1. Introduction

Over recent years, photonic crystal (PhC) nanobeam cavities [1–4] have attracted increasing attention, due to their high quality factor (Q), small mode volume, small foot print and no limitation of free spectrum range (FSR). Many applications based on PhC nanobeam cavities have been proposed, including nanobeam lasers [5–7], filters [8, 9], routers [10] and sensors [11–13]. For most of these applications, one of the fundamental requirements is to design and fabricate the PhC nanobeam cavities working at the target wavelength. However, the resonant wavelengths are very sensitive to the dimensional variations caused by the fabrication process variations [14].

Many methods have been proposed to compensate the fabrication variations. Active thermal tuning [15–17] is one of the common methods used to solve this problem, however, this will lead to high power consumption and device complexity when an array of cavities are integrated on a single chip [18]. Another way to tune the resonant wavelength is the post-fabrication trimming. Laser assisted oxidation [19, 20] and photo-induced oxidation [21] can individually tune the resonant wavelength, however, the tunable wavelength range using these methods is limited. Wet chemical digital etching [22] and atomic layer deposition [23, 24] can be used to trim the resonant wavelength over a large range, but the cavities fabricated on the same chip are difficult to be individually controlled. Electron-beam bleaching of chromophore doped polymer cladding has also been demonstrated [25], however, such effect causes a great deal of reliability concern since refractive index drifts over time due to densification and structural relaxation.

In this paper, we demonstrate that the resonant wavelengths of the PhC nanobeam cavities can be individually post tuned by selective electron beam exposure and development. Instead of using the electron-beam bleaching effect which may cause reliability issue, the post-trimming proposed in this paper is realized by exposing the cladding polymer layer with different doses. A kind of polymer - SU-8 [26] is utilized as the cladding layer of our PhC nanobeam cavities and exposed by electron beam lithography with different doses. The experimental results show that the thickness of the SU-8 cladding can be individually and precisely controlled. The transmission spectrums of the PhC nanobeam cavities were measured before exposure, after exposure and after development, respectively. By comparing the transmission spectrums, we observed that the resonant wavelength can be post-tuned as large as 30 nm.

2. Design and analysis

The PhC nanobeam cavities are designed based on the Silicon-On-Insulator (SOI) platform with the thickness of 220 nm for the silicon layer and 2 µm for the buried silica layer. 700 nm thick SU-8 is adopted to be the top cladding. The refractive index of the silicon core, the silica buffer layer and the SU-8 cladding are 3.46, 1.44 and 1.57, respectively. The PhC nanobeam cavities are formed by modulating the width of the silicon stacks, and the schematic is given in Fig. 1(a). The three-dimensional finite-difference-time-domain (3D-FDTD) method [27] is utilized to simulate the PhC nanobeam cavities. Figure 1(b) shows the electric field distribution, in which the black lines indicate the profile of the silicon stacks. The lattice constant is chosen to be 420 nm to keep the resonant wavelength of the PhC nanobeam cavities near 1550 nm. To obtain high Q factor, we quadratically modulated the widths of the dielectric stacks from $W_y\left(0\right)$ in the center to $(W_y\left(i_{max}\right)$ on the both sides ($W_y\left(i\right)=W_y\left(0\right)+i^2(W_y\left(i_{max}\right)-W_y\left(0\right))/i_{max}{}^2$, $i$ increases from 0 to $i_{max}$). Figure 1(c) shows the schematic of the cross-section for the PhC nanobeam cavities. The electric field distributions of the cross section for the PhC nanobeam cavities with $W_y\left(0\right)$ = 400 nm, $W_y\left(0\right)$ = 450 nm, and $W_y\left(0\right)$ = 500 nm are presented in Figs. 1(d), 1(e) and 1(f), respectively. From these figures, it is easy to find that the electric field is well confined in the PhC nanobeam cavities with larger $W_y\left(0\right)$. Therefore, increasing the width of $W_y\left(0\right)$ is a way to reduce the influence of the fabrication variations on the resonant wavelengths. However, to keep the PhC nanobeam cavities working at the target wavelength, smaller lattice constant should be designed for larger $W_y\left(0\right)$, which will increase the fabrication difficulty. From the above analysis, the parameters for the PhC nanobeam cavities are chosen to be: a = 420 nm, $W_x$ = 210 nm, $W_y\left(0\right)$ = 450 nm, $W_y\left(i_{max}\right)$ = 800 nm and $i_{max}$ = 17. And the effective mode volume of the PhC nanobeam cavities is calculated to be 1.282${(\lambda /n_{\text{Si}})}^3$ (defined by $\text{V}={{\displaystyle \int }}^{\text{}}\text{dV ε}{\left|\text{E}\right|}^2/{\left[\text{ε}{\left|\text{E}\right|}^2\right]}_{\text{max}}$).

 

Fig. 1 (a) The schematic of the PhC nanobeam cavities, in which the lattice constant a = 420 nm, $W_x$ = 210 nm, $W_y\left(0\right)$ quadratically increased from $W_y\left(0\right)$ = 450 nm at the center to $W_y\left(i_{max}\right)$ = 800 nm at the both sides, and $i_{max}$ = 17. (b) The electric field distribution of the PhC nanobeam cavities simulated by 3D-FDTD. The black lines indicate the profile of the silicon stacks. (c) The schematic of the cross-section for the PhC nanobeam cavities. The electric field distributions of the cross section for the PhC nanobeam cavities with $W_y\left(0\right)$ = 400 nm (d), $W_y\left(0\right)$ = 450 nm (e), and $W_y\left(0\right)$ = 500 nm (f), respectively.

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3. Fabrication and measurement

The PhC nanobeam cavities are fabricated on the SOI platform with the thickness of the silicon layer of 220 nm and the silica layer of 2µm. The positive tone e-beam resist (PMMA 950K) is spin coated onto the SOI wafer, and baked on the hot plate at 180°C for 20 minutes. The PhC nanobeam cavity patterns are defined by the e-beam lithography (Raith150 II) at 20KV acceleration voltage with the exposure dose of 200$\text{μC}/{\text{cm}}^2$, and developed in a methyl isobutyl ketone (MIBK): isopropyl alcohol (IPA) (1:3) mixture. Then we transferred the device patterns onto the silicon layer by inductively coupled plasma reactive-ion-etching (ICP-RIE) with a gas mixture of SF₆ and C₄F₈. The residual resist is removed by acetone in ultrasonic cleaner for 20 minutes and then rinsed in de-ionized (DI) water. In order to couple the optical mode from the optical fiber, another overlay exposure and a shallow etching (70 nm) are used to fabricate the grating couplers with the period of 630 nm and the duty cycle of 50:50 on both the input and output waveguides. Figure 2(a) is the microscope image of the fabricated PhC nanobeam cavities with the grating couplers at both the input and output parts. Figure 2(b) shows the scanning electric microscope (SEM) picture of the cavity part indicated by dashed frames in Fig. 2(a).

 

Fig. 2 (a) The microscope image of the fabricated PhC nanobeam cavities with the input/output grating couplers. (b) The SEM image of the cavity part indicated by the dashed frames in (a).

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Then, the SU-8 (from MicroChem) with the thickness of 700 nm is spin coated onto the device wafer as the top cladding. We measure the resonant wavelengths for the PhC nanobeam cavities as the references. The schematic of post-trimming process is shown in Fig. 3, in which the green region indicates the exposed area. Each PhC nanobeam cavity is exposed by electron beam with different doses at 30KV acceleration voltage with a spot size around 20 nm. The exposure doses we used in the experiment linearly increase from 0.5$\text{μC}/{\text{cm}}^2$ to 3$\text{μC}/{\text{cm}}^2$ by a step of 0.1$\text{μC}/{\text{cm}}^2$. A post exposure bake is implemented on the hot plate at 95°C for 5 minutes. After that, we record the resonant wavelengths for each cavity. Finally, the wafers are developed in propylene glycol monomethyl ether acetate (PGMEA) for 25 seconds and rinsed into IPA for 15 seconds. Then, the PhC cavities are characterized again to compare the resonant wavelength shifts.

 

Fig. 3 The schematic of the post-trimming process. The thickness of the SU-8 cladding can be precisely and individually controlled.

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For the characterization, we use the tunable laser (Agilent 81600B) with the wavelength ranging from 1520 nm to 1610 nm as the light source to measure the transmission spectrums of the PhC nanobeam cavities. The polarization of the light output from the tunable laser is adjusted by the polarization controller. The grating couplers at the input and output parts of PhC nanobeam cavities are used to couple the TE-like mode from the optical fiber. And the output optical signal of the PhC nanobeam cavities is detected by the power meter (Agilent 81635).

Figure 4(a) shows the measured and simulated Q factors of the PhC cavities with different thickness of the SU-8 cladding. From this figure, The Q-factors are even higher for the PhC cavities after treatment. This is because the confinement of the PhC cavities with thinner cladding (the case after treatment) will be higher than which with thicker cladding (the original case). The tendency of the measured Q agrees well with the simulated result. The derivation in absolute Q values is due to the fabrication imperfections. The inset figure of Fig. 4(a) shows the transmission spectrum of PhC nanobeam cavities after development, in which the black circles are the experimental data, while the red line indicates the Lorentz fit. The full width at the half maximum (FWHM) of the Lorentz fit is 95 pm, which indicates a Q factor of 1.6 × 10⁴. As discussed above, we have measured the transmission spectrums of the PhC nanobeam cavities before exposure, after exposure and after development, respectively. The resonant wavelength shifts for the PhC nanobeam cavities before and after exposure with different doses (without development) are shown in Fig. 4(b). From this figure, we can find that the resonant wavelengths of the PhC nanobeam cavities keep nearly unchanged regardless of the exposure dose. It is evident that there is no electron-beam bleaching effect for the SU-8 cladding.

 

Fig. 4 (a) The measured and simulated Q factors of the PhC cavities with different thickness of the SU-8 cladding. The inset figure in (a) shows the transmission of the PhC cavities after development, in which the black circles are the experimental data, while the red line is the Lorentz fit. (b) The resonant wavelength shifts for the PhC nanobeam cavities after the exposure (without development) using different exposure doses. (c) The resonant wavelength shifts and the thickness of the SU-8 cladding with different exposure doses (after development). (d) The relationship between the simulated resonant wavelength shift of the PhC nanobeam cavities and the thickness of the SU-8 cladding.

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We thereby compare the resonant wavelengths before exposure and after development. The relationship between the wavelength shifts and the exposure doses is shown in Fig. 4(c) with the black squares. The resonant wavelength shift decreases along with the increase of the exposure dose. For the exposure dose larger than 1.5$\text{μC}/{\text{cm}}^2$, the wavelength shift is almost unchanged. The measured largest wavelength shift of the PhC nanobeam cavities shown in Fig. 4(c) is about 30 nm (the resonant wavelength for the cavities with the SU-8 cladding exposed at the dose of 0.5$\text{μC}/{\text{cm}}^2$ is shorter than 1520 nm, which is out of the wavelength range for our experimental setup). Due to the fabrication errors, the measured resonant wavelengths of the PhC cavities are shorter than the simulation results.

We check the thickness variation for the SU-8 cladding exposed with different doses. The red dots in Fig. 4(c) represent the measured thickness for the SU-8 cladding by the step profiler. The measured SU-8 cladding thickness increases with the exposure doses. To confirm that the wavelength shift of the PhC nanobeam cavities is caused by the change of the SU-8 cladding thickness, we investigate the influence of the thickness (ranging from 250 nm to 1.5µm) on the resonant wavelength of the PhC nanobeam cavities. The simulation results are shown in Fig. 4(d). The resonant wavelength shift decreases as the increase of the thickness of the SU-8 cladding, when the thickness is less than 600 nm. The resonant wavelength of the PhC cavity with the SU-8 cladding thickness of 3 µm is used as reference. The experimental wavelength shifts of the PhC nanobeam cavities agree well with the simulation results. From Figs. 4(b) and 4(c), we can find that the exposure and the development will not change the refractive index of the SU-8 cladding, and the resonant wavelength shifts of the PhC cavities come from the decrease of the thickness of the SU-8 cladding. We have measured the same cavities one week after the first measurement. The results are consistent with the original ones, which means that the refractive index of SU-8 will not drift overtime. Since the resonant wavelength of the PhC nanobeam cavities can be individually tuned, this method is suitable to post-trim the PhC nanobeam cavity arrays.

4. Conclusion

In this paper, we demonstrated that the resonant wavelength of the PhC nanobeam cavities can be post tuned by selective electron beam exposure and development. Being exposed by e-beam lithography with different doses, the thickness of the SU-8 cladding can be individually and continuously controlled ranging from 150 nm to 650 nm. Using this method, the resonant wavelengths of PhC nanobeam cavities can be post-tuned as large as 30 nm. To confirm that the resonant wavelength shift is caused by the change of the SU-8 cladding thickness instead of bleaching, we analyze the relationship between the resonant wavelength and the thickness of the SU-8 cladding. The experimental wavelength shifts agree well with the simulations. Although the post-trimming of PhC nanobeam cavities is demonstrated in this paper, we believe that this method is applicable to the other type of cavities such as the ring resonators.