IMPACT OF MINIATURIZATION ON THE CURRENT HANDLING OF ELECTROSTATIC MEMS RESONATORS Manu Agarwal 1 , Harsh Mehta 1 , Robert N. Candler 2 , Saurabh A. Chandorkar 1 , Bongsang Kim 1 , Matthew A. Hopcroft 1 , Renata Melamud 1 , Gaurav Bahl 1 , Gary Yama 2 , Thomas W. Kenny 1 and Boris Murmann 1 1 Departments of Electrical and Mechanical Eng., Stanford University, Stanford, CA, USA 2 Robert Bosch Corporation (Research & Technology Center), Palo Alto, CA, USA ABSTRACT This paper studies the scaling of nonlinearities with miniaturization in double-ended-tuning-fork (DETF) MEMS resonators. We find that the increase in resonant frequency associated with beam length reduction strongly improves current handling; e.g. shortening the beams by a factor of 5 results in a 100- fold increase in sustainable signal current. Using the nonlinear models and scaling observed in this work, we present considerations for optimization of the resonant structure design and the electrostatic gap size. 1. INTRODUCTION Electrostatic MEMS resonators have become an attractive and viable alternative to quartz crystal resonators, especially for timing/frequency reference applications [1]. Many of the advantages offered by these resonators, such as integration with CMOS, lower cost and low form factors will be more pronounced for smaller (miniaturized) micro-structure resonators. High current handling is needed to attain large signal-to-noise-ratio in oscillator circuits tailored for precision frequency references. As in quartz, the current handling is limited by the amplitude- frequency (A-f) nonlinear effect [2]. This effect increases the relative far-from-carrier noise floor and also induces mixing of amplitude noise into close-to- carrier phase noise [3]. In this work, we study the impact of miniaturization on the nonlinear characteristics, and hence current handling, in electrostatically coupled MEMS resonators. The presented experimental results confirm existing models for the A-f effect [4] and provide design insight towards optimizing MEMS resonators for high precision frequency reference oscillators. Fig. 1 shows a schematic of the resonant structure, the resonant mode shape, and a partial SEM cross section of the devices used in this study. The devices were fabricated using an epi-seal encapsulation process [5] using a <100> SOI wafer with a device layer thickness of h = 20 µm and an Fig. 1. Schematic showing the double ended tuning fork resonator with length L. The resonance mode is also shown, along with a partial SEM cross-section of the wafer scale encapsulated resonator. electrostatic gap size of d = 1 µm. The beam lengths were oriented along the [110] direction. Fig. 2 shows the resonant frequencies (f 0 ) and quality factors (Q) of the measured devices. 2. THEORETICAL MODELS In this section, we briefly summarize existing analytical models for the A-f effect and current handling [4, 6, 7]. Using the solution to the nonlinear equation for low damping oscillations [8], we can