# Coupled D33 Mode-Based High Performing Bio-Inspired Piezoelectric MEMS Directional Microphone
## 2 Regular and Proposed D33 Modes
Both unit cells were modeled on a 300 \(\upmu\)m \(\times\) 300 \(\upmu\)m diaphragm of a 10 \(\upmu\)m thick silicon (with aYoung's modulus of 130 GPa, speed of sound of 8433 m/s and Poisson's ratio of 0.28). The diaphragm was fixed from the left side by making a 40 \(\upmu\)m \(\times\) 300 \(\upmu\)m anchor. Then, following [PERSON] et al. [19], each modeled unit cell was covered by an air medium with 300 \(\upmu\)m \(\times\) 300 \(\upmu\)m dimensions with a 50 \(\upmu\)m thickness as shown in Figure 2a,b, respectively, for unit cells of regular and proposed D33 modes. Under the physics-controlled meshing, the simulated sensitivity under the application of 1 Pa of sound pressure at 1 kHz frequency is shown in Figure 3a,b, respectively, for the regular and proposed D33 modes. The unit cell of the proposed D33 mode showed a 7.96% enhanced sensitivity compared to the regular D33 mode. Both unit cells were simulated using the parameter taken from [19]. Thus, a further simulation was performed by varying the parameters of the IDTs to understand the effectiveness of the proposed D33 mode. To do that, a parametric sweep study was performed by varying the width of the IDT from 5 \(\upmu\)m to 60 \(\upmu\)m and the spacing between the IDTs from 30 \(\upmu\)m to 90 \(\upmu\)m. In the simulations, both unit cells from Figure 2a,b were used. Figure 4a shows the comparison between the unit cells of regular and proposed D33 modes, where the simulations were performed by varying the width of the IDT. It can be noticed that the unit cell of the proposed D33 mode constantly showed a higher voltage than the regular D33 mode. Then, the parametric sweep study was performed for spacing between IDTs from 30 \(\upmu\)m to 90 \(\upmu\)m. As shown in Figure 4b, the unit cell of the proposed D33 mode gave constantly higher responses than the  
Figure 2: Modeling of unit cells in terms of the acoustic-piezoelectric interaction with the finite element method (FEM) in COMSOL: (**a**) unit cell of regular D33 mode, and (**b**) unit cell of proposed D33 mode. regular D33 mode over a wide range of spacings. Moreover, in both simulations, the local minimum voltage occurred due to the ratio of the width and spacing (Figure 4a) [22] and the ratio of the spacing over the thickness of the whole diaphragm (for Figure 4b). Besides, the presence of the strain in the sensitivity formula presented in Equation (1) was simulated and shown in Figure S1a,b, respectively, for the unit cells of the regular and proposed D33 modes. The unit cell of the proposed D33 mode showed a 1.96% enhancement in strain over the regular D33 mode. Furthermore, the elastic strain energy (\(\mathbf{\beta}\)) was also enhanced by 6.09%, as shown in Figure S1c,d. Along with the elastic strain, the displacement of the proposed D33 mode was enhanced by 3.32% as shown in Figure S1e,f. Nevertheless, the current density (A/m\({}^{2}\)) showed a 15.9% decrease as compared to the regular D33 mode due to the minimized capacitance as shown in Figure S2a,b. Moreover, the enhanced electric potential (V) and charge (q)--followed by enhanced strain--showed a 5.9% enhancement of electric energy (E\({}_{e}\)) by, E\({}_{e}\)= V \(\times\) q [26] as shown in Figure S2c,d.