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.