Theory of spontaneous-emission lifetime of Wannier excitons in mesoscopic semiconductor quantum disks

Abstract

A theoretical study of the spontaneous-emission lifetime of Wannier excitons in mesoscopic quantum disks is presented. We begin by introducing our experiments on the spontaneous emission of free and bound excitons in the ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP quantum wells. Using magneto-optical measurements, we show that excitons are localized at a certain potential minima below 20 K and that the bound excitons have a lifetime that is about 30 times longer than free excitons. To analyze the diamagnetic shifts of exciton resonance, we presented the effective-mass equation of bound excitons in quantum wells under a magnetic field. We derive a theoretical formula for the exciton spontaneous-emission lifetime in meso- scopic quantum disks by expanding the wave function for center-of-mass motion into a Fourier series and by applying the wave-vector selection rule between the radiation field and each Fourier component. The mesoscopic disks approach macroscopic quantum wells as the disk diameter increases above the exciton resonant wavelength and approach microscopic quantum dots as the radius decreases below the exciton Bohr radius. We show that the formula continuously connects the two limiting cases via mesoscopic regions and that the lifetime increases two orders of magnitude as the radius decreases in the ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP system, for example. Experimental results on the spontaneous emission of bound excitons in ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP quantum wells support our theoretical prediction.