Unified formulation of excitonic absorption spectra of semiconductor quantum wells, superlattices, and quantum wires

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Abstract
The problem of hydrogenic systems placed into strongly anisotropic media is solved exactly by using a metric space with a noninteger dimension α (1108, 1384 (1957)] in the three-dimensional case, and by Shinada and Sugano [J. Phys. Soc. Jpn. 21, 1936 (1966)] for two-dimensional media: this model includes contributions of bound states and of the so-called unbound states, which are responsible for an enhanced absorption continuum above the interband energy gap. At high energies, this continuum tends to behave like the α-dimensional valence-to-conduction joint density of states. The versatility of this approach should be particularly useful for modeling and improving the dynamic properties of optical modulators, for which not only the energy gap, but also the dimensionality of the excitonic absorption onset is modulated.