integrated ODP metrology with floating n&k’s
06/01/2009
One of the major contributions to the optical critical dimensions metrology uncertainty is the variations in optical properties (n&k’s) of film stack materials. It is wellknown that the optical properties of materials depend heavily on process conditions, such as operating conditions of deposition tools. However, in traditional approaches, n&k values have been used as fixed inputs in a scatterometry model that might result in significant metrology error. We describe an integrated scatterometry system used in a real production environment.
Patrick Kearney, Junichi Uchida, Tokyo Electron Europe Limited, Dresden, Germany; Dmitriy Likhachev, Timbre Technologies, Santa Clara, CA USA; Göran Fleischer, Qimonda, Dresden Germany
Advanced DRAM manufacturing demands rigorous, tight process control using high measurement precision and accurate, traceable, highthroughput metrology solutions. Scatterometry is one of the advanced metrology techniques that satisfies these requirements, and has been implemented in semiconductor manufacturing for some time for monitoring and controlling critical dimensions and other important structural parameters.
A significant improvement in CD data accuracy was achieved following implementation of a new floating n&k’s option for the optical digital profilometry (ODP) system. To achieve desired subnm accuracy in scatterometry measurements for advanced processes, we must pay scrupulous attention to every detail of the scatterometry modeling and measurement. Further work is needed to better understand the impact of n&k’s variations on tooltotool matching.
Methodology
Data was collected using a TEL Compact Critical Dimension integrated Reflectometer (CCDi) at the Qimonda 300mm fab in Dresden. The CCDi with the integrated Profiler Application Server (PAS) is called iODP. TEL ODP 2006EP Timbre software was used to model the structures and to float the n&k’s of several materials in the stack.
The CDSEM data will be used as reference metrology. This brought the challenge of matching two different measurement tools and matching data from different sampling plans and different measurement points, both on the structure and on the wafer. To this end, we derived an ODP function that finds the best height on the structure and adds the corresponding slope and offset to match with the CDSEM.
Scatterometry has been an industry standard for years While there have been many applications where fixed n&ks were used, scatterometry is still sensitive to changes in the underlying layers. This often leads to problems when correlating data to reference metrology, as imagebased metrology is independent to these changes. Increasingly, studies have shown the influence of n&k variation in higher technology nodes [13]. By using the floating n&k feature in ODP 2006EP to better characterize the changes in the underlying layers, we produced more accurate CD outputs that correlate better with reference metrology.
In this advanced litho DRAM application, implementation of floating n&k’s for the Material 3 layer was absolutely necessary. A pragmatic approach for matching to CDSEM and thereby bringing about the timely implementation of ODP data into production is also shown.
Floating n&k feature
Structures on a semiconductor wafer can be measured using scatterometry tools such as reflectometers and ellipsometers. The measured diffraction signal is used to determine the properties and profile of the structure. In scatterometry, the accuracy of a model (with regard to the data it generates) is a very important consideration [4].
One of the most important input parameters for the diffraction models are the optical properties of materials being used (i.e., the n&k’s). In the traditional scatterometry approach, the optical functions (n&k’s) of film stacks have been used as fixed inputs in a scatterometry model; therefore, the process engineers have to assume that there is no significant impact on measurement results by small deviation from preextracted n&k’s. However, the n&k’s of many materials on actual production wafers will always vary from the fixed values used in the model. These variations can significantly affect scatterometry results. [1,2]
Variable n&k’s is an advanced software feature. If there is a material anticipated to have some variations in the optical properties, the n&k values can be modeled (with some floating parameters) in the software. Then this model can be used as the material for one or more layers in the scatterometry model. Currently, the ODP 2006EP software includes multiple dispersion models that can be applied to model the optical properties of most of the materials used in current semiconductor production.
Figure 1. The n&k dispersion model setup in ODP 2006EP. The information is for material 3. 
For this study the TaucLorentz (TL) dispersion model [5,6] was selected.

Here, ε_{2}(E) is the imaginary part of the complex dielectric function, A is the oscillator’s amplitude, E_{0} is the energy of the Lorentz peak, Γ is the broadening parameter, E_{g} is the band gap, θ(E  E_{g}) is the Heaviside step function. The real part of the TL dielectric function is obtained by performing a KramersKronig integration of ε_{2}(E). Although the TL optical model is still an empirical relation (since there is no generally acceptable theoretical explanation), it has multiple advantages and was used successfully for various amorphous semiconductors. We used four oscillators in the TL model and floated the 0)A parameter, which corresponds to the amplitude of the first oscillator (Fig. 1). This parameter had highest sensitivity to the n&k variations we observed in our study.
Although it is possible to vary more than one parameter within the TL dispersion model, this can lead to a multipleparameter correlation issue. For this application, we found that it was not necessary to float any more parameters in the dispersion formula.
Matching to CDSEM
We used a combination of scatterometry data and reference data from CDSEM. This means that, regardless of which system is more accurate or precise, the scatterometry data have to correlate well with the reference metrology data. After a scatterometry library is built, the conventional method for implementing into production is:
 Pick one production wafer;
 Measure the wafer on a CDSEM and all the scatterometry tools in the fab;
 Calculate wafer mean CD for each of the tools;
 Calculate offset from CDSEM and each scatterometry tool;
 Apply the offset to the scatterometry library recipe.
The drawbacks with this procedure include: a single production wafer does not represent the population of wafer data; the value that the CDSEM reports as bottom or top CD may be measured at a different height on the structure from scatterometry’s bottom and top CD’s (e.g., CDSEM bottom CD may correlate better with scatterometry middle CD); there is no allowance for slope between the data sets; and the data is matched on a point to point comparison, whereas in production we match lot averages.
Therefore, for this implementation, we derived a new pragmatic approach for matching to CDSEM called “ODPfunction” (ODPf). The ODPfunction concept is to use production data >100 lots (more statistically robust); do the correlation using a moving average (MA) of 5 lots; use a combination of slope and offset (although slope is not a new concept we did not implement it with offset as standard practice); and find the grating height at which the best correlation can be achieved.
ODPf calculations
The formula for best height CD(x) can be expressed in a simple linear function:
In ODP, the top CD (TCD) is calculated as the average CD from a height of 80100% on the structure, and is therefore the CD at 90% height (assuming a trapezoid profile). Similarly, the bottom CD (BCD) is calculated at a height of 0???20% on the structure and is, therefore, the average CD at 10% height.
We can then express TCD and BCD in terms of a & b:

From equations 3 and 4 we can derive new equations 5 and 6:

By inserting equations 5 and 6 into equation 2 we can express the equation for best height as:

We can use another linear function to match the ODP data to CDSEM data:

Here c0 is the offset between ODP and CDSEM and c1 is the slope. If we then substitute equation 7 into 8 we get the following expression:

We then entered this formula along with the data from SEM and ODP into a thirdparty statistical software package JMP. JMP converges the data to find the best matching height, offset, and slope. These parameters are entered into the TEL PAS so that the scatterometry production measurements can begin.
Experimental results
The litho grating structure. The application under study consists of repeated lines and spaces of photo resist on a stack of unpatterned materials. Resist pitch was usual for litho; line space ratio was 1:1.
A process called additive or progressive stack n&k extraction has to be performed on each of the materials before ODP modeling can begin. With additive stack n&k extraction, each material has blanket wafer made and measured on standalone spectroscopic ellipsometer (SE) such as Woollam’s M2000 or KLATencor’s ASETF5. From these measurements, the n&k dispersion tables were derived (fixed n&k’s). With these tables, several assumptions generally are made, such as n&k’s remain constant across the wafer; n&k’s remain constant from wafer to wafer; and the n&k’s remain constant from lottolot (and tooltotool).
For some materials, these assumptions are valid (simple oxides like SiO_{2}, stoichiometric silicon nitride Si3N4, undoped crystalline Si). However, for most materials, the optical properties are not as stable and depend on multiple factors (such as deposition conditions and techniques, material composition, mechanical conditions, film thickness, temperature, etc.) and this can lead to essential errors in the CD measurements if the fixed n&k’s are used.
ODP 2006EP model selection
There are several analytical tools within the ODP 2006EP software that help determine the best model for the application. The Libre tool will supply correlation coefficients for the parameters used and give information on whether the model is stable or not, and hardware precision numbers. We used Libre along with other analytical tools to compare models that had both floating and fixed n&k’s for stability. The correlation tables showed that the largest correlation coefficient for the fixed n&k model was 0.8722 between resist and material 3 thicknesses. And the largest correlation coefficient for the floated n&k model was 0.8809 between material 4 and material 3 thicknesses. Even though this may indicate a disadvantage to the floating n&k model, the correlation numbers are very similar and below the recommended limit value of 0.95. For both models the correlation tables show good results.

Hardware precision (HP) 3 sigma information is also provided. HP is a calculation of uncertainty in parameter value due to system noise. These numbers generally should be <1.0nm for each parameter. From Tables 1 and 2, both the fixed and the floating models show HP numbers below 1.0nm, indicating that both models are stable. The fixed has slightly lower numbers; however, the values are comparable.

One other thing to look for in the HP numbers is that no one parameter has a value that is one order of magnitude different from the other parameters. This would indicate that the parameter in question was too sensitive and its spectral signal too big, potentially masking the sensitivity of the other parameters. However, in the fixed and floating models, this does not occur, indicating stability.
The precision numbers calculated in Libre were derived from regressions, but there are also precision and error calculations made when the libraries are generated. The precision numbers for both models are below 1nm and are comparable with each other. Similar to the Libre precision numbers, this indicates that the libraries are stable. Also the error numbers for the libraries are relatively low. Both the fixed and floating n&k libraries show the error values below 1nm. This indicates that both libraries are stable.
Figure 2. The GOF difference between floating and fixed n&k models. 
Further data on the stability of the model is seen in the goodness of fit (GOF). With GOF, the closer the number is to 1, the better the fit between measured and calculated spectra. The floating n&k model consistently produces a higher GOF than the fixed one (Fig.2).
This is not surprising, as the floating n&k model has an extra degree of freedom with which to fit. Even though the floating n&k model does have a higher GOF, the GOF Δ is relatively small (average Δ =0.00072). However, if we look at plots of the regressions, we can clearly see that the improvement in fitting happens over a relatively large part of the wavelength range. This increases the chances of affecting sensitive regions of the spectra. There is only one main region where the fixed n&k model fits better: 890???920nm. However, this gain is relatively small when compared to the floating n&k model.
Comparison with reference metrology
The error and precision and correlation data show that both models are stable. Also, the GOF data shows a slight advantage to the floating n&k model. However, the real acid test is how well the libraries correlate with the reference metrology (CDSEM). In our first comparison we looked at 31 wafers with 7pts measurements on each wafer for ODP. After processing the raw spectra through the fixed and floating n&k libraries, the average of each wafer was calculated. Each wafer was also measured by the CDSEM and the wafer average was taken. This data was then processed using

and JMP software. Because of a lack of variation in the sample data, we fixed the c1 value to 1.
Figure 3. Residual CDs for the floating and fixed n&k’s libraries. 
The ODPfunction coefficients between floating and fixed n&k models are very similar, with the best height around the middle CD (51% from the bottom). In both cases, the offset is ~15.6xx nm. The ODPfunction CDs were then compared to CDSEM in a 5pts moving average. In actual production, the data that is fed to the dose controller that looks at it over a moving average based over several lots. For this reason, we used a moving average method over 5 lots to compare the two libraries’ outputs. The data in Fig. 3 are the residuals between the CDSEM output and the ODPfunction outputs. From this plot we can see that floating n&k library is matching better to the CDSEM data than the fixed. We can see an improvement in 3s of 0.2775nm in the floating n&k library.
Figure 4. Tool A MA matching (CDSEM & ODPf). 
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Implementation into production
To implement the ODP function, we must calculate separate coefficients for each tool. Also, in the new set of data we compare lot averages as opposed to wafer averages shown previously. The comparison of CDSEM data with the ODP functions over a 5 lot moving average are shown in Figs. 4 and 5. Both tools show reasonable outputs for matching to CDSEM. Tool A results show a significant improvement over tool B, with several possible causes: sample size too small, different hardware, scanner, track, metrology, etc. Even though there is this difference, the 3s numbers are reasonable for both tools.
Figure 5. Tool B MA matching (CDSEM & ODPf). 
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Conclusion
The results led to the assertion that using the floating n&k feature in ODP 2006EP can significantly improve matching to CDSEM while maintaining model stability. By implementing the ODP function, we were able to match the ODP data at the best height with slope and offset coefficients. The ODP function along with floating n&k’s offers a more robust and faster method of matching to reference metrology, and thus opens the way for production monitoring and control.
Acknowledgments
The authors thank Dr. Youxian Wen at Timbre Technologies and Heiko Weichert and Sebastien Egret at Tokyo Electron Europe. ODP is a trademark of Tokyo Electron Limited. ASETF5 is a trademark of KLATencor Corporation. M2000 is a trademark of Woollam.
References
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Patrick Kearney may be reached at Tokyo Electron Europe Limited, German Branch, Moritzburger Weg 67, 01109 Dresden, Germany; ph. +49 35188385867; Patrick.Kearney@tel.com.