Simple method for calculating exciton binding energies in quantum-confined semiconductor structures

We present a simple, general method for calculating the binding energies of excitons in quantum-confined structures. The binding energy is given by an integral (over the electron and hole coordinates perpendicular to the confining layers) of a prescribed function weighted by the squares of the electron and hole subband envelope functions. As a test of the method, we calculate the binding energies for heavy- and light-hole excitons in a rectangular GaAs/${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As quantum well as functions of the well width. Very good agreement with previous results is obtained over a wide range of quantum-well widths. Also, we determine the binding energies for heavy-hole excitons as functions of electric field in a GaAs/${\mathrm{Al}}_{0.35}$ ${\mathrm{Ga}}_{0.65}$As asymmetric coupled-quantum-well structure. Our results compare favorably with those obtained in a treatment in which coupling of the electron subbands via the electron-hole Coulomb interaction is considered. Our method should be applicable to a variety of complex quantum-confined semiconductor structures for which more rigorous approaches require extensive numerical calculations.