Квантовый транспорт в полупроводниковом нанослое с учетом поверхностного рассеяния носителей заряда

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.

XXIV Международный симпозиум Нанофизика и наноэлектроника", Нижний Новгород, 10-13 марта 2020 г. Влияние граничных условий на высокочастотную электропроводность тонкого проводящего слоя в продольном магнитном поле

The problem of the high-frequency conductivity of a thin conductive layer in a longitudinal magnetic field is solved in terms of kinetic approach taking into account diffuse-mirror boundary conditions. Specularity coefficients of layer surfaces are assumed to be different. An analytical expression is derived for dimensionless integral conductivity as a function of dimensionless parameters: layer thickness, electric field frequency, magnetic induction, chemical potential and surface specularity coefficients. The limiting cases of a degenerate and non-degenerate electron gas are considered. A comparative analysis of theoretical calculations with experimental data is carried out. The method to determine specularity coefficients and mean free path of charge carriers from the longitudinal magnetoresistance of a thin metal film is illustrated.

Relaxation Processes in a Quantum Wire with Parabolic Confinement

Analytical expressions are found for the mobility of a degenerate electron gas in a quantum wire for three scattering mechanisms: on ionized impurities and on piezoacoustic and deformation acoustic phonons. The expressions allow one to analyze the concentration, temperature, and dimensional dependences of the electron mobility.

Interlude: Quantum Ideal Gases

The previous chapters having been about purely gravitational and orbital phenomena alone, this chapter introduces microphysical processes and relevant quantities. Adaptive conversions between units have already appeared in previous chapters, and now Planckian units are introduced for convenience in writing formulas, and the conversion to and from standard SI is explained. Planckian units continue to be used throughout the rest of the book. While the topic of quantum ideal gases (a photon gas, a degenerate electron gas, and of course a classical gas) is standard material in physics classes, they are briefly presented here, in an especially concise way using Planckian units. The physics at these tiny scales will be key in determining the macroscopic behaviour of stars and stellar objects in subsequent chapters.