Phonon-Assisted Electroabsorption

Recently several experiments have been reported on electroabsorption spectra in indirect-bandgap materials. These observations refer essentially to the change in absorption produced by an applied electric field $\mathcal{E}$ in the material under study. The particular photon-energy region explored has been that where phonon-assisted interband absorption obtains. Usually, considerable structure appears in the experimental curves. The absorption change $\Delta \alpha$ varies quite radically with photon energy both in amplitude and in sign. All theories extant on the phenomenon of electroabsorption are concerned with direct-bandgap transitions. In the light of recent experimental results, however, in the neighborhood of indirect transitions, it is appropriate to calculate the electroabsorption spectrum for phonon-assisted processes in order to have a more applicable theoretical model with which to compare experimental results. The present paper reports just such a calculation. A formula for $\Delta \alpha$ is presented in the case of phonon-assisted interband absorption.