^{1}

^{2}

^{*}

^{1}

^{1}

We have investigated the energy states of a one-dimensional electron gas and analyzed the temperature dependence of the density of states. It is shown that with increasing temperature due to thermal broadening of quantum, levels are blurred.

The current stage of development of solid state physics is characterized by the fact that the main object of study is increasingly not becoming massive semiconductor crystals and thin films, multi-layer thin-film structures, conductive yarns and crystallites. The small size of these structures, in which a direction is comparable to the de Broglie wave, according to the laws of quantum mechanics leads to a change in the energy spectrum of charge carriers [

The main dimensional quantum structures are structures with two-dimensional electron gas-epitaxial film MIS structure, heterostructure, etc.; dimensional structure with gas-kvanto¬vye yarn or wire; structure with zero-dimensional gas-quantum dots, boxes, crystallites.

Structures in which the movement of charge carriers is free only along one axis, and along the other two limited two-dimensional quantum well, are known as quantum wires or wires. The energy spectrum associated with the movement of charge carriers across the quantum wire is discrete due to the size quantization; and associated with the movement along the filament is continuous. The charge carriers are in such a one-dimensional electron gas [

Quantum yarn is one-dimensional electronic system where the electron motion is severely restricted in both directions of the three axes and along the thread remains free [

The aim of this work is to study the effect of temperature on the thermodynamic density of states of a quantum wire.

This work is devoted to studying the effect of temperature on the density of states of the one-dimensional electron gas (OEG). Thermal broadening of the levels described using statistics Shockley-Read-Hall [

The range of media in a one-dimensional pit is [

Here,

Here,

From (2) we have

Hence, we obtain expressions for the 1D density of states [

Here,

Plot the functions _{1} = 10^{−8} m and L_{2} = 1.5 ´ 10^{−8} m.

Let us now consider how we can describe the effect of heat on the broadening of the thermodynamic density of states. Its accounting functions via GN (i.e. the derivative of the probability by thermal energy generation energy states E) is given in [

Here,

The considered energy interval

Supplying (4) to (7), we obtain

Plot the temperature dependence of the density of states by Formula (8) at different temperatures believing.

The density of states of the two-dimensional electron gas, quantum wire is similar to the density of states of a three-dimensional electron gas in a quantizing magnetic field. The difference between the density of states of these systems due to the fact that the distance between the discrete states in a bulk semiconductor is determined by the magnitude of the magnetic field, and in the quantum filament transverse dimensions of two-dimensional quantum well. Due to the interaction of the electrons with the lattice vibrations peak heights density of states decreases and the width increases.

the density of states of the one-dimensional electron gas is strongly oscillating electron energy functions. With increasing temperature, the density oscillations subside, and at high temperatures turn into monotonically increasing function of energy

On the basis of this work, we can conclude that the temperature dependence of the density of the Kantian threads due to thermal broadening of discrete energy states. Thermal broadening of states can be described by the temperature dependence of the probability of filling the energy levels. At temperatures where the thermal kT energy of the electrons is much smaller than the distance between adjacent discrete levels ΔE_{nl}_{,}, thermal broadening is not significantly altered the density of states and the peaks in the density of states plots will stand out sharply. The increase in temperature due to the thermal broadening of the peaks of the density gradually eroded discrete levels. At temperatures of the order of kT distances between leveled kT ≤ ΔE_{nl}, density thermodynamic states are smoothed. Thus, the thermodynamic state density of electrons in the quantum wire is temperatures low power oscillating function at high temperatures, and it is converted into a monotonically increasing function of energy.

P. J. Baymatov,A. G. Gulyamov,1 1,A. B. Davlatov,B. B. Uzakov, (2016) Broadening Thermal Energy Levels and Density States Quasi One-Dimensional Electron Gas. Journal of Applied Mathematics and Physics,04,706-710. doi: 10.4236/jamp.2016.44081