An Analytical Capacitance Model of Temperature-Sensitive, Large-Displacement Multimorph Cantilevers: Numerical and Experimental Validation

This paper presents a new experimentally validated analytical capacitance macromodel for microelectromechanical systems large-displacement cantilever beams. The presented model successfully captures 1) the deformed cantilever shape under large-displacement conditions and when the beam is subjected to simultaneous thermal and residual stresses; 2) the electric field and capacitance between the curled beam and an electrode underneath it from room temperature to over 200 ^°C. All analytical models are verified through finite-element analysis and, for the first time, experimentally validated for deflections over 120 μm and temperatures above 200 ^°C. We start by extending a multimorph model originally proposed to analyze piezoelectric actuators, to also consider thermal and residual (postfabrication) strains under large-displacement conditions. The model is experimentally validated through measurements conducted on SiO₂/Ti/Au cantilevers fabricated on silicon wafers. The average error between the measured and simulated displacements is less than 4% and 3% at the beam midpoints and tips, respectively, for the entire range of 20-250 ^°C . Capacitance measurements conducted to over 200 ^°C show an average deviation from the macromodel of 6.4% over the range of 20-213 ^°C. The standard deviation for capacitance error is 5.4%, and the maximum error is 15.3%.