System, method, and non-transitory computer-readable medium for tuning the sensitivity of a modulated wafer and determining a process window for the modulated wafer

Abstract

Embodiments of the present application relate to systems, methods, and non-transitory computer-readable media for tuning the sensitivity of a modulated wafer and determining a process window for the modulated wafer. The present invention provides a system, method, and non-transitory computer-readable media for tuning the sensitivity of a modulated wafer and determining a process window for the modulated wafer. The sensitivity of the die of the modulated wafer is dynamically tuned based on a single set of parameters. In addition, the process window for the modulated wafer is determined based on a specific nominal process window of the parameters determined previously.

Description

[0001] This application is a divisional application of the patent application for invention titled "Systems, Methods, and Non-Transitory Computer-Readable Media for Tuning the Sensitivity of a Modulated Wafer and Determining a Process Window for a Modulated Wafer" with application number 201780068639.5 and filing date November 20, 2017.

[0002] Related Applications

[0003] This application claims the benefit of U.S. Provisional Patent Application No. 62 / 425,029, filed on November 21, 2016, the entire content of which is incorporated herein by reference. TECHNICAL FIELD

[0004] The present invention relates to the inspection of modulated wafers, and more particularly to the sensitivity tuning and process window characterization of modulated wafers. BACKGROUND OF THE INVENTION

[0005] Currently, defects in a wafer can be detected by comparing a target die on the wafer with a reference die on the wafer. An inspection system accomplishes this by taking images of the target and reference dies for comparison purposes. Specifically, defect detection typically involves performing two separate comparisons to produce two separate results, one comparison between the target die and one of the reference dies, and the other comparison between the target die and the other of the reference dies. Any similarity between the two separate comparison results is typically used as an indicator of a defect in the die. The detected defects are then used as a basis for qualifying the design of the wafer (e.g., determining design regions that are systematically prone to defects) and further for characterizing the process window (e.g., the parameters within which the manufacturing tool can fabricate the wafer within the design specifications) used by the manufacturing tool that fabricated the wafer.

[0006] PRIOR ART Figure 1 A conventional layout of a wafer is shown, which has multiple target dies in column 102, each target die being the same pattern modulated (i.e., magnified) by different combinations of parameter (e.g., focus (F) and exposure (E)) values, and the wafer further has multiple reference dies in columns 104, 106 on either side of the column of target dies and each reference die being a nominal (i.e., unmodulated) version of the same pattern. Thus, for any particular one of the target dies in column 102, the reference die from column 104 and the reference die from column 106 can be used to detect a defect in the particular target die (see block 108). Although the reference dies are shown as adjacent to the target dies, this is not necessarily always the case. For example, in other wafer configurations, the reference die for any particular target die can be the closest but not necessarily adjacent reference die to the particular target die.

[0007] Unfortunately, traditional methods related to defect detection described above involve inefficient and thus time- and resource-intensive techniques. By way of example only, current methods for process window characterization (e.g., Process Window Qualification (PWQ) methods) require numerous scan iterations, including individual tests for each die, and the individual tests further involve individual scans for each modulation of the die.

[0008] To accommodate the limitations mentioned above, current methods further involve individually estimating inspection sensitivity for each modulation. This can be achieved using an Initial Threshold Finder (ITF), but in any case requires a preliminary scan of each modulated die to evaluate the defect rate of the modulated die and assign a sensitivity to the modulated die such that subsequent inspection scans of the modulated die are performed based on the assigned sensitivity.

[0009] Accordingly, there is a need to address these and / or other problems associated with the prior art. SUMMARY OF THE INVENTION

[0010] In one embodiment, a system, method, and non-transitory computer-readable medium for determining a process window for a modulated wafer are provided. In use, a first region of interest is defined for a wafer having a plurality of dies modulated in different ways according to at least two parameters. Additionally, a first defect scan of the wafer is performed based on the first region of interest, and the result of the first defect scan is obtained. Further, a first nominal process window is determined for a first parameter of the at least two parameters based on the result of the first defect scan and based on an attribute space. Additionally, a second nominal process window is determined for a second parameter of the at least two parameters based on the result of the first defect scan and based on the attribute space. Additionally, a predicted process window for the wafer is determined based on the first nominal process window and the second nominal process window. Additionally, a second defect scan of the wafer is performed within the predicted process window based on a final region of interest, and the result of the second defect scan is obtained. Further, a final process window for the wafer is determined based on the result of the second defect scan.

[0011] In another embodiment, a system, method, and non-transitory computer-readable medium for tuning the sensitivity of a modulated wafer are provided. In use, from a wafer having a plurality of dies that are modulated in different ways according to at least two parameters, the following are identified: a first die having a low modulation relative to the modulation of the plurality of dies; a second die having a medium modulation relative to the modulation of the plurality of dies; and a third die having a high modulation relative to the modulation of the plurality of dies. Additionally, based on a Taylor series expansion function, a first-order offset is estimated from the first die and a separate second-order offset is estimated from each of the second die and the third die. Further, an inspection is performed on the wafer, for each die of the wafer undergoing the inspection: (a) a dynamic offset corresponding to the noise level in the die is calculated using the first-order offset estimated from the first die and the second-order offset estimated from the second die, and (b) the dynamically calculated offset is applied as the sensitivity to the die. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 An exemplary layout of a wafer according to the prior art is shown.

[0013] Figure 2A A block diagram illustrating an embodiment of a non-transitory computer-readable medium including program instructions executable on a computer system to perform one or more of the computer-implemented methods described herein is shown.

[0014] Figure 2B A schematic side view of an embodiment of an inspection system configured to detect defects on a fabricated device is shown.

[0015] Figure 3 A method for determining a process window for a modulated wafer according to one embodiment is illustrated.

[0016] Figures 4A to 4E Illustrates a first pass implementation of a method according to another embodiment Figure 3 of

[0017] Figure 5 A method for tuning the sensitivity of a modulated wafer according to one embodiment is illustrated.

[0018] Figure 6 A graph illustrating a polynomial model according to another embodiment, by which the sensitivity of a modulated wafer is tuned, is shown.

[0019] Figure 7The graphical illustration shows a graph of a linear model according to another embodiment, and the sensitivity of the modulated wafer is tuned by the linear model. Detailed Description

[0020] The following description discloses methods for tuning the sensitivity of a modulated wafer and determining a process window for the modulated wafer, as well as systems and non-transitory computer-readable media for performing the methods. It should be noted that the various embodiments described below can be implemented in the context of any inspection system (e.g., wafer inspection, mask inspection, laser scanning inspection system, etc.), such as the inspection system referenced below Figure 2B described inspection system.

[0021] One embodiment relates to a non-transitory computer-readable medium that stores program instructions executable on a computer system for performing the methods mentioned above. In Figure 2A is shown one such embodiment. Specifically, as Figure 2A shown, the computer-readable medium 200 includes program instructions 202 executable on the computer system 204. The computer-implemented method includes the steps of the method described below with reference to Figure 5 described. The computer-implemented method for which the program instructions can be executed can include any other operations described herein.

[0022] The program instructions 202 for methods implementing methods such as those described herein can be stored on the computer-readable medium 200. The computer-readable medium can be a storage medium, such as a magnetic disk or optical disk or magnetic tape or any other suitable non-transitory computer-readable medium known in the art. As an option, the computer-readable medium 200 can be located within the computer system 204.

[0023] The program instructions can be implemented in any of a variety of ways, including program-based techniques, component-based techniques, and / or object-oriented techniques, as well as other techniques. For example, ActiveX controls, C++ objects, JavaBeans, Microsoft Foundation Classes ("MFC"), or other techniques or methods can be used to implement the program instructions as needed.

[0024] The computer system 204 can take various forms, including a personal computer system, an image computer, a host computer system, a workstation, a network appliance, an Internet appliance, or other devices. In general, the term "computer system" can be broadly defined to encompass any device that has one or more processors that execute instructions from a memory medium. The computer system 204 can also include any suitable processor known in the art, such as a parallel processor. Additionally, the computer system 204 can include a computer platform with high-speed processing and software as a stand-alone or networked tool.

[0025] Additional embodiments relate to a system configured to perform the methods mentioned above. In Figure 2B an embodiment of this system is shown. The system includes an inspection system 205 configured to produce an output for components fabricated on a wafer (or other device). The system also includes one or more computer systems configured to perform the operations described below with reference to Figure 3 and 5 . One or more computer systems may be configured to perform these operations according to any of the embodiments described herein. The computer systems and the system may be configured to perform any other operations described herein and may be further configured as described herein.

[0026] In Figure 2B the embodiment shown, one of the computer systems is part of an Electronic Automation Design (EAD) tool, and the inspection system and the other of the computer systems are not part of the EAD tool. For example, these computer systems may include the computer system 204 described above with reference to Figure 2A . For example, as Figure 2B shown, one of the computer systems may be the computer system 208 included in the EAD tool 206. The EAD tool 206 and the computer system 208 included therein may include any commercially available EAD tool.

[0027] The inspection system 205 may be configured to produce an output for components fabricated on the wafer by scanning the wafer with light and detecting the light from the wafer during the scan. For example, as Figure 2B shown, the inspection system 205 includes a light source 220, which may include any suitable light source known in the art. The light from the light source may be directed to a beam splitter 218, which may be configured to direct the light from the light source to the wafer 222. The light source 220 may be coupled to any other suitable elements (not shown) such as one or more condenser lenses, collimating lenses, relay lenses, objective lenses, apertures, spectral filters, polarization components, and the like. As Figure 2B shown, the light may be directed to the wafer 222 at a normal incidence angle. However, the light may be directed to the wafer 222 at any suitable incidence angle including near-normal and oblique incidence. Additionally, the light or multiple light beams may be directed to the wafer 222 at more than one incidence angle sequentially or simultaneously. The inspection system 205 may be configured to scan the light over the wafer 222 in any suitable manner.

[0028] Light from the wafer 222 can be collected and detected by one or more channels of the inspection system 205 during a scan. For example, light reflected from the wafer 222 at an angle relatively close to normal (i.e., specularly reflected light when the incidence is normal) can pass through the beam splitter 218 and thus reach the lens 214. The lens 214 can include refractive optical elements, such as Figure 2B as shown. Additionally, the lens 214 can include one or more refractive optical elements and / or one or more reflective optical elements. The light collected by the lens 214 can be focused onto the detector 212. The detector 212 can include any suitable detector known in the art, such as a charge-coupled device (CCD) or another type of imaging detector. The detector 212 is configured to produce an output in response to the reflected light collected by the lens 214. Thus, the lens 214 and the detector 212 form one channel of the inspection system 205. This channel of the inspection system 205 can include any other suitable optical components (not shown) known in the art.

[0029] Since Figure 2B the inspection system shown in is configured to detect specularly reflected light from the wafer 222, the inspection system 205 is configured as a bright-field (BF) inspection system. However, this inspection system 205 can also be configured for other types of wafer inspection. For example, Figure 2B the inspection system shown in can also include one or more other channels (not shown). The other channels can include any of the optical components (such as lenses and detectors) described herein that are configured as scattered light channels. The lenses and detectors can be further configured as described herein. In this way, the inspection system 205 can also be configured for dark-field (DF) inspection.

[0030] The inspection system 205 can also include a computer system 210 configured to perform one or more steps of the methods described herein. For example, the optical elements described above can form the optical subsystem 211 of the inspection system 205, and the inspection system can also include a computer system 210 coupled to the optical subsystem 211. In this way, the output generated by the detector during a scan can be provided to the computer system 210. For example, the computer system 210 can be coupled to the detector 212 (e.g., through one or more transmission media, shown by the dashed line in Figure 2B that can include any suitable transmission media known in the art), such that the computer system 210 can receive the output generated by the detector.

[0031] The computer system 210 of the inspection system 205 can be configured to perform any of the operations described herein. Additionally, the computer system 210 can be configured to perform any other steps described herein. Further, although some of the operations described herein may be performed by different computer systems, all of the operations of the method can be performed by a single computer system (such as the computer system of the inspection system 205 or a separate computer system). Additionally, one or more of the computer systems can be configured as a virtual inspector, such as the virtual inspector described in U.S. Patent No. 8,126,255, issued to Bhaskar et al. on February 28, 2012, which is incorporated by reference as if fully set forth herein.

[0032] The computer system 210 of the inspection system 205 can also be coupled to another computer system that is not part of the inspection system, such as the computer system 208, which can be included in another tool such as the EAD tool 206 described above, such that the computer system 210 can receive the output generated by the computer system 208 (which can include a design generated by the computer system 208). For example, the two computer systems can be effectively coupled by sharing a computer-readable storage medium (such as a foundry database) or can be coupled by a transmission medium (such as the transmission media described above) such that information can be transferred between the two computer systems.

[0033] It should be noted that provided herein Figure 2B to generally illustrate the configuration of an inspection system that can be included in the system embodiments described herein. Obviously, the inspection system configurations described herein can be modified to optimize the performance of the inspection system, as is typically done when designing a commercial inspection system. Additionally, the systems described herein can be implemented using existing inspection systems (such as the 29xx / 28xx series tools commercially available from KLA-Tencor Corporation) (e.g., by adding the functionality described herein to an existing inspection system). For some such systems, the methods described herein can be provided as an optional functionality of the system (e.g., in addition to the other functionality of the system). Alternatively, the systems described herein can be designed "from scratch" to provide a brand-new system.

[0034] Figure 3 Illustrates a method 300 for determining a process window for a modulated wafer according to one embodiment. As shown in operation 302, a first region of interest is defined for a wafer having a plurality of dies modulated in different ways according to at least two parameters. The wafer can be as described above with reference to the prior art Figure 1configured to include a plurality of dies (target dies) modulated in different ways according to at least two parameters as described. These parameters can be exposure, focus, etc., and the modulation can be any magnification (positive or negative) of one or more of the parameters. U.S. Patent No. 8,213,704, incorporated herein by reference, discloses techniques for modulating dies of a wafer.

[0035] A first region of interest can be defined for a wafer as a unique pattern in which defect detection will be performed, and thus the first region of interest can be identified from an image of the wafer as a set of connected image pixels representing the unique pattern. The first region of interest can have any shape and size, but is a sub - part of a final region of interest where defect detection will ultimately be performed as mentioned below. In one exemplary embodiment, the first region of interest can be designated as "dense fine lines". For example, this region of interest can be pre - configured for method 300 (e.g., by a user, etc.) based on a determination of the defect rate occurrence that may occur within the process window based on the first region of interest.

[0036] Additionally, as shown in operation 304, a first defect scan of the wafer is performed based on the first region of interest. Specifically, the first defect scan of the wafer is performed within the first region of interest. In one embodiment, a single - tone tuning scan (OSTS) inspection of the wafer can be used to perform the first defect scan. U.S. Patent No. 9,518,934, issued on December 13, 2016 to Chen et al., the entire content of which is incorporated herein by reference, discloses an implementation of OSTS. As another option, an OSTS using a standard MDAT algorithm and known defect down - sampling techniques can be employed. MDAT is a defect detection method used by a wafer inspection tool commercially available from KLA - Tencor Corporation of Milpitas, California. U.S. Patent No. 7,440,607, issued on October 21, 2017 to Lin et al., the entire content of which is incorporated herein by reference, discloses an implementation of MDAT. As yet another option, the method 500 described below can optionally be implemented for the first defect scan. Figure 5 as described.

[0037] In operation 306, the results of the first defect scan are obtained. The results can indicate defects within the first region of interest. Additionally, as shown in operation 308, based on the results of the first defect scan and based on an attribute space, a first nominal process window is determined for a first parameter of at least two parameters. By way of example only, the first parameter for which the first nominal process window is determined can be a focus parameter. Additionally, the attribute space refers to any predetermined one or more attributes by which defects can be characterized, such as position, size, polarity, etc.

[0038] In one embodiment, the attribute space may include defect polarity. In this embodiment, a first nominal process window may be determined by tracking defect polarity for, for example, bright defects (i.e., defects that are brighter than their background, which may be caused by overfocusing resulting in gaps in lines on the die) and dark defects (i.e., defects that are darker than their background, which may be caused by underfocusing resulting in bridges between otherwise separated lines on the die). For example, a certain number of bright defects detected for each different value of a first parameter (e.g., focus) may be tracked, as well as a certain number of dark defects detected for each different value of the first parameter. The value of the first parameter at which the number of bright defects is lowest (hereinafter Parameter1Value1) and the value of the first parameter at which the number of dark defects is lowest (hereinafter Parameter1Value2) may define the first nominal process window. In other words, the first nominal process window may include the modulation between Parameter1Value1 and Parameter1Value2. In another embodiment, a polynomial fit of the defects may be used to determine the first nominal process window. In any case, the first nominal process window excludes the modulated die having values of the first parameter (e.g., focus) outside the first nominal process window.

[0039] Further, as shown in operation 310, a second nominal process window is determined for a second parameter of at least two parameters based on the results of the first defect scan and based on the attribute space. By way of example only, the second parameter for which the second nominal process window is determined may be an exposure parameter. In any case, the second nominal process window is determined based on the same attribute space as the attribute space used to determine the first nominal process window.

[0040] Again, in one embodiment, the attribute space may include defect polarity. In this embodiment, the second nominal process window may be determined by tracking defect polarity for, e.g., bright defects (i.e., defects that are brighter than their background, which may be caused, e.g., by overexposure resulting in gaps in lines on the die) and dark defects (i.e., defects that are darker than their background, which may be caused, e.g., by underexposure resulting in bridges between otherwise separated lines on the die). For example, a certain number of bright defects detected for each different value of a second parameter (e.g., exposure) may be tracked, as well as a certain number of dark defects detected for each different value of the second parameter. The value of the second parameter at which the number of bright defects is lowest (hereinafter Parameter2Value1) and the value of the second parameter at which the number of dark defects is lowest (hereinafter Parameter2Value2) may define the second nominal process window. In other words, the second nominal process window may include the modulation between Parameter2Value1 and Parameter2Value2. In another embodiment, a polynomial fit of the defects may be used to determine the second nominal process window. In any case, the second nominal process window excludes modulated dies having values of the second parameter (e.g., exposure) outside the second nominal process window.

[0041] Additionally, as shown in operation 312, a predicted process window for the wafer is determined based on the first nominal process window and the second nominal process window. For example, the predicted process window may combine the first nominal process window and the second nominal process window. In one embodiment, the predicted process window may be determined by downsampling the wafer using the first nominal process window and the second nominal process window such that the predicted process window includes dies having modulated parameters within both the first nominal process window and the second nominal process window.

[0042] Furthermore, as shown in operation 314, a second defect scan of the wafer is performed within the predicted process window based on the final region of interest. Specifically, the second defect scan of the wafer is performed within the final region of interest. As described above, the final region of interest may include the first region of interest area described above as a sub - part thereof. In one embodiment, a monotonic tuned scan (OSTS) inspection of the wafer may be used to perform the second defect scan. As another option, an OSTS using a standard MDAT algorithm and known defect downsampling techniques may be employed. As yet another option, the method 500 described below may optionally be implemented for the second defect scan. Figure 5 as described.

[0043] As shown in operation 316, the results of a second defect scan are obtained. The results may indicate defects within the final region of interest. Additionally, as shown in operation 318, based on the results of the second defect scan, a final process window for the wafer is determined. This can be accomplished using methods known in the art. Optionally, as additional steps (not shown) after operation 318, a predetermined PWEC sampling algorithm may be used to further refine the final process window.

[0044] The inventive method 300 can thus predict a process window based on a region of interest smaller than the final region of interest to be concerned with, and then use the predicted process window to determine the actual process window for the final region of interest of the wafer. Thus, in one embodiment, method 300 illustrates a two-pass method for process window characterization of a modulated wafer, where (1) the first pass (operations 302 to 312) uses a region of interest smaller than the second pass (operations 314 to 318), and (2) the second pass is performed within the smaller (predicted) process window. Thus, both (1) and (2) will reduce the number of iterations that would otherwise be required by the prior art (which scans each modulated die of the wafer with respect to the final region of interest), and thus reduce the time to arrive at the result (determining the final process window for the wafer).

[0045] Figures 4A to 4E Illustrating according to another embodiment Figure 3 an implementation of the first pass of the method of Figure 4A is shown. Specifically, Figure 4A a wafer is shown having dies that are modulated in different ways using different combinations of values of a focus parameter (F) and an exposure parameter (E). The Figure 4A modulated wafer is subjected to Figure 3 the first pass described in method 300 of Figure 4B to obtain defect detection results, and a nominal focus process window is determined based on those results (as shown in Figure 4C ), the nominal focus process window eliminating some of the modulated dies in the modulated wafer (as shown in Figure 4B ). Specifically, Figure 4C a graph is shown that maps defect polarities in association with changes in focus parameter values to determine the nominal focus process window.

[0046] A nominal exposure process window is also determined based on the defect detection results obtained during the Figure 3 first pass described in method 300 of Figure 4D , the nominal exposure process window eliminating some other modulated dies (as shown in Figure 4E ). Specifically, Figure 4DShow a graph that maps defect polarities in association with changes in exposure parameter values to determine a nominal exposure process window. Figure 4E Show the modulated die (i.e., marked with an X) outside both the nominal focus process window and the nominal exposure process window. Thus, Figure 4E Show the remaining modulated die (i.e., not marked with an X) within the predicted process window for the Figure 4A wafer. Figure 3 Method 300 of Figure 4E can then use the predicted process window shown in

[0047] Figure 5 Illustrate method 500 for tuning the sensitivity of a modulated wafer according to one embodiment. In one embodiment, method 500 is performed at runtime (e.g., for defect detection). Thus, the sensitivity of the modulated wafer can be dynamically (i.e., instantaneously and automatically) tuned by a computer system via this method 500. As described below, method 500 can dynamically adjust the sensitivity offset and its derivative based on the noise level.

[0048] As shown in operation 502, identify the following from a wafer having multiple die that are modulated in different ways according to at least two parameters: a first die having a low modulation relative to the modulation of the multiple die; a second die having a medium modulation relative to the modulation of the multiple die; and a third die having a high modulation relative to the modulation of the multiple die. For example, the wafer can be the same wafer as described above with respect to Figure 3

[0049] In one embodiment, a predefined ranking of the die on the wafer can be used to identify the first die, the second die, and the third die. The ranking of each die can vary with the modulation of the die. Thus, the first die can be identified (selected) based on its low ranking (e.g., relative to other rankings), the second die can be identified (selected) based on its intermediate ranking (e.g., relative to other rankings), and the third die can be selected based on its high ranking (e.g., relative to other rankings). Of course, the specific rankings based on which the first die, the second die, and the third die are identified can be preconfigured. Additionally, when classifying multiple die according to each of those specific rankings, the first die, the second die, and the third die can then be identified randomly or systematically for each of those specific rankings. However, of course it should be noted that the first, second, and third die can be identified in any way to obtain a sampling across the various modulations of the wafer.

[0050] ​In addition, as shown in operation 504, based on a Taylor series expansion function, a first-order offset is estimated from the first die and a separate second-order offset is estimated from each of the second and third dies. The Taylor series expansion function can be a predefined function that serves as a model for a noise-adaptation formula, as described in more detail below. In one embodiment, the first-order offset estimated from the first die can be the zero-order term in the Taylor series expansion. In another embodiment, the separate second-order offsets estimated from each of the second and third dies can be the first-order terms in the Taylor series expansion applied to the second and third dies. In an exemplary embodiment, the first-order offset includes a parameter (e.g., gray scale) offset (e.g., threshold) where a defect is detected. The first-order offset estimated from the first die can be non-zero.

[0051] Furthermore, as shown in operation 506, an inspection of the wafer is performed. In an exemplary embodiment, the inspection can be an OSTS inspection. In the current operation 506, for each die undergoing inspection, the inspection (a) dynamically calculates an offset corresponding to the noise level in the die using the first-order offset estimated from the first die and the second-order offset estimated from the second die, and (b) applies the dynamically calculated offset as a sensitivity to the die.

[0052] In one embodiment, the inspection can be performed on the dies of the wafer having a primary die type. Thus, optionally, the inspection can be performed only on a subset of all the dies of the wafer. A typical feature of the MDAT is an MDAT file that defines which dies of the wafer have the primary die type. The MDAT file can also define other dies of the wafer having a secondary die type, which can be of interest for an optional secondary inspection (e.g., as described below).

[0053] In one embodiment, the function shown in Table 1, which is stated for illustrative purposes only, can be used to dynamically calculate an offset corresponding to the noise level in the die.

[0054] Table 1

[0055] Offset = (maximum(first order offset, second order offset_second die x Noise),

[0056] where Noise is the noise level in the die.

[0057] Note that the sensitivity applied to a particular die can control the number of defects detected for the particular die, where a lower sensitivity results in fewer defects being detected compared to a higher sensitivity. The sensitivity of a die is dynamically calculated by using the function shown in Table 1, and the sensitivity can have a direct correlation with the noise detected for the die. Specifically, the sensitivity of the die of a wafer can linearly decrease (i.e., be detuned) as the noise of those dies increases, as Figure 7 shown in. This can allow lower modulated dies to be over-tuned and allow higher modulated dies to be detuned. Additionally, by dynamically calculating the sensitivity of each die based on the first-order offset estimated from a first die and the second-order offset estimated from a second die (as described above), a single test can be used to determine the sensitivity using a single set of parameters (i.e., the first-order offset estimated from the first die and the second-order offset estimated from the second die), and thus the requirement of the prior art to perform separate tests for each die can be avoided.

[0058] As an option, additional inspection of the wafer can be performed on the dies of the wafer having a secondary die type. This additional inspection can be prompted by the user, or can be configured to be automatically prompted (e.g.) when the dynamically calculated offset corresponding to a higher modulated die results in too high a sensitivity such that too many defects are being detected. By way of example only, when the maximum number of defects to be detected per die and / or per wafer has been set, additional inspection can be prompted when the higher modulated die results in the maximum number of defects being met.

[0059] Accordingly, the secondary die type can include these higher modulated dies. For each other die of the wafer that undergoes additional inspection, other offsets corresponding to the other die are dynamically calculated using the first-order offset estimated from the first die and the second-order offset estimated from a third die. This can be achieved using the function shown in Table 1, where the second-order offset is estimated from the third die instead of the second die. Then, the other offsets are applied as other sensitivities to the corresponding dies. By using the second-order offset estimated from the third die, the offset can increase at a rate higher than the rate at which the offset would otherwise be calculated when using the second-order offset estimated from the second die in proportion to the noise. This means that when calculated using the second-order offset estimated from the third die, the offset can allow higher modulated dies to be inspected without the maximum number of defects being met. Figure 6 A polynomial model showing the offset related to the noise, including different trajectories of the offset for higher modulated dies having higher noise.

[0060] This method 500 avoids the need in the prior art for multiple tests being set for different modulated dies and thus performing separate calculations to estimate inspection sensitivity individually for each die of a wafer. Specifically, a single test of the method 500 of the present invention can be used to determine the sensitivity of a die, as described above. Thus, method 500 makes test prescription management of a wafer more feasible than test prescription management required in the prior art. In addition, method 500 can reduce inspection time by more than twice that required by the prior art.

[0061] In addition, method 500 can increase the sensitivity of low-modulation dies while also reducing over-detection of excessive defects in high-modulation dies by corresponding reduced sensitivity. This can be achieved by using OSTS. This is in contrast to the prior art that specifically includes ITF, which is prone to detuning low-modulation dies and over-tuning high-modulation dies, resulting in low sensitivity in low-modulation dies or over-detection of excessive defects in high-modulation dies. For this reason, method 500 provides a more efficient and accurate technique for tuning the sensitivity of a modulated wafer as compared to the more time-consuming and resource-intensive methods of the prior art.

[0062] Although various embodiments have been described above, it should be understood that the embodiments are presented by way of example and not limitation. Accordingly, the breadth and scope of the preferred embodiments should not be limited by any of the exemplary embodiments described above, but should be defined only in accordance with the appended claims and their equivalents.

Claims

1. A non - transitory computer - readable medium storing a computer program product, the computer program product having code executable by a processor to perform a method, the method comprising: Identifying each of the following from a wafer having a plurality of dies modulated in different ways according to at least two parameters: A first die having a low modulation of the modulation relative to the plurality of dies, A second die having a medium modulation of the modulation relative to the plurality of dies, and A third die having a high modulation of the modulation relative to the plurality of dies; Estimating a first - order offset from the first die and a separate second - order offset from each of the second die and the third die based on a Taylor - series expansion function; Performing an inspection on the wafer, for each die of the wafer subjected to the inspection: (a) Dynamically calculating an offset corresponding to the noise level in the die using the first - order offset estimated from the first die and the second - order offset estimated from the second die, and (b) Applying the dynamically calculated offset as a sensitivity to the die.

2. The non - transitory computer - readable medium according to claim 1, wherein the first die, the second die, and the third die are identified using a predefined ranking of each die in the plurality of dies, and the ranking of each die varies with the modulation of the die.

3. The non - transitory computer - readable medium according to claim 1, wherein the first - order offset is non - zero.

4. The non - transitory computer - readable medium according to claim 1, wherein the offset corresponding to the die is dynamically calculated using the following function: Offset=(maximum(first - order offset, second - order offset of the second die multiplied by the noise)), where the noise is the noise level in the die.

5. The non - transitory computer - readable medium according to claim 1, wherein the inspection is performed on the dies of the wafer having a primary die type.

6. The non - transitory computer - readable medium according to claim 5, further comprising performing an additional inspection of the wafer on the dies of the wafer having a secondary die type, wherein for each other die of the wafer subjected to the additional inspection, the additional inspection: (a) Dynamically calculating an other offset corresponding to the noise level in the other die using the first - order offset estimated from the first die and the second - order offset estimated from the third die, and (b) Applying the other offset as an other sensitivity to the other die.

7. The non - transitory computer - readable medium according to claim 6, wherein the additional inspection is prompted by a user.

8. A method executed by a processor, the method comprising: Identifying each of the following from a wafer having a plurality of dies modulated in different ways according to at least two parameters: A first die having a low modulation of the modulation relative to the plurality of dies, A second die having a medium modulation of the modulation relative to the plurality of dies, and A third die having a high modulation of the modulation relative to the plurality of dies; Estimate a first-order offset from the first die and estimate separate second-order offsets from each of the second die and the third die based on a Taylor series expansion function; Perform an inspection on the wafer, for each die of the wafer that undergoes the inspection: (a) Dynamically calculate an offset corresponding to the noise level in the die using the first-order offset estimated from the first die and the second-order offset estimated from the second die, and (b) Apply the dynamically calculated offset as a sensitivity to the die.

9. An inspection system, comprising: A processor for: Identify each of the following from a wafer having a plurality of dice that are modulated in different ways according to at least two parameters: A first die having a low modulation relative to the modulation of the plurality of dice, A second die having a medium modulation relative to the modulation of the plurality of dice, and A third die having a high modulation relative to the modulation of the plurality of dice; Estimate a first-order offset from the first die and estimate separate second-order offsets from each of the second die and the third die based on a Taylor series expansion function; Perform an inspection on the wafer, for each die of the wafer that undergoes the inspection: (a) Dynamically calculate an offset corresponding to the noise level in the die using the first-order offset estimated from the first die and the second-order offset estimated from the second die, and (b) Apply the dynamically calculated offset as a sensitivity to the die.

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