Investigation of the effect of quantum well width on the binding energy of excitons to neutral donors

Observations of bound exciton states in some bulk semiconductor materials has shown the validity of Haynes' rule, namely that the binding energy of the exciton to a donor is a multiple 1/ξ (say) of the binding energy of the electron to the donor (i.e., the neutral donor binding energy E_D), although in other bulk materials more general linear dependencies are required. Quantum well structures (QWS) typically exhibit such donor hound exciton complexes. There are several points of difference however, E_D is a function of donor position, the donor distribution is unknown and interface roughness could also influence the donor bound exciton emission. Hence in order to determine whether a generalised form of Haynes' rule can be applied to excitons bound to donors in quantum wells of varying width requires a careful combination of theory with experiment. The binding energies of the donors at various positions in each well region must be calculated with due allowance made for the effects of interface roughness. A presumed distribution of the donor concentration is then made and, on the assumed validity of Haynes' rule, the lineshape of the bound exciton emission calculated. Comparison with the observed emission spectra will then give insight into whether Haynes' rule is satisfied as a function of position and well width in QWS. This analysis has been carried out for a series of single quantum wells, all of different widths and all grown in the same sample by the technique of molecular beam epitaxy. A careful analysis of all the data showed that Haynes' rule is not applicable—i.e., the observed exciton energies are not a constant multiple of the donor binding energy for QWS of different well width.