**2. Design**

The AlN MEMS accelerometer is composed of four supported beams and two proof masses. The schematic structure is as shown in Figure 2. It contains four layers, the SiO2 layer, the bottom electrode layer (Mo), the AlN layer, and the top electrode layer (Ti/Pt). The parameters are listed in Table 1. The SiO2 layer works as the support and insulation. The bottom electrode is connected to the ground. The top electrodes, which are serpentine, are placed on the supported beams. They contain the drive electrode and sense electrode. The drive signal is applied on the drive electrode. Due to the piezoelectric effect, the electric field will excite a mechanical strain. This strain will lead to a stress σ, which is the in-plane direction. Moreover, the stress can drive the structure to vibrate.

$$
\sigma = E\_{ALN} \frac{\mathcal{U}}{d\_{AllN}} d\_{31} \tag{1}
$$

where *EAlN* is the Young's modulus of AlN. *dAlN* is the thickness of the AlN film. *U* is the drive voltage. *d*31 is the piezoelectric coefficient of AlN. According to the reported references [17,18], the *d*31 = −2.6 pm/V.

**Figure 2.** The structure of the aluminum nitride (AlN) MEMS accelerometer. In addition, the detailed analysis of the core beams (B1, B2, B3, B4).

**Table 1.** The structure parameters of the AlN MEMS accelerometer.


To maximize the electromechanical signal, the top electrodes on the core beams are designed as serpentine electrodes. The sizes and the position of the serpentine electrodes come from the stress simulation. Figure 3a shows the stress simulation. The top electrodes are designed according to the stress distribution [11]. ABCDEFG is the line of the top electrode. Figure 3b shows the stress distribution. There are nearly no opposite sign charges on the top electrode. Therefore, a maximized electromechanical signal can be collected by the serpentine electrodes. Table 2 lists the parameters of each material.

**Figure 3.** The stress simulation of the AlN MEMS accelerometer (**a**); the stress distribution along the top electrode (**b**).


**Table 2.** The parameters of each material from COMSOL Multiphysics library.

Due to the AlN piezoelectric effect, the MEMS structure is excited to resonate in-plane by the drive signal [19]. The resonant mode is simulated by the software COMSOL Multiphysics. The simulation result is shown in Figure 4. The two proof masses vibrate reversely. The positions of the anchors are the nodes. There is no displacement and no stress. This means there will be no anchor loss. The quality factor of this accelerometer will increase [20].

**Figure 4.** The displacement resonant mode of this AlN MEMS accelerometer.

The proof masses vibrate along the x-axis. The acceleration is along the z-axis. When an acceleration → *a* applies on the entire structure, the supporting beams will deform in the z-axis. The stiffness coefficient *kz* will change. As a result, the resonance frequency *fx* will shift with the z-axis acceleration. The detailed derivation is in reference [15].

$$f\_{\mathbf{x}} = f\_{\mathbf{x}0} \left( 1 - \frac{1}{2} \frac{\Delta k\_{\mathbf{x}}}{k\_{\mathbf{x}0}} \right) = f\_{\mathbf{x}0} \left( 1 - \frac{3a}{E\_z} \frac{Lm}{\mathbf{wt}^3} a \right) = f\_{\mathbf{x}0} \left( 1 - \mathbb{C} \frac{Lm}{\mathbf{wt}^3} a \right) \tag{2}$$

where *f* x0 is the in-plane resonance frequency at static state. And *k*x0 is the stiffness coefficient along x-axis at static state. *C* is a constant. L is the length of the beam. w is the width of the beam. t is the thickness of the structure.

The sensitivity of this accelerometer is proportional to *Lm*w*t*<sup>3</sup> . In order to increase the sensitivity, the mass and the length of the beam should be increased. In this work, the AlN MEMS accelerometer is a thin-film structure. The whole thickness of the structure is 2.05 μm. The size of the proof mass is increased to 500 μm × 500 μm.

Due to the lattice mismatch, there will be a residual stress in the actual accelerometer structure. The mean value of the residual stress is more than 500 MPa. This residual stress will lead the MEMS structure to bend out of plane, as shown in Figure 5a. To simplify the simulation and show the trend of the whole curve, the residual stress is set to 5 MPa, which is less than the actual value. Figure 5b shows the simulation result with the residual stress. The AB part which includes zero g, is monotonically increasing. This part is the range of this accelerometer.

**Figure 5.** The deformation of the structure under the residual stress (**a**); the sensitivity curve of this AlN MEMS accelerometer simulated with the residual stress (**b**).
