Finite Element Analysis of the Effects of Package Induced Stress on Micromechanical Resonator Temperature Stability

Vacuum encapsulation of RF disk and beam resonators is often needed to maintain high quality factor and frequency stability. Conventionally, this is performed at the wafer level by anodic, eutectic, fusion, or glass frit bonding. After wafer dicing, packaging proceeds with die attach to the package substrate and plastic over molding. This process leads to many contacts between materials of different coefficients of thermal expansion (CTE) resulting in package-induced stress. The focus of this work is to determine the effect of this stress on the temperature stability of micromechanical resonators via finite element analysis (FEA), for applications that do not require attachment to a printed circuit board, such as the sensors in the original vision of Smart Dust. The simulation is separated into two main parts: (a) package analysis and (b) resonator analysis. The package is analyzed in a static structural environment, recording mesh model nodal displacement on the packaged die surface, yielding displacement boundary conditions specific for each of the selected package models. These boundary conditions are then applied to the anchor nodes of the resonator in a separate prestressed modal analysis to determine modal frequencies of the desired mode shapes. Results indicate that package-induced stress depends mostly on die thickness and die attach CTE. Thinner dies and die attach material with very high CTEs tend to induce more stress in the die. The temperature stability of packaged resonators, when compared to their unpackaged counterparts, is influenced very slightly by the package alone. Thinner dies improve temperature stability very slightly, although there is residual stress in the die itself, which may lead to mechanical failure of the package. Of the resonator geometries investigated, the clamped-clamped beam is the most susceptible to package-induced stress, because of the large anchor contact area to the substrate. The centrally anchored disk, although directly anchored to the substrate, contacts a much smaller area, and thus, its temperature stability is unaffected by package-induced stress. Although it has large anchors, the free-free beam is levitated by support beams, and so, its temperature stability is only slightly affected. Finite element models are solved using the commercial FEA software package ANSYS 14.5.