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 recombination processes [1]. The temporal delay between the individual equal energy fs-laser pulses was varied between 0 and 5 ps for quantification of the transient carrier densities in the conduction band of the laser-excited silicon. Additionally, cumulative effects were considered to account for multiple irradiation sequences. The results of the numerical analyses reveal the importance of carrier generation and relaxation processes in fs-LIPSS formation and quantitatively explain the two time constants of the delay dependent decrease of the rippled area observed experimentally [2]. Evidence is presented that (i) a threshold carrier density must be exceeded transiently turning the semiconductor to a metallic state and that (ii) interference between a surface plasmon polariton and the laser radiation is required to trigger the fs-LIPSS formation. [1] T.J.-Y. Derrien, J. Krüger, T.E. Itina, S. Höhm, A. Rosenfeld, J. Bonse, Opt. Express 21, 29643-29655 (2013). [2] S. Höhm, A. Rosenfeld, J. Krüger, J. Bonse, Appl. Surf. Sci. 278, 7-12 (2013).