Elsevier

Physics Letters A

Volume 311, Issue 1, 5 May 2003, Pages 60-66
Physics Letters A

The effect of an intense laser field on magneto donors in semiconductors

https://doi.org/10.1016/S0375-9601(03)00456-0Get rights and content

Abstract

The laser-field dependence of the binding energy of shallow-donor impurities in graded, and square quantum wells under the external magnetic field is calculated by a variational method and in the effective mass approximation. We have shown that, not only the ‘dressed’ potential, but also the shape of the confinement potential, the strength of the external magnetic field parallel to the growth direction, and the impurity position play very important roles in the determining the binding energy of a hydrogenic impurity.

Introduction

The development of very intense laser fields has provided an opportunity to explore the properties of matter in strong electromagnetic fields that greatly exceed the Coulomb binding fields in an atom. The effect of an intense high-frequency laser field on the physical properties of bulk semiconductors has been discussed and analyzed in the literature [1], [2], [3], [4], [5], [6].

To date, there exists a significant literature delay with the effect of external fields on the physical properties of the semiconductor heterostructures has attracted the attention of many researches in the last decades [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. More recently, these studies have been extended low-dimensional semiconductor heterostructures under intense electric fields, created by an applied AC voltage or a high-intensity THz laser [17], [18], [19], [20]. As is well known, the external electric field has important consequences for the electronic and optical properties of the structure. Fanyao et al. have reported calculation of the binding energy of an axial donor hydrogenic impurity in ideal, infinite, cylindrical quantum wire placed in an intense, high-frequency laser field [17]. They have also presented calculations of the binding energy of an on-center donor hydrogenic impurity in a quantum dot in an intense laser field [18]. It was found that the binding energy of an impurity in the low-dimensional systems decreases with increasing the laser-field amplitude [21], [23]. Also it is shown that, although the individual external electric field themselves act in a way to lower the binding energy of the impurity, one might accomplish a reduction of the weakening effects by considering the joint action of the two external fields [18]. Oliveira et al. have used the dressed-band approach to treat the interaction of a laser field with semiconductor GaAs–(Ga,Al)As quantum wells and dots [20]. They suggest that the strong localization of the electronic and impurity states due to the quantum well and quantum dot and enhanced by laser confinement may result useful for manipulation of electronic and donor states in some proposed solid-state based quantum computers. A electron in a semiconductor nanostructure under the action of a magnetic field perpendicular to the growth direction of and monochromatic electromagnetic radiation, linearly polarized in a direction perpendicular to the magnetic field is considered by Perez-Maldonado et al. [21], and they have observed a symmetry breaking in the quasi-energy spectra for intensities greater than a critical value. It was also found that, when an in-plane magnetic field is applied the nonlinear effects appear in superlattices for lower radiation intensities and for radiation polarized in any direction perpendicular to the magnetic field [24].

In this Letter we consider the magnetic field effect on the binding energy of a hydrogenic impurity placed in a graded quantum well (GQW) in the additional presence of a intense, high-frequency laser field, taking into account the laser ‘dressing’ effects on the both impurity Coulomb potential and the graded confinement potential [17]. It was shown that, not only the ‘dressed’ Coulomb potential, but also ‘dressed’ confinement potential, and impurity positions plays very important roles in the determining the binding energy of a hydrogenic impurity [17], [18], [19]. Nevertheless to the best of our knowledge, there is no study on the effect of an intense laser-field on the polarizability of a donor in a graded quantum well.

Section snippets

Theory

The method used in the present calculation is based upon a nonperturbative theory that has been developed to describe the atomic behavior in intense high-frequency laser fields [22], [23]. We assume that the radiation field can be represented by a monochromatic plane wave of frequency ω. For linear polarization, the vector potential of the field in the laboratory frame is given by A(t)=eA0cosωt, where e is the real unit vector of the polarization. By applying the time-dependent translation rr+α

Dressed binding energy

By changing the Al concentration x in the G1−xAlxAs one obtains a linearly changing conduction band profile as shown in Fig. 1. The functional form of the confinement potential V(z) is given as, V(z)=V0Θ|z−L/2|+V04zL/2+1Θ|L/2−z|, where V0 is the conduction band offset at the interface, L is the well width, and Θ is the step function.

Before preceding further and applying the above described dressed potential theory to our particular graded quantum well system, we write down the Hamiltonian of a

Results and discussion

For numerical calculations, we take, m=0.0665m0 (where m0 is the free electron mass), ε=12.58 and the aluminum concentration x=0.39. The position of the donor impurity is given as (xi,0,0) the barrier height V0 is obtained from the 60% (40%) rule of the band-gap discontinuity ΔEg for donor (acceptor) states for aluminum concentration x⩽0.45, such that the band-gap is direct at the Γ point and ΔEg is given by [31] as, ΔEg=1247x (meV).

The calculated impurity binding energies of a graded and

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