Combined Effect of Electron and Lattice Temperatures on the Long Intersubband Relaxation Times of Ge/SiGe Quantum Wells

In this work we have experimentally and numerically studied the non-radiative intersubband (ISB) relaxation in n-type Ge/SiGe quantum well (QW) systems. Relaxation times have been probed by means of pump-probe experiments. An energy balance model has been employed to interpret the experimental differential transmission spectra and to assess the relevance in the non-radiative relaxation dynamics of both electron and lattice temperature as well as of the carrier density. The comparison between experimental data and theoretical simulation allowed us to calibrate the interaction parameters which describe the electron-optical phonon scattering in 2D Ge systems. Characteristic relaxation times has been calculated and compared with those of GaAs QWs as a function of the 2D electron density, of the subband energy separation, and of the lattice and electronic temperature. We found that ISB relaxation times for the Ge/SiGe systems are generally shorter than what previously calculated when the electron distribution was neglected. Nonetheless, our main result is thatthe relaxation time in Ge/SiGe QW systems is longer than 10 ps, also for transition energies above the Ge optical phonon energy, up to 300 K. Furthermore, we obtained that the relaxation times are at least one order of magnitude longer than in GaAs-based systems.