Physica E: Low-dimensional Systems and Nanostructures
Optical properties of a magneto-donor in a quantum dot
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 () 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 aswhere 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 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 ( 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)
- et al.
Phys. Rev. B
(1994) Phys. Rev. B
(1981)et al.J. Vac. Sci. Technol. B
(1984)- et al.
Semicond. Sci. Technol.
(2002) - et al.
Solid State Electron.
(1986) - et al.
Phys Rev. B
(1993) - et al.
Phys Rev. B
(1998) - et al.
Semicond. Sci. Technol.
(2002) - et al.
J. Phys.:Condens. Matter
(2001) - et al.
Semicond. Sci. Technol.
(1995) - et al.
Phys. Stat. Sol. (b)
(2003)
J. Appl. Phys.
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