Hydrostatic pressure and electric and magnetic field effects on the binding energy of a hydrogenic donor impurity in InAs Pöschl–Teller quantum ring

https://doi.org/10.1016/j.spmi.2011.11.005Get rights and content

Abstract

We consider the effects of electric and magnetic fields as well as of hydrostatic pressure on the donor binding energy in InAs Pöschl–Teller quantum rings. The ground state energy and the electron wave function are calculated within the effective mass and parabolic band approximations, using the variational method. The binding energy dependencies on the electric field strength and the hydrostatic pressure are reported for different values of quantum ring size and shape, the parameters of the Pöschl–Teller confining potential, and the magnetic field induction. The results show that the binding energy is an increasing or decreasing function of the electric field, depending on the chosen parameters of the confining potential. Also, we have observed that the binding energy is an increasing/decreasing function of hydrostatic pressure/magnetic field induction. Likewise, the impurity binding energy behaves as an increasing/decreasing function of the inner/outer radii of the quantum ring nanostructure.

Highlights

► The binding energy is an increasing or decreasing function of the electric field. ► The binding energy is an increasing function of hydrostatic pressure. ► The binding energy is a decreasing function of magnetic field induction. ► The binding energy is an increasing function of the inner radii of the ring. ► The binding energy is a decreasing function of the outer radii of the ring.

Introduction

Growth of semiconductor nanostructures has attracted much attention due to their potential applications in electronic and optoelectronic devices [1]. In this context, the fabrication of semiconductor quantum rings (QRs) has triggered a strong interest in the realization of the kind of quantum topological phenomena that are expected in small systems with simply-connected geometry [2]. Lorke et al. first observed far-infrared optical response in self-assembled QRs, revealing a magneto-induced change in the ground state from angular momentum l = 0 to l = −1, with a flux quantum piercing the interior [3].

The application of an electric field along the growth direction of the heterostructure gives rise to a polarization of the carrier distribution with a consequent energy shift of the quantum states. Such effects may introduce considerable changes in the energy spectrum of the carriers, which could be used to control and modulate the output of optoelectronic devices. It is possible to mention a rather large There are many works related to the theoretical investigation of electric field effects on electronic states and optical properties of QRs [4], [5], [6].

The studies about the influence of the hydrostatic pressure on the electronic and impurity states have proven to be significant in the understanding of some optical properties of semiconductor heterostructures [7], [8]. Morales et al. have considered the simultaneous effects of hydrostatic pressure and electric field on shallow donor impurity states in quantum well (QW) [9]. Kasapoglu [10] reported the combined effects of hydrostatic pressure and electric field on the binding energy of a shallow-donor impurity in a double QW. Restrepo et al. have investigated the combined effects of hydrostatic pressure and electric field on the impurity-related self-polarization in multiple QW [11]. The effects of hydrostatic pressure and in-growth direction applied electric and magnetic fields on donor binding energy and photoionization cross section as well as in excitons in cylindrical quantum dots (QDs) have been considered by Barseghyan et al. [12]. Duque et al. [13] studied the simultaneous effects of hydrostatic pressure and electric field on the donor binding energy in vertically-coupled QDs. On the other hand, there are also reports from Mora-Ramos et al. on the effect of hydrostatic pressure on exciton properties in cylindrical GaAs quantum dots [14], [15].

Evolving techniques of crystal growth allow for accurate doping and composition alloy control in such a way that it is possible to tailor distinct conduction and valence band potential energy bending profiles in nanosystems. Among the different proposals for one-dimensional modulated confining potentials we can mention the one known as Pöschl–Teller (PT) [16], [17], [18], [19], [20], [21]. Two particularly interesting features of the PT potential are its tunable asymmetry and the fact that the corresponding Schrödinger equation is exactly solvable in analytic form in the absence of applied fields. Depending on the values chosen for its two characteristic parameters one can switch from a symmetric to an asymmetric 1D profile situation [17]. Several applications of the PT potential in semiconductor heterojunction devices and optical systems have been suggested by Tong [18], [19]. Between them we have, for example, its use in noise reduction in resonance tunneling devices and other devices [19]. Given the possibility of configuring an intrinsic asymmetry of the conduction band energy even for zero field, Radovanovic et al. took advantage of this potential function to investigate several intersubband absorption properties in PT-based confined systems [20]. Likewise, Yildirim and Tomak studied in particular the nonlinear optical properties associated to the PT potential [21], and also the nonlinear changes in the refractive index resulting from its tunable asymmetry [22].

Many studies published in recent years have considered heterostructure systems in which one finds some preserved symmetries, either due to the specific system configuration or because the given configuration of the applied external perturbations. In quantum dot and rings, we have the particular case of the azimuthal symmetry [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. Most theoretical works have been developed in the effective mass approximation, with the use of different methods like the variational or perturbative techniques as well as expansions of the wave function of the confined states in terms of appropriate orthonormal basis. The calculations have been performed in systems such as: (1) single hole and electron carriers in QRs [23], [24] and in double QRs [25], (2) shallow donor and acceptor impurity levels in abrupt rectangular QRs under the presence of crossed magnetic and electric fields [26], [27], [28], (3) shallow impurities in symmetrical paraboloidal and hemi-paraboloidal QDs [29], and (4) exciton complexes in single and vertically coupled type-II QDs under perpendicular magnetic field [30], [31], [32], nanoring double QWs [33], and narrow-gap InSb cylindrical layer QD [34]. The main results can be summarized as follows: (1) the exciton energy levels are non-equidistant and split up in only two levels in magnetic field, reflecting the ringlike geometries, (2) the Aharanov–Bohm oscillations of exciton characteristics predicted for one-dimensional rings are not present in finite-width systems, and (3) the presence of the applied electric field changes the selection rules for the different considered transitions.

Since none of the previous works have considered the combined effects of hydrostatic pressure and electric and magnetic fields, in this article we investigate the effects of hydrostatic pressure and applied electric and magnetic field on donor impurity states in InAs PT-QRs. The choice for a PT confining potential is made aiming at a prospective study of impurity-related possible nonlinear optical properties in the asymmetric variant of this kind of systems. In the work we obtain the impurity binding energy as a function of the hydrostatic pressure and electric field for several values of the height of the QR; for several values of the parameter of the PT confining potential, and for different configurations of the inner and outer radii and applied magnetic field induction. The calculation uses the effective mass and parabolic band approximations, within a variational procedure. The article is organized as follows. In Section 2 we describe the theoretical framework. Section 3 is dedicated to the results and discussion, and finally, our conclusions are given in Section 4.

Section snippets

Theoretical framework

Fig. 1 presents a pictorial view of the QR considered in this work. In the graphics there are shown the dimensions of the heterostructure (inner and outer radii and height), the direction of the applied electric and magnetic fields, and the electron and impurity positions.

In the present work we shall considered a fixed impurity location: on the plane zi = L/2, with radial position ρi = (R1 + R2)/2. The effective mass Hamiltonian for a hydrogenic donor impurity in an InAs QR under the influence of

Results and discussion

In Fig. 2 we present our result for the binding energy of a donor impurity as a function of the applied electric field in InAs PT-QR for the zero pressure case. The calculation considered three different values of the QR height. From the observation of the curves in the figure it becomes clear that the binding energy is a decreasing function of the electric field strength. Also, one notices that the influence of the electric field is stronger for larger values of the QR height. In order to

Conclusions

In this article we have studied the combined influences of hydrostatic pressure and applied electric and magnetic fields on the donor impurity states in a cylindrically shaped InAs quantum ring with Pöschl–Teller confining potential along the axial direction. In general terms it can be concluded that the electric field causes a reduction of the impurity binding energy in symmetric Pöschl–Teller potentials. In the asymmetric configuration the influence of the field is mixed. It causes the

Acknowledgments

C.A.D. and M.E.M.R. thank CONACYT (Mexico) and COLCIENCIAS (Colombia) for support under the 2009–2011 Bilateral Agreement “Estudio de los efectos de la presión hidrostática y la mezcla de estados de conducción sobre la estructura electrónica y los estados excitónicos en nanoestructuras basadas en semiconductores III–V”. M.E.M.R. also acknowledges support from Mexican CONACYT through grant CB-2008-101777. C.A.D. is grateful to the Colombian Agencies CODI-Universidad de Antioquia (Estrategia de

References (40)

  • V.A. Harutyunyan et al.

    Physica E

    (2007)
  • V.A. Harutyunyan

    Appl. Surf. Sci.

    (2009)
  • E. Kasapoglu

    Phys. Lett. A

    (2008)
  • R.L. Restrepo et al.

    J. Luminescence

    (2011)
  • M.E. Mora-Ramos et al.

    Physica E

    (2010)
  • B.Y. Tong

    Solid State Commun.

    (1997)
  • B.Y. Tong et al.

    Phys. Lett. A

    (1997)
  • J. Radovanovic et al.

    Phys. Lett. A

    (2000)
  • I. Filikhin et al.

    Physica E

    (2006)
  • M. Zuhair et al.

    Physica E

    (2009)
  • M.G. Barseghyan et al.

    Physica E

    (2010)
  • D. Bimberg et al.

    Quantum Dot Heterostructures

    (1999)
  • J.M. Garcia et al.

    Appl. Phys. Lett.

    (1997)
  • A. Lorke et al.

    Phys. Rev. Lett.

    (2000)
  • V.A. Harutyunyan

    J. Appl. Phys.

    (2011)
  • M. Chandrasekhar et al.

    High Pressure Res.

    (1992)
  • M. Chandrasekhar et al.

    Philos. Mag. B

    (1994)
  • A.L. Morales et al.

    J. Phys.: Condens. Matter

    (2002)
  • M.G. Barseghyan et al.

    Eur. Phys. J. B

    (2009)
  • C.M. Duque et al.

    Eur. Phys. J. B

    (2010)
  • Cited by (28)

    • Hydrogen-like donor impurity states in strongly prolate ellipsoidal quantum dot

      2023, Physica E: Low-Dimensional Systems and Nanostructures
    View all citing articles on Scopus
    View full text