A study of a finite element model for the chemical mechanical polishing process

Abstract

In this paper, relative velocity at a given point on the wafer was first derived. The revolutions of wafer and pad are assumed the same and the axisymmetric uniformly distributed pressure form is given. Thus, a 2D axisymmetric quasic-static model for chemical-mechanical polishing process (CMP) was established. Based on the principle of minimum total potential energy and axisymmetric elastic stress-strain relations, a 2D axisymmetric quasic-static finite element model for CMP was thus established. In this model, the four-layer structures including wafer carrier, carrier film, wafer and pad are involved. The von Mises stress distributions on the wafer surface were analysed, the effects of axial, hoop, radial and shear stresses to von Mises stress and the effects of axial, hoop, radial and shear strains to deformation of the wafer were investigated. The findings indicate that near the wafer centre, von Mises stress distribution on the wafer surface was almost uniform, then increased gradually with a small amount. However, near the wafer edge, it would decrease in a large range. Finally, it would increase dramatically and peak significantly at the edge. Besides, the axial stress and strain are the dominant factors to the von Mises stress distributions on the wafer surface and the wafer deformation, respectively.

A study on the stress and nonuniformity of the wafer surface for the chemical-mechanical polishing process

“…4a shows the correlation between the calculated von Mises stress distributions and the distance from the wafer centre. [8] To understand much more about the variations of the lower and flatter parts of the von Mises stress distributions in Fig.4a, the scale in the y axis of this part is magnified and plotted in Fig.4b. Figs.…”

“…The profile of the stress distribution is similar to that described by Wang et al [6], but the site of the peak stress is somewhat different. Lin and Lo [8] established a two-dimensional axisymmetric quasicstatic model for CMP and developed a two-dimensional axisymmetric quasic-static finite element model for CMP. They found that the profile of the simulated von Mises stress distributions is similar to that of the experimental removal rate.…”

Simulated Effects of Measurement Noise on Contact Measurements Between Rough and Smooth Surfaces

“…This is the equivalent of saying that every asperity is compressed within itself without expanding laterally. Although the pad material will expand under compression, we estimate the strain to be about 0.03 and therefore negligible, assuming Poisson's ratio for our surface is no greater than 0.1 [19]. Figure 3 is a cross section of the original Gaussian surface, which is shaded in dark gray.…”

Conformal polishing approach: Tool footprint analysis

“…[1][2][3][4] The CMP is based on a rotating table, a polishing head and a suspension pad, where the surface of the wafer moves across the pad, under pressure, in the presence of slurry abrasive. The mechanical movement and the downward force are applied to the wafer by the machine.…”