^{1}

^{2}

^{2}

One-band effective mass model is used to simulation of electron gas properties in quantum well. We calculate of dispersion curves for first three subbands. Calculation results of Fermi energy, effective mass at Fermi level as function of electron concentration are presented. The obtained results are good agreement with the experimental dates.

In semiconductors, InAs and InSb of the conduction band are characterized by a strong nonparabolicity and recently intensively studied heterostructures based on them [

In [^{11} to 8 × 10^{12} cm^{−2}. In this work has been found increase of the effective mass of almost 2 times.

The purpose of this work―the calculation of: 1) subbands dispersion curves, 2) the density of states of 2D electron gas and 3) concentration dependence of effective mass in Fermi level for InAs/AlAs QW with width L = 15 nm.

It is shown that an abrupt change in the density of states leads to a peculiar change in the concentration dependence of effective mass.

Consider a single QW with width L (area A―InAs), concluded between barriers with height V (area B―AlAs). The energy is measured from the bottom of the band of the bulk InAs.

In the one band effective mass approximation, the solution of the three-dimensional Schrödinger equation can be represented as

, (1)

, (2)

Here

, (3)

, (4)

we find the dispersion equation

here

Nonparabolicity of conduction band well takes into account by formulas

where,

To describe the statistics of electrons, Equation (5) is non convenient because it is not solvable with respect to E or k. Therefore, we replace Equation (5) is by simple approximation

InAs (A) | AlSb (B) | |
---|---|---|

E_{g}, eV | 0.42 | 2.37 |

D, eV | 0.38 | 0.75 |

E_{P}, eV | 21.2 | 20.85 |

m(0), [m_{0}] | 0.023 | 0.11 |

V, eV | 0 | 1.35 |

where, E_{n}―is bottom of n-th subbands. Now, approximation (8) is the best solution of (5). However, values of E_{n} in (8) now are obtained from Equation (5) at k = 0 by use numeric method.

For InAs/AlSb QW with L = 15 nm, we have: E_{1} = 0.0454 eV, E_{2} = 0.158 eV, E_{3} = 0.304 eV, and for case L = 6 nm we have: E_{1} = 0.163 eV, E_{2} = 0.509 eV, E_{3} = 0.903 eV.

Calculated dispersion curves from Equation (5) and approximation (8) are compared in

From

The total electron concentration is

where

According (8) we have

, (10)

where

In Equation (10), the terms in the sum should be positive. The negative terms in

From (10), we can estimate the critical concentrations of

with the well width L = 15 nm can be found

This estimation is close to experimental measured date _{c}_{2} = 6.87 × 10^{12} cm^{−2}.

The dependence

These fractures occur at the critical concentrations of

The thermodynamically DOS of electron gas at Fermi level

According approximation (8), the electron effective mass at the Fermi level (cyclotron mass)

The dependence

This dependence can be obtained from Equations (10) and (12) by changing the Fermi energy in the range

This figure shows also the dependence of experimentally measured value of the effective masses (cyclotron mass)

In this study are provided useful approximation (8) of subband dispersions and simplified Equation (10) to calculate the statistics of a degenerate electron gas in heterostructured InAs/AlSb QW, which satisfactorily describes the experimental results [

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

Gulyamov, G., Abdulazizov, B.T. and Jamoldinovich, B.P. (2016) Effects of Band Nonparabolicity and Band Offset on the Electron Gas Properties in InAs/ AlSb Quantum Well. Journal of Modern Physics, 7, 1644-1650. http://dx.doi.org/10.4236/jmp.2016.713149