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Jeng, Yeau-Ren; Tsai, Hung Jung

doi:10.1023/a:1021036611070

Cited by 15 publications

(6 citation statements)

References 10 publications

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“…For example, ␥ ϭ ϱ, 1, and 0 designate longitudinal, isotropic, and transverse roughness, respectively. The flow factors obtained by the perturbation approach and coordinate transformation 27,28 are ⌽ ¯xy S ϭ ⌽ ¯yx…”

Section: Theoretical Modelmentioning

confidence: 99%

“…The flow factors method has been applied to bearings, magnetic head/disk interface, ultrathin film lubrication, and grain flow lubrication. [24][25][26][27][28] The average lubrication equation used in this study was developed in an earlier paper of ours 27 and is based on Haff's grain flow theory and the Patir/Cheng flow factors method. In the present paper, the average lubrication equation is used to investigate the effects of CMP grain flow and pad roughness.…”

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confidence: 99%

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Improved Model of Wafer/Pad Powder Slurry for CMP

Jeng

Tsai

2003

J. Electrochem. Soc.

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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...

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Section: Theoretical Modelmentioning

confidence: 99%

mentioning

confidence: 99%

Improved Model of Wafer/Pad Powder Slurry for CMP

Jeng

Tsai

2003

J. Electrochem. Soc.

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“…The flow factors method has been applied to grain-flow lubrication. [29][30][31] Yu et al 32,33 presented a CMP model that combined the polishing pad roughness and slurry hydrodynamic pressure effects to consider the influence of the down force, platen velocity, and pad roughness. In Yu's model, the contact force of the polishing pad and wafer was handled using an elastic asperity microcontact model proposed by Greenwood and Williamson 34 ͑GW model͒.…”

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confidence: 99%

Elasto-Partial Hydrodynamic Contact Model for Chemical Mechanical Polishing

Tsai

Jeng

Huang

2006

J. Electrochem. Soc.

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Chemical mechanical polishing ͑CMP͒ has become a primary technique for the planarization of semiconductor wafers in submicrometer device fabrication. Increasing demands for high uniformity and dimensional precision make previously discountable levels of asperity, powder slurry, and wafer-pad contact significant. In this study, an improved model considering both the elastic microcontact mechanism and the grain flow with roughness effects is proposed. The model applies the average lubrication equation with the partial hydrodynamic lubrication theory and elastic microcontact theory proposed by Greenwood and Williamson. The external force acting on the wafer is supported by the partial hydrodynamic slurry pressure in the noncontact area and the surface asperity contact force in the contact area. This model predicts slurry flow film thickness under a variety of the CMP parameters, including applied load, rotation speed, particle size, and pad roughness. The results compare well with experimental data in the literature. Furthermore, the contact ratio of area and removal rate are studied and discussed.

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“…the modified dimensionless Reynolds equation (10) or (12) for directional roughness structure can be expressed as…”

Section: Discussionmentioning

confidence: 99%

“…Second, using the stochastic concept, a film-averaging model for hydrodynamic lubrication of rough surfaces was constructed by Christensen [10]. By applying this Christensen stochastic model, the one-dimensional hydrodynamic bearing with rough surfaces is considered by Turaga et al [11] and the average lubrication equation for grain flow is solved by Jeng and Tsai [12] to analyse the performance of rough slider bearings. The studies by Hsu et al [13], Chiang et al [14] and Naduvinamani et al [15] take into account further the combined effects of surface roughness and flow rheology upon the static characteristics of the system.…”

Section: Introductionmentioning

confidence: 99%

Linear Stability Analysis of a Rough Short Journal Bearing Lubricated with Non-Newtonian Fluids

et al. 2004

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On the basis of Stokes theory and the Christensen's stochastic model, the combined effects of couple stresses and surface roughness on the instability threshold of hydrodynamic rotor bearings are theoretically studied. The film pressure is solved from the generalized stochastic non-Newtonian Reynolds-type equation and applied to evaluate the equilibrium solution of a short journal bearing. By using the linear theory, the eight oil-film stiffness and damping coefficients as well as the vibrational stability boundary were determined. According to the results obtained, the presence of couple stresses accompanied with a longitudinal roughness provides an increase in the values of stiffness coefficients K XX , K XY and K YX as well as the damping coefficient C XX , and results in a higher stability threshold speed. Whereas, when compared to the smooth bearing lubricated with couple stress fluid, a decrease in the threshold speed is found in the case of transverse roughness.

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Untitled

Cited by 15 publications

References 10 publications

Improved Model of Wafer/Pad Powder Slurry for CMP

Improved Model of Wafer/Pad Powder Slurry for CMP

Elasto-Partial Hydrodynamic Contact Model for Chemical Mechanical Polishing

Linear Stability Analysis of a Rough Short Journal Bearing Lubricated with Non-Newtonian Fluids

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