Extracting the Young's Modulus and Stress Gradient of Thin Films from the Pull-in Voltage of a Micro Curled Cantilever Beam

This paper presents a high-precision algorithm for extracting the Young's modulus and stress gradient of thin films from the pull-in voltage measurement of a micro curled cantilever beam made of thin film materials. The algorithm considers the important issues including the fringing fields, the electromechanical coupling, and the stress-induced initial curling of the micro structures. The deviation of the extracted Young's modulus and stress gradient from the reality are below 4%. The present algorithm is very applicable to the wafer-lever testing of MEMS devices since the driving and response signals are both electric, the present algorithm could be accomplished using existing semiconductor testing equipments through probing on the bonding pads of devices.