Extracting theYoung's Modulus andStress Gradient ofThin Films fromthePull-in Voltage ofaMicroCurled Cantilever Beam

This paperpresents a high-precision algorithm for extracting theYoung's modulusandstress gradient ofthinfilms fromthepull-in voltage measurement ofa microcurled cantilever beammadeofthinfilmmaterials. Thealgorithm considers theimportant issues including thefringing fields, the electromechanical coupling, andthestress-induced initial curling ofthemicrostructures. Thedeviation oftheextracted Young's modulusandstress gradient fromthereality arebelow4%.The present algorithm isveryapplicable tothewafer-lever testing of MEMS devices since thedriving andresponse signals areboth electric, thepresent algorithm couldbe accomplished using existing semiconductor testing equipments through probing on thebonding padsofdevices. testing structures anditsextracting algorithm. Themotivation ofthepresent paperistodevelop amethodtoextract the Young's modulus andstress gradient ofthinfilms; moreover, suchmethod isexpected tobecompatible withthewafer-level testing inICindustry. Therefore, thebestchoices ofthe actuating andmeasuring method arebothelectrical. Besides, thedesign ofthetesting structure should besimple since the algorithm forextracting themechanical parameters from electrical signal issimpler forsimpler testing structure. To realize theidea ofMEMS wafer-level testing compatible with IC industry, theauthors select theelectrostatic actuating method andmeasuring thecapacitance variation todetect the pull-in voltage ofthemicro testing beams. We design asimple testing structure that isamicrocurled cantilever beam.Both thefabrication andextracting algorithm areverysimple. The extracting algorithm considering thefringing field capacitance aswellasthedistributed deformation ofthetesting beamsand isdeveloped basedontheenergymethod. Therequired equipment isonly anAgilent 4285Aprecision LCRmeterthat canapply DC bias voltages onthetesting beamsandmeasure thecapacitance variations precisely. We demonstrate the commoncases ofpolysilicon; thepolysilicon film deposited by low-pressure chemical vapordeposition (LPCVD).The extracted Young's modului andstresses gradient agree very well withtheexperimental data. p 1011 ~~~~~~x go ~~~w(x)