Physics-based electromigration modeling and assessment for multi-segment interconnects in power grid networks

Electromigration (EM) is considered to be one of the most important reliability issues for current and future ICs in 10nm technology and below. In this paper we focus on the EM stress evaluation for one-dimensional multi-segment interconnect wires in which all the segments have the same direction, which is a common routing structure for power grid networks. The proposed method, which is based on integral transform technique, could efficiently calculate the hydrostatic stress evolution for multi-segment metal wires stressed with different current densities. The new method can also naturally consider the pre-existing residual stresses coming from thermal or other stress sources. Based on this new transient EM assessment method, a full-chip assessment algorithm for power grid networks is then proposed. The new algorithm is also based on the IR-drop metrics for failure assessment of the power grid networks. However, it finds the precise location and time of EM-induced void nucleation by directly checking the time-changing hydrostatic stresses of all the wires. The resulting EM assessment method can ensure sufficient accuracy of the EM verification for large scale power grid networks without sacrificing the efficiency. The accuracy of the proposed transient analysis approach is validated against the numerical analysis. Also the resulting EM-aware full-chip power grid reliability analysis has been demonstrated and compared with existing methods.