Temperature-dependent photoluminescence in Ge: Experiment and theory

We report a photoluminescence study of high-quality Ge samples at temperatures 12K≤T≤295K, over a spectral range that covers phonon-assisted emission from the indirect gap (between the lowest conduction band at the L point of the Brillouin zone and the top of the valence band at the Γ point), as well as direct gap emission (from the local minimum of the conduction band at the Γ point). The spectra display a rich structure with a rapidly changing line shape as a function of T. A theory is developed to account for the experimental results using analytical expressions for the contributions from LA, TO, LO, and TA phonons. Coupling of states exactly at the Γ and L points is forbidden by symmetry for the latter two phonon modes, but becomes allowed for nearby states and can be accounted for using wave-vector dependent deformation potentials. Excellent agreement is obtained between predicted and observed photoluminescence line shapes. A decomposition of the predicted signal in terms of the different phonon contributions implies that near-room temperature indirect optical absorption and emission are dominated by "forbidden" processes, and the deformation potentials for allowed processes are smaller than previously assumed.