Pressure sensing can provide rich interaction force information related to the object and is of significant importance in artificial intelligence input devices [1], electronic skin [2,3], organ system medical pressure monitoring [4], gas-pressure monitoring [5], and industry applications [6]. Piezo-resistivity-based pressure sensors making use of physic-electronic transduction are the most common sensor type because of their easy signal readout capability. Many micronanostructures, such as ultrathin gold nanowires [7] and urchin-like hollow carbon spheres [8], were proposed to enhance transduction efficiency. However, electronical sensors still suffer electromagnetic interference, a narrow working temperature range, a small pressure measurement range, and large temperature cross-sensitivity, which make them unusable in a harsh environment. For example, pressure sensing at a high-temperature compressor can play an important role in aeroengine investigation and its active control [9–11]. The compressor exit temperatures are on the order of ∼700°C, which prevents the use of traditional electronical sensors without a complex cooling method. In addition, temperature interference is a nerve-wracking obstruction for sensor performance, since the large and unstable temperature cross-sensitive characteristics of the sensor will deteriorate the measurement even if the sensor survives at high temperatures.

In recent years, fiber-optic pressure sensors fabricated by employing the microelectromechanical systems (MEMS) technology [12–16] have attracted a great deal of attention because of the feasibility of mass production and high consistency. Anodic bonding technology is the usual way to form a sealed vacuum Fabry–Perot (F–P) microcavity between glass and silicon. The pressure sensitivity can be easily adjusted by designing the thickness of elastic silicon diaphragm and the microcavity diameter. Due to the microcavity diameter of MEMS, fiber-optic pressure sensors are not limited to the diameter of the optical fiber [17]; a ∼kPa pressure sensitivity can be easily reached. However, in a wide temperature range, temperature cross-sensitivity is inevitably a severe problem. The temperature cross-sensitivity mainly arises for two reasons. One is the residual gas trapped in the microcavity. Although the anodic bonding process is carried out under a high vacuum condition, some gas will be produced and trapped in the microcavity because of the chemical reaction essence of the anodic bonding process. The residual gas will shrink or expand with temperature change and produce an undesirable force on the inside face of the pressure-sensing diaphragm. The other reason is the thermal stress at the interface between silicon and glass. The thermal stress caused by the thermal expansion mismatch between different materials will cause nonlinear variation of temperature cross-sensitivity. The two factors together lead to worse temperature-related stability and therefore deteriorate the measurement precision. The problem can be relaxed with Au/Au thermal-compression bonding to some degree by reducing gas production and relieving thermal expansion mismatch with an Au film as a buffer layer [14].

Using real-time temperature measurement to compensate for the pressure-temperature cross-error is an alternative method. For example, a hybrid fiber-optic Fabry–Perot interferometer (FPI) fabricated by double-sided anodic bonding of a through-hole-array-structured glass wafer and two silicon wafers for simultaneous pressure and temperature measurement was proposed [15], or temperature information was obtained by fluorescent material glued near the anodic bonding structure [16]. Nevertheless, the degree of temperature compensation effectiveness will depend largely on the temperature stability of the sensor. The compensation may fail in high-precision measurement when the thermal stress has not been eliminated completely. Therefore, reducing temperature cross response is an essential issue to be solved in order to improve pressure measurement accuracy under a wide dynamic temperature range.

In this paper, an all-silicon dual-cavity fiber-optic pressure sensor is proposed and demonstrated. A silicon substrate and a silicon diaphragm with etched cylindrical cavity are bonded together by silicon/silicon direct bonding to form a sealed vacuum F–P cavity for pressure sensing. The vacuum cavity and the silicon substrate act as two microcavities in series connection. We theoretically analyze the effect of thermal stress and residual gas pressure on pressure measurement, which indicates that the low-temperature cross-sensitivity can fundamentally improve the accuracy of pressure measurement over a wide temperature range. The all-silicon structure fabricated with direct bonding solves the problem of interface thermal mismatch, gas building up in the sealed microcavity, and additional reflective coating. The experiment results show that the pressure sensitivity is of ∼33.034nm/kPa under air pressure ranging from 20 to 280 kPa. The pressure-temperature cross-sensitivity of the proposed pressure sensor is as low as ∼5.96Pa/°C, which verifies that the thermal stress and residual gas issues have been overcome. To our best knowledge, this sensor presents the lowest pressure-temperature cross-sensitivity among the optical fiber pressure sensors with the capability of surviving high temperatures up to 700°C. Moreover, the silicon microcavity can be used for simultaneous temperature sensing, which is also a useful input and can be used for the further temperature compensation process. The optical fiber pressure sensor is promising for a wide range of applications, especially for pressure detection under a wide temperature range.

With our proposed all-silicon structure, there is almost no thermal stress at the bonding interface. Thus, Eqs. (10) and (11) will be simplified to constant values as A and B, SP=−2(sd+1−2ν1E1h0)=A,STc=2(α1h0+sdPR0T0)=B.(12)The pressure-temperature cross-sensitivity of FP1 is calculated as STc/SP, which is mainly induced by the residual gas pressure PR0. Owing to the silicon direct bonding technique, the gas production is avoided during the bonding process, and hence the residual gas will be reduced. Thus, the all-silicon fiber-optic pressure sensor provides an approach to improving the pressure measurement accuracy from the root of the material and fabrication technique.

FP2 can be used for temperature sensing because silicon owns a high thermo-optic coefficient and heat conductivity coefficient. Similarly, the relationship between OPD of FP2 and the change of pressure and temperature can be written as OPD2=2L20[1+α2(T−T0)][1−1−2ν2E2(P−P0)]⁢[n20+β(T−T0)],(13)where β refers to the thermo-optic coefficient of silicon, and L20 and n20 refer to the original cavity length and refractive index of silicon at T0. Actually, over a large temperature range, β is not a constant with temperature [21]. It is approximately linear with temperature as β=β0+κ(T−T0), where β0 is the thermo-optic coefficient at T0, and κ=1.82×10−7. Ignoring the part α2β(T−T0)2 in Eq. (13), we have OPD2=2L20[1−1−2ν2E2(P−P0)][n20+(β0+α2n20)(T−T0)+κ(T−T0)2].(14)

The pressure cross-sensitivity SPc of FP2 can be expressed as SPc=∂OPD2∂P=−2L201−2ν2E2[n20+(β0+α2n20)(T−T0)+κ(T−T0)2].(15)The maximum of SPc is calculated to be −7.492×10−3nm/kPa when the temperature changes 700°C. The effect of pressure on OPD2 is only 7.492 nm under 1 MPa pressure variation (according to the parameters of FP2 we describe in the following fabrication section), and hence is negligible compared to the temperature sensitivity of FP2 (111.613 nm/°C). Therefore, Eq. (14) can be simplified as OPD2=2L20[n20+(β0+α2n20)(T−T0)+κ(T−T0)2].(16)

The temperature sensitivity ST can be expressed as $$\begin{gathered} ST=∂OPD2∂T=2L20[β0+α2n20+2κ(T−T0)] \\ =C+2D(T−T0), \end{gathered}$$(17)where C=2L20(β0+α2n20), and D=2L20κ.

According to Eqs. (12) and (17), the variation of OPDs corresponding to FP1 and FP2 can be expressed as a matrix to realize pressure and temperature simultaneous measurement, [ΔOPD1ΔOPD2]=[AB0C][ΔPΔT]+[0D(ΔT)2].(18)It is worth noting that besides passive temperature sensing, the silicon cavity can also be used as an active temperature optical-control medium. 980 nm light can be absorbed by the silicon cavity to heat the sensor [22], which is useful for the sensor under a low-temperature environment to avoid ice formation, or deicing in aviation applications.

The all-silicon sensing chip is fabricated by employing MEMS technology. A silicon-on-insulator (SOI) wafer with a device layer of 100±0.5μm thickness and a double-sided polished silicon wafer with 300±10μm thickness are chosen as the materials. The size and the orientation of the two wafers are both 100 mm and ⟨100⟩.

According to the thin plate or small deflection theory [19], the maximum deformation of silicon diaphragm should be less than 20% of its thickness to ensure that the deformation changes linearly with external pressure. Thus, the maximum measurement pressure is about 385 kPa. The experiment was carried out when the temperature of the thermostat was stabled at −20°C, 0°C, 20°C, 40°C, and 60°C. At each temperature, the pressure was controlled to increase from 20 to 280 kPa, with a step of 20 kPa.

On the other hand, as Fig. 8(b) shows, the OPD of FP2 remains almost unchanged with pressure increasing to 280 kPa, which demonstrates that the silicon microcavity FP2 is insensitive to pressure.

From Fig. 10(a), it can be observed that OPD of the vacuum cavity FP1 shifts with temperature linearly with a low-temperature cross-sensitivity of 0.256 nm/°C and 0.261 nm/°C, corresponding to the heating and cooling process, respectively, which is a little smaller than the theoretical value. This is because Young’s modulus of silicon decreases with increasing temperature. Since the experiment was carried out over a large temperature range, the silicon diaphragm deformation increased under the same external pressure. On the other hand, the lower linearity and coincidence in Fig. 10(a) further verified the complication of temperature interference, such as the tiny difference of two silicon wafer materials and tiny gas existence.

In Fig. 10(b), the OPD response of the silicon cavity FP2 exhibits a quadratic relation with temperature, with no hysteresis. The fittings to the heating and cooling data give the first-order coefficients of 121.670 nm/°C and 124.185 nm/°C, respectively, and the second-order coefficients of 1.05822×10−4nm/(°C)2 and 1.06166×10−4nm/(°C)2, respectively, which agree well with the theoretical value of 111.660 nm/°C and 1.09320×10−4nm/(°C)2.

In summary, from the discussion above, the sensor shows the ultralow temperature cross-sensitivity and excellent stability during the high-temperature cycle experiment. Pressure and temperature can be simultaneously obtained by solving the following matrix equation:[ΔOPD1ΔOPD2]=[−33.0340.1970122.928][ΔPΔT]+[00.105994×(ΔT)2],(19)where ΔOPD1 and ΔOPD2 are in the unit of nanometers, and the units of ΔP and ΔT are in kilopascals and °C, respectively. The values of A, B, C, and D are the average of the experiment data. What is more, as shown in Table 1, compared with the other reported fiber-optic pressure sensors, the pressure sensor proposed in this paper not only has a larger pressure sensitivity but also exhibits an ultralow pressure-temperature cross-sensitivity of ∼5.96Pa/°C. The high-pressure sensitivity and low-pressure temperature cross-sensitivity make the optical pressure sensor attractive for high-temperature pressure measurement applications, such as compressors of aeroengines.Table 1.

Comparison of the Proposed Fiber-Optic Pressure Sensors in Terms of Structure, Pressure Sensitivity, Temperature Cross-Sensitivity, and Pressure-Temperature Cross-Sensitivity

In this paper, we theoretically analyzed the factors that influence the temperature cross-sensitivity of a microcavity pressure sensor. An all-silicon dual-cavity fiber-optic pressure sensor was successfully fabricated. The sensing chip comprises two silicon layers, which are bonded together by direct bonding. A sealed vacuum F–P microcavity was formed between the silicon substrate and the silicon diaphragm for pressure sensing. The silicon substrate acts as the second solid microcavity for temperature sensing. The sensor can eliminate the influence of thermal stress and residual pressure greatly. The experiment results showed that the ultralow pressure-temperature cross-sensitivity of ∼5.96Pa/°C was successfully obtained. In addition, the sensor can survive a temperature of up to 700°C. Therefore, the proposed fiber-optic pressure sensor provides an excellent candidate for pressure measurement in harsh and complicated environments.