Electro-Thermal-Mechanical Modeling of one-Dimensional Conductors, Whiskers, and Wires Including Convection, and Considering Tin, Bismuth, Zinc And Indium
This work provides analytical solutions to the temperature rise of one-dimensional conductors such as whiskers and wires. Whisker growth from metal surfaces of electrical connectors and other components has shown itself to create reliability issues. If a whisker grows in a location that bridges between two conducting surfaces not previously electrically connected, a short can occur, resulting in faulting components. The current passing through the whisker or wire will cause its temperature to rise due to Joule heating. This can eventually cause the conductor to melt, which can than disconnect the short circuit. Therefore, whisker shorts are limited by this melting current. thermal fields of a solid cylindrical conductor including the heat convection, which dissipates some of the heat and reduces the temperature rise. This work examines the influence of convection on the melting of a shorted whisker via a finite difference model that considers the temperature dependent conductivities when solving the coupled one-dimensional heat and electrical conduction equations. Finally, the properties of tin, indium, bismuth and zinc are considered in modeling whisker melting since they are all known to form whiskers.