Introduction

In civil, military, and aerospace domains, high-g accelerometers are extensively employed to measure penetration signals1,2,3,4,5, particularly in the context of penetrating-weapon blast fuzes and shielding-facility characteristics. Precise measurement of the penetration-acceleration curve, which is related to the fixed depth and predetermined layer detonation of the munition, is important for the development of penetration-weapon systems6,7,8. The shock accelerometer and test system face significant challenges in this harsh environment, with the impact loads incurred during penetration reaching hundreds of thousands of gravity accelerations9,10,11. This requires the accelerometer to have an excellent dynamic-response characteristic. To fulfil the requirements for high-amplitude and large-pulse-width shock-signal measurements, research on high-g accelerometers must first be conducted.

High-g accelerometers mainly include piezoresistive and piezoelectric accelerometers, due to the large “zero drift” of piezoelectric accelerometers12,13; piezoresistive accelerometers became the mainstream technology route. Sensitivity and natural frequency are directly coupled in conventional piezoresistive high-g accelerometers because the piezoresistor is placed directly on the support beam14,15,16,17,18,19,20,21,22. This means that it is impossible to improve these two indicators simultaneously. Shock accelerometers typically have natural frequencies below 400 kHz to guarantee adequate sensitivity23,24,25. Researchers have produced self-supporting accelerometers by separating a piezoresistor (piezoresistive beam) from the support beam to reduce this coupling relationship4,26,27. When a self-supporting accelerometer is subjected to acceleration, most of the strain energy is concentrated on the piezoresistive beam, which has very small dimensions, thereby generating large stresses on the piezoresistive beam and improving the accelerometer sensitivity. Moreover, the support beam has greater stiffness, which increases the natural frequency of the accelerometer. For example, Endevco (USA) produced the high-g accelerometer known as the 7270A-200K28, which has a measurement range of 200,000 g, with a natural frequency of up to 1.2 MHz and a sensitivity of 0.1 µV/V/g. Robert Kuells et al.29 designed a monolithic integrated triaxial high-g accelerometer30,31, the sensor had a sensitivity of 0.65 μV/g/V and natural frequency of 1.5 MHz in the x- and y-axes, but its z-axis natural frequency was only 500 kHz.

High-g accelerometers based on the pure axial deformation of piezoresistive beams have been developed to further improve their performance5,32. Pure axial deformation can significantly increase sensitivity while maintaining the natural frequency33,34,35,36,37. Zou et al. developed a new monolithic integrated triaxial high-g accelerometer38,39. Its structure was designed based on the above idea, and the test results indicated a sensitivity of 0.2–0.4 µV/V/g and a high natural frequency of approximately 1.4 MHz. Jia et al. developed a double-ended fixed high-g accelerometer with a range of 100,000 g40, the pure axial deformation was realized with a sensitivity of 1.586 μV/g/3 V and a natural frequency greater than 500 kHz. However, in these studies, pure axial deformation necessitated the construction of specific structural relationships, which were typically provided only by the specific position of the piezoresistive beam. This not only increased the design time but also easily changed the position of the piezoresistive beam owing to fabrication errors, which prevented the realization of a pure axial-deformation condition.

To simplify the design process, this study proposes a monolithic integrated triaxial high-g accelerometer with position-independent pure axial-deformation piezoresistive beams. It is realized by synchronous deformation between the two ends of the piezoresistive beams and does not require complex theoretical calculations and design. Finite-element modelling is used to model both the static and dynamic performances of the accelerometer. The fabricated high-g accelerometer is packaged in a miniaturized titanium-alloy shell, and its performance is evaluated using the Hopkinson bar system. Test results show that the designed accelerometer achieves ultra-high natural frequency (>1.5 MHz) and high sensitivity (å 1.15 μV/g/5 V) in all three axes.

Result and discussion

Design and model

Figure 1a, b show the proposed monolithic integrated high-g accelerometer. The accelerometer is composed of three layers: a glass cover, a silicon structure, and a glass backplane. To measure the impact acceleration signals in the corresponding directions, the silicon structure has three measuring units: x, y, and z, each of which has two measuring subunits. The measuring units for x and y are arranged perpendicularly and share the same structure. The structure of the x and y measurement units is improved based on our previous research on the 100,000 g accelerometer41.

Fig. 1: Model and structure of the high-g accelerometer.
figure 1

a Glass-silicon-glass accelerometer structure. b Overview of high-g accelerometer without a glass cover. c Subunit structure of x and y measuring units. d Subunit structure of z measuring units. e Enlarged view of areas (i), (ii), and (iii) in (b), which shows the piezoresistor numbers of each measuring unit and operating circuit (iv) of the triaxial accelerometer

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As illustrated in Fig. 1c, for x and y measuring units, in each measuring subunit, the two masses are connected to the frame via support beams, whereas the other ends are connected to each other via hinged beams to form a double-ended fixed-support structure to obtain high natural frequencies. Two groups of piezoresistive beams are located between the two masses, and each group comprises two piezoresistive beams forming one piezoresistor, as shown in (i) and (ii) of Fig. 1e. As shown in Fig. 1d, the support beam of z measuring unit is connected to the mass on one end and to the frame at the other end. It is also fixed to the glass backplane at the bottom. The two subunits differ depending on whether the support beams are located inside or outside the two masses. Each subunit of the z measuring unit has six piezoresistive beams, and each group of three forms a piezoresistor. Four piezoresistors per measuring unit produce a Wheatstone full bridge output, as shown by the distribution and identification of piezoresistors in (iii) of Fig. 1e. Table 1 lists the values for the dimensions of the accelerometer, which are labelled in Fig. 1c, d.

Table 1 Values for every dimension of the high-g accelerometer
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Working principle

When the external acceleration causes stress on the piezoresistor of the piezoresistive accelerometer, changing the resistance value, its output sensitivity S is

$$S=\left\{\begin{array}{lll}\frac{\Delta R}{aR}{V}_{in}=\frac{{\pi}_{l}{\sigma}_{l}-{\pi}_{t}{\sigma }_{t}}{a}{V}_{in}&({\sigma }_{t}\,\ne\, 0)\\ \frac{\Delta R}{aR}{V}_{in}=\frac{{\pi }_{l}{\sigma}_{l}}{a}{V}_{in}=\frac{\Delta L}{aL}{V}_{in}&({\sigma }_{t}=0)\end{array}\right.$$
(1)

where R is the resistance value of the piezoresistor when it is not stressed, ΔR is the change in the resistance when the piezoresistor is subjected to stress, a is the acceleration, Vin is the supply voltage, πl is the longitudinal piezoresistive coefficient of the piezoresistor, πt is the transversal piezoresistive coefficient, σl is the axial stress on the piezoresistive beam, σt is the transverse stress, and \(\Delta L\) is the axial strain of the piezoresistive beam. For accelerometers with piezoresistive beams that are not purely axially deformed (\({\sigma }_{t}\,\ne\, 0\)), the presence of transverse stresses not only disperses the deformation energy but also negatively affects the output sensitivity. When the piezoresistive beam undergoes pure axial deformation (\({\sigma }_{t}=0\)), only axial stresses exist in the piezoresistive beam, which maximizes the utilization of deformation energy and increases the sensor sensitivity.

The y-unit is used as an example to explain the working principle because the structures of the x and y measuring units are the same. Acceleration in y-direction applied to the accelerometer causes a synchronized deflection movement between the two masses, as illustrated in Fig. 2a. This leads to a synchronized movement of both ends on the piezoresistive beam, leaving with only 2ΔL of axial strain and no transverse relative strain. At this time, the piezoresistive beam is deformed by the bending moment M and tensile or compressive force F, as shown in Fig. 2b. F generates an axial tensile or compressive stress \({\sigma }_{l}\), and moment M places the piezoresistive beam in a pure bending state, producing a gradient axial stress \({\sigma }_{\Delta l}\). Stress \({\sigma }_{\Delta l}\) is divided by the neutral surface, and the upper and lower stresses are equivalent but directed in opposite directions; thus, their effects on the piezoresistor are balanced. Therefore, only the axial stress \({\sigma }_{l}\) exists inside the piezoresistive beam, which is in a condition of pure axial deformation.

Fig. 2: Working principle of each measuring unit.
figure 2

a Deformation of y measuring unit when subjected to y-direction acceleration. b Pure axial-deformation state of the piezoresistive beam in (a). c Deformation of the z measuring unit when subjected to z-direction acceleration

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The pure axial deformation of the accelerometer can be easily realized without the need for intricate theoretical calculations and design processes, as reported in previous studies5,40,42. This is because the criterion of pure axial deformation is consistently satisfied when the piezoresistive beam is placed between the two masses, regardless of the change in position D1.

Figure 2c shows the operation of the z measuring unit when az is applied. The masses of both subunits are deflected in opposite directions by acceleration az owing to the various positions of the support beams, which results in opposite states of deformation (tensile or compressed) for the piezoresistive beams of the two subunits. At this time, the piezoresistive beam is only subjected to a tensile or compressive force F caused by the synchronized movement of the two masses, and the piezoresistive beam is in a pure axial-deformation state. The four piezoresistors, Rz1–Rz4, form a Wheatstone full-bridge circuit for the output.

Static stress simulation

The finite-element software ANSYS Workbench was employed to analyse the sensitivity, natural frequency, and modal characteristics of a high-g accelerometer. The silicon material properties used in the simulation include a density of 2330 kg/m³, an elastic modulus of 1.7 × 10¹¹ Pa43, and a Poisson’s ratio of 0.28. The boundary conditions were defined by applying fixed constraints to the bottom surface of the glass backplane, while an acceleration of 200,000 g was independently imposed along each principal direction.

Figure 3a–c depicts the deformation of each measuring unit along with the corresponding stress distribution under an applied acceleration of ax = 200000 g. Figure 3a shows the stress distribution of the x- measuring unit, which is mainly concentrated in piezoresistive beams Rx1–Rx4, and the stress distribution of the piezoresistive beam is uniform. As shown in Fig. 3b, the average axial stress (i.e., y-direction stress) of the piezoresistor is approximately \({\sigma }_{lx}\)=59.07 MPa. The transverse stress, including the x-direction and z-direction components, remains negligible (<0.1 MPa), except in the localized stress-concentration region at the interface between the piezoresistive beam and the proof mass. Consequently, the piezoresistive beam undergoes predominantly pure axial deformation, which enhances sensitivity and optimally utilizes the available deformation energy. The stress distributions in the piezoresistive beams in the y and z measuring units are shown in Fig. 3c. While the stress distribution on the piezoresistive beams is nonuniform, the stresses in the front and rear halves of each piezoresistive beam along the axial direction are opposite to each other, indicating that their influences on the resistance change in the piezoresistive beam offset each other. Therefore, the resistance values of the piezoresistors (Ry1–Ry4 and Rz1–Rz4) in the y and z measuring units do not change. Given an initial resistance of R for each piezoresistor, the resistance change resulting from tensile stress is ΔRx for Rx1 and Rx3, and compressed stress is −ΔRx for Rx2 and Rx4. Figure 3i shows the output circuit of the high-g accelerometer at ax = 200,000 g. Using Eq. (1), the simulation sensitivity and cross-sensitivity are calculated as follows:

$$\left\{\begin{array}{l}{S}_{xFEM}=\frac{{V}_{xout}}{{a}_{x}}=\frac{\Delta {R}_{x}}{{a}_{x}R}{V}_{in}=\frac{{\pi }_{l}{\sigma }_{lx}}{{a}_{x}}{V}_{in}=\frac{{\pi }_{44}{\sigma }_{lx}}{2{a}_{x}}{V}_{in}=1.093\,{\rm{\mu }}{\rm{V}}/{\rm{g}}/{\rm{5V}}\\ {S}_{yFEM-cross}=0\\ {S}_{zFEM-cross}=0\end{array}\right.$$
(2)

where \({\pi }_{44}=1.48\times {10}^{-9}{{\rm{m}}}^{2}/{\rm{N}}\)43,44 is the piezoresistive coefficient of the p-type doping, Vin = 5 V is the supply voltage, and Vxout is the output voltage of the x measuring unit.

Fig. 3: Simulation of static stress distribution of the high-g accelerometer.
figure 3

Stress distribution simulation in piezoresistive beams of x (a, b), y, and z (c) measuring units when ax = 200000 g. d Stress distribution in piezoresistive beams of each measuring unit when ay = 200,000 g. Stress distribution in piezoresistive beams of z (Figs. 3e and 3f) and x/y (Figs. 3g and 3h) measuring units when az = 200,000 g. Output circuit of accelerometer when ax = 200,000 g (Fig. 3i), ay = 200,000 g (Fig. 3j), and az = 200,000 g (Fig. 3k)

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When acceleration ay = 200,000 g is applied, the stress distribution on the piezoresistive beam of each measuring unit is as shown in Fig. 3d, in which the average stress of the y measuring unit is approximately \({\sigma }_{ly}\)=58.84 MPa. At this point, the stress distribution in the x measuring unit is the same as that in the y measuring unit, as shown in Fig. 3c. Therefore, the piezoresistor resistance of x measuring unit remains unchanged, and its output voltage is zero. The average stresses of the piezoresistive beam in the z measuring unit are 2.47 MPa (Rz1), −2.47 MPa (Rz2), −2.47 MPa (Rz3), and 2.47 MPa (Rz4). The change in resistance in the y measuring unit piezoresistors Ry1–Ry4 caused by the stress at this point is ΔRy, and the change in the z-measuring-unit piezoresistors is ΔRa. Its output circuit is illustrated in Fig. 3j, where the simulation sensitivity and cross-sensitivity can be calculated as follows:

$$\left\{\begin{array}{l}{S}_{xFEM-cross}=0\\ {S}_{yFEM}=\frac{{V}_{xout}}{{a}_{y}}=\frac{\Delta {R}_{y}}{{a}_{y}R}{V}_{in}=\frac{{\pi }_{l}{\sigma }_{ly}}{{a}_{y}}{V}_{in}=\frac{{\pi }_{44}{\sigma }_{ly}}{2{a}_{y}}{V}_{in}=1.086{\rm{\mu }}{\rm{V}}/{\rm{g}}/{\rm{5V}}\\ {S}_{zFEM-cross}=\frac{{V}_{zout}}{{a}_{z}}\\\qquad\qquad\qquad=\frac{1}{{a}_{z}}\left(\frac{{R}_{z1}-\Delta {R}_{a}}{{R}_{z1}}-\frac{{R}_{z4}-\Delta {R}_{a}}{{R}_{z4}}+\frac{{R}_{z2}+\Delta {R}_{a}}{{R}_{z2}}-\frac{{R}_{z3}+\Delta {R}_{a}}{{R}_{z3}}\right){V}_{in}\\\qquad\qquad\qquad=\frac{1}{{a}_{z}}\left(\frac{-\Delta {R}_{a}+\Delta {R}_{a}+\Delta {R}_{a}-\Delta {R}_{a}}{R}\right){V}_{in}\\\qquad\qquad\qquad=0\end{array}\right.$$
(3)

Figure 3e, f depict the stress distribution in the z measuring unit when az = 200,000 g is applied in the z-direction. The piezoresistive beam experiences pure axial deformation, exhibiting only axial stresses, where the average axial stress is \({\sigma }_{lzI}\)= 55.52 MPa (Rz1 and Rz2) and \({\sigma }_{lzII}\)= 54.84 MPa (Rz3 and Rz4). The deformation of the x or y measuring unit under the effect of az is shown in Fig. 3g, and the stresses in the piezoresistive beams are Rx1 = Rx2 = Rx3 = Rx4 = −47.04 MPa and Ry1 = Ry2 = Ry3 = Ry4 = −49.18 MPa. The x and y measuring units have identical structures; however, their different placements on the chip result in different boundary conditions, which explains why the stresses in the two units differ. The resistance changes in the piezoresistors at this time are assumed to be ΔRzI (Rz1 and Rz2), ΔRzII (Rz3 and Rz4), ΔRb (Rx1 - Rx4), and ΔRc (Ry1 - Ry4). The output circuit is shown in Fig. 3k, and the simulated sensitivity and cross-sensitivity of the accelerometer are as follows:

$$\left\{\begin{array}{ll}{S}_{xFEM-cross}&=\frac{1}{{a}_{z}}\left(\frac{{R}_{x1}+\Delta {R}_{b}}{{R}_{x1}}-\frac{{R}_{x2}+\Delta {R}_{b}}{{R}_{x2}}+\frac{{R}_{x3}+\Delta {R}_{b}}{{R}_{x3}}-\frac{{R}_{x4}+\Delta {R}_{b}}{{R}_{x4}}\right){V}_{in}\\&=\frac{1}{{a}_{z}}\left(\frac{\Delta {R}_{b}-\Delta {R}_{b}+\Delta {R}_{b}-\Delta {R}_{b}}{R}\right){V}_{in}\\&=0\\ {S}_{yFEM-cross}&=\frac{1}{{a}_{z}}\left(\frac{{R}_{y1}+\Delta {R}_{c}}{{R}_{y1}}-\frac{{R}_{y2}+\Delta {R}_{c}}{{R}_{y2}}+\frac{{R}_{y3}+\Delta {R}_{c}}{{R}_{y3}}-\frac{{R}_{y4}+\Delta {R}_{c}}{{R}_{y4}}\right){V}_{in}\\&=\frac{1}{{a}_{z}}\left(\frac{\Delta {R}_{b}-\Delta {R}_{b}+\Delta {R}_{b}-\Delta {R}_{b}}{R}\right){V}_{in}\\&=0\\ {S}_{zFEM}&=\frac{1}{{a}_{z}}\left(\frac{{R}_{z1}-\Delta {R}_{zI}}{{R}_{z1}}-\frac{{R}_{z4}+\Delta {R}_{zII}}{{R}_{z4}}+\frac{{R}_{z2}-\Delta {R}_{zI}}{{R}_{z2}}-\frac{{R}_{z3}+\Delta {R}_{zII}}{{R}_{z3}}\right){V}_{in}\\&=-\frac{2}{{a}_{y}}\left(\frac{\Delta {R}_{zI}+\Delta {R}_{zII}}{R}\right){V}_{in}\\&=-\frac{1}{{a}_{y}}\left[\frac{{\pi }_{44}({\sigma }_{lzI}+{\sigma }_{lzII})}{2}\right]{V}_{in}\\&\text{}=1{\rm{.018}}{\rm{\mu }}{\rm{V}}/{\rm{g}}/{\rm{5V}}\end{array}\right.$$
(4)

To summarize, the developed monolithic integrated triaxial accelerometer simulated triaxial sensitivities of 1.093 μV/g/5 V (x-axis), 1.086 μV/g/5 V (x-axis), and 1.018 μV/g/5 V (z-axis). The simulated cross-sensitivity of the three measuring units is zero; however, testing and evaluation of the constructed high-g accelerometer are necessary because of the actual fabrication errors that result in imperfect piezoresistors. However, as shown in Fig. 3a, e, g, the maximum stress of the high-g accelerometer under 200,000 g of acceleration is 77.52 MPa, which is less than the fracture stress of the single-crystal silicon micro-mechanical structure (approximately 300 MPa).

Modal simulation and frequency-response analysis

The accelerometer must have a high natural frequency and a wide working bandwidth to match the measurement requirements because the penetrating weapon experiences a high amplitude, a high dynamic range, and the fast amplitude-change characteristics of the shock acceleration. The finite-element approach is used to perform modal and frequency-response analyses to identify the frequency range in which the accelerometer is appropriate for vibration detection and to prevent resonance and signal distortion when the accelerometer is utilized.

Sinusoidal acceleration loads with frequencies of 0–2 MHz are applied in the three directions. Figure 4a shows that the first-order natural frequency of the accelerometer is 1.57 MHz, which is the natural frequency of the z measuring unit based on its vibration pattern. Therefore, a sinusoidal load is applied in the z-direction. The frequency response and vibration-phase angle of the accelerometer are shown in Fig. 4b. Its resonance peak coincides with Fig. 4a, and the operating bandwidth is calculated to be 0–0.74 MHz (±3 dB).

Fig. 4: Modal and frequency-response analyses of high-g accelerometers.
figure 4

a First vibration mode. b Frequency-response analysis using az = 200,000 g. c Second vibration mode. d Frequency-response analysis with ax = 200,000 g. e Third vibration mode. f Frequency-response analysis with ay = 200,000 g

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As shown in Fig. 4c, the vibration pattern reveals a second-order natural frequency of 1.578 MHz, which is the natural frequency of x measuring unit. Consequently, a sinusoidal load is applied in the x-direction. Figure 4d displays the frequency response and vibration phase angle of the accelerometer. Its resonance peak aligns with the natural frequency in Fig. 4c, and the operating bandwidth of the x measuring unit has been calculated to be 0–0.76 MHz (±3 dB).

Similarly, Fig. 4e shows the third-order natural frequency of the accelerometer at 1.586 MHz, which is the natural frequency of the y measuring unit. Figure 4f displays the frequency response and vibration phase-angle variation when a sinusoidal load is applied in the y-direction, and the theoretical operating bandwidth of the y measuring unit is calculated to be 0–0.78 MHz (±3 dB). Although the x- and y-axis measuring units share the same structure, the differences in their positions and arrangement directions on the chip lead to changes in the boundary conditions, which, in turn, result in different natural frequencies.

Fabrication and packaging

The fabricated monolithic integrated triaxial-accelerometer chip is shown in Fig. 5a, with the overall chip dimensions of 6.5 mm × 4.4 mm × 1.41 mm (length × width × height). Figure 5b shows the accelerometer chip after removing the glass cover, and the structural photographs of each measuring unit is shown in Fig. 5c–e. The partially enlarged image displays the detailed structure of the piezoresistive beam/piezoresistor, and clearly exhibits the regions of boron-ion heavy doping, boron-ion light doping, and lead holes. The piezoresistor resistances of the x and y measuring units are measured as Rx ≈ Ry ≈ 4.85 kΩ and the z measuring unit was Rz ≈ 7.3 kΩ. For details on the fabrication process of the accelerometer chip, please refer to the Materials and Methods section below.

Fig. 5: Chip and package of the high-g accelerometer.
figure 5

a Fabricated high-g accelerometer with glass cover. b High-g accelerometer structure without glass cover. SEM image of the x (c), y (d), and z (e) measuring unit. f Miniaturized titanium package for high-g accelerometers

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As shown in Fig. 5f, we selected a titanium-alloy material for the accelerometer shell because of its high strength and low weight. The accelerometer and package construction must withstand a strong impact signal throughout the test procedure; therefore, this material is selected to guarantee package reliability. The accelerometer chip is fixed on the titanium-alloy shell with an epoxy-resin adhesive and protected using a potting adhesive. The glass cover serves to protect the moving structures, including support beams, proof mass, and piezoresistive beams, preventing adhesion of the potting adhesive from obstructing their motion and consequently affecting acceleration measurements. The overall dimensions of the packaged accelerometer (excluding the screw structure) are 14 mm × 14 mm × 6 mm (length × width × height).

Testing and discussion

The dynamic performance and sensitivity of the fabricated high-g accelerometer are calibrated using a Hopkinson bar impact-test system45,46, as shown in Fig. 6a, b. The high-g accelerometer is securely fastened to the end of the rigid calibration bar using the titanium-shell screw threads. A specific half-sine pulse signal is produced when the projectile strikes the other end of the calibration bar, owing to the compressed air that is controlled and released by the control system. The pulse waveform produced by the projectile is modified using a pulse shaper. Because of the high rigidity of the calibration bar, the pulse signal is attenuated and dispersed very little during its propagation to the accelerometer and the end of the calibration bar. The acceleration input of the accelerometer is determined by measuring the vibration at the end of the calibration bar using a laser Doppler interferometer. The data-acquisition system collects the output voltage produced by the high-g accelerometer and transmits it to a computer for data processing.

Fig. 6: Testing of the high-g accelerometer.
figure 6

a Schematic of Hopkinson-bar test system. b Hopkinson-bar test system for high-g accelerometers. c Test curves and d local amplification of the shock stage of the y measuring unit with 91,459.13 g input

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The compressed-gas pressure is varied to generate different acceleration pulse signals, and the output curves of the designed high-g accelerometer under different shock accelerations are collected and compared with those of the laser Doppler interferometer. Laser Doppler measurements revealed that the acceleration amplitude ranges from 9000 g to 200,000 g, with a shock pulse width varying between 10 µs and 50 µs. The higher the amplitude, the smaller the shock pulse width. The output voltage of the accelerometer is proportional to the input acceleration. Figure 6c presents the laser Doppler interferometer signal alongside the output signal of the y-axis measuring unit under an input acceleration of 91,459.13 g. The shock peak is magnified locally in Fig. 6d, revealing a pulse width of 22.4 μs and an output voltage of 111.7 mV at this point.

The output signals of each measuring unit at different accelerations are obtained, as shown in Fig. 7a–c, and the peak voltages of the different measuring units in the high-g accelerometer are recorded. The output signals of each measuring unit are linearly fitted to obtain a measuring sensitivity of 1.212 μV/g/5 V with a nonlinearity of 1.25% for the x measuring unit, 1.223 μV/g/5 V with a nonlinearity of 1.97% for the y measuring unit, and 1.165 μV/g/5 V with a nonlinearity of 2.81% for the z measuring unit. The natural frequencies of each measuring unit are obtained by performing a fast Fourier transform on the output voltage of the accelerometer in Fig. 6c, as shown in Fig. 7d–f. The x, y, and z measuring units measure natural frequencies of 1.531, 1.524, and 1.516 MHz, respectively.

Fig. 7: Sensitivity and natural frequency of the high-g accelerometer.
figure 7

Measuring sensitivity of the x (a), y (b), and z (c) measuring units. Measuring natural frequencies of x (d), y (e), and z (f) measuring units

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Table 2 presents a comparison and error analysis of the measured sensitivity and natural frequency derived from the simulation and experimental tests. This shows that the sensitivity obtained from the experimental test increases compared with the simulation results, whereas the natural frequency decreases, which is in accordance with the constraint relationship between the sensitivity and natural frequency. The main reasons for this difference are the fabrication error of the accelerometer chip and the interference of the package on the output signal.

Table 2 Performance comparison between the test and simulation
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The figure of merit (FOM), defined as follows, is introduced as a standard for evaluating the overall performance of high-g accelerometers to facilitate comparisons with other high-g accelerometers:

$$\text{FOM}={S}_{m}{f}_{m}^{2}$$
(5)

where Sm is the measurement sensitivity, and fm is the first-order measurement natural frequency. A performance comparison between the high-g accelerometers built in our study and those in other works is displayed in Table 3. The high-g accelerometer developed in this study has a greater FOM than those in prior works, and concurrently combines high sensitivity and natural frequency. Moreover, unlike most triaxial high-g accelerometers, the measuring units in this study exhibit similar sensitivity and natural frequency, ensuring consistent overall performance of the triaxial accelerometer.

Table 3 Performance comparison of the high-g accelerometer fabricated in our work with other papers
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Conclusion

In this study, a monolithic integrated triaxial high-g accelerometer was designed, fabricated, and tested. By using the synchronized deformation of the two ends of the piezoresistive beam, pure axial deformation of the piezoresistive beam could be easily realized, which in turn ensured high sensitivity and natural frequency. Simulation results were utilized to prove the correctness of the design idea. The test results showed that the measurement sensitivities of the x, y, and z measuring units of our fabricated high-g accelerometers were 1.212, 1.223, and 1.165 μV/g/5 V without amplification, respectively, and the measurement natural frequencies were 1.531, 1.524, and 1.516 MHz, respectively. The design concept in our study can be used to design other high-performance piezoresistive sensors and simplify the design process.

Materials and methods

The accelerometer is fabricated using a Silicon on Insulator (SOI) wafer with the following specifications: N-type (100) crystal orientation, resistivity ranging from 1 to 10 Ω·cm, a device-layer thickness of 10 μm, a buried oxygen layer thickness of 1 μm, and a substrate layer thickness of 400 μm. The fabrication process for the accelerometer is depicted in Fig. 8a–m.

  1. (a)

    Plasma-enhanced chemical vapour deposition (PECVD) was used to deposit a 300 nm SiO₂ mask layer on both sides of the SOI wafer, serving as a mask for light doping and backside gap etching.

  2. (b)

    The SiO₂ layer was photolithographically patterned and subsequently lightly doped with boron ions at an injection concentration of 1 × 1015 cm−3. This produced a resistance of approximately 300 Ω/square in this region, forming the piezoresistor of the accelerometer.

  3. (c)

    A 400-nm SiO2 and SiNx composite mask layer is sputtered after removing the SiO2 mask layer. Subsequently, an ohmic contact region is formed by heavy doping with boron ions at a concentration of 5 × 1016 cm−3, resulting in a resistance of approximately 10 Ω/square in the doped area. The silicon wafers are then annealed in nitrogen for 1 h at 1000 °C to produce a uniform ion distribution in the doped region.

  4. (d)

    The mask layer is removed from the ohmic contact area, followed by the sputtering of a Cr/Au (20 nm/200 nm) layer to create the metal leads and pads.

  5. (e)

    Reactive ion etching (RIE) with a 2 μm etching depth is used to generate the backside moving gap of the mass after the photolithography and patterning of the backside SiO2.

  6. (f)

    The substrate layer of the accelerometer structure is formed by deep backside etching using deep reactive ion etching (DRIE) with a photoresist as the mask.

  7. (g)

    Then, 200 nm Al is sputtered on BOROFLOAT33 (BF33) glass to prevent the electrostatic attraction of the mass to the glass during subsequent anodic bonding.

  8. (h)

    Using an anodic bonding technique, the SOI wafers are bonded to the BF33 glass for 20 min at 350 °C and a bonding voltage of 1200 V.

  9. (i)

    Patterned SiO2/SiNx composite film layers and front-side etching using ICP are used to construct the device-layer portion of the high-g accelerometer structure.

  10. (j)

    The buried oxygen layer is then etched using RIE to finish the silicon structural component of the high-g accelerometer.

  11. (k)

    The motion gap and glass via holes (for exposing metal pads) on the BF33 glass cover are etched using the laser-etching process, with the motion gap being etched to a depth of 50 μm.

  12. (l)

    The glass cover is coated with a glass frit for bonding.

  13. (m)

    Glass-frit bonding is used to join the accelerometer and glass-cover plate. Bonding temperature and pressure are set at 450 °C and 5 atm, respectively, and the process takes 60 min.

Fig. 8: Fabrication process of high-g accelerometers.
figure 8

a PECVD SiO2 mask layer. b Boron lightly doped to form piezoresistive region. c Boron heavy doping to form an Ohmic contact region. d Sputtered-metal leads and pads. e ICP back-side etching to create a motion gap. f Backside DRIE to form the substrate layer of the accelerometer. g Sputtered metal layers used to prevent adhesion during anodic bonding. h Anodic bonding. i Front-side ICP etching. j Removal of the buried oxygen layers. k Laser etching to create front-motion gap. l Coated glass frit adhesive layer. m Bonded accelerometer glass cover

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The use of SOI silicon wafers and ICP/RIE dry etching technology is one of the mainstream process routes for making MEMS accelerometer chips. Although it will increase the manufacturing cost, but SOI and dry etching can control the structure size more precisely and improve the sensor performance, making the sensor conform to the design index. In this paper, we use the SOI buried oxygen layer as the stop layer of the back-side dry etching, which can precisely control the thickness of the piezoresistive beam and ensure the performance of the sensor. After bonding, laser-cutting technology is employed to dice the wafer into individual high-g accelerometer chips, completing the fabrication process.