Background

High-g accelerometers have been widely used in vehicle crash test, automotive air bag and shock detection applications. It is important to reduce the size of the sensor to extend the field of applications. Silicon microfabrication technique makes it possible to reduce size of the sensor as well as the production cost through batch fabrication, making it suitable for mass production. In previous researches, fabricated high-g accelerometers measure the acceleration in one-axis [1–6] or three-axis with three proof masses [7]. Compared with a three-axis accelerometer with multiple proof masses, a monolithic three-axis accelerometer is free from axis-alignment error and has advantages of smaller device size, better uniformity of the measurement signals in three sensing directions [7]. Design and analysis of monolithic three axis high-g accelerometers have been reported before [8–10], however, to our best knowledge, no actual device and experimental results were reported.

In this work, we developed a monolithic piezoresistive high-g three-axis accelerometer. The detailed description for the design, fabrication and characterization is given in the following.

Design and fabrication

Device and circuit design

It is desired for an accelerometer to have wide sensing range as well as the sensing capability in triaxial directions independently to be used to measure unpredictable and random-directional acceleration inputs. For this purposes, we designed mechanical structures and electrical circuits as shown in Fig. 1. Single proof mass is suspended by thin eight beams, and sixteen p-type silicon piezoresistors are formed at the top surface of the beams. We used eight beams to increase the modal frequency of the unwanted rotational mode of the proof mass, and to arrange the piezoresistors symmetrically (Fig. 1a, b). For an acceleration applied to the proof mass, resistance change caused by beam deformation (Fig. 1a) is measured as voltage difference using external circuits. One of the possible applications of the fabricated accelerometers could be shock detection in mobile devices. The small size of the accelerometer chip may allow its attachment to various components inside the mobile devices, such that we can estimate the actual acceleration values applied to each component. When a mobile device is dropped at a height of 1.5 m, a few thousand times of the gravitational acceleration is applied by the impact [11]. Thus, we set the target sensing range at around 20,000 g, and the dimension of the silicon structures were designed such that the maximum stress in the beams generated by the 20,000 g axial acceleration does not exceed 1 GPa. Since the known yield stress of silicon is 7 GPa, we considered a safety factor of 7 based on our drop testing experience and considering the unexpected factors such as fabrication errors. External measurement circuits are shown in Fig. 1c. In order to detect acceleration in three-dimensional space and rebuild its vector components in three-axial directions, sixteen piezoresistors and four external resistors are divided into three groups to form Wheatstone bridge circuits for detection. The resistance changes of piezoresistors for the acceleration in each of x, y and z directions is shown in Table 1. When the resistance of piezoresistors are changed, Vout_x for Z-axis bridge circuit is given by

$$V_{out\_z} = \frac{r}{{\left( {1 + r} \right)^{2} }}\left( {\frac{{\Delta R_{6} + \Delta R_{8} }}{{R_{6} + R_{8} }} - \frac{{\Delta R_{2} + \Delta R_{4} }}{{R_{2} + R_{4} }} + \frac{{\Delta R_{14} + \Delta R_{16} }}{{R_{14} + R_{16} }} - \frac{{\Delta R_{10} + \Delta R_{12} }}{{R_{10} + R_{12} }}} \right) \times \left( {1 - \eta_{{A_{z} }} } \right)V_{in}$$
(1)
$$\eta_{{A_{z} }} = \left[ {\frac{{\left( {\frac{{\Delta R_{6} + \Delta R_{8} }}{{R_{6} + R_{8} }}} \right) + \left( {\frac{{\Delta R_{2} + \Delta R_{4} }}{{R_{2} + R_{4} }}} \right) + \left( {\frac{{\Delta R_{14} + \Delta R_{16} }}{{R_{14} + R_{16} }}} \right) + \left( {\frac{{\Delta R_{10} + \Delta R_{12} }}{{R_{10} + R_{12} }}} \right)}}{{\left( {\frac{{\Delta R_{6} + \Delta R_{8} }}{{R_{6} + R_{8} }}} \right) + \left( {\frac{{\Delta R_{2} + \Delta R_{4} }}{{R_{2} + R_{4} }}} \right) + \left( {\frac{{\Delta R_{14} + \Delta R_{16} }}{{R_{14} + R_{16} }}} \right) + \left( {\frac{{\Delta R_{10} + \Delta R_{12} }}{{R_{10} + R_{12} }}} \right) + 2}}} \right]$$

where r = (R6 + R8)/(R10 + R12) = (R2 + R4)/(R14 + R16) and ηAz is nonlinear variable of the bridge circuit. The nonlinear term is always zero and r = 1 from Fig. 1c and Table 1, when all the resistors are identical [12]. Accordingly, the simplified equations of the output signal are expressed as follows:

$$V_{out\_x} = \frac{1}{4}\left( {\frac{{\Delta R_{1} + \Delta R_{5} }}{{R_{1} + R_{5} }} + \frac{{\Delta R_{3} + \Delta R_{7} }}{{R_{3} + R_{7} }}} \right)V_{in}$$
(2)
$$V_{out\_y} = \frac{1}{4}\left( {\frac{{\Delta R_{9} + \Delta R_{13} }}{{R_{9} + R_{13} }} + \frac{{\Delta R_{11} + \Delta R_{15} }}{{R_{11} + R_{15} }}} \right)V_{in}$$
(3)
$$V_{out\_z} = \frac{1}{4}\left( {\frac{{\Delta R_{6} + \Delta R_{8} }}{{R_{6} + R_{8} }} - \frac{{\Delta R_{2} + \Delta R_{4} }}{{R_{2} + R_{4} }} + \frac{{\Delta R_{14} + \Delta R_{16} }}{{R_{14} + R_{16} }} - \frac{{\Delta R_{10} + \Delta R_{12} }}{{R_{10} + R_{12} }}} \right)V_{in}$$
(4)

Acceleration in particular axis is measured by corresponding bridge circuit and the unwanted change of resistance because other axial acceleration is cancelled out. When the sensor is under x-axial acceleration Ax, the same amount of compressive stress is applied to R9 and R15, while the same amount of tensile stress is applied to R11 and R13 due to the symmetric arrangement. Resultantly, ΔR9 = ΔR15 = −ΔR11 = −ΔR13 and the change of output voltage Vout_y becomes zero [Eq. (3)]. Similarly, Vout_x and Vout_z are measured by each bridge circuit.

Fig. 1
figure 1

a Schematic of the fabricated accelerometer and deformation under applied axial acceleration. b Arrangement of sensing piezoresistors. c Circuit diagram for three Wheatstone bridges

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Table 1 Resistance changes of piezoresistors with axial acceleration
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Fabrication

The 3-axis accelerometer was fabricated by micromachining technique as shown in Fig. 2. A double-side polished, n-type, (1 0 0) oriented 4-inch silicon-on-insulator (SOI) wafer was used as a starting material. The thickness of device layer, substrate layer and buried silicon dioxide layer are 5, 500 and 1 μm, respectively. First, silicon dioxide (SiO2) layers were grown on both sides of SOI wafer by thermal oxidation (a). After the SiO2 was patterned and etched, contact pads and p-type piezoresistors were formed by implanting boron ions with the concentration of 5 × 1019 atoms cm−3 (b). Then 300-nm-thick SiO2 layer was deposited on the top surface as an insulating layer using plasma-enhanced chemical-vapor deposition. Etching via holes (c) for interconnection was followed by metallization to form contact pads (d). The top SiO2, device layer and buried SiO2 layer were sequentially etched to form proof mass and mechanical beams (e–f). Finally, the handle layer was deep-etched from backside to release the beams (g). It is noted that the proof mass is defined on the 500 μm-thick substrate layer, and is attached to the beams defined on the 5 μm-thick device layer.

Fig. 2
figure 2

Microfabrication process flow: a SiO2 growth on SOI wafer. b Patterning and ion implantation to form contact pads and piezoresistors. c SiO2 deposition and via hole patterning. d Al deposition and patterning. e Patterning and sequential etching of top SiO2, device Si layer. f Buried SiO2 from the topside. g Patterning and dry-etching of handle Si layer from the backside

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Results and discussion

Figure 3 shows optical images of the fabricated accelerometer fixed and wire-bonded on a flexible PCB. The device chip size was 1.4 mm × 1.4 mm × 0.51 mm. For calibration, both the reference accelerometer and the fabricated accelerometer were attached on a rigid metal block and this rail-guided block was dropped from various heights to apply different amount of impact to the accelerometers. The input voltage applied to the Wheatstone bridges was 5 V and an output signal was measured by an oscilloscope. The initial average resistance of sixteen fabricated resistors was 30.3 kΩ. Gauge factor (GF) of piezoresistor is defined and simplified as:

$$GF = \frac{{\frac{\Delta R}{R}}}{\varepsilon } = \frac{{\pi_{eff} \sigma }}{{\frac{\sigma }{E}}} = \frac{1}{2}\pi_{44} E$$
(5)

where ε, π eff , π 44 and E denote the strain, effective piezoresistive coefficient, shear piezoresistive coefficient (85 × 10−11 Pa−1) and Young’s modulus of silicon (163 GPa), respectively [12]. Thus the average gauge factor of the piezoresistors is calculated as 69.3.

Fig. 3
figure 3

Optical images of the fabricated accelerometer; An enlarged image of accelerometer attached on flexible PCB (left). Optical image of the accelerometer compared with a ten-won coin (right)

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Presented in Fig. 4a–c are the test results of the fabricated accelerometer. The drop test was repeated five times and error bars represent the variation of voltage difference. Figure 4 shows that the sensor can measure each of three axes acceleration with low cross-axis sensitivity. The sensitivities for axial accelerations, Sx, Sy, Sz on the X-, Y-, Z-axes were 0.2433, 0.1308, 0.3068 mV/g/V and resolutions were 24.2, 29.8, 25.4 g, respectively. The linearity of each directional measurement is calculated as LAx = 0.978, LAy = 0.918 and LAz = 0.997 by least-square fitting. For a specific axial direction, the output signal of the corresponding resistor increased with increasing acceleration, while the others remained constant. Consequently, the fabricated accelerometer is able to detect acceleration in arbitrary direction by vector summation of all three output signals. Although there exist number of non-ideal factors including microfabrication error, misaligned attachment, and electrical noise that may cause cross-axis sensitivity, nonlinearity, and non-zero output voltage, the developed accelerometer can measure both the magnitude and direction of high-g acceleration in arbitrary direction.

Fig. 4
figure 4

Output signals as a function of axial accelerations on the a X-, b Y-, and c Z-axis bridge circuit

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Conclusions

A high-g three-axis accelerometer using single proof mass has been designed, fabricated, and tested. The size of the fabricated accelerometer chip is 1.4 mm × 1.4 mm × 0.51 mm, and the accelerometer is suitable for impact test of portable electronic devices to evaluate mechanical robustness. To decompose acceleration in arbitrary direction into x, y and z components with minimal cross-talk among each axis, we designed sixteen piezoresistors and four external resistors that construct three Wheatstone bridge circuits. The accelerometer could also be applied to detect high-g shock of projectiles or vehicles.