Pad Asperities Research Articles

A model for chemical–mechanical polishing of a material surface based on contact mechanics

A new contact-mechanics-based model for chemical–mechanical polishing is presented. According to this model, the local polish rate is controlled by the pressure distribution between features on the wafer and the polishing pad. The model uses an analysis based on the work by Greenwood to evaluate this pressure distribution taking into account pad compliance and roughness. Using the model, the effects of pattern density, applied down-force, selectivity, pad properties, etc. on the evolution of the wafer surface can be readily evaluated. The interaction between individual pad asperities and the wafer pattern is investigated in detail. It is shown that the pressure distribution between an asperity and the wafer surface is discontinuous at edges of features that have different nominal polish rates and that this pressure discontinuity dominates the polish rate and dishing of narrow features. The model is implemented as an algorithm that calculates the evolution of the profile of a set of features on the wafer during the polishing process. The model can be applied to chemical–mechanical polishing used for oxide planarization, metal damascene or shallow trench isolation.

A Physical Model for Dishing during Metal CMP

A physically based model for dishing during metal chemical mechanical polishing (CMP) is presented. The control of dishing is important for advanced damascene metal interconnect technologies. However, the modeling of dishing is still in an initial phase. Material removal mainly takes place at the contact areas between the rough polish pad and the substrate. Therefore, a numerical model of the contact area of the pad and wafer, and the number of contacts and the size distribution of the contact areas as function of polish parameters and pad properties, was developed. The number of contacts appeared directly proportional to the applied pressure. In addition, the contact size distribution was strongly dependent on pad morphology. It was weakly dependent on the applied pressure and the Young’s modulus of the pad. Thereafter the dishing phenomenon was modeled using these results. For an arbitrary linewidth, the metal was removed by two groups of pad asperities, one group with contact size smaller than the linewidth (group S) and one with contact size larger than the metal linewidth (group B). By considering the material removal rate of these two groups of asperities separately and using a modified form of Preston’s law, a model was developed that describes the dishing during (over)polishing for an arbitrary metal line. The model contains one free parameter. The model was compared with experimental results obtained from state-of-the-art copper CMP. Excellent agreement was observed between data and the model. © 2003 The Electrochemical Society. All rights reserved.

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.

Improved Model of Wafer/Pad Powder Slurry for CMP

Chemical mechanical polishing (CMP) 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. © 2003 The Electrochemical Society. All rights reserved.

The Effect of Interactions Between Water and Polishing Pads on Chemical Mechanical Polishing Removal Rates

The elastic properties of polishing pads critically affect polishing results during chemical mechanical polishing (CMP) of integrated circuit substrates. The ability of water to plasticize polishing pads and the resulting effects on pad performance were investigated. Water is hypothesized to penetrate the surface of the polishing pads, disrupting hydrogen bonds between adjacent polymer molecules within the pads and altering the pad elastic modulus. Infrared spectra obtained using an attenuated total reflection technique were used to confirm the effect of water on the polishing pad structure. Contact with deionized water reduced the pad elastic modulus due to the formation of a hypothesized soft layer on the pad surface. Removal of the soft layer from the pad, as occurs during conditioning, increased observed CMP removal rates. Experiments on a commercial dual-axis polisher using a noncommercial process showed decreased oxide removal rates as the duration of the pad exposure to water increased. A pad asperity-wafer contact model was developed. This model indicates that if the surface of the pad asperities is softened by the penetration of water compared to the bulk pad, then the asperities will deform to a greater degree under the applied load than in the absence of the softening. As a result, the effective pad-wafer contact area for a given applied load will increase and the average pad-wafer separation will decrease, causing the applied load to be carried by a larger number of asperity-wafer contacts and reducing the local load on the wafer surface. The reduced local loads will contribute to reduced polishing rates, consistent with experimental observation. The maximum depth of penetration of water into the pad surface was estimated to be ∼20 μm. © 2002 The Electrochemical Society. All rights reserved.

Surface Removal Rate in Chemical-Mechanical Polishing

Variation of the surface removal rate with down pressure, pad asperity, and relative velocity in chemical-mechanical polishing (CMP) was studied. A phenomenological model for contact of pad asperities with abrasive particles and wafer is described. The functional dependence of the polishing rate on pressure and velocity was found to be related to the distribution of pad asperities. Simple argument based on the mechanical contact theory suggests that the linear variation predicted by Preston's equation follows when the pad asperities have a random distribution. The sublinear dependence of the removal rate, however, is obtained when the pad asperities have a wavy distribution. The use of the statistical least-square method is suggested as a way to determine the relationship between the removal rate and pressure for different industrial pads used in CMP processes. CMP polishing planarization surface removal

Mathematical modeling of polish-rate decay in chemical-mechanical polishing

A model is presented for polish-rate decay in chemical-mechanical polishing based on the Greenwood-Williamson theory of contact between a smooth surface (a wafer) and a rough surface (the polishing pad). The model assumes that polishing causes pad asperities to wear, with high asperities wearing faster than low asperities. Model predictions of the time dependence of polish-rate decay compare favorably with experiments.

A Model for Mechanical Wear and Abrasive Particle Adhesion during the Chemical Mechanical Polishing Process

Abrasive particle-surface interactions are analyzed and processes of surface removal by adhesive and abrasive wear mechanisms during chemical mechanical polishing (CMP) are studied. The mechanical contact theory is used, and a model for interactions of pad asperities with abrasive particles and wafer is developed. The cases of hard and soft pads and dilute and dense slurries are analyzed. A model for the particle-scale surface removal process in the chemical-mechanical polishing is developed. The influence of abrasive particle adhesion to the surface is included in the analysis. Variations of polishing rate with pressure, abrasive particle size, and concentration, as well as pad characteristics (including asperity distribution and asperity elastic and plastic deformation) are studied. The functional dependence of the polishing rate on pressure and velocity was found to be related to the distribution of pad asperities. The linear variation predicted by Preston’s equation follows when the pad asperities have a random distribution. The sublinear dependence, however, is obtained when the pad asperities have a wavy distribution. The results also show that the abrasive particle adhesion affects the CMP process. The model predictions are presented in graphical form and are compared with the available semiempirical correlations and discussed. © 2001 The Electrochemical Society. All rights reserved.

Submicron particle removal in post-oxide chemical-mechanical planarization (CMP) cleaning

Particle removal models for soft-pad buffing (the second-step polishing with DI water) and mechanical brush-cleaning processes are proposed and the removal forces are evaluated and compared with the average particle adhesion force to the oxide wafer surface resulting from the primary polishing (the first-step polishing with slurry). The hydrodynamic force due to the fluid flow is too small to remove slurry particles by itself and particles are most likely removed from the surfaces by the pad or brush asperity contact forces and the hydrodynamic drag force together. This conclusion is consistent with the experimental observations.

Mechanism for Subambient Interfacial Pressures While Polishing With Liquids

This paper reports the results of a model for predicting the development of subambient pressures during the polishing of flat hard substrates by sliding against a compliant pad in the presence of a slurry (liquid). This work is an extension of our prior experimental work on the polishing of single crystal silicon wafers with polyurethane pads and high pH slurries containing silica particles. Subambient pressures have important implications in the polishing rate and uniformity of silicon and, therefore, in the manufacture of large-scale integrated circuits. The subambient pressure is the result of pad asperity compression at the wafer leading edge followed by elastic reexpansion beneath the wafer due to the nonuniform wafer/pad contact stress. Liquid is expelled from interasperity voids where high leading edge contact stress causes asperities to be compressed. Lower contact stress behind the leading edge causes asperity reexpansion leading to recreation of interasperity voids and subambient liquid pressures. A Poiseuille like in-flow of liquid from the sides of the wafer limits the value of the subambient pressure. Numerical simulations predict subambient pressures as a function of liquid viscosity and relative velocity of the pad and wafer and the pad and wafer mechanics which follow the same trend as the experimental data. [S0742-4787(00)01702-1]

Particle Adhesion and Removal in Chemical Mechanical Polishing and Post‐CMP Cleaning

A new model including the effects of polishing pressure and platen speed on particle penetration depth in chemical mechanical polishing (CMP) processes is derived based on the particle adhesion theory, the surface plastic deformation, and the pad‐wafer partial contact. The predicted particle penetration depth is in good agreement with the experimental surface roughness data. Particle removal models in the final polishing and mechanical brushing/cleaning processes are proposed, and the removal forces are evaluated. The lift force in the hydrodynamic boundary layer is too small to lift particles off the surface and particles most likely roll off the surfaces by the drag force plus the contact forces from the pad or brush asperities. The effects of pressure, rotation speed, pad hardness, and chemical addition in post‐CMP are also addressed. © 1999 The Electrochemical Society. All rights reserved.

Interfacial Pressure Measurements at Chemical Mechanical Polishing Interfaces

We have found that the entrainment of a slurry between a silicon surface and a polyurethane pad will cause the generation of subambient pressure at that interface. These pressures cause the silicon to be further impressed into the pad. We have measured these pressures and this paper reports on the pressure distribution maps over an area beneath a 100mm diameter silicon wafer. The pressures are generally not uniform. The leading 2/3 of the wafer has subambient pressures of the order of 50kPa and the trailing 1/3 of the wafer has positive pressures of approximately 10kPa. The reasons for the subambient pressures is related to the dynamics of the compression of pad asperities, the boundary effects of the silicon edge, the rebound of the asperities, and re-infiltration of the slurry.

Mechanisms of Chemical-Mechanical Polishing of SiO2 Dielectric on Integrated Circuits

One of the fundamental mechanisms of chemical-Mechanical polishing (CMP) is the mechanical interaction between the wafer and polishing pad. This interaction was simulated in experiments. The vertical displacement of the wafer with respect to the polishing pad, the fictional drag of the wafer against the pad, and the pressure of the slurry trapped between the wafer and pad were measured. These experiments were performed over a range of commercially common CMP conditions. In addition, polishing rates were measured for CMP performed under induced hydrodynamic conditions where the wafer was separated from the pad by a film of slurry. It was found that no appreciable polishing occurred under hydrodynamic CMP conditions. Under commercial CMP conditions, it was found that the wafer contacts the polishing pad asperities as evidenced by near-zero wafer displacement and high friction coefficients (˜0.4). It was also found that pad conditioning (intentional roughening) causes a suction force to develop between the wafer and pad. This suction force draws the wafer into further contact with the pad, by as much as 20 μm, and corresponds to peak slurry vacuum pressures of 12 kPa (1.7 psi). Presented as a Society of Tribologists and Lubrication Engineers paper at the World Tribology Congress in London, United Kingdom, September 8–12, 1997