Polarizabilities of shallow donors in inverse V-shaped quantum wells under laser field

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Abstract

The effect of the high-frequency laser field on the subband structure and on polarizabilities of the shallow donors in a GaAs/GaAlAs inverse V-shaped quantum well for different Al concentrations at the structure center is investigated. Calculations are performed in the effective-mass approximation. It is shown that the polarizability decreases with the increasing of the laser intensity and this effect is stronger for high Al concentration at the well center. Our results are in agreement with previous calculations for square and graded quantum wells.

Introduction

In recent years, there is a great interest in studying some original quantum wells (QWs) with a wide variety of confining potential shapes such as parabolic, half parabolic, graded and V-shaped [1], [2], [3], [4], [5], [6], [7], [8], [9]. Chen et al. [10] have prepared an inverse parabolic QW; an inverse V-shaped quantum well can also be grown using the same technique.

The application of an electric field to these structures causes a polarization of the carrier distribution and a shift of the quantum energy states. These effects generate considerable changes in the energy spectrum of the carriers, which can be used to control and to modulate the output intensity of devices. The effect of the applied electric field on the binding energy of the shallow donor in QWs was investigated in previous studies [11], [12], [13], [14], [15]. More recently, such studies have been extended to low-dimensional structures in the intense laser field created by THz lasers [16], [17], [18].

In this paper we have studied the effect of the laser field on the binding energy and on polarizabilities of on-center donor in a GaAs/Ga1−xAlxAs inverse V-shaped quantum well (IVQW) with different Al concentrations at the well center.

Section snippets

Theory

We assume an electron subjected to a time-independent potential V(r) and under the action of a laser radiation field represented by a monochromatic plane wave of frequency ω. For a linear polarization, the vector potential associated with the radiation field is given by A(t)=eA0cos(ωt), where e is the unit vector of the polarization. By applying the time-dependent translation rr+α(t) the time-dependent Schrödinger equation describing the interaction dynamics was transformed by Kramers

Results and discussion

Fig. 2 displays the laser-dressed potential of the L=100 Å GaAs/GaAlAs polarized well, V=Vb(z, α0)+eFz, at several values of α0, F, and σ parameters. The corresponding ground-state subband energies are also plotted. We can see that in the presence of the laser field the shape of the confinement potential is changed and the “dressed” energy eigenvalues are blueshifted in agreement with the previous works [9], [24], [25].

As α0 increases, the heights of the central V-shaped and the lateral barriers

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