Exciton quantization and polariton propagation in semiconductor slabs: From semi-infinite crystals to quantum wells

Variational wave functions are proposed for the two lowest states of excitons in thin slabs. They are shown to be reliable for CdS slabs of thickness L larger than 2.5 exciton radii $a_B$. The energy difference between them is close to that found by quantizing the center-of-mass motion in a slab of effective thickness L-2d, where d is the transition-layer depth. This approximate rule becomes exact for L>16$a_B$. The calculated optical properties show that absorptance maxima and transmittance minima are in close correspondence with CdS exciton levels for L̊, where polaritonic effects are not important.