Stable state of interconnect under temperature change and electric current

This paper considers aluminum interconnects in the presence of insulators, vias, and shunts. Subject to a temperature change and a direct electric current, such an interconnect evolves - after a complicated sequence of events - into a stable state with a segment of aluminum depleted near the cathode, a linear distribution of pressure in the rest of the line, and no further mass diffusion. The electric current continues in the shunt layers where aluminum is depleted; the multilayer interconnect never opens, but its resistance has increased to a saturation level. Several aspects of this stable state are discussed, including the condition under which the high pressure near the anode does not cause the surrounding insulator to crack; the dependence of saturation resistance on shapes, materials, and loads; and the time scale for the interconnect to evolve to the stable state. Should a circuit tolerate a variable resistance up to saturation, the interconnect would function forever. Implications of this possibility are also discussed.