Macromodeling Temperature-Dependent Curl in CMOS Micromachined Beams

摘要

Temperature sensitive curling is commonly observed in MEMS structures fabricated using a standard CMOS process. In this paper, a macromodel for vertical and lateral curling effects is derived by extending thermal multimorph theory for cantilever beams. Stresses induced by temperature change are lumped to form equivalent force and moment sources at the two ends of a beam. The macromodel is added onto an existing mechanical beam model which is used to build and simulate MEMS in a schematic view. Strain in the polysilicon layer of the CMOS microstructure leads to piezoresistance. The macromodel implementation includes computation of strain. The deflections in the lateral and vertical directions from simulations using the macro-model match finite-element analyses to within 3% and match experimental measurements to within 15%.