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We report results of experimental investigations into a through-focus method relevant to sub-wavelength feature dimension measurement. The method linearizes the partial derivative values of a focus indicator with respect to minimum intensity order, and hence permits determination of pitch using a classical linear method. By evaluating the variations in focus indicator of the different captured images obtained at various focal positions, the through-focus curves show a response to sub-resolution changes in the grating structure. The results suggest that sub-wavelength feature dimensions can be evaluated using regular optical microscopes by implementing the through focus method.
©2005 Optical Society of America
1. Introduction
Because of the continued rapid development of the semiconductor industry, there is a continued requirement to reduce the feature dimensions of integrated circuits. Metrology tools must also be improved to meet the even more severe requirement of measurement precision and accuracy. The approach used to measure sub-wavelength features is important because it is strongly related to device-size measurement accuracy; furthermore, it affects the yield of integrated chip manufacturing. Optical imaging methods are commonly thought to face challenges for nanos-tructure analysis that involve the limitation of resolution of a metrology tool beyond the Rayleigh criterion. Optical interference leads to errors in the determination of the location of lines and, therefore, errors in feature dimension measurements. Thus, reliable measurements based on a theoretical model or enhanced algorithms are required. The through-focus method has been studied in previous papers for edge detection and enhancing overlay tool performance [1–3]. Multi-peaked focus plots were observed from the imaging tools when the target includes sub-resolution lines. The behavior is more pronounced when arrays of lines are used.
We developed a method that is based on the through-focus metric, and which does not require a detailed understanding and separation of the proximity effects between features. In this report that demonstrate that we can use a focus quality metric calculated from a sequence of images acquired as the target is moved through focus for our purpose. We have evaluated several different focus criteria for images acquired by bright-field microscopy [4–9], including gradient energy, standard deviation, contrast, Laplacian and total intensity. They were chosen because of their widespread use in semiconductor manufacturing and other industries. The best, but not the only, focus metric is “Gradient Energy”, an image-based focus analysis method that has been used since 1980[10,11]. The gradient energy is determined by applying the operator Q on the image intensity, where Q is defined by:
The discrete gradient may be implemented in numerous ways. We chose the Sobel method in order to reduce sensitivity to noise [12]. The standard deviation method is defined as the standard deviation of the image pixel values from the mean of all included pixels.
The total intensity is simply the sum of the pixel values:
The Laplacian is computed from the second derivative of the pixel values:
Contrast is defined from the minimum and maximum image intensity:
In all cases in which algorithms are compared to one another their responses are normalized to their peak values. Standard deviation was found to be the best criterion of the five tested for the pitch and critical dimension measurement. Our method linearized the partial derivatives values of the focus position with respect to minimum intensity order, and hence permits determination of pitch using classical linear method.
2. Experimental measures
2.1 Pitch measurement
For this study we used 150mm diameter test wafers manufactured with the NDL (Nano Device Laboratory, Taiwan) 0.35μm process. The exposure tool was an I-line 365 nm aligner. Two groups of test grating targets (an etched silicon oxide grating layer on a silicon wafer, and an etched silicon grating) of approximately 25 μm outside dimensions were designed and fabricated. All experiment data herein were implemented using an automated overlay metrology tool, an Accent Q200. Figure 1 shows the bright-field microscope measurement system layout. The CCD camera acquired the image, and then a series of through-focus images were acquired while the sample stage was moved continuously along the optical path (tool Z axis). The Z position was adjusted between −16μm and 16μm from best focus position in increments of 0.1μm. The data is acquired using a fixed signal acquisition mode such that the gray scales are absolute. Figure 2 shows four examples of the images acquired for a grating with linewidth/spacing dimensions of 0.5μm/0.5μm. Each image is 512 × 512 8-bit. These data were acquired with 0.3 illumination NA, 0.5 collection NA, and illumination centered at 550nm with 50nm FWHM.
Fig. 2. (a) The focused image of the grating with 0.5μm line-width and 0.5μm spacing. The defocused image with (b) 2μm (c) 5μm (d) 10μm focus offset
Figure 3 shows the response of the various focus algorithms to the periodic pattern of the etched silicon wafer. The focus measures were normalized to each have the same peak value of unity by dividing by the maximum value of their focus measures. We define the first local minimum along the negative focus offset as order -1, the second local intensity minimum as order -2, and so on. The same procedure was used for picking the local intensity minima with positive focus offset as orders 1, 2 and so on. The focus response was calculated within the region window marked with a red frame as shown in Figure 3. In general the total intensity algorithm showed very little variation between out-of-focus and in-focus images. The contrast of the image is also not a good indicator of image focus due to its low sensitivity to variation of the image with defocus. The Laplacian showed poor sensitivity in side lobe defocused image intensity, which is a key phenomenon in our application. The gradient energy metric provides the sharpest main peak discrimination while the standard deviation metric discriminates the side lobes more sharply. Thus we used the standard deviation algorithm as our best focus criteria for pitch measurement. The relationship between the focus offset and the Z position of the local minimum intensity orders can be used to measure the pitch of the grating, as will be discussed in the following sections.
Figure 4 shows the response of the various algorithms to the periodic silicon dioxide gratings. The etched SiO2 layer thickness is around 100 nm. Similar observations were obtained as with the bare Si grating target - the gradient energy metric provides the sharpest main peak discrimination; the standard deviation metric discriminates the side lobe more sharply. The difference in the side lobe profiles in Figure 3 and Figure 4 demonstrate that the response depends on the material composition of the artifact.
Table 1 gives details of the silicon dioxide grating structures available. The thickness of grating layer is 100 nm. Five grating samples with the dimension of linewidth/spacing are 0.5/0.5 μm, 0.5/1.0 μm, 1.0/1.0 μm, 1.0/1.5 μm, and 1.0/2.0 μm respectively.
Fig. 3. Top: The focus measures of the etched silicon grating target (0.5μm linewidth/0.5μm spacing); bottom left: focused image with selected measurement window; bottom right: grating intensity profile.
Fig. 4. Top: The focus measures of the etched SiO2 grating target (0.5μm linewidth/0.5μm spacing); bottom left: focused image with selected measurement window; bottom right: grating intensity profile.
Table 1. Sample wafer for pitch measurement.
2.2 Critical Dimension measurement
For this study we used 100mm test wafers with the e-beam direct writing process (Nano Technology Research Center, Taiwan) in order to get narrower linewidth. The thickness of the developed photoresist grating layer on top of the Silicon wafer is around 110 nm. Table 2 gives details of the test wafer structures available. The images were acquired with an Accent Optical Technologies Caliper élan overlay tool. Once again, 512×512 pixels images of the target pattern were acquired. These data were acquired with 0.3 illumination NA, 0.5 collection NA, and 50nm FWHM illumination centered at 550nm. The standard deviation algorithm was used as our best focus criteria for critical dimension measurement.
Two groups of test targets with fixed pitch 800 nm and 1200 nm were designed and fabricated. The photoresist grating layer was developed on top of Silicon substrate wafer. The minimum pitch for which the tool can image the line structure within the gratings is set by the tool resolution at about 800nm.
Table 2. Sample wafer for CD measurement
3. Through focus measurements
3.1 Pitch measurements
Figure 5 shows plots of focus position versus minimum intensity order Z position from etched SiO2 grating targets with the same linewidth and pitch as the grating targets on the etched SiO2 wafer. The through-focus images were acquired for 0.5μm/0.5μm, 0.5μm/1.0μm, 1.0μm/1.0μm, 1.0μm/1.5μm, 1.0μm/2.0μm (linewidth/spacing) grating targets. The relationship between focus position (focus offset) and local minimum intensity order were linear, as shown in Fig. 5. The partial derivatives of these linear curves is plotted against the grating pitch in Fig. 6. The plot demonstrates that the slope of the focus position divided by the order depends linearly on the grating pitch. The slope of the fitting curve is approximately 1.42. The fitted line and the experimental results agree within 4%. This result shows that the through-focus information for a grating does contain information related to its dimensions, and that a relationship exists which could be used as a basis for measurement. However, the method only works for if the grating pitch is large enough to be resolved by the imaging microscope, and simpler methods of determining the pitch are available. The true interest of this method arises because the through-focus data allows us to extract information about the width of the lines in the grating, even though they are smaller than the resolution limit of the tool.
3.2 Critical dimension sensitive measurements
Figure 7 shows the through-focus response as a function of linewidth and a grating pitch of 800nm for three linewidth/spacing combinations of 200nm/600nm, 400nm/400nm and 600nm/200nm. The linewidth was varied by 200nm, keeping all other dimensions constant. It can be seen that through focus response shows strong dependence on and good sensitivity to the line width. The response level at the subsidiary peak positions is particularly interesting with substantial variations in contrast and intensity. These data show a significant change in contrast and response level when comparing different linewidths. Although the absolute lateral positions of the peaks in the focus metric curves are one measure of the sensitivity to changes in linewidth and geometry, these data show an alternative approach by comparing the contrast or amplitude difference.
Figure 8 shows the through-focus response as a function of line width and pitch 1200nm for five line-width/spacing combinations at 200nm/1000nm, 300nm/900nm, 400nm/800nm, 900nm/300nm and 1000nm/200nm grating targets.. In order for this method to work it is necessary for the grating pitch to be large enough (compared to the resolution of the tool) that there is some modulation visible in its image. The imaging tool operates with a NA of 0.5, and hence a grating with pitch 800nm is the finest that can be resolved. Increasing the aperture of the imaging tool will reduce its resolution limit, allowing finer pitch gratings to be used – to 450nm, for example, if the NA is increased to 0.9. The depth of field will also be reduced by an increase in NA, requiring shorter movements around focus but ideally with improved Z resolution if the data quality is to be kept at the same levels. Similar effects would apply to operation at shorter wavelengths. Both increasing NA and reducing imaging wavelength should allow the capability of the method to be extended to smaller CDs. In this way, a demonstration of an ability to measure CD from the data reported in this work should allow extension to smaller CDs to be anticipated.
For constant pitch the period of the modulation of the through-focus metric is constant, as was demonstrated in figure 6 and can be seen again in figures 7 and 8 where the location of the minima do not change with CD. However, the relative magnitude of the maxima in the focus metric plots changes strongly with CD, even when the CD is much smaller (<200nm at least) than the tool resolution (800nm). In semiconductor process control applications we are concerned with controlling the width of lines in arrays where the pitch will not change significantly, which is precisely the situation investigated here.
The very strong changes in the through-focus signature with CD suggest that it is possible to use this data to measure the width of the lines in the grating. A similar situation arises in the use of scatterometers, where a change with incident angle or wavelength in the first-order scattered signal from a grating can be characterized to allow information about the grating – including the line CD – to be determined. It is normal to use rigorous models when interpreting the signature from a scatterometer, and ideally the same approach should be applied to the through-focus data presented here[13,14]. But no such model currently exists, and because imaging systems are more complicated than scattering ones, this may not be a practical route. Empirical methods remain possible, however. We can characterize the variation of key features in the though-focus metric from a reference grating against its line CD and use that information to estimate the linewidths in a test grating. The obvious advantage of this method is that it removes the need for a very accurate image formation model, but at the expense of the requirement for a calibration sample and potential complications if other grating dimensions (for example the layer thickness, or the side-wall angle of the lines) change.
Fig. 5. The minima in the focus plot against order for the (a) 0.5μm/0.5μm (b) 0.5μm/1.0μm (c) 1.0μm/1.0μm (d) 1.0μm/1.5μm (e) 1.0μm/2.0μm (linewidth/spacing) grating target pattern.
Fig. 6. The plot of partial derivative of focus position with respect to minimum intensity order versus pitch. The slope of the fitting curve is approximately 1.42.
Fig. 7. Through focus intensity of grating targets as a function of linewidth at pitch 800nm (linewidth/spacing combinations at 200nm/600nm, 400nm/400nm and 600nm/200nm).
Fig. 8. Through focus intensity of grating targets as a function of linewidth at pitch 1200nm for five linewidth/spacing combinations (200nm/1000nm, 300nm/900nm, 400nm/800nm, 900nm/300nm and 1000nm/200nm).
4. Summary
This work has demonstrated that a through-focus metric from a regular optical imaging microscope is sensitive to the dimensions of nano-scale features in a grating. It can be used to evaluate the pitch and critical dimension of an array of lines and possibly of multilevel structures. By evaluating the variations of the different captured images through analysis of the optical images intensity obtained at various focal positions, the through focus curves experimentally demonstrate sub-resolution sensitivity with grating structures. For the most part overlay measurements are essentially pitch measurements between two layers and are well-suited to image-based analyses, thus the through-focus method has its potential application in overlay metrology, and more, for the process control in future semiconductor manufacturing.
Overall, the data indicate that for bright-field mode the standard deviation is the most suitable focus algorithm of those tested for our purpose. We evaluated the focus response from a grating on the Z spacing of the peaks for CD measurement. The strong response of focus intensity signature to CDs well below the tool resolution might be usable to characterize these nano-scale features.
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