Asperity Deformation Research Articles

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

This paper describes a two-dimensional, multiscale, material removal model for chemical–mechanical planarization that includes: (i) asperity deformation; (ii) bulk pad deformation; (iii) wafer compliance; (iv) carrier film deformation; (v) slurry flow; (vi) material removal by abrasive particles in the slurry. A finite element method is used to establish the relationship between the contact stress and the deformation of an idealized asperity made of a hyperelastic material. The total local stress due to the multitude of asperities is computed using the Greenwood–Williamson approach. The wafer deformation, bulk pad deformation, and slurry film thickness are then evaluated from the estimated contact stresses and hydrodynamic fluid pressures. The material removal rate on the wafer is computed as a function of position on the wafer. The wafer scale material removal rate results show large changes in rate near the wafer’s edges, as often seen in practice, with very uniform removal across most of the wafer surface. The computational algorithm used to calculate the contact stresses, slurry fluid pressures, material removal rates, and the global force and moment balances is summarized.

Asperity deformation, lubricant trapping and iron fines formation mechanism in cold rolling processes

Contact conditions in cold rolling are decisive to improve quality and final aspect of rolled strip. The control of contact conditions is obtained by a good combination of process parameters, such as normal and tensile force, forward slip and lubrication regime. To understand and to optimise contact at roll–strip interface, a simulation test was developed in our laboratory. The upsetting rolling test (URT) permits reproduction of the main contact conditions for cold rolling. The URT is able to simulate and to define the influence of rolling parameters on the iron residue quantities, and on the quality of the final surface. In accordance with finite element simulations, we can estimate a mean Coulomb’s friction coefficient. A very good correlation was found between experimental and numerical results. A complementary finite element model has been developed to predict the local behaviour of surface asperities during cold rolling. In this simulation at local scale, the roughness and trapping of lubricant are introduced, in addition to the pressure force and forward slip. It has been found that forward slip and reduction ratio modify the plastic strain behaviour of asperity through pressure and shear force. Thus, we are able to define the quantity of iron residues, as a function of the local plastic strain and the plastic energy solutions.

Detection of shaft-seal rubbing in large-scale power generation turbines with acoustic emissions. Case study

Rubbing between the central rotor and the surrounding stationary components of machinery such as large-scale turbine units can escalate into severe vibration, resulting in costly damage. Although conventional vibration analysis remains an important condition monitoring technique for diagnosing such rubbing phenomena, the non-destructive measurement of acoustic emission (AE) activity at the bearings on such plant is evolving into a viable complementary detection approach, especially adept at indicating the early stages of shaft-seal rubbing. This paper presents a case study on the application of high-frequency acoustic emissions as a means of detecting and verifying shaft-seal rubbing on a 217 MVA operational steam turbine unit. The generation of AE activity is attributed to the contact, deformation, adhesion and ploughing of surface asperities on the rubbing surfaces of the rotor and stator.

Abrasive wear between rough surfaces in deep drawing

In tribology, many surface contact models are based on the assumption that surfaces are composed of a collection of small asperities of which the tips are equally sized and spherically shaped and have some kind of statistical height distribution. This approach was used in 1966 by Greenwood and Williamson and was successfully followed by many researchers during the following decades. The statistical representation of surface topography enables calculation of contact forces and asperity deformations with reasonable accuracy using well established equations. Although this approach has proven to be suitable for static contact situations, alternative representations of the surface topography are required when modelling abrasive wear. In the current work an elastoplastic contact model is developed in which a representation of the surface topography is obtained by best fit approximations of the micro-contacts, obtained from real, measured surface height data. In this deterministic surface representation, the tips of the contacting asperities are assumed to have an ellipsoidal shape. Given the material parameters and contact conditions, the load and deformation of a single asperity can be computed. Subsequently, the wear induced by each individual asperity is obtained by inserting its size and shape and the conditions into a “single asperity micro-abrasion model”. By summing the contributions of all individual asperities, the total abrasive wear volume is obtained. The results of the developed abrasive wear model are compared with results obtained using a statistical approach.

Inverse analysis of material removal data using a multiscale CMP model

This paper describes a mechanical model for a representative dual axis rotational chemical mechanical planarization (CMP) tool. The model is three-dimensional, multiscale and includes sub-models for bulk pad deformation, asperity deformation, lubrication based slurry flow, carrier film deformation, wafer compliance and material removal by abrasive particles in the slurry. With the model, material removal rate (MRR) can be determined as a function of stress applied to the wafer, relative sliding speed, and material and geometric parameters of the pad and slurry. Experimental material removal rate profiles obtained from Cu polishing experiments performed on a wafer without rotation are analyzed as an inverse problem. We use MRR data to predict local CMP conditions such as fluid film thickness, fluid pressure and contact pressure. The results are consistent with available experimental and analytical information. This inverse technique offers promise as an improved method of CMP model verification.

A Locally Relevant Wafer-Scale Model for CMP of Silicon Dioxide

Wafer-scale pressure distributions developed previously are combined with locally relevant models for asperity deformation and contact pressure during chemical mechanical planarization (CMP) based on the Greenwood and Williamson model. This combined model is used to predict local and wafer-scale removal rates. The resulting predictions are compared to wafer-scale experimental data obtained in an IPEC 472 polishing platform. In addition, the model is used to investigate the nature of pad-particle-wafer contact during CMP and its changing nature as a result of variations in abrasive particle diameter, slurry solid weight percentage, and changes in pad surface morphology. It has been established that the model is sensitive to pad surface morphology, in agreement with experimental observations. Two conclusions are drawn: (i) pad topography is a key aspect to be understood and optimized in CMP and it is necessary to collect pad surface topography data in order to accurately model a CMP material removal process. © 2003 The Electrochemical Society. All rights reserved.

Evaluation of wear mechanisms of Y-TZP and tungsten carbide punches

Tool wear is one of the major concerns in the tooling industry. A comparative evaluation of different tool materials and tool wear will help preventing frequent replacement of tools thus reducing the costs incurred due to such replacements. In this paper, tool wear mechanism of tetragonal zirconia polycrystal (TZP) punch is compared with that of commercially available WC (tungsten carbide) punch during stamping. The tool life for the TZP punch was found to be over 2.5 times higher than that of commercial tungsten carbide. The worn-out tools were analysed using scanning electron microscope and optical microscope for studying the tool wear mechanisms. Tool wear and chemical action possibly cause the failure of the tungsten carbide punch, whereas wear of TZP punch is predominantly caused by mechanical shearing of asperity and plastic deformation. Due to their inherent high melting point and the absence of the second-phase binder, ceramics materials do not soften at higher temperature unlike the carbide tools. Hence, they can be used at high cutting speeds without initiating deformation/diffusion wear. This assists in improving the tool life significantly. In addition, TZP ceramics is inert, corrosion resistant and non-wetting when contacting metals. Exposed carbide grains act as a site for increased wear and metal pickup during precision, high-speed metal stamping and forming. Moreover, cobalt-depleted carbide tools can create burring of the strip being stamped, leading to poor part quality. The performance of TZP punch tool will be evaluated thoroughly based on experimental data in this paper.

A Multiscale Elastohydrodynamic Contact Model for CMP

We present a three-dimensional multiscale elastohydrodynamic lubrication (EHL) contact model for chemical mechanical planarization (CMP) based on satisfying the fundamental mechanical force and moment balance equations appropriate for a rotational CMP tool. We describe surface-surface and fluid-surface interactions in conditions where pad asperities are in direct contact with the wafer and the effective film thickness is comparable in size to the roughness of the bounding surfaces. A hyperelastic material is used for our asperity scale model to account for large deformations of the soft polymer asperities. We iteratively solve the soft elastohydrodynamic contact problem, i.e., the solid-solid contact problem coupled with fluid pressure, until the global force and moment balances are satisfied for given operating conditions. The multiscale model computes contact stress across the wafer surface due to asperity deformation that is, in turn, caused by the externally applied load and interfacial slurry pressures. Finally, a relative measure of material removal rate across the wafer is represented by the computed local asperity contact stress. Flat, concave, and convex rigid wafers are considered. The work of this paper focuses on understanding fundamental mechanical aspects of CMP and presents a methodology to simulate mechanical aspects of the CMP process. © 2003 The Electrochemical Society. All rights reserved.

Modeling of the inlet zone in the mixed lubrication situation of cold strip rolling

In this paper a method to simulate the oil thickness and length of elastic deformation in the inlet zone of cold rolling has been developed. The mixed film lubrication model was adopted to describe the behavior of the lubricant and asperity deformation. The elastic Von Karman equation was used to describe the elastic deformation of strip in the inlet zone. The length and lubricant film thickness of the inlet zone can be obtained by a numerical method. Results of simulations show that the reduction, rolling speed, back tension have a significant influence on the lubricant film thickness and the inlet zone length.

Multiscale material removal modeling of chemical mechanical polishing

This paper describes a multiscale model for material removal during conventional chemical mechanical polishing (CMP). Three spatial scales are considered in the integrated model: (i) abrasive particle scale; (ii) asperity scale; (iii) wafer scale. The model is based on the deformation of hyper-elastic asperities attached to a linear-elastic pad. ANSYS is used to perform finite element analyses of a single asperity to obtain the relations between the deformation of the asperity, and the contact stress and area. Those relations are used in an extended Greenwood–Williamson model to compute the local average contact pressures on the pad. The material removal model includes the abrasive wear caused by local contact stress between the abrasive particles and the wafer, the distribution of asperity heights, and the plastic deformation of the wafer. The material removal rate results for unpatterned wafers are used to predict the material removal rates on a feature. The results of a computer simulation of material removal and the time evolution of a feature are shown. Two FEM based codes, ANSYS and EVOLVE are used; the former for the contact stress analysis and the latter to generate a new surface.

Effects of Friction on the Contact and Deformation Behavior in Sliding Asperity Contacts

Finite-element analyses are carried out to study the effects of friction on the contact and deformation behavior of sliding asperity contacts. In the analysis, on elastic-perfectly-plastic asperity is brought in contact with a rigid flat at a given normal approach. Two critical values of the normal approach are used to describe the asperity deformation. One is the approach corresponding to the point of initial plastic yielding, and the other at the point of full plastic flow. Additional variables used to characterize the deformation behavior include the shape and size of the plastic zone and the asperity contact size, pressure, and load capacity. Results from the finite-element analysis show that the two values of critical normal approach decrease significantly as the friction in the contact increases, particularly the approach that causes plastic flow of the asperity. The size of the plastically deformed zone is reduced by the friction when the contact becomes fully plastic. The reduction is very considerable with a high friction coefficient, and the plastic deformation is largely confined to a small thin surface layer. For a low friction coefficient, the contact size, pressure and load capacity of the asperity are not very sensitive to the friction coefficient. For a moderate friction coefficient, the contact pressure is reduced and the junction size increased; the load capacity of the asperity is not significantly affected due to the compensating effects of the pressure reduction and the junction growth. For a high friction coefficient, the pressure-junction compensation is not longer sufficient and the asperity load capacity is reduced. The degree of the friction effects on these contact variables depends on the applied force or the normal approach. Although the analyses are conducted using a line-contact model, the authors believe that the effects of friction in sliding asperity contacts of three-dimensional geometry are essentially the same and the same conclusions would have been reached. These results may provide some guidance to the modeling of rough surfaces in boundary lubrication, in which the asperity friction coefficient can be high and vary significantly both in time and from one micro-contact to another. Presented at the 57th Annual Meeting in Houston, Texas May 19–23, 2002

Effect of Lubricant Quantity and Surface Topography on the Frictional Behaviour of Can Body Stock

The friction of can body stock, alloy AA3104, with various surface topographies and lubricant coating weights was studied by means of a capstan test, which goes some way towards simulating the drawing process. The coefficient of friction varies significantly as a function of lubricant load. The friction decrease with increasing lubricant weight and then plateaus, remaining constant independent of further lubricant weight increases. A significant difference in coefficient of friction for samples tested while oriented along the rolling direction vs. oriented in the transverse direction has been interpreted in terms of a picture of severe asperity deformation at low lubricant loads and was related to the surface topography of the sheet. A simple model of mixed lubrication provides a reasonable correlation between the real area of metal/tool contact obtained from the capstan test measurements and the contact area derived independently from sheet topography.

A Micro-Contact Model for Boundary Lubrication With Lubricant/Surface Physiochemistry

A model is developed to study the tribological behavior of sliding micro-contacts. It provides a building block to the modeling of tribo-contacts in boundary lubrication. Three contact variables are calculated at the asperity-level by relating them to the state of contact and the state of asperity deformation. These variables include micro-contact friction force, load carrying capacity and flash temperature. The deformation of the contacting asperity is either elastic, elasto-plastic, or fully plastic. Furthermore, the asperity may be covered by the lubricant/additive molecules adsorbed on the surface, protected by a surface oxide layer or other chemical reaction films, or in direct contact with no boundary protection. The possibility of the contact in each of these three states is represented by a corresponding contact probability. A numerical method is developed to determine the contact state and contact variables in the course of an asperity-to-asperity collision. The asperity flash temperature, which governs the kinetics of lubricant/surface adsorption/desorption, is first calculated by integrating the Jaeger equation over the contact area and in time. Then, the probability of contact covered by an adsorbed film is determined using the Volmer adsorption isotherm, and the probability of contact protected by the oxide layer is estimated using a classical wear theory. For elastic/elasto-plastic deformation of the asperity, the friction coefficient is given by the linear combination of the friction coefficients of the three contact states with their contact probabilities as the weighting factors. For fully plastic deformation of the asperity, the contact pressure and friction force become dependent of each other. The shear stress is approximated by a linear function of the contact probabilities, and the contact pressure and friction coefficient then calculated. Meanwhile, the influence of fresh surface generation due to plastic flow on the contact probabilities is also modeled. Insights are provided into the asperity collision through numerical studies of a sample problem. In addition, parametric studies are carried out to analyze the effects of lubricant and surface parameters on the micro-contact severity and its load capacity.

거친 표면간의 미세 접촉에서의 표면력 해석

In a micro-scale contact, capillary force and van der Waals interaction significantly influence the contact between asperities of rough surfaces. Little is, however, known about the variation of these surface forces as a function of chemical property of the surface (wet angle), relative humidity and deformation of asperities in the real area of contact. A better understanding of these surface forces is of great necessity in order to find a solution for reducing friction and adhesion of micro surfaces. The objective of this study is to investigate the surface forces in micro-scale rough surface contact. We proposed an effective method to analyze capillary and van der Waals forces in micro-scale contact. In this method, Winkler spring model was employed to analyze the contact of rough surfaces that were obtained from atomic force microscopy (AFM) height images. Self-contact of OLC( diamond like carbon) coatings was analyzed, as an example, by the proposed model. It was shown that the capillary force was significantly influenced by relative humidity and wet angle of the OLC surface. The deformation of asperities to a critical magnitude by external loading led to a considerable increase of both capillary and van der Waals forces.<br/>

Tribological evaluation of AISI 304 stainless steel duplex treated by plasma electrolytic nitrocarburising and diamond-like carbon coating

In previous studies we have demonstrated that the tribological performance of stainless steels can be improved by applying a duplex surface treatment of plasma electrolytic nitrocarburising (PEN/C) and plasma-immersion ion-assisted deposition (PIAD) of a diamond-like carbon (DLC) coating. Diffusion-hardened layers between 15 and 60 μm thick, consisting primarily of expanded austenite, provide improved wear resistance and enhanced load-bearing capacity for the PIAD DLC low-friction coating. In this paper, further investigations are reported regarding the tribological and mechanical properties of these duplex treatments in wear tests against sintered WC–Co and SAE 52100 chromium–steel counterfaces using a low frequency (5 Hz) reciprocating-sliding ball-on-plate geometry with a ball diameter of 10 mm loads between 10 and 25 N. The friction coefficients remained remarkably similar for this range of loads (i.e. μ=0.09–0.13 and 0.24–0.32 for WC–Co and SAE 52100 counterface materials, respectively). The primary wear mechanism observed is one of mild asperity deformation and polishing and, in extreme cases, localised delamination of the DLC coating. The volumetric wear coefficient was almost constant for loads up to 15 N, particularly when sliding against WC–Co, where material loss from the ball counterface is less severe than with SAE 52100, despite the higher contact pressure at an equivalent load. No failure of the DLC coating was observed for 10 and 15 N loads against WC–Co and at up to 25 N against SAE 52100 steel. Scanning electron microscopy was employed to assist in the evaluation of the wear behaviour and failure mechanisms, with energy dispersive X-ray (EDX) analysis used to investigate material transfer to the coated surface.

A theoretical model for rock joints subjected to constant normal stiffness direct shear

Abstract The authors have conducted an investigation into the behaviour of rock joints subjected to direct shear. Both concrete/rock and rock/rock joints were investigated. The behaviour of rock/rock joints is important for the assessment of stability issues involving rock masses (e.g. rock slope stability). Concrete/rock joints are vital to the assessment of performance of concrete piles socketed into rock, rock anchors and concrete dam foundations. This investigation included an extensive series of direct shear tests under a range of stress boundary conditions. The rock used for the tests was a soft artificial siltstone, called Johnstone. The results from the tests on concrete/Johnstone joints have been presented in Seidel and Haberfield (Geotech. Testing J. (2002), accepted for publication) and on Johnstone/Johnstone joints in Fleuter (MEngSc Dissertation, Department of Civil Engineering, Monash University, Australia, 1997) and Pearce (Ph.D. dissertation, Department of Civil Engineering, Monash University, Australia, 2001, in preparation). This paper describes the theoretical models developed to simulate the observed behaviour, including asperity sliding, asperity shearing, post-peak behaviour, asperity deformation and distribution of stresses on the interface. These models have been combined into a micro-mechanical simulation of joint shear. Comparisons between program predictions and measured performance are presented and discussed.

A Model for Determining the Asperity Engagement Height in Relation to Web Traction Over Non-Vented Rollers

The traction developed between a thin flexible web, wrapped around a non-vented, rotating cylindrical roller is studied experimentally and theoretically. A series of eight webs representing a wide range of surface roughness characteristics are traction-tested against the same roller over a wide speed range. A mathematical model that couples air film pressure, web deflection, and asperity deformations is used to model the web/roller interface. An optimization technique is used to estimate the asperity compliance function parameters based on the experimental results and the mathematical model. A new model for determining the asperity engagement height, for surfaces with non-Gaussian peak height distribution, is proposed when the roughness of both surfaces is taken into account. Results are presented that indicate the viability and utility of the new methods.

Adhesion between weakly rough beads.

Cohesion effects are of prime importance in powders and granular media, and they are strongly affected by the roughness of the grain surface. We report measurements of the adhesion force between surfaces of Pyrex having a nanometric roughness, with a surface force apparatus. The two surfaces are immersed in liquid n-dodecane. The adhesion force measured is much smaller than expected in the case of smooth surfaces. We find that the adhesion force depends on the maximal load that has been applied on the surfaces, but does not depend on the time during which they have been in contact. We propose a model of plastic deformation of the small asperities in a macroscopic Hertz contact which is in good agreement with the experimental data.

Contact pressure between two rough surfaces of a cylindrical fit

Contact pressure, an important parameter for analysing and evaluating the contact behaviour, is always an interesting subject. The greater part of studies and results concentrates upon the contact, friction, wear, tear and lubrication for the cases of the rough contact. The tight fit is a current process of assembly for transmitting a force or a torque between a shaft and a hub with the help of friction effects. Contact surfaces play an important role in accounting for their capacities. The standards are based on the thick cylinder theory and does not take into account the surface textures and the asperity behaviour, although it is quite normal and useful to have rough surfaces, one is obliged to specify the very smooth contact surfaces. One obvious factor is that the smoother the surface is, the higher the manufacturing cost is. Moreover, having smooth surfaces does not result in a large friction coefficient. This paper, based on different precedent studies on roughness contact, bears, in mind on speciality of the tight fit problem, the distribution, the evolution of pressure, the plastic deformation of asperity and its influence on the pressure, in the objective to build a new method for computing the tight fitting pressure in a cylindrical tight fit [Influence de l’état de surface sur les caractéristiques d’un assemblage fretté, Thèse de l’ENSAM, France, 1998].

Computer-controlled lapping system for granite surface plates

This paper describes a two-dimensional, multiscale, material removal model for chemical–mechanical planarization that includes: (i) asperity deformation; (ii) bulk pad deformation; (iii) wafer compliance; (iv) carrier film deformation; (v) slurry flow; (vi) material removal by abrasive particles in the slurry. A finite element method is used to establish the relationship between the contact stress and the deformation of an idealized asperity made of a hyperelastic material. The total local stress due to the multitude of asperities is computed using the Greenwood–Williamson approach. The wafer deformation, bulk pad deformation, and slurry film thickness are then evaluated from the estimated contact stresses and hydrodynamic fluid pressures. The material removal rate on the wafer is computed as a function of position on the wafer. The wafer scale material removal rate results show large changes in rate near the wafer’s edges, as often seen in practice, with very uniform removal across most of the wafer surface. The computational algorithm used to calculate the contact stresses, slurry fluid pressures, material removal rates, and the global force and moment balances is summarized.