The near sub-wavelength and deep sub-wavelength ripples on monocrystalline silicon were formed in air by using linearly polarized and high repetition rate femtosecond laser pulses (f = 76 MHz, lambda = 800 nm, tau = 50 fs). The effects of laser pulse energy, direct writing speed and laser polarization on silicon surface morphology are studied. When the laser pulse energy is 2 nJ/pulse and the direct writing speed varies from 10 to 25 mm/s, the near sub-wavelength ripples (NSRs) with orientation perpendicular to the laser polarization are generated. While the direct writing speed reaches 30 mm/s, the direction of the obtained deep sub-wavelength ripples (DSRs) suddenly changes and becomes parallel to the laser polarization, rarely reported so far for femtosecond laser irradiation of silicon. Meanwhile, we extend the Sipe-Drude interference theory by considering the thermal excitation, and numerically calculate the efficacy factor for silicon irradiated by femtosecond laser pulses. The revised Sipe-Drude interference theoretical results show good agreement with the periods and orientations of sub-wavelength ripples. (C) 2015 Elsevier B.V. All rights reserved.