XIE Jianbing, YUAN Weizheng, and CHANG Honglong

Micro and Nano Electromechanical Systems Laboratory, Northwestern Polytechnical University, Xi’an 710072, China

1 Introduction

Micromachined gyroscopes are increasingly used in numerous consumer and automotive applications, primarily due to their small size, light weight, low cost, low power and high reliability. A variety of micromachined gyroscopes utilizing different drive and sense methods have been developed since the late 1980s[1–13], such as the double gimbal micro gyroscopes[1], tuning fork gyroscopes[2–3,12–13],surface acoustic wave resonator gyroscope[4], double linear vibratory gyroscope[5–6], decoupled angular velocity gyroscope[7–8], symmetric decoupled gyroscope[10–11]. Most of them are silicon based vibratory sensors, which utilize the energy transfer between two vibrating modes of a mechanical structure[1].

The earliest vibratory gyroscope, presented in 1993, has only one moveable inertial mass[2–3], the motion of the drive mode transmits to the inertial mass directly, at the same time, the motion is also transferred to the sense mode,thus creates the mode coupling. The mode coupling will lead to a quadrature error, which is considered as very harmful to the gyroscope. Similarly, the motion of the sense also can lead to a quadrature error.

To decrease mode coupling, a number of micromachined vibrating rate gyroscopes, which use separate oscillation modes for drive and detection have been developed[5–8]. In these gyroscopes, the sensing mass is separated from the inertial mass by some independent beams. Therefore, the inertial sense mass has one degree of freedom(DOF), the mass two DOFs, so that feedback from the sense mass to the inertial mass is suppressed and the quadrature is reduced[6–8]. But the coupling between drive mass and inertial mass still exists. Some subsequent study reported a more desirable structure by using three movable masses,inertial mass, drive mass and sense mass[9–11]. Due to its symmetric structure, the coupling between any two masses has been eliminated successfully.

In this paper, we presented a novel MEMS gyroscope with decoupled oscillation modes. Also, we used a three masses system, the drive mass is placed inside the main frame mass and the sense masses outside. In this way, we can make the best of the layout area, and obtain maximal inertial mass, which is very helpful to reduce the mechanical noises. The gyroscope is designed and analyzed through multi-port-element network(MuPEN) method[14]and fabricated through a simple one-mask SOI process.

2 Design of the MEMS gyroscope

2.1 Theory of operation

In general, the vibratory gyroscope shows maximum sensitivity when the driving and sensing mode frequencies are exactly matched. However, the gyroscopes that using the same spring in the driving and sensing modes show nonlinear behaviour when the difference of the driving and sensing mode frequencies are smaller than 100 Hz. To reduce the mode coupling effect that results from interference between the driving and sensing mode, the newly designed gyroscope has independent springs for driving and sensing mode.

Fig. 1 shows the schematic diagram of the vibratory gyroscope, which is achieved by using three moveable masses and two types of one-dimensional springs. The first type spring restricts the motion of the drive mass to y-axis.Similarly, the second restricts the motion of the sense mass to x-axis.

Fig. 1. Schematic diagram of the vibratory gyroscope

In this design the drive and main frame masses are forced by the come driver at resonance along the y-axis,and the Coriolis acceleration induced by rotation around the z-axis is sensed capacitively along the x-axis. The governing equations of the gyroscope having external driving force are as follows:

Where mx, λx, kxare mass, damping and spring coefficient of x-axis, respectively, my, λy, kyare mass, damping and spring coefficient of y-axis, respectively, Fyis driving force,Fxis Coriolis force, and ? is input angular rate.

When the z-axis speed is match more smaller than the natural frequency of driving mode and sensing mode, and the angular speed is constantly invariable, namely, ?=0, the equation may go a step further simplification as follows:

If there is no any external force in sensing mode, namely,Fy=0, at the same time, the Coriolis force coupled from sensing mode to driving mode is mach more smaller than the driving force, than the Coriolis force can be ignored and the governing equations may be simplified as follows:

Eqs. (5) and (6) are the ideal equations of gyroscope motion.

2.2 Structure of the gyroscope

The schematic of the fabricated micro gyroscope can be represented as shown in Fig. 2. The inertial mass is driven together in the x-axis at the driving mode by two drive electrodes. If an angular rate is applied in the z-axis, then the inertial mass moves in the x-axis by the Coriolis force.That is, the micro gyroscope estimates the input angular rate by sensing the displacement of the inertial mass induced by the Coriolis force.

Fig. 2. Schematic drawing of the gyroscope

As shown in Fig. 2, the inertial mass has three parts such as the main frame mass, outer mass and the inner mass. The main frame mass is connected to inner mass with 4 driving springs, at the same time, the inner mass is connected to the anchor with two decouple beams. When the driving voltage is applied on the driving electrodes on the side of the inner mass, the main frame mass and the inner mass is driven to a linear oscillation along the y-axis with the driving mode resonant frequency.

When the gyroscope rotates around the z-axis, Coriolis force arise, which cause an oscillation along the x-axis. In this direction, the high stiffness of the inside decouple beams suspension effectively suppresses the linear oscillation of the sense mass, so it will not follow the movement of the frame mass in the x-axis. Similarly the outer mass can only move in x-axis. Therefore, the mode coupling between drive and sense mode has been successfully decreased by using decouple beams.

2.3 Modeling and simulation

For the design of the gyroscope, system level simulation is used to predict the frequencies of the drive and sense mode. Fig. 3 shows the system level model of the gyroscope based on multi-port-element network(MuPEN)method. MuPEN method can presented rapid modeling and simulation of system-level behaviors of MEMS with multiple coupled energy domains. The model of the gyroscopes consists of 4 kinds of components, namely,mass, 3D beam, electrostatic comb and anchor.

Fig. 3. System level model of the gyroscope based on MuPEN

Fig. 4 shows the amplitude frequency response and phase frequency characteristics of the designed gyroscope in system level simulation. The frequencies of driving mode and sensing mode are 4.67 kHz and 4.83 kHz,respectively. The sensing mode is designed with 160 Hz higher frequency than the driving mode because of electrostatic tuning and fabrication tolerance. The average quality factor(Q-factor) of an individual gyroscope die is analyzed to be about 669 for the driving mode and about 671 for the sensing mode at atmosphere pressure. Fig. 5 shows the simulation of step response for displacement of the outer mass, inner mass, and the main frame mass in driving mode. The displacement of the inner mass and the main frame are both 212 nm, at the same time, the displacement of the outer mass is just 71.3 pm, only the 1/3 000 of the inner and main frame mass. It is mean that the displacement of main frame mass has not transfer to the outer mass, the couple between driving and sensing mode has bean decoupled successfully.

Fig. 4. Amplitude frequency response and phase frequency characteristics of the designed gyroscope

Fig. 5. Step response for displacement of the masses in driving mode

After the system-level design, we obtained the detail design parameters of the gyroscope. Fig. 6 shows the solid model of the designed gyroscope for the quarter view of the gyroscope (Fig. 6(a)) and comb fingers and release holes(Fig. 6(b)).

Fig. 6. Solid model of the gyroscope

3 Fabrication Process

The decoupled vibratory gyroscope shows in Fig. 7 is fabricated with the SOI wafer in order to achieve a high Q-factor. The SOI wafer is 500 μm thick with a 5 μm thick insulating SiO2layer and a 30μm thick device layer. The device layer, which is the gyroscope structure, is P-type with (100) orientation having a resistivity of 0.01–0.02 ? · cm.

Fig. 7. Cross-sectional view of the fabrication process flow

Fig. 7 illustrates the cross-sectional view of the fabrication process flow, which can be described as follows:Step (a): The fabrication begins with a P-type single-crystalline silicon wafer. Highly doped silicon wafer was used because it does not require an additional doping step. Step (b): Photoresist(PR) mask is deposited and patterned to transfer the structures. Step (c): The inductively coupled plasma etching(ICP) is used to vertically etch the device layer of the SOI wafer to form the moving structures of the gyroscope[15–16]. Step (d):Hydrofluoric acid is used to release the sacrificial SiO2layer, and a sublimation method is employed to release structure in order to prevent the suction phenomenon. Step(e): We use magnetron sputtering to generator a thin film metal to reduce the contact resistance. Step (f) is the wire bonding.

4 Experimental Results

Fig. 8 shows micrograph of fabricated gyroscope. The overall size of the fabricated gyroscope is approximately 3 mm×4 mm. The measured drive-mode frequency response is about 4.821 kHz, as shown in Fig. 9, and the simulated response of the gyroscope is 4.67 kHz. The relative error is 3.1%. The Q-factor of the drive-mode is 600, little smaller than simulation,

Fig. 10 shows the measured random variation of the output bias of the fabricated gyroscope for zero-rate input.Fig. 11 shows the resulting characteristics for determining the scale factor and nonlinearity of the output response of the microgyroscope. The gyroscope demonstrates a scale factor of 8.9 mV/((°)·s), and the R2-nonlinearity of the measured scale factor is better than 0.4% within ±80°/s full-scale.

Fig. 8. Micrograph of fabricated gyroscope

Fig. 9. Measured drive-mode frequency response

Fig. 10. Measured random variation of the output bias of the fabricated gyroscope

Fig. 11. Resulting characteristics for determining the scale factor and nonlinearity of the output response of the microgyroscope

5 Conclusions

(1) A MEMS gyroscope on the SOI substrate with decoupled oscillation modes was successfully designed and fabricated.

(2) The coupling between driving and sensing mode has been successful reduced using decouple beams.

(3) The gyroscope is fabricated with single mask process,having 30 μm thick single crystalline silicon structure without residual stress. Measurements results show that the scale factor of the gyroscope is 8.9 mV/((°)·s) and the Q-factor is as high as 600 at atmosphere pressure.

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