On the exciton binding energy in a quantum well

B. Gerlach; J. Wuesthoff; M. O. Dzero; M. A. Smondyrev

doi:10.1103/PhysRevB.58.10568

paper

On the exciton binding energy in a quantum well

arXiv:cond-mat/9803353 · doi:10.1103/PhysRevB.58.10568

Abstract

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy $E_{b}$ of the exciton. Based on these bounds, we study the dependence of $E_{b}$ on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from $1 R y$ at large widths to $4 R y$ at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value $1 R y$ for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a $G a_{1 - x} A l_{x} A s / G a A s / G a_{1 - x} A l_{x} A s$ quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.

32 pages, ReVTeX, including 9 figures

On the exciton binding energy in a quantum well

Abstract

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