SPIE Proceedings [SPIE Optics & Photonics - San Diego, CA (Sunday 13 August 2006)] Novel Optical...

Optical Illumination and Critical Dimension Analysis Using the Through-focus Focus Metric Method

Ravikiran Attota*, Richard M. Silver and James Potzick

Precision Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899

ABSTRACT

In this paper we present recent developments in optical microscope image analysis using both, best focus optical image as well as those images conventionally considered out of focus for metrology applications. Depending on the type of analysis, considerable information can be deduced with the additional use of the out of focus optical images. One method for analyzing the complete set of images is to calculate the total “edge slope” from an image, as the target is moved through-focus. A plot of the sum of the mean square slope is defined as the through-focus focus metric. We present a unique method for evaluating the angular illumination homogeneity in an optical microscope (with Köhler illumination configuration), based on the through-focus focus metric approach. Both theoretical simulations and experimental results are presented to demonstrate this approach. We present a second application based on the through-focus focus metric method for evaluating critical dimensions (CD) with demonstrated nanometer sensitivity for both experimental and optical simulations. An additional approach to analyzing the complete set of images is to assemble or align the through focus image intensity profiles such that the x-axis represents the position on the target, the y-axis represents the focus (or defocus) position of the target with respect to the lens and the z-axis represents the image intensity. This two-dimensional image is referred to as the through focus image map. Using recent simulation results we apply the through focus image map to CD and overlay analysis and demonstrate nanometer sensitivity in the theoretical results. Keywords: Optical critical dimension (OCD) metrology, Through-focus focus metric, Through-focus image map, Angular Optical illumination, Köhler factor, Overlay, Process control, Defect analysis

1. INTRODUCTION It is common to assume that the optical microscope image obtained at the best focus is the ideal image for information content and subsequent analysis. However, it is likely that the out of focus images too contain useful information. The utility of these out of focus images depends on the type of analysis performed and the application in question. In this paper, we present different types analyses which use the complete set of images, including both the best focus image as well as the out of focus optical images (i.e. the complete set of through focus optical images) and apply these techniques to optical metrology applications in semiconductor manufacturing.

2. THROUGH-FOCUS FOCUS METRIC In this section we describe one method for analyzing the complete set of through focus optical images [1-7]. An optical image of an infinite line grating can be represented as an intensity profile as shown on the right side of Fig.1. As the target is moved through the focus, different intensity profiles are acquired as shown in Fig.1. For the purposes of this paper, the sum of the mean square slope of an optical intensity profile is defined as the focus metric. A plot of the focus metric as the target is moved through the focus is called the through-focus focus metric (TFFM)[1]. The TFFM is one of the common approaches through which the best focus image is identified [8, 9]. The TFFM profile typically has a single peak when imaging a single line. The image at the peak focus metric value is usually considered to be the best focused image. However, the TFFM of a line grating, which exhibits complex optical interference of the scattered fields, shows multiple TFFM peaks as shown in Fig. 2 [2]. As the target is moved through the focus, the contrast of the optical image initially increases and reaches a peak value (Peak 1 in Fig. 2). This is followed by a decrease in the contrast. At a particular focus position (Point ‘a’) the contrast in the image completely disappears. This ----------------------------------------- * [email protected]

Novel Optical Systems Design and Optimization IX, edited by José M. Sasian, Mary G. Turner,Proceedings of SPIE Vol. 6289, 62890Q, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.681231

Proc. of SPIE Vol. 6289 62890Q-1

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is again followed by an increase in the contrast until it reaches Peak 2 followed again by a decrease in the contrast. TFFMs that exhibit multiple peaks as shown in Fig. 2 have several interesting applications. In the following sections we discuss two of these applications.

2.1 Through-focus Focus Metric for Illumination Analysis In this section we describe an application of the TFFM for illumination analysis in an optical microscope configured with Köhler illumination [6]. Köhler illumination is one common approach to obtaining uniform illumination. A simplified schematic of a Köhler illumination configuration is shown in Fig. 3. Each point on the back focal plane of the condenser lens produces an illumination plane wave at a specific angle at the object plane. In the current section formation of an image in an optical microscope with Köhler illumination is studied using optical simulation tools. In our optical simulations, uniform illumination at the back focal plane is represented by a tiled aperture with a discrete set of equal magnitude numbers which represent the illumination intensity for each given angle (for a circular illumination) as shown in Fig. 4(a). Each number produces a plane wave with magnitude as given by the value for that tile. If the source is incoherent, each plane wave is considered incoherent. For an incoherent source, each individual plane wave produces an independent image. The final image is the incoherent sum of all the individual images formed by scattering from each of the individual illuminating plane waves.

Through Focus Intensity Profiles

Through Focus Sample Movement





Figure.1 The method of obtaining through focus optical intensity profiles using an optical microscope.

Figure 2. A typical simulated TFFM profile for line array exhibiting proximity effects. Insets are intensity profiles at the indicated focus positions. The optical image has high contrast at peaks 1 and 2, while it has very low contrast at point “a” as shown by an arrow. Parameters for simulation: Line width=140 nm; Line height=200 nm; Pitch=600 nm; Illumination NA =0.4; NA=0.8; Wavelength=546 nm. Si lines on Si substrate. Zero position represents top of the substrate.

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Figure 3. A simplified schematic of a Köhlerillumination. Each point on the back focalplane produces an illumination plane wave at aspecific angle.

Figure 4. Back focal plane intensity is represented by a matrix of numbersin the simulations. Simulations were made using (a) complete circular, (b)right semicircular and (c) left semicircular illuminations at the back focalplane.



For simplicity, the illuminating plane waves are divided into positive and negative angles of illumination as shown in Fig. 3. All of the plane waves below the optical axis are bundled into negative angles of illumination while all of the plane waves above the optical axis are bundled into positive angles of illumination. A uniformly illuminated back focal plane shown in Fig. 4(a) produces uniform, equal magnitude negative and positive angles of illumination. Illuminating only one half of the back focal plane shown in Fig. 4(b) produces only the negative angles of illumination. Similarly, illuminating only the other half of the back focal plane produces only the positive angles of illumination (Fig. 4(c)).

Based on the division of angles shown in Fig. 3, optical simulations of a line grating were carried out for the three different types of illumination illustrated in Fig. 4. The resulting through-focus intensity profiles for each individual illumination condition are shown in Fig. 5. The following observations can be made from this result. Intensity profiles from only the negative or only the positive angles of illumination are different and their shape changes with focus position. The final image formed by all the incident angles is the incoherent sum of the images formed by only the negative and only the positive angles of illumination. The sum of the slopes contained in an intensity profile is a measure of the image content. When the maximum or the minimum intensities in the images formed by only the negative and only the positive angles of illumination overlap, the resultant final image has the highest contrast content as shown in window 11 of Fig. 5. Window 16 shows the instance where there is minimum overlap in the peak values, which results in the lowest contrast final image. Images formed by only negative or only positive angles of illumination do not produce low contrast images. However, when the intensities are summed they then produce a low contrast final image.

In window 16 the image focus position corresponds to point ‘a’ in Fig. 2. By moving the sample focus position in small incremental steps, a point is reached about the point ‘a’ where the sum of the negative and the positive illumination images produces an almost constant image intensity response. This situation results in an extremely low final image intensity contrast i.e. the intensity profile is nearly flat. The focus metric value (i.e. sum of the slopes) of this image is nearly zero. Further examination of the images at this focus position provides additional insight into the illumination analysis.

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Figure 5. Simulated through-focus image intensity profiles of a line grating. The lower overlapping curves in each window are the intensity profiles for only the negative angles and only the positive angles of illumination. The above curve is the intensity profile for all the angles of illumination. Each window is at different focus position. Y-axis is the intensity in arbitrary units, x-axis is the distance. Profile of only one pitch length is shown in the figure. Input parameters for the simulation: Line width = 200 nm, Line height = 200 nm, Pitch = 600 nm, Illumination NA = 0.4, Collection NA = 0.8, Illum. Wavelength = 546 nm, Si line on Si substrate.



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Uniform illumination of the entire back focal plane produces the constant intensity profiles shown schematically in Fig. 6(a). The dotted line is the image intensity profile produced by only the negative incident angles, the dot-dash line is the image intensity produced by only the positive incident angles, and the solid line is the image intensity profile produced by all of the incident angles of illumination. In this example both the negative and the positive incident angles are illuminated at 100 % intensity. As explained above, this results in an extremely low contrast final image. The focus metric has near zero value. However, when the intensity of all the positive incident angles is uniformly reduced to 80 % of the negative incident angles, the sum of the negative and the positive illumination profiles no longer produces a constant intensity profile as shown in Fig. 6(b). This results in a higher contrast final image. Further reduction in all of the positive incident angles uniformly increases the contrast of the final image as shown in Figs. 6(b) to 6(d). Consequently, the focus metric value, which is a measure of the total slope content, increases with increasing contrast for the profiles of the sort shown here. This analysis of the simulation shows that increasing intensity differences between the negative and the positive angles of illumination increases the focus metric value at the point ‘a’ (Fig. 2). The simulated TFFM profiles using different levels of the negative and the positive incident angle intensity are shown in Fig. 7. As expected, the focus metric value at point ‘a’ increased with increasing intensity difference between the negative and the positive incident angles of illumination. From the above discussion we can conclude that the magnitude of the focus metric at point ‘a’ (Fig. 2) is an indication of the asymmetry in the angular illumination intensity. Based on this observation an experimental attempt was made to analyze the asymmetry in the angular illumination

for a poorly aligned and a well-aligned Köhler illuminated microscope. The experimental details are as follows. A 100 µm x 100 µm scatterometry target with approximately 229 nm wide, 230 nm tall, 540 nm pitch array of lines was imaged through the focus at 100 nm increments using an optical microscope with 0.8 collection NA, 0.4 illumination NA, 546 nm illumination wavelength and at 50X objective magnification. Through focus images were acquired for two perpendicular target orientations. In the analysis, the entire field of view was divided into 50 rows and 50

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Figure 6. Schematic intensity profiles for the negative angles, the positiveangles, and all the angles of illumination at the focus position ‘a’ (Fig. 2).Percentage of the left half intensity compared to the right half is indicated inthe figure. Length of the profile equals to one pitch.

Figure 7. TFFM profiles at reduced left half back focal plane intensity. Percentage of the left half intensity compared to the right half is indicated in the figure.

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columns. TFFM profiles were calculated for each of the 50 x 50 locations. The resulting normalized minimum focus metric values at point ‘a’ were obtained for each of the 50 x 50 locations for the two perpendicular orientations. A plot of the resultant minimum focus metric values across the field of view indicates the asymmetry in the angular illumination. The experimental results for the poorly aligned microscope are presented in Fig. 8. In the three-dimensional image on

the left side, the x-y axes represent the field of view and the z-axis represents the magnitude of the focus metric at point ‘a’ (Fig.1). The results show that the poorly aligned microscope has a large angular illumination asymmetry across the field of view. For this configuration of the microscope an arrow shows the location in the field of view with the lowest value of the focus metric. Based on the discussion above, this location in the field of view for this microscope setup shows the best angular illumination symmetry, i.e. an image of a symmetric line at this location should produce the best symmetric profile fro this microscope setup. Other locations in the field of view, because of

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Figure 8. The experimental evaluation of the asymmetry in the angular illumination for the poorly aligned microscope. The X-Y axes represents a 40 µm x 40 µm field of view and the Z-axis is the focus metric in the left side figure. The right side figure is a two dimensional projection of the left side three dimensional figure. The best symmetric illumination location in the field of view is shown by an arrow. A target with approximately 229 nm wide, 230 nm tall, 540 nm pitch array of lines (100 µm x100 µm) was imaged using an optical microscope with 0.8 collection NA, 0.4 illumination NA and 546 nm illumination wavelength at 50X objective magnification.

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Figure 9. Experimental evaluation of asymmetry in the angular illumination for the well-aligned microscope. X-Y axis represents 40 µm x40 µm field of view and Z-axis is the focus metric in the left side figure. The right side figure is a two dimensional projection of the left side three-dimensional figure. A target with approximately 155 nm wide, 230 nm tall with 600 nm pitch array of lines (100 µm x100 µm) was imaged using an optical microscope with 0.8 collection NA, 0.38 illumination NA and 546 nm illumination wavelength at 50X objective magnification.



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their asymmetric illumination, will produce asymmetric image intensity profiles. The asymmetry in the illumination increases the further one moves from the location of best symmetry. It can also be observed that for this microscope setup the location for best angular symmetry does not coincide with the center of the field of view. The well-aligned microscope has much better angular illumination symmetry as shown in Fig. 9. However, even this microscope setup has some angular asymmetry at the lower left corner in the field of view. Here the entire field of view was divided into 30 rows by 30 columns for the analysis.

2.2 Through-focus Focus Metric for CD Analysis The shape of the TFFM is sensitive to the experimental conditions [2]. It depends on target parameters such as critical dimension (CD), line height, pitch, sidewall angle and its optical properties. It also depends on microscope settings such as illumination numerical aperture, collection numerical aperture, illumination wavelength, optical aberrations and quality/homogeneity of illumination. If all the parameters, except one such as CD, are known with a high degree of accuracy, then it is possible to evaluate the one unknown parameter by comparing the experimental TFFM with that

Figure 10. Mean experimental TFFM profiles for the 6 target locations selected, normalized to the bigger focus metric peak. SEM measured CD values and their standard deviations are indicated in the figure in nanometers.

Figure 11. Simulated TFFM profiles for 146 nm to 156 nm bottom CDs at 0.36 illumination NA. Other input parameters are: Line height=230 nm, Pitch=601 nm, collection NA = 0.8, Illum. Wavelength=546 nm, Si lines on Si substrate.

Figure 12. Plot of normalized left peak intensity vs. CD for the simulations and the experiments.

Figure 13. Measured CD values using SEM, and the through-focus focus metric method using the optical microscope.



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determined from the optical simulations. In this section we present evaluation of CDs using the TFFM. Evaluation of the effective illumination NA is presented elsewhere [2]. An etched Si focus exposure matrix wafer was used for this study. The CDs and pitches of the targets in the selected die were measured using a calibrated critical dimension-scanning electron microscopy (CDSEM). The line height and the sidewall shape were obtained using a calibrated atomic force microscopy (CDAFM). Measured pitch was 601 nm ± 0.2 nm and the measure line height was 230 nm ± 0.1 nm. CD-SEM measured line widths for the selected targets are 146.15 nm, 150.26 nm, 153.2 nm, 154.3 nm, 155.4 nm and 156.9 nm. The selected targets were imaged through the focus in 100 nm step size increments using an optical microscope with 0.8 collection NA, 0.37 effective illumination NA, 546 nm illumination wavelength, and 50X objective magnification. Each experiment was repeated at least three times. The mean, normalized TFFM experimental profiles are presented in Fig. 10 along with the measured CDSEM values and their standard deviations. This shows good experimental sensitivity to nanometer changes in the CD using the TFFM method. Figure 11 shows the simulated normalized TFFM profiles for CDs from 146 nm to 156 nm in 2 nm increments. Based on the similarities in appearance between the simulated and the experimental TFFM profiles, we evaluated the CD values for the targets selected. Figure 12 shows the normalized left peak focus metric value as a function of CD for both the simulations and the experiments. The curve in the figure labeled simulation is a plot of the simulated left peak focus metric values versus the CD values used as inputs to the simulations. The curve labeled experimental is a plot of the experimental left peak focus metric values versus the SEM measured CD values. By matching the intensity of the experimental focus metric value with the simulated focus metric value, CDs for all of the selected targets can be evaluated based exclusively on modeled results without reference to the SEM data as shown in Fig. 13. In this initial attempt to quantitatively measure CDs with the TFFM method based strictly on modeling results, good agreement was observed between the SEM and the optical TFFM method.

3. THROUGH-FOCUS IMAGE MAPS In this section we present another technique related to the TFFM method which uses information from the out of focus images to enhance the image-based analysis. Simulated optical images are used here to demonstrate the method. Optical images from a target of interest are obtained at different focus positions (through focus). For a two-dimensional target such as a line grating, each image at a given focus position can be reduced to an intensity profile. As the target is moved through the focus, each focus position results in a different intensity profile, as shown in Fig. 1. Here, the x-axis represents the position on the target and the y-axis represents the optical intensity (the right side of

Figure 14. The simulated TFIM obtained for an infinite line grating. Only one pitch distance TFIM is shown here. LW=40 nm, LH=100 nm, Pitch=600 nm, Illumination NA=0.4, Collection NA=0.8, illumination wavelength=546 nm, Si line on Si substrate.

Figure 15. The simulated TFIM obtained for an isolated line. LW=40 nm, LH=100 nm, Illumination NA=0.4, Collection NA=0.8, illumination wavelength=546 nm, Si line on Si substrate.

Figure 16. The simulated TFIM obtained for a finite line grating. LW=35 nm, LH=100 nm, Pitch=105 nm, Illumination NA=0.4, Collection NA=0.8, illumination wavelength=546 nm, Total number of lines simulated=9, Si line on Si substrate.



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Fig.1). The same through-focus intensity profiles can be combined and plotted such that the x-axis represents the position on the target, the y-axis represents the focus position and the z-axis represents the optical intensity. The resultant simulated through-focus image map (TFIM) is shown in Fig. 14 for an infinite line grating (only one pitch length of the image is shown here). Similarly, the simulated TFIM of an isolated line is shown in Fig. 15, and a finite line grating having a pitch much smaller than the illuminating wavelength, is shown in Fig. 16. 3.1 The Analysis At this point we make the assumption that the signature from a through focus interference pattern formed by the scattered light forms a unique signature for a given target. A small change in the dimension is likely to result in a discernible change in the resulting TFIM (although it is recognized that measurement noise can play a significant role in detectability to changes). Based on this, two types of analyses can be performed by making use of the TFIMs. In the first type of analysis, we apply the TFIMs to identify changes in target dimensions. Applications of this type are primarily process control related for critical dimension and overlay analysis. In the second type of analysis, if accurate theoretical modeling capabilities exist, TFIMs can be applied to the determination of actual feature dimensions in metrology applications, similar to image-based CD analysis except that we utilize the out of focus images explicitly. The caveat with regards to accurate modeling is important in that theory to experiment comparisons with robust, detailed agreement remains elusive. 3.1.1 The Analysis to Determine a Change in the Dimension

A small change in the dimension of a target produces a corresponding change in the TFIM. Comparing two TFIMs from different targets one can identify that a change in target dimension has occurred. Although one can compare and identify changes in many ways, here we present a method based on image map differences. Although this method can be applied to any of the targets discussed in this paper, in the current analysis we demonstrate the approach for an isolated line (several wavelengths from any nearby features), since this is one of the more difficult targets to analyze accurately. TFIMs were simulated for small changes in the target dimensions shown in Fig. 15. Three different dimensional changes were analyzed. They are a one nanometer change in the line height, a one nanometer change in the line width and a one-degree change in the sidewall angle. Comparison of the TFIMs with small changes in the dimension shows that they all appear similar. However, a simple subtraction of any two TFIMs highlights the difference between them. This we call difference in the TFIMs (DTFIM) and is shown in Fig. 17.

Figure.17. The simulated difference in the TFIM (DTFIM) obtained for isolated lines shown in Fig. 15. (a) one nanometer change in the line height (b) one nanometer change in the line width and (c) one degree change in the sidewall angle. Illumination NA=0.4, Collection NA=0.8, illumination wavelength=546 nm, Si line on Si substrate.

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The following observations can be made from the DTFIM. It may be feasible to identify a small change in the dimension of the target using this method, depending on the measurement noise, sensitivity, monotonic response, items that have not yet been investigated in depth. Notice, however, that a small change in the line height, the line width or the sidewall angle individually shows a very different DTFIM response. This is an important result and we have confirmed similar simulation-based results for several different types of targets. By evaluating the DTFIM, it may be possible to identify the dimension of the target that has changed. The same method was applied for overlay analysis as shown in Fig. 18. In the case of the finite line grating shown in Fig. 16, every alternate line was shifted by 1 nanometer to the right (1 nm overlay error). The DTFIM between zero offset and 1 nm offset overlay, shown in Fig. 9, demonstrate a potential application for this approach to overlay analysis.

3.1.2 The Analysis to Determine the Dimension of the Target The utility of the TFIM approach in metrology is based on the assumption that any given target produces a unique TFIM. This assumption was satisfactorily tested for a single case of an isolated line target using simulations. This requires a database of the simulated TFIM for all the possible combinations of the target dimensions for the given experimental conditions. The experimental TFIM can then be compared with the database. The simulated TFIM from the library, which best matched that of the experimental TFIM provides the dimension of the target. Currently we anticipate practical limitations with this approach for metrology, first and foremost due to the accuracy of the simulations. At present accurate, robust modeling is an issue.

4. CONCLUSIONS Similar to the best focus optical images, out of focus optical images contain useful information. However, depending on the application, out of focus images need to be analyzed differently to obtain the desired results. In this paper we presented two related, but different types of analysis performed on the through focus images to obtain desired information primarily for optical metrology applications. The first approach is the through-focus focus metric (TFFM). It is defined as a plot of the mean square slope of an image as the target is moved through focus. Line gratings with pitch in the order of the illumination wavelength produce multiple peak TFFMs with a minimum of near zero focus metric value between any two peaks. Using the simulations, we have shown that the magnitude of the focus metric value at the minimum between any two peaks increases with increasing angular illumination asymmetry for a Kohler illumination setup. We have shown that by monitoring this minimum focus metric value across the field of view, it is possible to evaluate the angular asymmetry of a given optical microscope. With the help of optical simulations, we have also demonstrated applications of the TFFM for critical dimension (CD) evaluation with nanometer sensitivity. The second method of analyzing the out of focus images is to align the optical intensity profiles such that the x-axis represents the position on the target, the y-axis represents the focus position and the z-axis represents the optical intensity, which results in a through focus image map (TFIM). We have demonstrated this method by making use of

Figure 18. The simulated DTFIM obtained for 1 nm difference in the overlay of alternate lines for finite line gratings shown in Fig. 16. LW=10 nm, LH=35 nm, Pitch=50 nm, Illumination NA=0.4, Collection NA=0.8, illumination wavelength=546 nm, Total number of lines simulated=9, Si line on Si substrate.

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optical simulations. A given small change in the dimension of the target produces a different TFIM. Based on the preliminary analysis, we have made the assumption that a given target produces a unique TFIM. Comparison of two TFIMs illustrates the difference in the targets. In this paper we used the difference in the TFIMs (DTFIM) to highlight the differences in the targets. We have demonstrated that for a given line or grating, change in the CD, the line height or the sidewall angle produces distinctly different DTFIMs. This enables one to identify the dimension that has changed. By comparing an experimental TFIM with that of a database of simulated TFIMs, it may be possible to determine the dimensions of a given target. Possible applications of this method include, CD metrology and overlay metrology, but will require satisfactory theory to experiment agreement.

ACKNOWLEDGEMENTS The authors would like to thank the Office of Microelectronics Programs of NIST for financial support and International SEMATECH for wafer fabrication support. The authors also would like to acknowledge Robert Larrabee, Thomas Germer, Michael Stocker, Heather Patrick, Bryan Barnes, Egon Marx, Jay Jun and Mark Davidson for assistance and useful discussions.

REFERENCES

1. R. Attota, R. M. Silver, M. Bishop, E. Marx, J. Jun, M. Stocker, M. Davidson, and R. Larrabee, “Evaluation of New In-chip and Arrayed Line Overlay Target Designs,” Proc. SPIE, Microlithography Vol. 5375, p. 395 (2004).

2. R. Attota, R. M. Silver, T. A. Germer, M. Bishop, R. Larrabee, M. T. Stocker, and L. Howard, “Application of Through-focus Focus-metric Analysis in High Resolution Optical Metrology” Proc. SPIE, Microlithography Vol. 5752, p. 1441-1449, 2005.

3. R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, “High resolution optical metrology” Proc. SPIE, Microlithography Vol. 5752, p. 67-79, 2005.

4. T.A. Germer, and E. Marx, “Simulations of optical microscope images of line gratings,” Proc. SPIE, Microlithography Vol. 6152, 2006.

5. Y. Ku, A. Liu, and N. Smith, “Through-focus technique for nano-scale grating pitch and linewidth analysis” Optics Express Vol. 13, p. 6699-6708, 2005.

6. R. Attota, R.M. Silver, M.R. Bishop, and R.G. Dixson, “Optical critical dimension measurement and illumination analysis using the through-focus focus metric,” Proc. SPIE, Microlithography Vol. 6152, 61520K (2006).

7. R. M. Silver, B. M. Barnes, R. Attota, J. Jun, J. Filliben, J. Soto, M. Stocker, P. Lipscomb, E. Marx, H. J. Patrick, R. Dixson, and R. Larrabee, ‘The limits of image-based optical metrology,’ Proc. SPIE Int. Soc. Opt. Eng., Vol. 6152, 61520Z (2006).

8. Eric Krotkov, “Focusing,” Int. Journal of Computer Vision, Vol. 1, p. 233 (1987). 9. S. Fox, R.M. Silver, E. Kornegay, and M. Dagenais, “Focus and edge detection algorithms and their

relevance to the development of an optical overlay calibration standard,” Proc. SPIE Vol. 3677, p. 95 (1999).



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