Differential Electroabsorption

Differential-electroabsorption spectra are calculated, using the Elliott theory of optical absorption by excitons, and are compared with experiments by Frova et al. at the direct ($M_0$) edge of Ge. The theory does not fit the data for any reasonable set of values of ${\epsilon }_0$, ${\mu }^{*}$, $E_{\mathrm{gap}}$, $\Gamma$, $〈c\left|\hat{\epsilon }·\overrightarrow{\mathrm{p}}\right|v〉$, and applied electric field strength. The discrepancies between theory and experiment can be understood qualitatively as due to nonuniformities in the applied electric field. The physics of electroabsorption is discussed with particular attention paid to the effects of excitons (i. e., the final-state Coulomb interaction) on both quasibound and continuum states of the electron-hole pair. In general, exciton theory predicts three phenomena omitted by the one-electron theory: (i) The excitons enhance the amplitude of the differential absorption both below and above the direct bandgap; (ii) the excitons increase the period of spectral oscillations of the electroabsorption signal above that predicted by Franz-Keldysh theory; and (iii) the first negative peak in the electroabsorption spectrum is due to the broadened zero-field bound-state excitons. The electron-hole interaction is responsible for a differential absorption which is both qualitatively and quantitatively different from that predicted by one-electron Franz-Keldysh theory—even when the applied electric field is so large that the discrete excitons are completely ionized.