High-frequency Magnetotransport in a thin Metal Layer with Variable Specularity Coefficients of its Boundaries
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RETICAL AND MATHEMATICAL PHYSICS
High-Frequency Magnetotransport in a Thin Metal Layer with Variable Specularity Coefficients of Its Boundaries P. A. Kuznetsova, O. V. Savenkoa,*, and A. A. Yushkanova aYaroslavl
State University named after P. G. Demidov, Yaroslavl, 150003 Russia *e-mail: [email protected]
Received January 28, 2020; revised April 3, 2020; accepted April 7, 2020
Abstract—A theoretical model of the conductivity of a thin metal layer placed in a longitudinal constant magnetic and alternative electric field is constructed, taking into account the diffuse-mirror boundary conditions. An analytical expression is obtained for the integral conductivity as a function of dimensionless parameters: layer thickness, electric field frequency, magnetic field induction and surface specularity coefficients. The dependences of the layer conductivity on the aforenamed parameters are analyzed. The results are compared with known experimental data. DOI: 10.1134/S1063784220120130
INTRODUCTION The investigation of electrical, optical, and galvanomagnetic properties of thin conductive layers are primarily associated with the rapid development of micro-, nano- and optoelectronics in recent decades. Thin layers are used as the basis of all semiconductor devices and integrated circuits, are employed to create multilayer solar cells, in present time active researches and developments are underway to increase their efficiency [1–5]. There are many works devoted to applying thin layers in photonics and nanophotonics [6, 7], microwave electronics [8, 9], etc. We know that the conductivity of a thin layer is less than the one of a macroscopic sample. Among the reasons explaining this difference, in addition to quantum size effects, there may be phenomena that have a classical explication. At room temperature, the mean free path of charge carriers lies in the range 10–100 nm in many typical metals, and 10–1000 nm in typical semiconductors [10, 11]. At the case when the layer thickness is much larger than the charge carrier de Broglie wavelength, which takes the value proportional to the interatomic distance (~0.3 nm) for metals and about 10 nm for semiconductors [10, 11], the classical kinetic description of size effects is valid. Modern technologies permit to create integrated circuit elements with a characteristic size of the order of nanometers. Therefore, the situation when it is necessary for problem solving to consider the charge carrier surface scattering, but to neglect the quantum effects, is realized in practice. Theoretical studies of the electrical properties of thin conductive films have been carried out since the first half of the 20th century. In [12], the model of dif-
fuse-mirror boundary conditions was proposed for the first time to solve the problem of the static conductivity of a thin metal film. Within the framework of this model, the concept of the surface specularity coefficient was introduced, which characterizes the relative number of electrons reflected specularly from the surface. In [13, 14], th
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