1. Introduction

With the continuous development of information technologies, the demand for MEMS devices has significantly increased. The MEMS gyroscope plays a key role in the market and has been used in vehicles, biomedical instruments, consumer electronics, industrial control, and other fields, due to its advantages such as small size, low cost, low power consumption and high reliability. In contrast, traditional gyroscopes typically have a large meter or sub meter size, are heavy and have high power consumption. As electronic products develop towards characteristics such as intelligence, mobilization and miniaturization, the power supply, sensors and other various elements used in the devices have suffered strict limitations. However, MEMS sensors can meet almost all of these strict specifications.

In the past few decades, the performance of the MEMS gyroscope has been improved greatly, but it still cannot take the place of traditional gyroscopes, such as fiber-optic and laser gyroscopes, in many applications. At present, the mechanical coupling between the driving mode and sensing mode is a significant barrier to performance enhancement. The coupling produces errors, and many non-ideal behaviors are mainly sourced from this^[1]. As an example, a quadrature error can usually achieve 1000$^\circ$/s, which means that only a 1$^\circ$/s quadrature demodulation error can cause a 17$^\circ$/s bias^[2]. Besides, phase noise in quadrature demodulation, which induces bias instability, makes things worse because of its random behavior. As a result of this, many attempts have been made to suppress the mechanical coupling^[3-6]. It has been demonstrated that a well-designed decoupled structure could efficiently restrain the undesired coupling and improve the performance of the gyroscope^{[7, 8]}. This decoupling approach has obvious advantages such as low cost and efficiency^[9]. Higher fabrication precision could ensure the performance of device, but it is costly and complicated. In addition, in most cases we can only produce a small performance enhancement this way. Eliminating cross-talk error during the demodulation process is a third option, but this does not provide a dramatic improvement.

In this work, we demonstrate a decoupled 100 $\mu$m thick bulk silicon vibratory gyroscope with a delicate anchor arrangement. A 4 inch SOI silicon wafer with a 100 $\mu$m epitaxial layer was used to make the structural layer of the device. The thicker structural layer induces a high elastic stiffness in the thickness direction and enlarges the cell capacitance of the comb finger electrodes. Moreover, with the same area, the bulk mass weight increases as the thickness rises, and the dynamics of the gyroscope indicate that a higher driving mass brings about higher sensing displacements. As a result, the spurious modes, like the out-of-plane mode, are suppressed to reduce deviations in the high elastic stiffness in the thickness direction. The large capacitance of the comb electrodes and the heavy bulk mass obviously profit the output of the gyroscope. In brief, the thicker structural layer in a delicate design benefits the performance of gyroscopes in many ways. But there is a tradeoff between increasing the thickness of the structural layer and fabrication precision. It is not difficult to understand why process difficulties rise as the structural layer thickness increases. According to the equivalent model, the vibratory gyroscope is comprised of two lumped mass-spring-damper resonators sharing the same mass where the resonance directions are orthogonal with each other. In this case, the mass is free to oscillate in the drive and sense directions, so the drive and sense modes seriously interact. To overcome the disadvantage, in decoupled gyroscopes the mass is divided into three parts, called the driving mass, the sensing mass and the proof mass. Usually, the driving and sensing mass are restrained to oscillate in the corresponding driving and sensing directions. The proof mass can oscillate in both directions and perform energy transfer, and meanwhile, it separates the driving mass and sensing mass to suppress mechanical coupling^[5]. Based on the above principle, we designed a decoupled gyroscope using a frame structure that nests the proof mass, which ensures that the drive motion is well aligned with the designed drive axis and minimizes the actual drive motion component along the sense detection axis. It also provides improved side stability and minimal parasitic sense-direction forces in the drive actuators. This paper will give more details about the fabrication and preliminary characterization.

2. Principle of operation and fabrication

In this paper, we propose a decoupled $z$-axis vibratory gyroscope. Figure 1 shows the layout of the SOI MEMS gyroscope. The drive direction is along the $x$ axis, the sense direction is along the $y$ axis, and the angular input axis is along the $z$ axis. The drive and sense modes are in-plane vibratory oscillators. In our design, the comb finger electrodes are used for both driving and sensing. More specifically, the gyroscope forms the drive oscillator and sense-mode accelerometer out of a mass suspended by eight flexible 1D beams above a substrate. The two anchor areas suspend the rigid frame with four sensing 1D springs, and the rigid frame is suspended and connected to the proof mass by four driving 1D springs. There are only two anchor areas suspending all the movable parts of the gyroscope, and the energy loss of the device can be decreased. The Coriolis force induced on the masses due to the drive vibration and angular rate input has to be transferred to the sense-mode accelerometer in an orthogonal direction. It should be noted that the mass block plays the roles of driving mass and proof mass, which means that the sense mode motion will affect the drive mode. The standard SOG (silicon on glass) process was used to fabricate the gyroscope, and the major process steps are illustrated in Fig. 2.

Pyrex 7740 glass was etched to form the bonding areas (Fig. 2a), which are bulge areas and suspend the movable parts of the gyroscope and the fixed parts of the electrodes. The wet etching process details are listed as follows. A mixed solution of hydrofluoric acid, hydrochloric acid and deionized water was used as the etchant. In order to study the influence of the temperature and the proportion of etchant, some experiments were completed to optimize the process factors. Finally, the wet etching processes were accomplished at 40 ℃ and for 10 min. The proportion of HF (49%), HCL (37%) and DI water was 50 to 5 to 80 (vol.), and the etching depth was approximately 10 $\mu$m to form the bonding areas. The above appropriate conditions could make the processes more repeatable and controllable. In fact, because the hydrofluoric acid-based etchants behave with strong transverse etching, the etching mask is the critical factor for glass wet etching. The commonly used mask is comprised of metal films such as Cr, Au and Cu. According to Refs. [10, 11], the Cr (50 nm) and Au (300 nm) films were deposited as the mask layer by magnetron sputtering.

A layer of Al film was deposited on the top silicon surface of the SOI wafer (Fig. 2b). The metal film can improve the ICP etching process and get a better trench profile. Then, SUSS SB6 was used to accomplish anodic bonding (Fig. 2c). Before the ICP process, the bottom silicon layer of the SOI wafer must be removed. It turns out that the TMAH (approximately 10 wt.%) wet etching of the SOI substrate at 90 ℃ has a negligible influence on the strength of the bonded wafer (Fig. 2d). Since the ICP etching depth reaches up to 100 $\mu$m, the buried oxide layer of the SOI wafer was left as the mask. Before oxide mask patterning, a metal pad must be made through the lift-off process, as shown in Fig. 2(e). Figure 2(h) shows the final cross-section of the device.

An SEM photograph of the SOI MEMS gyroscope is shown in Fig. 3.

3. Results and characterization

In this section, the performance test and related results will be illustrated and discussed. Figure 4 shows the test board of the MEMS gyroscope.

After the processes are finished, the wafer is scribed and the gyroscope dies are vacuum packed. Then, the packaged device is used to form a test board, as shown in Fig. 4. Some grippers are used to fix the test board to the test table horizontally. The test conditions are listed in Table 1. Specifically, the test circuit comprises two subcircuits. One loop is for the drive resonator of the gyroscope. The output of the sensing mode is detected and demodulated in the sensing subcircuit. For the sake of stable linearity, we utilize the closed loop to drive the gyroscope and make the amplitude fixed. In other words, amplitude stabilization is applied. To do this, an AGC (automatic gain control) is used. In the sensing subcircuit, the multiplier is used for demodulation.

Since the gyroscope is vacuum packed, the measurement can be accomplished under atmospheric pressure. The gyroscope shows middle-level performance. We believe that the mode mismatch influences device performance; the driving mode resonant frequency is 3.02 kHz and the sensing mode resonant frequency is 3.24 kHz.

When an angular velocity of -10 deg/s is applied to the device, its response curve is as displayed in Fig. 5. Then, an angular velocity ranging from -100 to 100 deg/s is used. The angular velocity versus the output is plotted in Fig. 6. The black dots correspond to the data collected during the test, and the red line is the fit curve. The scale factor, zero-rate offset and nonlinearity can all be specified from the fit curve exactly.

Before the exact values of the scale factor set and zero-rate offset set are provided, the related formulas will be listed and the computing methods will be explained briefly^[12]. The gyroscope output caused by unit angular velocity is called the scale factor. It can be computed by calculating the slope of the straight line that can be fitted by the least squares method to the input-output data. In the $\overline x$ term, ‘-’ is the average operation of the variable, similarly hereinafter. The scale factor is expressed as:

$\begin{equation} \label{eq1} {\rm SF}=\frac{\overline {xy} -\overline x \, \overline y }{\overline {x^2} -\overline x ^2}. \end{equation}$

(1)

Variable $x$ is the input data of the MEMS gyroscope, and variable $y$ is the output data.

The scale factor nonlinearity can be calculated by Eq. (2), and the scale factor asymmetry represents the difference in the scale factors in the original and reverse directions.

$\begin{equation} \label{eq2} r=\frac{\overline {xy} -\overline x\, \overline y }{\sqrt {(\overline {x^2} -\overline x ^2)(\overline {y^2} -\overline y ^2)} }. \end{equation}$

(2)

The zero-rate offset is the product of the average angular rate output for each sample interval and the gyro scale factor. Before the zero-rate offset stability is calculated, an Allan variance of the test data must be computed. The Allan variance in fact evaluates the total deviation induced by various error sources^[13]. In our work, the zero-rate offset stability is considered and it equals the value of the Allan mean square error, which located at the zero slope line segment of the log-log plot of the Allan variance curve, which has been fitted by the least squares method.

$\begin{equation} \label{eq3} \mathit{\overline \Omega} _{k} (\tau)= \frac{1}{\tau}\int_{t_k}^{t_{k}+\tau} \mathit{\Omega} (t) {\rm d}t, \quad \tau=n\tau _0, \end{equation}$

(3)

$\begin{equation} \label{eq4} \sigma ^2(\tau)= \frac{1}{2}\left\langle \left({\mathit{\overline \Omega} _{k+n} -\mathit{\overline \Omega} _{k}^2}\right) \right\rangle = \frac{1}{2\tau ^2}\left\langle \left({\theta _{k+2n} -2\theta _{k+n} +\theta _{k}^2}\right) \right\rangle . \end{equation}$

(4)

The average angular rate output for each sample interval $\tau$ ($\tau _0$ is sample duration) is expressed as Eq. (3) and the Allan variance as Eq. (4), where $\left\langle \right\rangle$ denotes an infinite time average, $\mathit{\Omega}$ is the angular velocity symbol, and $\theta$ is angular.

The scale factor is 1.316 $\times$ 10$^{-4}$ V/(deg/s), which is slightly small because of the mode mismatch. The scale factor nonlinearity and scale factor asymmetry are 1.87% and 0.36%, respectively.

Finally, we come to the conclusion that the MEMS SOI vibratory gyroscope behaves with mid-level performance. There are two obvious reasons that affect the performance of the device. The first is the imperfection of the fabrication processes, and the second is the mismatch between the driving and sensing modes. When further measurements have been made, the impact of fabrication imperfection on performance can be estimated. The performance parameters can be compared with commercial devices and some of the other published devices when the full set of parameters has been tested.

4. Conclusions

An SOI MEMS vibratory gyroscope is presented in this paper. Bulk micromachining technology was used to fabricate the gyroscope. This forms the drive oscillator and the sense-mode accelerometer out of a mass suspended by eight flexible 1D beams above a substrate. To decouple the drive motion and sense motion, a frame structure that nests the proof mass is used, and because the device was vacuum packaged, the performance test was achieved under atmospheric pressure. The scale factor is 1.316 $\times$ 10$^{-4}$ V/(deg/s), the scale factor nonlinearity and asymmetry are 1.87% and 0.36%, the zero-rate offset is 7.74 $\times$ 10$^{-4}$ V and the zero-rate stability is 404 deg/h, respectively. Further tests are now needed, and the promotion of the fabrication has been made constantly.