Magnetic field effect on the energy levels of an exciton in a GaAs quantum dot: Application for excitonic lasers

Abstract

The problem of an exciton trapped in a Gaussian quantum dot (QD) of GaAs is studied in both two and three dimensions in the presence of an external magnetic field using the Ritz variational method, the 1/N expansion method and the shifted 1/N expansion method. The ground state energy and the binding energy of the exciton are obtained as a function of the quantum dot size, confinement strength and the magnetic field and compared with those available in the literature. While the variational method gives the upper bound to the ground state energy, the 1/N expansion method gives the lower bound. The results obtained from the shifted 1/N expansion method are shown to match very well with those obtained from the exact diagonalization technique. The variation of the exciton size and the oscillator strength of the exciton are also studied as a function of the size of the quantum dot. The excited states of the exciton are computed using the shifted 1/N expansion method and it is suggested that a given number of stable excitonic bound states can be realized in a quantum dot by tuning the quantum dot parameters. This can open up the possibility of having quantum dot lasers using excitonic states.

Thermodynamic properties of Aharanov–Bohm (AB) and magnetic fields with screened Kratzer potential

“…Again, Jahan et al [37] studied the problem of an exciton trapped in a Gaussian QD of GaAs in both 2D and 3D in the presence of a B -field using the Ritz variational method [38], the 1 N expansion method [39], and the shifted 1 N expansion method [40,41]. The ground state energy and the binding energy of the exciton were obtained and compared with results in literature.…”

Hydrogenic impurity effect on optical properties of Wannier-Mott exciton confined in a spherical quantum dot with Kratzer potential under magnetic field

“…For further presentation, we only present results and equation related to the relative motion of the system. The relative part of the Hamiltonian for the excitonic system in the absence of magnetic field using effective mass approximation is(for details please see [9,20])…”

“…Analog to electron-proton bound systems in solid-state physics, in semiconductor nanomaterials, we have electron and hole pairs whose bound state is called an exciton, which is the result of Coulomb interaction. Between confined electron and hole, the study of exciton in QD breeds a new arena of application as shown by various researchers in earlier studies [20].…”

An off-center endohedrally confined hydrogen molecule

“…[30][31][32][33][34][35][36][37][38][39][40][41][42][43] The properties of confined systems have been studied using various confinement models depending on the applications considered. Some of the most frequently studied are the spherical hard wall, [44][45][46][47][48] the finite barrier, [49][50][51] the Gaussian-well potential, [52][53][54] the square-well potential 55,56 and a combination of Woods-Saxon potentials. 57,58 Moreover, these models usually consider the system to be at the center of the cavity as an initial approximation; however, to achieve a more realistic analysis, other possible positions should also be taken into account to see how this affects the energy levels and other properties of the confined species.…”