Geometric approach to determine the binding energy of quasi-two-dimensional biexcitons

Abstract

We improve upon the simple method of Singh et al. [Phys. Rev. B 53, 15 909 (1996)] to calculate the biexciton binding energy in quasi-two-dimensional (2D) quantum wells. Optimizing the geometric configuration, a simple and analytical expression for the ratio of the binding energy of a 2D biexciton to that of an exciton, ${E}_{b}^{\mathrm{xx}}{/E}_{b}^{x},$ is derived. It is found that the geometric configuration of a positronium-molecule-like biexciton is a square and that of a hydrogen-molecule-like biexciton is a tetragon. The average interparticle distances as functions of \ensuremath{\sigma} are also determined. The theory is applied to GaAs, ZnSe, and ${\mathrm{Cd}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{Se}$ quantum wells and the result of ${E}_{b}^{\mathrm{xx}}{/E}_{b}^{x}$ thus obtained agrees with the experimental results.