Fundamental Tribological and Removal Rate Studies of Inter-Layer Dielectric Chemical Mechanical Planarization

Transcription

1 Jpn. J. Appl. Phys. Vol. 42 (2003) pp Part, No. 0, October 2003 #2003 The Japan Society of Applied Physics Fundamental Tribological and Removal Rate Studies of Inter-Layer Dielectric Chemical Mechanical Planarization Ara PHILIPOSSIAN and Scott OLSEN Department of Chemical and Environmental Engineering, University of Arizona, Tucson, Arizona 8572, USA (Received March 4, 2003; accepted May 27, 2003; published October 9, 2003) In this work, real-time coefficient of friction (COF) analysis, in conjunction with a new method for approximating the, is used to determine the extent of normal and shear forces during chemical mechanical planarization (CMP) and to help identify the tribology of the system. A new parameter termed the tribological mechanism indicator is defined and extracted from the resulting Stribeck curves. The information on COF, tribological mechanism indicator and inter-layer dielectric (ILD) removal rate results in a series of universal correlations to help identify polishing conditions for optimized pad life and removal rate. Results further show that abrasive concentration, surface texture and pad grooving dramatically shift the tribology of the system from boundary lubrication to partial lubrication. Trends are explained using several models based on area of contact between wafer and abrasive particles, the extent of lubricity of the system and the compliance of the pad in micro- and macro-scales. [DOI: 43/JJAP ] KEYWORDS: chemical mechanical planarization (CMP), tribological mechanism, removal rate, coefficient of friction (COF). Introduction In Chemical Mechanical Planarization (CMP), one area that can potentially impact inter-layer dielectric (ILD) removal rates is the coefficient of friction (COF) associated with the pad, wafer and slurry abrasive particles. Given the limited reported effects of the coefficient of friction on silicon dioxide wafers,,2) it would be of interest to establish potential correlations between the slurry abrasive concentration, the coefficient of friction, and the amount of material removal during CMP. This work has been based on the premise that during planarization, the coefficient of friction (COF) in the pad-slurry-wafer region affects ILD removal rate, thus necessitating a fundamental understanding and control of the magnitude of forces involved in the process. Given the above postulation, identification of the tribological mechanism and determination of key factors contributing to the extent of pad-slurry-wafer contact will be critical. 2. Theory and Experimental Procedure 2.Tribology and removal rate measurements A :2scaled version of a Speedfam-IPEC 472 polisher was constructed. Table I shows the appropriate scaling factors for each parameter and a numerical comparison between the typical values of the scaled polisher and those of the full-scale polisher. The slurry s kinematic viscosity and the fluid film thickness between the pad and the wafer were assumed to be the same between the two systems. Therefore, Reynolds Number was used to scale the platen and wafer speeds (i.e., the relative pad-wafer velocity in the scaled model was matched to that of the full-scale model). The scaled polisher s platen-to-wafer diameter ratio and slurry flow rate normalized by the platen area corresponded to the values for the full-scale polisher. For wafer pressure, ranges typically found on an industrial polisher were applied to the scaled setup. The scaled polisher and its associated accessories are shown in Fig.. A modified industrial drill press with the ability to rotate and apply an appropriate amount of down pressure was used as the wafer carrier. A carriage, equipped with dead weights mounted on a traverse, provided variable pressure onto a gimbaled wafer carrier. The conditioner, consisting of a 76-mm diamond disc, was spring-loaded onto the pad. Two stepper motors allowed the conditioning disc to rotate and sweep independently across the pad. To measure the shear force between the pad and the wafer during polish, a sliding table was placed beneath the scaled polisher. The sliding table consists of a bottom plate held stationary by its attachment to the steel table, and an upper plate that the polisher is set upon. A photograph of this setup is shown in Fig. 2. When the wafer and pad are engaged, the upper plate slides with respect to the bottom plate in only one direction due to Table I. Scaling factors used in constructing the scaled polisher. Parameter Scaling factor Speedfam-IPEC 472 Scaled polisher Down pressure 4 psi 4 psi Relative pad-wafer Relative pad-wafer Platen speed Reynolds velocity of velocity of number 0.5 m/s 0.5 m/s (30 rpm) 55 rpm Platen diameter/ Dplaten /D wafer 5 cm/20 cm 3 cm/0 cm Wafer diameter Slurry flow rate Platen surface area 25 cc/min 80 cc/min 637 Fig.. Images of the scaled polisher showing the diamond disc conditioner, the drill press and the traverse assembly.

2 6372 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN Strain Gauge Fig. 2. Polisher Slider Sliding friction table with strain gauge. friction between the pad and wafer. The degree of sliding is quantified by coupling the two plates to a load cell. The load cell is attached to a strain gauge amplifier that sends a voltage to a data acquisition board. The apparatus was calibrated to report the force associated with a particular voltage reading. Tribological and removal rate data was taken on Rodel IC- 000 flat, perforated, k-groove, and x y pads. Rodel IC-400 k-groove pads were also examined, in addition, to Freudenberg FX-9 perforated and flat pads. Prior to data acquisition, the pad was conditioned for 30-min using Fujimi s PL-427 slurry. The abrasive content for pad conditioning was identical to the experimental abrasive concentration. The conditioning consisted of using a 00-grit diamond disk at a pressure of 0.5 PSI, rotational velocity of 30 RPM and disk sweep frequency of 30 per minute. Conditioning was followed by a 2-minute pad break-in with a silicon dummy wafer. Tribological and removal rate data were acquired under the following conditions:. In-situ conditioning at 30 RPM and 20 oscillations per min. Applied wafer pressures of 2, 4 and 6 PSI. Relative pad-wafer average linear velocities of 0.3, 0.62 and 0.93 m/s. Slurry flow rate of 80 cc/min. Slurry abrasive concentrations of 2.5, 6.25, 9, 2.5, 8.75 and 25 percent solids by weight 2.2 Sommerfeld number To understand the dominant tribological mechanism present when polishing interlayer dielectrics, Stribeck curves are presented using a dimensionless grouping of CMPspecific parameters, called the Sommerfeld number. So ¼ U ðþ p eff where is the slurry viscosity, U is the relative pad-wafer velocity, p is the applied wafer pressure, and eff is the effective fluid film thickness. Determination of U and are fairly straightforward as the latter can be measured experimentally for a given slurry, while the former depends on tool geometry and the relative angular velocity of the platen and the wafer. Wafer pressure is the applied downforce divided by the contact area between the wafer and the pad. Each pad type consists of a different surface area due to different grooving configurations, so each pad will experience a different pressure when subjected to the same downforce. To account for this, a dimensionless parameter, is used to scale the wafer pressure. is expressed as: ¼ A up-features ð2þ A flat The equation states that is equal to the area of the upfeatures divided by the area of a flat pad. This means that is equal to the percent up area for a given type of pad. The term = is subsequently multiplied by applied pressure to determine the actual pressure experienced by the wafer. Alpha is unity for IC-000 and FX-9 flat pads, and 0.9, 0.86, 0.83 and 0.76 for IC-000 perforated, FX-9 perforated, IC- 000 and IC-400 k-groove, and IC-000 x y pads, respectively. The use of is important when operating in boundary lubrication, where the wafer, pad and abrasive particles, are engaged in intimate contact, such that it is unlikely that a hydrostatic or buoyant force exists due to the fluid supporting the wafer. In addition to the lack of a fluid film in boundary lubrication, the grooves and perforations associated with different types of pads aid in removing any excess slurry from the pad-wafer interface. Pads that possess communicative grooves, such as x y pads, are more likely to remove any excess slurry because the grooves talk to one another, and extend off to the edge of the pad. Pads, such as perforated and k-groove, can be referred to as non-communicative. The perforations and concentric circles associated with these two types of pads do not extend off to the edge of the pad. Without this communication between grooves, the lack of channeling may increase the probability of a fluid film developing, which could aid in supporting some of the applied pressure from the wafer. In spite of the fact that on the macro-scale, perforated and k-groove pads appear to possess non-communicative grooving configurations, Ali et al. 3) demonstrate that pad conditioning forms micro-scratches on the pad surface, thereby opening pores of the pads and channeling slurry between the grooves and perforations on the pad surface. This creation of micro-scratches makes the k-groove and perforated pads somewhat communicative and reduces the likelihood of maximum slurry entrainment in the grooves. Without a full perforation or groove, it is unlikely that the wafer load is supported by the fluid. For certain cases in this study where the pad, wafer, and abrasive particles, are engaged in partial lubrication, the presence of a thin fluid film separating the wafer and pad is likely, where the use of the correction factor,, may not be totally accurate. In partial lubrication, the actual pressure experienced by the wafer may be between the applied pressure and the corrected pressure based on the application of. However, Levert 4) experimentally measured a suction or negative fluid pressure beneath the wafer at polishing pressures of 30,000 Pa (4.35 PSI) and relative pad-wafer

3 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN 6373 velocities of 0.7m/s. These operating conditions are favorable to partial lubrication schemes studied in this research and Levert s results suggest that the applied load is supported by solid-solid contact between the wafer and the pad asperities. With this noted, it is possible, that even in mixed lubrication, the correction factor of is necessary. The remaining calculations in this work are carried out using as a correction factor. The final parameter necessary for calculating the Sommerfeld number is the effective slurry film thickness. Different researchers have demonstrated different methods for calculating eff. DELIF, or dual emission laser induced fluorescence, is used by Lu et al. 5) and by Rogers et al. 6) to measure the hydrodynamic fluid film thickness of flat pads. This technique has its limitations as it can only calculate the film thickness for flat pads using glass wafers. Lawing 7) calculates the value of in the Sommerfeld number using the average surface roughness (R a ) of the pad. His method does not account for the depth of slurry entrained in the perforations or grooves. This study combines the technique used by Lawing while also accounting for the additional slurry entrapped in the grooves or perforations. In this study, the following expression was derived for calculating eff : eff ¼ R a þð Þ groove ð3þ First, the pad roughness was measured for each of the pad types studied using a Dektak 3ST surface profiler. The average roughness, R a, of the pad is defined as the arithmetic average value of the vertical deviation of the profile from the centerline: 4) R a ¼ jz i j ð4þ n i¼ where n is the number of points on the centerline at which the profile deviation z i is measured. Pad roughness values were taken at slow and medium speeds on the surface profiler and the average value of the resulting two measurements was used as the value of the pad surface roughness. Relative standard deviation for surface roughness was less than 0% for all the values measured. Having calculated the average surface roughness for each pad type, the final parameter necessary for calculation of eff is the groove or perforation depth of each pad. Slurry is transported to the wafer through these grooves and perforations, so they must be included in calculating the effective slurry film thickness. The groove or perforation depths for each pad were physically measured and the values for each pad are used to calculate the effective fluid film thickness. 2.3 Coefficient of friction and the stribeck curve The coefficient of friction is defined as the ratio of the shear force (F shear ) to the normal force (F normal ): COF ¼ F shear ð5þ F normal The plot of coefficient of friction vs. the Sommerfeld number is known as either the Stribeck Gumbel curve or the McKee Petrof curve. For simplicity, this is referred to as the Stribeck curve in this paper. The Stribeck curve is beneficial in CMP applications since it gives direct evidence toward the X n Coefficient of Friction COF Fig. 3..0E-03 Boundary Lubrication.0E-02 h ~ 0.0E-0 Partial Lubrication h >> Ra Hydro-dynamic Lubrication extent of contact or wear between the rotating wafer, the rotating pad, and the encased abrasive particles. When plotting the coefficient of friction as a function of the Sommerfeld number, according to Ludema s definition 8) three major modes of contact can be envisaged (Fig. 3). The first mode of contact is known as boundary lubrication. In the boundary lubrication regime, all solid bodies are in intimate contact with one another. Slurry abrasive particles may be embedded in the pad or directly press upon the wafer. This regime generally occurs at lower values of the Sommerfeld number. At the onset of boundary lubrication, the Stribeck curve acquires a flat shape. Further decreases in the Sommerfeld number do not change this shape as the pad and wafer remain in intimate contact, so the coefficient of friction remains constant. Furthermore, the fluid film thickness is small in this regime, with the separation distance between the wafer and pad at a minimum. In boundary lubrication, larger values of coefficient of friction are expected due to the close proximity of sliding and wear between the wafer and the pad. Additionally, if material removal rate is assumed to be predominantly due to waferpad contact, then it can also be assumed that removal rates will likely be influenced by values of the coefficient of friction. The second mode of contact occurs at intermediate values of the Sommerfeld number. This regime is typically referred to as the partial or mixed lubrication regime. In this mode, the wafer and the pad are not in intimate contact with one another. Some abrasives may be in contact with the pad or wafer, but much less than in the case of boundary lubrication. A fluid film layer will develop partially separating the wafer and the pad. In this case, the fluid film thickness will be similar to that of the roughness of the pad. As the Stribeck curve transitions from boundary lubrication to partial lubrication, the slope of the line measuring coefficient of friction becomes negative. Finally, the hydrodynamic lubrication mode of contact occurs at larger values of the Sommerfeld number. In this.0e+00 h ~ Ra Generic Stribeck curve based on Sommerfeld number.

4 6374 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN regime, smaller values of removal rate and the coefficient of friction are common. Furthermore, the fluid film layer separating the pad and the wafer is much larger than the roughness of the pad. With a larger film thickness, very little contact exists between the wafer and the pad. From the generic Stribeck curve, it is evident that the derivative of the coefficient of friction is zero, (i.e.) it reaches a minimum at the end of partial lubrication or at the onset of hydrodynamic lubrication. As even larger values of the Sommerfeld number are approached, the slope of the line turns slightly positive and the coefficient of friction begins to increase minimally. This nominal increase in the coefficient of friction is most likely attributed to an occurrence of eddies in the flow field. At large values of pad-wafer velocity, the flow underneath the wafer cannot remain constant or laminar forever and the fluid flow likely switches to a transitional or turbulent region, causing slight increases in the coefficient of friction. 2.4 Average coefficient of friction and the tribological mechanism indicator The average coefficient of friction for any series of polishes can be calculated using equation 6) where the term COF i refers to the coefficient of friction for a given wafer pressure and pad-wafer velocity. COF ¼ COF i ð6þ n i¼ It is apparent that Stribeck curves operating in different regions of lubrication may yield similar values of average coefficients of friction. For example, two hypothetical Stribeck curves shown in Fig. 4 have the same average coefficient of friction, yet each engages in different lubrication regimes. Typically, when there is a line with zero or slightly positive slope at smaller values of the Sommerfeld number, the pad and wafer are engaged in boundary lubrication. In contrast, a Stribeck curve with a negative slope is indicative of partial lubrication. To distinguish between analogous coefficients of friction for different types of pads and abrasive concentrations, this Fig. 4. Coefficient of Friction (unitless) E-03.0E-02 X n.0e-0.0e+00 Different Stribeck curves yielding similar coefficients of friction. COF K-Groove COF = (So) 05 R 2 = Flat COF = 0.085(So) -884 R 2 = Fig. 5. Values of describing boundary lubrication for an IC-400 k-groove pad at 25% solids and partial lubrication for an IC-000 flat pad at 2.5% solids. paper establishes that when plotting COF vs. Sommerfeld number on a linear scale, a power function, as in equation, 7) can be used to adequately describe its shape: COF ¼ A ðsoþ ð7þ where So denotes the Sommerfeld number of interest, A is a constant coefficient, and is an indicator of the lubrication regime. For this study, when is 0 boundary lubrication dominates. A negative value of, describes the extent of partial lubrication, such that with decreasing values of, the extent of partial lubrication increases. If material removal rate is assumed to be dominated by contact between the wafer and pad, increased lubricity and smaller values of are expected to lead to decreased material removal while larger, positive values of should promote material removal. Figure 5 shows two examples of. One describes boundary lubrication, the other describes partial lubrication. This figure depicts a Rodel IC-400 k-groove pad polishing at 25% abrasive concentration, and a Rodel IC-000 pad at 2.5% abrasive concentration. For this example, the correlation coefficients, R 2, is equal to and 0.86, respectively. 2.5 ILD removal Most removal rate models have been adapted from early studies of glass polishing. To date, several models have been proposed to describe the amount of material removed during a given polishing time. The most widely adopted polish rate (or removal rate, in the case of CMP) equation is the one proposed by Preston, 9) which states that the removal rate is proportional to the product of the applied pressure and the relative velocity of the substrate in contact with the pad. Equation (8) takes the form: RR ¼ k Pr p U ð8þ where RR is the removal rate, U is the relativ pad-wafer velocity, p is the actual pressure, and k Pr is Preston s constant which itself depends on the chemical and mechanical aspects of the process. Figure 6 is a representative removal rate plot for data collected in this study.

5 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN E-09 Removal Rate ( m/sec) 5.00E E E E-09 COF FX-9 perforated IC-400 k-groove FX-9 flat IC-000 perforated IC-000 flat.00e E Platen Speed x Wafer Pressure (Pa-m/sec) Fig. 6. Prestonian removal rate model for 9% solids using FX-9 flat pad. Fig. 8. Stribeck curves at 9% abrasives with Fujimi PL-427slurry. 3. Results and Discussion 3.Stribeck curves As a general trend, Figs. 7to 9 indicate that, for a given pad, as abrasive concentrations increase, the coefficients of friction decrease and the Sommerfeld numbers increase. The latter is due to an increase in slurry viscosity at larger abrasive concentrations. Figure 7displays tribological data for 2.5% abrasive content (by weight) using both Freudenberg and Rodel pads with different grooving configurations. It must be noted that each data point represents the average of 3 polishing runs. The repeatability associated with measuring COF and the Sommerfeld number was estimated to be approximately 5 and 0%, respectively. Using Fig. 3 as a reference, the shapes of the individual curves indicate that IC-000 perforated and x y pads immediately result in partial lubrication at low Sommerfeld numbers. FX-9 and IC-000 flat pads exhibit boundary lubrication at smaller Sommerfeld numbers and transition to partial lubrication as Sommerfeld numbers are increased. The maximum average coefficient of friction, 0.539, occurs in the IC-400 pad with a standard deviation of 0.0. The IC-000 x y pad has the smallest average coefficient of friction at with a standard deviation of 3. Standard deviations for all other pads at this abrasive concentration are less than Figure 8 shows Stribeck curves associated with a 9% abrasive concentration. Again, all k-groove pads remain in boundary lubrication along with the FX-9 perforated pad. All COF FX-9 perforated IC-000 perforated IC-400 k-groove FX-9 flat IC-000 flat Fig. 7. Stribeck curves at 2.5% abrasives with Fujimi PL-427 slurry. COF FX-9 perforated IC-400 k-groove FX-9 flat IC-000 perforated IC-000 flat Fig. 9. Stribeck curves at 25% abrasives with Fujimi PL-427slurry. other pads transition to partial lubrication at higher Sommerfeld numbers. The IC-000 x y pad shows the steepest slope as it transitions to partial lubrication. FX-9 perforated pads have the largest average coefficient of friction (0.322), while IC-000 x y pads have the lowest (8). The standard deviation for the x y pad is 0.07and for the FX-9 perforated pad is The standard deviations for the remaining pads are less than 0.06 at this abrasive concentration. Following the trends of earlier data, Fig. 9 indicated that the k-groove pads, even at 25% solids, remain in boundary lubrication. Although FX-9 perforated pads begin in partial lubrication, the coefficient of friction increases slightly at Sommerfeld numbers larger than This shift might indicate a transition to hydrodynamic lubrication. IC-000 perforated and x y pads coefficient of friction decrease as well until they reach a Sommerfeld number of , at which point they begin to increase slightly. Finally, both IC-000 and FX-9 flat pads exhibit decreasing coefficients of friction while engaged in partial lubrication. The friction at this abrasive concentration decreases by 55 and 66%, respectively, for IC-000 flat and FX-9 flat pads when compared to the coefficient of friction at the largest Sommerfeld number. The average coefficient of friction was largest for IC-400 k-groove pads at 0.39 and smallest for IC-000 x y pads at Standard deviations are similar to other concentrations studied, with none being

6 6376 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN larger than In deciding the more favorable region of operation, partial lubrication may offer increased pad life over boundary lubrication, however, boundary lubrication offers greater stability, control, and enhanced predictability in removal rates and within-wafer-non-uniformity (WIWNU). By definition, boundary lubrication possesses constant values of coefficient of friction throughout a wide range of Sommerfeld numbers while partial lubrication shows decreasing values of coefficient of friction with increasing Sommerfeld number. Based on the above explanation, more consistent removal rates are to be expected for boundary lubrication. For example, at a wafer pressure of 6 psi and a relative pad wafer linear velocity of 0.3 m/s, removal rates are much more consistent (i.e. conditions of boundary lubrication) compared to 2 psi and 0.93 m/s (i.e. conditions of partial lubrication). Note that these two operating conditions yield identical p U values and according to Preston s equation, the removal rates must be identical. In the former case, runto-run variability in removal rate is 5% while in the case of partial lubrication, run-to-run variability in removal rate has been shown to be as high as 5%. k Pr (/Pa) E-2 E-3 E-4 E COF avg -.0 β Fig. 0. Coefficient of friction, tribological mechanism indicator, and Preston s constant as a function of silica content for an pad. k Pr (/Pa) k Pr (/Pa) E-2 E-3 E-4 E E E E E Average coefficient of friction, tribological mechanism indicator, and Preston s constant as a function of slurry abrasive concentration Figures 0 through 2 give examples of the average coefficient of friction, tribological mechanism indicator, and Preston s constant for various types of pads and abrasive concentrations. Figure 0 shows that for the IC-000 k- groove pad, an increase in abrasive concentration causes a decrease in average coefficient of friction, while increasing and the Preston s constant. The average coefficient of friction seems to correlate linearly to Preston s constant at abrasive concentrations in excess of 9%, while seems to follow Preston s constant throughout the entire range of abrasive concentrations studied. Figure displays results associated with the FX-9 perforated pad. In this case, k Pr and follow the same general trend throughout the entire range of abrasive concentrations studied. That is, at abrasive concentration lower than 9% they both trend upward, followed by a gradual downward trend as abrasive concentration is further increased. The average coefficient of friction shows a steady decline from 2.5 to 25% solids. Figure 2 depicts a Rodel IC-000 perforated pad operating at different abrasive concentrations. For this pad, the average coefficient of friction and the tribological mechanism indicator mimic Preston s constant throughout the entire range of abrasive concentrations. The fact that maximum coefficient of friction for all types of pads occurs at 2.5% abrasive concentration is intuitive, given the following analogy: abrasive particles can be thought of as nano-sized ball bearings positioned between two flat, yet somewhat compressible surfaces. In the case when very few ball bearings exist, given a certain normal pressure, the two surfaces can still interact with each other and contact one another depending on the extent of roughness and hardness of the two surfaces. As the number of ball bearings is increased, less friction is created and the two surfaces can slide with greater ease with respect to one another. In the case of CMP, as fewer particles are entrained beneath the wafer, friction between the wafer and pad is much greater. As abrasive concentration is increased, the addition of extra particles increases the lubricity of the system, thus reducing shear forces. When the wafer and pad are less likely to grab these particles, coefficient of friction decreases COF avg β Fig. 2. Coefficient of friction, tribological mechanism indicator, and Preston s constant as a function of silica content for an IC-000 perforated pad COF avg β Fig.. Coefficient of friction, tribological mechanism indicator, and Preston s constant as a function of silica content for a FX-9 perforated pad.

7 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN 6377 For all types of pad studied, except for k-groove pads, Preston s constant exhibits a local maximum at approximately 0% abrasive concentration with local minima occuring at the lowest and highest abrasive concentrations, depending on the type of pad used. This behavior is explained as follows: As reported by Mahajan et al., 0) and based on earlier findings by Brown et al., ) it is demonstrated that as abrasive concentration increases, removal rate of SiO 2 films increases until around 2% abrasive concentration, where further increase in abrasive concentration yields no change in material removal rate. It must be noted that Mahajan studied the effect of abrasive concentration up to 5% solids. To account for this phenomenon, Mahajan utilized the surface area based model proposed by Brown, which states that polishing rate depends on the total contact area between the abrasive particles and the surface being polished. The contact area as a function of particle size and abrasive concentration is given by the following expression: Preston's Constant (/Pa).40E-3.20E-3.00E E E E E E+00 FX-9 Flat FX-9 Perforated IC-400 k-groove IC-000 Flat IC-000 Perforated Average Coefficient of Friction RR / A / C where A is the contact area, C 0 is the abrasive concentration, and is the particle diameter. A smaller particle diameter and a larger abrasive concentration will result in a larger contact area between pad and wafer, thus leading to larger material removal rates. On the other hand, this paper assumes a constant particle diameter, as only one slurry type was used for experimentation. Based on the results shown in Figs. 0 through 2, removal rates do not follow the results presented by Mahajan at larger abrasive concentrations (except in the case of k-grooved pads). This necessitates the development of a new mechanism, which accounts for pad grooving and higher abrasive concentrations. The mechanism proposed in this study, is comprised of two phases of interest. Phase occurs at low abrasive concentrations (ranging from 2.5 to about 9%). And phase 2 occurs at high abrasive concentrations (from 9 to 25%). When these two phases are considered in conjunction with the average coefficient of friction data depicted in Figs. 3 through 5, the following model can be postulated. In phase, removal rate does not depend on average coefficient of friction and follows the contact area model proposed by Brown and Mahajan, since pad surface sites are not fully occupied by abrasive particles. In this phase, increasing abrasive concentration leads to an increase in removal rate. In fact, when using eq. (9) as a fitting function, which contains a concentration term to the one-third power, an average R 2 value of 0.90 is obtained for all types of pads tested. 2) This lends further credence to the notion that Brown s model applies to low abrasive concentrations tested in this study. Contrary to Phase, in Phase 2, all surface sites are assumed to be fully occupied with abrasive particles. Therefore, further addition of particles does not impact contact area. In this case, the wafer is more likely to make contact with its closest abrasive particles and will not interact with the abrasives adsorbed on the pad surface. Depending on the type of pad (excluding k-groove), addition of particles will further increase the lubricity of the system, thus reducing shear forces and hence, removal rates. This phenomenon is observed in this research for various pad types studied. ð9þ Fig. 3. Preston s constant vs. average coefficient of friction for abrasive concentrations of 9% or larger. Additionally, as slurry viscosity is increased, fluid film thickness will also increase, leading to less intimate contact between pad and wafer at larger abrasive concentration. 3) This increase in fluid film thickness will decrease the coefficient of friction, thus decreasing average removal rate. 3.3 Correlation studies Figure 3 shows that removal rate (i.e. Preston s constant) and average coefficient of friction are linearly related at slurry abrasive concentrations of 9% or larger (i.e. in Phase 2 of the model described above) for all types of pads studied. Error bars on the x-axis denote minimum and maximum values of average coefficient of friction for the types of pads studied, while error bars on the y-axis denote minimum and maximum values of Preston s constant for a minimum of three repeat experiments. This is the first reported relationship between the average coefficient of friction and removal rate for various types of pad and suggests the presence of a universal relationship between the two factors. The tribological mechanism indicator,, shows a similar linear relationship to Preston s constant at abrasive concentrations of 9% or larger (Fig. 4). Increasing the removal rate would require increasing the value of, or the extent of contact between the pad and the wafer. Figure 4 can be a particularly useful tool for an IC manufacturer. For instance, with all else being constant, the manufacturer may not want to use a k-groove pad. While the k-groove pad does posses the largest Preston s constant (i.e. greatest removal rate), the fact that it is engaged in boundary lubrication ensures it will achieve the greatest amount of wear. From Fig. 4, the FX-9 flat or FX-9 perforated pads may be the two best choices for optimizing material removal rate while causing the least amount of pad wear. It must be noted that in Fig. 4, the two tribological mechanisms considered are boundary lubrication and partial lubrication since values of observed were not low enough to also

8 6378 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN Preston's Constant (/Pa).40E-3.20E-3.00E E E E E E+00 FX-9 Flat IC-000 Flat FX-9 Perforated IC-000 Perforated Tribological Mechanism Indicator (β) IC-400 k-groove Fig. 4. Preston s constant vs. tribological mechanism indicator for abrasive concentrations of 9% or larger. include hydrodynamic lubrication. While the newly discovered relationships shown in Figs. 3 and 4, have a great industrial utility, they fall short of explaining why different pads function differently. For instance, the above relationships do not explain the fact that the k-groove pads always show the largest Preston s constant and largest average coefficient of friction, while IC-000 x y pads always exhibit the smallest Preston s constant and average coefficient of friction. To account for these differences, the pad storage modulus has also been considered. Figure 5 is a plot of Preston s constant vs. the average storage modulus for each type of pad, in the temperature range of 20 to 40 C. Preston's Constant (/Pa).40E-3.20E-3.00E E E E E E+00 FX-9 Flat FX-9 Perforated IC-000 Perforated Storage Modulus (MPa) IC-000 Flat Fig. 5. Preston s constant vs. the average storage modulus for abrasive concentrations of 9% or larger. It is evident that an inverse linear relationship exists between Preston s constant and average storage modulus. In this case, the k-groove pad, which is the softest, provides the largest removal rates. The pad with the largest average hardness, the x y pad, displays the smallest removal rates. It should be noted that the IC-400 k-groove pad is not analyzed in terms of average pad storage modulus in this paper for two reasons. First, the sub-pad melts on the stage when large temperatures are encountered in the Dynamic Mechanical Analyzer (DMA) measuring process. Second, the non-homogeneous composite of the porous polyurethane upper pad and the fibrous, softer, sub-pad would not give a true representation of the pad s bulk properties. Additional studies by Stavreva et al., 4) Brown, ) and Stiegerwald 5) show that softer, more compressible pads yield larger removal rates, further rendering support to this claim. For a constant normal force, a softer pad will experience a greater shear force at the leading edge of the wafer during polish. The reason for this is 2-fold. First, on a macro-scale the softer pad will become further compressed at the leading edge of the wafer in response to the applied normal load. This compression will subsequently result in the formation of a barrier, which the wafer has to overcome continuously during its motion on the surface of the pad. Second, on a micro-scale, the pad asperities in the wafer-pad region will tend to collapse due to the relative softness of the pad. These two phenomena will combine to increase the net shear force between the wafer and the pad and hence the coefficient of friction for the softer pad as compared to the harder pad. A argument can also be used to explain the effects of pad storage modulus on. The collapse of pad asperities, and to a lesser extent, the collapse of groove structures for the softer pads, will enhance the extent of direct contact between the wafer and the pad 6) and hence result in a larger (and even positive) value of. 4. Conclusions A new definition for the Sommerfeld number was presented with applications specifically tailored to CMP. The Sommerfeld number, used in conjunction with the coefficient of friction, and tribological mechanism indicator,, present an enhanced method of describing the extent of contact between the pad, wafer, and slurry abrasive particles. In addition, the effect of parameters such as pad type, pad manufacturer, wafer pressure, pad-wafer average linear velocity, and slurry abrasive concentration, were shown to have a significant impact on the average coefficient of friction, tribological mechanism indicator,, and ILD removal rates. Furthermore, a two-phase model relating average coefficient of friction and Preston s constant was verified. At abrasive concentrations ranging from 2.5 to 9%, the amount of material removed was consistent with the previously reported contact area model at lower abrasive content. At abrasive concentrations between 9 to 25%, removal rate was directly influenced by the average coefficient of friction. A similar correlation was seen between Preston s constant and. These relationships at larger abrasive concentrations were beneficial in optimizing material removal rates while minimizing contact between the pad and wafer so as to inflict minimal damage to the pad.

9 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt., No. 0 A. PHILIPOSSIAN and S. OLSEN 6379 An inverse linear relationship between the average pad storage modulus and Preston s constant was seen at abrasive concentrations of 9% or larger. The pad, which was the softest, displayed the largest removal rates and average coefficients of friction, while the IC-000 x y pad, which was the hardest, showed the smallest removal rates and coefficients of friction. These phenomena were explained using a pad compliance model. On the macro-scale, a softer pad would become further compressed at the leading edge of the wafer in response to an applied normal load. This compression combined with the formation of a deeper trench in the pad increased the net shear force between the pad and wafer. This increase in shear forces for softer pads produced an increase in the values of the coefficient of friction, and thus, an increase in removal rates at abrasive concentrations greater than or equal to 9%. On the micro-scale, the pad asperities were believed to collapse more readily with a softer pad, 6) thus enhancing the extent of contact between the pad and wafer. This increase in contact produced larger values of for softer pads. Harder pads, like the IC-000 x y, were susceptible to less asperity collapse, resulting in smaller values of. Acknowledgements The authors wish to express their gratitude to Fujimi Corporation for slurry donation, and to Rodel-Nitta Company and Freudenberg Corporation for donation of IC-000 and FX-9 pads. The work was funded by the NSF/SRC Engineering Research Center for Environmentally Benign Semiconductor Manufacturing. ) A. K. Sikder, F. Giglio and J. Wood: J. Electron. Mater. 30 (200) ) A. K. Sikder, S. Thagella, U. C. Bandugilla and A. Kumar: Mater. Res. Soc. Symp. Proc. 697 (200). 3) I. Ali and S. Roy: Solid State Technol. 40 (997) 85. 4) J. A. Levert: Ph. D. Thesis, Georgia Institute of Technology, Atlanta, GA ) J. Lu, J. Coppeta, C. Rogers, V. Manno, L. Racz and A. Philipossian: Mater. Res. Soc. Symp. Proc. 63 (2000) E.2.. 6) C. Rogers, J. Coppeta and L. Racz: J. Electron. Mater. 27 (998) ) A. S. Lawing: Proc. 7th Int. Chemical-Mechanical Planarization for ULSI Multilevel Interconnection Conference (CMP-MIC), 2002, p.. 8) K. C. Ludema: Friction, Wear, Lubrication: A Textbook in Tribology (CRC Press, 996). 9) F. J. Preston: J. Soc. Glass Technol. (927) 24. 0) U. Mahajan, M. Bielmann and R. K. Singh: Mater. Res. Soc. Symp. Proc. 556 (2000) 27. ) N. J. Brown, P. C. Baker and R. T. Maney: Proc. SPIE 340 (98) 42. 2) S. F. Olsen: Master of Science Thesis. Department of Chemical and Environmental Engineering. University of Arizona (2002). 3) S. R. Runnels and L. M. Eyman: J. Electrochem. Soc. 4 (994) ) Z. Stavreva, D. Zeidler, M. Plotner and K. Drescher: Appl. Surf. Sci. 08 (997) 39. 5) J. M. Steigerwald, S. P. Murarka and R. J. Gutmann: Chemical Mechanical Planarization of Microelectronic Materials (John Wiley & Sons, New York, 997). 6) F. G. Shi and B. Zhao: Appl. Phys. A 67 (998) 249.