Introduction

Micro-electromechanical systems (MEMS) sensors are widely used in various industries such as industrial production and healthcare1,2,3,4. With advantages like high performance and compact size, they have become essential components in modern engineering. In many harsh industrial applications, such as aerospace and turbine engine chambers5, aircraft fuel systems6, automotive combustion chambers7, and oil and gas exploration wells8, it is essential to continuously monitor the internal pressure under harsh conditions to ensure the structural integrity and health of these systems. Therefore, there is an urgent need for MEMS-based pressure sensors that exhibit high temperature and vibration robustness to monitor dynamic pressure within these industrial systems, thereby facilitating effective health management and system optimization9.

At present, pressure sensors based on the piezoresistive effect are more suitable for pressure monitoring in harsh environments than other types of sensors, such as capacitive10, fiber optic8, and piezoelectric11 sensors, due to the directness and high linearity of their output voltage or current signals, the simplicity of their acquisition and processing circuits, and the feasibility of achieving high-reliability micro-packaging12,13. Extensive research has been conducted on piezoresistive pressure sensors for harsh environments. Among these, silicon-on-insulator (SOI) sensors14,15, which utilize a SiO2 dielectric layer, and silicon-on-sapphire (SOS) sensors16, which employ an Al2O3 dielectric layer, have shown leakage currents reduced by three orders of magnitude compared to Si PN junctions. However, due to differences in thermal expansion coefficients, these components can generate significant thermal stress at high temperatures, limiting the operating temperature of these sensors to below 400 °C17.

In recent years, silicon carbide (SiC) semiconductors have been widely studied in fields, such as sensors18,19,20,21,22, radiation detectors23, resonators24, power semiconductor devices, and integrated circuits25 due to their almost inert chemical properties, superior thermal mechanical properties, high breakdown voltage, and wide bandgap electronic properties26. SiC polytypes including 3C-SiC, 4H-SiC, and 6H-SiC with certain doping concentrations exhibit obvious piezoresistive effect27,28,29,30. Therefore, constructing typical epitaxial SiC PN junctions to build sandwich structures has gradually become an effective pressure-sensing solution in extreme temperature environments31. Compared to 3C-SiC sensors, 4H and 6H-SiC sensors can operate at extreme temperatures due to the use of bulk SiC substrates that are homogeneous with the P and N-type SiC epitaxial films to build “all-SiC”, avoiding thermal expansion mismatch between heterogeneous materials32,33,34,35,36. However, there are still challenges in achieving high accuracy (high linearity, good repeatability, and low hysteresis) in all-SiC dynamic pressure sensors in harsh environments with extreme temperature and vibration coupling. Okojie et al. developed a 6H-SiC pressure sensor with a working temperature of 600 °C, which features a circular diaphragm and four piezoresistors arranged radially to form a Wheatstone bridge, achieving a nonlinearity of −0.27% FSO37. Shang et al. proposed a 4H-SiC pressure sensor with piezoresistors arranged along the circumference of a circular diaphragm, achieving an accuracy of 0.29% FSO and a maximum test temperature of 250 °C38. Our group proposed a 4H-SiC pressure sensor prepared by femtosecond laser processing with a hysteresis of 0.17%/FSO, nonlinearity of 0.20%/FS, resonant frequency of 60.11 kHz, and operating temperature of 350 °C39. There are also some studies to improve the sensor’s stability by improving the packaging40.

This paper presents the MEMS 4H-SiC piezoresistive pressure sensor family for harsh environments. These sensors leverage the piezoresistive coefficients of 2.4 × 10–11 and –1.0 × 10–11 Pa–1 of heavily doped N-type 4H-SiC with a doping concentration of 2 × 1019 cm−3, which is reported for the first time. The sensor family comprises eight distinct design configurations, each featuring a piezoresistor arrangement optimized to match the stress distribution characteristics of square or circular elastic diaphragms. The diaphragms are fabricated through a combination of mechanical grinding and deep reactive ion etching. To address the issue of fatigue failure typically associated with traditional wire bonding under high-temperature conditions, we propose a novel leadless packaging solution for the 4H-SiC pressure sensor. This advanced design allows the sensor to function reliably within a temperature range of −50 to 600 °C. Furthermore, the stability of the 4H-SiC pressure sensor is rigorously validated through a high-temperature random vibration coupling test. The family design and preparation of the 4H-SiC piezoresistive sensors provide a systematic solution for pressure sensing in harsh environments.

Design and fabrication

Piezoresistive effect of heavily doped N-type 4H-SiC

For SiC crystals, those with a doping concentration level below 1017 cm−3 are usually referred to as low doping concentration, those with a doping concentration level of 1018 cm−3 are referred to as medium doping concentration, and those above 1019 cm−3 are referred to as high doping concentration. Due to limitations in epitaxial processes, the doping concentration of 4H-SiC generally does not exceed 1020 cm−3. The doping concentration of 4H-SiC used for piezoresistive devices is generally between 5 × 1018 and 1 × 1019 cm−3. We used an N-type 4H-SiC with a high doping concentration of 2.0 × 1019 cm−3 as the functional layer providing the piezoresistive effect. The doping depth of this N-type 4H-SiC layer is 1.95 μm, and the measurement results were obtained through dynamic secondary ion mass spectrometry (D-SIMS), as shown in Fig. 1a. Then there is a P + 4H-SiC doped with aluminum, which can form an effective PN junction isolation with N-type SiC to suppress the leakage current of the device at high temperatures. We prepared 4H-SiC bending beams to test the piezoresistive effect of the N + 4H-SiC, as shown in Fig. 1b. Preparation of 4H-SiC bending beams is compatible with the process of the pressure chips, which is described below. The setup for testing the piezoresistive effect of 4H-SiC is shown in Fig. 1c. The longitudinal and transverse resistances of Rl and Rt are prepared from N + 4H-SiC, which are used to measure the longitudinal and transverse piezoresistive coefficients of π‘11 and π‘12, respectively. Firstly, the 4H-SiC’s elastic modulus (E) is measured using a three-point bending method in Fig. 1d by

$$E=\frac{F{L}_{1}^{3}}{4B{h}^{3}\varDelta y}$$
(1)

where F is the applied force, Δy is the deformation displacement, L1 is the beam effective length between the two support ends, B is the beam width, h is the beam thickness. The elastic modulus is 492.60 GPa according to Eq. (1). Then, the piezoresistive effect of 4H-SiC is tested by the cantilever beam method, as shown in Fig.1e. The effective length for free deflection of the cantilever beam is 30 mm. Given that the height of the piezoresistor (~2 μm) is significantly smaller than the thickness of the sample, the strain experienced by the piezoresistor can be approximated as the surface strain at the location of the piezoresistor, which is calculable as follows:

$$\varepsilon =\frac{6F{L}_{2}}{EB{h}^{2}}$$
(2)

where L2 is the length of the free deflection end of the cantilever beam. The force-displacement testing curve of the 4H-SiC bending beam is recorded in Fig. 1f. The strain results calculated according to Eq. (2) can be verified through the finite element analysis of COMSOL. As shown in Fig. 1g, the FEA result of the strain at the resistance location is only 3.4% different from the calculated result of Eq. (2). The resistance changes of Rl and Rt are measured respectively, and the relationships between the resistance change rates and the corresponding strain are plotted in Fig. 1f, g. GF is generally used to quantify the piezoresistive effect, which is defined as the fractional alteration in the resistance per unit strain: GF = ∂R/R/ε. The applied stress/strain changes 4H-SiC’s carrier density and mobility, resulting in a distinct change in resistivity. The resistivity relative change (∂ρ/ρ) can also be presented as a function of the induced stress (σ), using a parameter defined piezoresistive coefficient (π): ∂R/R = ∂ρ/ρ = πσ. MEMS diaphragms are typically used to eliminate out-of-plane stress components. Therefore, the resistivity change is usually written as the sum of the longitudinal and transverse effects

$$\frac{\partial R}{R}=\pi {\text{'}}_{11}{\sigma }_{l}+\pi {\text{'}}_{12}{\sigma }_{t}$$
(3)

where σl is longitudinal stress, which is parallel to the current direction, σt is transverse stress, which is perpendicular to the current direction, π‘11 and π‘12 are the longitudinal and transverse piezoresistive coefficient, respectively. So the transverse GFt and longitudinal GFl of the 4H-SiC sample are calculated to be 11.6 and −4.6, respectively. Accordingly, π‘12 and π‘11 are 2.4 × 10−11 and −1.0 × 10−11 Pa−1, respectively. This is the first report on the piezoresistive coefficient test results of N-type 4H-SiC with a high doping density of 2 × 1019 cm−3, providing a theoretical basis for the design of highly doped SiC piezoresistive devices.

Fig. 1: 4H-SiC piezoresistive coefficient test.
Fig. 1: 4H-SiC piezoresistive coefficient test.
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a D-SIMS of the concentration and depth of nitrogen doping in N-type 4H-SiC epitaxial layer. b Fabricated 4H-SiC beams. c Setup for testing 4H-SiC’s piezoresistive effect. d Three-point bending test for 4H-SiC’s elastic modulus. e Cantilever beam bending test for 4H-SiC’s piezoresistive coefficients. f Force–displacement curve of the tested 4H-SiC bending beam. g Strain versus displacement of the 4H-SiC beam calculated by COMSOL. The relationships between the resistance change rate of h longitudinal piezoresistor Rl and i transverse piezoresistor Rt and their corresponding strains. Insets: optical microscope images of the longitudinal and transverse piezoresistors

Design of 4H-SiC pressure sensor family

The typical structure and exploded view of a 4H-SiC pressure sensor is shown in Fig. 2a. Four N-type 4H-SiC piezoresistors are connected in series to form a semi-open loop Wheatstone bridge on the 4H-SiC diaphragm. C-type and E-type diaphragm structures are typical elastic-sensitive components of pressure sensors. Compared to other combination forms of sensor elastic diaphragms with surface crossbeams and back islands41,42,43, circular and square flat diaphragms are the preferred elastic deformation structures for SiC pressure sensors due to their simplicity and ease of manufacturing44. Assuming that the diameter/length of the circular/square diaphragm is 2a and the thickness is t. A polar coordinate w(r) is used to represent the radial and tangential stress σr and στ at any point of a circular diaphragm as

$$\left\{\begin{array}{l}{\sigma }_{{\rm {r}}}=\frac{3p}{8{t}^{2}}[{a}^{2}(1+\mu )-{r}^{2}(3+\mu )]\\ {\sigma }_{\mathrm {{\tau }}}=\frac{3p}{8{t}^{2}}[{a}^{2}(1+\mu )-{r}^{2}(1+3\mu )]\end{array}\right.$$
(4)

where p is pressure, μ is Poisson’s ratio, h is the diaphragm thickness. A cartesian coordinate w(x, y) is used to represent the stress component σx along x-axis and the component σy along y-axis at any point of a square diaphragm as

$$\left\{\begin{array}{l}{\sigma }_{x}=-0.51p\frac{{a}^{2}}{{h}^{2}}[{(1-{(y/a)}^{2})}^{2}(1-3{(x/a)}^{2})+\mu {(1-{(x/a)}^{2})}^{2}(1-3{(y/a)}^{2})]\\ {\sigma }_{y}=-0.51p\frac{{a}^{2}}{{h}^{2}}[{(1-{(x/a)}^{2})}^{2}(1-3{(y/a)}^{2})+\mu {(1-{(y/a)}^{2})}^{2}(1-3{(x/a)}^{2})]\end{array}\right.$$
(5)
Fig. 2: Design of 4H-SiC pressure sensor family.
Fig. 2: Design of 4H-SiC pressure sensor family.
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a Schematic diagram of a typical 4H-SiC pressure sensor and its explosion view. b Normalized stress distribution calculated from COMSOL of the circular and square diaphragms and their stress distribution curves along the diaphragm centerlines. c Eight sensor schemes with circular and square diaphragms and different piezoresistors configurations. d Dimensions of SiC piezoresistors of R1, R2, R3, R4. e Position parameters of SiC piezoresistors of d1, d2, d3

The normalized stress distribution calculated from COMSOL of the 4H-SiC circular and square diaphragms and their stress distribution curves along the centerlines are shown in Fig. 2b. The 4H-SiC pressure sensor family includes eight design schemes of A–H, depending on the diaphragm shape, piezoresistor arrangement and size, as show in Fig. 2c. Figure 2d shows the dimensions of the single-folded and multiple-folded SiC piezoresistors in the sensor design schemes. For a circular diaphragm, both σr and στ are axisymmetrically distributed with respect to the center line of the circular diaphragm. On the same path, the variation trend of σr is greater than that of στ. σr is greater than στ at the circumferential boundary of the diaphragm, and σr is equal to στ at the center of the diaphragm. This feature indicates that the piezoresistors on the circular diaphragm can be arranged around the diaphragm circumference edge, as shown in schemes A and E. The absolute stress difference of this scheme is large, which is conducive to the differential output of the Wheatstone bridge. In addition, the four piezoresistors arranged in schemes B and F deform radially, resulting in good consistency. For a square diaphragm, the stress components σx and σy are distributed axisymmetrically with respect to the center line. On the same path, the change trend of σx is greater than that of σy. The absolute value of σx is greater than the absolute value of σy at the boundary points of the left and right sides of the square diaphragm, and σx is equal to σy at the center of the square diaphragm. This feature indicates that the piezoresistors on the square diaphragm can be arranged at the midpoint of the four sides of the square diaphragm, where the stress distribution is more concentrated, as shown in scheme C. There is also a stress concentration at the square diaphragm center, so the sensor scheme D can also have differential output. Given that the piezoresistive effect of silicon carbide is weaker than that of silicon, optimizing the position parameters of the piezoresistors is crucial to achieving high sensitivity in SiC pressure sensors. There are three position parameters d1, d2 and d3, which can configure the relative position of the piezoresistors, as shown in Fig. 2e. The relationships between the full scale outputs of the eight sensors and the three position parameters d1, d2 and d3 are obtained by parameterized calculation, as shown in Fig. 3a. The optimal position parameters and their corresponding sensor output sensitivities are shown in Table 1. Figure 3b illustrates the distribution of von Mises stress and the electric field on the eight sensors under a maximum pressure of 5 MPa, as obtained through COMSOL simulations. Figure 3c presents enlarged views of the electric potential and surface current density of the SiC piezoresistors in schemes G.

Fig. 3: Finite element analysis of 4H-SiC pressure sensor chip.
Fig. 3: Finite element analysis of 4H-SiC pressure sensor chip.
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a Parameterized calculation of position parameters d1, d2 and d3 for obtaining optimized sensor sensitivity. b The coupled distribution results of the von mises stress and electric potential of the eight sensors simulated by COMSOL. c Enlarged views of SiC piezoresistors in scheme G. The white arrow represents the direction of surface current density

Table 1 Optimized position parameters and corresponding sensitivities of 4H-SiC pressure sensor family calculated by COMSOL
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Fabrication of 4H-SiC pressure sensor chips

The SiC pressure sensors are prepared based on a 4-in. (0001) 4H-SiC wafer with a thickness of 350 µm. The fabrication flow of a four-mask process is shown in Fig. 4a. In step I, the P+ and N + 4H-SiC epitaxial layers are deposited on the 4H-SiC substrate by low-pressure chemical vapor deposition (LPCVD) respectively. In step II, the substrate thickness is reduced to 150 µm by mechanical grinding. In step III, Cr/Au seed layer deposition and Ni metal micro-electroplating are used to form an etching mask with a micron thickness. The 80 µm-thick SiC elastic diaphragms are prepared through DRIE. The scanning electron microscope (SEM) image of the etched sidewall morphology is shown in Fig. 4b. In step IV, after magnetron sputtering of the Ni mask, an inductively coupled plasma (ICP) etching is used to achieve the patterning of N-type 4H-SiC embossed piezoresistors. In step V, depositing 400 nm SiO2 by plasma-enhanced chemical vapor deposition (PECVD) and corrode the contact windows by BOE, where the contact layers of Ni (50 nm)/W (100 nm) are patterned by the magnetron sputtering and lift-off. The metallization process is completed by rapid thermal annealing at 1000 °C to establish the ohmic contact with the SiC piezoresistors. According to the transmission line model, the square resistance Rs is 124.28 Ω/square. In step VI, TaSi2 (400 nm)/Pt (100 nm) are successively deposited and form a diffusion barrier layer on the contact layer to delay the intrusion of oxygen atoms into the contact. The metal lead layer of Ti (400 nm)/Pt (100 nm) is deposited to build the Wheatstone bridge. The sensor Wheatstone bridge and its ohmic contact regions are shown in Fig. 4c. Figure 4d indicates the prepared 4H-SiC pressure sensor wafer. Finally, the 4H-SiC pressure sensor is divided by laser cutting. The photos of the sensor family are described in Fig. 4e. Each sensor chip’s size is 4.5 × 4.5 mm.

Fig. 4: Fabrication processes and the 4H-SiC pressure sensor chip.
Fig. 4: Fabrication processes and the 4H-SiC pressure sensor chip.
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a Fabrication process flow for 4H-SiC pressure sensors. b SEM of the etched sidewall morphology of SiC pressure sensor back cavity. c The sensor Wheatstone bridge and its enlarged view of ohmic contact regions. d The prepared 4H-SiC pressure sensor wafer. e Photographs of the 4H-SiC pressure sensor family

Leadless package of 4H-SiC pressure sensor

Wire bonding is the mainstream method for packaging microelectronic devices. The devices are usually attached to the packages by inorganic epoxy adhesive. However, the de-soldering temperature of the lead solder joint and the operating temperature of the inorganic epoxy adhesive usually do not exceed 350 °C, which limits the high-temperature advantages of the SiC sensors. We propose a leadless package to overcome the temperature limitations mentioned above, as shown in Fig. 5a. In the leadless package structure, we designed a SiC shim that is homogenous with the SiC sensor chip and an AlN header with a thermal expansion coefficient similar to that of SiC, to reduce thermal stress between the connecting materials. The 4H-SiC shim and AlN header each feature a central through-hole to accommodate sensor diaphragm deflection, as well as five through-holes aligned with the sensor’s metallized pads for electrical contacts. We achieved low-stress connection between the leadless package structure components through glass frit sintering at 700 °C, which mainly includes three parts: bonding of SiC chip and SiC shim by medium-layer of glass frit, as shown in Fig. 5b, bonding of SiC shim and AlN header by medium-layer of glass frit, as shown in Fig. 5c and direct connection between external pins and sensor chip pads by nano conductive silver paste, as shown in Fig. 5d. We obtained the thermal stress distribution of the leadless package sensor structure and the flip-chip SiC sensor surface under high and low temperature environments through FEA, as shown in the Fig. 5e. Figure 5f details the thermal stress distribution along the central line path on the of the sensor surface within the package at different temperatures. The thermal stress distribution in the sensor diaphragm area is relatively uniform, with areas of concentrated thermal stress appearing outside the edges of the diaphragm.

Fig. 5: Sensor leadless package and thermal stress analysis.
Fig. 5: Sensor leadless package and thermal stress analysis.
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a Profile diagram of 4H-SiC pressure sensor leadless package structure. The low-stress connections between the components of b SiC pressure sensor chip and SiC shim; c SiC shim and AlN header; d external pins and SiC sensor chip pads. e The thermal stress distribution of the leadless package sensor structure and the flip-chip SiC sensor surface. f Thermal stress distribution along the central line path on the of the sensor surface within the package

Results and discussion

Static performance characteristics

Schematic of the SiC pressure sensor performance testing platform is illustrated in Fig. 6a. The pneumatic piston gauge provides air pressure for the SiC pressure sensors. A digital source meter (Keithley, 2601B) is used to provide a constant excitation signal for SiC pressure sensors. A digital multimeter (Keithley, DMM6500) is to record the output signal of SiC pressure sensors. A low temperature test chamber (ESPEC, STH-120, temperature range −60 to 150 °C) and a high temperature chamber furnace (Hefei Kejing, KSL-1200X-M, temperature range 23–1200 °C) are used to provide test temperature environments for the sensors. We calculated the errors of nonlinearity ξN, repeatability ξR and hysteresis ξH through three consecutive repeated calibrations. Accuracy of the sensor is calculated by

$${\xi }_{{\rm {A}}}=\sqrt{{\xi }_{{\rm {N}}}^{2}+{\xi }_{{\rm {R}}}^{2}+{\xi }_{{\rm {H}}}^{2}}$$
(6)
Fig. 6: Experimental platform, static and temperature performance of the 4H-SiC pressure sensors.
Fig. 6: Experimental platform, static and temperature performance of the 4H-SiC pressure sensors.
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a Setup of the 4H-SiC pressure sensor performance testing platform. b The high-temperature pressure performance testing of SiC pressure sensor. c Static air pressure calibration results of SiC pressure sensors family of schemes A–H. d Temperature drift of SiC pressure sensors’ zero outputs in –50 to 600 °C. Error bars are scaled 5 times larger. e Temperature coefficients of zero output of SiC pressure sensors. (f) Working lines for pressure calibration of SiC pressure sensors in –50 to 400 °C. g Temperature drift of sensitivities and temperature coefficients of sensitivities of SiC pressure sensors. h The comparison of the normalized index for the operating temperature range, sensitivity, pressure range and accuracy of the SiC pressure sensors

Table 2 shows the static performance characteristics of the SiC pressure sensors family. Figure 6b presents radar charts illustrating the test indicators for eight sensor schemes. It is evident that sensors B and E exhibit excellent comprehensive static performance. The real-time calibration results of one cycle of loading and unloading are shown in Fig. 6c. Among the four schemes with circular diaphragms, the SiC pressure sensors with piezoresistors arranged along the diaphragm all edges (scheme A, E) have higher sensitivities than those with piezoresistors arranged at diaphragm center and edges (scheme B, F). The four schemes with square diaphragms have the similar results: sensors with piezoresistors arranged along the diaphragm all edges (scheme C, G) are more sensitive than those with piezoresistors arranged at diaphragm center and edges (scheme D, H). In the design family, scheme E has the highest sensitivity of 1.93 mV/V/MPa. Scheme B achieves the highest accuracy of 0.18% FSO for SiC piezoresistive pressure sensors in current research.

Table 2 Static performance characteristics of the 4H-SiC pressure sensor family
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Temperature coefficient of zero output

The availability of SiC pressure sensors in harsh environments is highly dependent on the temperature stability of the reference zero output voltage. We tested schemes B and G in the SiC pressure sensor family at low and high temperatures, which have circular and square diaphragms, as well as different resistor arrangements, respectively. The temperature stability of the reference zero output voltage of SiC pressure sensor is expressed by the temperature coefficient of zero output (TCZ), which is calculated as follows:

$${\rm{TCZ}}=\frac{y({T}_{1})-y({T}_{0})}{{y}_{{\rm {FS}}}({T}_{1}-{T}_{0})}\times 100 \%$$
(7)

where T0 is room temperature, T1 is test temperature, y(T0) is zero output at T0, y(T1) is zero output at T1, yFS is full scale output (FSO) of the sensor at room temperature. Figure 6d shows the variation of the zero output of the sensors in −50 to 600 °C. In the low temperature range (<25 °C), the zero output voltage increases gradually with the decrease of temperature. In the high temperature range (>25 °C), the zero output voltage increases negatively with the increase of temperature, then gradually returns to zero, and then increases positively. Within the range of –50 to 200 °C, the zero output drift of the two SiC pressure sensors is almost identical. Generally, the temperature at which the sensor’s zero output undergoes a monotonic change is defined as the inflection temperature, while the temperature at which the sensor’s zero output returns to zero is defined as the recovery temperature. The inflection temperature of sensor B is about 200 °C, and the recovery temperature is about 400 °C. While the inflection temperature of sensor G is about 400 °C, and the recovery temperature is about 540 °C. The difference of the above inflection temperature is mainly attributed to the non-uniformity of thermal stress distribution in different SiC sensor chip structures. The sensor’s zero output recovery is due to the release of the sensor’s thermal stress. Figure 6e shows TCZs of the SiC pressure sensors in –50 to 600 °C. The TCZ of sensors B and G at 600 °C are only 0.10%/°C and 0.08%/°C, respectively. This means that the leadless packaging connection through thermal stress matching can suppress the zero output to a sufficiently low level, making the SiC piezoresistive pressure sensors acceptable for both high and low temperature operations, which would be regarded as a preliminary success.

Temperature coefficient of sensitivity

The temperature coefficient of sensitivity (TCS) of the sensor reflects the sensor’s sensitivity drift under different application temperatures. The equation for calculating TCS of the SiC pressure sensor is as follows:

$${\rm{TCS}}=\frac{{y}_{{\rm {FS}}}({T}_{1})-{y}_{{\rm {FS}}}}{{y}_{{\rm {FS}}}({T}_{1}-{T}_{0})}\times 100 \%$$
(8)

where T0 is room temperature, T1 is test temperature, yFS (T1) is FSO at T1, yFS is FSO at T0. Figure 6f shows the working lines of the SiC pressure sensor G in response to 0–5 MPa pressure in the temperature range of −50 to 400 °C. The sensor’s sensitivity drift is mainly caused by the negative correlation between SiC piezoresistive coefficients and temperatures. Figure 6g shows the sensor’s sensitivities at each test temperature point and the variation of TCS calculated according to Eq. (7) with temperature. It can be found that the sensor’s sensitivity gradually decreases with the increase of temperature, and its TCS is only 0.10% FSO/°C at 400 °C and 0.17% FSO/°C at −50 °C. Such a small TCS means that the 4H-SiC pressure sensors can lend itself to effective compensation over a wide temperature range. The comparison of our developed leadless packaged 4H-SiC pressure sensor with other SiC pressure sensors based on the piezoresistive effect principle, in terms of normalized index, is shown in Fig. 6h.

Dynamic pressure testing of shock tube

The dynamic characteristics of the 4H-SiC pressure sensor is tested to verify its ability to withstand impact pressure under operational conditions. The shock tube which provides step-pressure is used to evaluate the dynamic pressure response of the prepared 4H-SiC pressure sensor, is set up at the Beijing Changcheng Institute of Metrology and Measurement, China, as shown in Fig. 7a. The steel shock tube consists of a 4 m long driver section and a 7 m long driven section, both with an inner diameter of 0.1 m, separated by an aluminum diaphragm. The 4H-SiC pressure sensor to be calibrated is securely mounted in the driver section using a steel flange. The drive section is filled with pressurized gas until the aluminum diaphragm ruptures, creating a shock wave that propagates into the drive section. The shock wave reflects off the end wall of the drive section, causing a rapid upward step change in the pressure inside the tube. The data acquisition system has a 12-bit A/D converter and a sampling frequency of 5 MHz. The rise time (tr) of the sensor, directly read from its response curve to the step-pressure in Fig. 7b, is 1 μs. This represents the time it takes for the sensors output to transition from 10% to 90% of the step response amplitude when excited by step-pressure. The result, with a resonant frequency of 243.7 kHz shown in Fig. 7c, demonstrates the sensor’s superior mechanical stability compared to other pressure sensors.

Fig. 7: Dynamic performance and temperature vibration coupling testing of the 4H-SiC pressure sensors.
Fig. 7: Dynamic performance and temperature vibration coupling testing of the 4H-SiC pressure sensors.
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a Setup of dynamic pressure test of shock tube. b Time domain response curve. Inset: enlarged display for rise time of the 4H-SiC pressure sensor. c Frequency domain response curve. d Setup of vibration and high-temperature coupling test. e The power spectral density (PSD) map of the input vibration excitation. f Working lines of the 4H-SiC pressure sensor of before and after being affected by vibration and temperature coupling loads. Inset: enlarged view for working lines

Vibration and high-temperature coupling tests

The ignition process of a solid rocket engine is a complex, unsteady process that involves high temperatures, high pressures, and vibrations. In order to determine the anti-interference ability of the SiC pressure sensor when exposed to the vibration environment of the turbofan, it is necessary to take the vibration test to simulate the vibration environment stress of the sensor in practice to ensure the reliability of the sensor. The best vibration testing method is random vibration to approximate the vibration environment in actual engines45,46. The vibration and high-temperature coupling test platform is shown in Fig. 7d, where the random vibration is provided by the vibration test table (VHR714H-5, Dongling Company). The power spectral density (PSD) map of random vibration test is shown in Fig. 7e, with a frequency range of 15–2000 Hz and a power spectral density of 1.0 g2/Hz. The sensor is installed on a three-axis mounting fixture, and by changing the installation position, the sensor can receive vibration excitation from the X, Y, and Z axes. The mounting fixture is fixed on the top of the electromagnetic vibration test bench and placed together in the temperature environment provided by the high-temperature test chamber. Due to the limitations of the high-temperature chamber, the testing temperature for coupled vibration is 150 °C. Working lines of the static calibration tests of the sensor are plotted in Fig. 7f, and the illustration shows a partial magnification of the working line. After room temperature vibration, the working line deviated by 0.19% from the initial state before vibration. After high-temperature vibration, the working line deviated by 0.30%, and the maximum deviation of the working line is 0.11 mV. This indicates that the developed sensor will exhibit robust reliability under actual, complex conditions.

Conclusion

This paper presents the development of a family of 4H-SiC pressure sensors based on the first-reported longitudinal and transverse piezoresistive coefficients of 2.4 × 10–11 and –1.0 × 10–11 Pa–1 of N-type 4H-SiC with a high doping concentration of 2 × 1019 cm–3. In our 4H-SiC pressure sensor family designs, the sensor featuring a circular diaphragm with four few-folded piezoresistors arranged at diaphragm center and two edges, demonstrates exceptional accuracy of 0.18% FSO. The sensor with a square diaphragm and four multiple-folded piezoresistors arranged along the diaphragm edges demonstrates superior high-temperature performance. The leadless packaged sensor exhibited a temperature coefficient of zero output of only 0.08%/°C at 600 °C, a temperature coefficient of sensitivity of 0.10% FSO/°C at 400 °C and 0.17% FSO/°C at −50 °C, respectively. The as-presented 4H-SiC pressure sensor provides a systematic solution for pressure monitoring applications in harsh environments, including extreme high and low temperatures, shock, and high vibration.