EXCITON BINDING-ENERGY IN EXTREMELY SHALLOW QUANTUM-WELLS

The usual approach to the problem of excitons in semiconductor quantum wells is to assume that both the electron or the hole are primarily l ocalized in the potential well regions defined by the band offsets, i. e., that the quantum wells are deep. We re-examine the problem of the exciton in the presence of a very shallow square well potential due to the (small) conduction and valence band offsets in a semiconducting h eterostructure. We show that the combined effects of the shallow well and the Coulomb interaction between the electron and the hole are equi valent to an effective potential acting on the center-of-mass of a thr ee-dimensional exciton. We calculate the shape of such a potential and show it to be satisfactorily approximated by the potential of a parab olic well.