# Patent

## Title
Method and system for detecting hotspots for photolithographically-defined devices

## Abstract

A method detects hot spots from overlay error data for photolithography defined device(s). The overlay error data corresponds to data for sites on a substrate for the photolithography defined device(s). The overlay error data is converted to residual overlay data, which indicates a residual overlay error for each of the sites. The residual overlay error is based on an expected overlay error for each of the sites. It is determined whether group(s) of overlay error sites are present. Each group includes at least two nearest neighbor sites that have the residual overlay error greater than a threshold. For each group of overlay error sites, it is determined whether the group fits a physical model, such as the derivative of a Gaussian, for a hotspot. Each group fitting the physical model is categorized as a hotspot. Hotspot parameters are determined for each group that fits the physical model.

## Background
BACKGROUND
Magnetic recording devices such as read or write heads as well as other micro devices are fabricated using photolithography. Typically, a photoresist layer is deposited. Selected areas of the photoresist layer are exposed to light. Corresponding portions of the photoresist layer are removed, forming a photoresist mask. One or more layers below apertures the photoresist mask may be removed or one or more layers deposited to form structures in the apertures. The photoresist mask is removed. This process is repeated to fabricate other layers in the photolithographically defined device. The device may thus be formed layer by layer.
Overlay refers to the match (or mismatch) between the desired locations of structures in different layers of the device. If a substrate were to be considered a planar surface described by x and y coordinates (z is perpendicular to the surface), then overlay error may be considered to be the actual x and y coordinates of a structure versus the designed x and y coordinates based on the previous layer(s). For example, the pole tip of a writer and a read sensor of a reader may be desired to be aligned in the cross-track direction. These structures are part of different layers formed at different times. Misalignments between the read sensor and pole tip may be due to overlay errors.
Overlay errors may be due to a variety of factors. For example, optical distortions may occur in the apparatus used to expose the photoresist to light. These distortions can cause offsets in the locations of regions exposed to light. The structures being formed may, therefore, be offset from their desired location and, therefore, be subject to overlay error. Another source of overlay error is hot spots. Hot spots occur because particulate contamination on the back side of the substrate. These micrometer to nanometer sized particles become trapped between the substrate and the holder, causing the substrate to deform. This deformation may result in a distortion of the features in the image being transferred to the substrate. Thus, significant overlay errors in the local area of the particle. The region in which such errors occur is termed a hot spot.
FIG. 1 depicts a conventional method for interrogating overlay errors that may be due at least in part to the presence of hot spots. The overlay data has been measured for one or more layers on the substrate. Based on this data, it is determined whether the overlay error (as measured by a) exceeds a particular threshold, via step 12. If so, then the wafer is further inspected, via step 14. In some cases, the inspection takes the form of a highly trained operator inspecting the overlay vector map. The overlay vector map indicates the magnitude and direction of distortions in the overlay. The operator may thus manually determine whether hotspots are present based on the character of the overlay vector map. Alternatively, the flatness of the substrate may be measured in a tool. These procedures may determine that there are small regions in which the overlay error is significant. These localized regions of high overlay error may correspond to the locations of hotspots. Thus, the presence and location of hotspots may be determined. A determination may then be made as to whether to pass the substrate for further processing, discard the substrate or rework the substrate due to the overlay error.
Although the conventional method 10 provides a mechanism for detecting and addressing overlay error, it is time consuming, less sensitive to hot spots than desired and operator dependent. Consequently, additional methods for dealing with overlay error are desired.



BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS
FIG. 1 depicts a conventional method for investigating overlay errors for a photolithographically defined device.
FIG. 2 is a flow chart depicting an exemplary embodiment of a method for detecting hot spots using a physical model of hotspots.
FIG. 3 depicts an exemplary embodiment of a system for detecting hot spots using overlay data and a physical model of the hot spots.
FIG. 4 depicts a portion of a substrate and a hotspot.
FIG. 5 depicts an exemplary embodiment of a physical model for a hot spot.
FIG. 6 is a flow chart depicting another exemplary embodiment of a method for detecting hot spots using a physical model of hotspots.
FIG. 7 is a flow chart depicting another exemplary embodiment of a method for detecting hot spots using a physical model of hotspots.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 2 is a flow chart depicting an exemplary embodiment of a method 100 for detecting hot spots for a photolithographically defined device using a physical model of the hot spots. For simplicity, some steps may be omitted, interleaved, performed in another order and/or combined. Each step may also include multiple substeps. The method 100 may be performed by one or more software components executing on one or more processors. For example, FIG. 3 is a block diagram a computing system 110 including processor(s) 112, memory 114 and user interface 116 that may be used in performing the method 100. The computing system 110 may be stand-alone or may be incorporated into an existing tool used in fabrication lines. For example, the computing system 110 may be part of an overlay measurement tool and/or an exposure tool. Referring to FIGS. 2-3, the method 100 is also described in the context of fabrication of a magnetic recording device, such as a read and/or write head residing on an AlTiC substrate. However, the method 100 may be used to detect hot spots for other devices and/or other substrates. In addition, one of ordinary skill in the art will recognize that multiple devices are generally fabricated on a single substrate. The method 100 uses overlay error data for the photolithography defined device(s). The overlay error data corresponds to data measured at sites on the substrate. For example, the overlay data may include spatial (e.g. x-y) variations in the locations of various structures measured at particular sites on the substrate. The locations may simply be a grid of sites across the surface of the substrate. For example, an array of sites across the surface of an AlTiC substrate on which multiple read and/or write heads are being fabricated may be used for obtaining overlay data for the method 100.
The overlay error data is converted to residual overlay data, via step 102. The overlay error data is the overlay error measured at each of the sites. The residual overlay data includes a residual overlay error for each of the sites. The residual overlay error is based on an expected overlay error for each site and the (measured) overlay error data. Stated differently, the expected overlay error may be removed from the overlay error data measured at each of the sites so that the residual overlay data remains for each site. For example, expected variations in locations of structures due to image distortion in the apparatus used to expose the photoresist may be modeled and subtracted from the overlay error data. These expected variations may be determined by a least squares regression fit of the measured overlay data at each site to a model for the image distortions (terms model). In other embodiments, other methods for removing other sources of overlay error from the overlay error data may be employed. Because the expected other sources of overlay error are removed from the overlay error data, the residual overlay data more closely corresponds to overlay errors due to hot spots.
It is determined whether one or more groups of sites having a large residual overlay error are present, via step 104. Step 104 includes determining sites that have a residual overlay error that exceeds a threshold. This determination may be accomplished mathematically using well known criteria. Any site having a residual overlay error greater than the threshold is deemed an outlier. Each group includes outliers that are nearest neighbors and that form a contiguous group. Each group thus includes a minimum of two nearest neighbor sites. Step 104 may include determining whether an outlier has a nearest neighbor outlier. If so, these two outliers/sites are collected together to form an initial group. It is determined whether there is a nearest neighbor outlier to any member of the initial group. If so, this new outlier is also made part of the group (e.g. forming an intermediate group). This process is continued on the intermediate group until the intermediate group contains all nearest neighbor outliers to those outliers already part of the intermediate group. Stated differently, the intermediate group is grown until there are no more nearest neighbor outliers. This final intermediate group is a group determined in step 104. The process may then be repeated for other outliers, forming other groups.
For each group of outliers formed in step 104, it is determined whether the group fits a physical model for a hotspot, via step 106. Each group that fits the physical model may be categorized as a hotspot. The physical model used in step 106 may be based on a Gaussian curve.
FIG. 4 depicts a substrate 120 during fabrication of photolithographically defined devices. A portion 124 of the substrate 120 is shown. A particle 122 is adjacent to the back side of the part 124 of the substrate 120. The particle 122 may be trapped between a chuck (not shown) that holds the substrate 120 and the substrate 120 itself. In the region 124, the substrate 120 deforms. The deformation is based upon the geometry and location of the particle 122 and may be approximated by a Gaussian curve. The residual overlay error due to the particle 122 corresponds to the deformation in the x-y plane described by a spatial derivative of the Gaussian. The residual overlay error may, therefore, be approximated by the first order spatial derivative of the Gaussian. FIG. 5 is a graph 130 depicting the first order spatial derivative of a Gaussian. The residual overlay error, E, that is the first spatial derivative of a Gaussian is given by:

E=A*{(x−x0),(y−y0)}*[exp(1/2)/w]*exp[(−(x−x0)2−(y−y0)2)/(2*w2)]

where the hot spot is centered on the point (x0, y0), has a width w and an amplitude A. In other embodiments, other and/or additional models for the overlay error due to hot spots may be used. For example, higher order corrections may be added to the Gaussian model described above.
Determining whether each group fits the above physical model for a hot spot may include multiple substeps. For example, a polygon may be determined for each group. The polygon encompasses all of the outliers (e.g. sites having residual overlay error greater than the threshold) in the group. The polygon may be a convex polygon. In addition, the polygon may be the smallest convex polygon that includes all of the outliers for the group. It may then be determined whether a circularness for the shape of the polygon for the group exceeds a particular threshold. The circularness of a polygon indicates how closely its perimeter and area match those of a circle. For example, a circularness parameter may be 4π(polygon area)/(polygon perimeter)2. The closer the circularness parameter is to one, the more the polygon matches a circle. If the circularness for the polygon does not exceed the threshold, the group may be discarded. This allows for groups of outliers that are a line or otherwise uncharacteristic of hot spots to be removed from consideration. The remaining groups having a sufficiently high circularness are hot spot candidates.
For each hot spot candidate, initial guesses for the amplitude (initial amplitude) and width (initial width) are made. In some embodiments, the initial amplitude is the largest overlay error in the group/hot spot candidate. The initial width may be determined based upon the radius of a circle having an area substantially equal to a polygon area of the polygon. A fitted width and a fitted amplitude are calculated for each hot spot candidate using the initial amplitude and the initial width and the physical model described above. Any hot spot having a fitted width less than the minimum spacing between sites may be rejected. This allows for calculated hot spots smaller than the distance between sites where data was measured to be rejected. A hotspot having the fitted width and the fitted amplitude being determined for each of the remaining hot spot candidate.
For each group of overlay error sites that fits the physical model, the parameters are determined, via step 108. For example, the location of the center (x0, y0), the amplitude and the width may be determined. Thus, the size, number and amplitude of the hotspot(s) may be determined. A decision may then be made as to whether to accept/pass the substrate for further processing, discard the substrate because the overlay errors are too large, or rework the substrate to attempt to correct errors in the overlay.
Using the method 100, hot spots may be automatically determined using overlay error data. More specifically, hot spots may be more quickly and easily found and quantified. For example, hot spots that may affect the alignment of the read sensor (not shown) and write pole (not shown) may be more rapidly identified and characterized. It may then be more easily determined whether to pass the substrate on for further processing, rework the substrate or discard the substrate. Because an operator no longer is required to manually inspect the overlay error and make such decisions, less time and training may be invested in the operator. In addition, operator bias and error in identification of the hot spots may be avoided. Thus, yield may be improved. The hot spot data determined using the method 100 may also remain available for later use, for example in improving production processes and reducing particulate contamination that gives rise to hot spots. Thus, fabrication of photolithographically defined devices, such as magnetic data storage devices, may be improved.
FIG. 6 is a flow chart depicting an exemplary embodiment of a method 150 for determining and characterizing hot spots for a photolithographically defined device using a physical model of the hot spots. For simplicity, some steps may be omitted, interleaved, performed in another order, combined and/or include substeps. The method 150 may be performed by one or more software components executing on one or more processors. For example, the method 150 may be implemented using the computing system 110 of FIG. 3. The method 150 is also described in the context of fabrication of a magnetic recording device, such as a read and/or write head residing on an AlTiC substrate. However, the method 150 may be used to detect hot spots for other devices and/or other substrates. In addition, one of ordinary skill in the art will recognize that multiple devices are generally fabricated on a single substrate. The method 150 uses overlay error data for the photolithography defined device(s). The overlay error data may be taken at an array of sites across the surface of the substrate on which multiple photolithographically defined devices are being fabricated. The method 150 is also analogous to the method 100. The overlay error data is spatial error data. Thus, the overlay error data may indicate a distance and direction that the structure for each site is offset. For example, the surface of a substrate may be described using x and y coordinates. The overlay error data indicates the offset in the ±x direction and/or the ±y direction for each site.
The overlay error data is converted to residual overlay data, via step 152. Step 152 is analogous to step 102. The residual overlay error is based on an expected overlay error for each site and the (measured) overlay error data. In step 152, the expected overlay error may be removed from the overlay error data measured at each of the sites so that the residual overlay data remains for each site. Because the expected other sources of overlay error are removed from the overlay error data, the residual overlay data more closely corresponds to overlay errors due to hot spots. The residual overlay error data is spatial error data, indicating the error of shift in the data at each site.
It is determined whether the spatial error data (i.e. the residual overlay error data) for each site exceeds a spatial error threshold, via step 154. This determination may be made using iterative calculations. Each site having the spatial error exceeding the spatial error threshold is considered to be an outlier. Thus, the outliers for the substrate are determined in step 154.
For the each outlier, it is determined whether another outlier is a nearest neighbor to the outlier, via step 156. The two nearest neighbor outliers form a current group.
The step of determining whether a nearest neighbor outlier exists for the outliers in the current group and adding these nearest neighbor outliers is repeated, via step 158. This step continues to be repeated until no additional nearest neighbor outliers are found. Thus, step 158 grows the current group until the current group no possible additional members are found. Thus, steps 156 and 158 form contiguous group(s) of outliers. Thus, steps 156 and 158 result in intermediate groups. Thus, the intermediate groups resulting may include those with individual outliers (which never grow) and those with multiple neighboring outliers (which have been grown).
If there are any intermediate groups with fewer than two nearest neighbor outliers as members, the intermediate group(s) are discarded, via step 160. Thus, any intermediate group with only a single site/outlier as a member is removed from consideration. Because they have an insufficient number of members, such individual outliers are deemed unlikely to be due to hot spots. The remaining groups include multiple, contiguous, nearest neighbor outliers. In an alternate embodiment, step 160 may be omitted. Steps 154, 156, 158 and 160 may be considered to be analogous to step 104 of the method 100.
For each group, the shape of a convex polygon including all of the outliers in the group is determined, via step 162. Various mechanisms for obtaining the polygons may be used in step 162. For example, a Jarvis March or gift wrap algorithm might be used. It is also determined whether the shape of the polygon for each group is sufficiently circular, via step 164. Step 164 may thus determine whether the circularness for the shape of the polygon for the group exceeds a particular threshold. Step 164 may include comparing the area of the shape to the perimeter. The groups for which the circularness for the polygon exceeds the threshold are retained, via step 166. Other groups are discarded. In other embodiments, other thresholds and/or other relationships may be used. For example, groups having a circularness of greater than or equal to the threshold might be retained. The remaining groups having a sufficiently high circularness are hot spot candidates.
For each hot spot candidate, initial guesses for the amplitude (initial amplitude) and width (initial width) are provided, via step 168. The initial amplitude may be the largest overlay error in the group/hot spot candidate. The initial width may be determined based upon the radius of a circle having an area substantially equal to a polygon area of the polygon. Each hot spot candidate is fitted to a physical model using the initial amplitude and initial width, via step 170. The physical model may be the spatial derivative of a Gaussian curve. In some embodiments, another physical model may be used or the gradient of the Gaussian may be supplemented with higher order corrections. For a Gaussian, a fitted width and fitted amplitude may be obtained in step 170. The fitted width for each hot spot candidate is checked against the spacing between sites. Any hot spot candidate having a fitted width less than the minimum spacing between sites are rejected, via step 172. Thus, steps 162, 164, 166, 168, 170 and 172 are thus analogous to step 106 of the method 100.
The fitted hot spot candidates may then be used to make various determinations. For example, the location of the center (x0, y0), the amplitude and the width may be determined from the fitted amplitude and fitted width obtained in step 170. Thus, the size, number and amplitude of the hotspot(s) may be determined. Further decisions may be made on the individual substrate tested. The data may also be used prospectively to improve processing of photolithographically defined devices.
The method 150 may share the benefits of the method 100. Hot spots may be more quickly and easily found and quantified. Decisions may be more quickly made on how to treat the substrate, for example whether to rework the substrate, and the data may be used to alter processing parameters to improve fabrication of devices on subsequent substrates. Operator bias and error may be avoided and yield improved. Thus, fabrication of photolithographically defined devices, such as magnetic data storage devices, may be improved.
FIG. 7 is a flow chart depicting an exemplary embodiment of a method 200 for determining and characterizing hot spots for a photolithographically defined device using a physical model of the hot spots. For simplicity, some steps may be omitted, interleaved, performed in another order, combined and/or include substeps. The method 200 may be performed by one or more software components executing on one or more processors. For example, the method 200 may be implemented using the computing system 110 of FIG. 3. The method 200 is also described in the context of fabrication of a magnetic recording device, such as a read and/or write head residing on an AlTiC substrate. However, the method 200 may be used to detect hot spots for other devices and/or other substrates. In addition, one of ordinary skill in the art will recognize that multiple devices are generally fabricated on a single substrate. The method 200 uses overlay error data for the photolithography defined device(s). The overlay error data may be taken at an array of sites across the surface of the substrate on which multiple photolithographically defined devices are being fabricated. The method 200 is also analogous to the method 100 and/or 150. The overlay error data is spatial error data. Thus, the overlay error data may indicate a distance and direction that the structure for each site is offset. For example, the surface of a substrate may be described using x and y coordinates. The overlay error data indicates the offset in the ±x direction and/or the ±y direction measured for each site.
The (measured) overlay error data is fit to expected distortions, via step 202. For example, the measured overlay error data may be least squares regression fit to the terms model for image distortions. The result of step 202 may be termed the fitted overlay data.
The fitted overlay data is subtracted from the measured overlay error data, resulting in residual overlay data, via step 204. Step 202 and 204 are analogous to step 102 and 112. The residual overlay error more closely corresponds to overlay errors due to hot spots. The residual overlay error data is spatial error data, indicating the error of shift in the data at each site.
It is iteratively determined whether the residual error data for each site exceeds a spatial error threshold using Chauvenet's criteria, via step 206. Each site having the spatial error exceeding the spatial error threshold is an outlier. Thus, the outliers for the substrate are determined in step 206.
For the each outlier, it is determined whether another outlier is a nearest neighbor to the outlier, via step 208. The two nearest neighbor outliers form a current group. For each current group, it is determined whether there are nearest neighbor outliers for the members of the current group, via step 210. Step 210 may then repeated, adding outliers to the current group, until the current group no longer grows, via step 212. Stated differently, step 210 is repeated until no additional nearest neighbor outliers are found for members of the group. If there are any groups with fewer than two nearest neighbor outliers as members, the intermediate group(s) are removed from consideration, via step 214. Thus, any intermediate group with only a single site/outlier as a member is removed from consideration. Each of the remaining groups include multiple, contiguous, nearest neighbor outliers. Steps 204, 206, 208, 210 and 212 may be considered to be analogous to step 104 of the method 100.
For each group, the smallest convex polygon including all of the outliers in the group is determined, via step 214. Stated differently, the convex hull for each group is determined in step 214. Various mechanisms, such as a Jarvis March or gift wrap algorithm, might be used in step 214.
The area and perimeter of each polygon is determined, via step 216. The area may be computed using Green's theorem implemented as a shoelace algorithm. However, other mechanisms for determining the polygon areas may be used. The perimeter of each polygon may be calculated by summing the length of all vector differences for the convex hull that was determined in step 214.
The shape value of each polygon is determined, via step 220. In some embodiments, step 220 includes determining the circularness for each polygon. The circularness for a group may be the quantity 4π(polygon area)/(polygon perimeter)2. The circularness of a circles is one. In other embodiments, another mechanism may be used to determine the circularness of the polygon for each group.
Groups that have a circularness that does not exceed a threshold are discarded, via step 222. In some embodiments, groups having polygons with a circularness of less than or equal to 0.5 are discarded. In other embodiments, other thresholds and/or other relationships may be used. For example, groups having a circularness of less than 0.5 might be removed. The remaining groups are hot spot candidates.
For each remaining group, initial guesses for the amplitude (initial amplitude) and width (initial width) are provided, via step 224. The initial amplitude may be the largest overlay error in the group/hot spot candidate. The initial width may be determined based upon the radius of a circle having an area substantially equal to a polygon area of the polygon for the remaining group.
Each hot spot candidate is fitted to a physical model using the initial amplitude and initial width, via step 226. The physical model may be the spatial derivative of a Gaussian curve. In some embodiments, another physical model may be used or the gradient of the Gaussian may be supplemented with higher order corrections. For a Gaussian, a fitted width and fitted amplitude may be obtained in step 226. The fitted width for each hot spot candidate is checked against the spacing between sites. Any hot spot candidate having a fitted width less than the minimum spacing between sites are rejected, via step 228. The remaining hot spot candidates are deemed hot spots. Thus, steps 216, 218, 220, 222, 224, 226 and 228 are thus analogous to step 106 of the method 100. The location of the center (x0, y0), the amplitude and the width for the hot spot may be determined from the fitted amplitude and fitted width. Thus, the size, number and amplitude of the hotspot(s) may be determined.
The method 200 may share the benefits of the methods 100 and/or 150. Hot spots may be more quickly and easily found and quantified. Decisions may be more quickly made on how to treat the substrate, for example whether to rework the substrate, and the data may be used to alter processing parameters to improve fabrication of devices on subsequent substrates. Operator bias and error may be avoided and yield improved. Thus, fabrication of photolithographically defined devices, such as magnetic data storage devices, may be improved.

## Claims

1. A method for detecting hot spots from overlay error data for at least one photolithography defined device, the overlay error data corresponding to data for a plurality of sites on a substrate for the at least one photolithography defined device, the method comprising:
converting the overlay error data to residual overlay data indicating a residual overlay error for each of the plurality of sites, the residual overlay error being based on an expected overlay error for each of the plurality of sites;
determining whether at least one group of overlay error sites is present in the residual overlay data, each of the at least one group including at least two nearest neighbor sites of the plurality of sites, each of the at least two nearest neighbor sites having the residual overlay error greater than a threshold;
for each of the at least one group of overlay error sites present, determining whether each of the at least one group of overlay error sites fits a physical model for a hotspot, each of the at least one group of overlay error sites fitting the physical model being categorized as a hotspot; and
determining a plurality of parameters for the hotspot for each of the at least one group of overlay error sites that fits the physical model, wherein the step of determining whether each of the at least one group of overlay error sites fits a physical model for a hotspot further includes:
determining a shape of a polygon for each of the at least one group of overlay error sites;
determining whether the shape has a circularness exceeding a shape threshold; and
retaining at least a portion of the plurality of the groups of overlay error sites having the circulamess exceeding the threshold to provide at least one hot spot candidate.

2. The method of claim 1 wherein the physical model is a Gaussian-based curve and the plurality of parameters include an amplitude, a width and a center location.

3. The method of claim 1 wherein the residual overlay data includes spatial error data and wherein the step of determining whether the at least one group of overlay error sites exists further includes:
determining whether a spatial error in the overlay error data for each of plurality of sites exceeds a spatial error threshold for each of the plurality of sites, each spatial error exceeding the spatial error threshold being an outlier;
for each of the outlier, determining whether an other outlier corresponding to an other site is in proximity to the outlier for a site, the other outlier and the outlier forming a current group; and
for each current group, repeating the determining step for the current group until the current group does not grow, thereby providing the at least one intermediate group.

4. The method of claim 3 wherein the step of determining the at least one group of overlay error sites further includes:
for each of the at least one intermediate group, rejecting any group including only a single site to provide the at least one group of overlay error sites.

5. The method of claim 1 wherein the step of determining whether each of the at least one group of overlay error sites fits a physical model for a hotspot further includes:
providing an initial amplitude and an initial width for each of the at least one hot spot candidate based on a largest overlay error and a circle having an area substantially equal to a polygon area of the polygon; and calculating a fitted width and a fitted amplitude for each of the at least the at least one hot spot candidate using the initial amplitude and the initial width, a hotspot having the fitted width and the fitted amplitude being determined for each of the at least the portion of the plurality of groups of overlay error sites.

6. The method of claim 1 wherein the step of determining the plurality of parameters further includes:
rejecting any hotspot having a fitted width less than a minimum spacing between the plurality of sites to provide at least one hotspot.

7. The method of claim 1 wherein the expected overlay error is an expected image distortion error.

8. The method of claim 1 further comprising:
determining whether to rework the substrate based on the plurality of parameters for each hotspot.

9. The method of claim 1 wherein the method is performed by at least one software component executing on at least one processor.

10. The method of claim 1 wherein the at least one photolithography defined device is at least one data storage device.