Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9837992 | Physica B: Condensed Matter | 2005 | 9 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Condensed Matter Physics
Authors
R.A. Escorcia, J. Sierra-Ortega, I.D. Mikhailov, F.J. Betancur,