Insights into copper electrochemical migration through numerical modeling and Monte Carlo simulation

• Diffusion and migration terms show an exponential pattern in the Nernst–Planck. • Ion diffusion and migration dominate ECM, with ratios varying over time and position. • The growth of dendrites is effectively modeled using the Monte Carlo simulation. Electrochemical migration (ECM) is receiving increased attention and requires further investigations due to the continuous miniaturization in microelectronics. A numerical ECM model for copper was developed which describes the anodic dissolution using two approaches: a constant anodic surface concentration and an increasing anodic dissolution rate, modeling the ion transport using the Nernst–Planck equation, simulates the dendrite growth was stochastically using the Monte Carlo method. The results of the numerical model were validated by water-drop (WD) tests using pure copper electrodes in a contaminant-free electrolyte. The validation process involved comparing the time to failure (TTF) values and the morphology of the dendrites. The incubation analysis of the numerical model reveals that diffusion dominates the early stages of the process, but eventually transitions into a diffusion-migration-controlled mechanism, with migration being higher near the anode and diffusion remaining dominant closer to the cathode. The Monte Carlo simulation demonstrated both efficiency and flexibility in modeling dendrite growth. The model also demonstrated that dendrite growth can be expressed as a function of copper ion concentration and the strength of the electric field across the gap between the cathode and anode. Our model could be a useful tool for ECM failure prediction and further ECM research as the digital twin of the ECM process.