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We have precisely measured the Raman shift of photonic crystal silicon heterostructure nanocavities for Raman laser applications. We utilized a near-infrared excitation laser of wavelength 1.42 μm in order to avoid local sample heating and exploited two high-Q nanocavity modes to calibrate the Raman frequency. The measured Raman shift was 15.606 THz (520.71 cm−1) with a small uncertainty of 1.0 × 10−3 THz. In addition, we investigated the compressive stress generated in a photonic crystal slab in which a ~5.1 × 10−3 THz blue shift of the Raman peak and a slight warpage of the slab were observed. We also demonstrated that the stress could be eliminated by using a cantilever structure.
© 2015 Optical Society of America
1. Introduction
Raman scattering has proved to be a useful phenomenon for examining the static stress of various silicon (Si) devices since the 1970s [1]. From the early 2000s, the Raman effect has also attracted attention due to its potential to add active functionality to pure Si devices [2–5]. The construction of Raman Si lasers using rib waveguide resonators represents an important advance in Si photonics [6–9]. The Raman effect has also been utilized in demonstrations of cascade lasing in the mid-infrared wavelength range [10], optical amplification [11–13], wavelength conversion [14], and optical modulation [15]. Raman-based Si photonics is thus a promising technology [16]. We have recently reported on a continuous-wave (cw) Raman Si laser based on a photonic-crystal (PC) high-quality (Q)-factor nanocavity, with a resonator size of 10 μm and an ultralow threshold of 1 μW [17]. Such a device may allow the integration of many silicon lasers in photonic circuits. Characterizing the Raman properties of Si nanocavities is important for enhancing the device performance.
Our nanocavity Raman Si laser utilizes two high-Q nanocavity modes to confine the pump light and Stokes Raman scattered light, which will hereafter be referred to as the pump mode and the Stokes mode, respectively. One of the key requirements for higher performance is that the frequency spacing between these modes should be matched to the Raman shift of Si with the accuracy of 1.0 × 10−2 THz taking account of the full width at half maximum (FWHM) for the Raman gain of Si, which is ~0.1 THz. However, it is well known that reported Raman shifts of Si vary within a certain error range, for example, 15.59 ± 0.03 THz (520 ± 1.0 cm−1) [18–20]. This is because the Raman shift is usually evaluated by Raman micro-spectrometers using short-wavelength excitation lasers, in which the absolute accuracy is relatively low due to local sample heating caused by the absorption of excitation laser light, the long measurement time needed, and temperature fluctuations of the atmosphere. It is also unclear whether the air holes and air-bridge structures comprising the high-Q nanocavities randomly affect these values due to local stress or deterioration of the crystal quality. Therefore, it is important to investigate the Raman shifts of high-Q Si nanocavities using a high-precision method.
In this paper, we report on the Raman spectroscopy of Si heterostructure nanocavities using a near-infrared excitation laser with a wavelength of 1.42 μm, which is not absorbed by Si. By exploiting the two high-Q nanocavity modes for frequency calibration (the pump mode and the Stokes mode), we can determine the Raman shift with an absolute accuracy of better than ± 2.0 × 10−3 THz. The average of our measured values was 15.606 THz (520.71 cm−1) with a small uncertainty of 1.0 × 10−3 THz. An essentially fixed nanocavity Raman shift is advantageous for the development of Raman lasers. In addition, we have investigated the compressive stress in high-Q nanocavities derived from the air-bridge structure, which caused a blue shift in the Raman scattering and a warpage of the slab. The stress could be eliminated using a cantilever structure. The deterioration of the crystalline Si was not observed for the nanocavities.
2. Sample structure and experimental setup
Figure 1(a) shows a schematic diagram of a typical measured nanocavity with a two-step heterostructure [21]. The lattice constant in the x-direction increases by 5 nm every two periods on approaching the center, which reduces the propagation band frequency. As a result, Fig. 1(b) shows that local optical confinement regions are generated at the lower-frequency edges of the first and second propagation bands, where two nanocavity modes with high-Q factors are formed [22]. We define the nanocavity modes arising from the first and second propagation bands as the Stokes and pump modes, respectively. The Si slab thickness is ~220 nm and the air hole radius is ~130 nm. We define the x-direction as the [100] crystalline direction of a (001) Si-on-insulator (SOI) substrate. These structural parameters are almost the same as those of our previously reported Raman laser sample [17]. The nanocavities were constructed from a SOI wafer (Soitec, SiO2 thickness: 3 μm, p-type, R > 13.5 Ωcm), and the PC slab was fabricated in the form of an air-suspended structure by removing the SiO2 layer underneath the patterned region [see Fig. 5(b)]. Details of the fabrication procedure are described in previous reports [17,23].
Fig. 1 (a) Schematic picture of a measured heterostructure nanocavity. The x-direction is defined as the [100] crystalline direction of a (001) SOI. (b) Band diagram of the nanocavity: fp is the frequency of the pump nanocavity mode, fS is the frequency of the Stokes nanocavity mode, FR is the Raman shift of the Si nanocavity, and fR is the frequency of the spontaneous Raman peak exciting the pump nanocavity mode.
This device configuration allows us to control the frequency spacing (Δ f) between the pump mode (fp) and the Stokes mode (fS) by changing the air hole radius. Although Δ f should be matched to the Raman shift (FR) for low-threshold Raman lasing, here we used nanocavity samples with slight mismatches. We define fR as the frequency of the spontaneous Raman emission peak observed when the pump nanocavity mode is excited at exactly fp. Δ fdetun. is the detuning between fR and fS. If Δ f and Δ fdetun. are measured with high accuracy, we can precisely evaluate FR for the nanocavities according to the relation FR = Δ f −Δ fdetun.. The merits of this method are discussed later.
Figure 2 shows the setup used to measure the resonant spectra of both nanocavity modes as well as the Raman scattering spectra. In both measurements, we used a tunable cw laser with transverse-electric polarization for the excitation. The two modes were excited through each excitation waveguide fabricated parallel to the cavity and the dropped light from the cavity in the direction vertical to the slab was measured. First, we determined Δ f by measuring fp and fS with a high-precision wavelength meter and a lock-in amplifier system. Details of this measurement are described in [22]. Second, we determined Δ fdetun. by measuring the Raman scattering spectrum using a monochromator with a liquid-nitrogen-cooled InGaAs-arrayed detector. Details are given in [17].
Fig. 2 Setup used to measure resonant spectra and Raman scattering spectra. The components indicated by parentheses and chevrons were used for resonant spectra and Raman spectra, respectively.
3. Precise determination of Raman shift
Figures 3(a) and 3(b) show the resonant spectra of the pump and Stokes nanocavity modes, respectively. As shown in the insets, the dropped light from the cavity in the direction vertical to the slab was measured. The absolute accuracy of the wavelength meter was ± 0.3 pm and the stability of the excitation laser was 0.1 pm, which result in an experimental error of ± 1.0 × 10−4 THz in determining Δ f. The sample temperature was stabilized at 294 K using a Peltier controller, which kept the temperature variation below 0.1 K for the entire measurement. This results in an error of ± 1.0 × 10−3 THz in the determination of Δ f. The FWHM for the pump nanocavity mode was ~10 pm, and that for the Stokes mode was ~1 pm, which correspond to Q factors of ~100,000 and ~1,000,000, respectively.
Fig. 3 (a) Resonant spectrum of the pump nanocavity mode. (b) Resonant spectrum of the Stokes nanocavity mode. (c) Raman spectrum measured while exciting the pump mode shown in (a). The insets illustrate how the nanocavity modes were excited.
Figure 3(c) shows the Raman scattering spectrum measured when only the pump nanocavity mode in Fig. 3(a) was excited. The excitation power coupled into the cavity was less than 1 μW, and the exposure time was only 2 minutes. This measurement is possible because the light coupled into the nanocavity interacts strongly with optical phonons due to the small volumes and high Q values of the nanocavity modes. We used a 500 mm-focal-length monochromator with a grating of 600 grooves/mm. Although these components are not superior to those in standard Raman spectrometers that use visible excitation lasers, Raman spectroscopy with high resolution is made possible here by the near-infrared wavelength range used (pixel resolution: 8.6 × 10−3 THz = 0.29 cm−1).
Because we used a nanocavity with a mismatch between Δ f and FR, a sharp peak enhanced by the Stokes nanocavity mode was observed in addition to the usual spontaneous Raman emission peak in Fig. 3(c). We were able to determine Δ fdetun. with higher precision than the pixel resolution by fitting both peaks with Lorentzian functions. By repeating the experiment, we found that the standard deviation in the measured value of Δ fdetun. was less than 1.0 × 10−3 THz.
Table 1 summarizes the measured values of Δ f, Δ fdetun., and FR for four different samples. We used nanocavities with 0.1 THz < |Δ fdetun. | < 0.2 THz such that both Raman peaks were clearly visible. The absolute accuracy in determining FR using the two spectral measurements is better than ± 2.0 × 10−3 THz. This value is 50 times smaller than the FWHM for the Raman gain of Si. The measured FR values lay in the range 15.606-15.607 THz and the average was 15.606 THz (520.71 cm−1). This represents the most reliable value yet reported in the study of nanocavity Raman lasers because the excitation configuration used here is the same as that for Raman laser operation [17]. An essentially fixed Raman shift, as observed here, is a favorable property for Raman laser applications. The small variation in the measured values also suggests that the formation of air holes comprising the nanocavities does not degrade the crystal quality. We note that a refractive index for air of 1.000268 was used for the pump and Stokes modes when converting the wavelengths to frequencies [24]. The use of an approximate value for the velocity of light, for example 3.0 × 108 m/s, leads to an error of ~1.0 × 10−2 THz.
Table 1. Summary of Raman measurement results for four nanocavities with air-bridge structures
It is important to comment on the merits of the method used in this study. Because the wavelengths of the two nanocavity modes can be precisely measured by the wavelength meter, FR can be determined with high accuracy. This procedure is similar to performing Raman spectroscopy with a 487.976 nm argon ion laser for excitation and a plasma line at 500.933 nm for calibration [25]. It should be emphasized that the wavelength of our excitation laser was 1.42 μm, corresponding to a photon energy lower than the band gap of Si. Furthermore, the excitation power was less than 1 μW, which is extremely small taking into account that the scattering is proportional to λ−4. It has been demonstrated that the heterostructure nanocavity with Q ~100,000 presents the heat effect in the range of the excitation power more than 10 μW [26]. Therefore, local sample heating due to absorption of the excitation laser, which is always a source of uncertainty in Raman spectroscopy, is negligible in our measurement. This is highly advantageous because the nanocavities have poor thermal diffusion due to the air-bridge structure.
4. Stress in photonic crystal slab
Next, we investigated the effect of stress in the nanocavities using a conventional Raman spectrometer with a 532 nm excitation laser (Nanophoton, Raman-11). Figure 4(a) shows a confocal laser scanning microscope image of a measured sample. Figure 4(b) shows the Raman spectra measured for the PC slab (solid line) and for the native SOI region (dotted line) where the sample was excited from the direction vertical to the slab. Here, the horizontal axis represents the wavenumber of the Raman shift in the conventional manner. The PC slab peak position was calibrated so as to match the Raman shift of the nanocavities (520.71 cm−1) determined in the above experiments. The Raman signal of the PC slab was more than 10 times larger than that of the SOI region because the periodic holey structure increases the surface area and allows extraction of the Raman scattered light with high efficiency.
Fig. 4 (a) Laser microscope image of a measured PC slab. The three line defects are the nanocavity and excitation waveguides. (b) Raman spectra measured at the position of the PC slab (solid line) and the SOI region (dotted line). (c) Raman shift profiles along the dashed line in (a) before (dotted line) and after (solid line) formation of the air-bridge structure. (d) Raman shift profiles for a cantilever PC slab sample. (e) FWHM of Raman peak for each structure.
We measured the Raman shift as a function of position along the dashed line shown in Fig. 4(a). The measurement was performed using stripe irradiation, where Raman signals from all positions on the line were detected simultaneously. The exposure time was 30 min and the excitation power was ~50 μW/μm2. The dotted line in Fig. 4(c) represents the signal from the PC slab before the air-bridge structure had been formed. The Raman shift remained almost the same along the line. The relatively large fluctuation in the SOI region was due to the low signal. The solid line in Fig. 4(c) represents the signal from a slab with an air-bridge structure. The Raman shift in the PC slab region increased by 0.4 cm−1 (1.2 × 10−2 THz) compared with that for the SOI region, indicating that the PC slab was under a uniaxial compressive stress of ~100 MPa. In contrast, the Raman shift was reduced by 0.3cm−1 at the interface between the PC slab and the SOI region, implying the presence of tensile stress.
Figures 5(a) and 5(b) display the mechanism by which stress arises. The SOI substrate used for fabrication initially experiences stress at the interface between the top Si layer and the SiO2 layer. This is generated during cooling after the high-temperature wafer fusion process because the thermal expansion coefficient of Si is five times larger than that of SiO2. Therefore, the top Si layer is under tensile strain whereas the SiO2 layer is under compressive strain [27]. When the SiO2 layer underneath the PC pattern is chemically removed, the SiO2 near the interface with the air gap is shifted horizontally toward the center of the PC slab, as indicated by the arrows in Fig. 5(b). Accordingly, compressive stress is applied to the PC slab, whereas tensile stress is generated at the interface with the SOI. We also note that these strains cause a slight warpage of the air-bridged slab. Figure 5(c) is a surface morphometric image of the slab measured by a scanning white light interferometer (Zygo). The air-bridged slab warps convexly with an angle of 1.5 degree to the native SOI surface.
Fig. 5 (a) Schematic cross-section of the PC slab before the air-bridge structure is formed. The compressive and tensile stresses are denoted in red and blue. (b) Cross-sectional view of the air-bridge PC slab. Arrows indicate shifts of the SiO2 layer to release stress. (c) Surface shape image of the air-bridge PC slab by a scanning white light interferometer. (d) Cross-sectional view of the cantilever PC slab. (e) Surface shape image of the cantilever PC slab.
The compressive stress could be eliminated using a cantilever structure, as shown in Fig. 5(d) where an air spacer is added to an edge of the PC slab. Figure 5(e) shows the surface shape, which clearly indicates that the air spacer prevents the slab from warping. Figure 4(d) is the Raman spectroscopy results for the cantilever slab. The curves were calibrated so that the values for the SOI are the same as those in Fig. 4(c). It is clearly observed that the blue shift at the PC slab was reduced, which indicates that the compressive stress could be eliminated by using the cantilever structure. It should be emphasized that no visible increase in the FWHM of the Raman peak was found in any of the samples as shown in Fig. 4(e). Therefore, it can be concluded that the fabrication process does not degrade the quality of the crystalline Si.
Table 2 summarizes the experimental results of the Raman measurements for the nanocavities with the cantilever structures using the method explained in section 3. The photonic parameters are the same as those for Table 1. The FR values were 15.601-15.602 THz and the average was 15.601 THz (520.54 cm−1), which are smaller than those in Table 1 by 5.1 × 10−3 THz (0.17 cm−1) since the compressive strain was eliminated. The reduced values agree well with the result in Fig. 4(d). The value of 15.601 THz for the PC slab suggests a Raman shift for crystalline Si without any stress. These knowledge about the strain effect would be important for the applications of photonic crystal devices. For example, the warpage of the slab shown in Fig. 5(c) might increases the optical loss of the waveguide and decreases the Q factor of the heterostructure nanocavities [28].
Table 2. Summary of Raman measurement results for four nanocavities with cantilever structures
5. Summary
In summary, we have precisely measured the Raman shift of Si heterostructure nanocavities with an absolute accuracy of better than ± 2.0 × 10−3 THz, which is 50 times smaller than the FWHM for the Raman gain of Si. The measured Raman shifts of our samples displayed little variation; the average value was 15.606 THz (520.71 cm−1). The construction of nanocavities with an essentially fixed Raman shift is advantageous for the development of Raman lasers. This value can also be applied to other types of PC devices [29–33]. In addition, we have investigated the effect of stress in high-Q nanocavities on the Raman shift. We found that the compressive stress derived from the air-bridge structure was added to the nanocavity, causing a blue shift of ~5.1 × 10−3 THz. We also found that the airbridge slab slightly warps due to the stress. In addition, we demonstrated that the compressive stress and the slab warpage could be eliminated using a cantilever structure. No evidence for deterioration in the quality of the crystalline Si of the nanocavities was found in any of our Raman measurements. These findings will be useful for various suggestions of PC Raman amplification devices [33–37], and helpful in enhancing the output power and the efficiency of the nanocavity Raman silicon lasers.
Acknowledgments
This work was supported by JSPS KAKENHI (grant number 23686015), the Asahi Glass Foundation, NanoSquare program, Future Pioneering Projects, and the CPHoST program.
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