Transient Nonlinear Electrothermal Behaviour of Functionally Graded Angled Metal Lines Under a Direct-Current Field

An alternative iterative scheme has been developed for the analysis of the transient electrothermal response of angled FGM conductor lines under a direct-current field. Material properties involved in the present coupled electrothermal analysis, like electrical resistivity, thermal conductivity, density, temperature coefficient of electrical resistivity and specific heat capacity, are assumed to be functions of space variables as well as temperature. The partial-differential equation that governs the transient, conduction–convection electrothermal problem has been derived, in which the space-dependent material properties are expressed as a function of material composition using a quadratic Sigmoid power-law model. The solution to the present nonlinear coupled initial-boundary-value problem is obtained by an iterative approach in conjunction with an implicit finite difference scheme. The resulting solutions of electric potential and temperature fields are used to determine relevant secondary variables of interest, like current density, temperature gradient as well as electrothermal heat flux, which can be readily used to predict electromigration failure of the FGM line under high current density.