Monte carlo simulation of Cu-resistivity considering size-effects

As interconnects scale down with generations, the line dimensions approach the electron mean-free-path for Cu of 39 nm which raise the resistivity of Cu considerably. The key size-dependent contributions are from electron-surface scattering, grain boundary scattering, and surface roughness-induced scattering. A new surface roughness model is introduced using a Gaussian probability density function and a Monte Carlo simulation is designed to include all the main three scattering mechanisms. The simulation results could predict the contributions of each mechanism when given certain conditions. At last, the previous analytical formula is modified to represent the rough surface effect more precisely.