# Coupled D33 Mode-Based High Performing Bio-Inspired Piezoelectric MEMS Directional Microphone
## 2 Regular and Proposed D33 Modes  
Figure 1a shows a unit cell of the regular D33 mode, which includes a pair of IDTs which are connected inter-digitally at MEs. Figure 1b shows the schematics of a unit cell of the proposed D33 mode. It includes three MEs, where two MEs are coupled and the other is placed in-between the coupled MEs with an equal inter-distance and different polarities. As a result, the coupled MEs form a uniform potential difference with the middle ME. After that, IDTs are patterned with an equal spacing, width and length. In both models, the sensitivity (V/Pa) forms of the external mechanical stimuli (i.e., 1 Pa sound pressure) can be analyzed following the piezoelectric circuit model [17; 19]. Figure 1c shows a circuit model which includes the induced charge (q), blocking capacitance (C) and induced voltage (V). The relationship of these parameters is given in [17; 18],  
\[V=q/C;\quad q=d_{33}S_{3}EA;\quad C=\varepsilon_{IDT}\times\frac{A_{s}-(A_{m}+A _{IDT})}{s-(\sum_{i=1}^{n}(W_{i}+L_{i}+w_{i}+l_{i})} \tag{1}\]  
where \(d_{33}\), \(S_{3}\), E, A, \(A_{s}\), \(A_{m}\), \(A_{IDT}\), w, W, l, L and s are the piezoelectric constant, induced strain, electric field, active area, area of electrode spacing, area of ME, area of IDT, width of IDT, width of main electrode, length of IDT, length of main electrode and spacing, respectively. Furthermore, \(\varepsilon_{IDT}\) is the effective material properties in 3-3 conditions and can be defined as the ratio of displacement to the electric field. In addition, \(i\) represents the number of unit cells, from 1 to N. Equation (1) suggests that the increasing of the IDTs and their spacing minimizes the capacitance, which enhances the sensitivity. This enhancement can be done by simply adding IDTs to the regular D33 mode, but it is necessary to have increased diaphragm dimensions. Moreover, the use of coupling does not require the device dimensions to be increased due to its orientation, which shows the significance of the proposed D33 mode. Besides, the use of a coupled D33 mode has some advantages over the regular D33 mode; for example, (1) it requires fewer fabrication steps in comparison  
Figure 1: Modeling of D33 mode, (**a**) unit cell of regular D33 mode, (**b**) unit cell of proposed D33 mode, (**c**) equivalent piezoelectric circuit of a unit cell of the regular and proposed D33 modes, (**d**) computer-assisted design (CAD) modeling of unit cell of the regular D33 mode and (**e**) CAD modeling of a unit cell of the proposed D33 mode. with the double-layered D33 mode, and as a result it is cost-effective [24], and (2) the shared IDTs of the middle electrode do not interact with each other due to them having the same polarity--instead, they have a uniform potential difference with coupled edge electrodes. To understand the effectiveness of the coupled D33 modes, both modes (Figure 1a,b) were modeled with regard to their acoustic-piezoelectric interaction using the finite element method (FEM) with COMSOL Multiphysics 5.2 version software, and electrical performances were simulated by applying 1 Pa of sound pressure at 1 kHz frequency in a frequency domain study. In both models, the ME and IDT were made of 1.02 \(\upmu\)m thick aluminum (with a Young's modulus of 70 GPa, speed of sound of 6320 m/s and Poisson's ratio of 0.35) and created on top of a 0.5 \(\upmu\)m thick aluminum nitride (AlN) structure. The AlN (with a [PERSON]'s modulus of 273 GPa, speed of sound of 5760 m/s and Poisson's ratio of 0.23) and aluminum structures along with their thicknesses were recommended by the PiezoMUMPs [25] since the authors fabricated the devices using multi-user MEMS processes (MUMPs), as discussed in Section 3. On the other hand, the width (w) of each IDT and the spacing between IDTs were 2.5 \(\upmu\)m and 10 \(\upmu\)m, respectively, as used by [PERSON] et al. [19], whereas the IDT's length in the regular D33 mode was 200 \(\upmu\)m; in the proposed D33 mode, this was reduced to 90 \(\upmu\)m to make space for the middle ME as shown in Figure 1d,e.