Static electromigration analysis for on-chip signal interconnects

With the increase in current densities, electromigration has become a critical concern in high-performance designs. Typically, electromigration has involved the process of time-domain simulation of drivers and interconnect to obtain average, root mean square (rms), and peak current values for each wire segment. However, this approach cannot be applied to large problem sizes where hundreds of thousands of nets must be analyzed, each consisting of many thousands of RC elements. The authors propose a static electromigration analysis approach. They show that the charge transfer through wire segments of a net can be calculated directly by solving a system of linear equations, derived from the nodal formulation of the circuit, thereby eliminating the need for time domain simulation. Also, they prove that the charge transfer through a wire segment is independent of the shape of the driver current waveform. From the charge transfer through each wire segment, the average current is obtained directly, as well as approximate rms and peak currents. The authors account for the different possible switching scenarios that give rise to unidirectional or bidirectional current by separating the charge transfer from the rising and falling transitions and also propose approaches for modeling multiple simultaneous switching drivers. They implemented the proposed static analysis approach in an industrial electromigration analysis tool that was used on a number of industrial circuits, including a large microprocessor. The results demonstrate the accuracy and efficiency of the approach.