The present application relates generally to measurement and evaluation of pattern features from images thereof, and, more particularly, to systems, methods, and devices for evaluating closed two-dimensional pattern features, for example, semiconductor device pattern features, from electron microscope images thereof.
A semiconductor manufacturing process forms one or more patterns on or in a substrate to form a semiconductor device. For example, photolithography transfers a pattern from a mask to photoresist on the substrate, thereby resulting in a photoresist pattern which serves as a template for subsequent material addition or removal steps in the formation of the semiconductor device. Because of variations in the semiconductor manufacturing process, the resulting pattern on/in the substrate may not always correspond sufficiently to the desired pattern. Variations in the resulting pattern may adversely affect device performance, especially when alignment and/or spacing between sub-millimeter scale features is important. For quality control purposes, feature sizes of a pattern are measured after forming of the pattern on/in the substrate to verify that the pattern satisfies desired tolerances. Such size measurements include, for example, measuring a width of a line pattern or a diameter of a hole pattern.
In order to evaluate size information of the formed patterns, images of the patterns after formation may be analyzed, for example, by extracting edges of the patterns and measuring a dimension of the pattern based on the extracted edges. When manufacturing semiconductor devices having small feature sizes (e.g., less than 1 μm), the images may be obtained using an imaging device sufficiently powerful to resolve the individual features of the pattern. For example, a scanning electron microscope (SEM) is used to obtain plan view images of the formed patterns.
For larger size features, the size measurements may focus on determining a dimension (e.g., width, length, diameter, etc.) of the formed pattern. Variations and/or roughness along the edge of the pattern may thus be trivial compared to the overall dimension of the pattern. For example, a 10-nm edge roughness for a 100-μm wide line pattern may be a relatively insignificant deviation. However, as feature sizes decrease, even minute variations introduced by edge surface roughness may result in a significant deviation in ideal device performance. For example, a 10-nm edge roughness for a 50-nm diameter hole pattern may be a relatively significant deviation. The measurement of formed patterns may thus include a measurement of edge roughness as well as pattern dimension. When applied to hole or dot patterns, the edge roughness is termed hole edge roughness. When applied to a small contact hole or dot patterns (e.g., with feature sizes less than 50 nm), the edge roughness is termed contact edge roughness (CER).
Embodiments of the present invention address the above-mentioned problems and limitations, among other things.
In embodiments, a measurement tool apparatus, which detects variations in hole or dot pattern features, extracts pattern-edge points along a pattern's circumference. The apparatus then calculates deviations of the pattern from a designed shape using the extracted edge points. Analyzing the deviations for a particular pattern yields one or more metrics for the pattern. Based on the one or more metrics, the apparatus calculates an index representative of the geometry of edge spokes of the pattern and/or the anticipated effect of edge spokes on device performance.
In embodiments, a system for evaluating a hole pattern in a semiconductor device pattern includes an image processing module and a pattern evaluation module. The image processing module extracts position information of an edge of the hole pattern from a critical dimension SEM (CD-SEM) image of the semiconductor device pattern. The pattern evaluation module fits a shape to points on the edge of the pattern and determines a deviation for each of the points from a corresponding point on an edge of the fitted shape. The pattern evaluation module also calculates a height index and a width index based on the determined deviations and a concavity parameter based on the extracted position information. The pattern evaluation module further calculates a roughness metric for the hole pattern based on the calculated height index and width index.
In embodiments, a system evaluates a semiconductor device pattern, which includes a hole pattern. The system includes a CD-SEM, an image processing module and a pattern evaluation module. At least one of the modules is integrated with the CD-SEM. The image processing module extracts position information of an edge of the hole pattern from a CD-SEM image of the semiconductor device pattern. The pattern evaluation module quantifies deviations of the edge of the hole pattern from an edge of an ideal shape fitted to the hole pattern. The pattern evaluation module also calculates a height index and a width index associated with the hole pattern based on the quantified deviations. In addition, the pattern evaluation module determines an electric field concentration for the hole pattern based on the calculated height index and width index.
In embodiments, a system for evaluating a hole pattern includes an image processing module and a pattern evaluation module. The image processing module extracts edge information of the hole pattern from a CD-SEM image. The edge information includes positions of a plurality of points on an edge of the hole pattern. The pattern evaluation module quantifies a difference in the position of each of the plurality of points from a position of a corresponding point on an edge of an ideal shape fitted to the hole pattern. The pattern evaluation module also calculates a height index and a width index associated with the hole pattern based on the quantified differences. In at least one embodiment, the height index is equal to
where m is the number of points on the edge of the hole pattern and Δri is the quantified difference for each said point. The width index is a length, ξ, for which an autocorrelation function applied to the deviation in a height direction along the circumference of the ideal shape has a value of 0.2. The pattern evaluation module also computes a roughness metric for the hole pattern based on the calculated height index and width index. The roughness metric is one of a sharpness parameter, which is equal to the height index divided by the width index, and an electric field concentration for the hole pattern.
The foregoing and other aspects, features, and advantages of the present invention will be better appreciated from the following description of embodiments, considered with reference to the accompanying drawings, wherein:
Embodiments will hereinafter be described in detail with reference to the accompanying drawings, wherein like reference numerals represent like elements. The accompanying drawings have not been drawn to scale. Any data presented in the accompanying graphs and figures is for illustration purposes only and may not represent actual data. Where applicable some features have not been illustrated to assist in the description of underlying features.
Edge roughness of a degraded hole pattern can cause an electric field concentration to occur at sharp tip projections, referred to herein as spokes, at an edge of the pattern. With reference to
In contrast, contact hole 106 has a spoke 110, which projects away from contact hole 104. Since the region of insulator 102 between holes 104 and 108 has been effectively increased by spoke 110, this type of defect may be less susceptible to electrical breakdown if a potential difference exists between contact holes 104 and 106. Because it projects toward the interior of the contact hole 106, such spokes 110 are termed herein concave spokes.
To evaluate CER of a hole or dot pattern, the pattern formed in/on the substrate is compared with an ideal shape, such as a designed shape or a fitted shape, to determine the variation of the edge from an ideal smooth contour. The standard deviation, σ, of the variations of the edge is used to characterize the edge roughness. The standard deviation provides a measure of the variability of the edge of the hole pattern. However, the standard deviation does not provide a measure of the sharpness of spokes, which plays a role in electric field concentration.
A self-correlation angle can be calculated from a local difference between the shape of a designed (or fitted) pattern and that of the formed pattern. This self-correlation angle is approximately equivalent to an angle 206 corresponding to the width of spoke 204 that exists at the edge of pattern 202, shown in
For example, when a pattern is an elliptical pattern, as shown in
Note that the performance of semiconductor devices may be sensitive to the sharpness of spokes in line patterns as well as hole patterns. As such, the self-correlation angle may provide a measure of the potential for electric field concentration due to edge roughness of line patterns as well. In view of the discussion above, the self-correlation angle of a spoke extending away from the interior of the pattern may be important in evaluating a pattern. However, while the self-correlation angle may provide an indication of sharpness, it does not always provide an accurate indication of the size or orientation of the spoke.
Accordingly, metrics are disclosed herein which take into account spoke and pattern features to appropriately characterize CER and the resulting effect on semiconductor device performance. Height and width indices may be determined for an imaged pattern. These indices provide a characterization of spoke geometry (e.g., size and sharpness) for the pattern. The height and width indices may be combined into a single roughness metric indicative of spoke severity. Alternatively, the height and width indices are used in the determination of potential electric field concentrations from the CER. A concavity parameter may be determined to determine the orientation of CER spokes, i.e., concave (projecting toward the interior of the pattern) or convex (projecting away from the interior of the pattern). Those patterns characterized as concave may be determined to have a minimal impact on device performance regardless of the size of the spokes, and thus may be ignored for the purposes of quality control measures.
For example, targets 522 may be individual chips or patterns on a semiconductor wafer. The sample 520 is supported by a microscope stage 518, which manipulates the position of the sample 520 with respect to the electron beam 512. The secondary electrons 524 emanating from location 522 are detected by a secondary electron detector 526. The secondary electrons 524 are used to generate an image of the sample 520 at target 522.
The measurement system 500 also includes a control module 528. Control module 528 may be integrated with the CD-SEM 502 or be a stand alone component, such as a programmed computer or processor. The control module 528 is operatively connected to and controls the various components of the CD-SEM 502, including the electron gun 508, the electromagnetic lenses 501 and 516, the deflector 514, and the microscope stage 518 to image sample 520. The control module 528 receives secondary electron data from the secondary electron detector 526, which is then used to form an image. Image data is stored in memory 532.
The measurement system also includes a critical dimension (CD) evaluation module 506. The CD evaluation module 506 receives the image data from the memory 532. Alternatively, the CD evaluation module 506 receives the image data directly from the control module 528. The CD evaluation module 506 includes a failure analysis module 530 and a memory 534. Image data from memory 532 is analyzed by the failure analysis module 530 to determine, among other things, the fidelity of the patterns on the sample 520 and the likelihood for failure based on pattern geometry. The results of the analysis are stored in memory 534.
It is noted that the various components of the control module 528 and the CD evaluation module 506 need not be embodied as separate components. Rather, modules 528 and 506 may be embodied as a single computer or processor 536, or as separate modules operatively connected together, such as independent computers or processors connected together using data transmission or interfacing means. The modules 506 and 528 may also be combined with one or more other modules, for example, as part of quality control processors or controllers in a semiconductor manufacturing line. Likewise, the memory devices 532, 534 may also be combined into a single memory device or separated into multiple memory devices.
Moreover, one or more of the modules 506 and 528 may be integrated with the SEM 502. Although separate components are illustrated in
Referring to
Image processing module 602 includes a pattern locating module 608 and an edge detection module 610. The pattern locating module 608 is configured to find a particular pattern of interest, such as a contact hole, in an image of the sample. The pattern locating module 608 may identify the pattern using one or more of pattern recognition, user input, or predetermined pattern coordinates, such as coordinates on a photolithographic mask used to create the pattern. Edge detection module 610 receives the image from the pattern locating module 608 together with information regarding the location of the pattern. Using image processing techniques, the edge detection module locates the edges of the pattern. The locating includes extracting coordinates of a position of a plurality of points along the edge of the pattern.
The pattern evaluation module 604 includes a shape fitting module 612, a deviation calculation module 614, a height index module 616, a width index module 618, a roughness metric calculation module 620, and a concavity parameter module 622. The shape fitting module 612 receives one or more images of the pattern as well as information regarding the coordinates of points on the edge of the pattern from the image processing module 602. The shape fitting module 612 approximates the formed pattern using a closed two-dimensional shape, such as an ellipse or other geometric shape that is represented by an analytical function. The deviation calculator 614 calculates a difference between the closed two-dimensional shape and the formed pattern by comparing the coordinates of the points on the edge of the formed pattern with corresponding points on the edge of the closed shape.
The difference between the closed two-dimensional shape and the formed pattern is used by various modules in the pattern evaluation module 604 to characterizing the formed pattern. For example, the height index module 616 and the width index module 618 calculate height and width indices, respectively, for the formed pattern. The roughness metric calculation module 620 calculates height and width indices to determine a roughness metric for the formed pattern. Concavity parameter module 622 uses the difference between the ideal shape and the formed pattern (and/or the coordinates of points on the edge of the formed pattern) to determine the orientation of CER spokes for the formed pattern. This orientation may be embodied as a concavity parameter, such as a number or label (e.g., “convex” or “concave”).
Wafer evaluation module 606 accumulates the roughness metrics and/or concavity parameters for all of the imaged patterns on the wafer to determine the quality of the patterns formed on the wafer. Wafer evaluation module may interact with a user or other components of a quality control process to provide an alert when a wafer does not meet certain threshold criteria. For example, the wafer evaluation module 606 may send a notice to a user via a display device or the like when a wafer index exceeds a predetermined threshold value.
Referring now to
At step 706, the module may detect the edge of the selected pattern. In particular, coordinates of a plurality of points (for example, an ‘m’ number of points) on the edge of the formed pattern are determined. The points may be equally spaced on the circumference of the formed pattern. The spacing may be chosen so as to provide sufficient discrimination based on the anticipated CER and size of the imaged pattern.
At step 708, the module fits an ideal shape, such as a closed two-dimensional shape, to the detected edge points. For example, a plurality of points on the edge of a formed pattern 804 may be determined, as shown in
A variety of different shapes and functions may be used to approximate the formed patterns. When the pattern has been designed as a perfect circle, the fitted shape is given by the function:
(X−Xc)2+(Y−Yc)2=R2, (1)
where Xc and Yc are the coordinates of the center of the circle and R is the radius of the circle.
When the formed pattern is designed as an ellipse, an elliptical function is used to approximate the formed pattern. An ellipse, as shown in
where Xc and Yc are the coordinates of the center 802 of the ellipse 800, a is the half-width of the ellipse along the minor axis 818, b is the half-width of the ellipse along the major axis 816, and θ is the angle 814 of the minor axis 818 with respect to the x-axis.
Various combinations of shapes can be used to approximate a formed pattern where a single closed form shape may not be sufficient. For example, when the designed pattern is an ellipse and the ratio of the long radius to the short radius is greater than 3, the elliptical function given by equation (2) may not adequately approximate the formed pattern. Accordingly, the shape shown in
where Xc and Yc are the coordinates of the center 802′ of the shape 800′, a is the half-width of the shape along the minor axis 818′, b is the length of the shape along the major axis 816′ between the center 802′ and the curved end portion, and θ is the angle 822 of the minor axis 818′ with respect to the x-axis.
Referring again to
Δri=ro−ri, (6)
where ri is the distance from center 802 to the point i on the fitted shape 800 and ro is the distance from the center 802 along the same radial line as ri to the formed pattern 804. Alternatively, Δri may be characterized as the distance from a point i on the fitted shape 800 and a corresponding point on the formed pattern 804 with the corresponding point lying along a line perpendicular to the circumference of the fitted shape 800 at the point i. In either case, when the formed pattern extends beyond the fitted shape, the deviation 806 is positive. When the formed pattern is within the bounds of the fitted shape, the deviation 808 is negative. The graph in
In addition to the deviation from the ideal shape (e.g., spoke height), the relationship of a particular point to the surrounding points on the edge of the formed pattern is also indicative of spoke geometry. Spoke width provides a measure of the circumferential extent of spoke 1004, and thus the relationship between adjacent points on the edge of the formed pattern. With reference to
Referring again to
The process repeats for each relevant pattern that is to be evaluated. The number of relevant patterns is a sampling of the total patterns on the wafer or of the total patterns in a chip on the wafer. Alternatively, the number of relevant patterns includes all patterns in a chip or subset of chips on the wafer. In yet another alternative, the number of relevant patterns includes all the patterns on the wafer. In still another alternative, all or a portion of the patterns on the wafer that are particularly susceptible to failure, either because of function or size, are evaluated. In step 714, it is determined if all relevant patterns have been evaluated. The process 700 repeats steps 704 through 714 until all relevant patterns have been evaluated, at which point the process terminates at 716.
According to a first embodiment 712a shown in
The height index is determined as a multiple of the standard deviation of the deviation distribution. For example, the height index is given by:
where σ is the standard deviation, m is the number of points on the edge of the formed pattern, and Δri is the deviation of the point i on the edge of the formed pattern from the ideal shape. If the deviation distribution is a normal distribution, 3σ is sensitive to large Δri while being stable against measurement error. Thus, in step 1204, the standard deviation, σ, is determined followed by the determination of the height index in step 1206.
The width index is determined using an autocorrelation function of the deviation in the height (or radial) direction from the edge of the fitted shape along the circumference thereof. In particular, the width index is equal to the auto-correlation length, ξ, as given by equations (8)-(10) below. The auto-correlation function is given by:
where s is a shift between the original deviations, Δri, and the shifted deviations, Δri+j, j is the number of data points of the shift s, and Δs is the average distance between adjacent data points (e.g., Pi and Pi+1) and is given by:
Δs=
The auto-correlation length, ξ, is the value of s for which:
Cr(ξ)=Ao. (10)
where AO is a predetermined constant.
For patterns formed in photo-resist, an Ao of 0.2 is appropriate. However, other values for determining the auto-correlation are also possible depending on, for example, the pattern material and shape, device layout, and/or quality control standards. An example of a plot 1100 of an auto-correlation function is shown in
The roughness index is computed in step 1212 as the ratio of the height index to the width index. As is evident, larger values for the height index indicate that a spoke extends farther from the ideal shape while smaller values of the width index indicate that a spoke is narrower. Thus, larger values of the roughness index represent spokes which are relatively large and/or sharp.
The process proceeds to step 1214 wherein a concavity parameter, φ, is determined. The concavity parameter, φ, is used to determine if the spoke or spokes along the edge of a formed pattern are concave or convex. As discussed above, convex spokes are of particular interest whereas concave spokes may not negatively affect device performance.
When using 3σ as the height index, the concavity parameter is determined from the skewness of the deviation distribution. Thus, the concavity parameter, φ, is calculated in step 1214 according to:
In step 1216, the value of the concavity parameter, φ, is evaluated. If the concavity parameter is greater than zero (i.e., skewness>0), this indicates that the pattern has convex spokes. The process advances to step 1218 wherein the pattern is labeled as convex. If the concavity parameter is less than or equal to zero (i.e., skewness≦0), this indicates that the pattern has concave or no spokes. The process advances to step 1220 wherein the pattern is labeled as concave.
According to a second embodiment 712b, shown in
The height index is determined as the maximum absolute value from the deviation distribution. For example, the height index is ΔRmax, where ΔRmax is given by:
ΔRmax=|Δrmax|=MAX(|Δri|), (12)
where Δri is the deviation of the point i on the edge of the formed pattern from the ideal shape, and Δrmax is the deviation having the largest absolute value. Thus, in step 1304, the maximum deviation, ΔRmax, is determined followed by the determination of the height index in step 1306.
While ΔRmax is sensitive enough to find the largest deviation that can contribute to the sharpest spoke, it should be noted that the largest deviation may also be due to measurement error. For example, variations in the edge of patterns observed by the CD-SEM may be due to local imaging fluctuations from electron beam charge build up.
As with the first embodiment, the auto-correlation function is evaluated to determine the value for the length which yields the desired constant, AO, in step 1308 (see equations (8)-(10) above). The resulting length, ξ, is selected as the width index in step 1310. The roughness index is computed in step 1312 as the ratio of the height index to the width index. As is evident, larger values for the height index indicate that a spoke extends farther from the ideal shape while smaller values of the width index indicate that a spoke is narrower. Thus, larger values of the roughness index represent spokes which are relatively large and/or sharp.
The process proceeds to step 1314 wherein the concavity parameter, φ, is determined. When using ΔRmax as the height index, the concavity parameter is determined based on the sign of the Δrmax which yields ΔRmax. Thus, the concavity parameter, φ, is calculated in step 1314 according to:
φ=Δrmax. (13)
In step 1316, the value of the concavity parameter, φ, is evaluated. If the concavity parameter is greater than zero (i.e., φ>0), this indicates that the pattern has convex spokes. The process advances to step 1318 wherein the pattern is labeled as convex. If the concavity parameter is less than or equal to zero (i.e., φ≦0), this indicates that the pattern has concave or no spokes. The process advances to step 1320 wherein the pattern is labeled as concave.
According to a third embodiment 712c, shown in
The deviations, Δri, are ranked according to magnitude. ΔR(x) represents one of the values in the ranking of deviations at a normalized index of x. In particular, the index x represents a ranking (e.g., Rank(Δri)) of one of the measured deviations, Δri, based on its magnitude with respect to the other measured deviations. The index x is normalized with respect to the total number of edge points, m. Thus, x can range from a minimum value of 1/m to a maximum of 1. When x is equal to 1, the value of ΔR(1) is equal to the deviation having the largest value of the measured deviations. When x is equal to 1/m, the value of ΔR(1/m) is equal to the deviation having the smallest (e.g., most negative) value of the measured deviations.
In this embodiment, the height index is determined as the ΔR(x) for a predetermined index of x. For example, the height index is given by:
The predetermined value of x may be selected based on experiential data and/or numerical simulation. For example, an appropriate value for x may be within a range from 0.7 to 0.9, such as 0.8. Note that in some cases, there may be no Rank(Δri)/m which is exactly equal to x. In such cases, the Δri that yields a Rank(Δri)/m closest to the predetermined index, x, may be used.
Thus, in step 1404, the deviations are ranked according to magnitude, and ΔR(x) is determined based on the predetermined x index value and the ranking. Following step 1404, the height index is set as ΔR(x) in step 1406.
Using the standard deviation as the height index for non-normal distributions may not indicate large deviations precisely. Thus, the use of ΔR(x) is particularly helpful when the deviation distribution is not a normal distribution. In addition, the robustness against measurement error increases with decreasing x from 1 in the case of ΔR(x).
As with the first embodiment, the auto-correlation function is evaluated to determine the value for the length which yields the desired constant, AO, in step 1408 (see equations (8)-(10) above). The resulting length, ξ, is selected as the width index in step 1410. The roughness index is computed in step 1412 as the ratio of the height index to the width index. As is evident, larger values for the height index indicate that a spoke extends farther from the ideal shape while smaller values of the width index indicate that a spoke is narrower. Thus, larger values of the roughness index represent spokes which are relatively large and/or sharp.
The process proceeds to step 1414 wherein the concavity parameter, φ, is determined. When using ΔR(x) as the height index, the concavity parameter is determined based on a normalized index, for which, ΔR(x)=0. That is, a normalized ranking is determined for the measured deviation, Δri, which is equal to zero. Note that in some cases, there may be no measured deviation which is exactly equal to zero. In such cases, the measured deviation which is closest to zero may be used. Thus, the concavity parameter, φ, is calculated in step 1414 according to:
φ=x′(ΔR(x′)=0). (15)
In step 1416, the value of the concavity parameter, φ, is evaluated and compared to the predetermined ranking index, x, used in the determination of the height index (e.g., ΔR(x)). If the concavity parameter is less than x (i.e., φ<x), this indicates that the pattern has convex spokes. The process advances to step 1418 wherein the pattern is labeled as convex. If the concavity parameter is greater than or equal to x (i.e., φ≧x), this indicates that the pattern has concave or no spokes. The process advances to step 1420 wherein the pattern is labeled as concave.
According to a fourth embodiment 712d, shown in
The height index is based on cumulative-probability-based deviation, ΔRcp(X), which is one of the values of the measured deviations, Δri, for which X percentage of the measured deviations have magnitudes at or below said value. X thus represents the percentage (or cumulative probability) of measured deviations having a magnitude at or below a certain value. When X is equal to 100, all values of the measured deviations are equal to or less than the value of ΔRcp(X). When X is equal to 0, all values of the measured deviations are greater than the value of ΔRcp(X).
In this embodiment, the height index is determined as the ΔRcp(X) for a predetermined value of X. The predetermined value of X may be selected based on experiential data and/or numerical simulations. For example, an appropriate value for X may be within a range of 70% to 90%, such as 90%. In this example, ΔRcp(90) would represent a selected deviation, Δri, at which 90% of the measured deviations have a magnitude equal to or less than the magnitude of the selected deviation, Δri.
When the distribution of the deviations for a pattern is not a normal distribution, the standard deviation may not precisely indicate large deviations. Employing ΔRcp(X) for the height index is useful in such situations. In addition, the robustness against measurement error increases with decreasing X from 100% for ΔRcp(X).
As with the first embodiment, the auto-correlation function is evaluated to determine the value for the length which yields the desired constant, AO, in step 1508 (see equations (8)-(10) above). The resulting length, ξ, is selected as the width index in step 1510. The roughness index is computed in step 1512 as the ratio of the height index to the width index. As is evident, larger values for the height index indicate that a spoke extends farther from the ideal shape while smaller values of the width index indicate that a spoke is narrower. Thus, larger values of the roughness index represent spokes which are relatively large and/or sharp.
The process proceeds to step 1514 wherein the concavity parameter, φ, is determined. When using ΔRcp(X) as the height index, the concavity parameter is determined based on the cumulative probability (e.g., the value of X′) for which the measured deviation is equal to or closest to zero (e.g., ΔRcp(X′)=0). Thus, the concavity parameter, φ, is calculated in step 1514 according to:
φ=X′(ΔRcp(X′)=0). (16)
In step 1516, the value of the concavity parameter, φ, is evaluated and compared with the predetermined value of X used in the determination of the height index. If the concavity parameter is less than X (i.e., φ<X), this indicates that the pattern has convex spokes. The process advances to step 1518 wherein the pattern is labeled as convex. If the concavity parameter is greater than or equal to X (i.e., φ≧X), this indicates that the pattern has concave or no spokes. The process advances to step 1520 wherein the pattern is labeled as concave.
According to a fifth embodiment 712e, shown in
The height index is determined based on the standard deviation and pattern size. In particular, the height index is given by:
where Co is the normalized variance, τ is the standard deviation, R is the average radius of the fitted shape, and M is a predetermined constant. Thus, in step 1704, the normalized variance, CO, is determined, followed by the determination of the height index in step 1706.
As with the first embodiment, the auto-correlation function is evaluated to determine the value for the length which yields the desired constant, AO, in step 1708 (see equations (8)-(10) above). The resulting length, ξ, is selected as the width index in step 1710. The roughness index is computed in step 1712 as the ratio of the height index to the width index. As is evident, larger values for the height index indicate that a spoke extends farther from the ideal shape while smaller values of the width index indicate that a spoke is narrower. Thus, larger values of the roughness index represent spokes which are relatively large and/or sharp.
The process proceeds to step 1714 wherein the concavity parameter, φ, is determined. When using the normalized variance, CO, as the height index, the concavity parameter is determined from the skewness of the deviation distribution. Thus, the concavity parameter, φ, is calculated in step 1714 according to:
In step 1716, the value of the concavity parameter, φ, is evaluated. If the concavity parameter is greater than zero (i.e., skewness>0), this indicates that the pattern has convex spokes. The process advances to step 1718 wherein the pattern is labeled as convex. If the concavity parameter is less than or equal to zero (i.e., skewness≦0), this indicates that the pattern has concave or no spokes. The process advances to step 1720 wherein the pattern is labeled as concave.
An alternative embodiment for the failure analysis module is shown in
Similar to the pattern evaluation module 530 of
Referring to
In step 2006, an image of the wafer is processed for a specific pattern. A user may select one of the patterns in the image, or the module may select a pattern for analysis based on a predetermined routine or map associated with the CD evaluation process. Alternatively, the pattern may be located using pattern recognition or from a predetermined protocol. The pattern is thus located in the image for further processing.
At step 2006, the module detects the edge of the selected pattern. In particular, coordinates of a plurality (m) of points on the edge of the imaged pattern are located. For example, the points may be equally spaced on the circumference of the imaged pattern. The spacing may be chosen so as to provide sufficient discrimination based on the anticipated CER and size of the imaged pattern.
At step 2008, the module fits an ideal shape, such as a closed two-dimensional shape, to the detected edge points. The process 2000 proceeds to step 2010. In step 2012, the module 530′ calculates a deviation between corresponding points on the formed pattern and on the fitted shape. This deviation is determined, for example, in a manner similar to that described above with respect to the other embodiments.
The process 2000 proceeds to step 2012. In step 2012, the module calculates a roughness metric and a concavity parameter for the formed pattern based on the calculated deviations for each point on the formed pattern edge. The process then proceeds to step 2014 where it is determined if all relevant patterns have been evaluated. The number of relevant patterns can include a sampling of the total patterns on the wafer or of the total patterns in a chip on the wafer. Alternatively, the number of relevant patterns includes all patterns in a chip or subset of chips on the wafer. In yet another alternative, the number of relevant patterns includes all the patterns on the wafer. In still another alternative, all or a portion of the patterns on the wafer that are particularly susceptible to failure, either because of function or size, are evaluated. The process 2000 repeats steps 2006 through 2014 until all relevant patterns have been evaluated, at which point the process terminates at 2018.
For example, step 2014 includes the process steps illustrated in
The height index is determined as a multiple of the standard deviation of the deviation distribution. For example, the height index is 3σ (see equation (7) above). Thus, in step 2104, the standard deviation, σ, is determined followed by the determination of the height index in step 2106.
In step 2108, the auto-correlation function, Cr(s), is evaluated to determine the value for the length which yields the desired constant, AO, in step 2108 (see equations (8)-(10) above). The resulting length, ξ, is selected as the width index in step 2110.
In step 2112, the E-field concentration for the pattern is determined. The E-field concentration is a function of the calculated height and width indices. The E-field concentration is based on simulated data for a variety of height and width indices. For example, a region of height and width indices which may result in fatal E-field concentrations for a particular pattern and/or semiconductor devices are obtained by simulation in step 2004. Using the results of the simulation, a contour map is constructed that visually shows detrimental areas as cross-hatched region 2302 in
In step 2112, using the height and width indices, the E-field concentration is extracted from the map data in
The process proceeds to step 2114 wherein a concavity parameter, φ, is determined. The concavity parameter, φ, is used to determine if the spoke or spokes along the edge of a formed pattern are concave or convex. As discussed above, convex spokes are of particular interest whereas concave spokes may not negatively affect device performance. When using 3σ as the height index, the concavity parameter, σ, is determined from the skewness of the deviation distribution (see equation (11) above).
In step 2116, the value of the concavity parameter, φ, is evaluated. If the concavity parameter is greater than zero (i.e., skewness>0), this indicates that the pattern has convex spokes. The process advances to step 2118 wherein the pattern is labeled as convex. If the concavity parameter is less than or equal to zero (i.e., skewness≦0), this indicates that the pattern has concave or no spokes. The process advances to step 2120 wherein the pattern is labeled as concave.
The E-field map could be used to determine the yield of a pattern or chip in a semiconductor device. For example, the production yield may not be sufficiently high if 20% or more of the observed patterns are in region 2302 of the E-field contour map. Therefore, an inspected wafer is sent to the next step in a manufacturing process only when fewer than three patterns are in region 2302. Since the example illustrated in
Process 700 and the accompanying variations for determining roughness metrics (or E-field concentration) and/or concavity parameters described with reference to
In some designs, it is impractical to inspect each pattern on the wafer due to the sheer volume of patterns thereon. Accordingly, a sampling of the chips on the wafer 2400, such as chips 2404, is selected for inspection while chips 2402 are not inspected, thereby significantly reducing inspection time. Chips 2404 may be randomly selected or symmetrically arranged around wafer 2400. As discussed above, convex spokes in patterns are more likely to result in performance degradation of the resulting semiconductor device. Whether based on all patterns on the wafer or a representative subset of the patterns on the wafer, the roughness index for patterns, which have been labeled as concave or have a concavity parameter indicative of concave spokes, is ignored or discarded in the generation of the wafer index. For example, the roughness index for a pattern having a concave spoke is reset to zero.
With reference to
In step 2508, the process checks if all measurement positions have been evaluated. If not, steps 2504-2508 are repeated for the next measurement position until all measurement positions on the wafer have been evaluated. The process proceeds to step 2510, wherein the wafer is evaluated based on the roughness metrics and concavity parameters. For example, nine chips 2404 on wafer 2400 are selected for inspection. The roughness metric for each hole pattern in a chip are averaged to generate a roughness metric for the entire chip.
Alternatively, the wafer evaluation module 606 generates a wafer index, based on the roughness metric for the inspected patterns, to determine if the wafer should continue in the manufacturing process. For example, the wafer index is determined as the average of the measured roughness metrics for the inspected patterns.
In another example, the wafer index is determined from the standard deviation of the roughness metrics for the inspected patterns. The wafer index may be 3σw, where σw represents the standard deviation of the roughness metric for the inspected patterns on each chip.
In yet another example, the wafer index is the number of inspected patterns for which the roughness metric exceeds a predetermined threshold. For
In still another example, the wafer index is based on a cumulative probability plot. The wafer index is determined as a selected value of the determined roughness metrics for which X percentage (i.e., the cumulative probability) of the roughness metrics are less than the selected value. Referring to
The wafer index thus provides an indicator of the quality of the patterns in/on the wafer. Such an indication is particularly useful when the patterns have not been permanently formed on the wafer. For example, in photolithography, photoresist patterns are temporarily formed on the semiconductor wafer as a template for subsequent material addition or deletion steps. If the pattern quality is unacceptable, the wafer may be recycled by removing and then re-applying the photoresist pattern.
A measurement evaluation process 2800 for use in inspecting photoresist patterns on a wafer as part of a semiconductor device fabrication process is shown in
The process proceeds to step 2806. In step 2806, a photoresist pattern is formed on the wafer using, for example, conventional photolithography. The photoresist pattern may be formed using other pattern transfer technologies, such as, but not limited to, LIGA, e-beam lithography, and EUV lithography. After the pattern is formed, the process proceeds to step 2808 wherein the formed pattern is imaged. The pattern may be imaged using, for example, a CD-SEM or other imaging apparatus capable of resolving the roughness features of the photoresist pattern.
Advancing to step 2810, the process calculates a wafer index based on the image of the patterned wafer. Step 2810 employs process 2500 of
The embodiments described herein have been chosen to best illustrate the principles of the invention and its practical application and to thereby enable others skilled in the applicable arts to utilize the invention. Various embodiments with various modifications depending on the particular use are contemplated. It is thus intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.
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Number | Date | Country | |
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20110176718 A1 | Jul 2011 | US |