Exciton binding energy in a quantum well

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 exciton Rydberg R at large widths to 4 R 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 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 Ga1-xAlxAs/GaAs/Ga1-xAlxAs quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive. [S0163-1829(98)08639-1].