Residual strain and resultant postrelease deflection of surface micromachined structures

Abstract

The mechanical behavior of surface micromachined structures is significantly affected by residual strains introduced in the manufacturing process. In this article we develop a relationship among residual strain, structure geometry, material properties and the resultant deflection upon release. Microstructures are more susceptible to the effects of residual strain than macromechanical structures for two reasons: (1) Surface layers are deposited at high temperatures and due to differential thermal expansion are subject to large and variable residual strains. (2) Many microstructures have large aspect ratios. Analytical solutions are presented in which beams are modeled as bilayer structures subject to uniform axial stresses and as monolayer structures with an arbitrary stress distribution. The predicted results compare favorably to experimental measurements of complementary metal–oxide–semiconductor surface micromachined beams.