^{1}

^{2}

^{*}

^{1}

^{1}

^{3}

With the help of mathematical models, the temperature dependence of the density of energy states was determined in a quantizing magnetic field. The influence of the effective mass at the temperature dependence of the density of the energy states in a strong quantizing magnetic field is investigated. The dependence temperature of density of energy states graph is obtained in a strong magnetic field for InSb.

In narrow-gap semiconductors, the effective mass of electrons is small, so that the quantization condition is observed in weak magnetic fields. In such conditions, the distance between Landau levels was greater than the

characteristic electron energy. In these conditions, it is possible to find the effective mass

tive mass is associated with transitions between Landau energy levels. However, if the dependence of the energy of the wave vector is not described by a quadratic form, for example, the electron in InSb energy levels of the

charge carriers in the magnetic field is not at equidistants, such as the cyclotron mass, but is given by _{z}.

The works [

The temperature dependence of the density of states is due to thermal broadening of discrete energy states [_{i} in the allowed band energy E is determined by the

exponential factor

The aim of this work is to study the influence changes in the cyclotron effective mass at the temperature dependence of the density of the energy states in a strong quantizing magnetic field.

In a strong magnetic field, the energy spectrum of free electrons and holes are undergoing serious changes, which is reflected by the density of the energy states. The dependence of the energy E of the electron with a quadratic ellipsoidal dispersion law in the magnetic field on the principal quantum number n, the number of quanta of the spin s, and the projection p_{z} momentum on the direction of the magnetic field H take the next view [

Here, g-factor is determined only by the orientation of the magnetic field H and does not depend on the quantity projection of the momentum p_{z}―pulse,_{z}―longitudinal effective mass.

The total density of energy states in a magnetic field, and the electronic system with a quadratic isotropic dispersion law excluding spinal splitting of the Landau levels can be written as [

where E is the energy of a free electron, ^{*} is the effective mass of the cyclotron,

At particular, if the energy spectrum is purely discrete, then the density of energy states is equal to the sum of δ-functions concentrated at the points of the spectrum E_{i}, where amplitude is

Thermal broadening of the levels in the magnetic field leads to a smoothing of discrete levels. Thermal broadening is considered by GN function. As in [

where

If the dispersion law is non-quadratic, but isotropic, for example, the electrons in III-V compounds and II-VI, the effective mass is a function of the wave number and energy. This means that the filling of the energy band effective mass of carriers will change [

The works [

[

where, E_{g}_{ }is bandgap, m is effective mass of the electrons at the bottom of the conduction band, E_{e}_{ }is energy of the electrons:

The use of several fitting parameters leads to ambiguity determining the value of

In the works [

Then the cyclotron effective mass can be represented as follows:

From here you can write the density of energy states as follows:

The effect of the change on the mass density of states in a magnetic field is considered. This can be considered as a deviation of the electron dispersion from parabolic.

In a strong magnetic field, continuous spectrum of energy states is strongly deformed and transformed into oscillating line. With increasing temperature, the discrete levels are washed away, and the density of the energy states is converted into a continuous spectrum. In the experiment, the density of states depends on the energy, and the temperature of the effective mass. The effective mass depends on energy; and cyclotron resonance depends on the effective mass. Thus, with increasing energy changes, the distance is between the peaks.

Changing

oscillations of the density of states are due to the Landau quantization that is observed. In this case, the measurements provide a continuous range of density of states. The detection of quantum levels is necessary to solve the inverse problem. In this case, it is necessary to find a discrete level due to the Landau quantization. For this, it is necessary to measure

At a constant effective mass (parabolic zone), the dependence of the energy density of states is given

between Landau levels, the curve of the density of states moved to larger values will shift the density of states, and travel up along the axis of the density of states. Conversely, if

Using the data of

We developed a method for determining the density of energy states in a quantizing magnetic field. With the help of mathematical models, the temperature dependence of the density of energy states in strong magnetic fields on semiconductors is determined. It is shown for the non-parabolic dispersion law that the density of states in a high magnetic field at an increased temperature coincides with the density of states in the sample without magnetic field. On the basis of this model, we used data on the high-temperature N_{s} to calculate the low-temperature density of states.

This work was supported by government grants of Uzbekistan F2-21 “Mathematical modeling of the determination of the density of surface states at the semiconductor-insulator”.

G.Gulyamov,U. I.Erkaboev,G. N.Majidova,M. O.Qosimova,A. B.Davlatov, (2015) New Method of Determining the Landau Levels in Narrow-Gap Semiconductors. Open Journal of Applied Sciences,05,771-775. doi: 10.4236/ojapps.2015.512073