Computational Solid Mechanics Modeling of Asperity Deformation and Pad-Wafer Contact in CMP

2007 ◽  
Vol 991 ◽  
Author(s):  
Bo Jiang ◽  
Gregory P. Muldowney
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Solid Mechanics ◽  
Real Contact Area ◽  
Formation Mechanisms ◽  
Stress And Strain ◽  
Finite Element Software ◽  
Real Contact ◽  
Deformation Mechanics ◽  
The Impact

ABSTRACTAsperity-scale pad deformation and dynamic pad-wafer contact area are crucial to the fundamental understanding of material removal and defect formation mechanisms in CMP. Pad asperity stress and strain are also central to characterizing pad wear rate during polishing and cut rate during conditioning. While it is very difficult to isolate and measure stress and strain in individual asperities, finite element modeling may be used in conjunction with experimental surface characterization to predict asperity-scale deformation and pad-wafer contact. Asperity sub-domains up to 1270 microns across are reproduced from three-dimensional point cloud data on porous polyurethane CMP pads obtained by confocal microscopy, meshed to high resolution, and analyzed using ABAQUS finite element software. Physical properties are derived from dynamic mechanical experiments. Pad stacks are simulated both with and without sub-pads. Results show that while a sub-pad increases pad-wafer contact area overall, it limits the local spreading of individual contact regions as polishing load increases. This finding identifies a direct mechanical origin of the trade-off in pad design between wafer-scale and die-scale planarity. As expected, the real contact area between a pad and wafer is much smaller than the cross-sectional or “bearing” area, but the difference is notably greater when a sub-pad is present. Values of asperity stress and strain under typical CMP polishing pressures reveal that plastic deformation takes place both on and beneath the contacting surface. Hence upon release of the polishing load the asperities do not fully rebound to their pre-compressed shapes. Each pass under the wafer thus reshapes the pad asperities such that a slightly different texture is presented upon the next pass. These deformation mechanics clarify the impact of top pad and sub-pad properties on real contact area, allowing better optimization of CMP pad performance.

scholarly journals A 3D study of the contact surface developed by the contact between the tires and the structural pavements

Exacta ◽  
2009 ◽  
Vol 6 (2) ◽  
pp. 197-208
Author(s):  
Alex Alves Bandeira ◽  
Rita Moura Fortes ◽  
João Virgílio Merighi
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Contact Area ◽  
Augmented Lagrangian Method ◽  
Numerical Results ◽  
Real Contact Area ◽  
The Real ◽  
Real Contact ◽  
Commercial Program ◽  
Contact Surfaces

The basic aim in this work is to present a new technique to analyze the contact surfaces developed by the contact between the tires and the structural pavements by numerical simulations, using 3D finite element formulations with contact mechanics. For this purpose, the Augmented Lagrangian method is used. This study is performed just putting the tires on the structural pavement. These tires and the structural pavement are discretized by finite elements under large 3D elastoplastic deformation. The real loads (of aircrafts, trucks or cars) are applied directly on each tire and by contact mechanics procedures, the real contact area between the tires and the pavement surface is computed. The penetration conditions and the contact interfaces are investigated in details. Furthermore, the pressure developed at the contact surfaces is automatically calculated and transferred to the structural pavement by contact mechanics techniques. The purpose of this work research is to show that the contact area is not circular and the finite element techniques can calculate automatically the real contact area, the real geometry and its stresses and strains. In the end of this work, numerical results in terms of geometry, stress and strain are presented and compared to show the ability of the algorithm. These numerical results are also compared with the numerical results obtained by the commercial program ANSYS.

A Finite Element Based Study on the Elastic-Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Shankar ◽  
M. M. Mayuram
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Plastic Material ◽  
Plastic Region ◽  
Real Contact Area ◽  
Real Contact ◽  
Perfectly Plastic ◽  
The Difference ◽  
Elastic Perfectly Plastic ◽  
Green Model

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios (ω∕ωc) for the evolution of the elastic core and the plastic region within the asperity for different Y∕E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y∕E ratio of the material.

Finite Element Analysis on Real Contact Area Based on Fractal Characterization

2013 ◽  
Vol 579-580 ◽  
pp. 517-522 ◽  
Author(s):  
Jia Chun Wang ◽  
Bo Qiang Xing ◽  
Teng Zhao
Keyword(s):  
Finite Element ◽  
Rough Surface ◽  
Contact Area ◽  
Smooth Surface ◽  
Thermal Conductance ◽  
Element Model ◽  
Real Contact Area ◽  
Process Data ◽  
Element Analysis ◽  
Real Contact

No surface in engineering is absolutely smooth. It is important to analyze and calculate the real contact area for a better understanding of friction, wear, lubrication and thermal conductance. To obtain the accurate real contact area between rough surface and smooth surface, a rough-non-rigid-smooth surface contact finite element model is proposed in which the rough surface is characterized by fracture theory. In finite element modeling and analyzing process, MATLABEXCEL and AutoCAD are used to process data, and the smooth surface is considered to be non-rigid body. Compared with the traditional modeling, this method can obtain data quickly and is closer to the actual situation.

scholarly journals A 3D study of the contact surface developed by the contact between the tires and the structural pavements DOI: 10.5585/exacta.v6i2.797

Exacta ◽  
2009 ◽  
Vol 6 (2) ◽  
pp. 197-208
Author(s):  
Alex Alves Bandeira ◽  
Rita Moura Fortes ◽  
João Virgílio Merighi
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Contact Area ◽  
Augmented Lagrangian Method ◽  
Numerical Results ◽  
Real Contact Area ◽  
The Real ◽  
Real Contact ◽  
Commercial Program ◽  
Contact Surfaces

The basic aim in this work is to present a new technique to analyze the contact surfaces developed by the contact between the tires and the structural pavements by numerical simulations, using 3D finite element formulations with contact mechanics. For this purpose, the Augmented Lagrangian method is used. This study is performed just putting the tires on the structural pavement. These tires and the structural pavement are discretized by finite elements under large 3D elastoplastic deformation. The real loads (of aircrafts, trucks or cars) are applied directly on each tire and by contact mechanics procedures, the real contact area between the tires and the pavement surface is computed. The penetration conditions and the contact interfaces are investigated in details. Furthermore, the pressure developed at the contact surfaces is automatically calculated and transferred to the structural pavement by contact mechanics techniques. The purpose of this work research is to show that the contact area is not circular and the finite element techniques can calculate automatically the real contact area, the real geometry and its stresses and strains. In the end of this work, numerical results in terms of geometry, stress and strain are presented and compared to show the ability of the algorithm. These numerical results are also compared with the numerical results obtained by the commercial program ANSYS.

Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects

2004 ◽  
Vol 19 (11) ◽  
pp. 3307-3315 ◽  
Author(s):  
Yeol Choi ◽  
Ho-Seung Lee ◽  
Dongil Kwon
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Contact Area ◽  
Indentation Depth ◽  
Indentation Load ◽  
Real Contact Area ◽  
Elastic Deflection ◽  
Contact Depth ◽  
Real Contact ◽  
Pile Up

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.

Unloading Process in Elastic-Plastic Contact of a Rough Surface With a Flat

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Finite Element ◽  
Rough Surface ◽  
Contact Force ◽  
Contact Area ◽  
Three Dimensional ◽  
Integral Form ◽  
Real Contact Area ◽  
Elastic Plastic ◽  
Real Contact ◽  
Approximate Equations

Three dimensional elastic-plastic contact of a nominally flat rough surface and a flat is considered. The asperity level Finite Element based constitutive equations relating contact force and real contact area to the interference is used. The statistical summation of asperity interaction during unloading phase is derived in integral form. Approximate equations are found that describe in closed form contact load as a function of mean plane separation during unloading. The approximate equations provide accuracy to within 6 percent for the unload phase of the contact force.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2005 ◽  
Vol 127 (2) ◽  
pp. 325-330 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2004 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

Impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β ≤ 1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β ≤ 1, and increases gradually for β > 1. Based on finite element results for the subsurface stress, strain, and velocity fields, and simple theoretical model that yields approximated closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β ≤ 1), and its validity was confirmed by favor comparisons with finite element results.

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