Combined effect of electron and lattice temperatures on the long intersubband relaxation times of Ge/Si_x Ge_1−x quantum wells

In this paper, we have experimentally and numerically studied the nonradiative 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 used to interpret the experimental differential transmission spectra and to assess the relevance in the nonradiative 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 two-dimensional (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 that previously calculated when the electron distribution was neglected. Nonetheless, our main result is that the 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.