Disentangling Elastic And Inelastic Scattering Pathways In The Intersubband Electron Dynamics Of N-Type Ge/Sige Quantum Fountains

n-type Ge/SiGe quantum wells have been suggested as a promising platform for the realization of a Si-compatible THz laser. Focusing on this material system, we have developed a numerical model to describe the intersubband carrier dynamics which restores the equilibrium after pulsed optical excitation in asymmetric coupled Ge/SiGe quantum wells. We take into account inelastic and elastic scattering processes and investigate different quantum-well geometries, doping densities, and excitation regimes. In this configuration space, we disentangle the effect on the overall dynamics of each scattering channel and provide intersubband relaxation times, finding larger values with respect to III-V based materials, thanks to the weaker electron-phonon coupling with respect to III-V compounds. Finally, the model is used to study and optimize the population inversion between the first- and second-excited subband levels and to assess its dependence on the lattice temperature, providing a sound theoretical framework to guide forthcoming experiments.