Raman silicon (Si) lasers based on high-quality-factor photonic crystal nanocavities are very compact and can operate at excitation powers of less than one microwatt. For the best performance, the nanocavity of the Raman Si laser has to be fabricated along the  crystal direction of the Si-on-insulator (SOI) wafer to enhance the Raman gain. On the other hand, Si photonic devices are usually fabricated along the  direction because crystalline Si can be easily cleaved along . This rotation by 45 degrees of the nanocavity with respect to the cleavable direction can be problematic for various applications. Here we report a Raman Si nanocavity laser fabricated on a modified (100) SOI wafer in which the crystal orientation of the top Si layer is rotated in plane by 45 degrees relative to the crystal direction of the support substrate. We observe room temperature continuous wave laser oscillation with a sub-microwatt threshold and a maximum energy efficiency of 5.6%. It is found that the photonic-slab warpage induced by compressive stress is reduced in this 45°-rotated SOI wafer.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Photonic functional devices fabricated on a silicon-on-insulator (SOI) wafer have small sizes due to the large refractive index difference between the top silicon (Si) layer and the buried-oxide-layer (BOX layer). They can be fabricated on large-diameter SOI wafers using a complementary metal–oxide–semiconductor (CMOS)-compatible process. Therefore, low-cost production of Si chips with highly-integrated optical circuits for optical communication seems possible and is expected to help reducing the power consumption of information technology devices [1–3]. Si photonic technologies are also promising for realizing compact and highly-sensitive sensors . To drive these optical devices, controllable light sources such as lasers are required. However, the realization of Si-based lasers using interband transitions has proven to be very difficult since Si is a semiconductor with an indirect bandgap [5–8]. To solve this problem, the utilization of stimulated Raman scattering (SRS) has been proposed because crystalline Si has a large Raman gain coefficient and is transparent for the optical communication bands in silica fibers [9–17]. The SRS concept has been successfully implemented in optically-pumped Si lasers using rib-waveguides. The Raman Si rib-waveguide lasers enable continuous wave (cw) operation at room temperature [18–20], but unfortunately the device size and the threshold power for lasing are too large for effective implementation in integrated circuits. As an alternative, photonic crystal (PC) devices have been studied [21–25] and we have developed a Raman Si laser based on a PC nanocavity [26–29]. The employed nanocavity design, which has a very small size and a high quality-factor (Q), allows for an ultralow threshold of one microwatt or even lower. As such, Raman Si nanocavity lasers are promising candidates for light sources in dense optical circuits based on Si technology. However, there are still some issues to be solved for the optimum integration.
Today, (100) SOI wafers are widely utilized in industry and thus constitute an important platform for Si photonics research. It is noted that crystalline Si can be cleaved along the  direction (or an equivalent direction). While a dicing saw can cut the wafer regardless of the crystal direction, it is difficult to directly form flat facets of waveguide edges by this technique. This issue is related to the fact that chipping and cracking are more likely to occur when using a dicing saw instead of cleaving . Therefore, cleaving is an important technique for photonics, used for the formation of waveguide facets and separation of small chips from a large substrate. In order to reduce the coupling loss at the waveguide edge and to increase the density of the integrated devices, Si photonic devices are usually fabricated along the  direction of the (100) SOI wafer.
To enable dense integration, the Raman Si nanocavity lasers have to be also fabricated on (100) SOI wafers. However, the nanocavity lasers should be fabricated along the  direction because the Raman gain for the nanocavity fabricated along  is twenty times larger than that for the cavity fabricated along  (in our laser device design) [23,26]. This results in a misalignment (by 45 degrees) between the cleavable direction of the wafer and the longitudinal direction of the Raman Si nanocavity laser, which is problematic for various applications.
To cope with this issue, we recently developed a Raman Si nanocavity laser on a modified (100) SOI wafer . This SOI wafer contains a top Si layer whose crystal orientation is rotated by 45 degrees with respect to the crystal direction of the support substrate (a 775-µm-thick Si crystal). Therefore, the  direction of the top Si layer is parallel to  of the support substrate. This wafer enables the design of a nanocavity laser whose longitudinal direction is perpendicular to the cleaved facet. Here we report the fabrication of a Raman Si nanocavity laser on the 45°-rotated SOI wafer, and we clarify that this approach results in a more suited laser design for integrated optical circuits. The structural properties of the fabricated sample are investigated using the X-ray diffraction (XRD), a scanning white-light interferometer (SWLI), and scanning electron microscopy (SEM). These measurements clarify the crystal direction of the SOI, the warpage of the PC slab due to the stress that is inherent to the top Si layer of a SOI wafer, and the cleavability of the wafer. Our results demonstrate that, compared to Raman Si nanocavity lasers that are fabricated on the conventional SOI wafer, the laser fabricated on the 45°-rotated SOI wafer exhibits no critical deterioration of optical properties. Hence, we consider that the SOI wafer with a 45-degree-rotated top Si layer is advantageous for implementing Raman Si nanocavity laser in dense optical circuits.
2. Nanocavity structure
Figure 1(a) illustrates the heterostructure nanocavity utilized for the Raman laser. The PC basically consists of a triangular lattice of circular air holes with a lattice constant (a) of 410 nm. A line defect of air holes defines the nanocavity. To form a heterostructure, the lattice constant a in the x-direction is increased by 5 and 10 nm in the areas that are closer to the center (light gray and dark areas, respectively) . The increase of a alters the two propagation band frequencies as shown in Fig. 1(b), and therefore two nanocavity modes with high Q are formed. We define the nanocavity modes arising from the first and second propagation bands as the Stokes and pump modes, respectively. The former is used to confine the Raman scattering light and the latter to confine the pump light in the cavity. The measured thickness of the Si slab employed in this work is 225.8 nm and the air hole radii are about 128 nm. These structural parameters are almost the same as those in our previous reports [26–28].
Figures 1(c) and 1(d) show both the x-components (Ex_pump and Ex_stokes) and y-components (Ey_pump and Ey_stokes) of the electric field distributions calculated for the pump mode and the Stokes mode, respectively. The field distributions were calculated by the three-dimensional (3D) finite-difference time-domain method. It is noted that the Ex_pump (Ey_pump) and Ex_Raman (Ey_Raman) distributions have different parity because they are generated from different propagation bands. On the other hand, the crossed field components, e.g. Ex_pump and Ey_stokes, have the same line symmetry and similar distributions. Therefore, the Raman scattered light can be strongly confined in the Stokes mode if the polarization of the light confined in the pump mode is rotated by 90 degrees (in plane) via the Raman scattering process.
Figure 1(e) presents the in-plane Raman scattering in a microscopic model for the cavity’s x-direction being parallel to the  direction of Si. Here, transverse-magnetic polarized waves are not considered since the two nanocavity modes shown in Figs. 1(b)−(d) are only available for the transverse-electric (TE) polarization . The purple spheres in Fig. 1(e) represent Si atoms, the grey lines are the projection of the covalent bonds onto the x–y plane, and the blue (red) arrows represent the pump light (Raman scattered light). As indicated with the wavy arrows, the polarization directions of the pump light and the Raman scattered light are orthogonal in the x–y plane in this geometry.
The Raman scattering process is theoretically described as explained in the following. When we define the three principle axes of the coordinate system (x,y,z) as , , and , the Raman tensors corresponding to the Γ point phonons of crystalline Si are represented by the following matrices [34,35],
3. 45°-rotated SOI wafer
Figure 2(a) shows a schematic of a conventional (100) SOI wafer. It consists of three layers: a thin Si layer (about 225 nm in this study) at the top, a buried-oxide (BOX) layer (3 µm thick), and a Si support substrate (775 µm). The wafer notch in the figure indicates the cleavable direction of Si. The air holes of the PC nanocavity are fabricated in the top Si layer.
Such SOI wafers are fabricated by thermal fusion bonding of two Si wafers [37,38]. Usually, the fusion bonding is performed with both wafer crystal directions being aligned as shown in Fig. 2(b). We have used this conventional SOI wafer in previous studies [26–28], but the resulting in-plane rotation of the cavity’s longitudinal direction by 45 degrees with respect to the cleavable direction causes problems for dense integration as explained in the introduction. Figure 2(c) shows the schematic diagram of the 45°-rotated SOI wafer utilized in this study. The fusion bonding for this wafer is performed with the top Si layer being rotated by 45 degrees relative to the Si support substrate. Therefore, the  direction of the top Si layer is parallel to the  direction of the support substrate. In fact, such 45°-rotated SOI wafers have previously been employed for the study of improved metal-oxide-semiconductor field-effect transistors [39,40]. For this work, we sourced the 45°-rotated SOI wafer from a substrate manufacturer. It is noted that the SOI wafer can only be cleaved along the  or [1–10] direction of the Si support substrate, because the thickness of the top Si layer is much smaller than that for the Si support substrate. As a result, the new wafer can be cleaved along the  or  directions of the top Si layer , which enables implementation of the Raman Si nanocavity lasers in integrated optical circuits. Since most Si photonic devices do not use optical effects that are sensitive to the crystal direction, their performance should not change when they are fabricated along the  direction. We confirm it for a wavelength filter using arrayed L3 nanocavities . A detailed comparison of high-Q heterostructure nanocavities fabricated along  and  directions will be soon reported in another work . Therefore, the Raman Si nanocavity laser and other Si photonic devices can be densely fabricated on the 45°-rotated SOI wafer.
We verify the crystal orientations of both SOI wafers using in-plane XRD (Rigaku, SmartLab). Figure 3(a) shows a schematic of the measurement. The SOI chips with size of 1 cm2 and same orientation of the (100) support substrate (aligned using the flat edge along <110>) are rotated by the azimuth angle φ while the detector position is fixed. This is the so-called φ-scan, which is useful to investigate the in-plane symmetry and crystal orientation . The diameter of the incident beam is 5 mm. In the present configuration, a part of the beam can strike the sidewalls and therefore, weak signals from the Si support substrate can also be detected. Figures 3(b) and 3(c) show the φ-scan spectra of Si (220), which has a large intensity and is easy to detect, for the conventional and the 45°-rotated SOI wafers, respectively. In Fig. 3(b), four large peaks are observed with a spacing of 90 degrees, which reflects the 4-fold symmetry of the Si wafer. In Fig. 3(c), the positions of the large four peaks are shifted by 45 degrees when compared to those for the conventional SOI wafer. The important feature is that the positions of the two small peaks indicated by the solid arrows coincide with those for the conventional SOI wafer. These two peaks originate from the Si support substrate and clearly indicate that the crystal orientation of the top Si layer of the modified SOI wafer is rotated by 45 degrees relative to the Si support substrate.
4. Fabricated sample
The Raman Si laser sample is fabricated on the 45°-rotated SOI chip by using the same procedure as previously reported [26–28,44–46]. After defining the PC pattern on the resist-coated chip by electron beam lithography, the pattern is transferred to the top Si layer by an inductively coupled plasma etching process using SF6-based gas. After the chip has been polished to about 80 µm thickness, the chip is cleaved into a piece with dimensions of 1.3 mm × 300 µm along the  direction of the Si support substrate. For this processing step, the chip is scribed from the backside surface (Si support substrate) using a diamond cutter. This piece is bonded to a small cubic block for optical measurements. Finally, the BOX layer underneath the PC pattern is selectively removed by a 48% hydrofluoric acid at room temperature, which results in an air-bridge structure that enhances the optical confinement of the PC slab. In this work, we did not employ any special procedure to reduce the surface absorption loss at the bottom side of the PC slab . It is noted that the thinning to less than 100 µm is not necessary if laser stealth dicing, which can be employed for mass production, is used . We confirmed that the 45°-rotated SOI wafer with thickness of 778 µm can be cleaved into a piece with dimensions of 2 mm × 800 µm along the  direction of the support substrate using stealth dicing.
Figure 4(a) shows a SEM image of the core part of the fabricated Raman laser device on the 45°-rotated SOI wafer. The central line defect is the heterostructure nanocavity. The upper line defect is a waveguide to excite the pump nanocavity mode. The lower waveguide is added to investigate the Stokes nanocavity mode and the extraction of Stokes light from the cavity via a waveguide, but is not essential for the laser operation. The SEM image evidences that the use of the 45°-rotated SOI wafer does not induce any degradation of the PC structure. Figure 4 (b) is the SEM image of the waveguide edge. The inset on the right side is an image of the corresponding location for the Raman Si laser sample fabricated on the conventional SOI wafer. Both samples were cleaved by the same method and the images prove that the accuracies of both cleavages are similar . Since the BOX layer between the top Si layer and the Si support substrate has an amorphous structure, the cleaved facet of the top Si layer is not atomically flat, even when the conventional SOI wafer is used. It is noted that the waveguide fabricated on the 45°-rotated SOI wafer extends perpendicular to the cleaved facet. Although the cleaved facet is used to introduce the pump light into the device in this study, such a coupling usually suffers high losses. To realize devices with low energy losses, methods for a direct connection of the optical fiber to the waveguide need to be studied .
Other approaches such as implementing only the core part of the Raman laser shown in Fig. 4 (a) on a conventional SOI wafer along the  direction while the other elements of the integrated optical circuits are fabricated along the  direction are possible but can involve disadvantages. For example, the latter design will require additional grating couplers. This not only complicates the circuit design but also increases the size of the circuit and the optical losses, and thus partially cancels the advantages of Si photonics. The PC shown in Fig. 1(a) has a 6-fold rotational symmetry due to the triangular lattice and therefore, it is difficult to steeply bend the PC waveguide by 45 degrees to enable pumping of the Stokes mode of the cavity while maintaining a low waveguide loss .
5. Experimental results
The optical properties of the fabricated sample are characterized using a conventional spectrum measurement. The light from a tunable cw laser, whose wavelength crosses the resonance wavelengths (λ) of the nanocavity modes while sweeping from short to long wavelengths, is focused on the cleaved facet of each excitation waveguide (the excitation light is set to TE polarization by a polarizer). When the incident wavelength matches the λ of either the pump mode or the Stokes mode, part of the excitation energy is extracted from the nanocavity as light emitted into the direction perpendicular to the slab. This emitted light is analyzed as a function of the excitation wavelength (details of the measurement method are given in ).
Figures 5(a) and 5(b) show the resonance spectra of the pump nanocavity mode and the Stokes nanocavity mode, respectively. The black circles represent the experimental data. The solid curves are fitting results using Lorentzian functions, from which we obtain the λ and the full width at half-maximum (Δλ). The pump nanocavity mode has a λ of 1429.168 nm and a Δλ of 11.32 pm. The values for the Stokes mode are λ = 1544.175 nm and Δλ= 0.83 pm. According to the relation Q = λ /Δλ for the quality factor, we estimate Q = 126,000 for the pump mode and Q = 1,860,000 for the Stokes mode. These Q values are similar to those obtained for the laser samples fabricated on the conventional SOI wafer [26–28]. It has been reported that the Q of the PC cavities decreases as the imperfections in radii and positions of the air holes increase [44–46,52,53]. Therefore, the high Q values estimated above indicate that the fabrication accuracy of the PC structures is not negatively affected by the use of the 45°-rotated SOI wafer. For efficient lasing via SRS, it is desirable that the frequency spacing between the two cavity modes, Δf, coincides with the Raman shift of the Si nanocavity, 15.606 THz [24,54]. The Δf for the present sample is 15.619 THz, that is, a detuning of the Δf from the Raman shift by 0.013 THz which is much less than the half width at half-maximum of the Raman gain (≈ 0.04 THz) . Accordingly, efficient lasing can be expected from our present device on the (100) SOI wafer with a 45-degree-rotated top Si.
The filled circles in Fig. 5(c) show the input/output characteristic of the Raman laser. In this experiment, the pump nanocavity mode is strongly excited by the cw laser. The Stokes Raman scattered light, which is emitted into the direction perpendicular to the slab [inset of Fig. 5(c)], is measured as a function of the excitation power (details of the measurement method can be found in the Appendix). The Stokes intensity rapidly increases by more than two orders of magnitude around the threshold power of 0.53 µW. This threshold is more than four orders of magnitude smaller than that for the Raman laser based on the rib waveguide  and thus evidences a high quality of the present Raman Si nanocavity laser. The highest energy efficiency of the present sample is 5.6%, which is obtained at 1.8 µW. An energy efficiency larger than 20% can be obtained in such a laser if the detuning of Δf is small [27,54]. The saturation of the laser output observed above pump powers of 2.0 µW is caused by the free carriers generated by two-photon absorption (same data in linear scale are shown in Fig. 8) [28,56,57]. Figure 5(d) shows the near-infrared (NIR) camera images of the nanocavity for an excitation with a pump power below (0.5 µW) and above the threshold (0.6 µW), and at optimum performance (pump power 1.8 µW). The laser oscillation is clearly visible with a standard InGaAs camera (FLIR SC2500, exposure time: 10 ms).
Figure 5(e) show the emission of Stokes light from the facet of the waveguide below the nanocavity [as shown in the inset of Fig. 5(c)]. These camera images demonstrate that a portion of the Raman laser light is simultaneously extracted via this waveguide while we investigate the laser properties via the vertical emission. From the intensity in Fig. 5(e) we roughly estimate that several tens of percent of the Stokes power in the present cavity are extracted by the waveguide. In order to realize dense optical circuits with various functions, it will be important to efficiently collect the Stokes light in such waveguides . For many applications, it is also important to increase the output power of the Raman laser up to several tens of µW. A larger output can be achieved by increasing the volume of the heterostructure cavity, optimizing the Q factors of the two resonant modes, and improving the fabrication process to suppress losses [28,58]. We note that higher-order resonant modes, which can also induce Raman lasing, appear in heterostructure cavities with larger volumes [23,59].
The open circles in Fig. 5(c) correspond to the results for the -aligned cavity fabricated on the conventional SOI wafer. For this sample we obtained Δf = 15.585 THz, Qp = 137,000, and Qs = 1,480,000. Although these values are comparable to that for our laser device on the 45°-rotated SOI wafer, the efficiency of the spontaneous Raman scattering in the low excitation range (below the threshold) for the device on the conventional SOI is about two orders of magnitude smaller. This difference in the emissiaon efficiencies is due to the Raman selection rule in Si and the different alignment of the cavities with respect to the  direction of the top Si layer [23,26]. The observed laser performance of the device fabricated along  of the top Si layer on the 45°-rotated SOI wafer is comparable to that observed from Raman lasers fabricated along  on conventional SOI wafers, although the detuning of Δf is slightly larger [26–28]. Therefore, it is concluded that the nanocavity-based Raman Si laser can be fabricated on SOI wafers with a 45°-rotated top Si layer without any degradation of the performance.
6. Stress in the PC slab
The cooling process after the thermal fusion bonding generates stress in the SOI wafer because the thermal expansion coefficient of Si is five times larger than that of SiO2 . The top Si layer of a SOI wafer and the BOX layer are subject to tensile stress and compressive stress, respectively, which results in a warpage of the air-bridge structure because the SiO2 near the interface to the air gap pulls towards the center of the PC slab . Because the stress in the Si slab can alter the absolute value of the Raman shift for the Si nanocavity, it is important to investigate the strain of the Raman Si nanocavity. Figures 6(a) and 6(b) present surface topographies of the PC slabs fabricated on the 45°-rotated SOI wafer and on the conventional SOI, respectively, measured by SWLI (Zygo NewView 100). The x and y axes correspond to those shown in Fig. 4(b). Both PC slabs investigated here warp with an angle of about 1.5 degrees. This indicates that the magnitude of the stress in the modified SOI wafer is almost the same as that in the conventional SOI. Therefore, the blueshift of the Raman shift that is induced by the compressive stress for the PC slab on the modified SOI, can be similar to that for the conventional SOI. In a previous study we determined a magnitude of ≈5.0 × 10−3 THz for the blueshift .
Figures 6(c)−(e) show the measurement results at a position close to the cleaved facet. The left data are the surface topologies while the right are the corresponding height profiles along the center line of the slab. Figure 6(c) is for the 45°-rotated SOI wafer. The cleaved facet is located at the position near x = 0 µm. Although the magnitude of the warpage varies depending on the x-position near the facet, the PC slab has a convex shape in the whole range of the 3D map. Figure 6(d) is for the conventional SOI where a variation of the warpage is also observed for positions close to the facet (x = 0 µm). It is noted that the variation is 1.6 times larger than that for the 45°-rotated SOI wafer. The variation of the warpage could increase the optical loss and rotates the polarization of the transmitted light . The smaller variation of the warpage in the PC slab that is fabricated on the 45°-rotated SOI wafer can be advantageous.
Figure 6(e) shows the results for another sample fabricated on the conventional SOI. The position of the cleaved facet is at x = 30 µm. It is noted that the slab has a convex shape near the facet but abruptly changes to a concave shape within a few tens of micrometers. This behavior is not suitable for optical interconnections. We confirmed that about half of the fabricated samples exhibit such a warpage when using a conventional SOI. On the other hand, this abrupt change of the warpage has not been observed in the Raman laser sample for the 45°-rotated SOI wafer and in the PC devices fabricated along  for the conventional SOI wafer. Therefore, the smaller variation in the topology close to the facet in the 45°-rotated SOI wafer should be due to the perpendicular alignment (the PC waveguide is perpendicular to the cleaved facet).
We demonstrate a Raman Si laser based on a high-Q PC nanocavity fabricated on a modified (100) SOI wafer whose top Si layer is rotated in plane by 45 degrees relative to the Si support substrate. Using this 45°-rotated SOI wafer, the nanocavity laser can be fabricated in the direction perpendicular to the cleaved facets of the wafer and the slab warpage at the cleaved facet decreases. These properties are advantageous for implementation in integrated optical circuits. We emphasize that the optical properties of the fabricated heterostructure nanocavity show no critical deterioration compared to the devices fabricated on the conventional SOI wafer. This modified design realizes cw lasing with a sub-microwatt threshold. We aim at fabricating Raman Si nanocavity lasers on a 300-mm 45°-rotated SOI wafer using CMOS-compatible processes [61–63], because the mass production of Raman Si lasers is essential for commercialization of this Si technology.
Figure 7 shows the experimental setup that is used to obtain the input/output characteristic of the Raman laser shown in Fig. 5(c). For excitation, we use the light from a cw tunable laser (Santec TSL-510), whose wavelength is tuned to the λ of the pump mode. The beam passes through a polarizer to obtain TE polarization and then the beam size is expanded with a beam expander to completely cover the pupil diameter of the objective lens (numerical aperture (NA) = 0.4), which is used to focus the light on the facet of the excitation waveguide. The coupling loss in this setup is about 10 dB. The sample is placed on a high-precision six-axis stage, and the sample temperature is stabilized at 296 K by using a Peltier element. When the pump nanocavity mode is strongly excited, stimulated Raman scattered light is emitted from the cavity via the Stokes nanocavity mode in the direction vertical to the slab. The emitted light is collected by another objective lens (NA = 0.5) placed on a three-axis stage. To efficiently couple the cavity emission into a fiber that guides the light to the monochromator, the position of the lens is precisely adjusted with help of a NIR camera. The Raman emission is measured by inserting a long-pass filter with a cutoff wavelength of 1500 nm. This ensures that the signal from the pump mode, which is simultaneously emitted from the cavity, is suppressed. The stimulated Raman emission (spontaneous Raman emission below the threshold) is resolved by a monochromator with a focal length of 500 mm and detected by a liquid-nitrogen-cooled InGaAs array. The plot on the right upper side in Fig. 7 shows the Raman scattering spectrum at an excitation power of 0.6 µW.
Figure 5(c) is produced by the same method as that in previous studies [26–28]. We measured the Raman scattering spectra for various excitation powers by adjusting the excitation wavelength in each measurement to the optimum value that maximizes the Stokes emission intensity. This maximized intensity for each excitation power is used to plot Fig. 5(c). The pump power coupled to the nanocavity is estimated using the following method: first, the power of the pump light emitted from the cavity to the upper vertical direction is measured at the threshold by an optical power meter (Thorlabs S132C) in front of the collection fiber, that is 0.106 µW. The total loss by the optics placed between the sample and the power meter is 0.4. The factor that accounts for the nanocavity emission geometry, i.e., emission into both upper (observed) and lower (not observed) directions, is 0.5. By using these values, the estimated threshold power is 0.106/(0.4 × 0.5) = 0.53 µW. We assume that the pump power coupled into the nanocavity is proportional to the input laser power. The Stokes power of Fig. 5(c) is estimated by a similar procedure. In this method, the pump light and Stokes light exiting the nanocavity to the adjacent waveguides are not considered since it is difficult to correctly measure the emitted powers from the edges. It is also noted that we assume that the coupling efficiencies to the objective lens are the 100% for both pump and Stokes light. This is because the efficiency considerably varies from the theoretical value for each nanocavity mode due to the random air-hole variations . The images shown in Fig. 5(d) are obtained from the sample under additional lamp illumination using the NIR camera.
New Energy and Industrial Technology Development Organization (NEDO); Toray Science Foundation; Support Center for Advanced Telecommunications Technology Research Foundation (SCAT); Japan Society for the Promotion of Science (JSPS) (15H05428, 18H01479); Kyoto Technoscience Center.
1. J. K. Doylend and A. P. Knights, “The evolution of silicon photonics as an enabling technology for optical interconnection,” Laser Photonics Rev. 6(4), 504–525 (2012). [CrossRef]
2. M. R. Billah, M. Blaicher, T. Hoose, P. I. Dietrich, P. M. Palomo, N. Lindenmann, A. Nesic, A. Hofmann, U. Troppenz, M. Moehrle, S. Randel, W. Freude, and C. Koos, “Hybrid integration of silicon photonics circuits and InP lasers by photonic wire bonding,” Optica 5(7), 876–883 (2018). [CrossRef]
3. K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015). [CrossRef]
4. K. Saurav and N. L. Thomas, “Probing the fundamental detection limit of photonic crystal cavities,” Optica 4(7), 757–763 (2017). [CrossRef]
5. J. M. Shainline and J. Xu, “Silicon as an emissive optical medium,” Laser Photonics Rev. 1(4), 334–348 (2007). [CrossRef]
6. T. Ihara, Y. Takahashi, S. Noda, and Y. Kanemitsu, “Enhanced radiative recombination rate for electron-hole droplets in a silicon photonic crystal nanocavity,” Phys. Rev. B 96(3), 035303 (2017). [CrossRef]
7. Y. Shi, Z. Wang, J. V. Campenhout, M. Pantouvaki, W. Guo, B. Kunert, and D. V. Thourhout, “Optical pumped InGaAs/GaAs nano-ridge laser epitaxially grown on a standard 300-mm Si wafer,” Optica 4(12), 1468–1473 (2017). [CrossRef]
8. R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691–694 (2018). [CrossRef]
9. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10(22), 1305–1313 (2002). [CrossRef]
10. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003). [CrossRef]
11. R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12(16), 3713–3718 (2004). [CrossRef]
12. A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12(18), 4261–4268 (2004). [CrossRef]
13. Q. Xu, V. Almeida, and M. Lipson, “Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides,” Opt. Express 12(19), 4437–4442 (2004). [CrossRef]
14. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004). [CrossRef]
15. M. Krause, H. Renner, and E. Brinkmeyer, “Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,” Opt. Express 12(23), 5703–5710 (2004). [CrossRef]
16. T. Liang and H. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 85(16), 3343–3345 (2004). [CrossRef]
17. R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005). [CrossRef]
18. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef]
19. H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007). [CrossRef]
20. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008). [CrossRef]
21. X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers,” Opt. Express 15(8), 4763–4780 (2007). [CrossRef]
22. X. Checoury, Z. Han, and P. Boucaud, “Stimulated Raman scattering in silicon photonic crystal waveguides under continuous excitation,” Phys. Rev. B 82(4), 041308 (2010). [CrossRef]
23. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013). [CrossRef]
24. D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “Raman shift and strain effect in high-Q photonic crystal silicon nanocavity,” Opt. Express 23(4), 3951–3959 (2015). [CrossRef]
25. Y.-H. Hsiao, S. Iwamoto, and Y. Arakawa, “Spontaneous and stimulated Raman scattering in silica-cladded silicon photonic crystal waveguides,” Jpn. J. Appl. Phys. 54(4S), 04DG02 (2015). [CrossRef]
26. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013). [CrossRef]
27. D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018). [CrossRef]
28. D. Yamashita, T. Asano, S. Noda, and Y. Takahashi, “Strongly asymmetric wavelength dependence of optical gain in nanocavity-based Raman silicon lasers,” Optica 5(10), 1256–1263 (2018). [CrossRef]
29. M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019). [CrossRef]
30. H. H. Jiun, I. Ahmad, A. Jalar, and G. Omar, “Effect of Laminated Wafer Toward Dicing Process and Alternative Double Pass Sawing Method to Reduce Chipping,” IEEE Trans. Electron. Packag. Manuf. 29(1), 17–24 (2006). [CrossRef]
31. Y. Yamauchi, M. Okano, S. Noda, and Y. Takahashi, “High-Q Nanocavity-Based Raman Laser Fabricated on a (100) SOI Substrate with a 45-Degree-Rotated Top Silicon Layer,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2018), paper Th1H.2.
32. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]
33. Y. Tanaka, S. Takayama, T. Asano, Y. Sato, and S. Noda, “A polarization diversity two-dimensional photonic-crystal device,” IEEE J. Sel. Top. Quantum Electron. 16(1), 70–76 (2010). [CrossRef]
34. D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides,” Opt. Lett. 28(20), 1954–1956 (2003). [CrossRef]
35. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(3), 412–421 (2006). [CrossRef]
36. Y. Inui, Y. Takahashi, T. Asano, and S. Noda, in Autumn Meeting Japan Society of Applied Physics, Abstract (The Japan Society of Applied Physics, 2012), 14p-B1-6.
37. W. P. Maszara, G. Goetz, A. Caviglia, and J. B. McKitterick, “Bonding of silicon wafers for silicon-on-insulator,” J. Appl. Phys. 64(10), 4943–4950 (1988). [CrossRef]
38. R. Stengl, T. Tanm, and U. Gösele, “A Model for the Silicon Wafer Bonding Process,” Jpn. J. Appl. Phys. 28(Part 1), 1735–1741 (1989). [CrossRef]
39. H. Sayama, Y. Nishida, H. Oda, T. Oishi, S. Shimizu, T. Kunikiyo, K. Sonoda, Y. Inoue, and M. Inuishi, “Effect of <100> channel direction for high performance SCE immune pMOSFET with less than 0.15 µm gate length,” Tech. Dig. of IEDM, 657–660 (1999).
40. T. Matsumoto, S. Maeda, H. Dang, T. Uchida, K. Ota, Y. Hirano, H. Sayama, T. Iwamatsu, T. Ipposhi, H. Oda, S. Maegawa, Y. Inoue, and T. Nishimura, “Novel SOI wafer engineering using low stress and high mobility CMOSFET with <100>-channel for embedded RF/analog applications,” Tech. Dig. of IEDM, 663–666 (2002).
41. Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, “Ultra-compact 32-channel drop filter with 100 GHz spacing,” Opt. Express 22(4), 4692–4698 (2014). [CrossRef]
42. J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental Fluctuation of Frequency Spacing Between the Two High-Quality Resonant Modes in a Raman Silicon Nanocavity Laser,” Submitted to IEEE J. Select. Top. Quant. Electron.
43. D. K. Bowen and B. K. Tanner, X-ray Metrology in Semiconductor Manufacturing (CRC Press, 2006).
44. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express 19(12), 11916–11921 (2011). [CrossRef]
45. H. Sekoguchi, Y. Takahashi, T. Asano, and S. Noda, “Photonic crystal nanocavity with a Q-factor of ∼9 million,” Opt. Express 22(1), 916–924 (2014). [CrossRef]
46. K. Maeno, Y. Takahashi, T. Nakamura, T. Asano, and S. Noda, “Analysis of high-Q photonic crystal L3 nanocavities designed by visualization of the leaky components,” Opt. Express 25(1), 367–376 (2017). [CrossRef]
47. T. Asano, Y. Ochi, Y. Takahashi, K. Kishimoto, and S. Noda, “Photonic crystal nanocavity with a Q factor exceeding eleven million,” Opt. Express 25(3), 1769–1777 (2017). [CrossRef]
48. W. H. Teh, D. S. Boning, and R. E. Welsch, “Multi-Strata Stealth Dicing Before Grinding for Singulation-Defects Elimination and Die Strength Enhancement: Experiment and Simulation,” IEEE Trans. Semicon. Manufact. 28(3), 408–423 (2015). [CrossRef]
49. G. Takeuchi, Y. Terada, M. Takeuchi, H. Abe, H. Ito, and T. Baba, “Thermally controlled Si photonic crystal slow light waveguide beam steering device,” Opt. Express 26(9), 11529–11537 (2018). [CrossRef]
50. H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly effective in-plane channel-drop filters in two-dimensional heterostructure photonic-crystal slab,” Jpn. J. Appl. Phys. 45(8A), 6078–6086 (2006). [CrossRef]
51. K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, K. Yamada, and Y. Takahashi, “Photonic Crystal Nanocavities with an Average Q factor of 1.9 million Fabricated on a 300-mm-Wide SOI Wafer Using a CMOS-Compatible Process,” J. Lightwave Technol. 36(20), 4774–4782 (2018). [CrossRef]
52. T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006). [CrossRef]
53. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]
54. D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A Sub-microwatt Threshold Raman Silicon Laser Using a High-Q Nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.
55. V. Sih, S. Xu, Y.-H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007). [CrossRef]
56. T. Liang and H. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1149–1153 (2004). [CrossRef]
57. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004). [CrossRef]
58. T. Asano and S. Noda, “Optimization of photonic crystal nanocavities based on deep learning,” Opt. Express 26(25), 32704–32716 (2018). [CrossRef]
59. Y. Takahashi, Y. Tanaka, H. Hagino, T. Asano, and S. Noda, “Higher-order resonant modes in a photonic heterostructure nanocavity,” Appl. Phys. Lett. 92(24), 241910 (2008). [CrossRef]
60. T. Iida, T. Itoh, D. Noguchi, and Y. Takano, “Residual lattice strain in thin silicon-on-insulator bonded wafers: Thermal behavior and formation mechanisms,” J. Appl. Phys. 87(2), 675–681 (2000). [CrossRef]
61. H. C. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100 µm Photonic Crystal Si Optical Modulators: Spectral, Athermal, and High-Speed Performance,” IEEE J. Sel. Top. Quantum Electron. 19(6), 127–137 (2013). [CrossRef]
62. Y. Ooka, T. Tetsumoto, N. A. B. Daud, and T. Tanabe, “Ultrasmall in-plane photonic crystal demultiplexers fabricated with photolithography,” Opt. Express 25(2), 1521–1528 (2017). [CrossRef]
63. K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, M. Mori, T. Asano, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic crystal nanocavities fabricated by CMOS process technologies,” Opt. Express 25(15), 18165–18174 (2017). [CrossRef]