# Simultaneous Detection of Relative Humidity and Temperature Based on Silicon On-Chip Cascaded Photonic Crystal Nanobeam Cavities

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

_{1}) are covered with SU-8 cladding to increase the sensitivity ratio contrast between RH sensing and temperature sensing. The air-mode nanobeam cavities (cav

_{2}) are coated with a water-absorbing polyvinyl-alcohol (PVA) layer that converts the change in RH into a change in refractive index (RI) under different ambient RH levels, thereby inducing a wavelength shift. Due to the positive thermo-optic (TO) coefficient of silicon and the negative TO coefficient of SU-8 cladding, the wavelength responses take the form of a red shift for cav

_{2}and a blue shift for cav

_{1}as the ambient temperature increases. By using 3D finite-difference time-domain (3D-FDTD) simulations, we prove the feasibility of simultaneous sensing by monitoring a single output transmission spectrum and applying the sensor matrix. For cav

_{1}, the RH and temperature sensitivities are 0 pm/%RH and −37.9 pm/K, while those of cav

_{2}are −389.2 pm/%RH and 58.6 pm/K. The sensitivity ratios of temperature and RH are −1.5 and 0, respectively, which is the reason for designing two different resonant modes and also implies great potential for realizing dual-parameter sensing detection. In particular, it is also noteworthy that we demonstrate the ability of the dual-parameter sensor to resist external interference by using the dual wavelength matrix method. The maximum RH and temperature detection errors caused by the deviation of resonance wavelength 1 pm are only 0.006% RH and 0.026 K, which indicates that it achieves an excellent anti-interference ability. Furthermore, the structure is very compact, occupying only 32 μm × 4 μm (length × width). Hence, the proposed sensor shows promising prospects for compact lab-on-chip integrated sensor arrays and sensing with multiple parameters.

## 1. Introduction

## 2. Design and Optimization of PCNCs

_{1}and cav

_{2}, which are placed on a buried silica layer. The cav

_{1}and cav

_{2}are connected by a Y-junction power splitter and a power combiner [27]. The cav

_{1}is coated with an SU-8 cladding (light yellow region), while the cav

_{2}is coated with a layer of PVA upper cladding (light blue region). The RIs of the silica layer (n

_{silica}), silicon core (n

_{si}), dry PVA cladding (n

_{PVA}), and SU-8 cladding (n

_{SU-}

_{8}) are, respectively, 1.45, 3.46, 1.49, and 1.57 [2,26]. The corresponding thickness of each layer is set to 2 μm, 220 nm, 2 μm, and 2 μm, respectively.

_{1}) and Figure 2b for air-mode nanobeam cavities (cav

_{2}). When introducing the frequency defect into the photonic band gap (PBG), we chose the usual method—i.e., quadratically modulating the radius of the holes.

_{1}and cav

_{2}are given in Figure 3a,d. For cav

_{1}, the periodicity a

_{1}= 375 nm remained unchanged. The radius of the circular hole decreased parabolically from center r

_{center}= 170 nm to r

_{end}= 120 nm on both sides in the taper region, r

_{i}= r

_{center}+ (i − 1)

^{2}(r

_{end}− r

_{center})/(N

_{t}− 1)

^{2}, in which i increases from 1 to N

_{t}and N

_{t}represents the number of taper region holes. The hole radius remains unchanged as r

_{end}= 120 nm and N

_{m}represents the number of holes in the mirror region. For cav

_{2}, the periodicity a

_{2}= 360 nm was kept fixed. The radius of the circular hole increased parabolically from center r

_{center}= 100 nm to r

_{end}= 130 nm on both sides in the taper region. The radius of the mirror region was set as r

_{end}= 130 nm. The two nanobeam widths were 700 nm. Figure 3b,e show the corresponding major electric field distribution along the PCNCs for the x–y plane when z = 0. Apparently, the optical mode was strongly confined inside the high-index silicon core (cav

_{1}) and low-index PVA cladding (cav

_{2}) area, respectively, leading to different light–matter interactions. The E

_{y}distribution in the x-direction is shown more clearly in Figure 3c,f, and it can be found that the light field distribution of the two resonant cavities was indeed different, leading to significant differences in the wavelength shift responses to the variations in the RH and temperature of the external environment.

_{t}and N

_{m}were investigated in detail by a series of individual 3D-FDTD simulations in the hopes of achieving a higher-quality (Q)-factor and high-transmission PCNCs. In Figure 4a, the dependence of the Q-factor and the resonant wavelength on N

_{t}for cav

_{1}is illustrated. As shown, with the increase in N

_{t}, the Q-factor improved and the resonant wavelength moved to a shorter wavelength. In ure 4b, the relationship between the Q-factor and the transmission on N

_{m}for cav

_{1}when N

_{t}= 12 is presented. Obviously, the Q-factor continued to increase but the transmission decreased significantly with the increase in N

_{m}. Here, to save the simulation calculation time while keeping a reasonable footprint, we chose a high transmission of 0.62 but a relatively low Q-factor geometry with N

_{t}= 12, N

_{m}= 2 in the following simulation, and the Q-factor could reach 2.2 × 10

^{4}. For cav

_{2}, the dependence of the Q-factor and the resonant wavelength on N

_{t}is displayed in Figure 4c. The Q-factor improved and resonant wavelength moved to a longer wavelength as N

_{t}increased. The relationship of the Q-factor and transmission on Nm for cav

_{2}when N

_{t}= 12 is presented in Figure 4d. For the same reason, N

_{t}= 12 and N

_{m}= 2 were chosen, while the Q-factor reached 2.0 × 10

^{4}and the transmission was about 0.63.

## 3. Dual-Parameter Sensing for RH and Temperature

#### 3.1. Basis of Dual-Parameter Sensing

_{2}, while the wavelength responses are kept fixed for cav

_{1}, since the light field is mainly localized inside the silicon. As seen in Figure 7b, by extracting the simulated data within the broad range of 40% RH~90% RH, the resonant wavelength shows an approximately linear relationship with the RH level for cav

_{2}. The slope of linear fitting represents the RH sensitivity, S

_{RH,cav}

_{1}(defined as dλ

_{cav}

_{1}/dRH) and S

_{RH,cav}

_{2}(defined as dλ

_{cav}

_{2}/dRH), which were calculated as 0 pm/%RH and −389.2 pm/%RH, respectively. Figure 7c plots the transmission spectrum with ambient temperature in the range of 300 K~340 K at a fixed RH = 40% RH. Because of the high negative thermo-optic (TO) coefficient of the SU-8 cladding (∂n

_{su-8}/∂T = −3.5(10

^{−4}K

^{−1}) and the positive TO coefficient of silicon (∂n

_{si}/∂T = 1.8(10

^{−4}K

^{−1}), the resonant wavelength responses present a blue shift for cav

_{1}and a red shift for cav

_{2}when the temperature rises. Figure 7d shows the fitting results of the wavelength shift. The temperature sensitivities, S

_{T,cav}

_{1}(defined as dλ

_{cav}

_{1}/dT) and S

_{T,cav}

_{2}(defined as dλ

_{cav}

_{2}/dT), were fitted as −37.9 pm/K and 58.6 pm/K, respectively. Correspondingly, the sensitivity ratios for RH and temperature were calculated to be S

_{RH,cav}

_{2}/S

_{RH,cav}

_{1}= 0 and S

_{T,cav}

_{2}/S

_{T,cav}

_{1}= −1.5.

#### 3.2. Analysis of Dual-Parameter Sensing

_{1}, Δλ

_{2}) and the changes in RH (ΔRH) and temperature (ΔT) are described as Equation (2):

_{RH,T}| ≠ 0—Equation (3) has a unique solution, which means that the presented structure can be applied to sense RH and temperature simultaneously. Therefore, ΔRH and ΔT can be represented by Equation (3):

_{1}(Δλ

_{i}

_{1}) and cav

_{2}(Δλ

_{i}

_{2}), and Equation (3) could be modified as follows:

_{error}) and temperature error (ΔT

_{error}) caused by external interference can be represented by Equation (6):

_{RH,T}| can be calculated as: |M

_{RH,T}| = S

_{RH,cav}

_{1}S

_{T,cav}

_{2}− S

_{RH,cav}

_{2}S

_{T,cav}

_{1}. Moreover, the smaller the maximum value of ΔRH

_{error}(ΔRH

_{error;max}) and ΔT

_{error}(ΔT

_{error;max}), the stronger the anti-interference ability, that is, the better the stability of the dual-parameter sensor. Therefore, the maximum external interference scope (ξ

_{RH}, ξ

_{T}) was introduced to evaluate the anti-interference ability [26], which is computable with the following equations:

_{RH}and ξ

_{T}, the smaller the ΔRH

_{error;max}and ΔT

_{error;max}, and the stronger the immunity to interference. The ξ

_{RH}as well as the ξ

_{T}of the dual-sensor previously proposed are 0.006 and 0.026, respectively, suggesting that the maximum RH and temperature test errors caused by the deviation of resonant wavelength 1 pm are merely 0.006% RH and 0.026 K. Therefore, the sensor proposed is expected to provide an excellent level of immunity from interference and shows a good stability. For comparison purposes, a summary of other structures based on RH and temperature sensors is given in Table 1.

## 4. Conclusions

_{1}) to improve the sensitivity ratio contrast, while and the other is coated with a water-absorbing PVA layer as the sensing cladding to detect the variation in RH. For cav

_{1}, the RH and the temperature sensitivity are 0 pm/%RH and −37.9 pm/K, while those of cav

_{2}are −389.2 pm/%RH and 58.6 pm/K. Note that the sensitivity ratios of RH and temperature are 0 and −1.5, respectively, ensuring the feasibility of achieving simultaneous detection. In addition, the anti-interference ability of the sensor is analyzed by using the dual-wavelength matrix method under external interference in the detection process. Moreover, the compact size of the structure is only 32 μm × 4 μm (length × width). With its compact size, simple design, competitive sensitivities, and excellent anti-interference ability, our proposed sensor will contribute to the future of on-chip integrated sensing systems and multifunctional detection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the proposed SOI-based cascaded photonic crystal nanobeam cavities (PCNCs) dual-parameter sensor. The dielectric-mode nanobeam cavities (cav

_{1}) are covered by SU-8 cladding (light yellow region), while the air-mode nanobeam cavities (cav

_{2}) are coated with a layer of PVA upper cladding (light blue region).

**Figure 2.**TE band diagram (

**a**) for cav

_{1}(

**b**) for cav

_{2}of the two independent PCNCs. Photonic bandgaps (PGB) are represented by light green regions.

**Figure 3.**(

**a**,

**d**) Top-view schematics of cav

_{1}and cav

_{2}, respectively. The two PCNCs are formed by modulating the radius of the holes quadratically to introduce a frequency defect. cav

_{1}and cav

_{2}are both strictly symmetric about the center blue dashed line. (

**b**,

**e**) The major electromagnetic field distribution (x–y plane with z = 0). (

**c**,

**f**) E

_{y}distribution along this cavity in the x-direction.

**Figure 4.**The dependence of the Q-factor and resonant wavelength on the N

_{t}obtained by 3D-FDTD simulations (

**a**) for cav

_{1}and (

**c**) cav

_{2}. The relationship between r and transmission on N

_{m}obtained by 3D-FDTD simulations (

**b**) for cav

_{1}and (

**d**) for cav

_{2}.

**Figure 5.**(

**a**) The transmission spectra of the Y-junction power splitter and combiner. (

**b**) The structure of the power splitter (at the incident end) and combiner (at the exit end). (

**c**) The electric field distribution near 1550 nm at the x–y plane when z = 0.

**Figure 6.**(

**a**) Transmission spectrum of the cascaded PCNCs. Peak1 and peak2 show the basic modes of cav

_{1}and cav

_{2}. (

**b**,

**c**) The corresponding major electromagnetic field distribution of PCNCs (x–y plane with z = 0).

**Figure 7.**(

**a**) Transmission spectra under various RH changes. (

**b**) The linear fitting of corresponding resonant wavelength during the time when RH changes from 0% RH to 90% RH in 10% RH steps (T = 300 K). (

**c**) Transmission spectra under different temperature. (

**d**) Linear fitting of relevant resonant wavelength shift versus different temperatures, from 300–340 K with 10 K steps (RH = 40% RH).

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## Share and Cite

**MDPI and ACS Style**

Ye, L.; Liu, X.; Pei, D.; Peng, J.; Liu, S.; Guo, K.; Li, X.; Chen, X.; Zhang, X.; Yang, D.
Simultaneous Detection of Relative Humidity and Temperature Based on Silicon On-Chip Cascaded Photonic Crystal Nanobeam Cavities. *Crystals* **2021**, *11*, 1559.
https://doi.org/10.3390/cryst11121559

**AMA Style**

Ye L, Liu X, Pei D, Peng J, Liu S, Guo K, Li X, Chen X, Zhang X, Yang D.
Simultaneous Detection of Relative Humidity and Temperature Based on Silicon On-Chip Cascaded Photonic Crystal Nanobeam Cavities. *Crystals*. 2021; 11(12):1559.
https://doi.org/10.3390/cryst11121559

**Chicago/Turabian Style**

Ye, Lun, Xiao Liu, Danyang Pei, Jing Peng, Shuchang Liu, Kai Guo, Xiaogang Li, Xuanyu Chen, Xuan Zhang, and Daquan Yang.
2021. "Simultaneous Detection of Relative Humidity and Temperature Based on Silicon On-Chip Cascaded Photonic Crystal Nanobeam Cavities" *Crystals* 11, no. 12: 1559.
https://doi.org/10.3390/cryst11121559