A silicon resonant pressure sensor based on thermal stresses matched structures

This paper introduced a silicon resonant pressure sensor based on thermal stress-matched structures to extend the operating temperature range. The sensor designed this time consists of an SOI wafer with a pressure-sensitive diaphragm for pressure sensing and two integrated resonators, a silicon wafer for vacuum packaging, and a glass wafer for additional stress isolation. The multilayer structures were bonded together to form a thermal stress-matched part to address the problem of temperature inflection points of conventional resonant pressure sensors within broad temperature zones. Finite element analyses optimized the sensor’s pressure- and temperature-sensitive characteristics. Micromachining based on eutectic and anodic bonding to fabricate sensor chips. Characterization results indicated the developed pressure sensor can work stably in a wide temperature range of -55∼125°C and has excellent fitting accuracy exceeding ±0.01% FS., which showed a better performance than previously reported counterparts.


Introduction
Pressure sensors based on MEMS technology offer several advantages, such as high accuracy, high resolution, and cost-effectiveness [1,2].These sensors found widespread applications in industrial control, aerospace, biomedicine, weather monitoring, and various other fields [3,4].
Resonant pressure sensors [5] worked in resonance principles of microresonators to measure pressure variations.Resonant pressure sensors provide outputs in the form of resonant frequencies, avoiding accuracy degradations due to analog-to-digital conversions and enhancing anti-interference capabilities.In comparison to piezoresistive [6] and capacitive sensors [7], resonant sensors offered attributes like high accuracy, high stability, and high long-term stability [8].
Conventional resonant pressure sensors, fabricated based on anodic bonding [9,10], silicon-tosilicon direct bonding [11], and eutectic bonding [12,13], show accuracies as high as 0.02%FS to 0.01%FS.Whereas, those sensors suffered compromised working temperature range (e.g.-55~125°C max), which limited the applications in industrial engines.The mismatches of thermal stress in multilayer sensor structures might be the main reasons for these limitations.
To solve this problem, a silicon resonant pressure sensor based on thermal stress-matched structures was proposed.The whole structures were designed by optimizing the temperature-sensing characteristics.Eventually, the sensor designed this time showed a high accuracy of ±0.01%FS in the temperature range of -55~125°C.Figure 1(d) shows that after simulation optimization of the sensor chip, the temperature sensitivity of the central resonator and the side resonator in the set temperature range -55~125℃ is 5.83Hz/kPa and 6.89Hz/kPa, respectively.The resonant frequencies of the two resonators showed monotonic temperature-sensitive characteristics, with the temperature increasing without any inflection points.Thus, a unique solution can be obtained in the temperature compensation algorithm based on the two frequencies of the optimized sensor.Firstly, clean a 4-inch SOI wafer using a standard wafer cleaning process (a i).The composite mask technology of silicon oxide and photoresist was used to etch pressure-sensitive film and lead holes on the base layer (a ii).Use DRIE to etch the designed device layers and HF to release the resonator (a iii).Sputter Cr/Au thin film on the silicon wafer surface and etch the cavity (a iv~vii).Ti metal is sputtered in the cavity as a getter to achieve high vacuum and gas-free in the vacuum cavity (a viii~ix).Then, the prepared SOI wafer and silicon cover plate were eutectic bonded.The glass layer was further bonded to the bonded substrate using anodic bonding (a x).Figures 2(b) and (c) show the sensor chip after the fabrications and the resonators under an infrared microscope.

Characterization
Figure 3(a) shows the sensor chip securely affixed to a Kovar pedestal through a combination of a PCB and silastic.The sensor electrodes are connected to the PCB pad using gold wires.
For testing purposes, the pressure sensor underwent evaluations in open-loop configurations within a testing setup, as depicted in Figure 3  The closed-loop circuit designed this time is shown in Figure 3(c).Amplifier I amplified the original resonator outputs, while Amplifier II reamplified the enhanced voltage signal.The signal was directed to the resonator's driving component to initiate vibrations.To ensure stable resonator outputs, an AGC circuit was integrated into the system.
Figure 4(a) shows the open-loop testing result of the center resonator, exhibiting the measured resonant frequency of 60.19kHz and the quality factor of higher than 20000.Closed-loop tests are shown in Figure 4 (b~d).The pressure and temperature sensitivities of the two resonators were ±41.5Hz/kPa and 6.5 Hz/°C, respectively, which matched the simulation results.

Conclusions
In this paper, a resonant pressure sensor based on thermal stress-matched structures was designed, and finite elements were simulated, fabricated, and tested.The thermal stressed matched sensor showed monotonic temperature sensitive characteristics in a wide temperature range of -55~125°C, which confirmed the high accuracy of ±0.01%within the wide working temperature range.
Figure 1(a) shows the composition of the resonant pressure sensor designed this time.It mainly includes SOI wafer, silicon cover plate, and glass layer.
Figure 2(a) shows the fabrication processes of the developed resonant pressure sensor.

Figure 2 .
Figure 2. Fabrication process and results.(a) Schematic of the fabrication flow chart (b) Images of fabricated sensor chips.(c) Resonators under infrared microscopy.Firstly, clean a 4-inch SOI wafer using a standard wafer cleaning process (a i).The composite mask technology of silicon oxide and photoresist was used to etch pressure-sensitive film and lead holes on the base layer (a ii).Use DRIE to etch the designed device layers and HF to release the resonator (a iii).Sputter Cr/Au thin film on the silicon wafer surface and etch the cavity (a iv~vii).Ti metal is sputtered in the cavity as a getter to achieve high vacuum and gas-free in the vacuum cavity (a viii~ix).Then, the prepared SOI wafer and silicon cover plate were eutectic bonded.The glass layer was (b).Specifically, an E5601B network analyzer was utilized to analyze resonant frequencies of Q factors and phase in the open-loop mode.A comprehensive performance test of the sensor was performed using a closed-loop circuit, pressure controller, and thermostat.

Figure 3 .
Figure 3. Package and test schematics.(a) of the developed sensor.(b) Open loop test system.(c) Closed-loop circuits and calibration test systems.The closed-loop circuit designed this time is shown in Figure3(c).Amplifier I amplified the original resonator outputs, while Amplifier II reamplified the enhanced voltage signal.The signal was directed to the resonator's driving component to initiate vibrations.To ensure stable resonator outputs, an AGC circuit was integrated into the system.Figure4(a)shows the open-loop testing result of the center resonator, exhibiting the measured resonant frequency of 60.19kHz and the quality factor of higher than 20000.Closed-loop tests are shown in Figure4(b~d).The pressure and temperature sensitivities of the two resonators were ±41.5Hz/kPa and 6.5 Hz/°C, respectively, which matched the simulation results.

Figure 4
Figure 4 Characterization results (a) open-loop test (b) pressure sensitivity (c) temperature sensitivity (d) comprehensive accuracy of the sensorFinally, the calibration test was carried out in the temperature and pressure ranges of -55~125℃ and 10~200kPa, and the results after polynomial fitting are shown in Figure4(d).The measurement error of the developed sensor is within 20Pa at -55~125 ℃ and 10~200kPa, which is better than ±0.01%FS.