Kinematic Optimization for Chemical Mechanical Polishing Based On Statistical Analysis of Particle Trajectories

The abrasive effect of particles is one of the basic mechanical actions in chemical mechanical polishing (CMP). In this paper, numerical simulations of particle sliding trajectories are performed to examine the influence of the kinematic parameters on the polishing uniformity of typical rotary-type CMP equipment. The trajectory simulations are carried out based on the kinematic analysis. The results reveal that the speed ratio α and the period ratio k_T0, which represent the coupling relationships among the three basic motions of CMP, are the two major factors affecting the trajectory distribution. Further, a trajectory density parameter is proposed to quantitatively evaluate the global uniformity of the trajectory distributions and to optimize the kinematic parameters for better uniformity. The statistical results of the trajectory density analysis reveal that the trajectory of the wafer edge is denser than that of the wafer central area. To obtain better trajectory uniformity, some particular values of α and k_T0, that is, α = 1 and k_T0=1, which imply that the basic motions have a special coupling relationship, should be excluded; the preferred kinematic parameter values for CMP are α = 0.91-0.93 and k_T0=5-7. This paper provides a basic guide to the kinematic parameter settings of CMP.