Ultra-Rapid Determination of Material Removal Rates Based Solely on Tribological Data in Chemical Mechanical Planarization

Single-run Stribeck + curves are constructed using real-time, high-frequency, shear force and normal force data from the wafer- slurry-pad interface during copper and cobalt (on ILD wafers) CMP in conjunction with multiple slurries, pads and conditioning discs at various pressures and relative velocities. To avoid having to perform actual polishing experiments to obtain blanket ﬁlm removal rates, “big data” sets from the same Stribeck + curves are used to construct new “Kinetic” curves to help infer relative blanket wafer removal rates. The “Kinetic” curves, which are based on the assumption that material removal is Prestonian, are eventually validated with actual removal rate studies involving different wafer types processed at various pressures-velocity combinations with the same pads, conditioning discs and slurries. A strong correlation is seen between the actual and “inferred” removal rates which renders credibility to our new ultra-rapid and ultra-low-budget approach for determining removal rates that does not require any wafer polishing nor any ﬁlm thickness metrology.

In CMP, a slurry containing chemicals and nanoparticles is first delivered to a rotating pad and allowed to form a thin film across its surface. A patterned wafer, having some gross topography, is next placed within a carrier and pressed face down against the pad which itself contains many surface asperities as well as deep grooves. Pad grooves facilitate the entry of fresh slurry into the pad-wafer interface. They also help move used slurry and polish byproducts away from the wafer's surface. Over time, chemical and mechanical effects remove the "up-features" of the wafer thereby resulting in local and global topographic planarization of the workpiece. This description, albeit simplified, indicates that frictional wear is an integral part of the CMP process since it causes the removal of the desired film on a patterned, or sometimes a blanket, wafer.
One way of understanding CMP is through tribological studies of the shear and normal forces as they can be exploited to remove a certain amount of material from the wafer. Over the past several years, our research team has successfully shown the utility of traditional Stribeck curves 1 in determining the lubrication mechanisms involved in the pad-slurry-wafer interface in CMP. [2][3][4] We have also introduced and shown that "Stribeck+ curves" provide more useful tribological information while dramatically reducing consumables as well as cutting down on the experimental time compared to traditional means. [5][6][7] The key point that we have emphasized throughout our published work is that Stribeck+ curves do not assume normal force to be constant throughout the polishing process as we can measure it (along with the shear force) instantaneously, and at frequencies of 1,000 Hz or more. If analyzed properly, "big data" resulting from such shear and normal force extractions can have many advantages as described in the following paragraph as well as in the Results and Discussion section of this work.
In our most recent studies, 8,9 we successfully, and for the first time, extended Stribeck and Stribeck+ curves to tribologically characterize retaining rings for copper and ILD applications. In all cases, 5-8 both type of curves yielded the same type of information and led to the same conclusions thereby lending credibility to the use of Stribeck+ curves which contain massive amounts of information while are much easier to obtain experimentally. In our latest work, 9 assuming that actual ring wear rate was proportional to COF × P × v (i.e. it followed a Prestonian relationship), 180,000 pairs of shear force and normal z E-mail: ara@email.arizona.edu force data points from the ring-slurry-pad Stribeck+ curves (generated during a 3-minute run) were used to construct new "Kinetic" curves that showed the relationship between an "inferred" ring wear rate and the pseudo-Sommerfeld number. Interestingly, validation studies involving extended wear tests of differently formulated retaining rings showed a correlation between actual and "inferred" wear rates, which has given us the motivation to propel our ideas to a new level.

Objective
The present work is based on our belief that the same methodology described above for rings can also be applied to metal CMP applications. That is, we are wondering whether "Kinetic" curves that are mathematically derived from Stribeck+ curves (based on pad-slurrywafer contact) and, as such, do not require any wafer polishing and film thickness metrology. If successful, our proposed methodology can significantly reduce process development and characterization time (something that all process engineers are striving to accomplish) thereby allowing for improved screening of the parameter space for CMP processes.

Experimental Apparatus and Test Procedures
All tests were done on an Araca APD-800 300-mm wafer polisher and tribometer equipped with proprietary force transducers suitable for acquiring real-time shear and normal force at high (i.e. up to 1,600 Hz) frequencies. 10 On this tool, the non-oscillating counterclockwise wafer carrier and its drive mechanism sit on a friction table attached to the frame. A load cell connected to the table measures the main component of the friction force vector, namely the shear force. This component runs perpendicular to the line connecting the platen and carrier centers. The carrier head does not use a contact retaining ring. Instead, a non-contact wafer backing film attached to a waterfilled template holds the wafer. The platen and its drive mechanism sit on four load cells that monitor the total normal force transmitted by the wafer to the pad. This includes both the applied load and any fluid forces that develop in the interface. All forces are measured at 1,000 Hz. There is no feedback between the normal force load cells and the carrier. Inside of the carrier, behind the wafer, there is an air chamber that applies the polishing force. An electro-pneumatic transducing regulator controls the chamber pressure. Pressure adjustments  can occur but are much slower than the force acquisition frequency.
The applied load has always been periodically checked and calibrated on a static platen.
In the case of the copper Stribeck+ studies, a single 300-mm blanket copper wafer was polished on CMC D100 pads using the PL-7106 slurry made by Fujimi flowing at 250 cc/min. When it came to Stribeck+ studies cobalt CMP, one 300-mm blanket interlayer dielectric (ILD) wafer was polished on a Fujibo H800-CZM pad using a proprietary cobalt buff-step slurry made by FujiFilm flowing at 200 cc/min. In the latter case, we used an ILD wafer instead of a cobalt-deposited wafer because our main objective was to see how the cobalt buff-step affected the removal of the surrounding dielectric. In each case, prior to running the Stribeck+ process and collecting force data, a new pad was broken in for 60 minutes (in the case of copper CMP) or 15 minutes (in the case of cobalt CMP). Deionized water was used during the break-in process.
For copper CMP, 4 very different types of conditioning discs were used as follows: 4S84SP4F5, 4K7530F6 and 43510F5 (all made by MGAM) as well as the Trizact B5 (made by 3M). In all copper CMP cases, the discs rotated at 95 RPM with a sweep frequency of 13 per minute. The downforce applied was 2.6 kg f . The same recipe was used for in-situ conditioning during copper wafer polishing. For cobalt (on ILD wafers) CMP, we used a Saesol CLC-S1-SASC disc which rotated at 36 RPM with a sweep frequency of 13 per minute. The downforce applied was 2 kg f . In this case, ex-situ conditioning was performed for 10 second before ILD wafer polishing. Both slurries were pre-diluted as per the manufacturers' specifications. For both copper and cobalt (on ILD wafers) CMP cases, the Stribeck+ curves were generated by performing only one 85-second polishing run with a series of gradual yet continuous changes (e.g. time-dependent ramp-ups and rampdowns) in polishing pressure and sliding velocity as shown in Tables I  and II. During each 85-second run, normal forces and shear forces were instantaneously measured at 1,000 Hz for the entire period, except for the first and last 5 seconds of the run (i.e. 75 seconds in total). There was a ramp-up or ramp-down step following each pressure-velocity combination which took approximately 2 seconds.
After conducting the single-wafer Stribeck+ tests and constructing the corresponding "Kinetic" curves that followed (see next section), for each wafer-disc-pad-slurry combination, we proceeded to perform removal rate validations studies by polishing multiple brand-new blanket wafers for 60 seconds at various pressures and velocities as shown in Tables III and IV. Removal rates were determined by measuring film thicknesses before and after polishing on 98 locations per wafer, averaging them, and finally dividing the difference in the two average values by the polish time. The same break-in and conditioning processes were used as were in the case of Stribeck+ studies.

Results and Discussion
The left-hand side plots in Figs. 1 to 5, show the Stribeck+ curves obtained in our study. The first 4 figures correspond to copper tests while the last figure is associated with the cobalt (on ILD wafers) experiments. Each curve is comprised of 75,000 data pairs (i.e. 75,000 shear force data points and 75,000 normal force data points, with the former divided by the latter) obtained by a single run at multiple pressures and velocities (with continuous ramp-ups or ramp-downs in between each condition) as detailed in the various steps of Tables I and II. The step number corresponding to a particular pressure and velocity is denoted atop each data cluster on the figures. In all cases, we observe that the processes stay in "boundary lubrication". This is in spite of the significant scatter observed at certain conditions. Large vibrations in the z-direction (e.g. up and down motion of the platen and/or the head) occur at low value of v/P as evident from the large slanted oval clusters seen in all four cases. [5][6][7] Compared to the other three discs, the MGAM 4S84SP4F5 conditioning disc seems to result in a more robust process (tribologically speaking) at low value of v/P as indicated by its smaller data cluster size. The nuances associated with the shape of each particular data cluster in the Stribeck+ curves cluster have been reported elsewhere in greater detail and are beyond the scope of this study. [5][6][7]9,11 Since the main objective of our study is to see if material removal rate can be inferred from the COF data, the same 75,000 data points for each Stribeck+ curve are replotted in the form of a new "Kinetic" curve, this time, with the ordinate representing COF × P × v. Here, we are assuming COF × P × v to be more or less proportional to the instantaneous removal rate of the wafer from a purely mechanical standpoint through Preston's equation. 12 Of course, we know, and have on numerous occasions shown that, copper and cobalt (on ILD wafers)  CMP processes, due to their tribochemical nature, are both chemically and mechanically activated, and that temperature plays an important role in determining the chemical rate constant for both processes as the activation energies for both cases has been shown to be around 0.5 eV. [13][14][15] However, in this study we have ignored the chemical effects altogether since there is no practical way of assessing, nor accounting for, them from the data sets in the Stribeck+ curves. Here, the notion of obtaining an indicator for instantaneous removal rate as a function of pressure and velocity from a single polish run, without doing any before and after film thickness measurements (which needs to be done for extended periods of time for multiple wafers processed at multiple pressures and velocities), is quite elegant and powerful. We think that, if validated, such analyses may someday become critical in reducing process development time while allowing process engineers to explore a wider parameter space during process development.
The "Kinetic" curve counterparts of the Stribeck+ curves are shown in the right-hand side plots of Figs. 1 to 5 as black scatter dots. Again, the step number corresponding to a particular pressure and velocity is denoted atop each data cluster. In all cases, the cluster shapes of the "Kinetic" curves are unique and the merging of the cluster that create ensembles of data point are quite complex.
To test our hypothesis that COF × P × v can be an indicator of removal rate, we proceeded to polish a total of 53 brand new 300-mm wafers (44 copper and 9 ILD wafers) through the conditions highlighted in Tables III and IV using the same slurries, conditioning discs and pads as those used in generating the Stribeck+ curves. The righthand side "Kinetic" curves of Figs. 1 to 5 also show the experimentally obtained removal rates (on the second abscissa and in the shape of circular symbols). Of the 53 discrete data points plotted, 51 of them fall atop their "Kinetic" curve counterparts while maintaining trends that are consistent with the overall shape and spirit of their individual "Kinetic" curves. It can be observed that the removal rates for cobalt (on ILD wafers) CMP exhibit larger deviations (when compared to their copper CMP counterparts in Figs. 1 to 4) when plotted alongside the "Kinetic" curve (Fig. 5). We believe that the cobalt (on ILD wafers) CMP process has kinetics that is different from the other 4 copper cases (hence the larger deviation discussed above). It must be noted that Stuffle et al. reported that the three copper CMP processes shown in Figs. 1 to 3 are non-Prestonian in which the two-step Langmuir-Hinshelwood model was successfully performed to simulate copper removal rates and the associated chemical and mechanical reaction rate constants. 13 Even with such non-Prestonian processes, the experimentally obtained removal rates are still consistent with the overall shape of their respective "Kinetic" curves. The results are our very first attempt at trying to show the probable utility of a "Kinetic" curve for a given process that does not require one to experimentally    obtain removal rates. Of course, more validation studies using different processes, consumable sets and wafer types at various pressures and velocities need to be done to render further credibility to our cause.

Conclusions
In this study, we constructed single-run Stribeck+ curves using real-time, high-frequency, shear force and normal force data from the wafer-slurry-pad interface during copper and (on ILD wafers) CMP. This was done with the appropriate set of slurries, pads and conditioning discs at various pressures and relative velocities for each application. To avoid having to perform actual polishing experiments to obtain blanket film removal rates, data from Stribeck+ curves were used to construct new "Kinetic" curves to help infer relative blanket wafer removal rates. The "Kinetic" curves were based on the assumption that material removal for both processes could be approximated using Preston's equation used in glass polishing. Our results next compared to actual removal rate studies on blanket wafers involving different wafer types processed at various pressures-velocity combinations with the same pads, conditioning discs and slurries. A strong correlation was seen between the actual and "inferred" removal rates which rendered credibility to our new ultra-rapid and ultra-lowbudget approach for determining removal rates that does not require any wafer polishing nor any film thickness metrology. Our results also indicated that the "Kinetic" curves were for the most part relevant to non-Prestonian CMP processes. The results were our very first attempt at trying to show the probable utility of a "Kinetic" curve for a given process that did not require one to experimentally obtain removal rates.