Model-based analysis for precise and accurate epitaxial silicon measurements
07/01/1998
Model-based analysis for precise and accurate epitaxial silicon measurements
Sylvie Charpenay, Peter Rosenthal, On-Line Technologies, East Hartford, Connecticut
Gerhart Kneissl, ADE Corporation, Westwood, Massachusetts
Carolyn Hoener Gondran, Howard Huff, SEMATECH, Austin, Texas
New model-based, Fourier transform infrared (FTIR) spectroscopy epitaxial silicon characterization techniques have significantly better accuracy and precision than current techniques. They also provide additional information about the doping profile. The new methods improve precision by a factor of 10, and accuracy by a factor of 2-10, extending the range of epi film characterization below 0.25 ?m. With today`s computers, this technique is fast enough for in-line applications with no degradation of system throughput, allowing for real-time process control.
The current trends in the semiconductor industry toward ever-thinner layers of epitaxial silicon (epi) are exceeding the capabilities of today`s nondestructive metrology techniques. These techniques typically employ infrared reflectivity with empirical (interferometric) thickness extraction algorithms, and perform the measurements off-line. Economics and the demand for increased productivity are driving the need for in-line and in-situ process sensors and control systems that can reduce waste as well as increase manufacturing accuracy through the use of feedback.
Epi wafers such as p/p+ are used instead of prime, polished wafers because of improved gate oxide integrity (GOI) and latch-up suppression. The improved GOI is due to the improved structural perfection of the epitaxial film as compared to residual polishing microdamage and grown-in microdefects in polished wafers such as crystal originated pits. As the technology generation approaches 180 nm, the demand for epi wafers will dramatically increase to meet the crystalline quality requirements for future ICs. Accurate determination of the epi layer thickness is critical since it affects subsequent process steps in IC fabrication such as the depths of the ion implanted retrograde well and the shallow trench isolation.
With increasingly smaller n+-p+ spacing in CMOS ICs, the epitaxial film thickness is driven to <2.0 ?m and eventually <1.0 ?m [1]. These thin epi layers are pushing the limits of current nondestructive metrology, which has significantly reduced precision and accuracy in this range. In addition, current epi metrology measurements are performed off-line, while improved process control for epi will be required through in-line real-time measurements. Here we discuss a new model-based epi film characterization technique that provides precise and accurate epi thickness measurements and extends the range of epi characterization to <0.25 ?m. It is also sufficiently fast for in-line applications, allowing real-time process control and feedback.
Methods to measure epi thickness
Current methods to analyze the epi thickness fall into two categories: destructive methods, such as secondary ion mass spectrometry (SIMS) and spreading resistance profiling (SRP), and nondestructive optical methods using infrared light. During SIMS analysis, the mass spectrometer detects and analyzes the secondary ions formed by ion sputtering the sample. One key issue for the calibration of the SIMS is the sputtering rate. SIMS is considered the most accurate profiling measurement method for epi, and provides a full profile of the dopant concentration with depth. In the SRP measurement, the sample is polished at an oblique angle to uncover the epi layer and substrate, and measurement of the sheet resistance along the polished surface generates the resistivity profile. Uncertainties of the SRP method include variations in the angle and the polished surface itself, as well as the proper modeling of carrier spilling. The fact that SIMS and SRP are destructive methods obviously confines their application to measuring a very small sample of wafers, with turn-around time that precludes their use for process control. Even with such limitations, these methods are important for estimating the accuracy of the nondestructive optical methods.
Commercial optical methods using FTIR spectroscopy instruments are currently employed to measure epi thickness on both product and test wafers. The basis of the FTIR measurement lies in the fact that the high-resistivity epi layer of lightly doped silicon and the low-resistivity, doped silicon substrate have different indices of refraction in the infrared range, due to their different free carrier concentrations. As a consequence, infrared reflectance measurements display interference effects that provide information on the epi layer thickness, as well as other parameters.
Basics of FTIR reflectance measurements
The heart of the FTIR is a scanning Michelson interferometer: a beam splitter separates incident light into two beams, one of fixed path length and the other of variable path length. The same beam splitter then recombines the two beams, creating interference between them. The difference in the travel distance between the two beams is called the optical path difference. The direct output of the spectrometer is an interferogram, which is a plot of light intensity vs. the optical path difference (mirror position) (Fig. 1). Fourier transform of the interferogram produces a "spectrum," i.e., a plot of light intensity vs. wavenumber (or wavelength). This spectrum is called a "single beam spectrum" and is the raw detector response vs. wavenumber. Absolute spectrum measurements are obtained by measuring the sample single beam spectrum, a background single beam spectrum (which accounts for all factors influencing the light intensity other than the sample), and by correcting the measured sample spectrum to the background spectrum. In the reflectance mode, the sample single beam is normalized to the single beam spectrum of a calibrated reference surface to yield the absolute reflectance spectrum (Fig. 1). Whether one considers the interferogram or the reflectance spectrum, the reflection dynamics at the sample surface affect the detected signal, and information about the sample can be extracted.
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Figure 1. The single beam spectrum (reflectivity vs. wavelength) is obtained from a Fourier Transform of the raw interferogram. The single beam spectrum is then normalized to a known reflectance standard to provide the absolute reflectivity spectrum (of an epi sample here).
Commercial FTIR methods
The current generation of commercial FTIR methods uses the interferogram to analyze the epi thickness. The interferogram displays a "centerburst," i.e., a high-intensity peak at the center (Fig. 1), which corresponds to a zero path difference. When analyzing an epi sample in reflectance, additional peaks are present in the interferogram. These peaks form due to the added beam travel in the epi film, and are present at path differences corresponding to one or several internal reflections in the film. The centerburst is thus accompanied by at least two "sidebursts" (more in the case of several reflections in the film), each separated from the centerburst by the optical distance the IR beam travels in the epi layer. For the first sideburst, this distance is approximately twice the product of the epi layer thickness and the film index of refraction, with the exact value depending on the angle of incidence. Consequently, the analysis of the position of the sidebursts provides information on the epi thickness. This method was widely adopted in the 1970s as computation requirements decreased from the elimination of the Fourier transform in the data analysis. With the improvement in computer technology over the last decade, this advantage is no longer significant and the interferogram sideburst method is hobbled by rather fundamental drawbacks that limit its reproducibility and accuracy.
One major problem is that the interferogram method is inherently a single-beam method, meaning that the signal shape of the interferogram, including the shape and location of the sidebursts, is influenced by the specific characteristics of each system. This causes variations of thickness readings from one tool to the next, thereby limiting the inter-machine correlation. Equally problematic is the "centerburst subtract method," required to extend the measurement range below 5 ?m. This subtraction step is necessary, since - for films around 5 ?m - the sidebursts are beginning to merge into the centerburst, making detection of the sidebursts in the raw interferogram impossible. Subtracting a "reference interferogram" (usually of an epi sample of very different thickness) allows removal of the effects of the centerburst under which the sidebursts are hidden. It is also designed to subtract out the interferogram signatures of the atmospheric absorption of CO2 and H2O, which tend to obscure the sidebursts. Aside from the practical difficulties of having to produce a set of special reference wafers, each of them "matching" the product to be measured, the main difficulty is to produce an exact duplicate of the sample centerburst. This and any slight shift in the relative centerburst position causes incomplete subractions leading to distortions of the sideburst, or potentially completely erroneous readings due to the peak detection program selecting a residual subtraction artifact instead of a true sideburst.
Another problem arises from the fact that the interferogram method assumes the phase difference of the two wavefronts (one reflected by the epi front surface and the second emerging from the epi/substrate interface) is due strictly to the thickness of the epi layer. In reality an additional phase shift occurs when the IR beam is reflected by the epi/substrate interface (the phase shift is due to the fact that the index of refraction of the epi is lower than that of the substrate). This additional phase term is a function of the probing wavelength and the carrier type and concentration in the substrate. The interferogram method cannot accurately account for this additional phase term, relying instead on an empirical correction and thereby reducing its accuracy. Finally, the doping profile at the interface epi/substrate (which varies with wafers suppliers) has an effect on the sidebursts` position and size, and consequently on the extracted thickness, thus introducing an unknown bias that cannot be accounted for by the interferogram-based algorithms.
Another FTIR-based method to measure epi thickness is used in the ASTM method F95-89. This method extracts the thickness not from the interferogram sidebursts` position, but from the analysis of the reflectance spectrum. As mentioned above, the reflectance spectrum of an epi sample displays interference fringes (Fig. 1) from the penetration of light in the epi film, the light being reflected at the epi/substrate interface. In the ASTM method, the position of the reflectance maxima and minima in the interference fringes are analyzed. The method uses essentially the same information as the interferogram method, i.e., the spacing of the interference fringes caused by the epi film. It is currently not widely used because of lack of support from FTIR manufacturers; the interferogram method has been sufficient so far to analyze films of thickness >2 ?m.
New model-based analysis
New model-based analysis methods are commercially available, providing more repeatable, reproducible, and accurate measurements of the epi thickness, and providing additional information on the doping profile [2-5]. These new methods are closer to the method described in ASTM F95-89 in their use of the infrared reflectance spectra than current commercial algorithms that use the interferogram analysis. Significant improvements over the ASTM method are present in the model-based methods. Instead of only recording minima and maxima, analysis of the entire spectrum reduces potential errors and provides additional information to extract the doping profile. The same observation can be made when comparing the new methods with the interferogram method: All the information in the interferogram is used, not just the position of the sidebursts. The new methods also usually account for the wavelength and doping dependence of the optical properties of the film and substrate. These complete analyses provide a superior measurement (in terms of precision and accuracy) of epi thickness, doping transition width, doping profile, and substrate doping and scattering rate. In addition, these model-based methods are applicable to more complex film stacks (e.g., multiple and graded layers, buried layers), which are impossible to analyze with the current commercial methods.
Reflectance measurement. In the new methods, an infrared reflectance spectrum of an epi silicon film is obtained from an FTIR (or some other hardware), following the procedure described above.
Analysis. During the analysis, a general multilayered reflectance model computes the simulated reflectance spectra. Each layer of the film stack is characterized by its thickness and its material-dependent parameterized dielectric function (DF). In addition, parametric models also describe the composition profile, e.g., "transition" layers due to up-diffusion from the substrate. The model parameters - such as thickness, dielectric function parameters, etc.- are adjusted iteratively to fit the measured spectrum. In the case of epi silicon, the fitting parameters are typically the unknown epi thickness, the transition layer thickness, and the doping of the substrate, which governs its dielectric function.
Silicon dielectric function model. For doped semiconductors such as silicon, the dielectric function depends on absorption due to multiphonons and free carriers. The multiphonon absorption contributes to a "background" dielectric function that is independent of resistivity over a wide range of doping levels. In the mid-IR range, the free carrier absorption is well modeled by the Drude approximation [6-8], which gives a linear relationship between the complex dielectric function and the free carrier concentration. For a quantitative determination of the carrier concentration, known values of other parameters such as the carrier effective mass and the carrier scattering rate (which both enter in the Drude model) are required. Resistivity and mobility data provide estimates of the effective mass, and fitting the reflectance data in the low wavenumber range allows calculation of the scattering rate.
Composition profile. A diffusion carrier concentration profile is typically present at the epi/substrate interface, with the shape and width of the profile varying significantly depending on the process conditions. Information on the concentration profile encoded in the reflectance spectrum can be extracted from the fit, along with the epi film thickness. In the analysis models, continuously graded concentration profiles (Fig. 2a) are segmented into multiple sublayers (Fig. 2b), and a dielectric function for each sublayer is specified based on its composition (Fig. 2c). The specific shape of the concentration profile depends on the complex processes of up-diffusion from the substrate, dopant evaporation during epi deposition, out-gassing from adjacent wafers in barrel-type reactors, and so on.
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Figure 2. Reflectance from a film stack: a) continuously graded film; b) a discretely segmented multilayered stack; and c) multilayered film stack reflectance model. d1 refers to the film thickness. DF1 refers to the dielectric function, and Mo is the incident medium index of refraction.
Results
Reflectance fits. Figure 3 shows model-based fits for 5- and 0.6-?m epi films. These calculations modeled the epi film as intrinsic silicon, the substrate as uniformly doped silicon. The transition layer was segmented into several sublayers, with the carrier concentration level rising through the sublayers from the epi film to the substrate. The figure shows that the model does an excellent job accounting for the shape of the interference fringe, including the decay at higher wavenumbers characteristic of the free carrier dielectric response.
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Figure 3. Measured (thin line) and fitted (thick line) epi reflectance spectra: a) 5-?m epi, b) 0.6-?m epi. The spike in b) is due to CO2 absorption in the optical path. The small CO2 range is excluded from the fit calculation.
Extraction of concentration profile. Figure 4 shows the influence of the substrate/epi film transition width on the reflectance, displaying the experimental reflectance of two films of similar epi thickness (as defined as the film thickness to 50% of the substrate level), but of varying profile width. The thick transition induces more damping of the fringes, as well as a shift in fringe position at high wavenumber. The effect of the exact shape of the concentration profile on the reflectance is also especially noticeable for wide transitions. For example, it is not possible to fit the spectrum of the thick-transition sample from Fig. 4 with a linear profile, while a curved interface profile (similar to a complementary error function) provides an excellent fit. Figure 5a compares the extracted profile for that sample to the experimental dopant profile (as measured by SIMS) and shows an excellent agreement. The predicted profile is plotted down to 2 ? 1017 cm-3, which is the sensitivity limit for the FTIR. Figure 5b shows the extracted curved profile compared with the experimental SIMS data for the sample from Fig. 4, which had the narrow concentration profile. We also obtained a very good agreement in that case.
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Figure 4. Influence of the width of the transition zone on the reflectance spectrum. The sample with the thin transition has an epi thickness of 2.135 ?m with a transition thickness of 0.16 ?m, while the sample with the thick transition has an epi thickness of 2.177 ?m with a transition of 0.68 ?m.
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Figure 5. Comparison of the extracted free carrier profile (line) with the measured SIMS dopant profile (circles) for: a) the wide-transition sample, and b) the narrow transition sample. Note that the carrier concentration is equal to the dopant concentration if all dopant atoms are activated.
Comparison of extracted parameters with other techniques. Comparisons of the extracted parameters to destructive SIMS and SRP measurements provide an assessment of the free carrier concentration profiling capability. A large number of p+ (boron-doped) samples from different manufacturers, and with different doping concentration profiles, was used. For all these samples, we compared two parameters extracted from the concentration profiles: the epi thickness, defined as the epi thickness to 50% of the substrate concentration, and the transition thickness, defined as the width of the region from 16 to 84% of the substrate concentration. Figure 6a shows the comparison of the model-based epi thickness values with SIMS and SRP measurements, as well as FTIR interferogram measurements. The extracted epi thicknesses compare extremely well (with no significant bias) to the SIMS measurements, which are considered to be the most accurate of the destructive measurements. On the other hand, the FTIR interferogram method measurements do not correlate well with the SIMS or SRP data, and appear to have significant "biases," as large as 200 nm, depending on the wafer type and manufacturer. These biases are expected to be even larger for thinner (< 1 ?m) epi.
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Figure 6. a) Correlation of epi thickness (defined as the epi film thickness to 50% of the substrate concentration) measured by SIMS with values from the new FTIR method, the interferogram method, and measured by SRP; b) correlation of transition thickness (defined as the region corresponding to 16-84% of the substrate concentration) measured by SIMS with values from the new FTIR method.
Figure 6b shows the correlation between the extracted transition thickness with SIMS data. The agreement demonstrates the applicability of a curved out-diffusion carrier profile model for all these samples from different sources. Note that information about the transition width is not available from the interferogram method.
Figure 7a shows the comparison of the fitted substrate carrier concentration with dopant concentration data from SIMS and carrier concentration from SRP. There is less correlation in that case than for the epi and transition thickness (the standard deviation of the difference between FTIR and SIMS is 1.3 ? 1018 cm-3). One reason is that the absolute dopant concentration is determined by SIMS with a precision of 10%, i.e., for our values, a precision of ~1 ? 1018 cm-3. It is also interesting to note that the FTIR and SRP data show the same variation (spread) in values compared to the SIMS data, and appear to support each other (Fig. 7b). Since both FTIR and SRP methods are sensitive to the carrier concentration - as opposed to the concentration of dopant atoms with SIMS - SRP and FTIR results should correlate better than SIMS and FTIR. The scatter in Fig. 7a may then also be due to carrier spill effects present in the FTIRand SRP measurements, but not affecting the SIMS measurement of dopant atoms.
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Figure 7. a) Correlation of substrate dopant concentration measured by SIMS with extracted values for substrate carrier concentration from the new FTIR method and SRP measurements; b) correlation of substrate carrier density measured by SRP and FTIR.
Conclusion
Model-based FTIR characterization of epitaxial silicon measurements is a promising new technique that provides information about the epi film thickness and doping profile. This new method has many advantages, in terms of precision and accuracy, over the current commercial techniques based on the analysis of the interferogram. Because model-based analysis eliminates the need for matching reference wafers and empirical adjustments, it improves the intermachine measurement precision by a factor of 10, and the accuracy by a factor of 5 to 10. These improvements allow more consistent interpretation and fusion of thickness data from multiple measurement stations or laboratories, and reduce the need for destructive measurements.
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SYLVIE CHARPENAY received her MS degree in materials science at the Institut National des Sciences Appliquees, Lyon, France in 1987, and her MS in metallurgy at the University of Connecticut in 1989. She is currently applications group leader at On-line Technologies Inc. 87 Church St., East Hartford, CT 06108; ph 860/291-0719, fax 860/289-7975.
PETER A. ROSENTHAL received his PhD degree in applied physics from Stanford in 1991, and has 16 years of experience in R&D and product management for technology related to materials characterization and process control. He is VP of semiconductor products at On-Line Technologies Inc., where he developed an R&D 100 award-winning integrated epi thickness sensor.
GERHART KNEISSL is the FTIR Product Marketing Manager at ADE Corp. He received a Diploma Engineer degree from the Institute of Technology in Graz, Austria, and his PhD degree in mechanical engineering from Oklahoma State University. Prior to joining ADE, he was the technical resources manager for confocal microscopy at Bio-Rad Laboratories, in Hercules, CA.
CAROLYN F. HOENER GONDRAN received her PhD degree in physical chemistry from the University of California at Berkeley for low-temperature optical studies on polyacetylene in 1988. After a postdoc on q-particles at the University of Texas at Austin, she started as an auger analyst at SEMATECH, where she now manages the materials analysis laboratory.
HOWARD HUFF received his BS degree in engineering science from New York University in 1960, his MS degree in physics from the Stevens Institute of Technology in 1962, and his PhD degree in metallurgy from M.I.T. in 1966. He joined SEMATECH in 1988, where he is a senior fellow and program manager for gate stack engineering and silicon materials.