Universal formulation of excitonic linear absorption spectra in all semiconductor microstructures

We present a generalization of the well-known exciton absorption calculations of Elliott [Phys. Rev. 108, 1384 (1957)], in the 3-dimensional case, and of Shinada and Sugano [J. Phys. Sec. Japan 21, 1936 (1966)], for 2-dimensional media : We calculate the optical absorption spectra of bound and unbound exciton states, by using a metric space with a noninteger dimension alpha (1 < alpha), Obtaining almost exactly the same theoretical lineshapes as those resulting from accurate but costly numerical approaches [Chuang et al. Phys. Rev. B, 43, 1500 (1991); Benner and Haug, Phys. Rev. B 47, 15750 (1993)].