The effect of linear and non-linear diffusion on exciton energies in quantum wells

This paper considers the technique of investigating diffusion processes via monitoring spectroscopically the ground state energy of an exciton confined in a quantum well. It is shown that the change in the exciton energy E-E₀ during linear diffusion, can be described by an empirical relationship E-E₀=(E^b_g-E₀)(1-exp{-γ√Dt/1_w}), where E^b_g is the band gap of the initial barrier material, D the diffusion constant and t the time. Detailed calculations accounting for the changes in the exciton binding energy have shown that the parameter γ∼1.5 for all wells of width 1_w ≥40 Å regardless of the material system. It is proposed that this relationship could be used to determine the linear diffusion coefficient D. Once D has been determined the relationship could then be utilized as a predictive tool, e.g., to determine the annealing time necessary to produce a given energy shift for a particular quantum well width. The paper goes on to discuss the effects non-linear diffusion processes could have on exciton energies in quantum wells. In particular, it is shown how detailed spectroscopy and annealing experiments when coupled with accurate modelling could be used to distinguish between constant and concentration dependent diffusion coefficients.