Cutting Behavior Simulation of a Chemical Mechanical Polishing Particle Using a Three-Dimensional Transient Atomistic FE Model with Nonlinear Spring-Damping Elements

摘要

During the grinding process, the cutting depth is much smaller than the size of a polishing particle. Therefore, under the small feed scale, polishing particles can be regarded as acting on the copper workpiece linearly. Based on this proposition, a three-dimensional transient atomistic FE model with nonlinear spring-damping elements was constructed. The simulated process involves first fixing the diamond particle on the polishing pad, then pressing down to a fixed depth of 3.7 A, and finally cutting across the copper metal layer that contains the wafer, at a speed of 300 m/s, to remove its atoms. On the basis of simulation results, cutting behaviors of 3D diamond polishing particles, the effect of the cutting nose shape (round, 120°, and 60°), and that of the copper metal layer size were investigated. Concerning the influence of the cutting nose shape, the results revealed that (1) As cutting proceeds, the copper workpiece undergoes an equilibrium stage, a down-pressed stage, and a traverse cutting stage; (2) the shape of the cutting nose affects surface roughness of the copper film, i.e., those processed using a round nose showed the best results and a 120° nose produced similar results as the round nose; (3) the diamond polishing particle is not in contact with the copper workpiece in the beginning, therefore the cutting force, down-pressed force, and lateral force are all zero and start to increase gradually as the diamond particle presses down. When polishing particles start to move horizontally at a speed of 300 m/s, the cutting force, down-pressed force, and lateral force increase with time. Since the cutting tool proceeds in the x direction, the lateral force (F_z) is relatively small and so has no significant effect on the cutting; and (4) the shape of cutting nose affects the cutting force and down-pressed force. A 60° nose has a significant influence on the cutting force (F_x) due to a smaller loading area, which leads to unstable cutting. Changes in the cutting force and down-pressed force when using the 120° and round nose show a similar trend, both resulting in stable cutting. Therefore, it can be deduced that a larger nose angle gives better cutting results. Concerning the effect of the copper workpiece size, the results revealed that: (1) when using 3D diamond polishing particles with a 120° nose on copper film of crystal sizes 24 × 6 × 12 and 24 × 6 × 8, the cutting tool is more restrained on both sides in the z direction due to the smaller dimension in that direction, which leads to a rough surface finish; and (2) for a 24 × 6 × 8 crystal, the cutting force and down-pressed force show slight increases.