Prediction of electro-thermal responses of non-uniform functionally graded metal lines under a direct current field

The electro-thermal response of thin, non-uniform functionally-graded metal lines subjected to a direct current flow is determined. The material properties associated with the problem are assumed to vary following a given functional relationship. The corresponding governing differential equations are derived in terms of variable electrical resistivity and thermal conductivity of the material. The solution of the boundary-value problem is then obtained numerically by using finite-difference technique. The electrical and thermal responses of a functionally graded metal line are presented in comparison with those of individual constituent metals. The results are claimed to be highly accurate and reliable, and are considered lobe a valuable guide to thermal analysis of modern electronic devices. (C) 2013 The Authors, Published by Elsevier Ltd.