Simulation of three dimensional grain growth for Cu-interconnects

The temporal evolution and morphology of three-dimensional (3-D) grain growth in Cu interconnect are simulated by phase-field model techniques. In the simulation, a new local free energy density function is proposed in which the field variables can be reduced from 200 to 20. By restraining the grain orientations in the side face of interconnect, the model is applicable to simulating the microstructure evolution of polycrystalline Cu-lines in addition to the conventional 2-D or 3-D grain topology. The dependence of grain size on the line width is analyzed systematically. With the obtained topology of Cu grains and morphology of the line boundary, the resistivity of Cu interconnects is estimated by conventional Monte Carlo simulation which are tested with different experimental data. These results are important for evaluation and optimization the Cu interconnect process.