Abstract
An exact closed-form solution of a model for excitons in degenerate semiconductors is presented. The optical absorption and luminescence spectra reduce to the Coulomb exciton absorption and luminescence (for both bound and continuum excitons) in the limit of vanishing free conduction electron density. In the high density limit, the free electron absorption and emission spectra are obtained. As the free conduction electron density decreases from infinite density, resonance-like structures appear and emerge from the continuum, forming bound exciton states. These continuum resonances should be observable in the absorption and emission spectra of degenerate semiconductors. As the model semiconductor becomes decreasingly degenerate, the optical spectra change continuously, with no evidence of an abrupt phase transition. The relation of this model to theories of x-ray spectra, Mott transitions, and enhanced interband transitions in free-electron metals is discussed.
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