Local shape deviations in semiconductor samples

Abstract

To provide a system and method for detecting a local shape deviation of a structural element in a semiconductor specimen.SOLUTION: A system and method includes: obtaining an image comprising an image representation of a structural element; extracting, from the image, an actual contour of the image representation; estimating a reference contour of the image representation indicating a standard shape of the structural element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically selected to be insensitive to local shape deviation of the actual contour; and performing one or more measurements representing one or more differences between the actual contour and the reference contour, the measurements indicating whether a local shape deviation is present in the structural element.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The subject matter of this disclosure relates generally to the field of testing semiconductor specimens, and more particularly to critical dimension (CD) metrology related to shape deviations of the specimens. [Background technology]

[0002] Current demands for high density and performance associated with ultra-large scale integration of fabricated devices require submicron features, increased transistor and circuit speed, and improved reliability. As semiconductor processes advance, pattern dimensions such as linewidths and other types of critical dimensions continue to shrink. Such demands require the formation of device features with high precision and uniformity, which in turn requires careful monitoring of the fabrication process, including automated testing of the devices while they are still in the form of semiconductor wafers.

[0003] Testing can be performed by using non-destructive testing tools during or after the production of the specimen to be tested. Testing generally involves directing light or electrons at a wafer and detecting photons or electrons from the wafer to generate a particular output (e.g., an image, a signal, etc.) related to the specimen. Various non-destructive testing tools include, by way of non-limiting example, scanning electron microscopes, atomic force microscopes, optical inspection tools, etc.

[0004] A test process can include multiple test steps. Test steps can be performed multiple times during the production process, such as after the production or processing of a particular layer. Additionally or alternatively, each test step can be repeated multiple times, for example, on different wafer locations or on the same wafer location with different test settings.

[0005] Test processes are used at various steps during semiconductor manufacturing to detect and classify defects on specimens, as well as to perform metrology-related operations. Test effectiveness can be improved by automating processes such as defect detection, automatic defect classification (ADC), automatic defect review (ADR), automated metrology-related operations, etc.

[0006] Traditional critical dimension (CD) metrology for process control is based on measuring the geometric dimensions of basic features such as lines and contacts. However, traditional CD metrics of such features, such as average contact diameter, average width, average Manhattan size, etc., sometimes fail to provide the necessary correlation with electrical metrology in large-scale semiconductor device production. Therefore, new metrology metrics for advanced process control need to be developed. Summary of the Invention

[0007] According to certain aspects of the presently disclosed subject matter, there is provided a computerized system for detecting local shape deviations of structural elements within a semiconductor sample, the system including a processing and memory circuit (PMC) configured to: obtain an image including an image representation of the structural element; extract from the image an actual contour of the image representation; estimate a reference contour of the image representation indicative of a standard shape of the structural element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically selected to be insensitive to the presence of local shape deviations of the actual contour; and perform one or more measurements indicative of one or more differences between the actual contour and the reference contour, the measurements indicating whether local shape deviations are present in the structural element.

[0008] In addition to the features described above, systems according to this aspect of the presently disclosed subject matter may include one or more of the following listed features (i) through (ix), in any desired combination or permutation that is technically possible. (i) The structural element has a shape selected from the group including elliptical, oval, rectangular, or a combination thereof. (ii) Local shape deviations are represented by local distortions of the actual contours that have relatively large deviations from the nominal shape of the structural element. (iii) The semiconductor sample is a memory device or a logic device. (iv) The actual contours are extracted using edge detection methods. (v) The loss function is a Welsch loss function. (vi) estimating the reference contour includes extracting a first sequence of points from the actual contour; transforming the sequence of points into a Fourier series characterized by a set of Fourier coefficients; optimizing values ​​of a subset of Fourier coefficients selected from the set of Fourier coefficients so as to minimize a loss function, the subset of Fourier coefficients having optimized values ​​constituting a Fourier descriptor of the reference contour; and performing an inverse Fourier transform using the Fourier descriptor to produce a second sequence of points constituting the reference contour. (vii) each of the one or more measurements indicates a difference between the radius of the actual contour and a corresponding radius of the reference contour; (viii) the PMC is further configured to apply a deviation threshold to the one or more measurements and report the presence of a local shape deviation when at least one measurement of the one or more measurements exceeds the deviation threshold. (ix) Local shape deviations are caused by physical effects during the manufacturing process of the semiconductor specimen, which, when detected, affect one or more electrical measurements of the semiconductor specimen.

[0009] According to another aspect of the subject matter of the present disclosure, there is provided a method for detecting local shape deviations of a structural element in a semiconductor sample, the method being performed by a processing and memory circuit (PMC), the method including: obtaining an image including an image representation of the structural element; extracting from the image an actual contour of the image representation; estimating a reference contour of the image representation indicative of a standard shape of the structural element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically selected to be insensitive to the presence of local shape deviations of the actual contour; and performing one or more measurements indicative of one or more differences between the actual contour and the reference contour, the measurements indicating whether local shape deviations are present in the structural element.

[0010] This aspect of the presently disclosed subject matter may include one or more of features (i) through (ix) listed above with respect to the system, mutatis mutandis, in any desired combination or permutation that is technically possible.

[0011] According to another aspect of the presently disclosed subject matter, a non-transitory computer-readable medium is provided that includes instructions, when executed by a computer, that cause the computer to perform a method for detecting local shape deviations of a structural element in a semiconductor specimen, the method including: obtaining an image including an image representation of the structural element; extracting from the image an actual contour of the image representation; estimating a reference contour of the image representation indicative of a nominal shape of the structural element, wherein the reference contour is estimated based on a Fourier descriptor representing the reference contour, wherein the Fourier descriptor is estimated using an optimization method based on a loss function specifically selected to be insensitive to the presence of local shape deviations of the actual contour; and performing one or more measurements indicative of one or more differences between the actual contour and the reference contour, wherein the measurements indicate whether local shape deviations are present in the structural element.

[0012] This aspect of the presently disclosed subject matter may include one or more of features (i) through (ix) listed above with respect to the system, mutatis mutandis, in any desired combination or permutation that is technically possible.

[0013] In order to understand the present disclosure and to appreciate how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a generalized block diagram of a test system in accordance with certain embodiments of the presently disclosed subject matter. [Figure 2] 1 is a generalized flow diagram for identifying local shape deviations of structural elements within a semiconductor specimen in accordance with certain embodiments of the presently disclosed subject matter. [Figure 3] 1 is a generalized flow diagram for estimating a reference contour of a structural element in a semiconductor specimen according to certain embodiments of the presently disclosed subject matter. [Figure 4] 10 is an exemplary graph depicting an estimated reference contour in the presence of local shape deviations in accordance with certain embodiments of the disclosed subject matter. [Figure 5] 1A-1C illustrate examples of measuring local shape deviations according to certain embodiments of the presently disclosed subject matter. DETAILED DESCRIPTION OF THE INVENTION

[0015] In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the present disclosure. However, it will be understood by those skilled in the art that the subject matter of the present disclosure may be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to obscure the subject matter of the present disclosure.

[0016] Unless otherwise indicated, as will be apparent from the discussion below, it is recognized that throughout this specification, discussions utilizing terms such as "measure," "obtain," "extract," "generate," "optimize," "perform," "select," "convert," "configure," "apply," "report," and the like refer to computer operations and / or processes that manipulate and / or transform data into other data, said data being represented as physical quantities such as electronic quantities and / or said data representing physical objects. The term "computer" should be interpreted broadly to encompass any type of hardware-based electronic device with data processing capabilities, including, by way of non-limiting example, the test systems, measurement systems, and respective portions thereof, disclosed herein.

[0017] The term "testing" as used herein should be broadly interpreted to encompass any type of metrology-related operation, as well as operations related to detecting and / or classifying defects in a specimen during production. Testing is performed by using a non-destructive testing tool during or after the production of the specimen to be tested. As non-limiting examples, the testing process can include one or more of the following operations performed on the specimen or portion thereof using the same or different testing tools: on-the-fly scanning (in a single scan or multiple scans), sampling, review, measurement, classification, and / or other operations. Similarly, testing can be performed prior to the production of the specimen to be tested and can include, for example, generating a test recipe and / or other setup operations. It should be noted that unless otherwise specified, the term "testing" or its derivatives as used herein is not limited with respect to the resolution or size of the inspection area. Various non-destructive testing tools include, as non-limiting examples, scanning electron microscopes, atomic force microscopes, optical inspection tools, etc.

[0018] The term "metrology" as used herein should be interpreted broadly to encompass any type of measurement of properties and characteristics of a sample performed using a test and / or metrology tool during or after the production of the sample to be inspected. As a non-limiting example, a metrology process can include generating a measurement strategy and / or performing on-the-fly measurements, e.g., by scanning (in a single scan or multiple scans), reviewing, measuring, and / or other operations performed on the sample or portion thereof using the same or different tools. Measurement results, such as measured images, are analyzed, e.g., by using image processing techniques. It should be noted that unless otherwise specified, the term "metrology" or its derivatives as used herein is not limited with respect to measurement technique, measurement resolution, or size of the inspection area.

[0019] As used herein, the terms "non-transitory memory" and "non-transitory storage medium" should be interpreted broadly to encompass any volatile or non-volatile computer memory suitable for the subject matter of this disclosure. The terms should be interpreted to include a single medium or multiple media (e.g., a centralized or distributed database and / or associated caches and servers) that store one or more sets of instructions. The terms should also be interpreted to include any medium that can store or encode a set of instructions for execution by a computer, causing the computer to perform one or more of the methods of this disclosure. Thus, the terms should be interpreted to include, but are not limited to, read-only memory ("ROM"), random access memory ("RAM"), magnetic disk storage media, optical storage media, flash memory devices, and the like.

[0020] As used herein, the term "specimen" should be interpreted broadly to encompass any type of wafer, mask, and other structure, combination and / or portion thereof, used to produce semiconductor integrated circuits, magnetic heads, flat panel displays, and other semiconductor manufacturing products.

[0021] As used herein, the term "defect" should be interpreted broadly to encompass any type of abnormal or undesirable feature formed on or within a specimen.

[0022] It will be appreciated that, unless otherwise stated, certain features of the presently disclosed subject matter, which are described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the presently disclosed subject matter, which are described in the context of a single embodiment, may also be provided separately or in any suitable subcombination. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the methods and apparatus.

[0023] With this in mind, attention is directed to FIG. 1, which illustrates a functional block diagram of a test system in accordance with certain embodiments of the disclosed subject matter.

[0024] The test system 100 shown in FIG. 1 can be used to test semiconductor specimens (e.g., wafers and / or portions thereof) as part of a specimen manufacturing process. As mentioned above, testing as referenced herein can be interpreted to encompass any type of metrology-related operation, as well as operations related to detecting and / or classifying defects on specimens during manufacturing. According to certain embodiments of the presently disclosed subject matter, the illustrated test system 100 includes a computer-based system 101 that can automatically perform one or more metrology operations on images acquired during specimen manufacturing. System 101 is also referred to as a metrology system, which is a subsystem of test system 100. Specifically, according to certain embodiments, the metrology operation can include critical dimension (CD) measurements related to local shape deviations of the semiconductor specimen.

[0025] The system 101 may be operatively connected to one or more test tools 120 configured to scan the semiconductor specimen and capture images of the semiconductor specimen for testing of the specimen. In some embodiments, at least one of the test tools 120 may have metrology capabilities and be configured to perform metrology operations on the captured images. Such test tools are also referred to as metrology tools.

[0026] As used herein, the term "metrology operation" should be broadly interpreted to encompass any metrology operation procedure used to extract metrology information related to one or more structural elements of a semiconductor specimen. By way of example, the metrology information to be extracted may indicate one or more of the following: dimensions (e.g., line width, line spacing, contact diameter, feature size, edge roughness, gray level statistics, etc.), feature shapes, distances within or between elements, associated angles, overlay information related to elements corresponding to different design levels, etc. In some embodiments, the metrology operation may include a measurement operation, such as, for example, a CD measurement, performed on a particular structure of the specimen.

[0027] The term "test tool" as used herein should be interpreted broadly to encompass any tool that can be used in a test-related process, including, by way of non-limiting example, imaging, scanning (in a single scan or multiple scans), sampling, reviewing, measuring, classifying, and / or other processes performed on a sample or portion thereof.

[0028] By way of example, the specimen may be examined with one or more low-resolution testing tools (e.g., optical inspection systems, low-resolution SEMs, etc.). The resulting data providing information about a low-resolution image of the specimen (referred to as low-resolution image data) may be sent to system 101 (either directly or via one or more intermediate systems). Alternatively or additionally, the specimen may be examined with a high-resolution tool (e.g., a scanning electron microscope (SEM) or an atomic force microscope (AFM) or a transmission electron microscope (TEM)). The resulting data providing information about a high-resolution image of the specimen (referred to as high-resolution image data) may be sent to system 101 (either directly or via one or more intermediate systems).

[0029] It should also be noted, without limiting the scope of the present disclosure in any way, that test tool 120 can be implemented as various types of test equipment, such as optical imaging equipment, electron beam equipment, etc. In some cases, the same test tool can provide low-resolution image data and high-resolution image data.

[0030] According to certain embodiments, one of the test tools is an electron beam tool, such as, for example, a scanning electron microscope (SEM). An SEM is a type of electron microscope that creates an image of a sample by scanning the sample with a focused beam of electrons. The electrons interact with atoms in the sample and create various signals that contain information about the sample's surface topology and / or composition. The position of the beam is combined with the intensity of the detected signals to create an image. SEMs can accurately measure features during the production of semiconductor wafers. By way of example, the SEM tool can be a critical dimension scanning electron microscope (CD-SEM) used to measure critical dimensions of structural features in an image.

[0031] System 101 includes a processor and memory circuit (PMC) 102 operatively connected to a hardware-based I / O interface 126. PMC 102 is configured to perform the processing necessary to operate the system, as described in further detail with reference to Figures 2 and 3, and includes a processor (not separately shown) and memory (not separately shown). The processor of PMC 102 can be configured to execute several functional modules in accordance with computer-readable instructions embodied in non-transitory computer-readable memory included in the PMC. Such functional modules are hereinafter referred to as being included in the PMC.

[0032] A processor as referred to herein may represent one or more general-purpose processing devices such as a microprocessor, a central processing unit, etc. More specifically, a processor may be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, or a processor implementing other instruction sets or a combination of instruction sets. A processor may also be one or more special-purpose processing devices such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), a network processor, etc. A processor is configured to execute instructions to perform the operations and steps discussed herein.

[0033] The memory referred to in this specification may include main memory (e.g., read only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM) or Rambus DRAM (RDRAM)), and static memory (e.g., flash memory, static random access memory (SRAM), etc.).

[0034] As mentioned above, in some embodiments, the system 101 can be configured to detect local shape deviations of structural elements within a semiconductor specimen. As used herein, local shape deviations (also referred to as grooving) refer to local distortions or deformations that have relatively significant deviations from a standard or ideal contour of a structural element. This is in contrast to global deviations, which refer to global or systematic deformations of a structural element, such as, for example, a global enlargement of the diameter of the structural element.

[0035] As used herein, a structural element or structural feature can refer to any original object of a sample having a contoured geometric shape or structure, possibly combined / superimposed with other objects (thus forming a pattern). Examples of structural elements can include, but are not limited to, generally shaped features such as contacts, lines, etc.

[0036] The local shape deviations referred to herein may be caused by physical effects during the manufacturing process of the semiconductor specimen, and if detected, such local deviations may affect certain electrical measurements of the semiconductor specimen, thereby potentially affecting yield.

[0037] As an example, localized deformations can appear in the pillars of vertical NAND (V-NAND) (also known as 3D-NAND) devices after the etching process. V-NAND is a type of nonvolatile flash memory in which memory cells are stacked vertically in multiple layers. The etching process can cause deformations in the sidewalls of the pillars of V-NAND devices, which can appear as rounded depressions or sharp protrusions. Such grooves can reduce the electrical barrier between cells, thereby causing electrical shorts and affecting device performance.

[0038] Current CD metrology measurements for process control of such structural features are based on a set of geometric parameters that define the shape of the structural feature. In the example of a contact, such parameters may include, for example, the contact top diameter (also referred to as top CD), the contact bottom diameter (also referred to as bottom CD), ellipticity, minor axis, and major axis. However, for advanced process development and mass production of complex features, these measurements are not sufficient to control the process steps of such features.

[0039] For example, in the above example of local deviations that occur in advanced 3D-NAND stair-forming processes, contacts with the same geometric parameters but different local shape deviations cannot be distinguished by conventional CD metrology measurement procedures. In other words, a contact with an ideal shape and a contact with a local shape deviation may have the same average contact diameter using current CD metrology metrics and therefore cannot be distinguished.

[0040] Therefore, when process control requires advanced analysis of local deviations from ideal shape, new metrology metrics are needed to be able to detect and measure such deviations. According to certain embodiments of the presently disclosed subject matter, a new metrology method is proposed to detect local shape deviations of structural elements with reference to a standard / ideal shape based on an optimization method. The proposed metrology method has been proven to provide better correlation with electrical measurements for advanced process control and to have improved accuracy in detecting local shape deviations and measuring deviations.

[0041] According to certain embodiments of the disclosed subject matter, functional modules included in the PMC 102 of the system 101 may include a contour estimation module 104 and a measurement module 106. The PMC 102 may be configured to obtain an image including an image representation of a structural element via an I / O interface 126. The image may be acquired by a testing tool 120, such as a CD-SEM tool. The contour estimation module 104 may be configured to extract an actual contour of the image representation from the image. The contour estimation module 104 may further be configured to estimate a reference contour of the image representation that indicates a nominal shape of the structural element. The reference contour may be estimated based on a Fourier descriptor representing the reference contour. The Fourier descriptor is estimated using an optimization method based on a loss function specifically selected to be insensitive to the presence of local shape deviations of the actual contour.

[0042] The measurement module 106 can be configured to perform one or more measurements that represent one or more differences between the actual contour and the reference contour. The measurements can indicate whether local shape deviations exist in the structural element.

[0043] The operation of the systems 100, 101, PMC 102 and the functional modules therein are further detailed with reference to FIGS.

[0044] According to certain embodiments, system 101 may include storage unit 122. Storage unit 122 may be configured to store data necessary to operate systems 100 and 101, such as data related to the input and output of systems 100 and 101, as well as intermediate processing results generated by system 101. By way of example, storage unit 122 may be configured to store images and / or derivatives thereof produced by test tool 120. As a result, images may be retrieved from storage unit 122 and provided to PMC 102 for further processing.

[0045] In some embodiments, the system 101 may optionally include a computer-based graphical user interface (GUI) 124 configured to allow user-specified input related to the system 101. For example, the user may be presented with a visual representation of the sample (e.g., by a display forming part of the GUI 124), including an image of the sample and / or a pictorial representation of structural elements. The user may be provided with options to define certain operational parameters via the GUI. In some cases, the user may also view operational results, such as one or more measurements, and / or further test results, in the GUI.

[0046] As described above, the system 101 is configured to receive one or more images of the specimen via the I / O interface 126. The images may include image data (and / or derivatives thereof) produced by the test tool 120 and / or image data stored in the storage unit 122 or one or more data repositories. In some cases, the image data may refer to images captured by the test tool during the production process and / or pre-processed images derived from captured images obtained through various pre-processing stages, etc. It is noted that in some cases, the images may include associated numerical data (e.g., metadata, craft attributes, etc.). It is further noted that the image data may include data related to a layer of interest within the specimen and / or data related to multiple layers of the specimen.

[0047] System 101 is further configured to process the received images and send the results (eg, CD measurements of the images) to storage unit 122 and / or test tool 120 via I / O interface 126 .

[0048] In some embodiments, in addition to test tool 120, test system 100 may include one or more test modules usable for testing of semiconductor specimens, such as a defect detection module, and / or an automatic defect review module (ADR), and / or an automatic defect classification module (ADC), and / or a metrology-related module, and / or other test modules. One or more test modules may be implemented as standalone computers, or their functionality (or at least a portion thereof) may be integrated with test tool 120. In some embodiments, measurements obtained from system 101 may be used by test tool 120 and / or one or more test modules (or portions thereof) for further testing of the specimen.

[0049] Those skilled in the art will readily recognize that the teachings of the presently disclosed subject matter are not bound to the system shown in FIG. 1 , and that equivalent and / or modified functionality may be combined or divided in other ways and may be implemented in any suitable combination of software, firmware, and / or hardware.

[0050] 1 can be implemented in a distributed computing environment, and the aforementioned functional modules included in PMC 102 can be distributed across several local and / or remote devices and linked by a communications network. It is further noted that in other embodiments, at least some of test tools 120, storage unit 122, and / or GUI 124 can be external to test system 100 and operate in data communication with system 101 via I / O interface 126. System 101 can be implemented as a standalone computer used in conjunction with a test tool. Alternatively, each of the functions of system 101 can be integrated, at least in part, with one or more test tools 120, thereby facilitating and enhancing the functionality of test tools 120 in test-related processes.

[0051] Although not necessarily so, the process of operation of systems 101 and 100 may correspond to some or all of the steps of the methods described with respect to Figures 2-3. Similarly, the methods described with respect to Figures 2-3 and their possible implementations may be realized by systems 101 and 100. It should therefore be noted that embodiments discussed with respect to the methods described with respect to Figures 2-3 can also be realized, mutatis mutandis, as various embodiments of systems 101 and 100, and vice versa.

[0052] Referring now to FIG. 2, a generalized flow diagram for identifying local shape deviations of structural elements within a semiconductor specimen is shown in accordance with certain embodiments of the presently disclosed subject matter.

[0053] An image of the sample can be acquired (202) (e.g., by PMC 102 via I / O interface 126, from test tool 120, or from storage unit 122) including a graphical representation of structural elements (also referred to as image structural elements) within the sample. In some embodiments, the image can be acquired by an electron beam tool such as an SEM. For example, an SEM tool as used herein can be a critical dimension scanning electron microscope (CD-SEM) configured to measure critical dimensions of structural elements / features of the sample based on the captured image. In some embodiments, the image can pertain to a particular layer of interest of the sample. For example, in a 3D-NAND device as described above, memory cells are stacked in multiple layers in the vertical direction. Elastic tension during the manufacturing process can cause deformation in particular device layers, which can be subject to the local deviation detection process of the present disclosure.

[0054] As discussed above, a structural element can refer to any original object formed on a sample having a contoured geometric shape or structure, and / or a combined / superimposed pattern of multiple such original objects. In some embodiments, a structural element can refer to any feature having a general shape selected from the group including ellipse, oval, rectangle, or any superposition / combination thereof. Examples of structural elements can include, for example, generally shaped features such as contacts, lines, etc. A structural element can be a 2D or 3D feature, and the image representation can reflect a 2D representation of the structural element.

[0055] A semiconductor specimen subject to the methods of the present disclosure can be any type of semiconductor device, including memory and / or logic devices, that may be compromised by local shape deviations as described herein. The present disclosure is not limited to any particular type or function of the semiconductor specimen.

[0056] For purposes of illustration and explanation, specific embodiments and / or examples of the subject matter of the present disclosure herein are described with respect to contact structural elements. This is not intended to limit the present disclosure in any way. It is recognized that the proposed methods and systems can be applied to other types of structural elements having various shapes as described herein.

[0057] The actual contours of the image representations of the structural elements can be extracted from the image (204) (e.g., by the contour estimation module 104 of the PMC 102). In some embodiments, the actual contours of the image structural elements can be extracted using an edge detection method. By way of example, the edge detection method can be implemented as a Canny or Sobel edge detection algorithm. Another example of an edge detection algorithm applicable to the present subject matter is described in U.S. Pat. No. 9,165,376, entitled "System, method and computer readable medium for detecting edges of a pattern," which is assigned to the assignee of the present patent application and is incorporated herein by reference in its entirety. As another example, the edge detection method can be implemented by using a segmentation algorithm based on gray-level statistical analysis of the image.

[0058] A reference contour of the image representation can be estimated (206) (e.g., by the contour estimation module 104 of the PMC 102). The reference contour represents the standard shape of the structuring element. Standard shape refers to the ideal or usual / normal shape of the structuring element as expected by the original design, without the presence of any local deviations. In some embodiments, the reference contour can be estimated based on Fourier descriptors representing the reference contour. Specifically, the Fourier descriptors can be estimated using an optimization method based on a loss function specifically chosen to be insensitive to the presence of local shape deviations of the actual contour.

[0059] As mentioned above, local shape deviation refers to a local distortion or deformation that has a relatively large deviation from the standard or normal shape of a structural element. Local shape deviation differs from edge roughness (which may be caused by various variations in the manufacturing process) in that shape deviation is local, whereas edge roughness exists along all edges, and the amplitude of the deviation is relatively significant (i.e., strong / large) compared to the fine roughness along the edge.

[0060] Such local deviations may be caused by physical effects during the sample manufacturing process, such as elastic tension of a particular layer of the semiconductor sample / device, and may affect the electrical measurements, thereby causing device performance impairment and yield loss. Therefore, it is considered as a kind of defect, and it is necessary to detect such deviation defects and measure their amplitude.

[0061] In order to measure the deviation of a structural element from a standard shape, it is necessary to estimate a reference contour that represents the standard shape of the structural element in the presence of the deviation. In particular, the estimation of the reference contour must be robust, i.e., insensitive to such relatively large deviations, so as to provide an estimated reference contour that can represent the standard shape regardless of the presence of such local deviations. Certain existing estimation methods, such as least-squares estimation, are used for this purpose, but, however, do not meet the required robustness with respect to such local deviations.

[0062] According to certain embodiments of the presently disclosed subject matter, a new method is proposed that provides a robust estimation of a reference contour of a structuring element that is insensitive to local shape deviations. Specifically, the reference contour can be estimated based on Fourier descriptors that represent the reference contour. The Fourier descriptors can be estimated using an optimization method based on a loss function specifically chosen to be insensitive to local shape deviations of the actual contour.

[0063] Fourier descriptors (FDs) can be generated using signal harmonic analysis (i.e., representing a function or signal as a superposition of fundamentals such as sine and cosine). FDs are used to represent the 2D closed shape / contour of a structuring element by the periodic structure of the contour, thereby allowing the contour to be described using a Fourier component representation. As an example, an elliptical shape of a structuring element can be represented using two Fourier components (corresponding to an FD of two Fourier coefficients), while a non-elliptical shape of a structuring element can generally be represented using five to seven Fourier components (corresponding to an FD of five to seven Fourier coefficients). Therefore, FDs can be estimated by identifying Fourier components with optimized weights (i.e., Fourier coefficients).

[0064] Referring now to FIG. 3, a generalized flow diagram for estimating a reference contour of a structural element within a semiconductor specimen is shown in accordance with certain embodiments of the presently disclosed subject matter.

[0065] A first sequence of points can be extracted from the actual contour (302). For example, the sequence of points<x[i],y[i]> (i=1,2,...n) can be extracted from the actual contour.<x[i],y[i]> (i=1, 2, ... n) represent the coordinates of n pixels of the actual contour of the image structure element. This sequence can be represented in the form of a complex number x[i] + j * y[i] and can be converted 304 into a Fourier series containing a set of Fourier components characterized by a set of Fourier coefficients. As an example, a sequence of n points extracted from the actual contour can be converted into a Fourier series containing a set of n Fourier components characterized by a set of n Fourier coefficients.

[0066] In some embodiments, the sequence of points<x[i],y[i]> First, polar coordinates<R[i],φ[i]> (e.g., by calculating the center of gravity (COG) of the actual contour and using the COG as the center of a polar coordinate system), where R(φ) is a periodic function. The sequence in polar coordinates can then be converted 304 into a Fourier series containing a set of Fourier components characterized by a set of Fourier coefficients. One example of such a Fourier series can be formulated as follows: R(φ)=a0+a1cos(2πφ)+b1sin(2πφ)+…+a K cos(2πKφ)+b K sin(2πKφ)+…

[0067] According to a particular embodiment, the subset of Fourier coefficients [a0, a1...a K ,b1…b K ] can be selected from the set of Fourier coefficients that characterize the Fourier series. A Fourier descriptor (FD) is a subset of the Fourier coefficients [a0, a1…a K ,b1…b K ]. By way of example, the number of Fourier coefficients K included in the subset can be predetermined. For example, K can correspond to the low frequency components of a Fourier series. As illustrated above, a non-elliptical shape of a structuring element can generally be represented using 5-7 Fourier components (corresponding to 5-7 Fourier coefficients). In some cases, K can be further determined based on the particular shape of the contour.

[0068] To estimate an FD that can accurately represent the contour, the values ​​of the Fourier coefficients need to be optimized, for example, using an optimization method. In some embodiments, the values ​​of a subset of the Fourier coefficients can be optimized in an optimization process to minimize a loss function (306), and the subset of Fourier coefficients with optimized values ​​can constitute a Fourier descriptor that represents the reference contour. An inverse Fourier transform can be performed (308) using the Fourier descriptor to produce a second sequence of points that constitutes the reference contour.

[0069] As mentioned above, the loss function used for optimization is specifically chosen to be insensitive to the presence of local shape deviations of the actual contour. Indeed, when estimating the normal shape of a structuring element, a robust loss function may be preferable compared to a non-robust loss function due to its insensitivity to large errors / deviations (i.e., robustness to the local shape deviations referred to herein), and can be used to perform estimations that are less affected by outliers than inliers.

[0070] An example of a non-robust loss function is the least squared error (LSE) or mean squared error (MSE), which are very sensitive to large errors (outliers), and the estimated fit based on such a loss function is heavily affected by outliers. An example of a robust loss function that is less sensitive to outliers is the Welsch loss function. Such robust loss functions can be designed by utilizing various robust penalties with specific properties.

[0071] A Fourier descriptor (FD) is a subset of Fourier coefficients [a0,a1…a K ,b1…b K ]. As formulated below,<r[i],φ[i]> But FD[a0,a1…a K ,b1…b K ] is the second sequence of points estimated by the inverse Fourier transform from r(φ)=a0+a1cos(2πφ)+b1sin(2πφ)+…+a K cos(2πKφ)+b K sin(2πKφ)

[0072] The Welsch loss function based on R(φ) and r(φ) can be formulated as follows:

number

[0073] As an example, the optimization method can be implemented as a first-order (gradient-based) line-search optimization scheme. A first rough fit with initial values ​​for a subset of Fourier coefficients is calculated and used as an initial starting point for optimization. At each iteration, a gradient can be calculated at the starting point, and a descent direction (e.g., anti-gradient direction) that results in a sufficient reduction in the loss function is identified. A step size is calculated that determines how far to move along that direction. After moving along the descent direction by the determined step size, a new starting point is derived and used to start the next iteration. The iterations can be repeated until convergence is reached (i.e., the error of the loss function reaches a minimum). A subset of Fourier coefficients [a] with optimized values ​​that allow the loss function to be minimized is identified. 0, a1…a K, b1…b K ] is the Fourier descriptor (FD) that represents the standard contour.

[0074] The inverse Fourier transform is the optimized value of FD[a 0, a1…a K, b1…b K ] and a second sequence of points that constitutes the estimated reference contour.<r[i],φ[i]> can be generated.

[0075] It should be noted that the Welsch loss function (and its particular formulation) as presented above is just one example of a robust loss function that can be used in the present disclosure to perform estimation of reference contours. Other robust loss functions, such as Cauchy-Lorentzian, Geman-McClure, Charbonnier, etc., can be used in combination with or instead of the above example.

[0076] Continuing with FIG. 2, after the reference contour of an image structure element is estimated as described above with reference to block 206 and FIG. 3, one or more measurements may be performed (208) (e.g., by measurement module 106 of PMC 102) that represent one or more differences between the actual contour and the reference contour. The measurements indicate whether local shape deviations (e.g., at least one local shape deviation) are present in the structure element. The local deviations detected and measured using the presently proposed method exhibit improved accuracy compared to other estimation methods.

[0077] As an example, one or more measurements may be performed at one or more points / pixels of the actual contour, and each measurement may indicate the difference between the radius of the actual contour (e.g., from the center of gravity (COG) of the reference contour to one or more points / pixels) and the corresponding radius of the reference contour (e.g., from the COG of the reference contour to one or more corresponding points / pixels in the reference contour).

[0078] In some embodiments, a deviation threshold can be applied to one or more measurements, and if one or more of the measurements exceed the deviation threshold, the presence of a local shape deviation can be reported. For example, a deviation threshold of 1 nm can be predefined, and measurements with differences greater than the threshold should be reported to the customer.

[0079] Referring now to FIG. 4, an exemplary graph illustrating an estimated reference contour in the presence of local shape deviations is shown, in accordance with certain embodiments of the disclosed subject matter.

[0080] The structural element in FIG. 4 is illustrated as a contact on a semiconductor sample having a standard elliptical / circular shape. Plot 400 (denoted by a circle symbol in the figure) represents the actual contour of the contact extracted from the image. As can be seen from plot 400, the contact appears to have local deviations in the shape of sharp protrusions. Plot 410 (denoted by a dot symbol in the figure) represents a first reference contour of the contact estimated using the estimation method of the present disclosure based on a robust loss function, such as the Welsch loss function. Plot 420 (denoted by a triangle symbol in the figure) represents a second reference contour of the contact estimated based on a non-robust loss function, such as the LSE loss function.

[0081] As shown, the first reference contour estimated based on the Welsch loss function closely resembles the standard contact shape (oval / circle), while the second reference contour estimated based on the LSE loss function is clearly affected by local deviations in the actual contact contour, causing it to appear to deviate from the standard contact shape. Therefore, the local deviations present in the contact cannot be detected using the second reference contour because the difference between the actual contour and the second reference contour is not significant enough to be detected as local deviations. However, by using the first reference contour, which is more accurate relative to the standard shape, the local deviations relative to the standard can be properly detected and the amount of deviation can be accurately measured.

[0082] Referring now to FIG. 5, an example of measuring local shape deviations according to certain embodiments of the presently disclosed subject matter is shown.

[0083] Graph 500 shows an actual contour 502 of a structuring element (having a standard shape of a rounded polygon) and a reference contour 504 of the structuring element estimated based on a non-robust loss function (i.e., not robust to local deviations), such as the L2 loss function. As shown, the structuring element has local deviations 503 in the shape of a rounded depression. Graph 500 also shows several measurements performed on the contour. By way of example, several radii are derived between the COG 501 of the reference contour and several points of the actual contour 502 to indicate locations along the actual contour where particular deviations are detected (the corresponding radii of the reference contour, and the difference between the radii, are not shown in the figure due to illustration limitations).

[0084] As shown, because the reference contour 504 was estimated incorrectly, differences between the two contours appear at many locations along the contours, resulting in many false alarms. Although real local deviations 503 are detected in the false alarms, the amplitudes of the real local deviations and the false alarms are very close to each other due to the incorrect reference contour 504, so the real local deviations may not be distinguished from the false alarms (e.g., when applying a deviation threshold).

[0085] Graph 510 shows the actual contour 502 of the same structural element and a reference contour 514 estimated using the disclosed estimation method based on Welsch's robust loss function. Graph 510 also shows several measurements performed on the contour. By way of example, several radii are derived between the COG 511 of the reference contour 514 and several points on the actual contour 502 to show where along the actual contour certain deviations are detected. Because the reference contour 514 is accurately estimated, the actual local deviations 503 can be distinguished from the rest of the false alarm deviations because their amplitudes differ from the amplitudes of the rest (e.g., when applying a deviation threshold).

[0086] According to certain embodiments, the local shape deviation estimation process described above with reference to Figures 2 and 3 may be included as part of a test strategy (in such case referred to as a metrology strategy) that can be used by system 101 and / or test tool 120 to test a specimen at runtime, e.g., to perform metrology operations on the specimen. Accordingly, the subject matter of this disclosure further includes systems and methods for generating a test strategy during a strategy-setting phase, the strategy including the steps described with reference to Figures 2 and 3 (and various embodiments thereof). It should be noted that the term "test strategy" should be interpreted broadly to encompass any strategy that can be used by a test tool to perform operations related to any type of test, such as those described above.

[0087] It should be noted that the examples provided in this disclosure, such as the illustrated structural elements of the contacts, the illustrated Welsch loss functions, the Fourier series representations, and the particular methods for measuring deviations as described above, are provided for illustrative purposes and should not be considered as limiting the disclosure in any way. Other suitable examples / implementations may be used in addition to or instead of those described above.

[0088] It should be noted that, although particular embodiments of the local shape deviation detection process of the present disclosure are described with respect to local shape deviations formed in contacts of a 3D-NAND device, this is not intended to limit the process of the present disclosure to application only to such structural elements and / or such semiconductor specimens. Additionally, the subject matter of the present disclosure may be similarly applied to any structural element and / or semiconductor specimen that may be impaired by such local deviations caused by various physical effects during the manufacturing process, regardless of its particular shape, type, or function.

[0089] Among the advantages of certain embodiments of the local shape deviation detection process described herein is the provision of a robust estimation of the normal shape of a structuring element that is not affected by the presence of local shape deviations, by using at least specific Fourier descriptors that represent the reference contour and by applying an optimization process to estimate the Fourier descriptors based on a specifically selected robust loss function.

[0090] By robustly estimating the reference contour representing the standard shape, the present disclosure can provide a direct measurement of local shape deviations that can be distinguished from edge roughness and have better correlation with electrical measurements for advanced process control. The detection of local shape deviations and the measurement of deviations have been proven to have improved accuracy.

[0091] It is to be understood that the present disclosure is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings.

[0092] It will also be appreciated that a system according to the present disclosure may be implemented, at least in part, in a suitably programmed computer. Similarly, the present disclosure contemplates a computer program readable by a computer for performing the methods of the present disclosure. The present disclosure further contemplates a non-transitory computer-readable memory tangibly embodying a program of instructions executable by a computer for performing the methods of the present disclosure.

[0093] The present disclosure is capable of other embodiments and of being practiced and carried out in various ways. Accordingly, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. As such, those skilled in the art will recognize that the conception upon which the present disclosure is based may readily be utilized as a basis for the designing of other structures, methods, and systems for carrying out some of the purposes of the subject matter of the present disclosure.

[0094] Those skilled in the art will readily appreciate that various modifications and variations can be made to the embodiments of the present disclosure described above without departing from the scope of the disclosure, which is defined by and within the scope of the appended claims. [Explanation of symbols]

[0095] 100 Test Systems 101 Computer-Based Systems 102 Processor and Memory Circuit (PMC) 104 Contour Estimation Module 106 Measurement Module 120 Testing Tools 122 Storage Unit 124 Graphical User Interface (GUI) 126 I / O interfaces Plot showing the actual contours of 400 contacts 410 Plot representing the first reference contour of the contact 420 Plot showing the second reference contour of the contact 500 graphs 501 Center of Gravity (COG) of Reference Contour 502 Actual Contour 503 Actual local deviation 504 Reference Contour 510 graphs 511 COG of reference contour 514 Reference Contour

Claims

1. 1. A computerized system for detecting local shape deviations of structural elements in a semiconductor specimen, the system comprising a processing and memory circuit (PMC), the processing and memory circuit (PMC) comprising: obtaining an image comprising a pictorial representation of the structural element; extracting from said image the actual contours of said image representation; - estimating a reference contour of the image representation indicating a nominal shape of the structuring element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically chosen to be insensitive to the presence of local shape deviations of the actual contour; performing one or more measurements representative of one or more differences between the actual contour and the reference contour, the measurements indicating whether local shape deviations exist in the structural element; 1. A computerized system configured to:

2. The computerized system of claim 1 , wherein the structural element has a shape selected from the group consisting of an ellipse, an oval, a rectangle, or a combination thereof.

3. The computerized system of claim 1 , wherein the local shape deviation is represented by a local distortion of the actual contour having a relatively large deviation from the nominal shape of the structural element.

4. 10. The computerized system of claim 1, wherein the semiconductor specimen is a memory device or a logic device.

5. The computerized system of claim 1 , wherein the actual contour is extracted using an edge detection method.

6. The computerized system of claim 1 , wherein the loss function is a Welsch loss function.

7. 2. The computerized system of claim 1, wherein the PMC is configured to estimate the reference contour by: extracting a first sequence of points from the actual contour; transforming the sequence of points into a Fourier series characterized by a set of Fourier coefficients; optimizing values ​​of a subset of Fourier coefficients selected from the set of Fourier coefficients so as to minimize the loss function, the subset of Fourier coefficients having the optimized values ​​constituting a Fourier descriptor of the reference contour; and performing an inverse Fourier transform using the Fourier descriptor to yield a second sequence of points constituting the reference contour.

8. The computerized system of claim 1 , wherein each of the one or more measurements indicates a difference between a radius of the actual contour and a corresponding radius of the reference contour.

9. 2. The computerized system of claim 1, wherein the PMC is further configured to apply a deviation threshold to the one or more measurements and report the presence of a local shape deviation when at least one measurement of the one or more measurements exceeds the deviation threshold.

10. 10. The computerized system of claim 1, wherein the local shape deviation is caused by a physical effect during a manufacturing process of the semiconductor specimen that, when detected, affects one or more electrical measurements of the semiconductor specimen.

11. 1. A computerized method for detecting local shape deviations of structural elements in a semiconductor specimen, said method being performed by a processing and memory circuit (PMC), said method comprising: obtaining an image comprising a pictorial representation of the structural element; extracting from said image the actual contours of said image representation; - estimating a reference contour of the image representation indicating a nominal shape of the structuring element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically chosen to be insensitive to the presence of local shape deviations of the actual contour; performing one or more measurements representative of one or more differences between the actual contour and the reference contour, the measurements indicating whether local shape deviations exist in the structural element; 10. A computerized method comprising:

12. The computerized method of claim 11 , wherein the structuring element has a shape selected from the group including an ellipse, an oval, a rectangle, or a combination thereof.

13. The computerized method of claim 11 , wherein the local shape deviation is represented by a local distortion of the actual contour having a relatively large deviation from the nominal shape of the structuring element.

14. The computerized method of claim 11 , wherein the actual contour is extracted using an edge detection method.

15. 12. The computerized method of claim 11, wherein the loss function is a Welsch loss function.

16. 12. The computerized method of claim 11, wherein said estimating a reference contour comprises: extracting a first sequence of points from the actual contour; transforming the sequence of points into a Fourier series characterized by a set of Fourier coefficients; optimizing values ​​of a subset of Fourier coefficients selected from the set of Fourier coefficients so as to minimize the loss function, the subset of Fourier coefficients having the optimized values ​​constituting a Fourier descriptor of the reference contour; and performing an inverse Fourier transform using the Fourier descriptor to produce a second sequence of points constituting the reference contour.

17. The computerized method of claim 11 , wherein each of the one or more measurements indicates a difference between a radius of the actual contour and a corresponding radius of the reference contour.

18. 12. The computerized method of claim 11, further comprising applying a deviation threshold to the one or more measurements and reporting the presence of a local shape deviation when at least one measurement of the one or more measurements exceeds the deviation threshold.

19. 12. The computerized method of claim 11, wherein the local shape deviation is caused by a physical effect during a manufacturing process of the semiconductor specimen that, when detected, affects one or more electrical measurements of the semiconductor specimen.

20. 1. A non-transitory computer-readable storage medium tangibly embodying a program of instructions that, when executed by a computer, causes the computer to perform a method for detecting local shape deviations of structural elements in a semiconductor specimen, the method comprising: obtaining an image comprising a pictorial representation of the structural element; extracting from said image the actual contours of said image representation; - estimating a reference contour of the image representation indicating a nominal shape of the structuring element, the reference contour being estimated based on a Fourier descriptor representing the reference contour, the Fourier descriptor being estimated using an optimization method based on a loss function specifically chosen to be insensitive to the presence of local shape deviations of the actual contour; and performing one or more measurements representative of one or more differences between the actual contour and the reference contour, the measurements indicating whether local shape deviations are present in the structural element.

Images