Modeling the temperature dependence of the discrete Landau levels in electronic semiconductors Abstract

Modeling the temperature dependence of the discrete Landau levels in electronic semiconductors
Abstract

Created a computer program (Maple 9.5) discrete Landau levels in electronic semiconductors. Using this program, the temperature dependence of the oscillations of the Landau levels in a strong magnetic field was calculated. Plots of the dependence of the oscillations of the Landau levels on temperature and magnetic field in electronic semiconductors are obtained. A model for determining the discrete Landau levels in narrow-gap semiconductors at high temperatures is constructed. The temperature dependence of the density of energy states of semiconductors in InAs is studied taking into account the dependence of the effective mass on energy in a strong quantizing magnetic field. The temperature dependence of the density of energy states was obtained taking into account changes in the cyclotron effective mass in a strong magnetic field.

Keywords:

1. 
   Introduction
   

It is known that with the help of oscillation phenomena it is possible to determine the basic physical quantities (longitudinal conductivity, magnetic susceptibility, thermoelectric power and other transport phenomena) in a quantizing magnetic field. In particular, oscillations of longitudinal electrical conductivity and oscillations of magnetic susceptibility provide valuable information on the energy spectra of free electrons in semiconductor structures. The temperature dependence of the energy spectrum of semiconductors is well explained by the thermal smearing of discrete energy levels [1-4]. The temperature dependence of the band gap is considered as a smearing of the energy states of both the conduction band and the valence band. In these works, it was assumed that the effective mass of the density of states does not depend on temperature. However, as shown by experiments [5–6], the effective mass of the density of states depends on temperature. These changes in the effective mass change the temperature dependence of the band gap. In addition, the effective mass is highly dependent on energy. These changes in the cyclotron effective mass change the dependence of the density of states on energy in a strong quantizing magnetic field [7-9].

The aim of this work is to create a computer program for calculating the temperature dependence of the discrete Landau levels in semiconductors, taking into account the cyclotron effective mass of electrons.

2. 
   Model
   

2.1. Determining the temperature dependence of the discrete Landau levels taking into account the effective mass of electrons.

In a strong magnetic field, the energy spectrum of free electrons and holes undergoes serious changes, which is reflected in the density of energy states. The dependence of the electron energy E with the quadratic ellipsoidal dispersion law in a magnetic field on the principal quantum number n, spin quantum number s and the projection pz of the pulse on the direction of the magnetic field H takes the following form [10]:

Here, the g-factor is determined only by the orientation of the magnetic field H and does not depend on the projection value p_z of the pulse, _В - Bohr magneton, m_z -longitudinal effective mass. The total density of energy states in a magnetic field of an electronic system with a quadratic isotropic dispersion law without taking into account the spinal splitting of the Landau levels can be written in the form [10]

where, E is the energy of a free electron, n = 0.1, ... is the number of Landau levels, m * is the effective cyclotron mass, and is the cyclotron frequency. If the energy spectrum is discrete (point), the Landau levels are equal to the sum of δ-functions and is determined by the following formula: