Table 1 Layer properties used in the ECM calculation
From: High frame rate ultrasonic flowmeter based on PMUT array with bidirectional acoustic beams
Symbol | Value | Description | Symbol | Value | Description |
|---|---|---|---|---|---|
r | 250 μm | Diaphragm radius | YPt | 168 Gpa | Young’s modulus of Pt |
Rte | 162 μm | Top electrode radius | \(\rho\)Pt | 21,450 kg/m3 | Density of Pt |
d | 625 μm | Pitch between adjacent cells | νPt | 0.38 | Poisson’s ratio of Pt |
tSi | 4 μm | Polysilicon thickness | YPZT | 70 Gpa | Young’s modulus of PZT |
\({t}_{{{SiO}}_{2}}\) | 0.5 μm | SiO2 thickness | \(\rho\)PZT | 7600 kg/m3 | Density of PZT |
tBE | 0.12 μm | Bottom Pt thickness | νPZT | 0.33 | Poisson’s ratio of PZT |
tPZT | 2 μm | Piezoelectric layer thickness | \({Y}_{{{Al}}_{2}{O}_{3}}\) | 400 Gpa | Young’s modulus of Al2O3 |
tTE | 0.1 μm | Top Pt thickness | \({\rho }_{{{Al}}_{2}{O}_{3}}\) | 3965 kg/m3 | Density of Al2O3 |
\({t}_{{{Al}}_{2}{O}_{3}}\) | 0.04 μm | Al2O3 passivation thickness | \({\nu }_{{{Al}}_{2}{O}_{3}}\) | 0.22 | Poisson’s ratio of Al2O3 |
tUSG | 0.4 μm | USG passivation thickness | YUSG | 72 Gpa | Young’s modulus of USG |
\({t}_{{{Si}}_{3}{N}_{4}}\) | 0.3 μm | Si3N4 passivation thickness | \(\rho\)USG | 2200 kg/m3 | Density of USG |
YSi | 160 Gpa | Young’s modulus of Si | νUSG | 0.17 | Poisson’s ratio of USG |
\(\rho\)Si | 2320 kg/m3 | Density of Si | \({Y}_{{{Si}}_{3}{N}_{4}}\) | 250 Gpa | Young’s modulus of Si3N4 |
νSi | 0.22 | Poisson’s ratio of Si | \({\rho }_{{{Si}}_{3}{N}_{4}}\) | 3100 kg/m3 | Density of Si3N4 |
\({Y}_{{{SiO}}_{2}}\) | 70 Gpa | Young’s modulus of SiO2 | \({\nu }_{{{Si}}_{3}{N}_{4}}\) | 0.23 | Poisson’s ratio of Si3N4 |
\({\rho }_{{{SiO}}_{2}}\) | 2200 kg/m3 | Density of SiO2 | d31 | –150 pm/V | Piezoelectric coefficient |
\({\nu }_{{{SiO}}_{2}}\) | 0.17 | Poisson’s ratio of SiO2 | \(\varepsilon\)r | 1200 | Relative dielectric constant |
