Influence of Static Electric Fields
If a static electric field is applied to a hydrogen atom, the well-known Stark effect shifts its energy levels towards lower energy and lifts degeneracies. For atoms, the Rydberg energy is typically much larger than the induced level shifts (accessible electric fields are usually smaller than a few 105V/cm). The situation is reversed for excitons in semiconductors. From perturbation theory, one obtains the result that the electric-field induced shifts are expected to be comparable to or even larger than the exciton Rydberg energy. But perturbation theory fails because electrons and holes are ripped apart by the field and true bound states do not exist. Owing to this field ionization, the exciton line broadens considerably and exhibits an absorption tail well below the excitonic resonance. With increasing fields, the resonance disappears before any appreciable shift is observed. Above the band edge, the electric field brings about an oscillatory behavior of the absorption coefficient. Both features, the oscillations and the absorption tail, were predicted long ago and constitute the Franz-Keldysh effect [156, 157, 158]. The corresponding theory, however, is insufficient to describe electroabsorption in bulk semiconductors quantitatively.
KeywordsAiry Function Transition Matrix Element Static Electric Field Uniform Electric Field Bloch Oscillation
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