EXCITON SPECTRA IN MULTI-SHELL OPEN SEMICONDUCTOR NANOTUBE

Abstract

The purpose of this paper is the theoretical investigation of electron, hole and exciton spectral parameters in multi-shell open cylindrical semiconductor nanotube composed of the semiconductors and AsGaAlxx−1.All analytical calculations are performed using the models of effective mass and rectangular potential barriers. Resonance energies and widths of electron (hole) quasi-stationary states are obtained within the exact solution of stationary Schrodinger equation and distribution function of the probability of quasi-particle location in the space of four inner shells of nanotube. The exciton Schrodinger equation is approximately solved using the modified Bethe variational method.The dependences of resonance energies and resonance widths on nanotube thickness are obtained and analyzed in the paper. Both the resonance energies and widths of quasi-stationary states of all quasi-particleas non-monotonously depend on nanotube thickness. Herein, at the functions of resonance energies one can see the sequence of horizontal and decaying plots, while at the functions of resonance widths the brightly visible maxima and minima are observed. Such behavior of electron, hole and exciton spectral parameters is quite caused by the complicated character of probability distribution of quasi-particles location in the space of multi-shell nanotube.The resonance widths of electron states are much bigger than that of the hole and the exciton binding energy is two orders smaller than the sum of size-quantized electron and hole resonance energies. Just therefore the dependences of resonance energies of exciton states on nanotube thickness in low-energy region of the spectrum are mainly caused by the peculiarities of electron and hole energy states and the exciton resonance widths almost coincide with electron ones.