The ground-state energy of an exciton in a parabolic quantum dot

Abstract

The shifted l/N expansion method is used to solve the effective-mass Hamiltonian for an interacting electron-hole pair in a quantum dot. The ground-state energy of an exciton parabolically confined in a quantum dot as a function of quantum dot size is obtained. Comparison shows our results are in excellent agreement with those of Que.

The energy level ordering in two-electron quantum dot spectra

“…Here R * and a * are used as units of energy and length, respectively. The complete discussion of the 1/N method can be found in [17,[28][29][30]. …”

“…The growing interest in this field is motivated by the physical effects and the potential device applications, both as electronic memories as well as optoelectronic devices to which many experimental [1][2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] works have been devoted. The effects of the magnetic field, which plays a useful role in identifying the absorption features, on the states of the interacting electrons, impurity [15] and excitons [17][18][19][20][21][22] confined in the QD have been intensively studied. Maksym and Chakraborty [8] have studied the eigenstate of interacting electrons, parabolically confined in the QD, in a magnetic field perpendicular to the plane of the QD and found that the Coulomb interaction has an important effect on the magnetic field dependence of the energy spectrum.…”

“…Following the previous work of the shifted 1/N expansion method [17,[28][29][30], we give here only the energy expression which is needed to produce the spectra of H r . The energy expression reads as,…”

Exciton States in a Quantum Dot With Parabolic Confinement

“…The electron-hole interactions in small semiconductor crystals and electronic states depending on QD size have been investigated by many researchers. 4,8,11 Electron systems under parabolic confinement are also attractive experimentally, dynamic and far infrared responses of these systems have been studied. 12 To study of excitonic systems in terms of the quantum effects of their size is important in low dimensional QDs rather than the bulk semiconductors.…”

“…15 Also, the ground state energy of an exciton in QD with parabolic confinement has been investigated and the ground state energy data depending on QD size has been studied. 11,16 The excitonic binding energy in a QD has been investigated via the variational method by converting the electron and hole coordinates to relative and center of mass coordinates and the ground state energy data depending on QD size has been published. 4 Generally, infinite barriers have been considered as a confinement potential of excitons 17 and exact numerical solution of this system has been calculated by Hu.…”