New Materials Integration

Optimizing the sizing and counting accuracy of CMP slurry large-particle counts

Leo H. Hanus, Clariant; and Stephen A. Battafarano and Andrew R. Wank, Rodel

CMP slurry large-particle count (LPC) data, which represent the tail of a particle-size distribution (PSD) above a threshold size, interest the semiconductor industry because such counts have been correlated to wafer defects.^1,2 However, that correlation does not always hold true because of measurement complexities involving the classification of defects, varying LPC composition, and other factors that affect LPC and defect measurement accuracy. To meet tight defectivity requirements, improved LPC and defect measurement techniques and a better understanding of the relationship between these variables are needed.

Available techniques for determining PSD range from chromatography to light scattering.^3–5 Of these methods, single-particle optical sizing (SPOS), which combines hydrodynamic particle focusing with light scattering or obscuration detection, has demonstrated the best potential for determining slurry LPCs. Slurry manufacturers and end-users often apply filtration to reduce LPCs and use SPOS tools to monitor the process. But LPC determination using SPOS tools can be difficult because of such instruments' sensitivity to random and systematic errors.

Sources of error include volume and flow-rate fluctuations, sampling inconsistencies (e.g., sample stability and homogeneity, and sampling and injection accuracy), and instrument issues (e.g., component malfunction, calibration, detector type and threshold, diluent type and background, and coincidence). Consistent use of a single method can produce measurement precision, but not necessarily accuracy. Sampling, instrument, and procedural variations can significantly affect both sizing and counting results. Because SPOS tools must be calibrated, accuracy also requires the development of a procedure that can be evaluated versus representative standards of known distribution.

The objective of the research described in this article was to quantify the impact of potential error sources and to develop an operating procedure designed to mitigate the most significant ones. Participants at six sites (representing four different companies) analyzed both silica and polystyrene standards using one type of optical sizer. The sources of error associated with this sizing tool and the measurement conditions used were then evaluated by comparing the results from the sites with the expected results for the standards.

Experimental Materials and Methods

Several types of samples were used in the study. Polystyrene standards with nominal sizes of 1, 3, 10, and 15 µm were purchased from Duke Scientific (Palo Alto, CA), and silica standards with sizes of 0.7, 2.6, and 3.3 µm were purchased from Bangs Labs (Fishers, IN). In the experiments discussed in this article, the sample labeled "multiple" is a mixture of these three silica standards. Two CMP silica production samples (designated 1201 and 1501) from Clariant (Charlotte, NC) were also investigated, and an additional sample was prepared by doping the 1201 CMP sample with the 0.7-µm silica standard.

The 15-µm polystyrene standard has a manufacturer-certified count of 3800 ± 722 particles/ml and was used as received. The 1- and 3-µm polystyrene standards (with known counts of 10⁹ and 5 X 10⁷ particles/ml, respectively) were used to prepare two separate series of five samples with known counts of 2.0, 1.5, 1.0, 0.5, and 0.2 million particles/ml. To create these sample series, the stock standards were homogenized, and analysis samples were then prepared from the homogenized stock via dilution with ultrapure DI water (18.2 M(omega)-cm and filtered to 0.2 µm) from a Milli-Q system from Millipore (Billerica, MA). The resulting samples were then homogenized and divided into containers for independent analysis at the six sites. No characterization information was sent with the samples to be analyzed so that participants at the sites would not be biased by the results prior to characterizing the samples.

The six participating sites used AccuSizer Model 780 SPOS systems manufactured by Particle Sizing Systems (Santa Barbara, CA). Site 1 employed an APS model, which has an automated sample-injection system, while all other sites used manual-injection models. The following instrument settings were used by all sites unless otherwise noted: a summation sensor, a 0.59-µm threshold, 128 bins, 60-ml vessel volume, and 100-µl sample injection volume. Sites 1 and 6 used autodilution, and all other sites used gravity drain operation. All volumes and flow rates (pipettor delivery, vessel fill, and gravity drain discharge volumes) were validated prior to the study by all sites, and the results were used to determine the counts per milliliter for each site.

Sample homogenization was controlled via moderate stirring. Each sample was stirred at the middle setting on a stir plate for 5 minutes and in the instrument vessel for 45 seconds prior to a measurement. Stirring was stopped during data acquisition to avoid the creation of bubbles.

Figure 1: Recovery ratio for the 1-µm sample series as a function of the expected counts for the six participant sites.

Each sample was measured three to five times to gauge measurement reproducibility. The baseline and sample sensor voltages and the coincidence level were monitored during each measurement to ensure proper instrument operation. Care was taken to avoid contamination by immediately closing the sample vials after a sample was removed and by keeping the pipettor tips and instrument vessel clean.

Counting Accuracy

Figures 1 and 2 show the count recovery ratio (measured count divided by expected count) obtained by the participant sites for the sample series consisting of 1- and 3-µm polystyrene standards, respectively. In Figure 1, vertical error bars are shown only for site 2 and site 4 data. Similar errors were seen for the other sites and ranged from 0.01 to 0.13, with an average of 0.08. No vertical error bars are shown in Figure 2 but were approximately 0.1 for all of the data points. Table I shows the counting results for the rest of the samples and for the 2 million-particles/ml 1- and 3-µm samples. The expected 15-µm count listed in the table was certified by the manufacturer; the other expected counts were calculated based on the dilution factor for the stock standard.

Figure 2: Recovery ratio for the 3-µm sample series as a function of the expected counts for four of the six participant sites.

Figures 1 and 2 indicate that particle-counting accuracy (but not necessarily counting precision, as Figure 3 shows) decrease as particle size and count decrease. The agreement among the sites was best for the 2 million-particles/ml 3-µm sample and worst for the 0.2 million-particles/ml 1-µm sample. Site 4's poor results, shown in Figure 1, were traced to an instrument malfunction. Site 2 initially had similar sizing-accuracy problems. These site results illustrate the need to periodically confirm an instrument's sizing and counting accuracy using representative standards, since personnel at those sites were unaware before the study that their instruments were malfunctioning. Troubleshooting prompted by the results for the 1-µm sample series led to the improved instrument operation demonstrated in the results for the rest of the study.

The lack of agreement seen in Figure 1 for the smallest samples probably resulted from sample instability over time rather than from signal-to-background limitations. While the 3-µm samples were analyzed within days of preparation, the 1-µm samples were analyzed weeks later. Figure 2, which shows an inverse relationship between counting accuracy for 3-µm samples and the dilution factor or equivalent sample injection volume, is thus more representative of instrument operation.

The inverse relationship between measured count and sample concentration indicated in Figure 2 is confirmed by the counting results for the 15-µm standard shown in Table I. Only sites 2 and 4 analyzed this size standard. Site 2 measured the sample without dilution and recorded an average count of 3374 ± 304 particles/ml, which is within the certified count range of 3800 ± 722. Site 4 first measured the sample diluted 12:1 with ultrapure water and obtained a count of 5103, which is outside the expected range. The site then
analyzed another sample of the standard without dilution and obtained a count of 3551 ± 104, which is within the expected range. If the smallest analysis channels are excluded from site 4's first measurement, the result is 3543, which is nearly equivalent to the second measurement.

Figure 3: Site 1's count measurements as a function of measured diameter for the 3-µm sample series.

Figure 3 shows a semilog plot of site 1's counting results for the 3-µm polystyrene sample series, and Figure 4 shows the same data normalized by the expected counts for the series. The secondary coincidence peaks in these figures occur at the size of the average orientation of overlapping particles in the detection plane. The other participant sites obtained results similar to those in Figure 3 for both the 1- and 3-µm polystyrene sample series. The repeatability of the results can be attributed to the methods used to conduct the study. However, as Figure 1 illustrates, taking steps to help ensure measurement precision does not guarantee counting accuracy.

Figures 1 and 2 suggest that a relationship exists between measured count rate and counting accuracy. To confirm this hypothesis, study participants calculated recovery ratios and count rates for the 2 million-particles/ml 3-µm sample as a function of sample injection volumes ranging from 3 to 500 µl. Results are shown in Figure 5, in which the solid lines are the count rates (plotted against the right-hand y-axis), the squares and diamonds are the recovery ratios based on mean total count (mean count divided by expected count), and the crosses are the recovery ratios based on measured peak count (peak count divided by maximum peak count). The vertical lines through some symbols are error bars for the measurements. For comparison purposes, the recovery ratios from Figure 2 are included in green, because the dilution series is equivalent to varying injection volumes.

Figure 4: Site 1's measured count distributions for the 3-µm sample series (from Figure 3), normalized by the expected counts for the series.

Figure 5 shows the impact of background noise on counting accuracy. For count rates of <1000 particles/sec, the recovery ratio exceeded the expected value of 1 because of the additive effect of background counts. If the smallest measurement channels (the channels most affected by background noise) were excluded from the analysis of site 2's results, recovery ratios of 1.00 ± 0.08 would be obtainable for all injection volumes <100 µl. However, simply subtracting the background does not solve the problem, and these channels cannot be excluded for typical slurry LPC measurements where the PSD tail is measured rather than a large unimodal peak.

Figure 5 also indicates that there is an upper limit to maximizing signal strength. For count rates that are higher than 3000 particles/sec, the recovery ratios and normalized peak ratios decrease with increasing injection volume. It is evident from Figures 3 and 4 that this decrease is a result of coincidence effects (the false counting of overlapping particles in the detection plane as single particles). The coincidence peaks in Figures 3 and 4 occur at approximately 1.67 times the sphere diameter (the average orientation of overlapping spheres in the detection plane). It is particularly clear in Figure 4, where dilution effects have been normalized, that these peaks grow larger as sample concentration increases. If these secondary peaks were "real," they would overlap as the primary peaks do. Unfortunately, for slurry LPC applications, coincidence begins to affect counting accuracy at a much lower sample concentration then expected, since SPOS systems are designed to operate at count rates as high as 12,000 particles/sec.⁶

Figure 5: Recovery ratios and count rates measured by sites 1 and 2 for the 2 million-particles/ml 3-µm sample as a function of injection volume.

Figure 6 shows the difference between extinction and summation detection techniques and gravity drain versus autodilution operation for the 2 million-particles/ml 3-µm sample. The overlapping lines of the same color indicate repeated measurements. The red, purple, and blue lines show gravity drain measurements employing an extinction sensor at a 1.5- and 2.0-µm threshold and the summation sensor at a 0.56-µm threshold. The green lines show autodilution measurements employing the summation sensor at a 0.56-µm threshold.

The difference between the results achieved using summation and extinction detection is magnified as the threshold increases, indicating that the difference is not simply linked to variations in sensor calibration. Increasing the extinction threshold affects both sizing and counting accuracy. This result agrees with those reported by other researchers, who studied the effect of using different types of SPOS instruments to size fumed silica and alumina slurries doped with varying amounts of polystyrene latex size standards.⁷ That work indicated that changing the sensor type (summation versus extinction) and bin spacing can lead to significantly different counting results for the same samples.

Figure 6: Site 2's count measurements for the 2 million-particles/ml 3-µm sample as a function of measured particle diameter and different instrument conditions.

The results in Figure 6 do not establish whether autodilution is a better technique for sample preparation than gravity drain operation. This conclusion was confirmed by comparing sizing and counting results from sites 1 and 6, which used autodilution, with those from the rest of the sites, which employed the gravity drain method. While the gravity drain technique can count all of the particles within the detection volume, it requires time-consuming preparation if little is known about a sample and the count rate is greater than the appropriate coincidence level.

Based on the results for the polystyrene standards, the study participants analyzed the silica standards and CMP silica production samples, achieving a rate of <3000 counts/sec through sample preparation. The CMP silica samples were not diluted before analysis because the count rate was already known to be below this level for a 100-µl injection. Figure 7 shows the modified recovery ratio (the measured count divided by the site-averaged measured count) obtained by four participating sites for the seven silica samples. The site-averaged measured counts were used to determine the recovery ratio because the expected counts for the samples were not known. The site-averaged count rates are listed in parentheses below the x-axis. Multiplying this number by 600 yields the site-averaged measured counts in particles per milliliter. Vertical error bars are shown for the data points.

Figure 7: Modified recovery ratio for the silica samples analyzed at four of the six participating sites.

The results in Figure 7 reveal the same general trends as the results for the polystyrene standards (Figures 1 and 2) in that the agreement in the sites' counts improves with increasing particle concentration (as quantified by the site-averaged count rate) and increasing particle size. However, the level of between-site agreement for the silica standards was worse than that for the polystyrene samples of the same relative concentration and size. This difference can be at least partly explained by the study design. Fewer silica than polystyrene samples were analyzed and less was known about their counts. Consequently, most of the silica samples contained <600,000 particles/ml, which yields a count rate of 1000 particles/sec, and had an effective size smaller than 2.5 µm. As Figures 1 and 5 show, the participant sites also had difficulty accurately counting polystyrene samples with these characteristics. Furthermore, simply correcting for background did not improve the agreement of the results obtained from the sites for the silica samples.

Figure 8: Site 1's count measurements for the 2.6-µm silica sample as a function of particle diameter and injection volume. The measured count rates are shown in the legend in parentheses next to the injection volume.

Coincidence effects and sample instability issues are additional explanations for the counting differences between the silica and polystyrene samples. Figures 8 and 9 show count distributions obtained by site 1 for the 2.6- and 0.7-µm silica samples, respectively, as a function of particle diameter and injection volume. An overlapping plot similar to the normalized results in Figure 4 would be expected, but these two figures depict significantly different distributions. Even at the lowest injection volume and count rate in Figure 8 (0.1 ml and 1579 particles/sec), there is a more significant coincidence peak than for polystyrene at the same count rate. Of even more concern in Figure 8 is that at high coincidence levels (3.5- and 7-ml injection volumes) a single peak occurs that is not distinguishable from the true primary peak of the sample.

At least some of the counting variation exhibited in the first part of the study can be attributed to sample instability resulting from dilution. The samples that were diluted the most yielded the most inaccurate results. To assess the impact of sample instability as a function of time, site 2 performed repeated measurements for all of the polystyrene sample series a month after performing the first measurements on these samples. The samples that had been diluted the least did not yield significantly different results when reanalyzed; however, the most-diluted samples, the 0.2 million- and 0.5 million-particles/ml samples, yielded significantly different counts and showed small peaks at sizes >200 µm.

Figure 9: Site 1's count measurements for the 0.7-µm silica sample as a function of particle diameter and injection volume. The measured count rates are shown in the legend in parentheses next to the injection volume.

By evaluating the equivalent of the 2 million-particles/ml sample, which did not yield different counting results over time, site 2 verified that the differences in the most-diluted samples did not result from count rate effects. The site performed the evaluation by injecting 10 times and 4 times as much of the 0.2 million- and 0.5 million-particles/ml samples, respectively. The results confirmed the existence of a sample instability effect, because the normalized per-milliliter counts were the same as had been recorded earlier that day with 100-µl injections rather than the counts expected for the 0.2 million- and 0.5 million-particles/ml samples or the results recorded a month earlier.

Sizing Accuracy

Table II lists the sizing results for the standards measured at the six participant sites. Missing data indicate that a site was not included in the measurement series. For the polystyrene standards, the maximum differences in the sizing results among the sites and between the sites and the expected results were 12% and 18%, respectively. Except for the 3- and 15-µm polystyrene standards (which were measured at four or fewer sites), the agreement between the sites and the expected results was better than the agreement among the sites, with average maximum differences of 6% and 12%, respectively. For the 1- and 10-µm polystyrene standards, the site-average size was within 2% of the expected size. For the silica standards, the agreement among the sites was about the same as for the polystyrene standards, with a maximum difference and an average maximum difference of 14% and 12%, respectively. However, the agreement between the sites and the expected results was much worse, with a maximum difference that was 52% lower than expected. All of the silica sizing results were lower than the expected size by at least 14%.

Instrument calibration issues are the most likely cause of the sizing differences shown in Table II. For the polystyrene samples, increasing the number of calibration standards in the size areas of interest and increasing the number of bins and their spacing consistency among the sites would probably improve the agreement level of the sizing results. For the silica samples, instrument calibration using silica standards rather than polystyrene standards could possibly improve the results. Figures 6, 8, and 9 show that instrument threshold size, sensor type, and sample injection volume can also impact sizing accuracy. Thus, improved sizing accuracy may be possible using different instrument conditions.

Conclusion

The research described in this article explored the errors associated with using an SPOS tool to characterize polystyrene and silica slurries with different types of PSD shapes in the >0.5-µm range. Study participants attempted to control, or quantified and corrected, variances related to sample homogenization, volumetric additions and discharges, diluent quality, and bin spacing. The effects of drain method (gravity versus autodilution), sensor type (extinction versus summation), and threshold level and sample injection volume (count rate) were among the areas studied. The investigators discovered that diluent type and regular confirmation of proper instrument performance are also critical factors.

It was found that if special care is taken to adhere to an operating procedure that ensures sample homogeneity, measurement precision (repeatability) is possible. However, measurement precision is not an indicator of counting or sizing accuracy. Counting and sizing accuracy were found to be functions of count rate. Sizing accuracy was also strongly dependent on instrument calibration. At increasing count rates >3000 particles/sec, coincidence leads to decreasing counts (underprediction of the true count), prediction of false coincidence peaks, and a broadening of the true PSD. At decreasing count rates <1000 particles/sec, background noise causes increasing overprediction of the true count, which cannot be corrected by simply subtracting the background counts. (However, a purer diluent source may solve this problem.) Because of coincidence effects, better accuracy is possible at lower counts. Nevertheless, better consistency was achieved among the study's six participant sites at higher counts (around 3000 particles/sec).

Most of the research effort reflected in this article focused on polystyrene size and count standards, which pose the simplest analysis case because of their simple PSDs (a single peak in a clear background) and because instrument calibration is based on polystyrene standards. Encouraging sizing and counting results were obtained for the polystyrene standards, being within 20% of the expected level for the recommended range of instrument operation. Similar accuracy was not achieved for the silica standards and CMP silica samples.

CMP silica samples pose a difficult analysis case because their measured LPCs can be composed not just of silica, but also of varying amounts of other materials. Additionally, their PSD shape is challenging. Typically, <0.2 ppb of particles that are >0.5 µm are present in bulk PSDs centered at 50 nm, and particles just below that size threshold may influence LPC analysis results. Slightly better agreement was obtained for silica standards than for the CMP silica samples because of the former's simpler PSDs. Silica samples similar to the polystyrene standard series discussed in this study will be analyzed in future research to uncover more about the difference between measuring LPCs of silica and polystyrene.

Acknowledgments

The authors would like to thank Clariant, Rodel and the personnel at each of the six sites who participated in the study.

References

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Leo H. Hanus, PhD, is a technical manager for performance nanocomposites at Clariant (Charlotte, NC), where he has worked for three years. Before joining Clariant, he completed postdoctorate work in chemical engineering at DuPont and the University of Delaware in Newark. Hanus has authored several works for a variety of books and journals and has also produced numerous papers. He received a BS in chemical engineering from Texas A&M University in College Station and a PhD in chemical engineering from the University of South Carolina in Columbia. (Hanus can be reached at 704/395-6715 or lhanus@clariant.com.)

Stephen A. Battafarano is a procurement strategist at Rohm and Haas in Philadelphia. Previously, he was a senior materials engineer at Rodel (Phoenix). He has spent more than 15 years in sales and marketing, operations, engineering, and product management for specialty chemicals and materials development at Union Carbide/Praxair Surface Technologies and Rodel. He received a BS in chemical engineering from Youngstown State University in Ohio. (Battafarano can be reached at 215/592-3147 or sbattafarano@rohmhaas.com.)

Andrew R. Wank is a quality department scientist at Rodel, where he has served for eight years. He is responsible for methods development in analytical chemistry, microscopy, image analysis, and machine vision applications. Before joining the company, he worked at Lanxide as a research and development technician and was responsible for research and development activities in the area of ceramic and metal matrix composites. He received a BS in biology from the University of Delaware in Newark. (Wank can be reached at 302/366-0500, ext. 6922, or awank@rodel.com.)