Current divisions and distributed Joule heating of two-dimensional grid microstructures
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TECHNICAL PAPER
Current divisions and distributed Joule heating of two-dimensional grid microstructures Zhongjing Ren1,2 • Jianping Yuan1 • Xiaoyu Su3 • Robert Bauer2 • Yang Xu2 • Sundeep Mangla4 Fernando Camino5 • Chang-Yong Nam5 • Ming Lu5 • Yong Shi2
•
Received: 29 October 2020 / Accepted: 3 November 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents current divisions and distributed Joule heating of two-dimensional (2D) grid microstructures. The current divisions on 2 9 2, 4 9 4, and n 9 n grid microstructures made of the same conductive beams are analyzed theoretically, and Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) are employed to determine the current division factors and directions under different voltage input cases. The equivalent resistances and Joule heating power are therefore derived. 2D 2 9 2 grid microstructures made of gold (60 nm in thickness) and those made of near-equiatomic NiTi (850 nm in thickness) for various independent voltage input cases are fabricated by electron-beam evaporation and co-sputtering, respectively. The equivalent resistances of these grid microstructures are measured by four-terminal resistance measurement at ambient conditions, which show a good agreement with the theoretical results. Further investigation on the electrical resistivities of evaporated gold layer (4.85 9 10–8 X m) and co-sputtered NiTi (1.23 9 10–5 X m) reveals that the influences of scale effect and fabrication process on the resistivity cannot be neglected. As such, it is found to be necessary to consider the materials’ resistivity in the fabricated grid microstructures before their electro-thermal analysis.
1 Introduction
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00542-020-05103-1) contains supplementary material, which is available to authorized users. & Zhongjing Ren [email protected] & Jianping Yuan [email protected] & Yong Shi [email protected] 1
National Key Laboratory of Space Flight Dynamics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
2
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
3
School of Automation, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
4
Downstate Medical Center, State University of New York, Brooklyn, NY 11203, USA
5
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
Active, reconfigurable microstructures for microactuators show wide uses in such applications as micro medical devices (Chun et al. 2010; Ghazali et al. 2020) and microrobots (Su et al. 2018), where a variety of miniaturized structures are created to satisfy diverse needs. The candidate materials for building such microstructures include metals (Sun et al. 2020a), polymers (Al-Zandi et al. 2018), ceramics (Galos et al. 2017a, b, 2018), and composites (Su et al. 2018). Generally, these microstructures can be des
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