Shaping interconnect for uniform current density

As the VLSI technology scaling down, the electromigration problem becomes one of the major concerns in high-performance IC design for both power network and signal interconnects. For a uniform width metal interconnect, the current flows through the driving point is much larger than that flows through the fan-out point since much of current bypasses to the ground through the parasitic capacitance. This causes the lifetime of driving point to be quite shorter than that of fan-out point due to electromigration. In order to avoid breakdown at the driving point, wire sizing is an effective solution. Thus we present a wire shape, of which the current density as well as the lifetime is uniform along the wire. SPICE simulation results show the uniformity of current density of this wire shape. Under the same current density bound, we demonstrate that chip area and power consumption are significantly reduced for this wire shape compared to the uniform width wire. The wire shape functions we derived are continuous. However, it is not necessary to ultra-accurately reproduce the continuous shape on the silicon, since we can round the continuous shape to the nearest available litho width and this will not degrade the uniformity of current density.