A method for mechanical characterization of capacitive devices at wafer level via detecting the pull-in voltages of two test bridges with different lengths

Abstract

The paper aims at developing a wafer-level testing method to examine Young's modulus and residual stress of structural materials of capacitive micro-devices by detecting the pull-in voltages of micro test beams made of the materials to be tested. We derive a formula that correlates the Young's modulus, residual stress and pull-in voltage of the micro test beams. The analytical model considers the fringing field capacitance, the distributed characteristics of the micro test beams and the electromechanical coupling effect. By the present method, one can extract Young's modulus and residual stress simultaneously by detecting the pull-in voltages of two test beams of different lengths. Three common structural materials used in micro-devices are demonstrated: mono-crystalline silicon, poly-silicon and aluminum. The extracted Young's moduli and residual stresses agree very well with the experimental measurement. The present method is expected to be applicable to the wafer-level testing in MEMS device manufacture and compatible with the wafer-level testing in IC industry since the test and the pickup signals are both electrical.