  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.
