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Using optical metrology to monitor low-k dielectric thin films

Feng Yang and William A. McGahan, Nanometrics; and Carol E. Mohler and Lisa M. Booms, Dow Chemical

Because controlling curing temperature and time is critical for producing high-quality spin-on dielectric thin films, rapid feedback from metrology tests on thermal process tools is needed to correct tool drift .

As device features of ULSI circuits continue to shrink, the capacitance of the interlevel dielectric (ILD) material becomes an increasingly limiting factor on the overall performance of these chips. An industrywide effort is under way to search for a next-generation low-k ILD material to replace traditional silicon dioxide. Many potential low-k materials belong either to the inorganic polymer family (e.g., organosilicates) or the organic polymer family.^1,2 The molecular structure of the cross-link network in these polymers is critical because it affects their electrical, thermal, and mechanical properties as well as their optical properties, such as index of refraction (n) and extinction coefficient (k). Because n and k values depend both on the electronic structure of a polymer and on its porosity, they can serve as good indicators for monitoring low-k polymer formation.

One low-k ILD material is SiLK from Dow Chemical (Midland, MI), a spin-on organic polymer that can be readily deposited using a conventional spin-coater. This dielectric thin film in its as-deposited state must undergo a thermal curing process to form a desired polymer structure and to achieve correct mechanical, thermal, and electrical properties. The curing process takes place at temperatures between 400° and 450°C in standard thermal-processing equipment (furnaces, ovens, or hot-plates). The cured resins have a dielectric constant of 2.65 and can withstand temperatures as high as 490°C. Their high thermal stability permits integration with current multilevel interconnect processes. However, because the polymerization of these resins is thermally activated, controlling the curing temperature and time is critical to producing high-quality cured films.^3,4 Thus, it is essential to have immediate feedback from metrology tests on thermal process tools to detect and correct tool drift promptly. This article discusses optical metrology methods for monitoring cured low-k dielectric thin films.

Thin-Film Optical Metrology

One of the most important advantages of optical metrology arises from its nondestructive nature, which permits measurements on product wafers and active device areas. In-line optical metrology can monitor the performance of thermal processing equipment by conducting real-time measurements on product wafers, thus eliminating monitor wafers and minimizing rework or loss of product wafers as a result of out-of-control equipment.

Thin-film optical metrology provides fast and precise real-time measurements of thin-film thicknesses and optical constants. In semiconductor manufacturing, spectroscopic reflectometry and ellipsometry are widely used optical metrology methods for measuring these parameters in-line. Thin-film metrology tools measure the reflectance or ellipsometric spectrum of thin films and extract values of thicknesses or optical constants.

Because there are a maximum of two independent optical measurement data ( and in spectroscopic ellipsometry) at each wavelength (), the maximum number of unknowns that can be determined in the whole spectrum is 2W (where W is the number of wavelengths). Materials with finite light absorption have two unknowns (n and k) at each wavelength and one additional unknown in the film thickness. Therefore, the total number of unknowns is double the number of wavelengths plus one--that is, 2W + 1. Because the number of unknowns resulting from 2W + 1 is at least one too many to be determined from available spectroscopic ellipsometry or spectroscopic reflectometry data, it is necessary to employ a dispersion model, which describes the functional dependence of n's and k's on wavelength based on N fit parameters. Therefore, the total number of unknowns becomes N + 1. As long as 2W N + 1, film thickness and optical constants can be determined simultaneously by numerically iterating N + 1 variables to fit spectra.

The results of the research discussed in this article on the use of optical metrology to monitor a low-k resin–curing process demonstrate that with a correct dispersion model, the n(), k(), and thickness values for a dielectric thin film can be determined from reflectance measurements. In the ultraviolet (UV) spectral region, the refractive indices values (RIs), or n()s, are found to correlate to the curing conditions. By measuring the variation of n, the degree of curing in the resin can be monitored. For example, at a wavelength of 314 nm, the RIs of dielectric thin films change systematically with the curing parameters of temperature and time.

Based on the relationship between the optical constants of resins and their curing parameters, a single-parameter empirical interpolation model for resin optical constants was developed. With this interpolation model, the curing of the resins can be readily monitored with an automated thin-film optical metrology tool that provides prompt feedback on the condition of the thermal processing equipment.

Sample Preparation and Instrumentation

For this study, a matrix of SiLK-I dielectric thin-film samples was prepared by varying the curing temperature and time. First, a spin-on process deposited resins on bare silicon wafers, which then went through a hard bake step at 310°C for 90 seconds and were subsequently cured on hot plates in a nitrogen ambient. The curing temperature varied from 400° to 470°C and the curing time from 30 to 360 seconds. The sample thicknesses were approximately 7400 Å.

To determine the optical constants n() and k() of these samples, a variable-angle spectroscopic ellipsometer (VASE) from J. A. Woollam (Lincoln, NE) was used.⁵ A very powerful off-line analysis instrument for the characterization of the optical properties of thin films, this instrument utilizes a monochrometer to control incident light wavelength so that only the light of a single wavelength is incident onto the sample during each measurement.⁶ It measures two ellipsometric data at each wavelength, and , and completes the spectrum by scanning through all wavelengths. This way, the measured and spectra truly represent the spectroscopic response of the sample. If a thin film's thickness is known, its n () and k() can be accurately determined by direct calculation from and values.

In general, organic polymers are transparent or nearly transparent in the visible spectral region, from which their thicknesses can be extracted by fitting that part of a spectrum using a Cauchy dispersion formula. Their complicated optical constant response in the UV spectral region can then be determined directly from and spectra.⁷ By choosing an appropriate dispersion model for the optical constants, the complicated n and k spectra from the VASE measurement results were parameterized. The production worthiness of the parametric dispersion model was tested by running it on a NanoSpec 8000XSE high-throughput thin-film metrology tool from Nanometrics (Sunnyvale, CA). This tool determines thickness values and the n's and k's of thin films by measuring and fitting spectroscopic reflectance spectra, spectroscopic ellipsometric spectra, or a combination of both. Its modeling capability and data-fitting algorithm enable the analysis of data from a wide range of materials and layered structures while simultaneously determining thickness and optical constants.⁸

Single-Parameter Empirical Interpolation

Using the VASE measurements, a spectral window between 280 and 340 nm was found where the RIs of the thin-film samples changed monotonically with cure temperature and time. Figure 1 shows the measurements for UV spectra only. In the visible-wavelength region, RI variation was not significant. As demonstrated in both Figures 1a and 1b, sensitivity to the curing parameters of time and temperature was highest at a wavelength of 314 nm. The total magnitude of the RI change was 0.065 at this wavelength. Figure 2 plots RI for all test samples at 314 nm, denoted as n(314 nm). Since the n(314 nm) value decreased when either the curing time or temperature was increased, the n(314 nm) variation can serve as an indicator of the degree of curing in the dielectric thin film. The reduction in the n(314 nm) value decreased as the temperature or time approached the high end of the curing process window, indicating that the curing process was nearly completed. After determining the correlation between curing parameters and optical constants, a single-parameter empirical interpolation model could be employed.

 

Figure 1: VASE measurements of the ultraviolet RIs of low-k resins cured under different conditions: (a) cure-time dependence; (b) cure-temperature dependence.

Figure 2: VASE measurements of RIs at 314 nm at different curing times and temperatures.

In a process-sensitive thin film, process parameter variations can lead to changes in the film's n() and k() values. That is the case for the cured resins investigated in this study. Monitoring the degree of curing in these dielectric thin films on an automated metrology tool requires a parametric dispersion model for the optical constants of these resins, which represents the functional dependence of n() and k() on in terms of a small number of adjustable parameters. This model should be able to describe the n() and k() of these resins cured under all conditions within the whole process window.

An empirical interpolation model is an effective single-parameter dispersion model whose adjustable parameter normally corresponds to a process-dependent physical property (e.g., the crystallinity of polysilicon or the alloy fraction ratio of SiGe).⁹ It consists of a database of optical constant spectra for a given material. Each spectrum corresponds to a specific process condition. When fitting reflectance or ellipsometry data of a sample prepared under unknown conditions (within the process window), the sample's optical constants are interpolated between known spectra in the database. With only one adjustable parameter, the correlation between thickness and optical constants can be minimized during data analysis.

To develop an empirical interpolation model for these low-k resins, optical constant spectra of five samples cured under different conditions were chosen. The n(314 nm) values of these samples, which are presented in Table I, were evenly distributed between the lowest and highest values in the process window. The term cure index was used to refer to the adjustable parameter in the model. A cure index value of 0 was assigned to the uncured sample, which had the highest n(314 nm) value, while an index of 1 was assigned to the cured sample with the lowest n(314 nm) value. The other three cured samples were evenly spaced between the samples with the highest and lowest n(314 nm) values. The cure indices were determined by proportioning the n(314 nm) values of the five samples between 0 and 1 as follows:

Cure index = [n(314 nm) – 1.9791]/[1.9161–1.9791]

Automated Production Metrology

The empirical interpolation model for low-k resins was tested on the automated thin-film metrology tool. Using the tool's reflectometer mode, both film thickness and optical constants were determined from a recipe set up to measure absolute UV-visible reflectance.¹⁰ Figure 3, which presents a reflectance scan-and-fit result based on the empirical interpolation model, shows an excellent match between the experiment and the model. To become production worthy, however, the metrology method must demonstrate high levels of precision, stability, accuracy, sensitivity, and throughput.

 

Figure 3: Fit result of reflectance data from low-k resin treated at 400°C for 300 seconds shows an excellent match between the experiment and the model.

The measurement precision and dynamic stability of the metrology tool were tested by examining several wafer samples that had varying film thicknesses or had been cured under different conditions. One of the worst cases was a 1000-Å-thick resin sample that was loaded 10 times and measured in five places at each load (one at the center and four around the edge). The results revealed that the standard deviation of n(314 nm) for 10 loads at each site was <0.001 and that the variation of the average value of n(314 nm) for five sites was also <0.001 from load to load. Since the uncertainty was <2% of the total range of the variation in n(314 nm) that may be induced by curing (about 0.063), it was concluded that this measurement technique provides sufficient precision and stability to monitor the curing process of these low-k resins. Table II lists the statistical results of the average thickness and n(314 nm) of each load.

 

Mean Standard Deviation Thickness (Å) 1064.8 1.14 n(314 nm) 1.929 <0.001

Table II: Statistical test results from a worst-case 1000-Å-thick sample that was loaded 10 times and measured at five places after each load.

By comparing n(314 nm) values measured by the automated in-line tool to the benchmark values from the VASE measurement, measurement accuracy could be evaluated. Figure 4 shows that the data points fit a straight line with a slope of 0.9788 and a y-intercept of 0.0441, indicating excellent correlation between the two types of measurements. This close match demonstrates that the refractive index measurements using the reflectometry mode of the in-line tool were accurate for monitoring the curing process.

 

Figure 4: Correlation between RI at 314 nm measured by the VASE and the automated metrology tool shows an excellent match between the two types of measurements.

The model's sensitivity to the curing process as well as the feasibility of determining the film thickness and optical constants simultaneously are seen in Figure 5, which plots three model-predicted reflectance spectra corresponding to three cure conditions: 30 seconds at 410°C, 30 seconds at 420°C, and 60 seconds at 420°C. All three spectra were generated based on the same thickness value of 7400 Å. The difference between the spectra is strictly a result of the difference in the degree of cure. Figure 5 clearly demonstrates that there is a significant difference among these spectra in the UV spectral region (between 310 and 400 nm), which can be readily measured by a reflectometer. Film thickness information, on the other hand, can be found in the period of the oscillating portion of the reflectance spectrum. By fitting a broadband UV-visible reflectance spectrum, film thickness can be measured quickly and reliably, and the cure-induced change in the resins can be monitored.

 

Figure 5: Reflectance sensitivity predicted by the empirical interpolation model for low-k resins under three different cure conditions; the difference between the spectra is a result of the difference in the degree of cure.

Measurement throughput depends on the speed of reflectometer data acquisition and analysis, as well as the focusing speed of the sample stage (e.g., the system's robotics). To boost the UV signal-to-noise ratio, a broadband measurement requires longer detector integration time than a visible reflectance measurement, leading to decreased throughput. The metrology tool used in this study performed measurements at five sites on an 8-in. wafer in approximately 1 minute with focusing on each site. New-generation spectrophotometer heads, robotics, and data-handling software are in the final testing stages, promising much improvement in measurement throughput.

Conclusion

In order to serve as adequate low-k ILD materials, organic spin-on polymers must be properly cured. In-line characterization of the curing process is crucial because it improves equipment efficiency, eliminates the need for monitor wafers, and reduces wafer scrap and wasted work. The curing process of low-k resins can be monitored with broadband reflectometry, and film thickness and the degree of curing can be calculated simultaneously. Because of its fine measurement spot size and pattern recognition capability, this technique can be used to monitor the curing process of low-k thin films on product wafers. The method described here for monitoring SiLK should be applicable to other low-k materials if the change in the optical constants induced by polymerization is monotonically related to the process parameter and the metrology tool is sensitive enough to measure the change in optical constants. Additonal studies must be performed to determine the feasibility of performing metrology measurements on product wafers with device structures and the efficacy of using integrated in-line metrology tools.

Acknowledgment

Portions of the material covered in this article were first presented at the Advanced Metallization Conference in Orlando, FL, September 28–30, 1999.

References

1. NH Hendricks, "The Status of Low-k Materials Development," in Proceedings of the Sixth International Dielectrics for ULSI Multilevel Interconnection Conference (Tampa, FL: IMIC, 2000), 17–26.
2. W Volksen et al., "Characterization of Porous Organosilicates for On-Chip Applications," in Proceedings of the Sixth International Dielectrics for ULSI Multilevel Interconnection Conference (Tampa, FL: IMIC, 2000), 67–76.
3. PH Townsend et al., "SiLK Polymer Coating with Low Dielectric Constant and High Thermal Stability for ULSI Interlayer Dielectric," in Proceedings of the Materials Research Society 476 (Warrendale, PA: Materials Research Society, 1997), 9–17.
4. S Allada, "Low K Adhesion Issues in Cu/Low K Integration," in Proceedings of the Second International Interconnect Technology Conference (1999), 161.
5. F Yang et al., "Investigation of Thermal Curing of an Organic Low-k Spin-On Dielectric by Variable-Angle Spectroscopic Ellipsometry" (paper presented at the 46th International Symposium of the American Vacuum Society, Seattle, October 25–28, 1999).
6. JA Woollam and PG Snyder, "Fundamentals and Applications of Variable Angle Spectroscopic Ellipsometry," Materials Science and Engineering B5 (1990): 279–283.
7. F Yang, M Tabet, and WA McGahan, "Characterizing Optical Properties of Red, Green, and Blue Color Filters for Automated Film Thickness Measurement," in Proceedings of SPIE 3332 (Bellingham, WA: International Society for Optical Engineering, 1998), 403–410.
8. WA McGahan et al., "Optical Characterization of TiN Thin Films," in Proceedings of the ASMC 96 (Piscataway, NJ: IEEE, 1996), 359–363.
9. WA McGahan, "Optical Characterization of Polycrystalline Silicon Thin Films," in Proceedings of SPIE 2725 (Bellingham, WA: International Society for Optical Engineering, 1996), 450–459.
10. VJ Coates, U.S. Pat. 5,045,704, 1991.

Feng Yang, PhD, is an applications scientist at Nanometrics in Sunnyvale, CA, specializing in optical data analysis for the development of thin-film metrology applications. Before joining the company, he worked as a staff scientist in the fields of ceramic thin-film deposition and device fabrication at Neocera (Beltsville, MD). He received a PhD in electrical engineering from the State University of New York at Buffalo in 1995. (Yang can be reached at 408/746-1600, ext. 183; or fyang@nanometrics.com.)

William A. McGahan, PhD, is chief scientist at Nanometrics. Before joining the company in 1995, he worked at J. A. Woollam (Lincoln, NE) in the area of development and applications development of spectroscopic ellipsometers. McGahan received BS, MS, and PhD degrees in electrical engineering from the University of Nebraska. He has published 46 papers on ellipsometry, magneto-optics, thermal characterization of materials, and semiconductor metrology; two chapters in textbooks on magneto-optical properties of materials and magneto-optical recording; and recently coauthored Spectroscopic Ellipsometry and Reflectometry with Harland Tompkins. (McGahan can be reached at 408/746-1600, ext. 123, or bmcgahan@nanometrics.com.)

Carol E. Mohler, PhD, is a research leader in the advanced electronics materials laboratory of Dow Chemical (Midland, MI). Since 1990 she has concentrated on the curing and oxidation of polymeric dielectric thin films. She received a BS in chemistry from the University of Michigan in Ann Arbor and a PhD in physical chemistry from the University of Wisconsin in Madison. (Mohler can be reached at 517/636-4770 or mohlerce@dow.com.)

Lisa M. Booms joined the advanced electronics materials laboratory of Dow Chemical in 1998. She is a process engineer supporting research and development of SiLK dielectric resin and supports customers on process issues. She received a BS from Saginaw Valley State University in University Center, MI. (Booms can be reached at 517/636-3667 or lmbooms@dow.com.)

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