Greenwood–Williamson Model Combining Pattern-Density and Pattern-Size Effects in CMP

Vasilev, Boris; Rzehak, Roland; Bott, Sascha; Kücher, Peter; Bartha, Johann W.

doi:10.1109/tsm.2011.2107756

Cited by 32 publications

(19 citation statements)

References 17 publications

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“…This point contact is specifically divided into two types, one is the top contact (Up), which is for fitting the peak of the parabola; the other is the bottom contact (Down), which is for the valley of the fitting parabola. Based on these two different contacts, the material removal rate of the original planar state is corrected [23]. After that, the removal rate (RR) for both cases is related to the polishing pad topography and the fitted graphical step curve.…”

Section: Model Based On Surface Topography and On-chip Graphics Densitymentioning

confidence: 99%

Review on modeling and application of chemical mechanical polishing

Zhao

Wei

Wang

et al. 2020

Nanotechnology Reviews

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AbstractWith the development of integrated circuit technology, especially after entering the sub-micron process, the reduction of critical dimensions and the realization of high-density devices, the flatness between integrated circuit material layers is becoming more and more critical. Because conventional mechanical polishing methods inevitably produce scratches of the same size as the device in metal or even dielectric layers, resulting in depth of field and focus problems in lithography. The first planarization technique to achieve application is spin on glass (SOG) technology. However, this technology will not only introduce new material layers, but will also fail to achieve the global flattening required by VLSI and ULSI technologies. Moreover, the process instability and uniformity during spin coating do not meet the high flatness requirements of the wafer surface. Also, while some techniques such as reverse etching and glass reflow can achieve submicron level regional planarization. After the critical dimension reaches 0.35 microns (sub-micron process), the above methods cannot meet the requirements of lithography and interconnect fabrication. In the 1980s, IBM first introduced the chemical mechanical polishing (CMP) technology used to manufacture precision optical instruments into its DRAM manufacturing [1]. With the development of technology nodes and critical dimensions, CMP technology has been widely used in the Front End Of Line (FEOL) and Back End Of Line (BEOL) processes [2]. Since the invention of chemical mechanical polishing, scientists have not stopped studying its internal mechanism. From the earliest Preston Formula (1927) to today’s wafer scale, chip scale, polishing pad contact, polishing pad - abrasive - wafer contact and material removal models, there are five different scale models from macro to the micro [3]. Many research methods, such as contact mechanics, multiphase flow kinetics, chemical reaction kinetics, molecular dynamics, etc., have been applied to explain the principles of chemical mechanical polishing to establish models. This paper mainly introduces and summarizes the different models of chemical mechanical polishing technology. The various application scenarios and advantages and dis-advantages of the model are discussed, and the development of modeling technology is introduced.

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Section: Model Based On Surface Topography and On-chip Graphics Densitymentioning

confidence: 99%

Review on modeling and application of chemical mechanical polishing

Zhao

Wei

Wang

et al. 2020

Nanotechnology Reviews

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“…As we know, in order to predict this pattern-dependent effect, contact mechanics and phenomenological geometry based chip-scale CMP models has been proposed to capture the within-chip nonuniformity of polished materials (dielectrics, copper, aluminum and oxides) and detect the hotspots of process variation in IC design layouts. 2,14,22,[30][31][32] Due to the significance of the contact behavior between the wafer surface and the pad in mechanical abrasion, one key aspect to model the CMP process is to construct a precise relationship between the removal rate and the contact pressure distribution on the patterned wafer surface. 33 The investigation of these chip-scale CMP models indicate that the pattern-dependent effect is quite important for ILD, STI, HKMG and copper damascene topography simulation.…”

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confidence: 99%

“…33 The investigation of these chip-scale CMP models indicate that the pattern-dependent effect is quite important for ILD, STI, HKMG and copper damascene topography simulation. [30][31][32][33] However, this effect has not been considered in W CMP model. Therefore, in order to obtain a good uniformity control of tungsten films, the influence of chemical reagent and interface pressure distribution on MRR should be investigated systematically to capture the polishing mechanism.…”

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confidence: 99%

“…A chemical reaction kinetics model is first proposed to construct a relationship between the removal rate and the chemical reagent and mechanical rate parameters by introducing steady-state equilibrium equation of chemical reactions. In order to describe the influence of the design pattern structures on the removal rate, Greenwood-Williamson (GW) contact theory 14,30 has been introduced in the present study to obtain an accurate contact pressure distribution. Then a closed-form equation of MRR can be constructed to systematically capture the synergistic coupling effect of chemical reaction and mechanical abrasion in the W CMP process.…”

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A Material Removal Rate Model for Tungsten Chemical Mechanical Planarization

Xu¹,

Cao²,

Liu³

2022

ECS J. Solid State Sci. Technol.

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A tungsten removal rate model is proposed in the chemical mechanical planarization (CMP) process to investigate the removal mechanism with consideration of the synergistic effect of chemical reaction and mechanical abrasion. Based on the fundamentals of steady-state chemical reaction and mechanical abrasion, a chemical reaction kinetics CMP model is first built up to relate the removal rate to the chemical reagent and mechanical rate parameters. Then the Greenwood-Williamson contact theory is introduced into the chemical reaction kinetics model to construct a closed-form equation of removal rate, which captures the synergistic coupling effect of chemical and mechanical interactions. Furthermore, the present model is verified by the collected experimental data and utilized to investigate the impact of the design pattern effects on the removal rate. The consistency of the model prediction and the experimental data as well as the removal characteristics of design pattern structures indicate that the new proposed tungsten CMP model can be adopted to elucidate the synergistic effect of chemical and mechanical interactions and perform the sensitivity analysis of the design pattern dependency on removal rate of tungsten films.

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“…Fan et al [16] established a physical model in which polishing parameters, such as dielectric thickness and step height on wafer surface and pad effective modulus and asperity height are considered. Vasilev et al [17] proposed a model which included effects of pattern-size based on a consideration of the roughness of the polishing pad. Urbach and Rzehak [18] studied the different frequency components of wafer pattern decay, observing different rates in the polishing process.…”

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Effects of Polishing Parameters on Evolution of Different Wafer Patterns During Cu CMP

Yan

2015

IEEE Trans. Semicond. Manufact.

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Chemical mechanical polishing (CMP) has been widely used in the IC industry. To specify proper polishing parameters for Cu CMP is a very important and difficult task. In this paper, by using the linear system method modeling the relationship between the contact pressure and topography of wafer, the evolutions of the wafer patterns under different polishing parameters are simulated and compared with experimental data. The wafer patterns contain square-wave features with different pitches and pattern densities. The effects and tradeoffs between different polishing parameters on the evolution of different wafer patterns are studied. It is found that high selectivity ratio can achieve small dishing, while small selectivity ratio can help to achieve small erosion and small differences among different patterns. Small down force and large Young's modulus of pad can achieve a good planar surface. Large Preston coefficient will have small erosion during one-material polishing, while small Preston coefficient will have small erosion in two-material polishing. Time point of changing polishing parameters is important to achieve an efficient polishing process and a planar surface.

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Greenwood–Williamson Model Combining Pattern-Density and Pattern-Size Effects in CMP

Cited by 32 publications

References 17 publications

Review on modeling and application of chemical mechanical polishing

Review on modeling and application of chemical mechanical polishing

A Material Removal Rate Model for Tungsten Chemical Mechanical Planarization

Effects of Polishing Parameters on Evolution of Different Wafer Patterns During Cu CMP

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