Exciton fractional dimension in semiconductor heterostructures arising from variational principle
We present a simple method for calculating the ground-state energy of an exciton in quantum confined structures. We express the exciton wave function as a product of the electron and hole one-particle wave functions with a variationally determined envelope function which describes the exciton intrin...
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Veröffentlicht in: | Physica. B, Condensed matter Condensed matter, 2005-01, Vol.355 (1), p.255-263 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We present a simple method for calculating the ground-state energy of an exciton in quantum confined structures. We express the exciton wave function as a product of the electron and hole one-particle wave functions with a variationally determined envelope function which describes the exciton intrinsic properties. Starting from the variational principle, we derive an one-dimensional wave equation for this envelope function and show that it describes a hydrogen-like atom in an effective isotropic space with the non-integer running dimension. We establish that this dimension runs from three, as the electron–hole separation is small for all heterostructures, to two in quantum well one in quantum well-wire and to zero in quantum dot, as the separation is large. The exciton ground-state energies are calculated for different confining potential shapes. Our results for GaAs-(Ga, Al)As heterostructures with square-well potential are in an excellent agreement with those obtained previously by means of other methods. |
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ISSN: | 0921-4526 1873-2135 |
DOI: | 10.1016/j.physb.2004.11.002 |