Thermal and nonthermal melting of silicon under femtosecond x-ray irradiation

As it is known from visible light experiments, silicon under femtosecond pulse irradiation can undergo the so-called 'nonthermal melting' if the density of electrons excited from the valence to the conduction band overcomes a certain critical value. Such ultrafast transition is induced by strong changes in the atomic potential energy surface, which trigger atomic relocation. However, heating of a material due to the electron-phonon coupling can also lead to a phase transition, called 'thermal melting'. This thermal melting can occur even if the excited-electron density is much too low to induce non-thermal effects. To study phase transitions, and in particular, the interplay of the thermal and nonthermal effects in silicon under a femtosecond x-ray irradiation, we propose their unified treatment by going beyond the Born-Oppenheimer approximation within our hybrid model based on tight binding molecular dynamics. With our extended model we identify damage thresholds for various phase transitions in irradiated silicon. We show that electron-phonon coupling triggers the phase transition of solid silicon into a low-density liquid phase if the energy deposited into the sample is above $\sim0.65$ eV per atom. For the deposited doses of over $\sim0.9$ eV per atom, solid silicon undergoes a phase transition into high-density liquid phase triggered by an interplay between electron-phonon heating and nonthermal effects. These thresholds are much lower than those predicted with the Born-Oppenheimer approximation ($\sim2.1$ eV/atom), and indicate a significant contribution of electron-phonon coupling to the relaxation of the laser-excited silicon. We expect that these results will stimulate dedicated experimental studies, unveiling in detail various paths of structural relaxation within laser-irradiated silicon.