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

Abstract

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 T 0 , 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 T 0 , that is, α = 1 and k T 0 = 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 T 0 = 5∼7. This paper provides a basic guide to the kinematic parameter settings of CMP.

Optimization of kinematic parameters in single-sided lapping

“…Znaczenie mają także geometria i materiał przedmiotów obrabianych. Ponadto siła docisku [9] oraz prędkości obrotowe, które są ściśle zwią-zane z parametrami i kinematyką obrabiarki, mają istotny wpływ na stan narzędzia, jakość oraz wydajność procesu obróbkowego [5,7,10].…”

“…Większość opracowanych modeli zużycia tarczy docierającej zakłada, że intensywność zużycia zależy od intensywności styku narzędzia z obrabianymi przedmiotami poprzez ziarna ścierne [7,10]. Jednym ze sposobów określenia intensywności kontaktu jest obliczenie gęsto-ści ścieżek ziaren ściernych.…”

“…-wartość średnia intensywności ścierania, N -całkowita liczba obszarów, na które podzielono tarczę docierającą [10].…”

Chemical mechanical polishing: Theory and experiment

“…Kinematic analysis reveals that the basic kinematic parameters significantly affect the velocity distribution, the sliding distance distribution, and the nonuniformity [7, 30−33]. Zhao et al [29] found that the intrinsic relations, especially the coupling relations among the basic motions, i.e., the rotary speed ratio of the wafer to the pad α and the period ratio of the reciprocating motion of the wafer to the rotary motion of the platen Friction 1(4): 306-326 (2013) k T0 , significantly affect the uniformity of the sliding distance of the wafer relative to the pad, and the distribution of the particle sliding trajectories [34]. For better uniformity, the speed ratio should be close to 1 (but should not equal to 1), and the reciprocating motion of the carrier is necessary.…”

Analysis of Disc Wear Based on Trajectory Simulation in Lapping Process

“…However, the influence of the wafer parameters and other processing parameters on lapping tool wear are not considered previously. Also some researches showed that the uniformity of the lapping tool surface trajectory was able to reflect the wear of lapping tool [6,7]. Therefore, combining with the knowledge of kinematics and establishing the model of lapping disc wear trajectory, this paper is carried out a detailed analysis on the relation between the distribution of disc wear trajectory and the lapping processing parameters.…”