Spectrum of an Electron Localized by Electrostatic Image Forces in Thin Semiconductor Layers

Abstract

The spectrum of an electron confined in a layer with the dielectric constant ϵ, embedded between two media with larger (ϵ> > ϵ) and smaller (ϵ< < ϵ) values of the dielectric constant is calculated. The dependence of the spectrum on the layer thickness and on the ratio between the dielectric constants of the layer and the media is calculated. It is shown that if the crystal thickness increases, the whole spectrum of electrons shifts into the region of negative energies and becomes quasi‐hydrogenic there.

Electron energy spectra in an elliptic quantum wire and elliptic nanotube

“…Hence it follows that to investigate the spectrum of dimensional quantization of quasi-particles in elliptic quantum wires with potential barrier of finite height and small eccentricity / f a ε = , it is better to use the method of variable separation retaining one term in expansion (6) that makes the main contribution to the formation of the given mixed quantum state than to neglect the quasi-particle penetration into the external medium. Taking advantage of the standard continuity conditions for the wave function and probability flux density [6,7] on the elliptic interface between the media, we obtain the dispersion equations for the electron energy spectrum in the elliptic quantum wire: No q ξ calculated by the method described in detail in [12]. Fig.…”

“…These problems were solved by different authors both for simple and multilayered spherical and cylindrical semiconductor nanostructures [5,6]. Based on the analytical expressions derived for the quasi-particle wave functions, their interaction was investigated, and renormalization of the energy spectrum resulted from this interaction was calculated [7,8]. For many nanostructures of simple geometrical shape, no exact solutions of the Schrödinger equation can be obtained.…”

Hole, impurity and exciton states in a spherical quantum dot

“…The presence of impurities in QD's can significantly change the localization states. First theoretical researches of impurity donor states in QD's were reported in [1][2][3][4][5][6], where exact solutions of the Schrödinger equation with the Coulomb potential interaction between particles were obtained. It is shown in work [6] that the exact solutions of the Poisson and Schrödinger equations for hydrogenic donor impurity being taken into account changes to some extent the electron spectrum as compared with results [1][2][3][4][5].…”

The effect of polarization charges on energy of univalent and bivalent donors in a spherical quantum dot

“…In [1][2][3][4][5][6][7][8][9][10][11] the attention was focused on the research of a univalent impurity. However, frequently the impurities in a QD have a valency greater than unity.…”