Optical properties of a magneto-donor in a quantum dot

https://doi.org/10.1016/j.physe.2005.04.005Get rights and content

Abstract

The optical-absorption spectra associated with transition between the ground state of a hydrogenic donor impurity to the second conduction levels in the presence of a magnetic field has been calculated for spherical CdSe quantum dot (QD) with infinite potential confinement, using a variational method and a perturbation method within the effective-mass approximation. We have found that as a consequence of the scaling laws, the absorption coefficient varies systematically as a function of QDs size. The application of the magnetic field may hinder the absorption coefficient of an on-center impurity and displace the threshold energy towards high energy if γ>1/R2 and towards low energy if γ<1/R2 for the 1s–2p transition. For all values of the magnetic field, the threshold energy of the transition 1s–2p+ is displaced towards high energy.

Introduction

Understanding of the effect of the quantum confinement on the impurity states in low dimensional structures is a very important subject in semiconductor physics. Electronic and optical properties of shallow impurities in quantum wells, quantum wires, and quantum dots (QDs) are strongly modified with the respect to the host materials due to the quantum-confinement effects. The electronic and optical properties of selectively doped semiconductor structures have been extensively studied [1], [2], because of their technological applications in electronic devices [3]. Within the effective-mass theory, the problem of shallow donor in semiconductor is equivalent to that of a hydrogen atom but with very different energy and length scales. However, exact solutions for shallow impurity states in the presence of magnetic fields are not available. Most theoretical studies on shallow impurities use a variational approach [4]. Other approximate methods such as the perturbation approach [5] and numerical solution of the Schrödinger equation [6] have also been developed. The application of the magnetic field modifies the symmetry of these states as well as the nature of the wave functions. Different experimental techniques have been used in the study of shallow impurity states in the presence of magnetic field such as magneto-spectroscopy and far-infrared spectroscopy. In order to determine the impurities optical properties such as absorption and photoluminescence spectra, nonlinear response, and the other properties in low dimensional heterostructures many researchers are interested in the study of the transitions between the impurity energy levels [1], [7], [8], [9], [10]. Most of these studies have concentrated on the low-energy hydrogenic-like transitions such as 1s–2p±. In Ref. [11] Silva-Valencia and Porras-Montenegro calculated the optical-absorption spectra associated with transitions between the (n=1) valence level and the acceptor impurity band for spherical GaAs QDs with infinite potential confinement. They have shown results both for one impurity and for a homogenous distribution of impurities inside the QD. They have found an absorption edge associated with transitions involving impurities at the center and a peak related to impurities at the edge of the QD. For all sizes of the QD the peak associated with impurities located close to the edge always governs the total absorption probability. However, to our knowledge there are neither theoretical nor experimental reports on the impurity-related optical-absorption spectra in QD associated with the ground state of a hydrogenic donor impurity to the first and second conduction levels of the QDs using an infinite confinement potential.

In this paper, we report a calculation of the absorption coefficient of a shallow donor in the presence of a magnetic field. The absorption process is considered as being a photo-excitation of an electron residing in the ground state of a hydrogenic donor impurity to the second conduction levels of the QDs. The energy is calculated by using a variational method in which the trial wave function takes into account the magnetic and the spatial confinements, and the Coulomb interaction. The paper is organized as follows: the analytical expression for the absorption coefficient of a shallow donor in QD is presented in Section 2, results and discussion are presented in section 3.

Section snippets

Theory

The Hamiltonian of a shallow hydrogenic impurity located at the center of the spherical QD in the presence of the magnetic field can be written in spherical coordinates and in the effective-mass approximation asH=-Δ-2r+γLz+14γ2r2sin2(θ)+V(r),where the first term is the kinetic energy of the electron of the impurity, the second term correspond to the potential energy of the impurity the third and the fourth terms correspond to the effect of magnetic field. The last term V(r) is the infinite

Numerical results and discussion

We have calculated the absorption coefficient of an on-center impurity, in the presence of a uniform magnetic field applied along the z-direction. In Fig. 1 we present 1s–2p+ transition energy as function of the dot radii for a set of magnetic field value running from 0 to 20 T. For small values of the dot radius (R<a* strong confinement), the transition energy is nearly insensible to the magnetic field variation. In this range of the dots radius the geometric confinement governs the magnetic

Acknowledgments

The authors (A.D.S and I.Z) gratefully acknowledge the Abdus Salam International Centre for Theoretical Physics, Trieste-Italy, where this work was initialized, for very kind hospitality and its support in the preparation of the results. This work was done within the framework of the Associate ship Scheme of the Abdus Salam ICTP.

References (23)

  • J.M. Shi et al.

    Phys. Rev. B

    (1994)
  • G. Bastad

    Phys. Rev. B

    (1981)
    J. Lee et al.

    J. Vac. Sci. Technol. B

    (1984)
  • A. Latagé et al.

    Semicond. Sci. Technol.

    (2002)
  • W.T. Masselink et al.

    Solid State Electron.

    (1986)
  • C. Wetzel et al.

    Phys Rev. B

    (1993)
  • P.W. Barmby et al.

    Phys Rev. B

    (1998)
  • A. Latgé et al.

    Semicond. Sci. Technol.

    (2002)
  • A. Bruno-Alfonso et al.

    J. Phys.:Condens. Matter

    (2001)
  • L.C. Lew Yan Voon et al.

    Semicond. Sci. Technol.

    (1995)
  • M. Pacheco et al.

    Phys. Stat. Sol. (b)

    (2003)
  • J. Silva-Valencia et al.

    J. Appl. Phys.

    (1997)
  • Cited by (20)

    • The effects of the dielectric screening, temperature, magnetic field, and the structure dimension on the diamagnetic susceptibility and the binding energy of a donor-impurity in quantum disk

      2022, Physica B: Condensed Matter
      Citation Excerpt :

      Furthermore, the rapid progress in semiconductor growth techniques, such as molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) has accelerated research in this area. The defining physical properties of these nanostructures are attractive not only from a fundamental scientific point of view, but also in the manufacture and subsequent operating of electronics and optical devices based on such systems [4–6]. It should be noted that the properties of semiconductor quantum disks (QDisks) are highly sensitive to internal and external perturbations such as compositions, electric and magnetic fields, size, impurities, temperature, hydrostatic pressure and radiation [7–11].

    • Linear and nonlinear absorption coefficients of spherical quantum dot inside external magnetic field

      2017, Physica B: Condensed Matter
      Citation Excerpt :

      Niculescu and Bejan [28] studied the optical properties of a pyramidal QD subjected the external magnetic field. Similarly, Xie [29], Sjojae and Vala [30] and Nasri and Bettahar [31] carried out the linear and nonlinear absorption coefficients of anisotropic QD, disk-like QD and triangular quantum ring inside external magnetic field. In the presence and absence of Gaussian white noise Mandal et al. [32] and Ganguly and his co-workers [33] studied the roles played by the electric, magnetic field and the confinement potential on the optical absorption coefficients.

    • Exploring diamagnetic susceptibility of impurity doped quantum dots in presence of Gaussian white noise

      2016, Journal of Physics and Chemistry of Solids
      Citation Excerpt :

      Magnetic field effects become more prominent at higher field strengths [16]. Application of magnetic field may diminish the absorption coefficient (AC) of an on-center impurity and shift the threshold energy towards high energy and low energy transitions [17]. Naturally we find a wealth of significant investigations on LDSS in presence of a magnetic field [18–42].

    View all citing articles on Scopus
    View full text