Efﬁciency of a CMP Pad at Removing Protective Material from Copper during CMP

The efﬁciency of a pad asperity and abrasives embedded between the asperity and wafer at removing the protective material on the surface of copper (removal efﬁciency) during chemical mechanical planarization (CMP) was determined experimentally using currentdensitiesfrominsituelectrochemicalmeasurementswhilepolishingwithaslurrycontainingBTA.Theremovalefﬁciencywasinsentitivetothepressureandslidingvelocity,butwasdictatedbythepadsurfacetopographyparametersandabrasiveconcentrationintheslurry.Ananalyticalestimatewasderivedbycomparingthetrajectoriesofapadasperityandtheabrasivesembeddedintheasperity.Comparisonoftheexperimentalandanalyticalestimatesuggeststhattheasperitiesaredeformedenoughbytheembeddedabrasivestocontactthesurfaceofcopperatabrasiveconcentrationsupto1wt%.Athigherconcentrationsupto5wt%,theasperitiesdeﬂectedtoalesseramount,makingtheforceexertedonthecopperincrease.Atthesehigherconcentrations,someofthecopperinteractingwiththesqueezedabrasiveswasplasticallydeformed,yieldinghigherremovalefﬁciencythanwhenelasticallydeformed.Theremovalefﬁciencycanbeusedasastandardmetricforassessingthematerialremovalabilityofvariousconsumablessuchasslurry,CMPpadandpadconditioner.©TheAuthor(s)2017.PublishedbyECS.ThisisanopenaccessarticledistributedunderthetermsoftheCreativeCommonsAttribution4.0License(CCBY,http://creativecommons.org/licenses/by/4.0/),whichpermitsunrestrictedreuseoftheworkinanymedium,providedtheoriginalworkisproperlycited.[DOI:10.1149/2.0351704jss]Allrightsreserved.

Chemical mechanical planarization (CMP) of copper is the key technology for the multilevel metallization of interconnects during the manufacture of integrated circuits. With scaling down of devices, the process requirements for copper CMP have become more challenging, requiring less variation in step height and fewer defects. Integration of fragile ultra low-k materials and even air gap structures with thinner barrier layers and narrow copper wiring to reduce the interconnect delay has created further constraints, such as low stress during the process and very low step heights. Addressing these challenges requires holistic understanding of the role of individual components of the copper CMP system and their interplay, so as to construct a robust model that predicts the material removal rate (MRR).
Despite awareness of the importance of the interplay between chemical and mechanical phenomena during copper CMP, few studies have investigated the true synergy. Tripathi et al. postulated a quasisteady state during copper CMP where the MRR of the protective layer on copper by a pad asperity is balanced by the rate of formation of the protective layer, until the next interaction by another asperity. 1,2 Based on this assumption, they postulated the MRR during copper CMP to be the sum of the dissolution rates for all sites on the copper and the removal rates of the protective layer, which can be determined from the oxidation rates. Choi et al. further extended the Tripathi's model so that the quasi-steady state assumption can be applied even when the protective layer on the surface of copper is less than a monolayer. 3 The kinetics of formation of the protective material on the copper surface in acidic solution containing BTA and glycine were determined by assuming the extended quasi-steady state. It was found that only a portion of the protective material present on the surface is removed by interaction with the asperities. It was also suggested that the abrasive particles embedded between a pad asperity and copper dislodge the copper under certain circumstances to generate debris that is subsequently dissolved by the complexing agent in the slurry. 4,5 The overall MRR is the sum of the rate of material removal by oxidation, which can be measured electrochemically, and the rate of removal of copper by mechanical detachment, which creates debris that may then be chemically dissolved and complexed in the slurry.
The presence of a protective surface layer is crucial for attaining planar wafer surfaces during copper CMP; this ensures that the wafer does not dissolve congruently, but rather that topographically protruding regions are removed selectively. Inhibitors such as BTA are typically added to the slurry to protect the recessed regions from being dissolved. While the formation of the protective layer has been studied widely, the removal of this layer is less understood; instead, studies of the removal of materials have focused on the copper itself, based on the study of oxide CMP. To address this gap in knowledge, the present paper quantitatively analyzes the removal of the protective materials during copper CMP. The fraction of the protective material removed by the abrading action of a pad asperity on which numerous abrasive particles are embedded is defined as removal efficiency. 4 The removal efficiency of a CMP pad was evaluated experimentally and analytically and the two compared.

Experimental
In situ electrochemical measurements were made during polishing using the apparatus shown in Figure 1 connected to a Gamry G300 Potentiostat. A three electrode electrochemical cell, housed in a  plastic beaker, was constructed on the table of a high precision machine tool (Matsuura MC-510VSS), which rotated the working electrode at high speed with high precision. The working electrode was a copper tube (99.99% purity from McMaster-Carr) with a 2 mm difference between the outer and inner diameters, so as to minimize the variation of sliding velocities relative to the CMP pad across the annulus. The copper tube was embedded in insulating epoxy, exposing an annulus at the bottom of the electrode, with a cross sectional area of 0.46 cm 2 . The surfaces of the copper electrode were insulated by epoxy except the bottom, where electrochemical reactions occurred and the corresponding current density was measured. The counter electrode was platinum mesh, placed under the polishing pad parallel to the copper electrode. A saturated calomel reference electrode (SCE) was placed in a Luggin capillary, and the tip of the capillary was located between the polishing pad and the counter electrode. An IC1010 (Rohm and Haas) CMP pad, through which four equispaced holes (4.76 mm diameter) were machined along the trajectory of the contact by the copper electrode ( Figure 2), was fixed to the bottom of the beaker. The purpose of the through holes on the CMP pad was to reduce the uncompensated resistance between the working electrode and the counter electrode and facilitate the delivery of slurry to the region between the working electrode and the pad. The pad was maintained parallel to the open surface of the copper electrode to ensure a uniform pressure distribution across the copper during polishing. The polishing slurry contained 5 wt% alumina particles (primary diameter of 20 nm and a median aggregate diameter of 150 nm, from Cabot Corporation) and 0.01 M glycine in deionized water (DI water), with or without 0.01 M benzotriazole (BTA). The pH of the slurry was adjusted to 4 using acetate buffer. All potentials are reported with respect to the SCE.
The pressure applied on the copper surface was adjusted by vertically moving the axis of the machine tool; the position was numerically controlled as precisely as one micrometer. The load applied during polishing was measured by a load cell (TUF-010-025-S from Loadstar Sensors) placed under the electrochemical cell. The sliding velocity of the copper surface over the polishing pad was adjusted by varying the rotational speed of the working electrode.
The copper electrode was potentiodynamically polarized from −0.8 V to 0.8 V at a scan rate of 5 mV/s. The copper electrode was conditioned at −0.8 V for 30 seconds before each scan to remove any oxides on the surface. In situ IR compensation was not applied because of the noise in the output data. Scans were obtained while rotating or not rotating the copper electrode. Several scans made for each condition confirmed good reproducibility.  The CMP pad was conditioned before each experiment with a diamond conditioner (GNP Technology) while irrigating with DI water. The exposed surface of the copper working electrode was polished for 30 seconds before each experiment with an IC1010 CMP pad using the same slurry specified above to flatten the entire surface including the epoxy insulating layer, followed by additional polishing using a commercial CMP slurry for 30 seconds to reduce the topography of the copper surface. The electrode was then immediately rinsed with DI water. Any remaining oxide on the copper surface was reduced by polarizing at −1.5 V for 5 seconds followed by −1.2 V for 10 seconds while abrading the working electrode on the pad. The potential was then stepped up to 0.6 V and the current was measured for 10 seconds while polishing. In situ IR compensation was applied using an integrated function of the potentiostat. Since the experimental results were highly dependent on whether the surface of the copper electrode and the top surface of the pad were truly parallel, this was ensured throughout the measurements. Figure 2 shows the pad surface after CMP when the bottom of the copper was well aligned with the top surface of the pad. The uniform annular trajectory of the copper electrode demonstrates that the exposed surface of the copper electrode interacted with a corresponding annulus of the pad. Polishing was conducted with different down pressures and sliding velocities while maintaining the potential of copper at 0.6 V. The same experiments were repeated, while exerting a down pressure but holding the electrode stationary, to compare with the data for the rotating electrode. Experiments were repeated at least three times for each condition. Figure 3 shows the efficacy of BTA at protecting the surface of copper over the entire potential range of the scan. At anodic potentials the oxidation rates of the copper were nearly two orders of magnitude lower when the slurry contained BTA, compared to the rates measured in the absence of BTA. Consistent with the experimental observations of Tripathi et al., 1 BTA also suppressed the current density at cathodic potentials, corresponding to reduction of oxygen, albeit less markedly. When the copper electrode slid over the CMP pad at 0.5 m/s under 24.8 kPa (3.6 psi) of down pressure in the presence of BTA, the current densities increased about two orders of magnitude in the anodic region, approaching the oxidation rates observed for the stationary electrode in the absence of BTA, demonstrating the efficacy of the abrading action in removing the protective layer on the surface of the copper.  Note that the current densities in the cathodic region also increased when the copper was polished in the presence of BTA. This implies that the inhibition by BTA at cathodic potentials was induced by physical adsorption of BTA and the abrading actions by pad asperities and abrasives easily removed the weakly sorbed layer of BTA from the surface. Figure 4 shows a typical chronoamperometry curve when the potential of copper was stepped up to an anodic potential, 0.6 V (SCE) while the copper electrode was polished. The current density decreased rapidly before stabilizing at a quasi-steady state after two seconds; thus the values for the first two seconds were excluded when evaluating the average current densities for each experimental condition. The initial decay of the current density (see the inset of Figure  4) was attributed to the adsorption of BTA on the oxide-free surface of copper despite the abrading action of the polishing pad. Capacitive charging of the macroelectrode was not considered because it was finished by 0.05 seconds in the absence of BTA (see filled circles in Figure 5) and the protective layer on the surface of copper would further reduce the time for the capacitive charging in the presence of BTA. 1 After the initial decay of the current, a quasi-steady state was reached where the current densities were nearly constant, implying that the overall fraction of sites occupied by BTA remained constant, although the exact location of the occupancy would change as the asperities swept the surface of the copper. The noise of the measured current densities was due to the rotation of the copper electrode; the frequency of the noise exactly matched that of the rotation. Figure 5 compares the decrease in the current densities over time for micro-and macro-electrodes, both of which were stationary, in a pH 4 aqueous solution containing BTA and glycine. It also shows that in the absence of BTA (upper curves) the current densities were almost constant after about 0.1 s. In the acquisition of the data shown in Figure 5, 5 wt% of alumina abrasives was added to the solutions used for the macro-electrode, whereas no abrasive was present in the tests using the microelectrode. Although stationary, the macro-electrode was in contact with the perforated CMP pad during the potentialstep chronoamperometry measurements, to allow comparison with the currents measured during polishing. It was of interest to compare the data obtained using a macro-electrode in the polishing slurry used in this work with the data obtained by Tripathi et al. 1 using a microelectrode in the same aqueous solution, but without added alumina particles, because the adsorption kinetics of BTA for this case were known. Because of the different geometries, the current densities for the micro-electrode at any given time were about 22.7 times larger than those for the macro-electrode (see inset of Figure 5). To aid the comparison the data for the micro-electrode were scaled down by a factor of 22.7 in the main plot of Figure 5. It is clear that, with this correction, the relative magnitudes of the current densities in the absence and the presence of BTA coincided for the macro-and microelectrodes over a protracted time period.

Results
The differences in geometry between the micro-and macro-electrodes leads to much better mass transport for the microelectrode, which is surrounded by a spherical region of electrolyte into which oxidized products can be transported. In contrast, the configuration of the copper macro-electrode parallel to the platinum counter electrode, separated by perforated CMP pad, yielded a restricted electric field and poorer ability for oxidized products to be transported from the electrode. Despite the difference in the magnitude of the oxidation rates for the two types of electrode, the intrinsic mechanism for passivation would be unchanged. Therefore, the approach used by Choi et al. 3 of considering the fractional coverage of the copper by Cu(I)BTA complexes as a function of time was adopted to examine the material removal efficiencies from the measured current densities. Figure 6 shows the average steady-state current densities of copper during polishing with different down pressures or sliding velocities. It is clear that the current densities in the absence of BTA, where protective material was not expected to form, were insensitive to the down pressure and sliding velocity. In contrast, the current densities in the presence of BTA, where some sites on the copper were expected to be protected, were always significantly lower than those in the absence of BTA, but increased steadily with down pressure and sliding velocity. This suggests that increasing pressure and velocity increased the amount of protective material removed from the surface of copper by the pad asperities and the abrasives embedded between the asperity and the copper or allowed less time for protective material to be adsorbed on the surface of copper, leaving more sites unprotected.

Discussion
Evaluation of the removal efficiencies from the experimental results .-Recalling the concept of a quasi-steady state, it is reasonable to assume that the steady current seen during polishing corresponds to a state in which the rate of removal of the protective material on copper is balanced by the rate of formation of new protective material. The removal of protective material by an asperity would be nearly instantaneous, whereas the protective material, Cu(I)BTA, reforms comparatively gradually, until the next interaction with another asperity as illustrated in Figure 7. The average duration of contact by a pad asperity on a given point on the copper, t as , was estimated assuming circular asperity and copper contacts: where d as is the average diameter of the circular contacts between the asperities and copper and v is the sliding velocity of the wafer over the pad. Equation 1 gives a maximum because the duration of the contact varies with the wear distances 1 across the circular contact, as shown in Figure 8. The growth of the protective material on the copper surface is dependent on the coverage ratio, or fraction of occupied sites immediately after interaction with a pad asperity, characterized as θ t 0 in Figure 9, and the interval until the subsequent contact by another asperity, defined as t as-as in Figure 9. Throughout the following analysis, a fraction of a monolayer of the protective material is assumed to be formed on the surface of copper during CMP, on the basis of the findings of Choi et al. 3 A complete monolayer of protective material is taken as a coverage ratio of unity.
The average time interval between two consecutive interactions of a given point on the surface of copper with asperities, t as-as , can be determined by equating it with the time required to completely sweep the surface of the copper wafer by the asperities: Wafer-pad asperity contact Coverage ratio, asperity-copper contact wear distance asperity-copper contact wear distance a as sp pe er rity ity--co cop pp per er c co on nt tact act w we ea ar r d di is st ta ance nce asperity-copper contact wear distance where N as is the number of asperities that contact the surface of a wafer, d as is the average diameter of the circular contact areas between asperities and a wafer and A w is the surface area of a wafer. The number of asperities that contact the surface of a wafer is calculated by the following expression: where r contact is the ratio of real area of contact between a CMP pad and a wafer to the nominal contact area and a as is the average contact area of an asperity contacting the copper. Thus, assuming a circular contact area between an asperity and a wafer the time interval between consecutive contacts by asperities at a point on the surface of copper is determined as: t as−as = πd as 4vr contact [4] where r contact is an increasing function of the down pressure 6,7 and d as can either increase or stay constant with the down pressure. Both can be experimentally characterized using confocal reflectance interference contrast microscopy (C-RICM) 6 or dual emission laser induced fluorescence (DELIF). 8 Once the experimentally observed average oxidation rate of copper is known, t 0 and t as-as can be determined from a plot of the oxidation rate of copper as a function of time elapsed since a bare surface of copper was raised to an anodic potential as illustrated in Figure  9. Since the measured oxidation rate, i measured , is the average of the current densities from the entire surface of the copper where some points have just been abraded by an asperity while others are waiting to be abraded, the exact location of t 0 can be determined using the following expression: idt t as−as [5] When a spot on the surface is abraded by an asperity, the oxidation rate at the point will increase immediately because the fraction of sites occupied by protective materials, θ t 0 is lowered. As time elapses until the interaction with another asperity, the protective material progressively accumulates, finally giving a coverage ratio of θ t 0 +tas−as .
Using these coverage ratios at a given point on the surface immediately before and after abrasion, the removal efficiency, η, can be defined as: This is the efficiency of an asperity and abrasives embedded between the asperity and copper in removing protective materials on the surface of copper. factor of 22.7 to account for the different mass transport in this configuration, as previously discussed. Table I shows these data, along with the intervals between consecutive asperity-copper interactions, the corresponding coverage ratios and the removal efficiencies. When estimating t as-as , the average area of the contact of an individual asperity with copper was assumed to be constant regardless of the applied pressure or the sliding velocity. However, the overall contact area ratio was considered to increase with increasing down pressure, due to the increase in the number of asperities that contact the wafer. 9 Data for the pad surface topography parameters, such as the average area of individual asperity-copper contacts and the real contact area ratio, which was linearly proportional to the down pressure, were not measured for the conditioned CMP pad used in this work. Instead, these data were adopted from experimental measurements made by Elmufdi et al. who used an IC1010 pad conditioned with SPD-01 or CG-181060 conditioner. 6 It was assumed that t as-as and a as values for the pad used in this work were similar to the values in Elmufdi et al. 6 The estimated intervals between consecutive asperity interactions in Table I were of the same order as the periodicity of the protective material formation and removal on the surface of copper derived by DeNardis et al. from spectral analysis of the coefficient of friction. 10 Figure 10 further illustrates the changes in the removal efficiencies with the down pressure or the sliding velocity when t as-as and a as values for SPD-01 or CG-181060 conditioners determined by Elmufdi et al. were used to evaluate the removal efficiencies from the measured current densities reported in Figure 6. Error bars indicate one standard deviation. No error bar is shown where the lower limit of the evaluated removal efficiency was larger than unity. The CG-181060 and SPD-01 conditioners yielded individual asperity-copper contact areas of 22 μm 2 and 11 μm, 2 respectively, with the real area ratio of contact being 0.100% and 0.135% of the total for 24.8 kPa down pressure. The removal efficiencies evaluated using these parameters were observed to be insenstitive to the down pressure or the sliding velocity, implying that the removal efficiency is principally a characteristic of process consumables rather than of the operating parameters. It is notable that the evaluated removal efficiencies were insensitive to the down pressure and the sliding velocity, regardless of the choice of the pad surface topography parameters, supporting our adoption of these parameters from the literature. In contrast, the removal efficiency was very sensitive to the scatter of the measured current density, especially when t as-as was large, due to the very rapid adsorption of BTA onto copper in a very short time after the copper was anodically polarized (the curve for the coverage ratio by Cu(I)BTA with time appears to be almost a step function; 3 this curve is schematically shown as a blue line in Figure 9). When t as-as is large, the positions of t 0 and t 0 + t as-as are distant, leading to a large difference in the coverage ratios at Error bars correspond to one standard deviation of the experimental data in Figure 6. Pad topography parameters for two types of pad conditioner were adopted from Elmufdi et al. 6 those moments. Any slight increase in the measured current density, corresponding to the oxidation rate curve shown as a green line in Figure 9, would shift the location of t 0 toward much smaller values, resulting in more difference in the coverae ratios at t 0 and t 0 + t as-as and thus an increase in the coverage ratio for a given t as-as .
Analytical prediction of the removal efficiency.-The removal efficiency was predicted analytically to compare with the removal efficiencies evaluated from the experimental data. The response of the protective material on the surface of copper, Cu(I)BTA, to the sliding motion of abrasive particles embedded between an asperity and the copper was considered. It was assumed that the embedded abrasive particles remove all the adsorbed Cu(I)BTA in their paths as they slide over the surface. Removal of the protective material by asperities in direct contact with the copper was neglected, because prior studies on polishing rates in the absence of abrasives indicated that pad asperities alone were ineffective at removing protective material. 11 Thus, one can estimate the fraction of the Cu(I)BTA on the surface that is removed by the squeezed abrasives under a pad asperity by comparing the areas swept by the asperity and by the embedded abrasives during the interaction: η = w abs w as [7] where w abs is the cumulative width of the sliding trajectories on the copper of all abrasive particles trapped under an asperity and w as is the width of the sliding trajectory of an asperity. It was assumed that an asperity and all the embedded abrasives slide in the same direction by the same distance. It was necessary to rule out overlapping paths followed by the abrasives when evaluating the cumulative width because once protective material has been removed by an abrasive particle, there is neither enough time, nor favorable mass transport to allow any more protective material to adsorb on the surface between consecutive interactions by abrasive particles embedded beneath the same asperity. The total width of the resultant sliding trajectories of the embedded abrasives under an asperity was calculated by summing the expected widths of the sliding trajectories of the individual abrasives: where (w ab ) i is the expected width of the sliding trajectory of the i-th abrasive particle. The expected width of the sliding trajectory of the second abrasive is reduced by the probability that it overlaps with the trajectory of the first abrasive. Figure 11 shows that the second abrasive can leave a new trajectory only when its sliding area had no overlap with the trajectory of the first abrasive particle, reducing the probability of the second abrasive removing protective material to 1 − (w ab ) 1 was . The same argument was applied to the remaining abrasives to determine the cumulative width of the sliding trajectories of all embedded abrasives.
It was assumed that the removed protective material did not redeposit on the surface of the copper; if it did, this would lower the removal efficiency. It was also assumed that the ability of abrasives to remove the protective material was not affected by the adherence of the removed protective material to the abrasives. Rolling of the embedded abrasives was not considered. If considered, it might reduce the evaluated removal efficiency because of the shorter moving distance than during sliding as illustrated in Figure 12. Since most of copper interacting with the sliding abrasives during CMP undergoes elastic deformation, 5 Hertz contact theory 12 was used to obtain the pressure induced in the copper by the force transmitted through the abrasive particle and the shape of the contact area. The width of the sliding trajectory of the first abrasive particle was estimated using Hertz contact theory 12 as follows: (w ab ) 1 = 2 r ab h e [9] where h e is the penetration depth of an abrasive particle into elastically deformed copper, which is also determined using Hertz contact theory: h e = 3 f ab 4E * r ab 1/2 2/3 [10] where f ab is the force transmitted by an abrasive to a wafer, E * = ( 1−ν 1 2 E 1 + 1−ν 2 2 E 2 ) −1 , E and ν are the elastic modulus and Poisson's ratio, respectively, and subscripts 1 and 2 denote the contacting materials; in this case copper and the abrasive, respectively. It was assumed that the presence of protective material on the surface of copper did not affect the indentation depth or the area of contact between the abrasive and copper because it is very soft and thin. If the copper is plastically deformed, the width of the contact and indentation depth is: (w ab ) 1 = 2 2r ab h p [11] where the indentation depth of plastically deformed copper, h p , is given by: h p = f ab πr ab H Cu [12] where H Cu is the hardness of copper. Note that in this case, only the leading edge of the area contacted by the abrasive particle supports the load applied by the abrasive while the abrasive ploughs on the surface of the copper.
To calculate the indentation depth of the embedded abrasives, the force applied on the abrasive f ab was estimated from the force applied on a pad asperity.
Force applied on a pad asperity.-The insensitivity of removal efficiencies to the down pressure in Figure 10 could be explained if the average area of an asperity-copper contact was independent of the down pressure. Although this may seem counterintuitive, and indeed is invalid if considering the contact area of a specific asperity, it is worth recalling that during copper CMP the number of asperities contacting a wafer is a small fraction of the total number of asperities. Hence the Gaussian distribution of asperity heights 13 can be approximated to an exponential distribution, which results in the number of contacts being proportional to the applied load. 9 The exponential distribution of pad asperities contacting the wafer was experimentally observed by Sun et al. 14 Combined with the experimental observation that the real overall contact area was linearly proportional to the down pressure, 6,7 the average area of each asperity-copper contact was regarded as independent of applied pressure. Thus the average force transmitted through an asperity (f as ) should be constant for a given pad and conditioning specifications: Pa as r contact [13] where P is the nominal down pressure applied on a wafer. Using the values used in this work, the average force per asperity was 0.2 mN or 0.5 mN when pad surface topography parameters for SPD-01 or CG-181060 conditioners, respectively, were used.
Number of abrasive particles embedded between an asperity and copper.-Alumina abrasives may agglomerate when the pH of a slurry, the ionic strength or additives in a slurry lower the zeta potential or compress the double layer enough to eliminate the electrostatic repulsion between the particles. 15,16 Ihnfeldt et al. 17 estimated the force required to break up the agglomerates using the equations developed by Brown et al. to calculate the shear strength of a powder. 18 Using their analysis, the lower and upper bounds of the force required to break up an agglomerate 20 nm in diameter were only 70 pN and 0.9 -4 nN, respectively. These forces are nearly three orders of magnitude smaller than the force transmitted to an embedded abrasive (discussed below), suggesting that any agglomerates that may have been present in the slurry during the experiments would have been broken up when squeezed between an asperity and copper. Therefore, it was assumed in the following analysis that only individual abrasive particles were present in the area between asperities and copper.
Slurry containing abrasive particles wets the CMP pad and was present between the pad and the wafer during the CMP process. Neglecting any forces that could influence the spatial distribution of abrasives around the pad asperities, such as electrostatic and van der Waals interaction between abrasive particles and the pad material, the local concentration of abrasive particles in the slurry squeezed between the pad and the copper was assumed to be identical to that in the bulk slurry, c wt , which is expressed as a ratio of the weight of abrasives to the total weight of the slurry. Further, assuming that the abrasive particles were rigid spheres with uniform radius, r ab , the number of abrasive particles that are embedded between an asperity and the copper,ñ ab , is determined as: 3c wt a as ρ slurr y 2πr ab 2 ρ ab [14] where ρ slurry and ρ ab are the density of slurry and abrasives, respectively. It was assumed that the number of embedded abrasives maintained a steady state in which abrasives in the slurry were continuously drawn into and discharged from the gap between the asperities and the copper as the wafer slid over the pad. The assumptions employed in this analysis are similar to those by Che et al., 19 Zhao et al. 20 and Bastawros et al. 21 The estimated number of abrasive particles embedded into an asperity is listed in Table II for various concentrations of abrasives in the slurry.
Force applied on an abrasive.-The force applied on an abrasive particle that is embedded between an asperity and copper was estimated by evaluating the upper and lower extreme situations where pad asperities are deformed by the embedded abrasive particles as shown in Figure 13. Note that pad asperities will be deformed by the applied force in preference over the abrasives and copper because the pad material has a much lower elastic modulus and hardness than copper and abrasives. The upper bound of the estimated force is obtained when the pad asperity is not deflected enough to contact the surface of the copper (Figure 13a). Thus the force applied to the asperity is supported only by the embedded abrasives. The upper bound of the estimated force on an abrasive, f ab-ub , is then: [15] The lower bound of the estimated force, f ab-lb , would occur when a pad asperity is deformed enough to completely encapsulate the abrasive particles and to contact the surface of the copper; so the force applied to the asperity is evenly distributed across all abrasive particles and the deformed asperity contacting the copper ( Figure  13c). Then the force on an individual abrasive particle is independent of the number of embedded abrasives, and dependent only on the cross-sectional area of the particle: f ab−lb = πr ab 2 ( f as /a as ) [16] As an intermediate case, if the pad asperities are deflected to partly contact the surface of the copper as shown in Figure 13b, the force applied on an abrasive will lie between those two extremes, and will be inversely proportional to the area of the contact between the deflected asperity and the copper. Thus the force applied on an embedded Table II. Number of abrasive particles embedded between an asperity and the wafer, force on an embedded abrasive particle, maximum shear stress and penetration depth induced by the applied force for different concentrations of abrasives. The down pressure, the sliding velocity and the diameter of abrasive were 24.8 kPa, 0.5 m/s and 20 nm, respectively. Pad topography parameters were from Elmufdi et al. 6 [17] where a as-def is the contact area between copper and the asperity that is deformed by the embedded abrasives.
The estimated upper and lower bound forces applied to an abrasive for the varied concentrations of abrasives are listed in Table II. The upper bound of the estimated force transmitted to each embedded abrasive particles decreased with increasing concentration of the abrasives, from 3.06 μN or 4.11 μN for 0.5 wt% of abrasives to 0.304 μN or 0.411 μN for 5 wt% of abrasives when pad topography parameters for SPD-01 or CG-181060, respectively were used. In contrast, the lower bound of the estimated force applied to an abrasive was 5.78 nN or 7.80 nN for pad topography parameters for SPD-01 or CG-181060, respectively, regardless of the concentrations of the abrasives.  Figure 13. Contact modes between a pad asperity and a copper wafer in the presence of abrasive particles in the slurry: an asperity is not deformed much, and does not itself contact the wafer (a) an asperity is deformed to partly contact the surface of a wafer (b) and an asperity is deformed enough to completely encapsulate the abrasives and to contact the wafer (c).
Prediction of the removal efficiency.-Applying this analysis to predict the removal efficiencies using Equation 7 and 8 for the experimental conditions 1 to 8 in Table I, removal efficiencies of 0.208 and 0.582 were obtained for the lower and upper bounds of the estimated forces, respectively when conditioning with an SPD-01 conditioner, assuming that the copper underwent elastic deformation only. If copper was considered to undergo plastic deformation, a removal efficiency of 0.678 was predicted for the upper bound of the estimated force. For a pad conditioned with a CG-181060 conditioner, the predicted removal efficiencies were 0.280 and 0.709 for copper elastically deformed by the lower and upper bounds of the estimated forces, respectively, and 0.844 for copper plastically deformed by the upper bound of the estimated force. Note that all the experimental conditions 1 to 8, other than conditions 1 and 2 for the CG-181060 conditioner, yielded the same experimental removal efficiencies for each conditioning specification because the average area of the asperities and copper contacts was assumed to be invariable. The experimentally determined removal efficiencies shown in Table I ranged between the analyticaly predicted value for copper elastically deformed by the lower bound of the force and the value for plastically deformed copper, which is physically valid.
To further examine the validity of the analysis, chronoamperometry measurements were made during polishing with various concentrations of abrasives in the slurry, with other conditions unchanged. Four different abrasive concentrations were used, namely 0.5, 1, 3 and 5 wt% of alumina abrasives in the slurry. The experimental data, analyzed by Equation 7 and 8, for pad topography parameters for either an SPD-01 or CG-181060 conditioner, yielded removal efficiencies indicated in Figure 14. The analytical prediction is presented as curves in Figure 14. The upper bound of the estimated force on an abrasive gave two different curves, one for the condition where the copper undergoes plastic deformation and the other for elastic deformation. However, the lower bound of the estimated force gave only a curve for elastic deformation of copper because the indentation depth is only a fraction of the diameter of a copper atom, 0.6 Å or 0.7 Å for pad topography parameters for SPD-01 or CG-181060, respectively, which is too small to initiate dislocations in the crystal lattice and hence plastic deformation.
The width of the trajectories of abrasives when the copper was plastically deformed was calculated using the nanohardness value, 15 GPa, obtained from molecular dynamic (MD) simulation of nanoindentation at appropriate length scales for copper CMP. 5,22,23 This value is nearly an order of magnitude larger than the hardness measured by nanoindentation with higher loads and deeper depths 24-28 due to the significant size effect. [29][30][31][32][33] The penetration depths caused by the force applied on an abrasive particle, used to determine the widths of the trajectories for different concentrations of abrasives in the slurry, are listed in Table II. The upper bound force estimate gave a penetration depth of the order of 1 nm for plastic deformation, which is of the same order as the roughness after copper CMP. 34,35 For lower concentrations of the abrasives, the experimentally evaluated removal efficiencies approximated well the analytical predictions for copper elastically deformed by the lower bound of the estimated force, regardless of the assumed pad surface topography parameters. This implies that the pad asperities supported by the abrasives were deformed enough to encapsulate the copper, such that the force applied to the embedded abrasive particles approached the lower bound of the estimate. In contrast, for higher abrasive concentrations the experimentally evaluated removal efficiencies exceeded the prediction for copper elastically deformed by the lower bound force estimate. This suggests that the pad asperities supported by the embedded abrasives were deflected to partly contact the surface of the copper as depicted in Figure 13b. As the concentration of the abrasive particles increased, the portion of the asperity (a as-def ) contacting the wafer decreased, so that a higher force was borne by the abrasives. This behavior would be expected, as the distance between the embedded abrasive particles decreased with increasing concentration of the abrasives. Nevertheless, the separation between the embedded abrasives remained much larger than the size of the abrasives; only 1.90% of area was occupied by the abrasive particles held under an asperity contacting the copper when 5 wt% abrasives was used, as indicated in Table II. The conclusion that deflected asperities completely or partly contacted the copper is consistent with the work of DeNardis et al. 10 and Li et al., 36 who deduced a contact mode during copper CMP from the slopes of experimentally obtained Stribeck curves. The contact mode during copper CMP was "partial lubrication", in which abrasive particles and slurry separate the pad asperities and the copper in part or "boundary lubrication", where the asperities, abrasives and copper are in direct contact. Both of the analyses in this work and the work of DeNardis et al. 10 and Li et al. 36 suggested that copper CMP does not operate in hydrodynamic lubrication mode.
The deviation of the removal efficiencies at higher abrasive concentrations might also have been attributed to increased instances of plastic deformation of copper by the abrasive particles sliding under a pad asperity. The upper bound of the force estimate at 3 or 5 wt% of abrasive concentrations in Table II is not enough to plastically deform the copper, because the shear stress induced in copper by the force is below the theoretical shear strength of copper, about 8 GPa, at this small length scale. 5 However, the local shear strength of copper may be reduced where the sliding abrasive particles have already abraded some of the surface, because of the increased defect density or generation of a surface roughened by plastic deformation. 5 With more abrasive particles present under an asperity, the possibility increases that a region on the surface of copper undergoes multiple abrasions, leading to more sites on the copper that could deform plastically. As a result, the overall removal efficiency by a pad asperity for these cases increased, because the contact area during plastic deformation is higher than that during elastic deformation.

Conclusions
The efficiencies of abrasive particles that are embedded into a pad asperity in removing protective material from the surface of copper during CMP were determined experimentally and analytically, then compared. The experimentally determined removal efficiencies were insensitive to the down pressure and the sliding velocity, agreeing well with the analytical analysis due to the insensitivity of the average contact area of a single pad asperity and copper to pressure. Comparison of the analytically and experimentally determined removal efficiencies for various concentrations of the abrasives in the slurry suggested that the pad asperities encapsulated the embedded abrasive particles and contacted the surface of the copper at abrasive concentration up to 1 wt%, so that minimum load is exerted to the copper by the abrasives. At higher abrasive concentrations, up to 5 wt%, the fraction of asperity and copper contact decreased, so that higher loads are applied to the copper by the embedded abrasives. With more abrasive particles in the slurry, the frequency of copper and embedded abrasive contacts under a pad asperity increases, increasing the possibility that the interaction will plastically deform the copper. This will eventually increase the contact area between the abrasive particles and the protective material on the copper surface, resulting in more removal of protective material by the abrasives.
In short, the removal efficiency is a function of consumable variables, such as the pad surface topography parameters, determined by the type of pad and the conditioning specification, and the concentration of abrasive in the slurry. The analytical and experimental approaches outlined in this work could be applied to compare the material removal ability of various consumables such as slurry, CMP pad and pad conditioner, using removal efficiency as a standard metric for comparison. More importantly, the analyses are essential for completing the mechanistic model that predicts the MRR during CMP proposed by Choi et al. 4 Once the number of abrasive particles that are embedded between a pad asperity and the wafer is known, the analytical solution given in this work can directly evaluate the removal efficiency of a set of consumables and eventually predict the MRR for a given processing and consumbles variables. The incomplete portion of the analysis, which is the influence of the slurry chemistry and the processing conditions on the behavior of the abrasive particles, must be understood to estimate the number of abrasive particles squeezed between a pad asperity and copper and hence to complement the mechanistic MRR model.