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Abstract
In this paper, a high sensitivity pressure sensor employing an internal-external cavity Vernier effect is innovatively achieved with the microelectromechanical systems (MEMS) Fabry-Perot (FP) interferometer. The sensor consists of silicon cavity, vacuum cavity, and silicon-vacuum hybrid cavity, which is fabricated by direct bonding a silicon diaphragm with an etched cylindrical cavity and a silicon substrate. By rationally designing the optical lengths of the silicon cavity and silicon-vacuum hybrid cavity to match, the internal-external cavity Vernier effect will be generated. The proposed cascaded MEMS FP structure exhibits a pressure sensitivity of -1.028 nm/kPa by tracking the envelope evolution of the reflection spectrum, which is 58 times that of the silicon-vacuum hybrid cavity. What’s more, it owns a minimal temperature sensitivity of 0.041 nm/°C for the envelope spectrum. The MEMS FP sensor based on internal-external cavity Vernier effect as the promising candidate provides an essential guideline for high sensitivity pressure measurement under the characteristic of short FP sensing cavity length, which demonstrates the value to the research community.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Pressure monitoring plays an irreplaceable role in traditional engineering such as the health monitoring of large building structures [1], petrochemical industry [2], aerospace [3] as well as in the field of human health surveillance [4,5]. In recent years, optical fiber pressure sensing technology has attracted widespread attention, because it is more in line with the needs of modern sensing technology than traditional electromechanical or electronic sensors [6,7]. In addition, in some extreme or special circumstances, the unique advantages of optical fiber pressure sensors become more prominent [8,9]. It has to be mentioned that low-cost optical fiber pressure sensors can still be fabricated according to actual production requirements without losing sensing performance [10]. The researchers use pressure to modulate the intensity, phase, wavelength, and polarization state of the transmitted light in optical fiber, and to achieve real-time measurement of the pressure. Pressure sensors based on Fiber Bragg Grating (FBG) and Fabry-Perot (FP) are the most widely studied and applied at present [11,12]. Embedding FBG into a diaphragm usually made of polymer materials to achieve pressure measurement is a research hotspot in the field of FBG pressure sensing [12,13]. As for FP pressure sensing, FP interferometers with Vernier effect and its harmonics are good choices and have also been studied in depth to improve the measurement sensitivity [14–17]. The internal-external cavity Vernier effect also provides an alternative solution for dual-parameter measurement [18]. However, it has to be mentioned that most optical fiber FP sensors are made by pure manual methods. Relying on the production process with poor repeatability such as cutting and welding may lead to low production efficiency and poor consistency of the sensor, which seriously restricts its further engineering development.
With the continuous progress of microelectromechanical systems (MEMS) technology in recent years, the optical fiber FP pressure sensor delicately combined with MEMS technology has been studied and reported successively, injecting new vitality into the field of optical fiber sensing [19–21]. Optical fiber MEMS FP sensor not only has the unique advantages of optical fiber, but also characterizes high consistency and mass production. In terms of the pressure sensing performance, it is generally superior to traditional fiber optic sensors. High-fineness fiber FP high-temperature pressure sensor has been prepared by anodic bonding silicon diaphragm and Pyrex glass with the assistance of high-reflection film [20]. The experimental results have been confirmed with pressure sensitivity of 55.468 nm/MPa and temperature coefficient of 0.01859 nm/$^{\circ }$C at 25$\sim$300$^{\circ }$C. The designed all-silicon FP interferometer pressure sensor can eliminate the influence of thermal expansion mismatch induced stress and chemical reaction induced gas generation, thereby substantially improving the measurement accuracy [21]. The precise optical path differences (OPD) measurement results demodulated by fast Fourier transform combined with the peak-tracing method demonstrate the pressure sensitivity with 33.066 nm/kPa at 20$^{\circ }$C. Although the proposed sensor can achieve the effect of accurate pressure demodulation, it has strict requirements on the length of FP cavity, which is not conducive to the improvement of sensitivity in a certain sense.
In point of fact, when the length of the vacuum cavity is designed to be short, it has an excellent effect on improving pressure sensitivity. However, there will also exist new problems. In the full spectral range, the low-frequency interference fringes have a very low proportion in the frequency domain. Besides, the low interference frequency of the vacuum cavity after fast Fourier Transform makes it extremely close to the direct component fundamental frequency, which is difficult to extract efficiently. Therefore, the frequency domain filtering method is not suitable. In order to solve the nerve-wracking obstruction, the internal-external cavity Vernier effect is designed to achieve high-sensitive pressure measurements employing the vacuum cavity with short length. Meanwhile, by tracking the envelope evolution of the reflection spectrum, it can avoid the insufficiency of frequency domain filtering method. High-sensitive pressure measurement fields can benefit from this type of sensor, such as oil exploration [2], aerospace [3], and biomedical applications [4].
Herein, internal-external cavity Vernier effect employing MEMS technology is proposed and verified by theoretical analysis and experiment for the first time in the literature. We take advantages of the silicon-silicon direct bonding process to fabricate the MEMS FP pressure sensor, which consists of a silicon cavity with a length of 500 $\mathrm {\mu }$m, a vacuum cavity with a length of 30 $\mathrm {\mu }$m, and a silicon-vacuum hybrid cavity. Subsequently, the silicon cavity serving as the internal cavity and the silicon-vacuum hybrid cavity serving as the external cavity performs optical path length matching to form internal-external cavity Vernier effect. One of its advantages is that the pressure sensitivity of the vacuum cavity can be obtained without fast Fourier transform and filtering technology. The experimental results demonstrate that the sensor provides a high pressure sensitivity of -1.028 nm/kPa for envelope spectral evolution and a temperature sensitivity of 0.041 nm/$^{\circ }$C, which are consistent with theoretical simulation analysis.
2. Sensor configuration and the operation principle
The schematic diagram of pressure sensor based on internal-external cavity Vernier effect employing MEMS technology is shown in Fig. 1(a), which is simply formed by an all-silicon sensing chip, silicon capillary, and introduced single-mode fiber (SMF) fixed with UV Light Adhesives. The all-silicon sensor chip consists of a silicon diaphragm with an etched cylindrical cavity and a thick silicon substrate through direct silicon-silicon bonding to form a silicon cavity (FP1), a sealed vacuum cavity (FP2), and a silicon-vacuum hybrid cavity (FP3). The simplified model of optical interference is shown in Fig. 1(b). The light emitted by the broadband light source propagates to the sensor chip through the SMF, passing through FP1 composed of reflectors M1 and M2, and FP2 composed of reflectors M2 and M3, and then reflects. It is vital to note that the outer surface of the thin silicon diaphragm is roughened so that light is not reflected. The total reflection spectrum is generated by the superposition interference of the three reflectors. Due to the low reflectivity of the three reflectors, it can be considered low-finesse interference, therefore, the reflected light can be considered as the result of triple-beam interference [22], which can be expressed as Eq. (1):
The calculated reflection spectrum for the sensor is shown in Fig. 2(a). It can be seen that the whole interference spectrum contains two frequency envelopes. The high-frequency fringes are the interference signal introduced by the silicon cavity, while the low-frequency fringes are caused by the interference of the vacuum cavity. Its envelope function is expressed as Eq. (3):
where A represents the amplitude of the envelope function. The phase information of the envelope spectrum is only related to $\phi _2$, independent of the silicon cavity. As shown in Fig. 2(b), silicon cavity with different lengths has no effect on the envelope spectrum, but affects the number and position of high-frequency fringes within a period shown in the insertion. Fortunately, we are only concerned with the envelope spectrum evolution caused by the pressure.
Fig. 1. (a) Schematic diagram of pressure sensor; (b) The simplified model of optical interference with three reflectors.
Fig. 2. Reflection spectrum: (a) the internal-external cavity Vernier effect sensor; (b) the sensor with different silicon cavity lengths (The parameters in the simulation are listed as follows: $n_1$=3.42, $L_1$=500 $\mathrm {\mu }$m, $n_2$=1 and $L_2$=30 $\mathrm {\mu }$m.)
Subsequently, the sensitivity amplification mechanism of the internal-external cavity Vernier effect sensor is described in detail. The vacuum cavity pressure sensitivity is shown in Eq. (4):
The pressure sensitivity of silicon-vacuum hybrid cavity according to the reference [23] is described in Eq. (5):
In Eq. (4) and Eq. (5), m represents the interference order. Instead of the traditional Vernier effect of two single-cavity optical path matching, in this structure, it is the optical path matching of the silicon-vacuum hybrid cavity and the single silicon cavity. The amplification factor [24] can be rewritten as Eq. (6):
The sensitivity of the envelope (7) can be deduced from the Eq. (5) and (6):
The above analysis further proves that the sensitivity of the envelope obtained by the internal-external cavity Vernier effect is exactly equal to that of a single vacuum cavity. By the action of the internal-external cavity Vernier effect, the low sensitivity of the original silicon-vacuum hybrid cavity can be amplified to the same sensitivity as that of the vacuum cavity. When the external pressure acts on the thin silicon diaphragm, it will affect the length change of the vacuum cavity. Figs. 3(a)–3(d) show the simulation results of the spectrum evolution caused by the change of vacuum cavity length. The length of the vacuum cavity $L_2$ increases from 30 $\mathrm {\mu }$m to 30.1 $\mathrm {\mu }$m, and the spectral shift of the silicon-vacuum hybrid cavity is 0.09 nm, as shown in Fig. 3(b). However, the spectrum of a single vacuum cavity is shifted by 5.2 nm, which is equivalent to the envelope shift of the internal-external cavity Vernier effect, as shown in Fig. 3(c) and Fig. 3(d). It must be worth mentioning that the variation of the vacuum cavity length has little effect on the high-frequency fringes of the silicon cavity. Compared with the silicon-vacuum cavity, the amplification factor $M$ is 57.78, which is consistent with the theoretical calculation value 58 in Eq. (6).
Fig. 3. Calculated spectrum (a) single silicon cavity; (b) silicon-vacuum hybrid cavity; (c) single vacuum cavity (d) envelope of the internal-external cavity Vernier effect.
The diaphragm-type FP cavity sensor designed in this paper employing MEMS technology converts the change of pressure into the vacuum cavity length $L_2$ by the micro-deformation of the diaphragm, and then realizes the pressure sensing function. Therefore, it is significant to analyze the deformation characteristics of the silicon diaphragm, which determines the sensing parameters such as sensitivity and measurement range. Next, the performance of silicon diaphragm is described in detail. For a round diaphragm of uniform thickness with clamped edges, diaphragm deflection caused by applying longitudinal pressure $P$ combined with a lateral load can be given by Eq. (8) according to reference [25]:
where $R_0$ is the radius of the vacuum cavity, $r$ is the radius distance from the center of SMF to the center of the vacuum cavity, $\nu$ and $E$ are the Poisson’s ratio and Young’s modulus of silicon respectively, and $t$ is the effective thickness of the elastic silicon diaphragm. $P_R$ is the residual pressure in the vacuum cavity, and $\xi$ is the modified parameter of the diaphragm deformation caused by the interface stress. The silicon/silicon direct bonding technology avoids the effects of interfacial stresses such as anodic bonding between silicon diaphragm and Pyrex glass, which is one of the advantages of the designed sensor. Furthermore, the influence of residual pressure is ignored and it is considered a vacuum cavity. The original cavity length $h$ is affected by the thermal expansion effect of silicon and the strain caused by lateral pressure [26], as shown in Eq. (9): where $h_0$ represents the corrosion depth of the vacuum cavity, $\alpha$ represents the thermal expansion coefficient of the silicon diaphragm, $P_0$ and $T_0$ represent the initial pressure and temperature, respectively. The length of vacuum cavity $L_2$ is Eq. (10):According to Eq. (4) and Eqs. (9)-(11), the pressure sensitivity of vacuum cavity by tracking the envelope evolution of the reflection spectrum can be expressed as Eq. (11):
The temperature sensitivity of vacuum cavity by tracking the envelope evolution of the reflection spectrum can be expressed as Eq. (12):
According to Eqs. (11) and (12), we simulated pressure sensitivity and temperature sensitivity of the central position of the vacuum cavity, that is, $r=0$. As shown in Fig. 4(a), the pressure sensitivity results with $h_0$ = 30 $\mathrm {\mu }$m of the designed sensor at a pressure range of 10-300 kPa and a wavelength range of 1500-1600 nm can be obtained. In Fig. 4(b), the extremely low temperature sensitivity of the pressure sensor at the central wavelength of 1550 nm is demonstrated. For the internal-external cavity Vernier effect, according to the above theoretical analysis, the behavior of the vacuum cavity is consistent with the evolution of the envelope spectrum that we focus on in our experiment.
Fig. 4. (a) The simulated pressure sensitivity results in the pressure range of 10-300 kPa and the wavelength range of 1500-1600 nm; (b) Temperature sensitivity results at the central wavelength of 1550 nm.
3. Sensor fabrication and validation
The all-silicon sensor chip consists of two layers of silicon wafers, which can be etched on either surface to obtain FP cavity. A Silicon-on-Insulator (SOI) wafer with device layer of 70 $\mathrm {\mu }$m thickness and a double-sided polished silicon wafer with the thickness of 500 $\mathrm {\mu }$m are selected as raw materials. These wafers are both 4 inches in size and <100> in orientation. In order to reduce the influence of the interfacial bonding strength on the deformation repeatability of the diaphragm, the etching is performed on the surface of the SOI wafer. For more key fabrication steps of the production process, please refer to our previous research [21], and no redundant description is given here. It should be noted that the etching depth at this time is 30 $\mathrm {\mu }$m and the thickness of the top silicon diaphragm is 40 $\mathrm {\mu }$m.
The all-silicon chip pressure sensor realized by MEMS technology has the advantages of mass production and high consistency. It breaks through the limitation of fiber cutting, aligning and splicing for the optical fiber FP sensor, and the problem of a limited number of single processing is also solved. Therefore, it is of great significance to study the FP sensor employing MEMS technology to promote its application and commercialization in the engineering field. The sensor chip after dicing is shown in Fig. 5(a). The SMF is aligned to the center of the silicon substrate of a single all-silicon chip through a glass ferrule, and then fixed with UV Light Adhesives, thus, the complete sensor is fabricated, as shown in Fig. 5(b). The reflection spectrum of the as-prepared sensor is shown in Fig. 5(c), exhibiting the Free Spectral Range (FSR) of 43 nm for envelope spectrum. It is consistent with the simulation results. The extra-frequency fringes between the high-frequency and the low-frequency fringes are related to the incomplete roughness of the top silicon diaphragm. The amplitude-frequency curve after fast Fourier Transform is shown in Fig. 5(d). These peaks indicated by the arrows correspond to the frequency components of vacuum cavity, silicon cavity and silicon-vacuum hybrid cavity, respectively. Other frequencies with smaller peaks are formed by multiple interference of the beam and can be ignored. The low-frequency signal of the vacuum cavity is too close to the direct component fundamental frequency, so it is difficult to extract it well through the band-pass filtering in the frequency domain. The envelope peak tracing method based on internal-external cavity Vernier effect is suitable for the short vacuum cavity to improve pressure sensitivity.
Fig. 5. (a) The sensor chip after dicing; (b) MEMS pressure sensor; (c) The reflection spectrum of the sensor; (d) Fourier transform amplitude frequency curve.
4. Experiments and discussion
The MEMS FP pressure sensor based on internal-external cavity Vernier effect is placed in the air pressure chamber, which is placed in the thermostat. The high precision controller (Honeywell ADT-222C) is used to accurately adjust the pressure with the precision of 0.02 kPa. The thermostat (ESPEC SETH-A-040U) has the precision of 0.5$^{\circ }$C to control the ambient temperature. The light emitted from the broadband light source (BBS) enters the prepared pressure sensor through the optical fiber circulator, and the reflection spectrum is received by optical spectrum analyzer (Yokogawa AQ6370, OSA). The pressure measurement setup is shown in Fig. 6.
The pressure response of the novel configuration we proposed is tested in the pressure range of 95 to 127 kPa. Limited by the wavelength range of broadband light source, the number of envelope waveforms observable in the optical spectrum analyzer is also limited. Therefore, broadband light source with wider wavelength range is needed to increase the range of unambiguous pressure measurement. In fact, according to thin plate or small deflection theory, the deformation quantity of silicon diaphragm changes linearly with external pressure when the maximum deformation is less than 20$\%$ of its thickness. As a result, the sensor is designed to measure a maximum pressure of approximately 385 kPa. The envelope spectrum evolution of reflection spectrum is shown in Fig. 7. With increasing pressure, it can be observed that the envelope spectrum exhibits a blue-shift phenomenon, which is in line with the above theoretical analysis. This is due to the reduction in the length of the vacuum cavity as the pressure increases, resulting in a blue-shift of the spectrum. Bearing in mind that the interference order is avoided in the tracking of envelope spectrum in an FSR range.
Fig. 7. (a) and (b) Envelope spectrum evolution of the sensor while the pressure increases from 95 to 127 kPa.
The data analysis exhibits that a good linear relationship and a high pressure sensitivity of -1.028 nm/kPa are achieved by tracking the peak of envelope spectrum, as shown in Fig. 8. Tracing the envelope of the reflection spectrum in the case of short FP cavity length solves the problem that the vacuum cavity length is close to the direct component fundamental frequency and cannot be demodulated in the frequency domain. In the process of increasing and decreasing the pressure, each data point has been measured more than five times. The standard deviations are less than 0.014 nm, and the resolutions are better than 13.62 Pa. It can be observed that the pressure sensitivity obtained in the experiment is slightly lower than the theoretical analysis result. On the one hand, the reason can be considered that the optical fiber center is not aligned with the vacuum cavity center of the all-silicon pressure sensor in the process of preparing the sensor. On the other hand, the reasonable error may originate from the deviation between the actual value of the silicon diaphragm and the length of the vacuum cavity and the theoretical value. When compared with other pressure sensors obtained by the optical fiber microstructure, the MEMS FP pressure sensor based on the internal-external cavity Vernier effect designed in this paper shows its ultra-high sensitivity by tracking the evolution of the spectrum, as shown in Table 1 More importantly, it is worth mentioning that when compared with the same type of sensor, the all-silicon dual-cavity structure [21], the research achieves higher pressure sensitivity by designing a short FP cavity length. Since the Ref. [21] studies the pressure sensitivity through the change of the OPD, it needs to be converted into the wavelength domain. According to Eq. (10) and Ref. [21], the connection between the pressure sensitivity $Sen2,P$ obtained by tracking the evolution of the reflection spectrum and the pressure sensitivity $SenOPD$ obtained by the change of the OPD can be obtained under the condition of ignoring the residual air pressure:
Table 1. Comparison of MEMS FP pressure sensor based on the internal-external cavity Vernier effect in terms of Structure, Pressure Sensitivity and Temperature Sensitivity.
Obviously, the pressure sensitivity is greatly improved thanks to its short FP cavity length. At the same time, the problem of inability to demodulate in the case of short cavity length is also avoided, which provides an innovative solution for high-sensitivity pressure measurement.
The temperature sensitivity of the sensor is then verified at 110 kPa. In the range of 0-80$^{\circ }$C, the evolution of envelope spectrum is shown in Fig. 9(a). Fig. 9(b) shows the relationship between temperature and envelope peak shift during the heating and cooling process, showing a good linear relationship, respectively. The standard deviations are less than 4.24$\times 10^{-3}$ nm. It can be obtained that the temperature sensitivity is 0.041 nm/$^{\circ }$C by tracking the evolution of the reflection spectrum. In a sense, this is normal. Taking into account the effect of thermal expansion of residual air pressure in the vacuum cavity will lead to an unexpected variation in the length of the vacuum cavity, which is ignored in our theoretical analysis. Accordingly, the fabrication process of the MEMS sensor can be improved to reduce the effect of residual gas pressure to achieve lower temperature sensitivity. The temperature sensitivity of the envelope is that of the vacuum cavity, since the silicon cavity does not affect the sensitivity of the envelope. Even if the silicon cavity owns high temperature sensitivity, it will not affect the envelope spectrum, which lays the foundation for the realization of the temperature-immune pressure sensors.
Fig. 9. (a) Envelope spectrum evolution of the sensor while the temperature increases from 0 to 80$^{\circ }$C; (b) Envelope peak wavelength versus temperature
5. Conclusion
In conclusion, on the basis of improving the pressure sensitivity, the internal-external cavity Vernier effect is used to solve the disadvantage that the vacuum cavity cannot be effectively demodulated by the frequency domain filtering technology when the length of the vacuum cavity is very short. Moreover, the internal-external cavity Vernier effect is innovatively realized by all-silicon FP sensor employing MEMS technology. The feasibility of the all-silicon FP sensor as a pressure sensor is expounded in detail from the perspective of theoretical analysis and experimental verification. The experimental results demonstrate a pressure sensitivity of -1.028 nm/kPa for the envelope spectral evolution, and a lower temperature sensitivity of 0.041 nm/$^{\circ }$C. In addition, the sensors realized by MEMS technology have good consistency and can be mass-produced, laying the foundation for the realization of product industrialization. It can be seen that the proposed sensor has prospects and potential in high-sensitive pressure measurement.
Funding
National Natural Science Foundation of China (62035006, 62075160, U2006216); Tianjin Research Innovation Project for Postgraduate Students (No.2021YJSB159).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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