Modeling and Analyzing Copper Dendrite Growth during Electrochemical Migration Using Monte Carlo Simulation

Electrochemical migration (ECM) has recently received increased attention, primarily due to the escalating risk of short circuits associated with the continuous miniaturization of microelectronic devices. As the spacing between conductive elements decreases, the likelihood of ECM-induced failures rises, necessitating a deeper understanding of the underlying mechanisms. This study presents a 2D computational model designed to simulate the ECM process in Cu. The model deterministically accounts for the anodic dissolution of Cu and the subsequent ion transport, while the stochastic nature of dendritic growth is captured through Monte Carlo simulation. To validate the accuracy and reliability of the proposed model, a series of water-drop (WD) tests were conducted using pure copper electrodes separated by a $200 \mu \mathrm{~m}$ gap distance, subjected to a constant 10 VDC bias, and a droplet from a contaminant-free electrolyte. The findings emphasize the versatility of Monte Carlo simulation in accurately replicating ECM behavior in Cu-based systems. By fine-tuning key simulation parameters, the model successfully predicts the Time-to-Failure (TTF) and effectively captures the characteristic tree-like morphology of Cu dendrites.