Stability of two- and three-dimensional excitonic complexes

The binding energies and other properties of the excitonic complexes (bound systems of electrons and holes) in two and three dimensions (2D and 3D) are calculated by a precise variational method. The mass ratios for the limit of the stability of $X_3^{+}\mathrm{}\left(\mathrm{eehhh}\right)\mathrm{}$ are determined in both 2D and 3D cases. Two excited states of the biexciton are found to remain bound for any mass ratio.