поле с учетом квантовой теории процессов переноса. Поверхностное рассеяние носителей заряда учитывается через граничные условия Соффера. Получено аналитическое выражение для модуля и фазы интегральной проводимости как функции безразмерных параметров: толщины слоя, частоты электрического поля, химического потенциала, параметров шероховатости поверхностей. Проведено сравнение полученных результатов для случаев вырожденного и невырожденного электронного газа и с известными экспериментальными данными.
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