Design and Modeling of Micro-glassblown Inverted-wineglass Structures Doruk Senkal, Mohammed J. Ahamed, and Andrei M. Shkel MicroSystems Laboratory, University of California, Irvine, CA, USA Email: {dsenkal, mahamed, ashkel}@uci.edu Abstract— This paper reports analytical and finite element models for predicting the final 3-D geometry of micro-glassblown inverted-wineglass and hemi-toroidal structures from a set of initial conditions. Using these methods critical geometric param- eters for wineglass resonator and gyroscope operation, such as shell thickness, shell height, stem type (hollow/solid), and stem diameter can be estimated from initial parameters. Analytical models for first order calculation of shell height and minor radius, as well as finite element models based on Arbitrary Lagrangian- Eulerian (ALE) methods for calculating the thickness of the shell and diameter of the stem structure are presented. Devel- oped models were validated against fabricated micro-glassblown structures and showed better than 10 % match to experimental results. Methods presented in this paper can be used to design micro-glassblown wineglass resonators with specific dimensions and resonance frequencies, essentially taking the guesswork out of the design process and significantly lowering the development time. I. I NTRODUCTION Recently, there has been a growing interest in 3-D MEMS wineglass resonator architectures for use in timing and inertial sensing applications due to potential advantages in symmetry, minimization of energy losses, and immunity to external vibrations [1]. Two common themes emerged in the literature for wafer- level fabrication of micro-wineglass structures: (1) thin-film deposition of the resonator material into a pre-defined mold [2]–[4] and (2) pressure induced plastic deformation of a device layer to form the 3-D shell structure (micro- glassblowing) [5]. Due to the self-correcting behavior of surface tension forces, micro-glassblowing process has potential advantages over conventional micro-machining techniques in terms of surface roughness, structural symmetry, and robustness to fabrication imperfections. For this reason similar fabrication processes emerged in the recent years, which rely on plastic deformation of the device layer to create micro-wineglass structures for rate integrating gyroscope and resonator applications. These processes include blow molding of bulk metallic glasses [6], micro-glassblowing of fused silica/ULE inverted-wineglass structures [7], [8], Fig. 1, and blow-torch molding of fused silica hemi-toroidal structures [9]. This material is based upon work supported by DARPA grant W31P4Q-11-1-0006 (Program Manager Dr. Robert Lutwak). 4 mm Fig. 1. Micro-glassblowing process can create arrays of inverted-wineglass structures on the wafer surface. Outer diameter of shells is 4 mm, over 100 shells were fabricated on a 4” wafer. Despite the recent advances in fabrication techniques for micro-glassblown structures, means to design a specific 3-D geometry based on initial geometric parameters have so far not been presented. Even though, a set of equations to predict the final geometry of micro-glassblown spherical shell structures were introduced in [10], accurate estimation of shell thickness was not possible and the equations did not extend to inverted-wineglass structures. This paper presents analytical and finite element models to predict the outcome of the micro-glassblowing process, which enables one to design photomasks and process parameters to obtain a specific 3-D shell geometry. II. DESIGN &MODELING In this section, first a brief description of the micro- glassblowing process will be presented. This will be followed by analytical expressions to predict the final micro-glassblown geometry and finite element methods to predict thickness of the shell structure and stem diameter. A. Micro-glassblowing of Inverted-wineglass Structures Micro-glassblowing process consists of four fundamental steps: (1) etching of cavities onto a substrate wafer, (2) bonding of a thin glass layer on top as to trap atmospheric 978-1-4799-0916-2/14/$31.00 ©2014 IEEE