Wannier-Mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity

A method is developed to obtain Wannier-Mott — exciton wave functions in semiinfinite crystals in the framework of the effective-mass approximation. An analytical approximation is shown to agree well with numerical wave functions and is used to compute exciton nonlocal polarizability (in closed form) and $s$-wave reflectivity. The results are compared with normal-incidence reflectivity experiments in CdS, ZnSe, GaAs, and InP, and the experimental line shapes are well reproduced. The existence of an intrinsic dead layer is confirmed and a new additional boundary condition is derived. It is shown that the spike, frequently observed at the longitudinal-exciton frequency, is due to extrinsic dead layers.