Optimal design of unimorph-type cantilevered piezoelectric energy harvesters using level set-based topology optimization by considering manufacturability

TL;DR

This work addresses designing unimorph cantilevered piezoelectric energy harvesters under manufacturability constraints. It introduces a level-set topology optimization framework that concurrently optimizes the silicon substrate and the piezoelectric film, with DRIE-oriented constraints to ensure microfabrication feasibility. The method targets specified eigenfrequencies and a minimum output voltage while maximizing electromechanical coupling via open-circuit and short-circuit eigenproblems, incorporating a substrate-dependent constraint to prevent unsupported piezoelectric regions. Numerical examples demonstrate manufacturable designs with enhanced coupling and controllable voltage, though tighter constraints reduce objective performance; the approach holds promise for practical fabrication-ready energy harvesters.

Abstract

In this study, we propose a design methodology for a piezoelectric energy-harvesting device optimized for maximal power generation at a designated frequency using topology optimization. The proposed methodology is adapted to the design of a unimorph-type piezoelectric energy harvester, wherein a piezoelectric film is affixed to a singular side of a silicon cantilever beam. Both the substrate and the piezoelectric film components undergo concurrent optimization. Constraints are imposed to ensure that the resultant design is amenable to microfabrication, with specific emphasis on the etchability of piezoelectric energy harvesters. Several numerical examples are provided to validate the efficacy of the proposed method. The results show that the proposed method yields optimized substrate and piezoelectric designs with an enhanced electromechanical coupling coefficient, while allowing the eigenfrequency of the device and the minimum output voltage to be set to the desired values. Furthermore, the proposed method can provide solutions that satisfy the cross-sectional shape, substrate-dependent, and minimum output voltage constraints. The solutions obtained by the proposed method are manufacturable in the field of microfabrication.

Figures (11)

• Figure 1: Concept of a piezoelectric energy harvester
• Figure 2: Steps of the DRIE process creating precise microstructures. (a) Application of resist: A layer of photoresist is applied to the surface of the material. (b) Photolithography: (1) A photomask is aligned over the photoresist-coated material. (2) UV exposure through the photomask transfers the pattern onto the photoresist. (3) The photoresist is developed, revealing the pattern. (c) Etching: (1) Etching begins in the exposed areas by exposing the surface to reactive ions. (2) Etching progresses to achieve the desired depth and pattern. (3) Etching is completed with precise control in the vertical direction. (d) Removal of resist: The remaining photoresist is removed, leaving behind the etched pattern.
• Figure 3: Illustration of the substrate-dependent constraint on the piezoelectric domain. The left side shows a "Constrained structure," where the piezoelectric material is properly supported by the substrate, ensuring mechanical stability and integrity. The right side shows a "Not constrained structure," where piezoelectric material is deposited without substrate support, leading to potential delamination or cracking.
• Figure 4: The design domains used in this study. 3D view: Visualization of the 3D structure showing the division into the piezoelectric design domain ($D_{pe}$) and the substrate design domain ($D_{sb}$). Side view: Cross-sectional side view illustrating the components contained within each domain. $D_{pe}$ is the design domain for the piezoelectric material, while $D_{sb}$ is design domain for the substrate material.
• Figure 5: Schematic illustration of the etching process for a unimorph cantilevered piezoelectric energy harvester. Initial configuration: Before any etching process begins. Step (a) Weight formation: The structure after etching from the backside to form the weight. Step (b) Beam and PZT formation: The structure after etching from the backside to form the silicon beam and PZT shapes. This step represents single-side etching. Step (c) Final PZT formation: The structure after etching from the front side to form the PZT shape differing from the beam. This step represents double-side etching.