Temperature dependence of the indirect-gap photoluminescence from Ge

Few experimental reports have been published to date on the temperature dependence of the photoluminescence (PL) from Ge, and no attempts have been made to model the spectra using the standard Van Rosbroeck-Schockley equation that relates absorption to spontaneous emission. This anomaly can be traced back to the fact that the standard textbook expressions for indirect absorption are not applicable to Ge¹ due to the proximity of the direct and indirect gaps. If such expressions are used to compute the PL, not even a peak is predicted.
We report here a PL study of high-quality Ge samples at temperatures 10 K ≤ T ≤ 300 K. The spectra display a rich structure with a rapidly changing lineshape as a function of T. We show that when the more realistic theory of LA-phonon assisted absorption from Ref. 1 is used to compute the PL, peaks at about the right energy are predicted. However, the agreement between theory and experiment requires the additional incorporation of “forbidden” channels involving LO and TA phonons. Analytical expressions for the absorption assisted by these phonons are derived, and the resulting expressions are combined to predict a PL spectrum in very good agreement with experiment.

¹J. Menéndez et al. Phys. Rev. B 96, 121201 (2017), Phys. Rev. B 98, 165207(2018).