Comparison of MEMS PZT Cantilevers Based on $d_{31}$ and $d_{33}$ Modes for Vibration Energy Harvesting

Abstract

<i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> mode microelectromechanical systems piezoelectric energy harvesters (PEHs) were fabricated and compared to investigate their output powers converted from vibration. Both types of devices have the same dimensions in a cantilever structure and aim to effectively couple vibration from ambient conditions. The resonant frequencies of the cantilevers are 243 Hz. Two types of devices were compared using mathematical equations based on an equivalent circuit model. The output power of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31</sub> mode PEH was 2.15 μW and 2.33 μW in experiment and modeling, respectively. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> mode PEHs generated output power ranging between 0.62 and 1.71 μW when the width of the interdigital electrode (IDE) is ranging from 8 to 16 μm and finger spacing is varied from 4 to 16 μm. The output power of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> mode device strongly depends on the dimensions of IDE. The analysis of material constant and electrode design was conducted in conjunction with developing a mathematical equation. The result predicts that the output power of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> mode PEH can be higher than that of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31</sub> mode PEH when the finger width is reduced to 2 μm and finger spacing is between 8 and 20 μm.