Specifying and evaluating thin-film metrology tools
06/01/1999
Thin-film metrology, crucial to semiconductor manufacturing, requires clear understanding of the definitions used within the context of individual applications. Together, precision, repeatability, and stability, when properly specified and evaluated, provide a fairly broad characterization of thin-film metrology tools. A metrology system may work well in production when meeting all the requirements for these parameters.
In many cases, thin-film metrology tool vendors and IC manufacturers use different terms to describe similar metrology characteristics, creating confusion among users. One approach, for example, is to unify metrology system characteristics with statistics [1]. This, however, is not sufficient because definition and application should be based on an understanding of the whole measurement process.
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By definition, optical thin-film measurements are not direct. To obtain correct and consistent results, optical effects, such as spectrum or polarization changes, must be measured accurately, and the film thickness calculation must be performed with an adequate optical model. The "interpretation" model may be much more significant for accurate thickness measurements than measurement accuracy.
Consider that an advanced metrology tool cycle consists of several operations that can affect the accuracy of measured optical parameters. These include positioning, alignment, focusing, transformation of light intensity into electrical signals, signal amplification and digitization, and calibration. Our view is that thin-film thickness measurement tools should be specified and evaluated in terms of precision, repeatability, stability, and accuracy.
Precision
Precision characterizes the statistical probability of measuring a true value of meaningful signal in the presence of stochastic noise. It is evaluated by multiple measurements in invariable conditions (e.g., 30 measurements on the same test site without changing tool setup and conditions, such as motion, focus, and amplification).
Assuming Gaussian noise, the measured value (x) is within the interval m+2s with a probability of ~95%, where m is the mean value and s the standard deviation of 30 measurements. Percent precision is defined as s/m x 100 and characterizes the capability of a measurement tool to carry out repeatable measurements. Precision depends directly on the signal-to-noise ratio (SNR) of the measurement tool (see figure). High precision is a necessary condition for any measurement, but it is not totally sufficient because other factors such as positioning accuracy and long-term stability can also affect measured values.
Repeatability
Repeatability characterizes the capability of a metrology tool to perform correct thickness measurements under varying conditions. It depends mainly on precision and positioning, focus, and calibration accuracy. Repeatability is usually determined in terms of statistical deviation of the measured thickness with multiple cycles of wafer loading, measurement, and unloading.
Repeatability evaluation depends on measurement conditions including uniformity of the measured film within the test-site and the ratio between measurement-spot size and test-site size (Table 1). The same precision and positioning accuracy may yield high values of repeatability for a uniform monitor wafer and low values for a patterned wafer, where the test-site area is similar to the measurement-spot size or the film within the test area is not uniform.
Even when a test site is small, the measured thin film may not be uniform, especially after chemical mechanical planarization. So, a single micron positioning error may cause unfavorable repeatability results. Preferably, repeatability tests should be performed on wafers with uniformly deposited layers, rather than on wafers after removal processes.
Stability
Stability describes a metrology tool`s ability to provide the same results from a wafer for a long period under the same recipe and setup conditions; in effect, stability is repeatability measured over time (e.g., three times a day, every day, for one week).
To exclude effects of test-site material instability and nonuniformity in stability measurements, it is necessary to use simple and stable structures, such as thick oxides on silicon after deposition, and to perform measurements on test sites at least several times larger than the measurement spot.
In stability testing, we assume the measured film is much more stable than the test system itself. However, even stable material such as SiO2 exposed to atmosphere and humidity may change its index of refraction and thickness by several angstroms from reversible hydrolysis [2]. In our lab, when evaluating the stability of interlayer dielectric oxides that were several angstroms thick (measured in water), we found thickness changes of several tens of angstroms over relatively long periods (these changes were greater for BPSG oxides than for TEOS oxides). Indeed, it is hard to find a sample for a stability test that provides thickness stability or even surface stability on the molecular level.
Interpretation of optical results
As noted above, optical metrology methods are indirect; thin-film measurements are an interpretation of optical parameters such as spectral reflectance or polarization change. Interpretation applies an optical model of the measured thin-film structure and the theory describing the interaction of light with the layers, each having different optical properties.
The optical model is usually a set of individual transparent layers between a semi-infinite (for analyzing wavelengths) substrate and ambient (Table 2). Each material in this structure is described by a complex index of refraction ñ = n - ik, where n is the index of refraction, i is checkmark-1, and k the extinction coefficient; this characterizes light refraction and absorption in the particular layer. If a spectral range is used as in spectrophotometry, n and k have to be defined as spectral functions in the measurement range via Cauchy coefficients [3] or other parameters. Spectral dispersion of some layers cannot be fitted to Cauchy equations, so they are usually presented in a table of n-and-k vs a number of wavelengths.
Interpretation theory is usually based on Fresnel equations for reflection on a specular surface, defining amplitude and phase of the electrical vector for p- and s-polarizations of the wavelength reflected from the boundary between two media with different values of ñ. Interpretation matches measurement results with theoretical results obtained for a given optical model by calculation with Fresnel equations. Matching is also called goodness of fit or the normalized difference between the two results, which is a quantitative criterion.
If the optical model is correct, if the interpretation theory is adequate, and if the fitting is confident, the film thickness obtained is considered accurate. Understanding all these "ifs" helps in understanding "accuracy." Consider the optical model of the multi layer stack in Table 2, which is typical for film-thickness measurements in semiconductor manufacturing. Several assumptions in this model simplify the interpretation process, but do not necessarily reflect the actual situation. These assumptions include that all layers are optically uniform through layer thickness and within the measurement spot; all boundaries are abrupt (i.e., step functions with no graded layers); Cauchy coefficients accurately describe the actual dispersion of a given material; and each layer in the measured stack has the same optical properties as the optical model.
The situation with interpretation theory is similar. For example, commonly used theory does not consider effects such as light scattering, partial polarization in case of spectrophotometry, actual spectral range and numerical aperture of light beam in case of ellipsometry, and other secondary effects that to some extent can have an impact.
To achieve better accuracy, we need a more sophisticated and detailed optical-modeling-and-interpretation theory. Since this is not simple, we have to look for a more practical way to evaluate the accuracy of a metrology system.
Accuracy
Accuracy can be defined as the degree of confidence of measurement results. It can be obtained by comparing a measurement with a scanning electron microscopy (SEM) cross-section (the most accurate metrology tool available today) or measuring a film thickness standard. The latter is simple and allows us to obtain the same measurement results on all metrology tools in a wafer fab. In practice, this method is far from perfect, however. Consider a typical film-thickness standard (Table 3). Despite obtaining very accurate measurement with a well-calibrated ellipsometer, the actual thickness value still de pends on the optical model: if the index of refraction is taken as 1.46, the oxide thickness is 6683Å. But if the index of refraction is calculated as 1.468, the thickness is 6626Å. The 57Å difference is greater than the estimated measurement error of 15Å (+1.5nm in Table 3).
Which result is actually true? No one knows. In addition, this calibration data is accurate for either of the two index of refraction values when using an ellipsometer with the same wavelength; but what about metrology with a different tool? There is no easy solution.
The definition of the accuracy for more complex layer structures is much more problematic. For example, different metrology tools may provide the same value for the thickness standard (a silicon dioxide layer on silicon), but very different results for the structure in Table 2. None of these systems can be defined as a reference tool, since the actual top layer thickness in this structure is not known.
This problem may be approached using film thickness standards certified by more accurate methods, such as atomic force microscopy or SEM and applied to actual multilayer structures, not just a SiO2-Si structure.
Interpretation of multilayer stacks
State-of-the-art metrology tools also need to cope with a variety of applications, which may be fairly difficult for optical measurements. Consider for example SiO2/poly/SiO2/Si, SiO2/Si3N4/SiO2/Si, SiO2/TiN/Ti/Al, and SiO2/TiN/WSi/SiO2/ poly/Si stacks. Most stacks are characterized, from the thickness measurement perspective, by two common features:
A current trend with thin-film metrology tools is to obtain more variables in each single measurement in order to provide simultaneous calculations of several unknown variables. Popular methods include spectrophotometry and spectral ellipsometry (i.e., measurement of reflectance or ellipsometric parameters for a number of wavelengths) [4], focused beam ellipsometry [5], and beam-profile reflectometry [6].
This trend assumes that more measured parameters are able to provide more unknown variables of the optical model that can be simultaneously calculated. But this concept might have some inherent problems of interpretation:
Based on long-term experience in thin-film metrology and in semiconductor manufacturing, we believe that the best approach for reliable metrology in production is a reduction in unknown variables to two or three. It is also important that chosen variables will differently affect the measured parameters, regardless of the measurement technique used for both spectrophotometry and ellipsometry.
There is no common solution to reach this goal; combining applied algorithms for interpretation and handling information available from processing will lead us in the right direction. We strongly believe that only close cooperation between process engineers and experts in thin-film metrology will provide the right solution for any application.
Conclusion
Precision is an important feature defining the potential capability of a metrology tool, but it does not prove anything about its compatibility to end-users` needs. Repeatability depends both on the metrology tool itself and on the size and uniformity of the measured test sites. When evaluating stability, it is important that the chosen measured object be much more stable that the metrology tool itself.
An inadequate optical model, applied in actual film thickness measurements for data interpretation, may cause a greater error of absolute thickness than the combined errors of the metrology tool. Currently, film thickness accuracy may be defined for a SiO2-Si structure only and for thickness ranges in which NIST-traceable standards exist. When deciding on a simultaneous calculation of two or three unknowns, one must consider that the accuracy of both the metrology tool and the optical model is limited, and the interpretation of the measured results may be problematic.
Acknowledgments
The author thanks David Scheiner and Gregory Guntzberg for providing measurement results, Giora Dishon for useful discussions, and Regula Alon for editing help.
References
References
1. R.J. Elias, "Statistical Process Control for Semiconductor Metrology Systems," Semiconductor International, p. 167, October 1996.
2. G. Hoffman, et al., "Optical investigation of the Si-SiO2 system, Acta Phys. Acad. Sci. Hung., V. 36, N4, p. 349, 1974.
3. W.A. Pliskin, "Refractive index dispersion of dielectric films used in semiconductor industry," J. Electrochem. Soc., p. 2820, Nov. 1987.
4. J.J. Estabil, M. Keefer, "A combined spectroscopic ellipsometer and spectrophotometer," Solid State Technology, p. 71, April 1995.
5. M. Haller, et al., "Multidomain ellipsometry for thin-film process control," Semiconductor International, p. 269, July 1998.
6. J.T. Fanton, et al., "Multiparameter measurements of thin films using beam-profile reflectometry," J. Appl. Phys., 73 (11), p. 7035, 1993.
Moshe Finarov received his PhD in semiconductor physics from the Technical University in Moscow. Over the last 20 years, he has held R&D positions in development of metrology and inspection equipment for the semiconductor, PCB, and LCD industries, publishing more than 50 papers. Finarov is director of technology and co-founder of Nova Measuring Instruments, Ltd., Weizmann Science Park, Rehovoth 76100, Israel; e-mail [email protected].