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Effects of measured spectral range on accuracy and repeatability of OCD analysis


07/01/2013







FRANZ HEIDER, Infineon Technologies, Villach, Austria; JEFF ROBERTS, JENNIE HUANG, JOHN LAM and RAHIM FOROUHI, n&k Technology, San Jose, CA


A broadband polarized reflectometry measurement, utilizing RCWA analysis, can be used to obtain detailed trench profile results.


There is a need for metrology to help control manufacturing processes for power semiconductors, where deviations from the desired structure geometry can affect device performance. Lithography and etch processes, specifically, create patterned structures, where the trench depth and width, or CD (critical dimension), must be tightly controlled. Traditionally, several techniques have been employed for this purpose, including cross-section Scanning Electron Microscopy (SEM), CD-SEM, profilometry, and Atomic Force Microscopy (AFM). Each method has its benefits and limitations, but none can provide detailed profile information with the combination of speed and measurement sensitivity of non-destructive optical metrology, based on broadband polarized reflectometry.


To demonstrate the capabilities of broadband polarized reflectometry, we performed measurements on power semiconductor samples using an optical metrology instrument, the n&k Olympian. One key aspect of this system is the relatively large wavelength range, extending from deep ultraviolet to near infrared wavelengths (190nm - 1000nm). This large range enables applications that would not be possible with the limited range of standard reflectometers (375nm - 750nm).


Measurement system


The n&k Olympian is a fully-automated metrology system for thin film and optical critical dimension (OCD or "scatterometry") measurements that uses broadband polarized reflectance. The data extends from the UV to NIR, with a separate optical system covering IR wavelengths up to 15,000nm. The measurement method is non-contact, non-destructive and high throughput, with typical measurement times (including the move, acquire, measure, and analyze steps) on the order of 5s per measurement point.


For the UV-NIR wavelength range, there are two light sources. UV light comes from a deuterium arc lamp, while visible and near-IR radiation is provided by a tungsten filament lamp. The source light is focused on the sample and directed to a spectrophotometer by a series of mirrors, creating a measurement spot diameter of 50??m and incident angle of 4?? from normal. The spectrophotometer contains a holographic diffraction grating and a photodiode array that separates the polychromatic beam into its individual wavelength components and records the reflectance at each wavelength, in one nanometer intervals. There is a rotating polarizer in the optical path enabling the collection of two sets of measurement data (S-polarized Reflectance and P-polarized Reflectance, or "Rs" and "Rp" respectively). When line/space grating structures are measured, the structures are oriented such that Rs data relates to the TE polarization and Rp data relates to the TM polarization.


To extract values for structure dimensions, a model of the measured area is created using n&k Analysis software. The software incorporates rigorously coupled wave analysis (RCWA) for periodic structures1 with Forouhi-Bloomer dispersion relations2, 3 for n and k. The model is used to calculate theoretical reflectance spectra. The structure dimension parameters, within the model, are varied using nonlinear regression analysis in order to obtain the best match between the experimental and calculated spectra. Inputs to an OCD structure model include the optical properties for all materials within the structure, which can be determined by measuring blanket film areas, and the structure pitch.


The measurement results are determined by converging on the maximum goodness of fit (GOF) value, which describes the similarity of the calculated reflectance of a modeled profile to the experimental reflectance. The variables within the model, including CD and depth, are reported as measurement results after the software determines that the GOF cannot be further improved by changing any of the values. A higher goodness of fit value generally means that the measurement results are consistent with the physical dimensions of the actual structure. If there is variation in neighboring features within the 50??m diameter measurement area, the results are considered to be the average dimensions.


To provide measurement results with this tool and technique, the area of interest must meet certain requirements. Typically, the measurement area is either the device structures, or within designed test areas meant to approximate the features found within the actual device. OCD test structures, including 2D line/space gratings or 3D hole arrays, must be repeated periodically, with a pitch less than 10??m.


Tapered trench measurement


To test the measurement capabilities of the n&k Olympian, Infineon Technologies created five silicon wafer test samples with line/space grating structures. Each sample was created using different process conditions, meant to represent possible unintended changes in the manufacturing process that could lead to differences in the dimensions of the grating structures, ultimately affecting the device performance. The samples were measured using both the n&k system and a cross section SEM, for comparison and determination of the approximate trench profile.


As shown in FIGURE 1, the tapered line/space grating structures have repeating spaces etched into silicon with a pitch of 1.7??m, nominal trench depth of 4??m, and space CD of 0.55??m. The pitch is based on the design layout and will not be affected by changes in the etch processing, so pitch is fixed within the analysis model. Trench depth and space CD are the parameters of interest that need to be measured. There were no materials besides silicon in the test structures, but oxides, nitrides, and poly-silicon are often a part of OCD structures, and the analysis software allows for the inclusion of multiple layers on the trench mesa (above silicon lines), at the bottom of the trench, or on the trench sidewall.





Figure 1: Cross-section SEM image of the tapered trench (left) and model of the trench structure within n&k analysis software (right). The model was created to be consistent with the trench profile seen in SEM images.
Figure 1: Cross-section SEM image of the tapered trench (left) and model of the trench structure within n&k analysis software (right). The model was created to be consistent with the trench profile seen in SEM images.

A review of the cross-section SEM image for the grating structure (Fig. 1) shows the trench profile for one of the samples with two distinct sections. From the top of the trench until a depth of ~800nm there was a fairly constant sidewall angle, while from the depth of ~800nm to the bottom the trench sidewall angle changes to be closer to normal. Subsequent SEM images show that this inflection point is consistently near a depth of 800nm from the top of the trench. These observations of the trench profile were used to develop the analysis model for the n&k Olympian. Neither an AFM nor a CD-SEM would be able to measure CD at the inflection point as well as at the top and bottom of the trench.


Based on the trench profile from cross-section SEM images, the analysis model was created to include space CD variables at three points (FIGURE 2): CD1 at the top, CD2 at 800nm from the top, and CD3 at 70nm from the trench bottom (to allow for some rounding at the trench bottom). There is good match between the SEM image and the schematic from the analysis software.





Figure 2: Cross-section view of the OCD model, drawn to scale. Pitch is fixed within the model, while CD1, CD2, CD3, and trench depth are measurement parameters. Sidewall angle values can be calculated from the results for CD and depth.
Figure 2: Cross-section view of the OCD model, drawn to scale. Pitch is fixed within the model, while CD1, CD2, CD3, and trench depth are measurement parameters. Sidewall angle values can be calculated from the results for CD and depth.

Each wafer was measured at 29 points using the n&k Olympian, while cross-section SEM images were taken at the center point for each sample. For the optical measurements, we considered two cases: 1) using the full wavelength range of the broadband polarized reflectometer (190nm - 1000nm), and 2) using a limited range typical of standard reflectometers (375nm - 750nm). This comparison was done to demonstrate the advantages of using a larger wavelength range, for this application. Other than the wavelength range, the modeling was identical for both cases.


Experimental Data


Without any data analysis, observations of the experimental data, Rs and Rp, can provide insight into the measurement sensitivity to the structure depth and CD values. Looking at the experimental data, we clearly see oscillations in the Rs data from 190nm - 450nm, and in the Rp data from 800-1000nm. For Sample 4, the oscillations in the Rs data have a limited wavelength range and only extend from 190nm ??? 350nm, as shown in FIGURE 3.





Figure 3: Experimental Rs and Rp Data for Sample 4, at 3 locations across the wafer. The data shows the areas of the spectra that are critical in distinguishing changes in trench depth and CD. The three locations appear to have differences in terms of experimental data, which relate to trench depth and CD, particularly from 190-350nm in Rs data and 800-1000nm in Rp data. A standard reflectometer with wavelength range of 375-750nm does not include data in the critical regions where there is good sensitivity to the trench depth and CD values, so measurement results using this limited wavelength range will be unreliable for Sample 4.
Figure 3: Experimental Rs and Rp Data for Sample 4, at 3 locations across the wafer. The data shows the areas of the spectra that are critical in distinguishing changes in trench depth and CD. The three locations appear to have differences in terms of experimental data, which relate to trench depth and CD, particularly from 190-350nm in Rs data and 800-1000nm in Rp data. A standard reflectometer with wavelength range of 375-750nm does not include data in the critical regions where there is good sensitivity to the trench depth and CD values, so measurement results using this limited wavelength range will be unreliable for Sample 4.

To further test measurement sensitivity, we can create an analysis model using the nominal structural dimensions. We calculate the theoretical polarized reflectance for the nominal structure and compare this to the experimental data. By changing the parameter values for depth and CD within the model and recalculating the theoretical reflectance, we can observe the effects of changing depth or CD on the reflectance spectra. Overall, the simulations confirm that reflectance measurements of the 190nm - 450nm and 800nm - 1000nm ranges are important to measurement of the trench profile.


The calculations also confirm that decreasing the CD values limits the wavelength range in the Rs and Rp data where there is sensitivity to the depth and CD values. This is consistent with the experimental data that is measured for Sample 4, which has smaller CD values and exhibits sensitivity to the trench depth and CD values only from 190nm ??? 350nm in the Rs data and 800nm ??? 1000nm in the Rp data. This suggests that a standard reflectometer, with wavelength range of 375nm ??? 750nm, will have limited measurement capabilities for this type of trench structure, particularly when the CD values are smaller.


SEM Comparison


In order to verify the results from the optical measurement system, we compared results from SEM cross-sections for CD and depth to the values obtained by the n&k Olympian. Using the full wavelength range, 190nm???1000nm, there is a good match between cross-section SEM results for depth and CD and the measured results from the broadband polarized reflectometer (FIGURE 4). Using a limited wavelength range, 375nm???750nm, with an analysis model that is otherwise identical, the results do not compare as well with the SEM data, particularly the trench depth of Sample 4.





Figure 4: Comparison of n&k results, both limited range (350nm - 750nm) and broadband (190nm - 1000nm), to cross section SEM results for Trench Depth (upper left), CD1 (upper right), CD2 (lower left) and CD3 (lower right). For CD1 and CD3, the results match SEM results equally well for the full and limited wavelength range. For Trench Depth and CD2, the results from analysis of the full wavelength range have good agreement with the SEM results, while results from the limited wavelength range do not match as well. Sample 4 results were expected to be inaccurate for the limited wavelength range, and the trench depth for Sample 4 does not match the SEM result.
Figure 4: Comparison of n&k results, both limited range (350nm - 750nm) and broadband (190nm - 1000nm), to cross section SEM results for Trench Depth (upper left), CD1 (upper right), CD2 (lower left) and CD3 (lower right). For CD1 and CD3, the results match SEM results equally well for the full and limited wavelength range. For Trench Depth and CD2, the results from analysis of the full wavelength range have good agreement with the SEM results, while results from the limited wavelength range do not match as well. Sample 4 results were expected to be inaccurate for the limited wavelength range, and the trench depth for Sample 4 does not match the SEM result.

The reason that Sample 4 measurements are inaccurate for trench depth, using the limited wavelength range, is related to the CD values. For Sample 4, the CD3 value measured by cross-section SEM is ~275nm, significantly lower than any of the other samples. For deep trenches in silicon, as the CD gets smaller the OCD interference fringes are reduced at longer wavelengths. Experimental data in the UV region is required for measurement of this structure, as shown by the broadband data.


In order to further test the measurement limitations, we performed simulations using the full wavelength range to see the effects of smaller CD values on the Rs spectra. As CD2 and CD3 get smaller, the amplitude of interference fringes decreases and the wavelength region is narrowed. With CD2 equal to 400nm and CD3 equal to 350nm, interference fringes are present from 190nm - 420nm. However, with CD2 equal to 300nm and CD3 equal to 200nm, interference fringes are only present from 190nm - 280nm. Therefore, as the CD values become smaller the system must include UV wavelengths in order to measure the trench depth and CD.


Wafer Uniformity


One advantage of an optical measurement system is the ease with which wafer uniformity maps can be created. While the cross-section SEM can show a detailed trench profile, it is both destructive and time consuming. With the broadband polarized reflectometer, however, wafer uniformity maps can be created in a few minutes, depending on the number of locations measured.





Figure 5: 29 Point Wafer Uniformity Results for Sample 4, 200mm wafer, as measured by broadband OCD. Dense mapping measurements are used to test the non-uniformity for depth and CD. Cross section SEM is typically done at a single point or a few points per wafer, so uniformity information is limited. The trench depth mapping shows a typical uniformity pattern after an etch process, with a center to edge effect, while CD1 is larger on the left side of the wafer, smaller on the right.
Figure 5: 29 Point Wafer Uniformity Results for Sample 4, 200mm wafer, as measured by broadband OCD. Dense mapping measurements are used to test the non-uniformity for depth and CD. Cross section SEM is typically done at a single point or a few points per wafer, so uniformity information is limited. The trench depth mapping shows a typical uniformity pattern after an etch process, with a center to edge effect, while CD1 is larger on the left side of the wafer, smaller on the right.

FIGURE 5 shows the wafer uniformity results for Sample 4 using the full wavelength range analysis (190nm ??? 1000nm) for both CD1 and trench depth, which cannot be accurately measured using the limited wavelength range (375nm ??? 750nm). The apparent wafer non-uniformity is common for samples after an etch process. For trench depth, there is a center to edge effect, with lower trench depth at the wafer center. For CD1, the largest CD value is on the left side of the wafer, with the smallest CD on the right side. The wafer non-uniformity is significant, which speaks to the importance of a multi-point measurement to verify that all points across the wafer are within specification. This would be extremely time consuming to achieve with cross section SEM measurements, but is much more practical with the n&k Olympian, where 25 points can be measured in about two minutes.


Conclusion


A broadband polarized reflectometry measurement, utilizing RCWA analysis, can be used to obtain detailed trench profile results. The system provides trench depth and CD results comparable to cross-section SEM, with a method that is both high-throughput and non-destructive. The capabilities have been demonstrated with the measurement of five samples that have undergone different processing conditions. In comparison to the limited wavelength range of standard reflectometers (375nm - 750nm), use of a wider 190nm - 1000nm wavelength range provides more sensitivity to the trench profile, and the ability to accurately measure trench structures with smaller CD values and deeper trenches.


Acknowledgement


We are very grateful to Georg Ehrentraut (Infineon Technologies) for etching the trenches across a wide range of process conditions.


References


1. Moharam, M. G., Grann, E. B., Pommet, D. A., Gaylord, T. K., "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. vol. 12, issue 5, p. 1068-1076, 1995.


2. A. R. Forouhi and I. Bloomer, "Optical Dispersion Relations for Amorphous Semiconductors and Amorphous Dielectrics", Physical Review B, 34, p. 7018, 1986.


3. A. R. Forouhi and I. Bloomer, "Optical Properties of Crystalline Semiconductors and Dielectrics", Physical Review B, 38, p. 1865, 1988.


FRANZ HEIDER, Infineon Technologies, Villach, Austria; JEFF ROBERTS, JENNIE HUANG, JOHN LAM and RAHIM FOROUHI, n&k Technology, San Jose, CA.



Solid State Technology | Volume 56 | Issue 5 | July 2013