A Multiphysics Coupled Electro-thermo-mechanical Model of Whisker Shorting

This work considers the behavior of a metallic whisker as it is causing a short circuit. This is achieved by using a coupled electro-thermo-mechanical numerical model (i.e. multiphysics finite elements). The shorted current passing through the whisker will cause it to heat and the temperature to rise. The temperature rise can cause the whisker to soften and stresses to grow. Eventually this could cause the whisker to melt or fail, which in turn breaks the short circuit. This work examines at what conditions this will occur for typical whiskers consisting of tin. The model is able to include temperature dependent properties such as resistivity and strength, which is difficult to accomplish in closed-form analysis. Based on the finite element model and existing theory, equations are also provided to make predictions of the maximum current that can be withstood by a typical whisker before its demise.