Reciprocal space of the substrate surface. The direction of the incident light projected on the substrate surface defines the direction of positive . , , and are experimentally measurable lengths proportional to , , and , respectively.
Early stage of ripple formation. AFM image suggesting an evolution of the surface with increasing number of laser pulses, until the proper conditions are achieved for the ripples to propagate. Specimen irradiated with 400 pulses of a single beam of -polarized light incident at . Laser fluence of ; He atmosphere at a pressure of . Ripple spacing from FFT: , much less than the theoretical lowest value of .
AFM image and inset with FFT of a mature LIPSS structure generated at near normal incidence with 400 pulses of a single beam of -polarized light at a fluence of . The direction of the projected electric field of the electromagnetic wave is also indicated.
AFM image of a specimen edge where incipient LIPSS can be observed. Laser fluence .
AFM image of sample irradiated with 2000 pulses at a laser fluence of , using a -polarized single beam at an incident angle of . FFT of the image on lower left shows two short arcs that reveal rotation of the vector (Fig. 1). The spacing measured in the lower right profile is , in very good agreement with formula (9) and with the value of obtained from the FFT.
AFM image of sample irradiated with 50 pulses at a laser fluence of . The ripples were produced using a -polarized single beam at an incident angle of . . Notice tiny little “fingers” in lower rim of fringes and asymmetry in fringe profile taken in downward direction.
(a) AFM image of sample irradiated with 2000 pulses of a -polarized single beam at an incident angle of . Laser fluence: . Lower left inset: FFT of the image showing two intense short arcs which are part of two circles that can be completed with the much fainter arcs close to the origin. A vector from the origin to any of the strong spots is proportional to the magnitude of the vector (Fig. 1). Lower right inset: profile from the lower to upper end along line shown in image. Notice the increase in the ripple amplitude. Measured spacing is , in very good agreement with formula (9). This spacing agrees with the value of derived from the FFT. (b) Magnified image of the region enclosed by a rectangle in (a). This region reveals the propagation of ripples (downward in the figure) from the region of fully developed ripples. The three profiles show ripple evolution at three different stages characterized by the groove depth (notice different scale in the ordinate of ).
Schematics of the two orientations of the beam shape for a Lloyd’s mirror configuration: (a) horizontal and (b) vertical.
Ripple structure obtained after 1000 laser pulses using a Lloyd’s mirror; edge orientation relative to beam (horizontal) is illustrated in Fig. 8, (a) -polarized light incident at an angle of . Profile in lower left from trace marked on the AFM image. Ripple spacing derived from FFT in lower right inset is .
Ripples obtained after 1000 pulses using a Lloyd’s mirror; configuration illustrated in Fig. 8(a). Nonpolarized laser light incident at .
AFM image of ripple structure produced with laser beam incident at , using a Lloyd’s mirror arrangement. The FFT in the inset is part of the circles in reciprocal space shown in Fig. 1. The distance between the two spots at the intersection of the two arcs equals . The distance is the intersection of the normal with the two arcs. The corresponding ripple spacings measured in the image are on the average 315 and . The ratio measured using the FFT image gives an angle of incidence of and spacings of 318 and [Eqs. (13), (17), (18), and (21)].
AFM image of region displaying a much distorted ripple structure produced at , using a Lloyd’s mirror arrangement. The FFT image shows that the vectors follow the grating equation and a significant number of them are present clearly outlining part of the allowed space shown in Fig. 1. The extra faint arcs shown in the FFT are harmonics of the Fourier transform. The values of and have been used to derive the values and check the value of (Table I).
AFM image of region displaying a fractured ripple structure produced at , using a Lloyd’s mirror arrangement. The FFT image shows that the vectors follow the grating equation and a significant number of them are present in order to clearly delineate all of the allowed space shown in Fig. 1. The values of and have been used to derive the values and check the value of (Table I).
Line spacing vs incident angle, for ripples formed using Lloyd’s mirror. Data are listed in Table II. Notice occurrence of ripples characterized by only one set of possible values at , those that run normal to the substrate/mirror edge. A transition can be seen to occur gradually between and .
Calculated temperature evolution at two locations distant during laser irradiation in silicon assuming that the spatial dependence of the fluence (in ) is given by . The lower curve is at (minimum of ) and the upper at (maximum of ). The inset shows the Gaussian temporal profile of the laser beam used for the calculation. Details of the calculation are given in the Appendix.
Ripple spacings and angles of incidence derived from FFT images versus calculated spacings and experimentally measured angles.
Nanofringe spacing at various angles of incidence of the laser beam on substrates, with Lloyd’s mirror attached— Total number of pulses: 1000.
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