We demonstrate that resonant wavelength of photonic crystal (PhC) nanobeam cavities can be individually post-fabrication tuned by electron beam irradiation. By measuring the transmission spectrum of the cavities before and after trimming, it is shown that resonant wavelength shifts are proportional to the scanning time and the acceleration voltage. Furthermore, larger resonant wavelength shifts can be achieved by scanning the region where the electric field is highly localized. The measurement results show that the resonant wavelength difference can be reduced from 5.5 nm (before trimming) to 0.4 nm (after trimming), while the quality factor of the cavities can be maintained.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Photonic crystal (PhC) nanobeam cavities [1–3] are being actively investigated due to the advantages of compact size, small mode volume, and high quality factor. They are valuable in a variety of applications including optical filters [4, 5], lasers [6, 7] and high sensitivity sensors [8,9]. Most of these applications require precise control of the cavity resonances to achieve desired functionalities. However, there is always a deviation between the theoretical designed resonant wavelengths and experimental realized ones due to the fabrication errors . Trimming techniques for compensation of the fabrication-induced resonance shifts are strongly required.
Active tuning techniques, such as the local heating through the thermo-optic effect [11, 12] or the carrier injection through p-i-n junctions , are the most common solutions. The tuning of resonant wavelength is reversible, but these methods require additional complicated fabrication processes and continuous power consumptions. Other approaches to address this issue are the permanent post-fabrication trimming techniques, where the induced refractive index change does not disappear after the applied trimming source is switched off . Wet chemical digital etching  and atomic layer deposition  can provide large wavelengths tuning range, but they cannot induce the refractive index change locally. In contrast, laser assisted oxidation [17, 18] and photo-induced oxidation  can individually tune the resonant wavelength, but the wavelength tuning range is limited. Photodarkening of a thin chalcogenide glass layer  and electron-beam bleaching of the chromophore doped polymer cladding  provide other solutions for post trimming but both strongly degrade the quality factor of the cavity. Eletron beam exposure is adopted to tune the resonance , but additional top polymer cladding is required.
In this work, we show that the resonant wavelength of a PhC nanobeam cavity can be individually tuned after fabrication by the electron beam irradiation. Electron beam irradiation compacts the silica substrate, following by inducing a stress on the silicon layer [23, 24]. Both these two effects increase the refractive index, thus a red shift in the resonant wavelength can be observed. We have characterized this tuning technique on arrays of dielectric mode nanobeam cavities. The measurement results show that this tuning technique can provide efficient post-fabrication trimming for the PhC nanobeam cavities.
2. Design and analysis
The cavity is designed based on the silicon-on-insulator (SOI) platform with a 220 nm silicon layer and a 2 μm buried silica layer. All the numerical calculations are performed with the three-dimensional finite-difference time-domain (3D-FDTD) package from the Lumerical FDTD solution . The schematic of the dielectric mode nanobeam cavity is given in Fig. 1(a). The cavity is formed in a straight waveguide with w = 500 nm by quadratically tapering the radii of air holes from Rcenter in the center to Rend on both sides, i.e., R(i) = Rcenter + (i-1)2(Rend – Rcenter)/(N-1)2. Figure 1(b) shows the band diagram of the PhC dielectric mode nanobeam cavity. The PhC structure with the hole on the sides forms the bandgap while the dielectric band of the PhC structure with the hole in the center is pulled into the bandgap. Tapering holes with gradually changed size are added on both sides to achieve high transmissions. According to the above analysis, the parameters of the PhC cavity are chosen as following: w = 500 nm, a = 340 nm, Rcenter = 90 nm, Rend = 25 nm, N = 25. The resonant wavelength is around 1548.71 nm and the electric field intensity profile of the resonant cavity mode is shown in Fig. 1(c). We find that the majority of the electric field locates at the central region of the cavity.
Although the advanced fabrication technologies improve the accuracy of the feature size greatly, the precise resonant wavelength control of the cavities is still challenging. We investigate the influence of the variation of the geometry parameters of the cavity on the resonances. Resonant wavelength shifts with respect to the variations of the waveguide width and the radius of the circle holes in the center are shown in Fig. 2. The shift rates are approximately 0.8 nm/nm and 2 nm/nm, respectively. In the simulations, we consider the two parameters separately. But for the real fabricated cavities, the shift rates may be even higher since all these geometry deviations may influence the resonances simultaneously.
3. Fabrication and characterization
The PhC nanobeam cavities are fabricated on the silicon-on-insulator (SOI) platform with a 220 nm silicon layer and a 2-μm oxide buried layer. A 310 nm thick positive tone electron beam resist (PMMA 950 K) is spin-coated onto the top of the wafer. Electron beam lithography (Raith150 II) is adopted to define the pattern at 20 KV acceleration voltages. The device patterns are then transferred from the resist to the silicon layer by inductively coupled plasma (ICP) etching with mixed gases of SF6 and C4F8. The residual resist is removed by acetone in the ultrasonic cleaner for 15 mins, and finally rinsed into the de-ionized (DI) water. Grating couplers with a period of 630 nm and a 50:50 duty cycle are fabricated at both input and output parts by another electron beam lithography process followed by a shallow etching (70 nm) to couple the light from the single mode fiber. Four cavities with the same parameters are fabricated on the same chip. The microscope and the scanning electron microscope (SEM) images of the fabricated PhC nanobeam cavities and the grating coupler are shown in Fig. 3.
To characterize the fabricated PhC nanobeam cavities, a continuous wave (CW) broadband amplified spontaneous emission (ASE) light source is used. Polarization sensitive grating couplers are used to couple the TE-like mode into/out the chip. The output optical signal is detected by an optical spectrum analyzer (OSA). Figure 4 shows the measured normalized transmission spectra of the PhC nanobeam cavities right after the fabrication. From the figure, it can be clearly seen that the resonant wavelengths for these cavities are around 1530 nm but the maximum difference between them is up to 5.5 nm. Such difference is due to the fabrication imperfections (waveguide width/hole radius variations), although all the parameters for the four cavities are designed to be the same. From Fig. 2, one can find that a 2 nm fabrication error will result in more than 3 nm resonant wavelength shifts and it’s not possible to avoid such a wavelength shift even using the state-of-art fabrication technologies.
Electron beam irradiation is then performed to tune the resonances of the fabricated cavities. The electron beam from the SEM is utilized as the trimming source. The aperture is kept at 10 μm. Three of the four fabricated cavities are irradiated with the SEM, and the left one is used for reference. In Fig. 5, resonant wavelength shifts of the cavities are plotted as a function of the scanning time. The resonant wavelength shifts are proportional to the scanning time, which is in accordance with that the resonant wavelength shifts are proportional to the compacted fraction .
The influences of the irradiation at different magnifications, scanned regions, and acceleration voltages are investigated. Figure 5(a) shows the resonant wavelength shifts at different magnifications. The rate of the wavelength shift to scanning time at 12K and 6K magnification are 0.209 nm/min and 0.063 nm/min, respectively. Almost four times enhancement has been observed by increasing the magnification. This is reasonable since the amount of the electron received by a unit area increased times with doubled magnification [as shown in the inset of Fig. 5(a)]. Figure 5(b) shows the resonant wavelength shifts at different irradiation regions. Larger wavelength shift can be obtained for the central irradiation compared to the one at side [as shown in the inset of Fig. 5(b)]. This can be explained that the tuning effect will be enhanced if the electron distribution matches the electric field distribution of the resonant mode [see Fig. 1(c)]. The tuning effect will also be influenced by the acceleration voltage, as shown in Fig. 5(c). The rate of wavelength shift to scanning time under 10 kV and 5 kV acceleration voltages are 0.136 nm/min and 0.07 nm/min, respectively. Electron beam under a higher acceleration voltage has higher energy and it is easier to compact the silica layer, thus a larger wavelength shift can be obtained. Furthermore, the ratio between wavelength shift rates is the same as the ratio of acceleration voltages. It indicates that the resonant wavelength shift is proportional to the acceleration voltage. From the above analysis, efficient tuning can be acquired by increasing the magnification and acceleration voltage, while keeping the irradiation region at the center of the fabricated cavity.
We finally investigate the post-trimming effect for the fabricated cavity arrays. The aim of the post trimming is to minimize the resonant wavelengths difference for the fabricated cavities. The measured normalized transmission spectra of the PhC nanobeam cavities after trimming are shown in Fig. 6(a). The maximum difference between their resonant wavelengths decreases from 5.5 nm (before trimming) to 0.4 nm (after trimming). This difference can be further decreased by trimming with a lower acceleration voltage or a smaller magnification. In Fig. 6(b), we compare the quality factor of the cavity before and after trimming using Lorentz fitting for the transmission spectra. The quality factor for the cavity before and after trimming is 35478 and 33536, respectively. It indicates that the electron beam trimming has a negligible effect on the performance of the cavity.
In summary, we demonstrated that the resonant wavelength of the PhC nanobeam cavities can be post-fabrication tuned by electron beam irradiation. Utilizing this method, the difference in the resonant wavelength due to the fabrication imperfections can be compensated. The influences of the irradiation at different magnifications, scanned regions and acceleration voltages are systematically investigated. The measurement results show that the resonant wavelengths can be precisely controlled while the performance of the cavity can be maintained with the proposed method. Although only the post-trimming for the PhC cavities is shown in this work, we believe that the method also works for the other type of cavities such as the ring resonators.
National Natural Science Foundation of China (Grant No. 61675178); National Key Research and Development Program (Grant No. 2016YFB0402502); the Fundamental Research Funds for the Central Universities.
References and links
1. Q. Quan, P. B. Deotare, and M. Lončar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010). [CrossRef]
5. X. Ge, Y. Shi, and S. He, “Ultra-compact channel drop filter based on photonic crystal nanobeam cavities utilizing a resonant tunneling effect,” Opt. Lett. 39(24), 6973–6976 (2014). [CrossRef] [PubMed]
6. K. Y. Jeong, Y. S. No, Y. Hwang, K. S. Kim, M. K. Seo, H. G. Park, and Y. H. Lee, “Electrically driven nanobeam laser,” Nat. Commun. 4(1), 2822 (2013). [CrossRef]
8. D. Yang, H. Tian, and Y. Ji, “High-Q and high-sensitivity width-modulated photonic crystal single nanobeam air-mode cavity for refractive index sensing,” Appl. Opt. 54(1), 1–5 (2015). [CrossRef] [PubMed]
9. W. Liu, J. Yan, and Y. Shi, “High sensitivity visible light refractive index sensor based on high order mode Si3N4 photonic crystal nanobeam cavity,” Opt. Express 25(25), 31739–31745 (2017). [CrossRef] [PubMed]
11. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010). [CrossRef]
12. W. S. Fegadolli, N. Pavarelli, P. O’Brien, S. Njoroge, V. R. Almeida, and A. Scherer, “Thermally controllable silicon photonic crystal nanobeam cavity without surface cladding for sensing applications,” ACS Photonics 2(4), 470–474 (2015). [CrossRef]
13. S. Ibrahim, N. K. Fontaine, S. S. Djordjevic, B. Guan, T. Su, S. Cheung, R. P. Scott, A. T. Pomerene, L. L. Seaford, C. M. Hill, S. Danziger, Z. Ding, K. Okamoto, and S. J. B. Yoo, “Demonstration of a fast-reconfigurable silicon CMOS optical lattice filter,” Opt. Express 19(14), 13245–13256 (2011). [CrossRef] [PubMed]
14. A. Canciamilla, F. Morichetti, S. Grillanda, P. Velha, M. Sorel, V. Singh, A. Agarwal, L. C. Kimerling, and A. Melloni, “Photo-induced trimming of chalcogenide-assisted silicon waveguides,” Opt. Express 20(14), 15807–15817 (2012). [CrossRef] [PubMed]
15. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoğlu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005). [CrossRef]
16. X. Yang, C. J. Chen, C. A. Husko, and C. W. Wong, “Digital resonance tuning of high-Q/Vm silicon photonic crystal nanocavities by atomic layer deposition,” Appl. Phys. Lett. 91(16), 161114 (2007). [CrossRef]
17. C. J. Chen, J. Zheng, T. Gu, J. F. McMillan, M. Yu, G. Q. Lo, D. L. Kwong, and C. W. Wong, “Selective tuning of high-Q silicon photonic crystal nanocavities via laser-assisted local oxidation,” Opt. Express 19(13), 12480–12489 (2011). [CrossRef] [PubMed]
19. F. Intonti, N. Caselli, S. Vignolini, F. Riboli, S. Kumar, A. Rastelli, O. G. Schmidt, M. Francardi, A. Gerardino, L. Balet, L. H. Li, A. Fiore, and M. Gurioli, “Mode tuning of photonic crystal nanocavities by photoinduced non-thermal oxidation,” Appl. Phys. Lett. 100(3), 033116 (2012). [CrossRef]
20. A. Faraon, D. Englund, D. Bulla, B. L. Davies, B. J. Eggleton, N. Stoltz, P. Petroff, and J. Vučković, “Local tuning of photonic crystal cavities using chalcogenide glasses,” Appl. Phys. Lett. 92(4), 043123 (2008). [CrossRef]
24. T. A. Dellin, D. A. Tichenor, and E. H. Barsis, “Surface Compaction in Irradiated Vitreous Silica,” Bull. Am. Phys. Soc. 21, 296 (1976).
25. Lumerical Solutions, Inc., http://www.lumerical.com