Fractional-dimensional approach for biexcitons in GaAs/AlxGa1−xAs quantum wells

The energy of a biexciton in a GaAs/AlxGa1−xAs quantum well structure with finite barriers is investigated by using the geometrical model of two-dimensional biexcitons proposed by Singh et al. [J. Singh, D. Birkedal, V.G. Layssenko, J.M. Hvam, Phys. Rev. B 53 (1996) 15909; I.-K. Oh, J. Singh, Phys. Rev. B 60 (1999) 2528]. A fractional-dimensional approach is used to obtain the binding energy of the biexciton in both square quantum wells and parabolic quantum wells. Theoretical results show that the binding energy of a biexciton in a finite quantum well exhibits a maximum with increasing well width. The ratio of the binding energy of a biexciton to that of an exciton in a quantum well structure is found to be sensitive to the electron-to-hole mass ratio and larger than that in the three-dimensional system. The results agree fairly well with previous experimental results. The results of our approach are also compared with those of earlier theories.