Bulk Polish Models

In Section II, we focus first on wafer-scale models, including macroscopic or bulk polish models (e.g., via Preston s equation), as well as mechanistic and empirical approaches to model wafer-scale dependencies and sources of nonuniformity. In Section III, we turn to patterned wafer CMP modeling and discuss the pattern-dependent issues that have been examined we also discuss early work on feature-scale modeling. In Section IV, we focus on die-scale modeling efforts and issues in the context of dielectric planarization. In Section V, we examine issues in modeling pattern-dependent issues in metal polishing. Summary comments on the status and application of CMP modeling are offered in Section VI. 

The modeling of polishing effects in CMP begins with two key issues what are the process-related dependeneies in the rate of removal of exposed surface material during polishing, and on what does the wafer-scale uniformity of that polish depend In this section, we begin with the modeling of polish or removal rate, and then consider models for the effects that impact the commonly observed nonuniformity in polish across the wafer. 

Chemical mechanical polishing appears to consist of two cooperating physical mechanisms [9]. First, chemical interaction of the slurry with material at the surface of the wafer weakens the surface to be polished. Second, the weakened surface is mechanically removed by a combination of slurry particles, polish pad asperities, and hydrodynamic effects. The extent 

The forward reaction is favored by the alkaline slurry solutions which result in breakage of the Si—O bonds. In metal CMP, oxidizing slurries are often used, resulting in faster removal rates. Since the contributions of the chemical and mechanical components are not well known, modeling efforts have focused on empirical approaches guided by physical intuition of process mechanisms. 

In a typical modeling approach, the material removal rate is modeled as a function of easily controlled process parameters. The most basic model is one that predicts the bulk rate of material removal in a macroscopic fashion. An empirical observation by Preston is widely used, in which the rate of material thickness reduction is proportial to the product of (a) the relative velocity between the wafer and the polish pad and (b) the pressure on the surface of the wafer  

---

The bulk nitride polish model is used when the nitride is exposed. At this phase, the goal is to predict the polish rate of the bulk composite material. Just before reaching the nitride, the surface is usually completely planar such... 

The first challenge to surface studies of model ceria surfaces is to produce a suitable Ce02 surface that can be mounted and manipulated within a UHV system. Typically bulk polished or cleaved single crystals, wafers or polycrystalline foils of the desired material are used for surface studies. This approach has been used in the case of Ce02. Ceria single crystals can be obtained commercially, and can be cut and polished to a desired orientation. Several studies on the (111) surface of bulk single crystal Ce02 have been reported." ... 

Reexamination of bulk and wafer-level modeling in the context of copper CMP is also underway. Due to the strong interaction between chemical and mechanical processes in copper polishing, consideration of the removal mechanisms as well as proper Preston-equation like modeling is being pursued [37,65]. More work is needed to produce effective and efficient wafer-level, feature-level, and die-level models for copper CMP, particularly as the industry moves to copper interconnect systems. 

A number of researchers have indicated the importance of pad surface roughness in determining polish rate and planari- (8,16,25) Pqj. example, Renteln and Coniff have demonstrated that polish rate increases with pad roughness. In addition, they argue that because of the increased porosity at the pad surface, the surface will exhibit a modulus lower than the bulk modulus. Mechanical behavior of the pad may then be modeled by considering the pad as two separate layers whose moduli add in parallel. 

---