Rippled area formed by surface plasmon polaritons upon femtosecond laser double-pulse irradiation of silicon: the role of carrier generation and relaxation processes

The formation of laser-induced periodic surface structures (LIPSS, ripples) upon irradiation of silicon with multiple irradiation sequences consisting of femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied numerically using a rate equation system along with a two-temperature model accounting for one- and two-photon absorption and subsequent carrier diffusion and Auger recombination processes. The temporal delay between the individual equal-energy fs-laser pulses was varied between $0$ and $\sim 4$ ps for quantification of the transient carrier densities in the conduction band of the laser-excited silicon. The results of the numerical analysis reveal the importance of carrier generation and relaxation processes in fs-LIPSS formation on silicon and quantitatively explain the two time constants of the delay dependent decrease of the Low-Spatial-Frequency LIPSS (LSFL) area observed experimentally. The role of carrier generation, diffusion and recombination are quantified individually.