Hydrodynamics of a Chemical-Mechanical Planarization Process
- PDF / 639,678 Bytes
- 6 Pages / 417.6 x 639 pts Page_size
- 108 Downloads / 262 Views
INTRODUCTION As the devices become more miniaturized in microelectronics industry, the required level of planarization calls for a more stringent thickness control, and the CMP process is expected to meet the planarity requirements. Modeling of the CMP process is often classified into two categories; wafer-scale model and feature-scale model. The characteristic length scale of the wafer-scale model is the gap between the pad and wafer which is in the order of 50 ýtm, and it attempts to describe the overall removal rate of the CMP process. The feature-scale model is for the length scale of typical device features on the wafer which is in the order of a few micrometers, and focuses on the local removal rate rather than the overall removal rate. The wafer-scale model which is most frequently referred to is Preston's equation'. According to this equation, the average removal rate is proportional to the applied normal force (or pressure) and the speed of the wafer relative to that of the pad. In another wafer-scale model, 2
Patrick et al. found that every point on the wafer experiences the same linear speed relative to
the pad if the wafer rotates with the same angular velocity as the pad. Their experiment confirmed that the variation of the local removal rate was affected by the relative angular velocity of the wafer and applied normal force (or pressure). Ouma et. al. 3 showed that the polishing rate near the edge of the wafer is higher than the center and this can be attributed to the reduced slurry flow at the interior of the wafer and the increased stress at the wafer edge. Runnel et al. 4 proposed a model which accounts for the fluid flow between the wafer and the pad. Wang et al. 5 presented a model correlating the non-uniformity with the Von Mises stress distribution, which is a combination of principal stresses. Several other studies attempted to account for various effects of slurry flow and the slurry-pad interaction on the removal rate and the nonuniformity across the wafer47 . The present study is a wafer-scale modeling which provides the three dimensional flow field of the slurry in the gap between the wafer and the pad which are assumed to be parallel to one another.
GOVERNING EQUATIONS A schematic of a CMP process is shown in Figure 1. A circular wafer of a radius Rk rotates with an angular velocity 0,2 about its center, whereas the pad with a much larger radius rotates with an angular velocity O.p and its center of rotation is a distance L away from the center of the 181
Mat. Res. Soc. Symp. Proc. Vol. 566 ©2000 Materials Research Society
x A
o./ •-'
,
/wafer
-
.......... . . ..!.. .'.. .. , i / "
~hi pad
(top view) (side view) Figure 1. Schematic of a CMP process wafer. Assuming that the pad and the wafer are rigid and parallel with a uniform gap of h and that the slurry in the gap is a Newtonian fluid, the governing equation for the slurry flow in the gap is given as V.u=O (1) P(u.Vu) =-Vp+A~V 2 u
(2)
Since the fluid motion is induced by the relative motion of the two parallel plates (i
Data Loading...
