The rate of energy transfer between electrons and phonons is investigated by a first-principles framework for electron temperatures up to Te = 50,000 K while considering the lattice at ground state. Two typical but differently complex metals are investigated: aluminum and copper. In order to reasonably take the electronic excitation effect into account, we adopt finite temperature density functional theory and linear response to determine the electron temperature-dependent Eliashberg function and electron density of states. Of the three branch-dependent electron-phonon coupling strengths, the longitudinal acoustic mode plays a dominant role in the electron-phonon coupling for aluminum for all temperatures considered here, but for copper it only dominates above an electron temperature of Te = 40,000 K. The second moment of the Eliashberg function and the electron phonon coupling constant at room temperature Te=315 K show good agreement with other results. For increasing electron temperatures, we show the limits of the T=0 approximation for the Eliashberg function. Our present work provides a rich perspective on the phonon dynamics and this will help to improve insight into the underlying mechanism of energy flow in ultra-fast laser-metal interaction.
Keywords: DFT; electron–phonon; energy transfer; laser; linear response.