Few-Body Syst (2009) 45: 71–76
DOI 10.1007/s00601-009-0009-8
H. Hassanabadi · A. A. Rajabi · S. Zarrinkamar ·
M. M. Sarbazi
Spectrum of Exciton in a Quantum Wire
Received: 27 October 2008 / Accepted: 12 December 2008 / Published online: 19 February 2009
© Springer-Verlag 2009
Abstract In the present work we obtain the wave function and the corresponding energy of exciton confined
within a quantum wire. What we do is to obtain the approximate analytical solution of the corresponding
Schrödinger equation for the quantum wire in the presence of Coulomb and confining terms. We then calculate
the energy and the binding energy of the exciton. By using the obtained energy of exciton, we calculate the
corresponding wave length. The comparison of the obtained wave length with the emitted wave length from
the semiconductor under study shows a good agreement with experimental results.
1 Introduction
The Coulomb interaction near the absorption edge leads to considerable changes in the optical properties of
matter. The Coulomb interaction leads to the formation of electron-hole pairs which are in the jargon called
excitons. The excitons are to some extent similar to positronium atom in which an electron is bound to a positron
through the Coulomb attraction. The electron in an exciton is bound to the hole and the resulted quasi-particle
is electrically neutral. An exciton can move like a free atom through the crystal. The existence of excitons
yields in intense absorption lines below the energy gap region. As a result of the Coulomb attraction, the photon
due to the exciton transition has less energy in comparison with the energy gap. Therefore, the phenomenon
of photon absorption in a crystal corresponds to direct formation of excitons in the media. Those excitons in
which the separation distance between the electron and the hole is large in comparison with the length the of
lattice unit cell are the so-called Wannier excitons which often occur in semiconducting combinations [1]. At
the other limit, if the excitons are such that the separation distance between the electron and the hole is less than,
or about, the length of the lattice unit cell, they are called Frenkel excitons. Nitride semicondoctors, because
of having wide energy gaps from the infrared to ultraviolet region, have found great applications in electronic
devices [2]. The photoluminescence method is one of the interesting methods in studying optical properties of
semiconductors. Also, one can use the magnetoluminescence to study the optical phenomena in the presence
of strong magnetic fields [3]. In Nitride semiconductors, after the electron-hole pairs are formed by laser stim-
ulation, they quickly form excitons as a result of Coulomb attraction and recombine afterwards. Wójs et al.
have studied the spectrum of excitons formed in quantum wells in both singlet and triplet states [4, 5]. Through
considering the Coulomb interaction among the electrons and the holes for Al
x
Ga
1-x
As / GaAs samples,
Riva et al. have studied the binding energy of trion by considering it as a function of the applied magnetic
H. Hassanabadi (B ) · A. A. Rajabi · S. Zarrinkamar
Physics Department, Shahrood University of Technology, P.O. Box 316, 3619995161 Shahrood, Iran
E-mail: h.hasanabadi@shahroodut.ac.ir
M. M. Sarbazi
Mechanical and Aerospace Engineering Department, Islamic Azad University,
Science and Research Branch, Tehran, Iran