EXCITONS IN EXTREMELY SHALLOW QUANTUM-WELLS

Excitons in extremely shallow semiconductor quantum wells are consider ed in the limit when both the conduction band and the valence band con fining potentials are small compared to the binding energy of a three- dimensional (3D) exciton. Under these circumstances it is found that t he quantization of the center-of-mass motion can make a sizable contri bution to energies of excitonic optical transitions. A simple effectiv e Hamiltonian is derived for describing this situation, with a potenti al that confines the motion of the exciton center of mass. The shape o f the potential is approximated either by a parabolic profile (when qu antum wells are narrow compared with the 3D exciton Bohr radius), or b y a rectangular potential (for wide quantum wells), and the resultant eigenvalue problem is solved accordingly. The results are compared to experimental data obtained in magnetooptical studies of ZnSe/Zn1-xMnxS e spin superlattices, giving excellent quantitative agreement.