Improved Model of Wafer/Pad Powder Slurry for CMP

Abstract

Chemical mechanical polishing ͑CMP͒ is a key technique for wafer global planarization. Increasing demands for high uniformity and dimensional precision make previously discountable levels of asperity and particle effects significant. However, particle size and pad asperity have not been considered simultaneously in previous literature. This study presents a grain flow model which applies the average lubrication equation with partial hydrodynamic lubrication theory, thereby analyzing slurry flow between wafer and pad and taking into account both grain flow and roughness effects. This model predicts slurry flow film thickness with various convex wafer curvature radii under a variety of the CMP parameters, including applied load, rotation speed, dome height, particle size, and pad roughness. Furthermore, the influence of particle size and pad asperity on removal rate is investigated. The results compare well with experimental data in the literature.Integrated circuit ͑IC͒ gates of 0.13 m and smaller are making it increasingly important to control thickness and planarity. Chemical mechanical polishing ͑CMP͒ is a popular technique to achieve global planarization of wafers for very large and ultralarge-scale integrated circuits. A typical CMP mechanism is shown in Fig. 1. The wafer is held inside a carrier and pressed onto a rotating pad under a user-defined polishing pressure while a powder slurry flows between wafer and pad. Because the CMP mechanism is inadequately understood and because higher levels of CMP performance are desired, significant research is being directed toward improved physically based models of the CMP process.Nanz and Camilletti 1 conducted a survey and compared the physical effects of CMP models up to 1995. Published CMP models are based mainly on contact mechanics, 2-6 slurry hydrodynamics, 7-10 or lubrication theory. 11 Recently, Tichy et al. 12 ͑1999͒ presented a two-dimensional CMP model including both contact mechanics and lubrication hydrodynamics. To account for pad compressibility, porosity, and slurry delivery effects, Thakurta et al. 13 used lubrication theory to describe lubrication regime ͑40-70 m slurry films͒ and contact regime ͑thinner films͒. Luo and Dornfeld 14 proposed a solidsolid contact model of the CMP process based on plastic contact over the wafer-abrasive interface and pad-abrasive interface. The fluid effect is attributed to the number of active abrasives, but the effects of slurry particles under hydrodynamic contact were not investigated. Liang et al. 15 in real-time CMP experiments investigated the wear behavior of polishing wafers and pads by comparing different polishing slurries with different additives. Under optical microscopy, they found that the polishing removal rate of wafers decreases with decreasing slurry particle size. Lu et al. 16 used dualemission laser-induced fluorescence ͑DELIF͒ to measure slurry thickness and friction force between wafer and polishing pad. They demonstrated that slurry thickness and friction force are dominantly dependent on the s...

The Flow Factors Considering the Elastic Deformation for the Rough Surface with a Non-Gaussian Height Distribution

“…Lunde and Tonder (6) studied the influence of boundary conditions in mixed lubrication analysis using the average flow model. Though the flow factor method was originally developed for hydrodynamic lubrication, it has been widely applied in EHL problems (PhanThien (7); Tripp and Hamrock (8); Sadeghi and Sui (9); Dong, et al (10)) and CMP analysis (Sundararajan and Thakurta (11); Jeng and Tsai (12)). Despite the popularity of the flow factor method, it has a serious shortcoming (Kumar,et al (13)).…”

“…[11] and [12] is generated using Johnson's translator system. The Johnson system of frequency curves based on the method of moments provides a family of curves that can be used to generate an equation for the distribution for which the first four moments (mean, σ , Sk, and K) are known.…”

“…Finally, the steps of the two-dimensional digital filter technique outlined earlier by Eqs. [6] to [12] are used to transform the non-Gaussian input sequence η to z. Figure 1 shows two-and three-dimensional surfaces generated numerically with the same σ = 1 µm and three different values of the skewness and the kurtosis.…”

An improved model considering elastic—plastic contact and partial hydrodynamic lubrication for chemical mechanical polishing

“…The contact force between polishing pad and wafer was handled using an elastic asperity micro-contact model (G-W model) proposed by Greenwood and Williamson [32]. Jeng and Tsai [33] proposed a CMP material removal rate model by using Haff's grain theory, hydrodynamic lubrication, and pad roughness. Jeng et al [34] used a micro-contact model to investigate the wafer-pad contact pressure.…”

Quantitative In-Situ Measurement of Asperity Compression Under the Wafer During Polishing

“…Slurry layer behavior interactions with the polishing pad and wafer during Chemical Mechanical Planarization (CMP) have been extensively studied both by computer modeling [1][2][3] and experimentation [4,5]. Knowledge of the pad/slurry/wafer interface provides insight into the physical processes that govern material removal rate.…”