Development of a Multi-Scale Electromigration Simulator Based on a Combination of Ultra Accelerated Quantum Chemical Molecular Dynamics and Kinetic Monte Carlo Methods Application to Cu Interconnects Lifetime Simulation

Abstract

We present a novel study on electromigration (EM) phenomena in Cu interconnects using a newly developed multi-scale simulator that consists on a combination of a device scale simulator based on a kinetic Monte Carlo (KMC) method and an atomic scale simulator based on ultra accelerated quantum chemical molecular dynamics (UA-QCMD). We have firstly demonstrated the simulation of the lifetime of Cu interconnects using the newly developed device scale simulator setting some suitable KMC probabilities for the void movement according to the regions in which it can be divided, i.e., the crystal grain and the grain boundary. The simulated values are shown to be in good agreement with experimental values. In an attempt to connect the device scale studies to quantum chemical instances of the system -since the correlation of probability of the void movement with, for example, activation energies or diffusion coefficients is important -we have developed an atomic scale simulator based on our original UA-QCMD method. In this atomic scale simulation, the electron wind force was evaluated using our original electrical conductivity prediction simulator based on KMC method which uses the electronic states from tight-binding quantum chemical (TBQC) calculation. Using this atomic scale simulator under the conditions of 475 K of temperature and 2:5 Â 10 10 A/m 2 of current density, we were able to successfully simulate the migration of a Cu atom from a lattice site to a vacant site by evaluating the electron wind force.