A new measure of value for CD metrology tools
12/01/2004
Analyzing the results of critical-dimension uniformity wafers from step-and-scan systems using different metrology tools revealed a random contribution to the overall CD variation that could not be attributed to the exposure tool or to the metrology tool's repeatability. A test and analysis method was developed to separate this random contribution from the test results. The level of this random CD variation, called the total test repeatability, is proposed as a new metric to compare CD metrology tools' ability to generate valuable CDU maps for exposure-tool characterization or feedback purposes.
Until now, the steady decrease of critical dimension (CD) has driven an equivalent reduction of its control budget. Recently, however, the updated ITRS shows an even greater proportional reduction in CD uniformity (CDU) [1]. The combination imposes challenges for all tools involved in the realization of the new CD nodes. For CD metrology tools, these are translated in requirements for resolution, repeatability, and accuracy. For example, the target for the MPU-gate CD control for the 90nm node is as low as 3nm 3σ. To measure and maintain this CD control, CD metrology precision for the 90nm node should be 0.6nm 3σ.
Today’s CD metrology tools show promising resolutions for future nodes [2], and the repeatability of current tools, already well below 1nm, should be well suited for the 90nm node. Continuous improvements are foreseen to follow the roadmap down to smaller nodes [3]. The application of metrology tools however, has been expanded from traditional sampling plans of a few points/wafer toward determination of CDU maps, across-wafer or across-field, for CD control applications or for qualification of exposure tools and tracks. This raises the following question: Is repeatability of a metrology tool a good figure of merit to determine its ability to measure such CDU maps?
Additional random CD variation
ASML is using various CD metrology tools to characterize capabilities of its scanner exposure systems. These metrology tools are state-of-the art and have excellent long-term repeatability characteristics, but the analysis of our data revealed some unexpected results. After removal of CD variation due to scanner and track, the observed residual variation could not be explained by the repeatability of the metrology tool alone. Two examples of such random CD variations are described below.
One wafer was measured on two different CD scanning electron microscopes (SEM) for the purpose of SEM matching. Apart from the average offset, the resulting CD readings from the SEMs for the same line showed large differences at random over the wafer. These differences ranged from –3nm to +3nm. Given the fact that both SEMs have a long-term repeatability of <1nm 3σ, this variation was surprisingly high. The exposure tool or track could be excluded as source of this variation because the same wafer was measured on both SEMs. Further scrutiny showed that the two SEMs measured the lines on the wafer at slightly different locations. Local linewidth variations (linewidth roughness, LWR) caused the SEMs to report different CDs for the same line (see section “Results with CD-SEM”).
A second set of wafers was measured using electrical linewidth measurements (ELM). The across-wafer and across-field fingerprints were removed from the data to eliminate exposure tool, etch, and track fingerprints. The remaining random CD variation was as high as 6nm 3σ. No correlation with other exposure tool characteristics was found. This variation could not be related to the metrology tool repeatability, which, for ELM, is 0.4nm 3σ. Instead, the level of these CD variations was related to the wafer properties - a very surprising result.
Aside from resolution and precision, another characteristic of the metrology tool or method affects its ability to accurately determine the CDU map required to monitor and control the CD capability of lithographic tools.
The following section describes a test and analysis method developed to quantify this random component in the data and separate it from the exposure-tool CD control capabilities. The experimental verification demonstrating the validity of this method is shown along with results for various CD metrology tools. In-depth analysis reveals some of the root causes and possible countermeasures. The data lead to conclusions about the value of this new figure of merit in comparing different CD metrology methods and tools.
Determining TTR
The phenomenon described above appears as a random CD variation in any kind of lithographic test and resembles the effect of metrology tool repeatability in a measurement. This CD variation appears only if the total test, not the metrology step, is repeated. It is therefore called total test repeatability (TTR).
 Figure 1. Layout of the features and fields over the wafers, as needed, to determine the TTR. |
Very much like the metrology tool repeatability, TTR is determined by comparing repetitive results of a test. This eliminates constant, systematic CD fingerprints caused by the reticle, exposure tool, and processing. Further steps in the method remove other CD variations originating from the exposure tool, processing variations, or wafer topography. All have some kind of fingerprint or local correlation, whereas the TTR is completely random. Proper filtering suppresses these other sources in the TTR analysis. Altogether, the following steps are taken to obtain the TTR (Fig. 1):
- A reticle is required with n pairs of similar features, separated by a very small distance (<200µm at 1×) between the two features in a pair. The features are called P1,n and P2,n, where n ranges from 1 to n.
- Two or more wafers are exposed with multiple fields, all under the same conditions. The field is indicated with index m; the number of fields is M. The wafer is indicated with index k; the number of wafers is K. The number of repeated pairs must be large enough, preferably n×(M×K − 1) ≥100.
- The wafers are processed and measured on the metrology tool under investigation.
- The difference between the two features in a pair is calculated as ΔPn,m,k = P2,n,m,k – P1,n,m,k.
- Flyers in the population of ΔPn,m,k are eliminated using a 4σ criterion.
- The wafer-to-wafer variance of this difference is calculated
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- The variances are averaged over the fields and feature pairs:
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- Finally, the TTR is derived from the average variance:
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The factor 
is needed because of the subtraction performed in step 4.
In this method, all systematic sources of CD variation are eliminated as follows:
- The reticle fingerprint and the field fingerprint of the exposure tool are eliminated by calculating the variances over each pair of features (step 6).
- Dose and focus variations of the exposure tool and the effect of wafer topology are eliminated by taking the pairwise difference of two similar features, close enough to experience the same local exposure conditions (step 4).
- Both steps 4 and 6 effectively eliminate the effects of all process variations.
In some instances, only one wafer is available; in these cases, the single-wafer TTR is estimated from the field-to-field variations of the pairwise differences. Prior to this, any remaining across-wafer fingerprint must be removed. This can be done by a fitting procedure that enables mathematical removal of across-wafer or across-field fingerprints [4].
Validation
The method developed to separate TTR from other sources of variations was validated in two different experiments.
First, the single-wafer method was compared to a two-wafer TTR analysis. Experimental conditions are given in the next section. The wafer was measured using ELM. The single-wafer analysis gave 1.5nm on the first wafer and 1.8nm on the second. The two-wafer analysis yielded 1.6nm, close to the average of the two single-wafer results. The across-wafer CD fingerprint was effectively removed by both methods: The average CD showed a clear offset/field, whereas the average variance was fully independent of the average CD/field.
In a second experiment, the first steps of the single-wafer TTR analysis were performed as described previously. The variance of the difference/feature pair was compared to the average difference between the features in the pair. There was no correlation at all, which indicates that the across-field reticle and exposure-tool CD fingerprints also were effectively suppressed by the TTR analysis method.
These experiments reveal a random CD variation that is significantly higher than the repeatability of the tool, and that this variation is independent of systematic across-wafer or across-field CD variations. TTR analysis was used to study CD-control measurement capabilities for three metrology platforms: CD-SEM, ELM, and CD scatterometry.
Comparing CD metrology methods
The wafers under investigation were exposed on ASML AT:1100 and AT:1200 step-and-scan systems using binary reticles that contained regular arrays of similar modules. Typically, 13 columns in the slit direction and seven rows in the scanning direction were used in the tests. Each module comprised at least a horizontal and vertical test structure. The CDs were 100, 90, and 80nm (at 1×); the line-to-space ratio ranged from dense (1:1) to isolated [or almost isolated (1:6) in the case of CD scatterometry]. The wafers were fully covered with exposed fields. In most of the tests, >4000 points were measured for a TTR analysis.
The following metrology tools were used in this investigation: Hitachi 9360 CD-SEM; ELMs with a Hitachi M711 etcher, Keithley F600 parametric tester, and Electroglas EG 5-300 prober; and CD scatterometry with a KLA-Tencor Spectra CD.
Based on our experience, the TTR results are more typical for a metrology technique and strategy than for the brand or model of the metrology tool.
Results with CD-SEM
The investigations on the CD-SEM characteristics were focused on the repeatability, variation in the matching data, TTR, and CDU test results. Experiments were performed on a CDU wafer with 80nm dense lines (1:1). Measurements were taken using two different sizes of the measurement box (500nm and 2.1µm); it has been proven that this has an impact on determining the average CD of a line [5].
The CD-SEM dynamic repeatability for these kinds of features was 0.9nm 3σ for the short measurement box (MB) and 0.8nm for the long MB. These numbers, obtained after correction for resist-line shrinkage, are typical results for this type of CD-SEM.
As mentioned in the introduction, a strange effect was observed when the very same wafer was measured on another CD-SEM (SEM B). SEM B had the same repeatability as the original CD-SEM (SEM A). The CDs measured on SEM B, however, did not correlate with the results from SEM A as well as expected. The differences showed a random variation from point to point of a few nanometers. Our hypothesis was that the MB was placed in different locations on each SEM. In combination with LWR, this could be the root cause of the random difference. Therefore, the measurements were repeated on the original SEM A, but with the position of the MB a few microns further down the line. This indeed had a dramatic effect: The repeatability between the original and the repeated measurement was as high as 3.5nm. Moreover, the difference showed the same random characteristic as the difference between SEM A and SEM B. These findings confirmed the hypothesis: LWR shows up in the CD-SEM measurements as a source of random CD variation. The traditional repeatability test does not reveal this finding because the repeated measurements are taken on the very same position of the line.
The effect had to show up in the TTR analysis. To investigate this in more detail, the TTR and LWR were determined for various exposure conditions, using a short MB. The TTR was again much higher than the SEM repeatability - its increase from 4.5-7nm 3σ being proportional to the LWR. This trend confirmed that LWR is the major factor in the CD-SEM TTR and degrades the capability to determine across-wafer or across-field CD maps.
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In the next experiment, a CDU wafer was measured and analyzed using both long and short MBs, for comparison. The CD variation was split into various contributions using a model approach [4], with results given in Table 1. Note that the TTR is a fully random CD variation, hence the variance adds linearly. Summations, differences, and averages of 3σ are therefore calculated by a quadratic equation. In this specific case, the difference is calculated as:
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All the results, except for the across-field CDU, showed a 2-3nm 3σ extra CD variation for the short MB compared to the long MB. These results indicated the impact of TTR on the measurements with a short MB. Roughly 55% of the residuals were dominated by the TTR. Again, the variance is used:
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In case of the long MB, the effect was less pronounced; still, a significant part of the reported across-wafer CD uniformities were actually due to the TTR effect. Note also that the dynamic repeatability of the short MB shows only a 0.4nm 3σ higher variation than the long MB.
The situation for the across-field CDU was different - effectively, a result of the averaging over multiple fields. The averaging reduced the impact of the TTR on the CDU. The additional CD variation in the across-field CDU determined with the short box was now 1.4nm, well below the across-field CDU itself. Not surprisingly, the slit and scan fingerprints of the across-field CDU were quite similar for both ways of measurement (Fig. 2) due to the averaging over a number of fields and over multiple rows or columns in a field.
In spite of the CD-SEM’s good repeatability, the ability to measure CD fingerprints of scanner field, reticle, or wafer is clearly hampered by sensitivity to LWR. A longer MB can suppress this effect. Typical TTR numbers with a long MB, in our application, are on the order of 2nm 3σ. Further reduction of the impact of this TTR can be obtained only by averaging multiple measurements at the cost of a longer measurement time.
Results with ELM
ELM is a method that excels in speed and repeatability; in our application, a repeatability of 0.4nm 3σ was measured. A low TTR was expected, too, because the length of the measured lines (80µm) should reduce the effect of LWR on TTR by a factor >6×, compared to long-box CD-SEM. In this section, the results of a TTR evaluation and the relation to the results of a scanner CDU test are presented and discussed.
It was previously mentioned that the wafer characteristics could influence the random CD variation found in a CDU test. To study this effect in more detail, a CDU test was repeated with wafers from different vendors, two from each source. Similar to in the CD-SEM section, the CD variation was split in various contributions and the TTR was determined for each wafer pair. The results are given in Table 2.
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The analysis shows TTR numbers between 2 and 3nm - clearly not as low as expected from ELM. Further analysis revealed a correlation to wafer type as follows: wafer A had a somewhat larger overall variation. After removal of the global (process) fingerprint, however, the remaining across-wafer CD variation for wafer B was slightly higher (4.9 vs. 4.7nm 3σ). The across-field fingerprints were not the source of this difference; they had an excellent match, with a correlation coefficient of 0.98. The correlation between across-field slit and scan fingerprints for both wafers types is shown in Fig. 3.
The residuals, obtained after subtracting the across-wafer and across-field fingerprints, were again significantly higher for wafer B than for wafer A: 3.3 vs. 2.7nm 3σ. Subtraction of the variances revealed an additional source of CD variation for wafer B, as high as 1.9nm 3σ. The analysis showed TTR numbers that accounted for ~60% of the residual CD variance. Clearly, the difference in TTR was largely responsible for the difference in residual CD variation.
A search for the root cause of the TTR pointed toward the local resistivity variation of the wafer as a possible root cause. The sheet resistivity must be known to convert electrical measurements into CDs. Global resistivity variations over the wafer are taken into account in the measurements by the use of Van der Pauw (VdP) test structures. There is no correction however, for local variations; they will appear as CD variations in the CD measurements.
In view of this, the local VdP variations were determined for both wafers and scaled to the average VdP; the TTR is calculated as a percentage of the average CD, with values of 4.4% and 5.4% for wafers A and B, respectively. Wafer B indeed had a larger VdP variation (1.8% vs. 0.7% for wafer A), although the magnitude and difference cannot explain the large value of the TTR.
Separate experiments with other wafer stacks, based on TiN conducting material [6], gave much lower TTR values, as low as 0.6nm 3σ. These results confirm that the properties of the conducting material used in ELM applications are at least one source of TTR and determine to what level ELM can reliably reveal CDU fingerprints. Again, the standard repeatability test did not reveal this source of variation in the measured CD simply because the very same wafer is measured repeatedly.
Results with CD scatterometry
CD scatterometry is gaining popularity. Due to the small hardware, the method is the preferred choice for in-line metrology applications. From a CD metrology perspective, scatterometry is interesting: CDs can be measured with a good repeatability [7], and additional shape information is obtained [8]. Since CD scatterometry uses a rather large spot to determine the average CD of a grating, the expectation was that TTR numbers would also be very low.
The model that was used for this CD-scatterometry TTR analysis consisted of a single trapezoid, with floating parameters: middle CD, pattern height, sidewall angle, and bottom antireflective coating thickness. The bottom CD - which should match the SEM measurement most closely - was calculated from these parameters. The dynamic repeatability was measured for 80nm lines with a pitch of 560nm (mimicking the behavior of isolated lines). The results for the middle CD were excellent: 0.12nm 3σ, while results for the bottom CD were “less good”: only 1.4nm 3σ. The large difference is due to the repeatability of the sidewall angle, which in this case was 0.52° 3σ.
This CD scatterometry tool was also used to measure wafer CDU fingerprint and from this to determine the scanner CD control. The results (Table 3) were analyzed using the middle and bottom CDs as metrics. Results for H and V were determined separately and averaged (RMS).
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For the middle CD results, the TTR is not as good as the repeatability, but still <0.5nm. The source of the middle CD TTR is not fully understood. Some investigations point to the combination of grating uniformity and positioning stability of the scatterometer’s measurement spot. Figure 4 shows the variation of measured CD with varying spotlight position within the grating. The variation is significant in view of the excellent repeatability. This small TTR has hardly any effect on the analysis results: The TTR is only 12% of the residual CDU and has virtually no impact on the measured wafer and field CD maps.
 Figure 4. Measured CD vs. position of the scatterometry spot. A variation of a few microns in the spot position causes >0.5nm variation in measured CD. |
For the bottom CD, the TTR is much higher -1.5nm, almost equal to the repeatability - indicating that this is the major contributor to the higher TTR. Also, the residual CD variations and the across-wafer CDU for the bottom CD are higher: Compared to the middle CD values, an additional 2.3nm was found, which is partly due to the higher TTR. Other sources of this variation are still unknown.
These results favor the use of middle CD to characterize CD fingerprints, but looking to the across-field CDU fingerprint, it appeared that there was actually no correlation between the average field fingerprint for middle and bottom CDs (Fig. 5). In the specific case studied here, this should not come as a surprise: With such small variations, the profile shape dominates the bottom CD. This shape will vary with the position in the die, due to subtle gradients in focus, for example. The middle CD is insensitive to profile changes and will not correlate to the bottom CD.
 Figure 5. Comparison between slit and scan across-field CDU measured at the middle CD (dashed line) and bottom CD (solid line). |
In the past, we have found excellent correlation between middle CD measured by CD scatterometry and CD measured by ELM. With the very low TTR, CD scatterometry using the middle CD appears to be the most appropriate technique to determine valuable CD fingerprints with minimal measurements.
Conclusion
>Various effects become random variations in CD measurements that affect the ability of a metrology tool to measure CD fingerprints of exposure tools, process tools, and reticles. The proposed metrology parameter, total test repeatability, is a better metric for these random variations than metrology tool repeatability alone. The TTR should be taken into account in particular when evaluating tools for integrated metrology applications, where a limited number of measurements are taken to determine and control CDU fingerprints over time.
Typically, the TTR is much larger than the metrology tool repeatability. The TTR for CD-SEM is dominated by linewidth variations and can be suppressed by a longer measurement box. For ELM, the choice of the stack and processing has an impact on the TTR, and, thus, on the measurement results.
Finally, scatterometry shows results that very much depend on the measurement parameter chosen. Using middle CD as the parameter of interest, the CD scatterometer outperforms the other tools, with a TTR as low as 0.4nm. This is a strong argument to use CD scatterometry metrology for CDU characterization, either standalone or in integrated metrology applications.
References
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Hugo Cramer, PhD, is group leader of CD analysis, imaging systems development, at ASML Netherlands BV, P.O. Box 324, 5500 AH Veldhoven, The Netherlands; ph 31/40-268-3319; fax 31/40-268-4550, e-mail [email protected].
Ton Kiers, Peter Vanoppen, Jeroen Meessen, Frans Blok, ASML, Veldhoven, The Netherlands
Mircea Dusa, ASML, Technical Development Centre US, Santa Clara, California
Stephanie Kremer received her BSc honors in physics and chemistry from Oxford U. and is an applications engineer in the areas of thin films and scatterometry at KLA-Tencor, 160 Rio Robles, San Jose, CA 95134.
This article is based on a paper that was originally presented at the SPIE 2004 Microlithography Conference (Metrology, Inspection, and Process Control for Microlithography XVIII, Proc. SPIE, Vol. 5375, pp. 1254-1264). Reprinted with permission from SPIE.