GENERAL FORMALISM FOR EXCITONIC ABSORPTION EDGES IN CONFINED SYSTEMS WITH ARBITRARY DIMENSIONALITY

Citation
P. Lefebvre et al., GENERAL FORMALISM FOR EXCITONIC ABSORPTION EDGES IN CONFINED SYSTEMS WITH ARBITRARY DIMENSIONALITY, Journal de physique. IV, 3(C5), 1993, pp. 377-380
Citations number
14
Categorie Soggetti
Physics
Journal title
ISSN journal
11554339
Volume
3
Issue
C5
Year of publication
1993
Pages
377 - 380
Database
ISI
SICI code
1155-4339(1993)3:C5<377:GFFEAE>2.0.ZU;2-5
Abstract
A metric space with a noninteger dimension alpha (1 < alpha) is used t o describe bound and unbound states of strongly anisotropic Wannier-Mo tt excitons, such as those confined in semiconductor superlattices, qu antum wells and quantum-well wires. Indeed, the relative motion of the electron-hole pair which constitutes such excitons can never be consi dered strictly 1D, 2D or 3D. We calculate the optical absorption spect rum, near a Van Hove singularity, for any arbitrary value of the dimen sionality alpha. The whole absorption spectrum is obtained from a sing le compact equation, much simpler than the existing models. This model is an exact generalisation of the calculations performed, in the effe ctive-mass approximation, for allowed transitions, by Elliott [Phys. R ev. 108, 1384 (1957)], in the 3-dimensional case, and by Shinada and S ugano [J. Phys. Soc. Japan 21, 1936 (1966)], for 2-dimensional media.