Description of the Magnetization Oscillations of a Silicon Nanostructure in Weak Fields at Room Temperature. The Lifshit
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CONDUCTOR STRUCTURES, LOW-DIMENSIONAL SYSTEMS, AND QUANTUM PHENOMENA
Description of the Magnetization Oscillations of a Silicon Nanostructure in Weak Fields at Room Temperature. The Lifshitz–Kosevich Formula with Variable Effective Carrier Mass V. V. Romanova, V. A. Kozhevnikova, V. A. Mashkova†, and N. T. Bagraeva,b,* a
Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251 Russia b Ioffe Institute, St. Petersburg, 194021 Russia *e-mail: [email protected] Received July 23, 2020; revised August 3, 2020; accepted August 3, 2020
Abstract—A formalism of the statistical approach to describing de Haas–van Alphen oscillations known as the Lifshitz–Kosevich formula is developed as applied to a low-dimensional system with an effective carrier mass depending on an external magnetic field. The statistical approach makes it possible to perform more detailed interpretation of the experimental results and analyze the interrelation of the dependence found by us of the effective carrier mass with the individual features of the structure of a silicon nanosandwich caused by the formation of negative-U δ barriers in its composition. Keywords: the Lifshitz–Kosevich formula, de Haas–van Alphen effect, silicon nanosandwich, effective mass, size quantization DOI: 10.1134/S1063782620120337
1. INTRODUCTION When studying the magnetic properties of electrons in thin layers of metals in the case of an arbitrary dispersion law, I.M. Lifshitz and A.M. Kosevich, having determined the quasi-particle energy levels in a magnetic field and calculated the oscillating part of the magnetic moment of a gas of such quasi-particles, derived general formulas for studying the de Haas–van Alphen effect [1, 2]. It should be noted that the statistical approach developed by I.M. Lifshitz and A.M. Kosevich [1, 2] has not lost its significance with the development of the fabrication technologies of low-dimensional structures and recording of their oscillations identified as the de Haas–van Alphen effect making it possible to adequately describe the observed phenomenon in general. Nevertheless, Schoenberg, having scrupulously considered the factors affecting the behavior of magnetization in thin layers of metals and in two-dimensional structures, showed that when describing the de Haas–van Alphen effect using the Lifshitz–Kosevich formula both additive diamagnetic and paramagnetic contributions to the structure magnetization, against the background of which the oscillations under investigation are observed, and the characteristics of oscillations themselves, notably, their scale and shape, should be discussed. [3]. Herewith, the result of calculating the † Deceased.
nonoscillating component of magnetization depends on the selected dispersion law, which determines the value of the phase correction γ [3]. Direct calculation of the phase correction is very problematic because of the fact that, as follows from [3, 4], its value can vary in a complex manner in an external magnetic field with an arbitrary dispersion law. However, the magni
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