MICROELECTROMECHANICAL INDUCTORS WITH HIGH INDUCTANCE DENSITY VIA MECHANICAL ENERGY STORAGE Vikram Divakar * , Yaxing Zhang, Justin C. Zito, Everett A. Salley and David P. Arnold Interdisciplinary Microsystems Group, Dept. Electrical and Computer Engineering, University of Florida Gainesville, FL, United States *Presenting Author: vikramdivakar@ufl.edu Abstract: This paper reports the design, fabrication and testing of microelectromechanical inductors (MEMIs) that show high electrical inductance by storing energy via a mechanically compliant flexure. The microfabricated MEMI structures comprise a simple electroplated Cu beam that is placed in a static magnetic field. Upon application of ac current, the conductor vibrates via electrodynamic interactions with the magnetic field. This electromechanical behavior manifests as a highly reactive (inductive) one-port electrical impedance. In this work, we explain the microfabrication processes and the subsequent characterization of a variety of test structures, which exhibit a peak quality factor up to 5.6 with net areal inductance densities of up to 3.5 H/mm 2 . These devices are envisioned as a passive energy storage component for exploring high-power-density electrical power converters. Keywords: Inductors, electrodynamic transduction, energy storage, passive components, power converters INTRODUCTION Inductors are an integral part of power electronic circuits. Nowadays, there is a great effort underway to miniaturize inductors to enable fully integrated single- chip electrical power converters [1-6]. This motivates the need for high-inductance-density and high-Q (efficient) microfabricated inductors with form factors that are amenable for integration or co-packaging with silicon integrated circuits (low profile and small areal footprint). Most research in this regard is aimed at increasing the inductance densities of microinductors by including high-permeability magnetic core material. For example, Xu et al. employed a soft magnetic CoZrTa thin film ring structures around copper spiral inductors to obtain a Q factor greater than 3 at 1 GHz [6]. At such high frequencies, the hysteretic and eddy current losses from the soft magnetic core lead to limit the efficiency of the inductor [7]. In general it has been difficult to realize magnetic-core based inductors with high inductance density and high quality factor. The key working principle of the proposed microelectromechanical inductor (MEMI) to achieve high inductance is that mechanical energy storage is used rather than magnetic field energy storage [8]. Mechanical energy storage mechanisms have been shown to possess high energy-density [9]. The device here is an electrically conducting slender beam mechanically supported at each end, as shown in Fig. 1. The device is electrically excited by an external circuit and is set into mechanical oscillation by virtue of a static magnetic field applied perpendicular to the length of the conductor but in plane with the substrate. This results in an electrodynamic actuation, where potential energy is stored via strain, and kinetic energy is stored via inertia of the moving beam. The mechanical energy storage “appears” like inductance due to the electromechanical coupling between the mechanical and electrical energy domains [10]. As will be shown, the apparent electrical inductance of the device can be substantially large, particularly near the mechanical resonance. This paper is a continuation of the work done by Zhang et al., where proof-of-concept results were demonstrated for macroscale devices [8]. Here, we report the fabrication and testing of microscale electromechanical inductors. The microelectro- mechanical inductors explored here operate at “easier- to-implement” kHz frequencies (rather than <100 Hz) and are physically much smaller. These devices are a step toward future development of compact, high- performance power conversion circuitry using these electromechanical energy storage elements. Fig. 1: Microelectromechanical inductor (MEMI) structure DEVICE MODEL The physics for the microscale devices remains the same as their macroscale counterparts as discussed by Zhang et al. [8]. The system can be modeled as a lumped system as shown in Fig. 2. The mechanical parameters such as the damping coefficient, equivalent mass, and equivalent spring stiffness are modeled as an resistance, inductance, and capacitance, respectively (b m , m m and C m =1/ k m ). The electrodynamic transduction is modeled as a gyrator with a gyration ratio denoted by K=Bl (units of T·m). The equivalent one-port circuit representation of the device is also shown in Fig. 2, where the mechanical domain circuit elements have been reflected across the gyrator as equivalent electrical circuit elements. The net electrical behavior appears as