Soft Elastohydrodynamic Lubrication With Roughness

Kim, Andrew T.; Seok, Jongwon; Tichy, John; Cale, Timothy S.

doi:10.1115/1.1494100

Cited by 14 publications

(14 citation statements)

References 7 publications

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“…Kim et al 13 presented a general outline for soft elastohydrodynamic lubrication ͑EHL͒ that considers the roughness effect. Lately, this work was extended to a 3D analysis 14 with the aid of ANSYS.…”

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confidence: 99%

A 3D EHL Simulation of CMP

Jin

Keer

Wang

2005

J. Electrochem. Soc.

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The extensive application of chemical mechanical polishing ͑CMP͒ in the semiconductor industry requires an understanding of the fundamental mechanisms involved. This paper integrates a group of mechanical models to give a framework for CMP modeling: a mixed three-dimensional ͑3D͒ soft elastohydrodynamic lubrication ͑EHL͒ model with asperity contact considered. The soft-pad mechanics, asperity-contact analysis, and slurry film description are three major components of this framework. Based on the results of a thin-layer contact analysis, the Winkler foundation model is selected to evaluate the pad deformation in bulk. By applying the macro-micro approach, the macroscopic view of the average fluid film thickness ͑average clearance͒ is related to microasperity contact. When CMP is implemented in a mixed lubrication regime, the soft polishing pad usually undergoes a displacement of the same scale as the slurry film, which may change the lubrication boundary considerably. Considering this effect, a modified Reynolds equation is derived, and a stronger coupling is found in the global force and moment balances. Finally, an effective iterative scheme is proposed and modeling results examined.Chemical mechanical polishing ͑CMP͒ is currently used to achieve global planarization over a long length/thickness scale and is being widely applied in the semiconductor industry. During a CMP process, a rotating wafer is pressed face down onto a moving, resilient thin polishing pad, while a polishing slurry containing abrasive particles and chemical reagents flows between the wafer and pad. The extensive utilization of CMP in integrated circuit ͑IC͒ manufacturing requires deep understanding of the CMP mechanisms.Nanz and Camilletti 1 presented a critical review of the CMP models developed prior to 1995 for pad bending, nonplanarity of a wafer, the effect of pad asperities, and slurry flow. Whereas various working conditions may weigh differently due to the factors mentioned previously, it is axiomatic that the contact between the polishing pad and the wafer is determined by the clearance between them. Bhushan et al. 2 pointed out that three contact scenarios, namely, direct contact, nondirect contact, and semidirect contact, may appear at the pad-wafer interface in CMP. Chekina et al. 3 developed an analytical solution for wafer surface evolution in a steady state on the basis of elastic contact mechanics. Zhao and Chang 4 developed an abrasive wear model for CMP on the basis of elastic-plastic microcontact mechanics. They first estimated a relationship among the real area of contact, the number of particles participating in wafer material removal, and the particle indentation depth into the wafer surface, and then derived a closed-form formula to address the material removal rate ͑MRR͒. Runnels and Eyman presented a nondirect-contact model for CMP based on a waferscale slurry flow analysis. 5 Supposing the wafer is completely separated from the polishing pad by the flowing slurry, the slightly tilted wafer with a curvature allows a...

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confidence: 99%

A 3D EHL Simulation of CMP

Jin

Keer

Wang

2005

J. Electrochem. Soc.

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“…It is interesting to note that subambient pressures are obtained over the whole wafer, and the pressure gradient almost matches up in magnitude with that of the pure contact pressure acting on the pad while being opposite in direction. Thus, the hydrodynamic pressures increase the contact stresses [4] due to the tilt of the wafer.…”

Section: Resultsmentioning

confidence: 99%

“…Introducing a parameter λ(x) to represent a ratio of the pad deformation to the total deformation, we can obtain the following relations [4]:…”

Section: Determination Of the Fluid Pressures Fluid Film Heights Comentioning

confidence: 99%

“…In a recent work [3], it was proposed that subambient pressures are the consequence of the interactions of the pad, asperities, and slurry flow. Kim et al [4] treated the 'soft' elastohydrodynamic lubrication (SEHL) problem of a compliant conformal rough surface. To examine the coupled soft pad/slurry flow effects, the model proposed in [4] makes use of contact mechanics and hydrodynamics, and the pad is treated as a thin elastic layer with plane strain assumptions.…”

Section: Introductionmentioning

confidence: 99%

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Material removal model for chemical–mechanical polishing considering wafer flexibility and edge effects

Seok

Sukam

Kim

et al. 2004

Wear

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“…In the region away from where chemical reaction is dominant, in which non-Prestonian behavior generally appears, this equation represents that the material removal rate of a wafer is proportional to the applied pressure on the wafer as well as to the relative velocity between the pad and the wafer. In CMP, recent research results [27,28] strongly support that the wafer and the pad are in direct contact during CMP, in which the abrasives are embedded in the pad asperities, so that twobody abrasion [29] is regarded as the dominant removal mechanism. Based on this observation, the relative velocity in Preston's equation is that between the tool and the workpiece to be finished.…”

Section: Interpretations Of Materials Removal Mechanism Associated Witmentioning

confidence: 98%