Numerical and Experimental Research of the Slurry Film in Chemical Mechanical Polishing (CMP)

2010 ◽  
Vol 102-104 ◽  
pp. 669-674
Author(s):  
Fei Yan Lou ◽  
Qian Fa Deng ◽  
Ju Long Yuan
Keyword(s):  
Film Thickness ◽  
Chemical Mechanical Polishing ◽  
Applied Load ◽  
Reynolds Equation ◽  
Rotation Speed ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Mechanical Polishing ◽  
Film Pressure ◽  
Minimum Film Thickness

A three-dimensional hydrodynamic lubrication model for chemical-mechanical polishing is presented based on the Reynolds equation and Reynolds boundary condition. By solving the Reynolds equation, the slurry film pressure distribution has been obtained. The effects of minimum film thickness and the wafer tile angle on the film pressure are analyzed, and the influence of the polishing applied load and rotation speed on slurry film thickness and tilt angle are discussed. At last, by experiment, it is found that the simulation results are similar to experiment results which film thickness is increasing with the increasing of rotation speed, decreasing of the applied load. It is proved that the simulation is reliable.

A Three-Dimensional Hydrodynamic Lubrication Model for Chemical-Mechanical Polishing Considering Pad Roughness

2010 ◽  
Vol 44-47 ◽  
pp. 1213-1217
Author(s):  
Fei Yan Lou
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Tilt Angle ◽  
Chemical Mechanical Polishing ◽  
Applied Load ◽  
Rotation Speed ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model

A three-dimensional hydrodynamic lubrication model based on lubrication theory is developed which accounts for pad roughness and slurry flow. The distribution of the slurry film thickness and pressure between the pad and the wafer are predicted using the model. The effects of the pad roughness, the polishing applied load and rotation speed on slurry film thickness and tilt angle are discussed. At last, a CMP experiment is carried out. It is found that the results are proved the three-dimensional model considering pad roughness agrees well with our experimental data. The results improve the previous models so that the CMP process can be better simulated using the model. Furthermore, they are useful in the processing of CMP and the design of the pad roughness.

scholarly journals Analysis of Starvation Effects on Hydrodynamic Lubrication in Nonconforming Contacts

1982 ◽  
Vol 104 (3) ◽  
pp. 410-417 ◽  
Author(s):  
D. E. Brewe ◽  
B. J. Hamrock
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Point Contact ◽  
Sharp Decrease ◽  
Reduction Factor ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Starvation Effects

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. The analysis is considered valid for a range of speeds and loads for which thermal, piezoviscous, and deformation effects are negligible. It is applied to a wide range of geometries (i.e., from a ball-on-plate configuration to a ball in a conforming groove). Seventy-four cases were used to numerically determine a minimum-film-thickness equation as a function of the ratio of dimensionless load to dimensionless speed for varying degrees of starvation. From this, a film reduction factor was determined as a function of the fluid inlet level. Further, a starved fully flooded boundary was defined and an expression determining the onset of starvation was derived. As the degree of starvation was increased, the minimum film thickness decreased gradually until the fluid inlet level became critical. Reducing the fluid inlet level still further led to a sharp decrease in the minimum film thickness. An expression determining the critically starved fluid inlet level was derived. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three-dimensional isometric plots and also in the form of contour plots.

Three-Dimensional Hydrodynamic Lubrication Analysis of Cylinder Liner-Piston Ring

2013 ◽  
Vol 871 ◽  
pp. 27-31
Author(s):  
Shi Feng Zhang ◽  
Shu Hua Cao ◽  
Jiu Jun Xu
Keyword(s):  
Piston Ring ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Cylinder Liner ◽  
Asperity Contact ◽  
Crank Angle ◽  
Minimum Film Thickness ◽  
Friction Analysis

This paper constructs a three-dimensional transient hydrodynamic lubrication model for cylinder liner-piston ring based on the three-dimensional transient average Reynolds equation and asperity contact model. A computer program was written with FORTRAN to calculate hydrodynamic lubrication, in which the surface roughness, the variable viscosity effect and the deformation of the circumferential direction of the cylinder liner are taken into account. The film pressure distribution in different crank angle during the stroke, minimum film thickness and friction are computed and analyzed with this program. This three-dimensional transient hydrodynamic lubrication model provides a design basis for the friction analysis of cylinder liner-piston ring.

Characterization and Control of Copper CMP with Optoacoustic Metrology

2001 ◽  
Vol 671 ◽  
Author(s):  
Michael Gostein ◽  
Paul Lefevre ◽  
Alex A. Maznev ◽  
Michael Joffe
Keyword(s):  
Film Thickness ◽  
Spatial Resolution ◽  
Chemical Mechanical Polishing ◽  
High Spatial Resolution ◽  
Mechanical Polishing ◽  
Length Measurement ◽  
And Control ◽  
Non Destructive

ABSTRACTWe discuss applications of optoacoustic film thickness metrology for characterization of copper chemical-mechanical polishing (CMP). We highlight areas where the use of optoacoustics for CMP characterization provides data complementary to that obtained by other techniques because of its ability to directly measure film thickness with high spatial resolution in a rapid, non-destructive manner. Examples considered include determination of planarization length, measurement of film thickness at intermediate stages of polish, and measurement of arrays of metal lines.

Influence of Surface Waviness on the Thermal Elastohydrodynamic Lubrication of an Eccentric-Tappet Pair

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
J. Wang ◽  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Surface Waviness ◽  
Film Pressure ◽  
Oil Film ◽  
Working Cycle ◽  
Temperature Oscillations ◽  
Minimum Film Thickness ◽  
Traction Coefficient ◽  
Oil Film Pressure

The effect of single-sided and double-sided harmonic surface waviness on the film thickness, pressure, and temperature oscillations in an elastohydrodynamically lubricated eccentric-tappet pair has been investigated in relation to the eccentricity and the waviness wavelength. The results show that, during one working cycle, the waviness causes significant fluctuations of the oil film, pressure, and temperature, as well as a reduction in minimum film thickness. Smaller wavelength causes more dramatic variations in oil film. The fluctuations of the pressure, film thickness, temperature, and traction coefficient caused by double-sided waviness are nearly the same compared with the single-sided waviness, but the variations are less intense.

EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling

2005 ◽  
Vol 219 (4) ◽  
pp. 285-290 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Validity Of Results ◽  
Erroneous Conclusion ◽  
Low Speeds ◽  
Lubrication Models ◽  
Circular Contact

When numerical and experimental results are compared to validate elasto-hydrodynamic lubrication (EHL) models, it is of utmost importance that grid-converged results are used. In particular at low speeds and high loads, solutions obtained using grids that are not sufficiently dense will exhibit an artificial trend that does not represent the behaviour of the continuous modelling equations. As it coincides with a trend observed in experiments this may lead to the erroneous conclusion that the theoretical model on which the numerical simulations are based is accurate. This risk is illustrated in detail. It is further shown that EHL models based on the Reynolds equation in a steady state circular contact predicts a positive film thickness as long as the grid used in the calculations is sufficiently dense. This has significant implications for the validity of results obtained using mixed lubrication models based on a Reynolds model and a film thickness threshold.

Effects of Surface Roughness and Additives in Lubrication: Generalized Reynolds Equation and its Application to Elastohydrodynamic Film

1987 ◽  
Vol 201 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P Sinha ◽  
J S Kennedy ◽  
C M Rodkiewicz ◽  
P Chandra ◽  
R Sharma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Molecular Size ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Minimum Film Thickness ◽  
Porous Matrices ◽  
The Mean ◽  
Generalized Reynolds Equation

To study the effects of surface roughness and additives in lubrication, a generalized form of Reynolds equation is derived by taking into account the roughness interaction zones adjacent to the moving rough surfaces as sparsely porous matrices and purely hydrodynamic film of micropolar fluid characterizing the lubricant with additives. A particular, one-dimensional form of this equation is used to study these effects on the elastohydrodynamic (EHD) minimum film thickness at the inlet, between two rough rollers. It is shown that for the low permeability of the roughness zone, the EHD film thickness increases as the mean height of the asperities increases, whereas for the high permeability it decreases. The EHD film thickness is also found to increase with the concentration of the additives and the molecular size of the particles. These results are in conformity at least qualitatively, with various experimental and theoretical investigations, cited in the paper.

scholarly journals Numerical Investigation of Pressure Profile in Hydrodynamic Lubrication Thrust Bearing

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Farooq Ahmad Najar ◽  
G. A. Harmain
Keyword(s):  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Pressure Profile ◽  
Grid Refinement ◽  
Average Value ◽  
Lubricant Oil ◽  
Pressure Profiles ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Grid Independence

Reynolds equation is solved using finite difference method (FDM) on the surface of the tilting pad to find the pressure distribution in the lubricant oil film. Different pressure profiles with grid independence are described. The present work evaluates pressure at various locations after performing a thorough grid refinement. In recent similar works, this aspect has not been addressed. However, present study shows that it can have significant effect on the pressure profile. Results of a sector shaped pad are presented and it is shown that the maximum average value of pressure is 12% (approximately) greater than the previous results. Grid independence occurs after 24 × 24 grids. A parameter “ψ” has been proposed to provide convenient indicator of obtaining grid independent results. ψ=|(Prefinedgrid-PRefrence-grid)/Prefinedgrid|, ψ≤ε, where “ε” can be fixed to a convenient value and a constant minimum film thickness value of 75 μm is used in present study. This important parameter is highlighted in the present work; the location of the peak pressure zone in terms of (r,θ) coordinates is getting shifted by changing the grid size which will help the designer and experimentalist to conveniently determine the position of pressure measurement probe.

scholarly journals Hydrodynamic lubrication of rough surfaces

1982 ◽  
Vol 383 (1785) ◽  
pp. 439-446 ◽  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Homogenization Method ◽  
Squeeze Film ◽  
Spatial Average

Using the two-space homogenization method we derive an averaged Reynolds equation that is correct to O (< H 6 > — < H 3 > 2 ), where H is the total film thickness and the angle brackets denote a spatial average. Applications of this mean Reynolds equation to a squeeze-film bearing with a sinusoidal or an isotropic surface roughness are discussed.

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