Effect of material composition distribution on the electro-thermal response of a non-uniform functionally graded metal line under a direct current field

The effect of material composition distribution on the electro-thermal response of a thin, non-uniform functionally graded metal (FGM) line is investigated under a direct current field. The distribution of material composition along the FGM line is expressed in terms of a general power-law function of space variable, which, in turn, suggests the corresponding distributions of material properties involved. The governing differential equations associated with the electro-thermal problem are derived in terms of variable electrical resistivity and thermal conductivity of the material. The solution of the coupled boundary-value problem is then obtained numerically using finite-difference technique. The electro-thermal response of the FGM line is obtained for different composition profiles and environmental conditions, which are discussed in light of comparison with those of individual constituent metal lines. (C) 2014 The Authors. Published by Elsevier Ltd.