Local Stress Field in Wafer Thinning Simulations with Phase Space Averaging

From an ingot to a wafer then to a die, wafer thinning plays an important role in the semiconductor industry. To reveal the material removal mechanism of semiconductor at nanoscale, molecular dynamics has been widely used to investigate the grinding process. However, most simulation analyses were conducted with a single phase space trajectory, which is stochastic and subjective. In this paper, the stress field in wafer thinning simulations of 4H-SiC was obtained from 50 trajectories with spatial averaging and phase space averaging. The spatial averaging was conducted on a uniform spatial grid for each trajectory. A variable named mask was assigned to the spatial point to reconstruct the shape of the substrate. Different spatial averaging parameters were applied and compared. The result shows that the summation of Voronoi volumes of the atoms in the averaging domain is more appropriate for spatial averaging. The phase space averaging was conducted with multiple trajectories after spatial averaging. The stress field converges with increasing the number of trajectories. The maximum and average relative difference (absolute value) of Mises stress was used as the convergence criterion. The obtained hydrostatic stress in the compression zone is close to the phase transition pressure of 4H-SiC from first principle calculations.