Inertial navigation requires a measurement with six degrees of freedom (DOF) in three-dimensional space, namely the ability to move forward or backward, up or down, left or right (translation in three perpendicular axes) combined with rotation about three perpendicular axes (pitch, yaw, roll). A micromachined inertial measurement unit (MIMU) is used to output signals proportional to the rotation and translational motion of a carrier in six DOFs from, respectively, micromachined angular rate sensors and acceleration sensors. Traditionally, these separated inertial sensors are mechanically mounted orthogonally in one or two substrates to output the three-axis angular rate and acceleration measurement signals [1]. In this mechanical assembling process, it is difficult to achieve exact mutual orthogonality between the sensors. Orthogonality aberrations degrade the accuracy of the subsequent processes, such as attitude determination or inertial navigation. A variety of multi-axis inertial sensors, such as tri-axis micro gyroscopes [2–4] or tri-axis micro accelerometers [5–8], can alleviate this misalignment problem in MIMU. Moreover, such technology allows the MIMU to be even smaller because the multi-axis sensing only requires one inertial mass. However, the cross-axis coupling within the multi-axis sensor limits the performance of the sensor. Designing a tri-axis sensor with only one inertial mass is a challenging task and requires a creative, clever design.

Integrated MIMU (IMIMU) technology can avoid the misalignment problem without tri-axis sensors. In IMIMU, different single-axis inertial sensors are fabricated simultaneously on a single chip with a surface or bulk micromachining process. Thus, the mutual orthogonality in IMIMU is inherently guaranteed by the design. Additionally, compared with tri-axis sensors, a single-axis inertial sensor is more rugged, and easier to design. Furthermore, cross coupling within a tri-axis sensor is successfully avoided. The first IMIMU was implemented using a surface micromachining process in 1998 [9]. It integrates three accelerometers, a dual-axis gyroscope, and a Z-axis gyroscope into a 1-cm² chip, including the interface circuitry. Luo Hao integrated two accelerometers and a gyroscope into a single chip using a surface process in 2003 [10]. It did not include an X/Y-axis gyroscope or a Z-axis accelerometer. Currently, surface micromachined IMIMUs have been commercialized successfully by Analog Devices, Inc (Norwood, MA, USA).

However, there is no report on bulk micromachined IMIMU so far. The major difficulty is the lack of a mature monolithic bulk micromachining process. Some monolithic bulk processes have emerged recently [11–15]. Unfortunately, they are not mature enough to realize a complex device like IMIMU. It is widely accepted that the bulk process could achieve better performance than the surface process for the inertial sensor. Today, inertial sensors with the highest accuracy [16,17] are nearly all fabricated by bulk micromachining process, where the larger proof mass can reduce mechanical noise to improve performance. Therefore, people usually utilize a two-chip integration scheme to realize bulk micromachined MIMU. In this two-chip approach, the six mechanical sensing elements are simultaneously fabricated on a chip and packaged with a circuit chip that reads out the various signals and generates the corresponding signal. Donato Cardarelli proposed a two-level conceptual MIMU design scheme based on the standard dissolved wafer process in 2002 [18]. However, no further fabrication or test results with this bulk micromachined MIMU have been reported. In our previous work [19], we established a two-chip MIMU using a bulk micromachining process. However, the yield rate of fabricating the mechanical chip is very low, which partially explains why there has not been a commercial bulk micromachined MIMU until now.

There are many difficulties when fabricating the six inertial sensors simultaneously through the bulk micromachining process. First, there is a tradeoff between area limitation and sensor performance. For a single inertial sensor, greater area usually means better performance because the performance is usually proportional to the inertial mass. However, greater area reduces the accuracy of micromachining process. In our bulk process, the minimum line width is 2 μm when the layout area is less than 8 mm × 8 mm. However, the minimum line width will become 10 μm when the layout area is larger than 10 mm × 10 mm. Therefore, a trade-off must be made to optimize a total of six sensors in a limited area. Secondly, the reactive ion etching (RIE) lag effect [20,21], which does not appear as a major problem in the surface micromachining, and notching effect [22] in deep RIE (DRIE) are challenges when generating a bulk micromachined MIMU. The six sensors inevitably have different line widths. Consequently, different etching depths caused by the RIE lag effect definitely hurt the performance of inertial sensors. Finally, the residual stress caused by the anodic bonding and chemical mechanical planarization (CMP) in the bulk process [23–24] cause a large mode mismatch for gyroscopes, which is a fatal bug for gyroscopes. In this paper, we present solutions to these problems to establish a bulk micromachined two-chip MIMU based on our previous work.

The proposed MIMU integrates two chips, as shown in Figure 1, where the letters A and G represent the accelerometer and gyroscope, respectively. The mechanical sensing element chip consists of sensing structures for six single-axis inertial sensors, i.e., three accelerometers and three gyroscopes. While the interface circuit chip consists of the six interface circuits that match the corresponding sensors. The two chips are packaged together to form the final MIMU device.

The first step when designing the bulk micromachined MIMU is to determine its topology for each single-axis inertial sensor based on a bulk process. The sandwich process or other processes with more than three structure layers are very complex and greatly reduce the yield rate to MIMU. A two-structure-layer process, as shown in Figure 2, is used to design the MIMU. Fabrication begins with a P-type single-crystalline silicon wafer. First, the photo resist (PR) is coated on the wafer to form the mask of anchors, as shown in step (a). In step (b), inductively coupled plasma (ICP) etching is used to etch shallow trenches to form anchors, and in step (c), PR is coated on the glass wafer. In step (d), a deep trench is wet etched on the glass wafer to increase the distance between the proof mass and the substrate. In step (e), a layer of metal is sputtered on the glass to form electrodes. In step (f), anodic bonding is used to bond the glass and silicon wafer together. At this step chemical mechanical polishing is used to reduce the thickness of the silicon wafer to meet the actual demand. In step (g), PR is coated on the back side of the silicon wafer. Finally, in step (h), ICP is used again to form moving structures, such as comb drives or damping holes.

It is obvious that the major process flow is similar to our previous one [19]. However, some improvements have been proposed to ensure an acceptable MIMU yield rate. The thickness of the proof mass was reduced to 65 microns from 80 microns. One additional mask was provided to add a trench in the glass to increase the distance between the proof mass and the substrate for some sensors, including the Z-axis gyroscope and X/Y-axis accelerometer. Thus, the slide film damping in these devices is greatly reduced to improve the quality factors for Z-axis gyroscopes because the MIMU is packaged at one atmosphere.

In this study, we use the most typical topologies for inertial sensors instead of novel designs to ensure a better yield rate because they have been verified in many ways. There are many typical topologies for accelerometers [25–30]. Most lateral accelerometers fabricated by surface or bulk micromachining processes can be used as the X/Y-axis accelerometer in the proposed MIMU. The vertical accelerometers, which require the sandwich process, cannot be used as the Z-axis accelerometer in the proposed MIMU. Finally the topologies of the accelerometers are chosen as shown in Figure 3. After experimental verification with the previous MIMU, the topologies are proved to be effective and are still used in this version of MIMU.

There are also many typical topologies for gyroscopes [31–36] that are compatible with the above-mentioned process flow. In the current version, there are many essential improvements on gyroscopes to increase the yield rate of the MIMU. The vibrating wheel gyroscope in the previous version was difficult to fabricate. Thus, we used the tuning fork gyroscope instead [31]. The Z-axis gyroscope with interdigitated electrodes in the sense mode [32] was difficult to fabricate because the large metal electrodes in the glass wafer are hard to remove. Therefore, we used a symmetrical Z-axis gyroscope topology [33] to replace it. Finally, the topologies of the gyroscopes are chosen as shown in Figure 4.

After choosing a feasible topology for each inertial sensor, we must determine the dimensions for each sensor. However, the MIMU consists of six separated inertial sensors, which means the usual device optimization approaches, such as a genetic algorithm (GA) [36] or simulated annealing algorithm (SAA) [37], are not suitable to be applied directly to MIMU design. Therefore, area occupations for each sensor should be determined first before the detailed design for the single sensor. In this paper, we propose an area optimization approach to establish the layout configuration for MIMU.

Various interface circuit design schemes exist. Here, we took some typical ones for accelerometers (Figure 10) and gyroscopes (Figure 11) in the MIMU. However, there are six different single-axis sensors in MIMU; the various signals will experience crosstalk. Therefore, special design in the interface circuit chip is needed to suppress the crosstalk. In addition to the necessary shielding, the proper choice of interface circuit frequency for the different sensors is also very helpful in suppressing crosstalk. Usually the noises of the operational amplifiers decrease with a higher frequency. Thus, we set the frequency of the interface circuit for gyroscopes to be higher than that of the accelerometers because the gyroscope is less sensitive than the accelerometer. Such a configuration is very helpful in reducing noise in the circuit.

As in the mechanical chip, a proper layout in the circuit chip can suppress crosstalk. The circuits for the gyroscopes were placed next to the circuits for the accelerometers. Furthermore, the circuits with similar frequencies were separated. The final layout configuration of the interface circuit chip is shown in Figure 12.

We used the process flow shown in Figure 2 to fabricate the designed MIMU. The fabricated chip is shown in Figure 13. We used the circuit board shown in Figure 14 to test the MIMU.

The frequency responses of the six sensors are shown in Figure 15. It can be observed that the resonant frequencies of the X/Y-axis accelerometer and Z-axis accelerometer are about 2,506 Hz and 2,084 Hz, respectively. The resonant frequencies of the drive mode and sense mode for the X/Y-axis gyroscope are 4,032 Hz and 4,048 Hz, respectively. The resonant frequencies of the drive mode and sense mode for the Z-axis gyroscope are 5,090 Hz and 5,132 Hz, respectively.

The scale factor plots of the six sensors are shown in Figure 16. It can be seen that the scale factors of the X/Y-axis accelerometer and Z-axis accelerometer are about 213.3 mV/g and 226.9 mV/g, respectively. The big nonlinearity exists just because the rough test method based on a triangle ruler. The accelerometers were tiled 0°, 30°, 45°, 60°, 90°, 270°, 300°, 315°, 330°, 360°, respectively, through a triangle ruler to generate multiple acceleration input. The scale factors of the X/Y-axis gyroscope and Z-axis gyroscope are about 2.2 mV/°/s and 10.8 mV/°/s, respectively.

Plots of the Allan variance analysis for the gyroscopes are shown in Figure 17. It can be seen that the bias stability of the X/Y-axis gyroscope and the Z-axis gyroscope are about 2,135 deg/h and 80 deg/h, respectively.

The noise floors of the six sensors are shown in Figure 18. It can be observed that the power spectral densities of the noise for X/Y-axis accelerometers, Z-axis accelerometers, X/Y-axis gyroscopes, and Z-axis gyroscopes are 258.7   μ V / Hz, 247.8   μ V / Hz, 692.4   μ V / Hz, and 86.3   μ V / Hz, respectively. Consequently the resolutions of X/Y-axis accelerometers, Z-axis accelerometers, X/Y-axis gyroscopes, and Z-axis gyroscopes are 0.0012   g / Hz, 0.0011   g / Hz, 0.314   ° / s / Hz, and 0.008   ° / s / Hz, respectively.

It is obvious that the performance is far from the navigation level [38]. The major reason for this low performance lies in the capacitive detection circuit. There are a significant amount of noise that reduces the capacitance detection capability far below the expected 10⁻¹⁹ F. If the interface circuit were improved, the performance of the sensors would be much better. Another phenomenon is that the performance of the X/Y-axis gyroscope is much worse than that of the Z-axis gyroscope, primarily because the big squeeze film damping for the out-of-plane motion in the sense mode of the X/Y-axis gyroscope is packaged at one atmosphere. The large damping greatly reduced the quality of the sense mode. In the future, the X/Y-axis gyroscope needs to be improved further to obtain a better performance, e.g., by using a larger layout area or a smaller resonant frequency, if identical performance is required for all three gyroscopes.

In this paper, we demonstrated a miniature bulk micromachined MIMU; a detailed design, the fabrication process and testing were all discussed for the first time. The proposed global area optimization approach is proved to be very effective to determine the layout configuration of the six single-axis sensors in the mechanical element chip. Moreover, the widely used common geometry patterns are also proved to effectively alleviate the RIE lag effect in bulk micromachining process. The test results show that the current MIMU achieves medium accuracy. With an improved interface circuit, this technology can yield better performance than the surface micromachined MIMU.