Le Journal de Physique IV 03 (1993) C5-377-C5-380
General formalism for excitonic absorption edges in confined systems with arbitrary dimensionalityP. LEFEBVRE, P. CHRISTOL and H. MATHIEU
Groupe d'Etudes des Semiconducteurs, CNRS, Université Montpellier II, Case courrier 074, 34095 Montpellier cedex 5, France
A metric space with a noninteger dimension α (1 < α) is used to describe bound and unbound states of strongly anisotropic Wannier-Mott excitons, such as those confïned in semiconductor superlattices, quantum wells and quantum-well wires. Indeed, the relative motion of the electronhole pair which constitutes such excitons can never be considered strictly 1D, 2D or 3D. We calculate the optical absorption spectrum, near a Van Hove singularity, for any arbitrary value of the dimensionality [MATH] . The whole absorption spectrum is obtained from a single compact equation, much simpler than the existing models. This model is an exact generalisation of the calculations performed, in the effective-mass approximation, for allowed transitions, by Elliott [Phys. Rev. 108, 1384 (1957)], in the 3-dimensional case, and by Shinada and Sugano [J. Phys. Soc. Japan 21, 1936 (1966)], for 2-dimensional media.
© EDP Sciences 1993