The supplementary Figures offer expanded computational details, including detailed band structures and densities of states for bulk Si, NiSi2, and CoSi2, as well as their respective supercells. Given that the NAMD method utilized in this research solely accounts for the Gamma point in k-space, the implementation of supercells with band unfolding enables the inclusion of contributions from a sufficient number of k-points, thereby guaranteeing an in-depth analysis of the phonon-assisted thermalization of charge carriers discussed in the maintext.