A Material Removal Rate Model for Aluminum Gate Chemical Mechanical Planarization

In this work, a new aluminum gate chemical mechanical planarization (CMP) model for material removal rate (MRR) is proposed in high-k metal gate (HKMG) process. Using the basic principles of steady-state oxidation reaction and mechanical abrasion mechanism, the combinational interaction of chemical and mechanical coupled effects on MRR was systematically described by process parameters, pad properties and concentration of oxidizer, and then balanced to construct an overall polishing rate. Because of the great significance of the slurry pH on MRR in CMP process, the effects of surface forces, including the influences of van der Waals (vdW) and double-layer (DL) forces simultaneously acted between the wafer and the particles were investigated. Meanwhile, the influence of particle sizes, abrasive loadings and zeta potentials of the wafer and particles on MRR was also analyzed. It is found that the attractive vdW forces strengthen the MRR, while the DL forces, calculated to be repulsive, lower the MRR. The magnitude of surface forces increases with a smaller particle size compared with the pad-particle force. When zeta potentials of the wafer and particles are considered as a function of slurry pH, the experimental trends for the MRR with slurry pH, applied pressure and abrasive loading were predicted well by the present model. Therefore, the governing equation of aluminum removal reveals some insights into the HKMG CMP process and can be utilized for optimizing and controlling the polishing rate of aluminum gate structures and performing sensitivity analyses of operating parameters. © The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0251503jss] All rights reserved.

With the steady shrinkage of the feature size and device geometry of modern integrated circuits (ICs), chemical mechanical planarization (CMP) has become the most important process choice for the surface planarization in the fabrication of advanced multilever ICs in microelectronic industry. 13][4] In CMP process, a rotating wafer with different types of design structures is pushed against a rotating polishing pad which is immersed in slurries containing chemicals and abrasive particles.Pattern structures on the wafer surface are first chemically passivated by slurry chemicals and then removed by effects of contact interactions of abrasive particles which are trapped between the pad and the wafer.The contact mechanism of the particles in the slurry provides the opportunity to remove the material from the wafer surface at an acceptable production rate. 5he material removal rate (MRR) which has been studied extensively from both a modeling and experimental standpoint depends sensitively on pattern geometry, process parameters, chemical reactions, pad properties and mechanical abrasion.If the CMP process is not properly controlled, excessive erosion of the dielectric layer or dishing of metal lines will result in great significant impact of the surface topography on the wafer yield.The introduction of porous ultra-low-k dielectrics and shrinking device sizes calls for more stringent requirements for the CMP process to control the MRR and planarity.The effects of the interaction between the wafer surface and the abrasive particles need to provide an adequate MRR and planar surface with minimal defects.
Up to now, numerous approaches have been proposed to predict the MRR of the wafer profile from different standpoints of the CMP process.][8][9][10][11][12] The influence of applied pressure, pad properties, particle size and concentration, wafer hardness, and their interactions on the MRR is also expressed. 13A wafer-level MRR model was proposed by combining a hierarchical model of the particle-wafer-pad interactions and an adhesive wear model. 14For z E-mail: xuqinzhi@ime.ac.cn in-depth understanding the slurry flow at the wafer-pad interface, 15,16 fluid hydrodynamics with mass transport model was also developed to depict the importance of the slurry flow to the CMP process.Moreover, the mixed lubrication model taking into account the compressibility of the pad and the mold of slurry delivery 17,18 is used to give reasonable predictions of the pressure profiles and removal rates. 4,19,208][29][30][31][32][33][34][35][36][37][38] The overall MRR is influenced by the existence of different compositions on the wafer surface, 31,34 resulting in the change of the wafer surface hardness, which affects the aggregate wear rate of the wafer material. 30,34,35,37n addition to the effect on the wafer hardness, slurry chemicals have also been shown to influence the zeta potential of abrasive particles and the wafer, 27,29,35,[39][40][41][42] where the slurry pH was the primary factor affecting the zeta potentials. 43The slurry pH and zeta potentials of particles and wafer surface could significantly affect the polishing performance.5][46][47] When the DL forces are attractive, the contact force between the wafer and abrasives becomes large, which causes the MRR for each abrasive particle to increase. 29,47The experimentally observed variation in MRR with a slurry pH was attributed to the effect of a slurry pH on the zeta potential, which influences the magnitude of DL forces.Moreover, the van der Waals (vdW) forces between the wafer and abrasive particles could also cause an increase of the MRR. 27,48The surface forces have a large effect on the agglomeration of the abrasive particles in the slurry and finally affect the removal rate. 49,50It has been pointed out that if the particles are at their isoelectric point, the particle aggregates can grow from a nanometer to a micrometer size in a relatively short time, causing undesirable, deep scratches on the wafer surface. 27,49lthough the effects of surface forces were illustrated to contribute to MRR, only few models 8,12,27 have been developed to understand the experimental phenomena.A MRR model which postulates the abrasive particles as spheres with hemispherical bumps on the surface was proposed to investigate the effect of the roughness of abrasive particles on the magnitude of the vdW forces. 48Furthermore, the DL forces were further considered in an extension of this model to understand the effect of slurry pH and DL forces at abrasive-wafer contact including their adhesion and repulsion. 12As for HKMG structures, none of aluminum CMP (Al-CMP) models have been proposed to incorporate the surface forces in the process of constructing the MRR model.As we know, for integrating the metal gate as well as the high-k gate oxide, HKMG technology is widely adopted by most of IDM and foundries due to its associated lower thermal budget, more stable threshold voltage, and improved performance from strain induced dummy gate removal. 4,26Poly opening polishing processing before dummy poly removed and Al-CMP implementing after work function metal deposition, have been developed to fabricate the HKMG products. 26,51During this process, there are several problems needed to solve, such as the conformal deposition of metal layers in the gate stack, precise gate height control, and minimum galvanic corrosion. 26,52,53However, the planarization process control of the aluminum gate has several challenges, which results in developing complex CMP tools and a special slurry recipe to control all the gate processing steps for proper device function and uniform parameter distribution. 54,55In HKMG CMP process, the passivation of Al gate in slurry plays a very important role and the combinational effect of polishing pad, abrasive particles, and chemical components leads to the material removal.Under the mechanical abrasion of abrasive particles and polishing pad, the unreacted sites and oxidants of the metal gate surface are removed and then carried out of wafer surface by the flowing slurry. 26Modeling this process involves describing the nature of the surface material formed, the chemical reactions, and the abrasive-film interactions, including the effects of surface forces.
In our previous work, 26 a physically based Al-CMP model is proposed to study the synergistic interactions between mechanical abrasion and chemical reaction.Although we systematically investigated the effects of mechanical abrasion and concentrations of different types of chemical reagents on MRR and metal gate height evolution in HKMG process, the effect of abrasive loading and the contribution of surface forces on MRR were not considered.Therefore, it is quite necessary to extend our previous method further to take into account the influence of these parameters unconsidered on the polishing planarity in order to achieve good MRR and surface topography control.
In this paper, a new Al-CMP material removal model has been explored to capture the synergetic effects of mechanical abrasion and chemical reaction process using the concepts of chemical-mechanical equilibrium and chemical reaction kinetics as a bridge to connect them.In addition to the force applied on the abrasive by the pad, the contribution of the surface forces acting between the wafer and the abrasive particles to the overall force equilibrium is considered.As a result of this consideration, the model enables the calculation of the MRR by including the effects of the vdW forces and the zeta potentials of the wafer and particles.It generally depicts the basic abrasive mechanism in the polishing process and gives a heuristic vision of the non-Prestonian behavior of Al-CMP.We validated our integrated synergistic model by comparing the results with some experimental data. 53In the experiment, 53 the aluminum alloy film diced out of 300 mm wafers was polished on a CETR CP-4 bench-top polisher, and IC-1000 K-groove pad was used and conditioned ex-situ for 1 min after each polish.Polishing pressures in the range of 1-4 psi, a slurry flow rate of 90 mL/min, platen/carrier speeds of 90/90 rpm, and the silica abrasives of average diameter 35 nm were used for the polishing experiments.The MRR was obtained by measuring the pre-and post-polish film thickness with a four-point probe and an interferometry-based technique.The experimental condition, process parameters and the removal rate values are quite typical in HKMG Al-CMP process, and the polishing behavior of the aluminum alloy film is very similar to that of aluminum. 53Therefore, the experimental data can provide an important data basis for model construction and be directly utilized for verification of the present Al-CMP model.The comparison indicates that the present model can be used to focus on the oxidation effects, abrasive particles, slurry pH, and surface forces on removal rate, describe and optimize the surface evolution control in HKMG Al-CMP process.
The remainder of the paper is organized as follows.In Sec. 2, the theoretical model is constructed and proposed.In Sec. 3, the results and discussion are described in detail.Finally, our conclusions are presented in Sec. 4 with a brief summary and discussion.

Modeling
During the model construction, some assumptions should be pointed out for clear understanding.7][58] In CMP process, the polishing pad will be replaced by a new one after polishing some wafers to keep it maintained at a certain roughness level for process performance stability.Before the new pad is formally employed for the CMP process, several blanket wafers are polished in advance to control the polishing process reaching a stable state.Moreover, during the polishing process, the pad can be effectively conditioned with a standard diamond grit conditioner to keep the MRR and uniformity of surface topography sustained in a reasonable range, and the dispersion state of the abrasive particles can also be kept. 53In order not to make the present model too complicated, the effects of consumables life and additive interaction with abrasives are not considered in this work.][61][62][63][64] The present model focuses on the synergistic effects of the material removal in aluminum CMP process, including providing a further understanding of the surface forces.With the development of the present model, various parameters considered are described in detail.
Chemical and mechanical removal mechanism.-InHKMG Al-CMP process, the formation of a composite layer of the wafer surface is a dynamic chemical process and the aluminum surface is first attacked by some chemicals in the slurry.The equilibrium coverage of the surface complex is largely dependent on the concentration of chemicals and the relative rates of the formation and decomposition reactions. 21,22he combination of chemical formation of the aluminum gate surface layer and its destruction by both chemical and mechanical processes leads to a steady state balance.In building the present model, the aluminum surface is modeled with the unreacted fresh surface [Al] and the reacted surface [Al(III)].The composite surface is assumed to have a random distribution of the above species and the total aluminum complex [ Al] T is described as: The chemical equilibrium reaction between aluminum and oxidizer (Oxi) in CMP slurry is achieved to form an oxide or hydroxide layer: where k 1 is the rate constant and [Oxi] is the concentration of the oxidizer in the slurry. 26Meanwhile, direct mechanical removal of the gate surface is postulated with the abraded reacted material δ and the detritus of unreacted aluminum δ flown into the slurry without re-depositing onto the complex surface.Therefore, the mechanical removal process of the aluminum can be expressed as: 4,26 Al(III) where k 2 and k 3 are the mechanical removal rate parameters, depending on the number of abrasive particles making contact and therefore on the polishing pressure, polishing speed and abrasive concentration in the slurry.Here, A denotes to the abrasive particle.Following standard methods of chemical kinetics, the local removal rates of oxidant [Al(III)] and unreacted sites [Al] are assumed to be proportional to the product of the mechanical removal constant and the probabilities of surface sites [ Al(III)] and [Al].Therefore, the material removal rate MRR of aluminum gate surface at any point is given as: [Al] T [5]   where M and ρ 0 denote the molecular weight and density of aluminum, respectively.
Steady-state removal rate.-Themass balance theory is utilized to eliminate the probability of the rate formula in Eq. 5 and the change rate of [Al(III)] can be expressed as: where the first term in the right hand side of the equivalence is for creation while the second term is for mechanical destruction of the surface film.When the steady-state of the polishing balance is achieved, the rate formation of [ Al(III)] is equal to the rate depletion, giving as: If we set the ratio of the species [ Al(III)] and the total aluminum surface sites [Al] T as ρ, then derive Eq. 7 again, and the following expression is obtained: Therefore, the MRR is derived as follows based on Eq. 5: It can be seen from Eq. 9 that the MRR depends on the concentration of oxidizer and the surface kinetic parameters k 1 , k 2 and k 3 also have an effect on the aluminum removal mechanism.The parameter k 1 is postulated as concentration-related and independent of positions, while parameters k 2 and k 3 are mechanical abrasion rates of reacted [Al(III)] and unreacted [Al], respectively.They are determined locally by polishing pressure, relative rotational speed, wafer-backing film, concentration of abrasives, particle radii and pad properties. 12,21,65everal possible dependences are available to describe this relationship, one of which can be given as: 65 [11]   where the proportionality parameters k 20 and k 30 determine the scale, K pad is the ratio of rate constants for particle adsorption and desorption from the pad.It can be represented as: where D is the abrasive diameter, and k is the corresponding parameter.The particle concentration [ A] in units of particles/volume is expressed as follows: 65 [A] = 6 πD 3 where M w A is weight percent for spherical particles and ρ s and ρ A are the densities of the slurry and particles.Moreover, the mechanical removal rate R 0 is captured by the following expression: 12 p−w E w− p [14]   where and κ S are amplitudes of a regular wavy surface and the curvature of the asperity submit, respectively.p 0 is the applied pressure, V is the relative velocity and f is the fill factor, which is defined as the ratio of number of particle per unit area divided by the number of particles at dense packing.E p−w is the composite Young modulus between the wafer and the pad and E w− p is the composite Young modulus between the wafer and abrasive particle.f w is the wafer-particle contact force and C w is defined as: 12 where W A is the thermodynamic work of the adhesion.The waferparticle contact force f w consists of the force transmitted through the pad-particle contact L p and surface forces between the wafer and the particle, including the vdW f vdw and electrical DL forces F ψ s− p with constant surface charge for a spherical particle and a plane surface: 12,27 [19] where E pad and υ pad are the Young modulus of the asperity and the Poisson ratio of the pad, respectively.A wsp is the effective Hamaker constant, ε r is the relative dielectric constant, ε 0 is the dielectric permittivity of vacuum, κ −1 is the double layer thickness and L is the distance of minimum approach.ψ 1 and ψ 2 are zeta potentials of the abrasive and the wafer. 27,66,67o evaluate the effect of DL forces on the MRR, the zeta potentials for different materials as a function of slurry pH must be known.As pointed out by Ramarajan et al., 45 they investigated the effect of slurry pH on the MRR of tantalum films polished by slurries containing silica and alumina particles.In the present model, the zeta potentials of silica was determined as a function of slurry pH and was described by a curve-fit equation: 12 Moreover, we assume that the [Al(III)] surface is composed of aluminum hydroxide for model simplicity.The zeta potential of [Al(III)] hydroxide is determined by specific experimental conditions, including temperature and components of the slurry.For conveniently capturing the basic characteristics of the studied system, a fit formula is given as 68 ψ Al(OH 33.9 cos π( pH−5.0)6.9 + 15.2(mV ) 4.7 ≤ pH ≤ 12 −18.5(mV ) pH ≥ 12 [21]  Finally, the MRR in Eq. 9 is rewritten as: ) unless CC License in place (see abstract

Results and Discussion
In this section, we will give a detailed analysis on the effects of the oxidizer concentration, abrasive loading and contact pressure on the material removal rate.The model is compared with the experimental data 52,53 and good agreement is obtained.Unless otherwise indicated, the specific values of the following parameters are set to be V = 0.5m/s, E p = 3M Pa, υ = 0.2, k 1 = 4.87×10 −6 m/s, M = 27g/mol and ρ 0 = 2.7g/cm 3 for convenience in the following simulation and verification. 12,26,27,65,69,70In CMP process, it is really very difficult to accurately measure the specific model parameters.For simplicity and convenience, these parameters in the present model are mainly selected from some published literatures. 12,26,27,65,69,70These values are generally adopted in CMP simulation or experimentally used for recipe configuration except for parameter k 1 .The chemical reaction rate parameter k 1 is fitted from the experimental values of the following subsections.Similarly, the parameters listed in Table I are adopted from references 12 and 27.

Effect of oxidizer concentration on MRR.-A simplification of
Eq. 22 can obtain different expressions for the material removal rate, which can be represented as a function of oxidizer concentration [Oxi] while other parameters are fixed as constant: where a, b and c are model parameters.
Figure 1 shows the effect of the oxidizer concentration on the removal rate, where there exists a simple relationship between the MRR and the oxidizer concentration.In the present simulation, the particle radius is 35 nm, the slurry pH is 6 and the applied pressure is equal to 4 psi.It is seen that the removal rate MRR enhances rapidly with the increase of the concentration [Oxi] at small values and then plateaus to a maximum at higher oxidizer concentration.The possible reason is that at low oxidizer concentration the surface coverage is low and any additional oxidizer in the solution has easy access to absorb onto the unreacted surface sites and then induce chemical reaction.While at high concentration the surface is effectively reacted and additional oxidizer in solution could not find more surface atoms to complex.In general, low oxidizer concentration leads to small surface coverage, while high concentration leads to nearly full coverage of aluminum hydroxide.This observation helps to explain the dependence of aluminum polishing rate on oxidizer concentration in the slurry.Moreover, another illustration of Fig. 1 is that the removal rate is the outcome of the competitive interaction between chemical and mechanical removal.The slope of MRR curves at small concentrations is determined by the chemical rate parameter k 1 , while the height of the plateau at larger values is dependent on the mechanical rate parameters k 20 and k 30 .At low oxidizer concentration, the mechanical abrasion rate is much weaker than the chemical production rate for the surface layer, which causes the mechanical parameters to become the limiting factor for the polishing rate.However, when the oxidizer concentration is large enough, the mechanical abrasion prevails against the chemical production of the aluminum surface.The chemical process becomes rate limiting, and increases of the oxidizer concentration will not significantly affect the material removal rate. 26Clearly, it can be seen from Fig. 1 that the variation behavior of the mechanical parameters k 30 and k 20 is consistent with the relationship of Eq. 22 by taking the limits of small and large values of the oxidizer concentration.
Effect of abrasive loading on MRR.-Furthermore, Eq. 22 can be transformed to show the dependence of aluminum polishing rate on abrasive loading by some simple algebraic manipulations: where a 1 , b 1 , c 1 and d are model parameters.
For constant abrasive loading M w A , there are more particles in the slurry when the diameter of the abrasive D is small than when D is large.According to Eq. 22, small abrasive particles can lead to large material removal rate compared with big ones.This conclusion deduced from the present model is consistent with the experimental observation that small abrasive particles polish faster than large ones in tungsten CMP. 71In effect, for constant abrasive loading M w A and particle concentration, there are simply more small particles than large ones in the slurry that are available to effectively remove the film from the aluminum surface.
The simulation shown in Fig. 2 presents the relationship between the abrasive loading and the removal rate when other conditions are fixed as constants.In the present calculation, the concentration of oxidizer is 0.003 mol/L, the particle diameter is 35 nm and the slurry pH is 6 which is same as the experiment. 53The fit values of the scale parameters in present MRR model are k 20 = 147.4    2 shows that the increase of the abrasive loading leads to the increase of the MRR.Meanwhile, with further increase of abrasive loading, the material removal rate curves also give an explanation that the MRR finally converges to the maximum value a 1 .
As is clearly shown in the figure, the present simulation which has revealed the dependence of polishing rate on abrasive loading in the slurry agrees well with the experimental data.Qualitatively, at relatively low loadings the pad has enough empty sites, and the added abrasive particles will go to these sites and become effective in Al-CMP process.At higher concentrations, with the increase of the abrasive loading, all of the pad sites are loaded and additional abrasive particles could not fit onto the surface.The abrasive particles either remain in the slurry or stack on the pad surface without adding to its polishing effectiveness, which leads to a plateau of the polishing rate. 21fect of applied pressure on MRR.-Similar to previous subsections, the MRR can also be simplified as a function of the polishing applied pressure p 0 with all other parameters held constant: where a 2 , b 2 and c 2 are model parameters.
Figure 3 shows the relationship between the polishing rate and the applied pressure.It is indicated that the increase of applied pressure results in the increase of removal rate.The experimental data also shows this behavior and the present model can qualitatively explain this variation trend.In particular, some studies indicate that the CMP polishing rate is linearly proportional to the applied pressure, but that the intercept is not zero.The discrepancy of the original Prestonian behavior at the limiting case of the pressure can be solved by the present model, since the MRR expects nonzero value over small ranges of pressure.The model explanation is consistent with the necessity of some initial energy for the abrasive to break through the surface layer, push into the hydroxide material, and then begin the circling process of fracture and material removal.In this part, the abrasive loading of silica is 1% and the fit parameters of k 20 and k 30 are 169.5 and 812.1, respectively.
In Al-CMP, the abrasive process is significantly different from the conventional glass polishing due to the nature of the abrasive-polishing pad system.In the mechanical step, the polishing pad presses abrasive particles against the aluminum surface which is contacted with the pad asperities.The pores of the polishing pad can be served as reservoirs for abrasive particles and the pad pulls the particles across the aluminum surface.The complex surface layer formed in the chemical reaction step is then removed.When the pressures are low, few of the abrasives are contacted with the surface layer.At higher pressures,  the abrasives are forced in the pad pores against the aluminum surface.The pad asperities are flattened out to provide additional contact area between abrasives and the aluminum surface.Because of these additional abrasive contacts, the mechanical polishing rate increases.
Otherwise, the mechanical polishing rate is also determined by the polishing speed, because more abrasive-aluminum surface contacts can occur per unit time at higher speeds.

Effect of slurry pH on MRR.-
To evaluate the present model further and determine the effect of slurry pH on MRR, a compact formula of MRR is necessary.However, as are shown in Eqs.14-22, there is a quite complicated nonlinear relationship between the present MRR and the slurry pH.Therefore, the simplified formula is not presented here to directly illustrate the function relations between MRR and pH value.To more conveniently investigate the variation of MRR as a function of slurry pH, the results are shown in Fig. 4. In this subsection, the model developed was implemented by using the parameters of the experimental conditions, 53 where the concentration of oxidizer is 0.003 mol/L, the abrasive loading of silica is 1%, the applied pressure is 4 psi, and the mean particle diameter is 35 nm in the simulation.The fit parameters are k 20 = 142 and k 30 = 2190.7.
It can be seen that a reasonable agreement between the results of the experiment and the model is illustrated in Fig. 4. The material removal rate first increases to a certain maximum and then it decreases with the increase of the slurry pH.This observation is attributed to the effect of DL forces varying in magnitude with slurry pH.In the model, the slurry pH influences the zeta potentials of the aluminum surface and the particle; therefore, the contact force between the wafer and the particle varies with increasing slurry pH.The maximum MRR occurs at around pH 8, as determined by the experiment and the model for the silica slurry.The electrostatic attraction between the positively charged aluminum surface and the negatively charged silica surface is the reason for the higher MRR at pH 8 while the electrostatic repulsion between the aluminum and silica surfaces at pH 10 can lower the MRR.As shown in Fig. 4, the present simulation under-predicts the maximum MRR value for the silica slurry.
Effect of other parameters on MRR.-To qualitatively investigate the effects of particle size on the material removal rate of Al-CMP, Eq. 17 can be rewritten as a function of abrasive particle size with other parameters held constant.The particle diameter has a large effect on the MRR, which can be illustrated from Fig. 5.The fitted parameters k 20 and k 30 are equal to 1500 and 1200, respectively.It is seen that the MRR decreases with the increase of the abrasive radius, which is consistent with the experimental data of tungsten CMP. 71oreover, with the increase of the chemical reaction parameter k 1 , the MRR slightly increases, which means that the increase of the aluminum hydroxide on the wafer surface can induce more material removal during the mechanical polishing step.This variation trend of the MRR with increasing parameter k 1 is consistent with our previous simulation work. 26therwise, the impact of the particle radius on the MRR as a function of pH values is also displayed in Fig. 6.Clearly, with increasing the particle radius, the effect of slurry pH on MRR becomes less prominent.Therefore, it can be predicted that the effect of the DL forces will be quite small when the particle radius is bigger than 100 nm based on the present model parameters.As for small particles, the pH value has the largest impact on the material removal rate, which can be seen from particle radius R = D/2 = 20 nm.At the same time, it is quite interesting that the values of slurry pH with different particle diameters are equivalent when the MRRs reach to their maxima.However, the magnitude of the peak intensity of MRR is different and influenced by the abrasive particle diameter.All the three simulations with different diameters have the same position of maximum peaks.This is because the zeta potentials for silica and aluminum hydroxide near pH 8 are relatively large and opposite in sign and it has no relations with the particle diameter.Moreover, when slurry pH is approximately less 9.7, small particle has a larger MRR.While the slurry pH is bigger than 9.7, the variation trend changes with increasing the pH value.The integrated interaction of the abrasive particle size and the slurry pH has a large effect on the material removal rate.The smaller the abrasive particle diameter is, the faster the gradient of the MRR changes, which directly leads to the intersection of the MRR curves.According to the present calculation, it can be predicted that the decreasing rate of the MRR will become quite slow when the abrasive particle diameter exceeds a threshold value.
Furthermore, the variation of the MRR as a function of slurry pH for different oxidizer concentrations is also studied and displayed in Fig. 7.It is assumed that the diameter of abrasives is 35 nm and the  scale parameters k 20 = 1500 and k 30 = 1200.It can be seen that the MRR increases with increasing oxidizer concentrations.The observation clearly shows that the effect of the oxidizer concentration on material removal rates becomes quite prominent when the slurry pH is in the range of 6 to 10.
It is known that if the surface forces are repulsive, then the surface forces have a negative effect on the MRR, causing the material removal rate to decrease.However, if the surface forces are attractive, the MRR will increase with the increase of the magnitudes of the vdW forces and DL forces.As is shown in Fig. 8, the MRR is plotted as a function of the slurry pH in the presence of the attractive van der Waals forces.It shows that the MRR increases with increasing the effective Hamaker constant, which is an indication of the magnitude of the vdW forces.

Conclusions
In this work, a new MRR model is proposed to give an overall polishing rate in HKMG Al-CMP process with considerations of integrated chemical and mechanical effects.The present model comprehensively takes the chemical effects and contact interactions to describe the material removal mechanism by different parameters such as process parameters, pad properties and oxidizer concentrations.The removal mechanism is verified by experimental data gathered from literatures under different conditions.The predicted results could provide both qualitative and quantitative insights into the influence of oxidizer concentration, abrasive loading, polishing pressure and slurry pH on aluminum removal rate.The effects of surface forces, including vdW forces and DL forces were investigated and the role of particle sizes and zeta potentials of the wafer and particles on MRR After the emphasis of Al-CMP mechanism, the model is further used to predict the effects of abrasive size, oxidizer concentration and effective Hamaker constant on MRR as a function of slurry pH.The removal rate is found to be strongly dependent on these parameters and displays nonlinear behaviors.For practice, the model has the potential to be used as a design tool to evaluate the influences of changes in oxidizer, abrasive loading, pH values and particle sizes, since it ascribes specific mechanisms to different parts of Al-CMP.It is possible that the model can give a quantitative description of abrasive-surface film interaction details and abrasive size dependences in specific process.Since the polishing rate is affected by how the applied pressure deforms the pad as it contacts the aluminum surface, the model can also inspire attentions about the nature of the polishing pad, including stiffness and asperity characteristics.Moreover, although the present model is mainly focused on the HKMG Al-CMP process, it can also be applied to general CMP conditions.The reason is that the present model formulation is nearly identical during the construction of the general CMP model, and the specific difference between the aluminum MRR and the general CMP equation is that the zeta potentials are different for different conditions.Therefore, the present MRR formula can be directly extended to the general CMP process without much extra manipulations, and the subsequent discussion of the model parameters is similar to present study.However, the present model still needs to overcome some challenging issues before it can yield further practical predictions of the aluminum polishing process.In fact, the HKMG Al-CMP modeling parameters are different for different slurry chemistries, pad types, polishing pressures and rotational speeds configured in different process conditions.The experimental determination of the mechanical removal parameters and the chemical reaction rate during CMP process is not an easy task at present.Moreover, the shear effect of the flowing slurry has been ignored in the present model, and it may play a role in determining the MRR in a real CMP process.The material removal mechanisms for these factors have to be further studied on a fundamental level in the future study.

Figure 1 .
Figure 1.MRR as a function of oxidizer concentration with pH = 6 and particle radius equal to 35 nm.

Fig.
Fig.2shows that the increase of the abrasive loading leads to the increase of the MRR.Meanwhile, with further increase of abrasive loading, the material removal rate curves also give an explanation that the MRR finally converges to the maximum value a 1 .As is clearly shown in the figure, the present simulation which has revealed the dependence of polishing rate on abrasive loading in the slurry agrees well with the experimental data.Qualitatively, at relatively low loadings the pad has enough empty sites, and the added abrasive particles will go to these sites and become effective in Al-CMP process.At higher concentrations, with the increase of the abrasive loading, all of the pad sites are loaded and additional abrasive particles could not fit onto the surface.The abrasive particles either remain in the slurry or stack on the pad surface without adding to its polishing effectiveness, which leads to a plateau of the polishing rate.21

Figure 3 .
Figure 3. MRR as a function of polishing pressure with abrasive loading of silica equal to 1%.

Figure 4 .
Figure 4. Comparison of MRR between simulation and experimental data as a function of pH.

Figure 5 .
Figure 5. MRR as a function of abrasive diameters with pH = 6.

Figure 6 .
Figure 6.MRR as a function of pH with different abrasive radii.

Figure 7 .
Figure 7. MRR as a function of pH with different oxidizer concentrations.