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The analysis of the density of states for electrons in single quantum well, the conduction band nonparabolicity take is account. It is shown that the degree of conduction band nonparabolicity pronounces depending on the energy density of states. With increasing temperature, a step change in the density of states smoothes and at high temperatures is completely blurred. Nonparabolicity dispersion law manifests itself in a wide range of temperatures. Calculations are carried out for the example of the quantum wells in InAs and InSb.

Recently, investigations of narrow band gap semiconductors InAs, InSb [

with a 2DEG with a concentration of up to

It is known that with an increase electron concentration

The purpose of this work is to obtain expressions for the DOS of 2DEG with allowance conduction band nonparabolicity and graphical analysis of the expressions. To study the effect of temperature on the DOS, the calculations will be carried out numerically for heterostructures of InAs and InSb based QW.

In the simplest approximation, the nonparabolic energy spectrum of the 2DEG can be represented as

Here,

In real situations, the energy levels

The dependence of

where,

According to (1-3), bottom n-th subband

Solving Equation (4), it is possible to determine of interband transition energy, for example

The figure shows that a simple model (4) gives qualitatively correct results only for wide quantum wells. For example, in QW width

T = 4.2 K | ||
---|---|---|

Compounds | InSb | InAs |

0.237 | 0.42 | |

0.014 | 0.023 | |

4.1 | 2.27 | |

−0.5 | −0.26 |

deformation of the structure due to mismatch of the lattice constant, and the effect of depolarizing shift unaccounted for in the model (4). Therefore, following a study of DOS carried out for the QW width

Knowing the energy spectrum of the electron gas can determine its DOS. To determine the DOS of 2DEG, we use the equation of the total number of particles. After summation over the spin degree it has the form

where

Writing

where,

Hence, we obtain the formula for DOS of 2DEG, where band nonparabolicity (3) is taking into account

or explicitly

Here

In the particular case when

Formula (9) can be rewritten as

where

is energy-dependent electron effective mass. It is also obtained from the definitions of the transport mass

taking into account the spectrum (1) and (3).

From these graphs follows that the band nonparabolicity can be lead to the following results:

-The bottom of each subbands moves down as compared to the parabolic case.

-This is clear from the fact that the bottom of the subbands is inversely proportional to the effective mass of

-The height of the jumps increases with energy, since it is proportional to

-Within each subbands the DOS increases linearly.

According to (9), the change of the DOS within each subbands must be square.

However, this amendment to the plot is weak, as for the structures of InAs, InSb the approximation

In letter [

where

Using (9) (14) and (15)

As seen from

At low energies steps completely disappear. With increasing energy, appear slight deviations to the provisions of the former steps of the respective discrete levels. With further increase of the energy―the thermodynamic DOS become a smooth curve, but nonparabolicity dispersion law manifests itself in a wide range of temperatures.

In this paper, the analysis of the density of states of the 2DEG in a single quantum is well. The calculations are performed for narrow-gap semiconductors InAs and InSb.

The nonparabolicity of conduction band leads to the following features of DOS:

-The bottom of each subband shifted downwards compared with parabolic case (

-The height of the jumps increases with energy, since it is proportional to

-Within each subband DOS increases linearly;

-With increasing temperature step change DOS smoothed and high temperatures completely blurred (

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

G.Gulyamov,P. J.Baymatov,B. T.Abdulazizov, (2016) Effect of Temperature and Band Nonparabolicity on Density of States of Two Dimensional Electron Gas. Journal of Applied Mathematics and Physics,04,272-278. doi: 10.4236/jamp.2016.42034