On the validity of haynes rule for the binding of excitonic complexes in low dimensions

Using a two-dimensional geometrical model and fractional dimension approach, it is found analytically that the ratio of the binding energy of a biexciton to that of an exciton is 0.228 in quantum wells and it is independent of the quantum-well width. This agrees very well with the results in GaAs and ZnSe quantum wells, and CuCl crystals and large quantum dots. It is suggested that, while Haynes rule may be valid for bulk, much higher ratios may be expected in lower dimensions.