Nov_Dec_AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | N O V E M B E R / D E C E M B E R 2 0 2 0 1 7 merely provide a starting point for pre- dicting performance of the fabricated devices [14] . Validation of the fundamental resonance frequency can be achieved through electrical input impedance modeling. The single PMUT cell mod- el was driven by a bipolar peak-to-peak voltage, 3 Vpp, and 1 MHz to 500 MHz sinusoidal signal to ensure that the lowest resonance frequencywas discov- ered. The modeling assumed a vacuum environment for calculation efficiency. Figure 3 displays a snapshot of the di- aphragm deflections at their centers in the PMUT model simulation. Figure 4 shows the electrical input impedance responses of the four diaphragms in the PMUT cell. Figure 3 shows the deflections of the respective diaphragm cross-sec- tions, which were coincident. In Fig. 4, all four diaphragms had the same elec- trical input impedance response. The fundamental resonance and anti-res- onance frequencies were found at 39.1 MHz and 40.3 MHz, respective- ly, satisfying a targeted resonance fre- quency range near 40 MHz. A water load was added above the PMUT cell so that the basic character- istics of the PMUT cell, center frequen- cy and bandwidth, could be simulated for the same environment as for water immersion experiments. Figure 5 re- vealed the center frequency and -6 dB bandwidth of the PMUT water model to be 37.6 MHz and {(44.8-32.7) ÷ 37.6) × 100 %} = 32.3 %, respectively. The model was driven by a bipolar peak- to-peak 3 Vpp, single cycle sine wave. The decreased center frequency, 37.6 MHz from 39.1 MHz, can be explained by the mass loading effect of the wa- ter on the diaphragms. The 32.3% bandwidth was relatively narrow for an imaging transducer, a feature that has been addressed by Kim et al. [8] , who found that the bandwidth narrowed as the number of PMUT cells increased in a flexible polymer substrate PMUT array. This article addressed increasing the bandwidth beyond that considered by Kim et al. [8] . RESULTS A 2D, 32x32 array model, com- prised of 256 (16×16) quad diaphragm PMUT cells and 1024 (32×32) moving di- aphragms, is now considered, as shown in Fig. 6. The 1024 (32×32) moving di- aphragms each have the same kerf, 11 µm, and the same pitch, 21 µm, and occupy a planar area of approximately 0.7 × 0.7 mm. Fig. 2 — Properties of PZT 8 applied to model thin-filmPZT. Fig. 3 — Snapshot of the quad diaphragmPMUT cell model running in vacuum for the electrical input impedance calculation.