1. Introduction

Resistance thermometers have been usually utilized to measure temperatures with uncertainties of ≤ 0.01°C [1], however, they are sensitive to environmental variables, such as mechanical shock and humidity. To solve this problem, photonics based temperature sensors have attracted increasing attentions, including fiber Bragg grating (FBG) sensors [2–4], temperature sensitive dyes based sensors [5] and silicon waveguides based temperature sensors [6]. Among them, on-chip integrated silicon temperature sensors have many advantages, such as small size, high complementary metal-oxide-semiconductor (CMOS) compatibility, and immunity to electromagnetic interference.

Over recent years, many silicon waveguides based temperature sensors have been demonstrated with good performances, such as micro-ring resonators [7–10], PhC nanobeam cavities [11] and waveguide Bragg gratings [12, 13]. However, the sensitivity of the silicon resonator based temperature sensors is limited to be about 80 pm/°C, due to the silicon TO coefficient of 1.810⁻⁴ [14–17]. Although by utilizing the Vernier effect, the sensitivity for the cascaded ring resonator-based temperature sensor is 293.9 pm/°C [18], the temperature resolution is limited to be 0.18°C due to its large envelope peak fitting error.

In this paper, we present the design, fabrication and characterization of a high sensitivity temperature sensor based on cascaded PhC nanobeam cavities. Two PhC nanobeam cavities are carefully designed: one with stack width modulated structure [19, 20] and the other one with parabolic-beam structure [21, 22]. The stack width modulated PhC nanobeam cavity is covered with SU-8 cladding which has a negative TO coefficient. There will be a blue shift of the cavity’s resonant wavelength as the increase of the ambient temperature since most of the light will be confined in the SU-8 cladding. The parabolic-beam PhC nanobeam cavity will have a red shift since most of the optical mode is confined in the silicon core which has a positive TO coefficient. The difference in the resonant wavelength shifts of the two cavities is detected and the sensitivity for the temperature sensor is greatly increased. The experimental results show that the sensitivity of the temperature sensor is about 162.9 pm/°C, which is almost twice as high as that of conventional silicon based resonator temperature sensors. Furthermore, the foot-print for the proposed high sensitivity temperature sensor is less than 420.

2. Design and analysis

The schematic of the proposed high sensitivity temperature sensor based on two cascaded individual PhC nanobeam cavities is shown in Fig. 1(a). The Silicon-On-Insulator (SOI) platform with a 220 nm silicon core layer and 2 $\text{μm}$ buried silica layer is adopted for the design. The refractive index of the silicon core, the silica buffer layer, PMMA and the SU-8 cladding are 3.46, 1.44, 1.49 and 1.57, respectively. To obtain a higher sensitivity, the optical mode for the SU-8 covered PhC nanobeam cavity is deigned to distribute more into the SU-8 region, while for the other one the optical mode is designed to be more confined inside the silicon area. The SU-8 covered PhC nanobeam cavity is formed by modulating the width of the silicon stacks, and the structure is given in Fig. 1(b). The widths of the dielectric stacks are quadratically modulated from $W_y\left(0\right)$ in the center to $W_y\left(i_{max}\right)$ on the both sides ($W_y\left(0\right)+i^2(W_y\left(i_{max}\right)-W_y\left(0\right))/i_{max}{}^2$, i increases from 0 to$i_{max}$). And the parameters are chosen to be: the lattice constant a = 400 nm, $W_y\left(0\right)$ = 480 nm, $W_y\left(i_{max}\right)$ = 800 nm, $W_x$ = 200 nm and $i_{max}$ = 17. The electric field distribution for the stack width modulated PhC nanobeam cavity is simulated by using three-dimensional finite-difference-time-domain (3D-FDTD) method [23], as shown in Fig. 1(c). From this figure, one can find that the electric field for stack width modulated PhC nanobeam cavity will penetrate more into the SU-8 cladding, therefore the interaction between light and SU-8 cladding can be enhanced. The confinement factor of the resonant optical mode distributed into the SU-8 cladding is calculated to be 70%. The parabolic-beam structure is used to form the other PhC nanobeam cavity given in Fig. 1(d). The width of the parabolic-beam PhC nanobeam cavity is parabolically tuned as $W_y\left(x\right)=W_y\left(0\right)+x^2(W_y\left(x_{max}\right)-W_y\left(0\right))/x_{max}{}^2$. The parameters are: the lattice constant a = 360 nm, $W_y\left(0\right)$ = 600 nm, $W_y\left(x_{max}\right)$ = 800 nm, r = 130 nm and the number of Gaussian mirrors N = 17 on each side. From the electric field distribution of the parabolic-beam PhC nanobeam cavity shown in Fig. 1(e), one can find that the resonant mode is well confined in the silicon region. One should note that the two cavities are working at different resonant wavelengths, thus there is no interference between the two arms of the pair of Y-junctions. We adopt such a structure just for the ease of measurement. The length of the two optical paths has no influence on the performance of the proposed temperature sensor.

 

Fig. 1 (a) The schematic of the proposed high sensitivity temperature sensor based on two cascaded PhC nanobeam cavities. (b) & (c) The schematic and the electric field distribution of the stack width modulated PhC nanobeam cavity with most of the optical mode penetrated into the SU-8 region. The parameters are chosen to be: the lattice constant a = 400 nm, $W_x$ = 200 nm, $W_y$ quadratically increased from $W_y\left(0\right)$ = 480 nm at the center to $W_y\left(i_{max}\right)$ = 800 nm at the both sides, and $i_{max}$ = 17. (d) & (e) The schematic and the electric field distribution of the parabolic-beam PhC nanobeam cavity with the optical mode well confined in silicon core. The parameters are: the lattice constant a = 360 nm, r = 130 nm, $W_y$ quadratically increased from $W_y\left(0\right)$ = 600 nm at the center to $W_y\left(x_{max}\right)$ = 800 nm at the both sides, and the number of Gaussian mirrors on each side N = 17. The black lines in (c) and (e) indicate the edges of silicon core.

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To investigate the sensitivity of the proposed temperature sensor, we have calculated the wavelength responses of the two cavities. The TO coefficients of silicon, silica, PMMA and SU-8 we used in the simulation are 1.8$\times$10⁻⁴, 1$\times$10⁻⁵, −1.2$\times$10⁻⁴ and −3.5$\times$10⁻⁴, respectively. To keep the resonant wavelength working near 1550nm, the lattice constants for the two PhC cavities are set to be 400 nm and 360 nm, respectively. Figures 2(a) and 2(b) show the influence of the widths of $W_y\left(0\right)$ and $W_x$ on the sensitivity and the Q factor for the stack width modulated PhC cavity. We can find that as the increase of $W_y\left(0\right)$ and $W_x$, the sensitivity and the Q factor will decrease. However, PhC cavities with small $W_y\left(0\right)$ and $W_x$ are difficult to fabricate. Thus, $W_y\left(0\right)$ and $W_x$ for the stack width modulated PhC nanobeam cavity are chosen to be 480 nm and 200 nm, respectively. The sensitivity and Q factor for the parabolic-beam cavity with different $W_y\left(0\right)$ and radius are shown in Figs. 2(c) and 2(d). The Q factor decreases as the increase of $W_y\left(0\right)$, while the sensitivity increases. And the highest Q factor is obtained when the radius is 130 nm. Considering the trade-off between the sensitivity and the Q factor, $W_y\left(0\right)$ and radius for the parabolic-beam cavity are chosen to be 600 nm and 130 nm, respectively. Figures 2(e) and 2(f) show the relationship between the simulated resonant wavelengths and the ambient temperature for the two PhC nanobeam cavities, as well as the Q factors. The sensitivities for the two PhC nanobeam cavities are calculated to be −98.7 pm/°C and 65 pm/°C, respectively. Thus, the total sensitivity for the designed cascaded PhC nanobeam cavities temperature sensor will be 163.7 pm/°C, which is twice as high as that of conventional silicon based resonator temperature sensors.

 

Fig. 2 (a) & (b) The influence of the widths of $W_y\left(0\right)$ and $W_x$ on the sensitivity and Q factor for the stack width modulated PhC nanobeam cavity, respectively. (c) & (d) The sensitivity and Q factor of the parabolic-beam cavity with different width of $W_y\left(0\right)$ and radius, respectively. (e) & (f) The calculated resonant wavelengths and Q factors as the increase of the ambient temperature for the two PhC nanobeam cavities.

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3. Fabrication and measurement

The SOI platform with a 220 nm silicon layer and a 2$\text{μm}$ silica buffer layer of is used to realize the proposed high sensitivity temperature sensor. A positive tone e-beam resist (PMMA 950K) is spin coated onto the SOI wafer, and the device patterns are defined by the e-beam lithography (Raith150 II) at 20KV acceleration voltage with the exposure dose of 200$\text{μC}/{\text{cm}}^2$. After the development, the inductively coupled plasma reactive-ion-etching (ICP-RIE) with a gas mixture of SF₆ and C₄F₈ is used to transfer the patterns onto the silicon layer. We removed the residual resist by acetone in ultrasonic cleaner for 20 minutes and then rinsed the device wafer into de-ionized (DI) water. In order to couple the optical mode from the optical fiber, the grating couplers with the period of 630 nm and the duty cycle of 50:50 are fabricated on both the input and output waveguides with another overlay exposure and a shallow etching (70 nm). Figure 3(a) shows the microscope image of the fabricated temperature sensors. Figure 3(b) is the scanning electric microscope (SEM) picture of the left Y junction. The SEM pictures of the two PhC nanobeam cavities are presented in Figs. 3(c) and 3(d), respectively.

 

Fig. 3 (a) The microscope image of the fabricated temperature sensors. (b) The SEM image of the left Y-junction. (c) & (d) The SEM pictures of the stack width modulated PhC nanobeam cavity and the parabolic-beam PhC nanobeam cavity, respectively.

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A 500 nm PMMA is then spin-coated onto the device wafer, and a third overlay exposure is used to define the opening window above the stack width modulated PhC nanobeam cavity. After the development, 2 $\mu m$ SU-8 (with the mass concentration of 10%) layer is spin-coated onto the opened window as the upper cladding. The gaps in the stack width modulated PhC nanobeam cavity can be well filled since SU-8 has a quite good mobility [24, 25].

A broadband light source (B&A technology OS8143) is utilized to characterize the fabricated temperature senor. The grating couplers at the input and output parts of the PhC nanobeam cavities are used to couple the light from the optical fiber. The output optical signal of the PhC nanobeam cavities is received by the optical spectrum analyzer (OSA) (Yokogawa AQ6370D). A thermistor is used to control the temperature of the device.

Figure 4(a) shows the measured spectra of the fabricated temperature sensor by controlling the ambient temperature from 30°C to 80°C with a step of 10°C. From this figure, we can find that as the increase of the ambient temperature, there is blue shift of the resonant wavelength for the SU-8 covered PhC nanobeam cavity, while red shift can be observed for the parabolic-beam PhC nanobeam cavity. Figures 4(b) and 4(c) show the relationship between the ambient temperature and the measured resonant wavelengths, as well as the Q factors for these two PhC nanobeam cavities, respectively. The Q factor for the stack width modulate PhC nanobeam cavity is about 2$\times$10⁴, while that for the parabolic-beam PhC nanobeam cavity is 2.8$\times$10⁴. The sensitivities for the two PhC nanobeam cavities are measured to be −99 pm/°C and 63.9 pm/°C, respectively, which show good agreement with the calculated results. The resonant wavelength difference between these two PhC nanobeam cavities with different ambient temperature is presented in Fig. 4(d). The sensitivity of the fabricated temperature sensor is around 162.9 pm/°C by linear fitting, which is almost twice as high as that of conventional silicon based resonator temperature sensors. By using the definition given in [26], the detection limit (temperature resolution) is calculated to be 0.08°C. We believe that it is possible to improve the resolution by increasing the Q factor of the PhC cavities. Since the glass transition temperature for SU-8 polymer is around 150°C, we estimate the temperature damage threshold to be 150°C. Considering the reported 6$\mu$s response time for the silicon based microring [7], we believe that the response/recovery time for the proposed sensor will be on the order of microseconds although we have not done the measurement.

 

Fig. 4 (a) The transmission spectra of the fabricated temperature sensor at different ambient temperatures. (b) & (c) The measured resonant wavelengths and Q factors as the increase of temperature for the SU-8 covered PhC nanobeam cavity and parabolic-beam PhC nanobeam cavity, respectively. (d) The wavelength difference between the two PhC nanobeam cavities as the increase of the ambient temperature. The temperature sensitivity is around 162.9 pm/°C by linear fitting.

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We have summarized the performances for different temperature sensors, as shown in Table 1. From this table, we can find that the sensitivity of the proposed temperature sensor is the highest comparing with other temperature sensors based on silicon resonators.

Table 1. Sensitivity, and Q Factor for Different Temperature Sensors.

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4. Conclusion

In this paper, we present the design, fabrication and characterization of a high sensitivity temperature sensor based on cascaded PhC nanobeam cavities. By combining the high positive TO coefficient of silicon with high negative TO coefficient of SU-8, the sensitivity for the proposed temperature sensor can be greatly improved. The experimental results show that the sensitivity is about 162.9 pm/°C, which is almost twice as high as that of conventional silicon based resonator temperature sensors. Since the sensitivity is enhanced, the proposed temperature sensor can be potentially used for an on-chip system combining with the integrated low resolution micro optical spectrometry such as an arrayed waveguide grating. Furthermore, the foot-print for the proposed high sensitivity temperature sensor can be very small, less than 4$\times$20${\text{μm}}^{\text{2}}$.