Electromigration and metalization lifetimes

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Abstract
A model has been developed to predict the lifetime τf of integrated circuit metalizations which operate at high dc densities Je. Grain-boundary electromigration, internal heat generation, and current crowding at growing voids dominate the rate processes that lead to failure. Joule heating of the stripe causes an initial temperature rise ΔT0 and heat flow into the substrate. If this rise is appreciable an instability exists in the stripe. When vacancies electromigrate down grain boundaries and precipitate on a suitable boundary, forming an elongated void, the electric current will be diverted. This is serious if the crack has a substantial length component perpendicular to the current flow which increases vacancy currents to the crack tip and the local heating. An analytical model considering these effects and the time for a crack to propagate across the stripe width yields a stripe lifetime integral which fits the form Pn =(1/2)(1+0.265γΔT0). Here γ=ΔH/kT2 is the temperature coefficient of the diffusion constant. Pn, the crack width, and the initial electromigration grain boundary flux then largely determine the stripe lifetime. The self-heating contribution ΔT0 is shown to be an important term in the interpretation of accelerated test data and for proper extrapolation to lower temperature-and-current stress levels. The stripe temperature coefficient of resistance and melting point are shown to have only secondary effects on lifetime. Lifetimes have a Je−n dependence with n varying from unity at low ΔT0 levels to 15+ for high ΔT0 levels and are determined by the stripe and heat-sink temperatures. For maximum stripe lifetimes, wide stripes with good thermal coupling to the heat sink are desirable.