Keywords: 
• Sipe-Drude模型 /
• 表面等离子体激元 /
• 低频率周期性波纹 /
• 双温方程

Abstract: The formation mechanism of low-spatial-frequency laser-induced periodic surface structure (LSFL) on singlecrystalline silicon irradiated by single femtosecond-laser pulse (pulse duration τ =150 fs and central wavelength λ =800 nm) in air is investigated theoretically based on the interference theory of Sipe-Drude model and surface plasmon polariton (SPP).In order to account for transient intrapulse changes in the optical properties of the material due to the excitation of a dense electron-hole plasma,we model the maximum of the electron density as a function of laser fluence by solving the generally accepted two-temperature equation and Drude model.The results show that both theories are applicable to explaining the LSFL formation on the high-excited silicon.In the Sipe-Drude theory,the factor η(k)is used to describe the efficacy with which the surface roughness at position k leads to inhomogeneous absorption of radiation.We find that the value of η(k) first increases until reaching a maximum at an electron density of 6 x 1021 cm-3 and then decreases with the laser fluence increasing.When the incident laser fluence is 0.38 J/cm2,which is the threshold for excited plasma,the period reaches a minimum value in a small range of the top.Besides,the law of period is calculated according to the relationship between the rη(k) and period.In the SPP theory,the ripple period on the highly excited silicon increases with the laser fluence increasing.Comparing the scopes of application of two theories,the Sipe-Drude theory is found to be suitable for the analysis of more extensive periodic surface structures,while the SPP theory is applicable only for the case that laser fiuence is close to the damage threshold.Moreover,our results are capable of explaining that the delay direction of periodic ripples are always perpendicular to the incident laser polarization direction by using the Sipe-Drude theory.When laser fiuence approaches to the damage threshold,the LIPSS period is calculated sightly to be below the laser wavelength.It also reveals that the periodic surface structures are approximately the same in the different polarization directions with the increase of incident angle.Taking into account a single pulse,the corrugation period decreases with the increase of angle of incidence in the S polarization direction.And under different polarizations,with the increase of incident angle,the changes of the ripple period show an opposite trend.The obtained dependence provides a way to better control the properties of the periodic structures induced by femtosecond laser on the surface of a semiconductor material,which is of great significance for understanding the formation of periodic structure of silicon surface,caused by femtosecond laser,and its application in the field of silicon materials processing.