A Dishing Model for STI CMP Process
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A Dishing Model for STI CMP Process Shih-Hsiang Chang Department of Mechanical Engineering, Far East College, 49, Chung-Hwa Rd., Hsin-Shih, Tainan 744, Taiwan, ROC. ABSTRACT It is well known that oxide dishing occurring in STI CMP leads to considerable sidewall and edge-parasitic conduction. Thus, a closed-form solution for quantitative prediction of oxide dishing is needed. A contact-mechanics-based approach to describe the steady-state oxide dishing occurring in STI CMP process is presented. The theory is validated through comparison with experimental data in the literature. Once validated, the model is used to quantify the effect of pattern geometry on oxide dishing. It is shown that the predictions of the model agree reasonably well with the experimental results measured in overpolishing time. INTRODUCTION Significant research efforts have been made to investigate the effects of process parameters and pattern geometry on oxide dishing for STI CMP [1-4]. In these studies, it was found that the amount of oxide dishing is sensitive to the pattern density, feature size and overpolishing time. Recent works by Boning and his colleagues [5,6] showed that dishing is also highly dependent on other pattern geometrical parameters such as the ratio of perimeter to feature area. A planarization length measured from the experiments can be used to characterize the influential range of a specific pattern on the neighboring area. Although a few semiquantitative dishing models [3,5] which can explain these experimental observations have been proposed, the dependence of oxide dishing on other important factors such as trench width, selectivity and pad properties was not explicit and the nonlocal pressure effect was not considered in these models. This paper begins with a brief description of the model used to calculate the steady-state oxide dishing occurring in STI CMP. Following this, the unknown pattern selectivity is estimated by matching the model results with the experimental data and quantitatively described by an appropriate function of trench width and pattern density. The model is then validated and applied to investigate the effect of pattern geometry on dishing in details. MODEL FORMULATION In this paper, the pad-wafer contact is modeled as a three dimensional quasi-steady state contact problem where a rigid wafer with surface shape f ( x, y ) comes into contact with an elastic half-space, as proposed by Chekina et al. [7]. Thus, the displacement of pad surface w( x, y ) and contact pressure p ( x, y ) are described by the relation [8] w (x, y) =
1−ν π E
2
∫
Ω
p (ς ,η )
1 ( x − ς ) 2 + ( y −η ) 2
dςdη
(1)
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subject to the boundary conditions w( x, y ) = f ( x, y ) + c, p ( x, y ) ≥ 0 ( x, y ) ∈ Ω (2) w( x, y ) > f ( x, y ) + c, p( x, y ) = 0 ( x, y ) ∉ Ω (3) where c is the normal penetration, E and ν the effective Young's modulus and Poisson's ratio of the pad, respectively. Here Ω is the total area of contact including the isolated real contact areas. The unknown penetration c can be obtained f
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