Results of researches concerning the properties of the two-dimensional (2D) degenerate electron gas in a single quantum well on the basis of the InAs/AlSb heterostructure are reported. The non-parabolic character of the InAs and AlSb conduction bands is described by a simplified Kane model. The dispersion curves for first three subbands are calculated, as well as the dependences of the Fermi energy, subband filling, and effective mass of electrons at the Fermi level on the total 2D electron concentration. The obtained results are in good agreement with experimental data.
An analysis is made of the low-temperature behavior of the chemical potential [Formula: see text] of a quasi-two-dimensional electron gas near the resonance point (at the bottom of the miniband) and far from it. Low-temperature analytical formulas for [Formula: see text] are obtained under the conditions of the existence of an arbitrary number of minibands. It is shown that with the increasing temperature near the resonance point, the chemical potential decreases linearly and exponentially slowly in the middle of the resonance points. Analytical formulas are compared to the numerical solutions.
A numerical calculation of the temperature dependence of the chemical potential and for various values of the filling factor [Formula: see text] of the Landau level is carried out. The degree of filling of each Landau level is found as a function of temperature. Analytical calculations were carried out in the model of an ideal Fermi gas both without taking into account the broadening of the Landau levels [Formula: see text] and taking into account their broadening [Formula: see text]. An analytical formula is found that describes the dependences of [Formula: see text] at [Formula: see text] and low temperatures. A low-temperature formula for the dependence of [Formula: see text] based on the Sommerfeld expansion is also given. The influence of the intra- and interlevel thermal excitations on changes in the chemical potential with temperature is discussed.
Numerical and analytical results of the investigation of the thermodynamic properties of a quasi-2D electron gas are presented. The density of states, the temperature derivative of the chemical potential, and the heat capacity of the gas at the resonance points and away from it are analyzed. It is shown that, in the dependence of the heat capacity on the chemical potential, there are additional steps at the resonance points. The width of the additional steps increases with temperature. With the increase in temperature, when the main steps are practically blurred, there are still visible marks from the additional steps.
For nonparabolic dispersion law determined by the density of the energy states in a quantizing magnetic field, the dependence of the density of energy states on temperature in quantizing magnetic fields is studied with the nonquadratic dispersion law. Experimental results obtained for PbTe were analyzed using the suggested model. The continuous spectrum of the energy density of states at low temperature is transformed into discrete Landau levels.
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