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A thermodynamic density of states, electron density in the subband and the entropy of the gas as function of the temperature and the total two-dimensional electron density are studied. Semiconductor conduction band dispersion is described by the simplified Kane model. Numerical simulation shows that with an increase in the total electron concentration, thermodynamic density of states at low temperatures changes abruptly and smoothes jumps at high temperatures. This change manifests itself in the peculiar thermodynamic characteristics. The results are used to interpret existing experimental data.

Recently, a large number of studies are devoted to the study of two-dimensional electron gas in a magnetic field [

In work [

It is known [

This work is devoted to the calculation of the thermodynamic DOS, the concentration of electrons in the subband and the entropy of a gas as a function of total concentration and temperature with allowance for the nonparabolicity of conduction band. It is shown that with increasing total concentration of electrons, thermodynamic DOS changes abruptly, and this leads to a peculiar change in the subband’s concentration and entropy. The results are compared with experimental data on the basis of the electron gas in the quantum well heterostructures, InAs/AlSb.

Consider a QW width L, concluded between the barriers of infinite height.

The energy is measured from the bottom of the bulk semiconductor. Dispersion law of electrons in the conduction band relies on nonparabolicity, and in the simplest case describe by two-band Kane model. In the effective mass approximation, the solution of the Schrödinger equation leads to the following dispersion

where

The total concentration and the concentration of electrons in the subbands defined by the relations

where

The thermodynamic DOS is defined as

The thermodynamic potential

With the help of the relations (2)-(5) can provide useful information about the behavior of the two-dimensional electron gas at varying temperatures and the total electron concentration. Calculations of the density of states and entropy are carried out by the example of InAs semiconductor. Used in the calculation of the band parameters of InAs semiconductor are shown in

Since the total concentration

The graph shows the temperature significantly influences the shape of

0.42 | |
---|---|

0.023 | |

2.27 | |

0.95 × 10^{13} |

Since the thermodynamic quantities―entropy, heat capacity, etc. is directly linked to the DOS, and then these values are also abrupt change.

The graph shows that the calculation of the thermodynamic quantities―nonparabo- licity effects are important. For example, at a concentration

Nature jumps in the concentration dependence of

The jump in the concentration dependence _{exp} = 15 nm.

With the growth of the total concentration of the first miniband is filled first, the

concentration continues to increase linearly until it begins filling the second miniband. When filling in the upper subband starts, a filling of the lower subband is slowing. In graphics appears a fracture. These fractures are caused by an abrupt increase in the DOS.

From

Our estimates show that if use a real value for the height of the potential barrier (say V ~ 1 eV) the calculated curve with L = 15 nm coincides better with the experimental data for comparison with L = 18 nm curve.

High temperatures and a wide QW leads to intensive filling of overlying subbands.

This paper, by using numerical simulation, studied the concentration of electrons in the subbands and the entropy of two-dimensional electron gas, depending on the temperature and the total two-dimensional electron density. To account for the conduction band nonparabolicity in the spectrum (1), a simple Kane model is used.

We have shown that an abrupt change in the DOS with increasing concentration (

We also presented numerical results dependences of subbands concentration as

function of total two-dimensional electron concentration (

This work was supported by the Scientific and Technical program Republic of Uzbekistan (Grant F2-OT-O-15494).

Gulyamov, G. and Abdulazizov, B.T. (2016) On the Thermo- dynamics of a Two-Dimensional Electron Gas with Non-Parabolic Dispersion. World Journal of Condensed Matter Physics, 6, 294-299. http://dx.doi.org/10.4236/wjcmp.2016.64028