2-D simulation of multilayered MEMS structures

Abstract

MEMS device structures, particularly those made using Surface-Micromachining, consist of thin layers of insulator, silicon, silicon dioxide, silicon nitride, metal or poly-silicon held at few points onto a thick silicon substrate. These heterogeneous layers resemble closely to laminas of composites used in building structures. For these heterogeneous material systems, involving Metal- Insulator-Semiconductor layers, there is usually an inherent two dimensional thermal contraction of the various layers upon cooling from a growth temperature of 1000 to 1200 C down to room temperature. The thermal stress, so developed, could result in static deformation as well change the dynamic characteristics of the micro-parts. Thin heteroepitaxial layers, with lattice mismatch with the single crystal substrate, can also result in a built in stress. External effects like electrostatic potentials and magnetic fields applied to a layered structure can also result in contractions or extensions of specific layers that respond to applied fields. A generic formulation of governing equations of equilibrium and compatibility has been developed for laminated structures with various in-built stress effects like difference in temperature of formation and use; difference in lattice constants of heteroepitaxial layers; effects that involve dimensional changes like piezoelectric effect and magnetostriction. This paper aims at demonstrating, through simulations of a test structure of a doubly suspended resonator, how these multi-layer structures could exploit the static deformations to result in a robust (temperature- insensitive) dynamic response. The static deformation for temperature changes in a bi-layer of aluminum and silicon dioxide is simulated on ANSYS. The results of ANSYS match very well with a fabricated test device.