A Study on the 0-Level Package Design of a High Accuracy Silicon MEMS Resonator

Finite element analysis (FEA) is employed in this work to calculate the induced stresses in a double clamped silicon resonator and estimate the shift in frequency due to induced stresses during processing. From the modeling results, it was found that the induced stresses in the resonator are in the order of 1 to 6 MPa. A parametric analysis done on the FEM suggested that the sensitive factors affecting the resonance frequency of the resonator are: (a) the distance between the anchor of the beam resonator and the sealing ring, (b) the width of the sealing ring and (c) the materials used in the sealing ring. The analysis indicates that a narrow sealing ring will reduce the stresses in the resonator, however a compromise between hermeticity and low induced stress has to be kept. Another possibility to reduce the shift in resonance frequency is to place the sealing ring at an optimal distance from the anchor points of the resonator, counteracting the local deformation of the sealing ring and the global warpage of the package. A stress-decoupling gap is also proposed to isolate the resonator from the deformations of the sealing ring