Excitonic Theory of Electroabsorption: Phonon-Assisted Indirect Transitions in Si and Ge

Abstract

The theory of indirect phonon-assisted optical absorption by semiconductors in a uniform electric field is developed with particular attention being paid to the effects of electron-hole correlations (excitons). The Coulombic electron-hole interaction is treated within the Wannierexciton effective-mass approximation. The physics of indirect electroabsorption is discussed, and it is found that exciton theory predicts an indirect absorption spectrum which is dramatically different, both qualitatively and quantitatively, from the spectrum predicted by one-electron theory (neglecting electron-hole correlations). The excitonic correlations are responsible for four qualitative features found in measured differential electroabsorption spectra but omitted by the one-electron theory: (i) The threshold for potical absorption by excitons lies at a lower energy; (ii) excitons cause a sharp drop on the high-energy side of the first differential electroabsorption peak; (iii) the amplitude of the differential absorption is enhanced by excitons; and (iv) excitonic spectra exhibit longer periods of spectral oscillations. These excitonic effects are analogous to effects previously predicted for direct transitions. Numerical calculations of the differential electroabsorption at the indirect edges of Ge and Si are compared with the data of Frova et al. and are found to be in excellent agreement with experiment.