Electromigration Reliability Modeling And COMSOL Simulation Method For Multi-branch Interconnect Trees

In high performance circuit design,thermal effect on electromigration(EM)reliability has become a recent major research for being a limiting factor.Due to the miniaturization of integrated circuits,the current density of metal interconnects increases sharply,the failure of interconnect tree caused by electromigration is becoming more and more serious,and EM reliability analysis is also attracting much attention.For EM modeling and assessment,one important problem is to perform fast EM time to failure analysis for practical interconnect layouts,such as clock and power/ground networks consisting of many multi-branch wires.However,existing EM modeling and analysis techniques are mainly developed for a single wire with constant temperature.In this thesis,a new analytic expression to calculate hydrostatic stress evolution for general multi-branch interconnect wire with multiple terminals is proposed,and EM failure time can be calculated by critical stress.This method is based on Korhonen's equation with blocked atom flux boundary conditions and continuity conditions of stress at terminals.Analytical solutions can be derived using a set of auxiliary basis functions with the complementary error function by Laplasce transform technique.We also propose a novel analytic method to calculate the stress evolution considering time-varying temperature effects during the void nucleation phase for those multi-branch interconnect trees.Experiment results show that the obtained analytic solutions match well with the numerical results by COMSOL simulation method and thus the proposed models can be used in traditional EM reliability analysis tools.We further demonstrate that using the first one dominant basis function approximation can decrease the error less than 2% error,which leads to very compact EM models with sufficient accuracy.Also,the proposed closed-form expression has been compared against electromigration simulator XSim and the eigenfunction method.The numerical results indicate that the proposed method has higher accuracy and faster convergence rate.