Inscribing diffraction grating inside silicon substrate using a subnanosecond laser in one photon absorption wavelength

Using focused subnanosecond laser pulses at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.064\,\upmu \hbox {m}$$\end{document}1.064μm wavelength, modification of silicon into opaque state was induced. While silicon exhibits one-photon absorption at this wavelength, the modification was induced inside \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$300\,\upmu \hbox {m}$$\end{document}300μm-thick silicon substrate without damaging top or bottom surfaces. The depth range of the focus position was investigated where inside of the substrate can be modified without damaging the surfaces. Using this technique, diffraction gratings were inscribed inside silicon substrate. Diffraction from the gratings were observed, and the diffraction angle well agreed with the theoretical value. These results demonstrate that this technique could be used for fabricating infrared optical elements in silicon.

In recent years, ultrafast laser processing inside transparent solid materials has been attracting interest as a tool of three-dimensional (3D) micro-nano processing technique [1][2][3] . For example, marking, inscribing waveguide, and selective etching inside glass have been reported [4][5][6][7] . In these research, non-linear optical phenomena, such as multi-photon absorption, is utilized for localized modification of materials. Now application fields of ultrafast laser processing inside glass is expanding such as microphotonics and microfluidics [1][2][3] .
Silicon is one of the most important material in modern technology. Its application field includes large-scale integrated circuits (LSIs), micro-electro-mechanical systems (MEMS) devices, and multi-pixel photodetectors. In these, semiconductor technology based on photolithography, which is a two-dimensional technique, is mainly used for fabrication. Recently research on the use of silicon as a near-infrared (NIR) photonic platform material is active. For such applications, 3D processing using lasers will be advantageous.
Silicon is transparent in the near-infrared range (the band gap of silicon is 1.12 eV, and corresponding wavelength is 1.11 µm ), thus use of an ultrafast laser in this wavelength range seems promising. However, unlike glasses, difficulty has been reported to process inside silicon with an ultrafast laser in the transparent wavelength region 8 . Thus, special methods have been executed, such as use of optical setup with extremely high numerical aperture of 2.97 9 , double pulse 10 , and use of high repetition rate laser [11][12][13] . In the study by Matthäus et al. 12 , waveguides were inscribed in longitudinal geometry starting at the exit surface then moved upstream, in this case the waveguide inscription was significantly facilitated by an imperfectly flat exit surface 13 . Very recently, it was reported that temporal contrast (pre/post-pulse, pedestal), which is laser technology dependent, of ultrafast laser pulses has a significant effect on the modification threshold energy 14 . Investigation using THz-repetitionrate pulse bursts also showed the effectiveness of peak-suppressed consecutive pulses for laser modification inside silicon 15 .
In contrast to ultrafast lasers, longer pulse lasers are effective for modification inside silicon. Verburg et al. reported modification inside silicon using laser pulse of 1.549 µm wavelength and 3.5 ns duration 16 . Tokel et al. used reflection on the back surface and fabricated modification inside silicon with 1.550 µm and 5 ns pulses 17 . In their method the length of modification along the optical axis was controlled by the number of pulses. They also reported fabrication of waveguide, and selective etching of modified region. Kammer et al. made modifications inside silicon with 1.552 µm wavelength and duration ranging from 800 fs to 10 ps, and reported that 10 ps pulses showed better reproducibility 18  Generally, one-photon absorption is not used for laser processing inside solid materials. Meanwhile, in cutting silicon substrate using internal modification, a Nd:YAG laser operating at 1.064 µm wavelength is used 23 , at this wavelength there is weak but non-negligible one-photon absorption (absorption coefficient of silicon at 1.064 µm about 9.7 cm −1 at 295 K) 24 . However, there have been no report on the use of one-photon absorption based fabrication for optical applications. One-photon absorption based fabrication could be more efficient than that based on multi-photon absorption, whereas there are possible drawbacks that energy loss due to absorption in pre-focal region, and limitation in the inscribing depth due to damaging surface and/or pre-focal region. In addition, a Nd:YAG laser operating at 1.064 µm is widely used. Thus it is worth investigating to apply one-photon absorption based fabrication in modification inside silicon. In this research, we used a subnanosecond Nd:YAG laser operating at 1.064 µm wavelength, and inscribed diffraction gratings inside silicon substrate without damaging top or bottom surfaces.

Results and discussion
Inscribing inside silicon substrate without damaging surfaces. At first, we examined the condition where we can inscribe modified lines inside silicon substrate without damaging top or bottom surfaces. For this, lines parallel to the surface were inscribed at different depths, experimentally sample position along optical axis was changed for each line, as shown in Fig. 1(a). Hereafter the sample position along optical axis is referred to as ascending distance d; d = 0 indicates the focus of laser was set at the top surface of silicon substrate, and positive value of d indicates the sample was moved to the laser source (accordingly, the focus was moved to the

Characterization of modification inside silicon substrate. Cross-section of silicon substrate with
inscribed lines was observed. The irradiation condition was the same as that in Fig. 1 (8.8 µJ , 50 µm/s), and d was set at 52 µm . The substrate was cleaved perpendicular to the inscribed lines, As seen in Fig. 3(a), a series of modified spots aligned in vertical direction (that is, the direction of laser irradiation) is observed. The presence of the vertically aligned spots indicates that completely 3D-localized modification was not realized yet, but the modification was localized in two-dimensions thus can be used in two-dimensional applications. Such a series of modified spots have been reported in nanosecond laser processing of silicon 25,26 . In these studies, modified spots were identified as voids. Li et al. explained that this phenomena is due to void formation and hydrodynamic phenomena occurring near the void induced by successive laser pulses 25 . We presume that similar phenomenon occurred in our case, while laser wavelength was different. Another possibility might be a phenomena related to the propagation of the absorption front to the upstream of the incoming laser 27,28 . In this case, however, the speed of propagation is about 1 µm /1 ns or less, thus it is difficult to explain the total length of the observed modified spots considering the pulse duration of 0.5 ns in the present study. In order to elucidate the nature of modified spots, micro-Raman spectra were measured at modified and unmodified spots (three spots each) on the cleaved face. Figure 3(b) shows the spectra around 520 cm −1 . Compared to the spectra from un-modified spots, the spectra from modified spots are broader and shifted to lower Raman shift. These changes can be explained by polycrystallization 29,30 or strain 31,32 . Grating and diffraction. Several gratings with different period and width of lines were inscribed. Pulse energy was 8.8 µJ , scanning speed was 50 µm/s, and d was 60 µm for all. Figure 4 shows one of the gratings observed with the NIR microscope transmitted illumination. Here 11 dark lines were inscribed with a lattice constant of 34 µm . The width of the dark lines were about 24 µm ; each line consists of six paths of inscription with a separation of 4 µm . As seen in Fig. 4, grating was inscribed inside silicon substrate as designed. In addition, this transmitted illumination image indicates that the inscribed grating is, at least in part, an amplitude grating, whereas Chambonneau et al. evaluated only the real part of the refractive index change in the lasermodified zone 20 .
Diffraction pattern from the gratings were observed in transmission geometry. Figure 5(a) shows the diffraction pattern from the grating of Fig. 4. The distance between the grating and the target paper was set at L = 150 mm. As seen, in addition to the strong zero-order line, diffraction lines up to 4-th order were observed. In this case, theoretically, first-order diffraction should be found at ±4.7 mm ( = L tan θ , where θ = sin −1 ( /�) is the first-order diffraction angle, is the laser wavelength, and is the lattice constant). The experimental result is in good agreement with the theoretical one. Dependence of first-order diffraction angle on the lattice constant is shown in Fig. 5(b). As seen, diffraction angle from the other gratings also agreed with the theory well. These results indicate that the fabricated gratings inside silicon substrate functioned as expected.

Conclusion
We have inscribed diffraction gratings inside 300 µm-thick silicon substrate using a subnanosecond laser of 1.064 µm wavelength. Although silicon exhibits non-negligible one-photon absorption at this wavelength, the gratings were inscribed without damaging top or bottom surfaces. The functionality of the inscribed gratings were demonstrated. So far, internal modification inside silicon substrate by laser pulse of 1.064 µm wavelength has been used for dicing. The present results indicate that the modification based on one-photon absorption can also be used for optical applications. Silicon is one of important infrared optical materials. This technique would be useful for fabricating amplitude optical elements in silicon.

Methods
N-type Si (100) substrates with a thickness of 0.3 mm, mirror-polished on both sides, were cut into 10 mm× 8 mm pieces, and used for experiments.  To observe the laser inscribed lines inside the substrate, a NIR camera (CONTOUR-IR digital, Electrooptic) was attached on the same microscope, and observed under transmitted or reflected illumination. Under transmitted illumination the dark (opaque) region in whole thickness of the substrate was observed, while under  www.nature.com/scientificreports/ reflected illumination only the top surface was observed. In both transmitted/reflected illumination, the light source was a halogen lamp (U-LH100IR, Olympus). A confocal Raman microscope (LabRAM HR Evolution, Horiba) was used for measuring Micro-Raman spectra.
For the observation of diffraction pattern from the fabricated gratings, non-focused laser beam at 1.064 µm wavelength was irradiated to the grating at normal incidence, and the pattern of transmitted (diffracted) light on a target paper was recorded by a digital camera (E-PM2, Olympus). The camera has week sensitivity at 1.064 µm ; laser beam appeared violet in the recorded images. Because of the observation angle, the image was slightly distorted. Thus, a cross mark and concentric circles were printed on the target paper as show in Fig. 6.