A SINGLE EQUATION DESCRIBES EXCITONIC ABSORPTION-SPECTRA IN ALL QUANTUM-SIZED SEMICONDUCTORS

The relative motion of the electron-hole pairs which constitute Wannie r-Mott excitons in semiconductor quantum wells, superlattices, and qua ntum wires can never be considered strictly 1-D, 2-D, or 3-D. We propo se an exact generalization of the well-known calculations of Elliott i n the 3-dimensional case, and of Shinada and Sugano for 2-dimensional media-we calculate the absorption spectrum by bound and unbound excito nic states, by using a metric space with a noninteger dimension alpha > 1. Whatever the dimensionality, i.e., for any quantum-sized structur e, the whole optical density spectrum ib obtained from a single compac t equation, in excellent agreement with experimental data and with the most accurate available theories. We present examples of calculated s pectra for quantum wells under applied perpendicular electric fields, and for quantum wires.