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Optical microscopy is sensitive both to arrays of nanoscale features and to their imperfections. Optimizing scattered electromagnetic field intensities from deep sub-wavelength nanometer scale structures represents an important element of optical metrology. Current, well-established optical methods used to identify defects in semiconductor patterning are in jeopardy by upcoming sub-20 nm device dimensions. A novel volumetric analysis for processing focus-resolved images of defects is presented using simulated and experimental examples. This new method allows defects as narrow as (16 ± 2) nm (k = 1) to be revealed using 193 nm light with focus and illumination conditions optimized for three-dimensional data analysis. Quantitative metrics to compare two-dimensional and three-dimensional imaging indicate possible fourfold improvements in sensitivity using these methods.
© 2013 Optical Society of America
1. Introduction
Nanotechnology and nanoscale imaging present new challenges to optical measurement methods. Some successes are widely known, such as scatterometry and parametric modeling of the reflected specular field for the determination of nanoscale dimensions of arrayed targets [1]. Capturing and measuring the entire scattered electromagnetic field has likewise been performed using optical microscopy [2]. Imaging platforms provide a highly localized probe of the intensity laterally and axially when collecting both in and out of focus images.
Optimizing both the measurement of the scattered field and the perturbations due to nanoscale imperfections, or defects, in an arrayed target are of critical importance to high-volume semiconductor manufacturing. Detectability is evaluated by subtracting a reference image from an image acquired from the sample under test, with a localized intensity difference possibly indicating a defect. Light-scattering instruments used for defect inspection rely on isolating subtle variations in the scattered field to identify defects. The looming challenge for optical patterned defect inspection as critical dimensions (CDs) decrease below 20 nm is the relative falloff in the defect’s scattered intensity. As defects approach the 10 nm scale, it has been shown that the scattered intensity to first order is proportional to CD6/λ4 based on Mie scattering theory [3]. Detection of such a diminished signal with reduced CD is made even more difficult by both instrument noise and subtle variations in the patterned features often referred to as wafer noise [4]. The noise directly affects the difference image and compromises defect detection. New approaches to the acquisition and processing of noise laden optical data are needed to perpetuate effective optical defect metrology.
We have previously shown that engineering the incident angle, wavelength, polarization, and focus position in an optical microscope are critical to extending high resolution optical metrology [5] and improving defect detectability [6]. This paper outlines a new approach to utilize the full three-dimensional scattered electromagnetic field to isolate the differential electromagnetic “signal” from deep sub-wavelength defects through collection and analysis of three-dimensional volumetric images acquired from focus resolved imaging. Tympel et al. previously reported a three-dimensional optical defect detection approach, which was applied to resolvable particulate contamination more than an order of magnitude larger than presented in this paper [7]. Three-dimensional extreme ultra-violet (EUV) mask defect detection has been proposed using coherent scattering stereoscopic microscopy with phase retrieval [8], and 20 nm wide defects have recently been observed from intensity and phase measurements using interferometric microscopy [9]. Here, sub-20 nm patterned defects are successfully detected using intensities by coupling through-focus microscopy from a bright field microscope with advances in three-dimensional volumetric image analysis. Selected qualitative comparisons between two- and three-dimensional defect differential images at λ = 193 nm illustrate the impending necessity of using three-dimensional methods. Defect metrics are presented that provide quantitative evaluations on a common footing between two- and three-dimensional imaging approaches.
2. Capturing and simulating images of intentional patterned defects
The basis of all simulations and experiments in this work is the 9 nm node SEMATECH Intentional Defect Array (IDA). The IDA offers a variety of defects (e.g., islands, bridges, extrustions) with an assortment of defect sizes; two types of bridging defects are used for illustration here with schematics and example scanning electron microscope (SEM) images shown in Fig. 1. Several dies were printed in an exposure matrix to vary the widths and quality of the features that were patterned in an e-beam resist exposure, leading to variations in wafer noise among dies. Critical dimensions of these defects were nominally scaled to the design rule (9 nm) of the patterned lines. SEM measurement of the lines and defects indicate that the maximum widths of these features are larger than their nominal values for all printed dies, as will be shown in Table 1.
Fig. 1 Scanning electron micrographs of patterned defects. a) “Bx” bridge. b) “By” bridge. Insets show schematics for simulation. c) Axis, angle definitions relative to the patterning. The heights of the lines are nominally 35 nm.
Table 1. Defect Metrics Comparisona
Simulation is performed by numerically evaluating the scattered field from these patterns with and without defects using the finite-difference time domain (FDTD) method [10]. To faithfully represent a single defect in a dense periodic array, the defect is placed in a single unit cell of the repeating nominal structure and then surrounded by a sufficient number of defect-free unit cells. This minimizes the artificial amplification of the defect signature due to optical resonances that result from the periodic numerical methods used in the FDTD simulation. Finite aperture and incident angle effects in incoherent Köhler illumination are accounted for by computing the scattering for several plane waves originating at a conjugate back focal plane. Simulated defect and reference images are obtained using Fourier optical imaging methods with the focal position z selected using the Helmholtz equation. Random and correlated noises are added to simulate realistic intensity backgrounds.
Experimental images were collected using the National Institute of Standards and Technology (NIST) 193 nm Microscope, described in detail elsewhere [11]. The full-field effective illumination numerical aperture (NA) is annular due to a catadioptric objective and ranges from 0.11 NA to 0.74 NA, as illustrated in the schematic in Fig. 2(a). Defects were also illuminated using dipole illumination as illustrated in Fig. 2(b). Since the patterns are highly repetitive, at each defect location and focus position, an image of the defect was collected as well as a “reference” image. In practice the reference image is obtained by laterally shifting the sample by a multiple of the periodic unit cell. The lateral shift in these experiments was within the field-of-view, thus experimental difference images in this present work often show two copies of the defect. While having a copy shifted a known distance empirically confirms the observation of the intentional defect, the three-dimensional technique described here does not require the use of this additional defect measurement, as shown through simulation.
Fig. 2 Orientation of full-field and dipole illumination relative to the patterned structure. a) Annular full-field illumination b) 0° and 90° dipole orientations with respect to the patterned lines.
Selected measured two-dimensional differential images appear as Fig. 3. These examples demonstrate the extremes of two-dimensional image-based inspection. Many measured defects yield images such as Figs. 3(a) and 3(b) that directly reveal defects that can be isolated using simple intensity and two-dimensional size thresholding algorithms. The optical defect signatures in Figs. 3(c) and 3(d) are highly impractical to detect in two-dimensional images. It is for such defects that three-dimensional volumetric analysis will be required.
Fig. 3 Two-dimensional absolute-value difference images for selected dies and defects. Defect widths as measured using SEM are decreasing from left to right, with defect width values specified in Table 1.
3. Establishing three-dimensional data sets for defect inspection
The goal of our technique is the accurate inspection of semiconductor patterned defects by thorough examination of the electromagnetic scattered field. Each two-dimensional image samples this field at a particular focal height z with each pixel yielding an intensity, I, that can be mapped to an (x, y) position on the sample. Multiple images can be collected or simulated through focus as illustrated in Fig. 4(a). In Fig. 4(b), each position (x, y, z) can be represented using a volumetric element, or voxel, with each voxel containing a single value for I. In this work, voxels are cubic with each simulated voxels edge sized 39 nm and experimental voxels sized 40 nm per side, matching the nominal pixel area. Experimental volumes are calculated using three-dimensional interpolation, as the z step size was 25 nm. Both the reference image data and the defect image data must be converted to volumes. Various multi-dimensional mathematical operations can be performed to increase the relative signal from the defect. In Fig. 4(c), experimental data are filtered using a three-dimensional fast Fourier transform (FFT) to remove the highest and lowest frequency noise.
Fig. 4 Steps in generating three-dimensional defect images. a) Selected 2D simulations performed through focus. b) The full simulation set stacked into a volumetric matrix c) Experimental data filtered using a 3D fast Fourier transform (FFT).
Figure 5 demonstrates the additional operations required to extract meaningful information from these three-dimensional volumes. For experimental data sets, subtle drifts in focal position or sample stage position necessitate sub-voxel realignment. Enhanced correlation coefficient (ECC) maximization [12] is performed to optimize the alignment simultaneously in all three spatial dimensions, shown schematically in Fig. 5(a). The ECC enables precise alignment of the defect volume to the reference volume with sub-nanometer precision through three-dimensional interpolation. The absolute value of a simulated difference volume is shown in Fig. 5(b), and it is from such a volume that the optical signature from a defect must be accurately identified. The scattering from the defect is isolated as the green isosurface in Fig. 5(c) with other artifacts shown in red.
Fig. 5 Volumetric analysis for defect detection. a) Correlation of experimental reference and defect matrices using a 3D correlation algorithm. b) Simulated difference volume with cut-out showing the optical signature of a defect. c) Application of intensity and size thresholds differentiate the defect’s primary optical signal (green) from random and correlated noise (red).
The data analysis protocol used for Fig. 5(c) exploits not just the (x, y) extent of the optical scattering intensities but also its relatively large extent in z. The difference volume is intensity thresholded to isolate higher intensity regions (subvolumes). The threshold is determined here by using a selectable multiple of the standard deviation of all voxels. Each region is inspected to determine if these cubic voxels have 26 nearest and next-nearest neighbors, ensuring maximum continuity in the x, y, and z axes. The number of pixels in each region is computed as well as its maximum width, height, and depth. This approach enables full utilization of the 3D nature of the data set.
Figure 6 shows fully processed simulations of 9 nm CD bridge defects situated in an array of 9 nm CD lines with the defect identified. The maximum extent in the z direction easily separates defects from the noise for two cases, and polarization is also seen to substantially enhance the defect scattering. Identification was optimized for the “Bx” defect using linearly polarized light along the x direction and for the “By” defect using y polarized light, while the realistic noise model suppresses the weaker signal for polarizations orthogonal to the bridge direction. This trend is verified using experimental and simulation results on similar bridge defects on the 22 nm node IDA [9]. The volumetric extent of the defects in Figs. 6(a) and 6(d) is at least 3 x 2 x 9 voxels, indicating a minimum focal range (z) of at least 350 nm and a spatial extent of at least 110 nm x 80 nm (x, y). For comparison, these defects are defined to be 9 nm in CD, 35 nm in height, and either 60 nm (“Bx”) or 51 nm (“By”) in length.
Fig. 6 Polarization-dependent detection of simulated defects in the presence of noise. a) “Bx” defect, x pol. b) “Bx” defect, y pol. c) “By” defect, x pol. d) “By” defect, y pol.
This new approach addresses key issues that traditionally limit conventional defect detectability. Our simulation noise model includes correlated and random noise to better represent experimental artifacts such as wafer noise, line edge roughness, camera errors, microscope aberration, and focus-dependent lens imperfections. Unlike random noise, these factors often extend throughout a given z range similar to a defect, although observations thus far indicate that the optical signal from such events may have smaller spatial extent. In Fig. 7, two copies of a “By” defect from the third die are found in the three-dimensional space. One isometric view and two projections are shown to illustrate the data set, and a two-dimensional slice through the processed volume is shown at an optimal z height for comparison. Figure 7(d) shows that even after choosing an optimized focal plane, a single 2D image is insufficient to identify this (16 ± 2) nm (k = 1) CD defect. Although several defects in this IDA, which was printed in a single patterning level, do not require a full three-dimensional analysis, inspection in a manufacturing environment will require measurement of sub-15 nm defects patterned in more complex multiple layers. This measurement methodology is expected to be of most benefit measuring these complex three-dimensional samples.
Fig. 7 Renderings of a volumetrically processed experimental difference volume with two copies of a defect signature identified. Defect corresponds to Fig. 3(d). a) 3D isometric view, b) YZ projection, c) XY projection, and d) XY slice through the centroid of one of the defects (green) and noise (red) identified at that height. Area thresholding can remove much of the noise in this plane, but unique isolation of the intentional defect in 2D is frustrated by the noise.
An important outcome of the volumetric analysis of these samples is that the optical response from the defect can be completely isolated with proper intensity, volume, and size thresholding. The interactions among these thresholds determine the utility of this methodology. Here, there are six thresholds placed on the data: intensity, total volume, nearest-neighbor, and the maximum extents in x, y, and z. The centroids of the two defect optical signatures were determined, then five parameters (all but nearest-neighbor) were varied during volumetric analysis of several defects. For most of these defects, the three-dimensional intensity threshold was dominant. Relatively low intensity threshold values yielded more than two “defect” subvolumes, leading to false positives while relatively high intensity thresholds produced one or two false negatives. In Fig. 8 the ratio between the true and false positive volumes is shown for variations in intensity threshold and the z extent threshold. The white band indicates that the detection of two copies of the defect optical signatures has been fully optimized. Although a comprehensive statistical analysis evaluating these thresholds is beyond the scope of this paper, statistical treatments for combining spatial extent testing and peak intensity thresholding have been introduced by Poline et al. for assessing the risk of error in analyzing three-dimensional positron emission tomography (PET) images [13].
Fig. 8 Signal to noise analysis of the volumetric defect detection method varying the intensity and extent in z. The signal to noise ratio (SNR) is defined here as the sum volume of positive defects detected divided by the sum volume of all false positives. The detection of two copies of the defect was optimal in the white band with no false positives. Black regions above and to the right of this band yielded less than two defect signatures (false negatives). Regions in red yielded false positives and calculable SNR. This graph corresponds to Die 3, Defect “By” (Fig. 7) with the “X” marking the parameter set used in that figure and for all other dipole-illuminated data in Table 1.
4. Computing defect metrics for quantitative comparison
Optical defect inspection on a qualitative level is binary (i.e., pass/fail), as in Fig. 7 in which two defect copies were correctly identified in three-dimensional volume while detection from a two-dimensional image is problematic. To quantitatively evaluate and compare detectability between two- and three-dimensional images, defect metrics are required that can reduce the information in the differential volume to a form enabling direct quantitative comparison. Two metrics have been developed, each of which is computed for “Bx” and “By” defects from three different dies as shown in Table 1. For these six defects, metrics are computed after volumetric processing has separated the defect subvolumes from the noise subvolumes as in Fig. 7, with the volume and centroid (xc, yc, zc) of each defect identified. For the two-dimensional image, an xy slice through the defect and noise subvolumes is extracted at the focal height zc of the larger defect as shown in Fig. 7(d).
The first metric reduces the larger defect subvolume into its xz and yz projections. The voxels are flattened such that each voxel with a given (xi, yi, zi) yields a pixel in (xi, zi) and (yi, zi), respectively. The areas of these data sets are compared against the area of this defect in the xy image. The second metric integrates the intensity of this three-dimensional defect differential subvolume, which is then compared with the integrated intensity of the defect in the two-dimensional image. Defect metric results for these two metrics are shown in Table 1.
As outlined in Section 3, intensity thresholding is critically important and is set using a multiple of the standard deviation of the absolute value of the intensity after 3D Fourier filtering, thus defect metric value comparisons should be made within individual rows in Table 1. The data clearly demonstrate that using three-dimensional data analysis improves defect sensitivity by at least a factor of four when using the integrated intensity metric and increases the area-based metric as much as fourfold or more. The improvements in these metrics stem from the greater extent of the optical signal along the z axis than its extents in x and y, as focus-resolved scanning yields changes in the phase information with little effect on the intensity, independent of defect size.
With additional tailoring of the Fourier filtering, adjustments to thresholding, and application of more sophisticated metrics, these sensitivities may improve further. An important research direction for this technique is the development of protocols that enable similar gains in sensitivity while performing measurements at fewer focal planes for more efficient throughput. Additionally, more investigation is needed to better understand the interplay between polarization and defect orientation. While detectability was highly polarization dependent in Fig. 6, experimentally, such a clear relationship is not observed on the present IDA, perhaps due to the three-dimensional shape of these defects.
5. Summary
Optical imaging methods for defect inspection are extensible through full use of the three-dimensional electromagnetic scattered field that has been perturbed by patterned defects. Deep sub-wavelength defects with widths as small as (16 ± 2) nm have been experimentally detected using this volumetric technique. Larger defects were visible using simpler two-dimensional image analysis, and two-dimensional imaging can be used when feasible. Simulation indicates that bridge defects with sub-10 nm critical dimensions will be detectable using λ = 193 nm light and three-dimensional data collection and analysis methods. As critical dimensions and pitches trend smaller, single images are likely to be insufficient for accurate defect detection. Through experimental demonstration, simulation, and quantitative comparison using defect metrics, this three-dimensional approach excels in sensitivity for smaller defects and should provide an essential solution to the known challenges ahead in defect metrology.
Acknowledgments
The authors thank Dr. Bin Ming for his assistance and training in obtaining SEM data and Dr. Jing Qin for her helpful discussions. This project was funded internally by NIST.
Certain commercial materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials are necessarily the best available for the purpose.
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