Numerical Simulation of Temperature-Voltage Relation in Electrical Contacts and Correction of Classical Kohlrausch's Equation

The increase in temperature caused by Joule heat is a very important concern to the electrical interconnections. The maximum temperature of contacts in these interconnections is not easily measurable, but can be calculated by the temperature-voltage relation, which is also called Kohlrausch's equation. In this paper, we build a finite-element model of spherical copper contact pairs for thermal-electrical coupled analysis. The material properties of the model involved are closely dependent on the temperature. By comparing simulation results with the calculation of the temperature-voltage equation, the accuracy of Kohlrausch's equation has been verified. Furthermore, the effects of electric current, side surface heat convection coefficient, and Lorenz coefficient on Kohlrausch's equation are investigated explicitly. It is determined that the calculation error of Kohlrausch's equation could be attributed to the assumed constant Lorenz coefficient, and then a correction method for Kohlrausch's equation is proposed.