3D reconstruction of semiconductor samples

Abstract

To provide three-dimensional reconstruction of a semiconductor specimen.SOLUTION: There is provided a system and a method comprising obtaining a first (respectively second) image of an area of a semiconductor specimen acquired by an electron beam examination tool at a first (respectively second) illumination angle and determining a plurality of height values informative of a height profile of the specimen in the area, the determination comprising solving an optimization problem which comprises a plurality of functions, each function being representative of a difference between data informative of a grey level intensity at a first location in the first image and data informative of a grey level intensity at a second location in the second image, wherein, for each function, the second location is determined with respect to the first location, or conversely, when solving the optimization problem, wherein a distance between the first and the second locations depends on the height profile and the first and second illumination angles.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The subject matter of this disclosure relates generally to the field of sample testing, and more specifically to automating sample testing. [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 speeds, and improved reliability. Such demands require the formation of device features with high precision and uniformity, which in turn requires careful monitoring of the manufacturing process, including automated testing of the devices while they are still in the form of semiconductor wafers.

[0003] Testing processes are used at various steps during semiconductor manufacturing to measure specimen dimensions and / or detect and classify defects in the specimen (e.g., automatic defect classification (ADC), automatic defect review (ADR), etc.). Summary of the Invention

[0004] According to certain aspects of the subject matter of the present disclosure, a system for testing a semiconductor specimen is provided, the system including a processor and memory circuit (PMC), the processor and memory circuit (PMC) configured to acquire a first image of an area of ​​the semiconductor specimen acquired by an electron beam testing tool at a first illumination angle and a second image of the area acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle, and determine a plurality of height values ​​providing information of a height profile of the semiconductor specimen within the area, the determining of the plurality of height values ​​including determining height values ​​solving an optimization problem, the optimization problem including a plurality of functions, each function providing information of at least a difference between data providing information of gray level intensity at a first location of the first image and data providing information of gray level intensity at a second location of the second image, and for each function, solving the optimization problem results in a second location being determined for a first location positioned away from the height profile within the area, the first illumination angle, and the second illumination angle, or the first location being determined for a second location positioned away from the first location depending on the height profile within the area, the first illumination angle, and the second illumination angle.

[0005] According to some embodiments, for a given function of the plurality of functions, the system is configured to determine height values ​​at locations within the area that are dependent on the first location or the second location determined for the given function.

[0006] According to some embodiments, for a given function of the plurality of functions, the system is configured to determine a height value at a location that depends on a first location, the height value, and a first illumination angle, or a second location, the height value, and a second illumination angle.

[0007] According to some embodiments, the optimization problem includes constraints that link some or all of the multiple height values ​​within the area.

[0008] According to some embodiments, multiple height values ​​are determined simultaneously as a solution to an optimization problem.

[0009] According to some embodiments, the system is configured to take into account the first estimate of the height profile to determine the plurality of height values.

[0010] According to some embodiments, the system is configured to determine a height value at a given location within an area that matches the expected variation in the height profile of the sample in the area that includes the given location.

[0011] According to some embodiments, the optimization problem includes a correction term that takes into account the dependence of the gray level intensity on the illumination angle.

[0012] According to some embodiments, the system is configured to perform a spatial alignment process of at least one of the data providing information on grey level intensities of the first image and the data providing information on grey level intensities of the second image.

[0013] According to some embodiments, for a given function of the plurality of functions, the first location and the second location are linked by a relationship that depends on the height value of the sample at the location where the height value is determined, the first illumination angle, and the second illumination angle.

[0014] According to certain aspects of the subject matter of the present disclosure, there is provided a method of testing a semiconductor specimen, the method comprising: acquiring, by a processor and memory circuit (PMC), a first image of an area of ​​the semiconductor specimen acquired by an electron beam testing tool at a first illumination angle and a second image of the area acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle; and determining a plurality of height values ​​providing information of a height profile of the semiconductor specimen within the area, wherein determining the plurality of height values ​​comprises determining the height values ​​solving an optimization problem, the optimization problem comprising a plurality of functions, each function providing information of at least a difference between data providing information of gray level intensity at a first location of the first image and data providing information of gray level intensity at a second location of the second image, and for each function, solving the optimization problem results in a second location being determined for a first location positioned away from the height profile within the area, the first illumination angle, and the second illumination angle, or the first location being determined for a second location positioned away from the first location depending on the height profile within the area, the first illumination angle, and the second illumination angle.

[0015] According to some embodiments, the method includes determining, for a given function of a plurality of functions, a height value at a location that depends on a first location, the height value, and the first illumination angle, or a second location, the height value, and the second illumination angle. Includes.

[0016] According to some embodiments, the optimization problem includes constraints that link some or all of the multiple height values ​​within the region.

[0017] According to some embodiments, multiple height values ​​are determined simultaneously as a solution to an optimization problem.

[0018] According to some embodiments, the method includes using at least one of a priori knowledge of the sample and measurements of two-dimensional critical dimensions of the sample (e.g., as constraints) in an optimization problem to determine a plurality of height values.

[0019] According to some embodiments, the method includes determining a height value at a given location within an area that fits the expected variation of the height profile of the sample in a region that includes the given location.

[0020] According to some embodiments, the optimization problem includes a correction term that takes into account the dependence of the gray level intensity on the illumination angle.

[0021] According to some embodiments, the method includes performing a spatial alignment process of at least one of the data providing information on grey level intensities of the first image and the data providing information on grey level intensities of the second image.

[0022] According to some embodiments, for a given function of the plurality of functions, the first location and the second location are linked by a relationship that depends on the height value of the sample at the location where the height value is determined, the first illumination angle, and the second illumination angle.

[0023] In accordance with certain other aspects of the subject matter of this disclosure, a non-transitory computer-readable medium is provided that includes instructions that, when executed by a processor, cause the processor to perform operations as described above.

[0024] Among the advantages of certain embodiments of the subject matter of the present disclosure is the ability to reconstruct the height profile of a sample using non-destructive methods. According to some embodiments, the proposed solution improves the accuracy for reconstructing the height profile of a sample. According to some embodiments, the proposed solution allows for a complete reconstruction of the height profile of a sample. According to some embodiments, the proposed solution provides specific local information about the height profile, such as the roughness of the sample. According to some embodiments, the proposed solution does not require identifying topo-points. According to some embodiments, the proposed solution takes into account constraints on the height profile, such as constraints derived from a priori knowledge of the height profile.

[0025] In order to understand the present disclosure and to see 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 description of the drawings]

[0026] [Figure 1] FIG. 1 is a generalized block diagram of a test system in accordance with certain embodiments of the presently disclosed subject matter. [Diagram 2] 1 is a generalized flow diagram of a method for determining a height profile of a specimen. [Figure 2A] FIG. 13 is a cross-sectional view of a sample illustrating the evolution of the height profile along an axis. [Figure 2B] FIG. 1 shows examples of grey level intensities of images acquired at different illumination angles. [Diagram 3] FIG. 3 illustrates a possible implementation of the method of FIG. 2. [Figure 4] FIG. 2 illustrates an example of a first estimate of a height profile of a sample. [Diagram 5] 1 is a generalized flow diagram of a method for performing spatial registration of gray level intensities of acquired images. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, those skilled in the art will understand 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.

[0028] Unless otherwise noted, and as will be apparent from the discussion below, throughout this specification, discussions utilizing terms such as "obtain," "determine," "take into account," "output," "execute," "solve," and the like, will be understood to refer to computer actions and / or processes that manipulate and / or transform data into other data, said data being represented as physical quantities such as electrons, and / or said data representing physical objects. The term "computer" should be interpreted broadly to encompass any kind of hardware-based electronic device with data processing capabilities, including, as a non-limiting example, system 103 and each of its portions disclosed in the present application.

[0029] 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.

[0030] The term "sample" as used herein should be interpreted broadly to encompass all types of wafers, masks, and other structures, combinations and / or portions thereof, used to produce semiconductor integrated circuits, magnetic heads, flat panel displays, and other semiconductor manufactured articles.

[0031] The term "testing" as used herein should be broadly interpreted to encompass any kind of metrology-related operation, as well as operations related to detecting and / or classifying defects in a specimen during production. Testing is performed during or after the production of the specimen to be tested by using a non-destructive testing tool. As non-limiting examples, the testing process can include on-the-fly scanning (in a single scan or multiple scans), sampling, reviewing, measuring, classifying, and / or other operations performed on the specimen or a portion thereof using the same or different inspection tools. 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 stated, the term "testing" as used herein or its derivatives are not limited with respect to the resolution or size of the inspection area. A wide variety of non-destructive testing tools include, as non-limiting examples, scanning electron microscopes, atomic force microscopes, optical inspection tools, and the like.

[0032] The term "design data" as used herein should be broadly interpreted to encompass any data that represents a hierarchical physical design (layout) of a sample. The design data may be provided by a respective designer and / or may be derived from the physical design (e.g., by complex simulations, simple geometric and Boolean operations, etc.). The design data may be provided in various formats, such as, as non-limiting examples, GDSII format, OASIS format, etc. The design data may be presented in vector format, grayscale intensity image format, or in other ways.

[0033] It will be understood that certain features of the presently disclosed subject matter that are described in the context of separate embodiments may also be provided in combination in a single embodiment, unless otherwise noted. Conversely, various features of the presently disclosed subject matter that 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 in order to provide a thorough understanding of the methods and apparatus.

[0034] 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 subject matter of the present disclosure. The test system 100 illustrated in FIG. 1 can be used to test a specimen (e.g., a wafer and / or a portion thereof) as part of a specimen manufacturing process. The illustrated test system 100 includes a computer-based system 103 that can automatically determine metrology-related information and / or defect-related information using images acquired during specimen manufacturing. The system 103 can be operatively connected to one or more low-resolution test tools 101, and / or one or more high-resolution test tools 102, and / or other test tools. The test tools are configured to capture images and / or review the captured images and / or enable or make measurements related to the captured images. The system 103 can further be operatively connected to a CAD server 110 and a data repository 109.

[0035] System 103 includes a processor and memory circuit (PMC) 104 operatively connected to a hardware-based input interface 105 and a hardware-based output interface 106. PMC 104 is configured to perform all processing necessary to operate system 103 (see methods described in Figures 2, 3, and 5 that may be performed at least in part by system 103), as described in further detail below, and includes a processor (not separately shown) and memory (not separately shown). The processor of PMC 104 can be configured to perform several functions according to computer-readable instructions embodied in non-transitory computer-readable memory included in the PMC.

[0036] The system 103 is configured to receive input data via the input interface 105. The input data may include data produced by the test tool (and / or derivatives thereof and / or metadata associated therewith) and / or data produced and / or stored in one or more data repositories 109 and / or in the CAD server 110 and / or another associated data depository. It is noted that the input data may include images (e.g., captured images, images derived from captured images, simulated images, synthetic images, etc.) and associated numerical data (e.g., metadata, handcrafted attributes, etc.). It is further noted that the image data may include data associated with the layer of interest and / or data associated with one or more other layers of the specimen.

[0037] The system 103 is further configured to process at least a portion of the received input data and send the results (or a portion thereof) via the output interface 106 to a storage system 107, a test tool, a computer-based graphical user interface (GUI) 108 for rendering the results, and / or an external system (e.g., a yield management system (YMS) of the FAB). The GUI 108 may be further configured to allow user-specified inputs related to the operating system 103.

[0038] As a non-limiting example, the specimen can be tested with one or more low-resolution testers 101 (e.g., optical inspection system, low-resolution SEM, etc.). Resulting data providing information of a low-resolution image of the specimen (hereinafter referred to as low-resolution image data 121) can be sent to the system 103 (directly or via one or more intermediate systems). Alternatively or additionally, the specimen can be tested with a high-resolution machine 102 (e.g., a subset of potential defect locations selected for review can be reviewed by a scanning electron microscope (SEM) or an atomic force microscope (AFM)). Resulting data providing information of a high-resolution image of the specimen (hereinafter referred to as high-resolution image data 122) can be sent to the system 103 (directly or via one or more intermediate systems). According to some embodiments, as described below, the high-resolution image of the specimen can be acquired by an AFM or a TEM (transmission electron microscope) and can be used in the calibration process (e.g., as ground truth).

[0039] It should be noted that image data may be received and processed along with its associated metadata (eg, pixel size, textual description of the defect type, parameters of the image capture process, etc.).

[0040] Upon processing the input data (e.g., low resolution image data and / or high resolution image data, optionally together with other data such as, e.g., design data, synthetic data, etc.), system 103 can send results (e.g., instruction related data 123 and / or 124) to any of the test tools, store the results (e.g., defect attributes, defect classifications, etc.) in storage system 107, render the results via GUI 108, and / or send the results to an external system (e.g., to a YMS).

[0041] Those skilled in the art will appreciate that the teachings of the subject matter of this disclosure are not bound by the system illustrated in FIG. 1 and that equivalent and / or modified functions may be integrated or divided in other manners and may be implemented in any suitable combination of software with firmware and / or hardware.

[0042] Without limiting the scope of this disclosure in any way, it should also be noted that the test tools can be implemented as various types of inspection machines, such as optical imaging machines, electron beam inspection machines, etc. In some cases, the same test tool can provide low-resolution image data and high-resolution image data. In some cases, at least one test tool can have metrology capabilities.

[0043] It is noted that the test system illustrated in FIG. 1 can be implemented in a distributed computing environment, and the aforementioned functional modules illustrated in FIG. 1 can be distributed across several local and / or remote devices and linked through a communication network. It is further noted that in other embodiments, at least some of the test tools 101 and / or 102, the data repository 109, the storage system 107, and / or the GUI 108 can be external to the test system 100 and operate in data communication with the system 103 via the input interface 105 and the output interface 106. The system 103 can be implemented as a stand-alone computer that can be used in conjunction with the test tools. Alternatively, each of the functions of the system can be at least partially integrated into one or more test tools.

[0044] Attention is now directed to Figures 2 and 2A, which illustrate a method of testing a semiconductor specimen.

[0045] The method includes acquiring (operation 200) a first image of an area of ​​a semiconductor specimen acquired by an electron beam testing tool at a first illumination angle 280 (see FIG. 2A). The electron beam testing tool may in particular correspond to a scanning electron microscope (SEM) as described with respect to reference 102 above.

[0046] The method includes acquiring (operation 210) a second image of the area of ​​the semiconductor sample acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle (e.g., the absolute value of the second illumination angle is different from the absolute value of the first illumination angle).

[0047] The first illumination angle 280 and the second illumination angle 281 are known and can be selected using an electron beam testing tool that includes optical and electronic elements that allow for the selection of the illumination angle. The illumination angle can be expressed, for example, as the angle between the incident electron beam and a vertical axis or plane 282 (e.g., perpendicular to the specimen).

[0048] According to some embodiments, multiple images (three or more) of an area may be acquired, which may have been acquired by an electron beam testing tool at a variety of different illumination angles.

[0049] The method further includes determining (operation 220) a plurality of height values ​​that provide information of a height profile 290 of the sample 283 within the area based on pixel intensities (gray level intensities) of the first and second images (as described above, in some embodiments, more than two images can be acquired and therefore more than two images can be used to determine a plurality of height values). The sample generally includes various features or structures (e.g., contacts, transistors, gates, etc.) and it is desired to determine their heights (also referred to as thickness or depth) in the area of ​​interest. FIG. 2A shows a cross-sectional view of the sample in the XZ plane (X-axis corresponds to reference 250, Y-axis corresponds to reference 251, and Z-axis corresponds to reference 252). As shown in the non-limiting example of FIG. 2A, the height profile 290 of the sample can vary along at least one axis (X-axis 250). In some embodiments, the height profile can vary along two or more axes.

[0050] The beam strikes (after impinging on the sample) a focal plane 285 (where, for example, an imaging detector can be located) to provide an image of the sample. Each image (first and second image) generally comprises at least a distribution of gray level intensities of pixels. A non-limiting example is shown in FIG. 2B, where the gray level intensity (axis 296) is plotted against the image location 295 (for example, along axis "X" shown as 250 in FIG. 2A). The first image is associated with gray level intensity 297 and the second image is associated with gray level intensity 298. If the height profile is constant along the "Y" axis (reference 251), the gray level intensity of each image can be, for example, averaged along the Y axis. However, this is not required.

[0051] FIG. 3 illustrates a possible implementation of the method of FIG.

[0052] As described above, an attempt is made to determine multiple height values ​​in order to reconstruct the height profile of the sample within an area.

[0053] Determining the height values ​​may include determining height values ​​that solve an optimization problem (operation 320). In some embodiments, the height values ​​may be determined simultaneously as a solution to an optimization problem (common to all height values), as described further below. In other embodiments, the height values ​​may be determined independently (e.g., an optimization problem may be solved independently for each height value).

[0054] The optimization problem includes a number of functions. The optimization problem is generally formulated as a minimization problem. Each function gives information of the difference between data giving information of the gray level intensity of a first location in a first image (the first image is obtained in operation 300) and data giving information of the gray level intensity of a second location in a second image (the second image is obtained in operation 310).

[0055] In particular, for each function of the optimization problem, the distance between the first location and the second location depends on the height profile 290 in the area, the first illumination angle 280, and the second illumination angle 281. Indeed, as will be further explained below, for a given point of the sample where the illumination beam hits, the first pixel is acquired at the first illumination angle and the second pixel is acquired at the second illumination angle. The distance between the first pixel and the second pixel depends on the height of the given point, the first illumination angle, and the second illumination angle. It is possible to formulate each function of the optimization problem based on the relationship between the location of the first pixel and the location of the second pixel and assumptions on the gray level intensity (the gray level intensity can be assumed, for example, to be substantially constant for the first pixel and the second pixel corresponding to the same point of the sample, or with a variation determined by a model and / or calibration). In some embodiments, as will be explained below, additional constraints and / or a priori knowledge may be used in formulating the optimization problem.

[0056] In some embodiments, one location is predetermined (e.g., a first location is provided as a known input to the optimization problem), and therefore, solving the optimization problem allows a height value to be determined (along with a second location that is linked to the first location by a height value).

[0057] In some embodiments, the optimization problem is solved iteratively to determine multiple height values.

[0058] In some embodiments, the optimization problem can be solved for multiple height values ​​simultaneously, which allows constraints linking multiple height values ​​to be taken into account, such as prior knowledge about the height profile, as described below.

[0059] This method allows height values ​​at multiple locations within the area to be determined. In some embodiments, a complete height profile is obtained for the area. For example, the height profile can be used for metrology purposes (e.g., to measure trends in the production process of one or more structural features). In some embodiments, since a complete height profile is obtained, local information about the sample, such as roughness, can be obtained. In some embodiments, the height profile can be used to detect defects (e.g., abnormal or undesirable features formed on or within the sample).

[0060] For each given function of the plurality of functions, a height value is obtained as an output of the optimization problem and is determined at a location within the area that is dependent on the first location or the second location. A specific example is provided below.

[0061] In some embodiments, after multiple height values ​​have been determined, the smallest height value may be set to a reference value (zero value) and all other height values ​​may be expressed relative to this reference value.

[0062] Returning to FIG. 2A, assume that a given portion 279 of a sample 283 is acquired at a first illumination angle 280 and, during another acquisition, at a second illumination angle 281 (different from the first illumination angle 280).

[0063] As shown in FIG. 2A, a given portion 279 is imaged by a first pixel located at a first location 270 in a first image.

[0064] 2A, the given portion 279 is imaged by a second pixel located at a second location 271 in the second image. The second location 271 is different from the first location 270.

[0065] The distance 268 between the first location 270 and the second location 271 depends on the height profile (particularly the height value 291 of a given portion 279 ), the first illumination angle 280 , and the second illumination angle 281 .

[0066] The gray level intensity of a first pixel located at a first location 270 may be assumed to be equal to the gray level intensity of a second pixel located at a second location 271. In other words, the gray level intensity may be assumed to be independent of the illumination angle. However, this is an approximation. In some embodiments, an attempt is made to correct this approximation when solving the optimization problem using a model and / or a calibration process.

[0067] The gray level intensities of the first and second images, the first illumination angle, and the second illumination angle are known. Therefore, it is possible to determine the corresponding height for each location in the area by solving an optimization problem in which the height value is the parameter to be optimized and the constraints of the optimization problem include minimizing a function (along with other constraints, if applicable) that represents the difference between the gray level intensities between a first location in the first image and a second location in the second image. As described above, for each function, one location (e.g., the first location) is provided as an input to the optimization problem, and the other location (e.g., the second location) is determined when solving the optimization problem.

[0068] A non-limiting example of an optimization problem is provided below.

[0069] Assume the following: - a first image is acquired with a first illumination angle α (corresponding to reference 280) and a second image is acquired with a second illumination angle β (corresponding to reference 281); - The given part 279 has height h 279 having - the first position 270 of the first image is x α Represented by - The second position 271 in the second image is x β Represented by - the grey level intensity of the first image is f(x), where x is the position along the axis "X" 250; the grey level intensity of the second image is g(x),

[0070] Using the notation above, x α =x β -h 279 (tan α-tan β) The result is as follows.

[0071] As shown above, (at least to a first approximation) f(x α )≒g(x β ) can be assumed. Therefore, the following optimization problem can be formulated (this formulation is provided only as an example and not as a limitation): h = argmin | g(x) - f(xh x (tan α-tan β))| 2 formula 1 It is.

[0072] In this formula, h x is unknown and can be determined for each value of x, where "x" corresponds to a (known) second location in the second image, and "xh x "tan α-tan β" corresponds to an (unknown) first location in the first image, which can be determined relative to the second location. As shown, the distance between the first location and the second location is determined by the first illumination angle α, the second illumination angle β, and the height profile (h to be determined). x ), where h is the output of the optimization problem.

[0073] For a given value of x given as input to the optimization problem, the gray level intensity (f(xh)) at the first location of the first image is given as shown in Equation 1. x The method attempts to minimize a function that gives information about the difference between data that gives information about the gray level intensity ("g(x)") of the second location of the second image and data that gives information about the gray level intensity ("g(x)") of the second location of the second image.

[0074] Therefore, the optimization problem can be solved for each value of x (eg, for each known location in the second image).

[0075] In some embodiments, g(x) (respectively, f(x)) can be determined as a continuous function based on an interpolation between pixel intensities of the second image (respectively, the first image). As a result, x (the second location) may not necessarily correspond to a "real" pixel location of the second image, but may correspond to an interpolated location between the real pixels of the second image. The same applies to the determined first location "xh x (tan α-tan β)".

[0076] The height value h determined as a solution to the optimization problem is placed at a second location, the location of which depends on the height value h itself and on the second illumination angle β.

[0077] In particular, in the optimization problem as formulated above, the height value determined for a value of x corresponds to the height of the sample at the location x+h tan β.

[0078] For example, x=x β So the height value h obtained is at location x β +h corresponds to the height value at tan β, which is an estimate of the height value of the given portion 279.

[0079] By solving an optimization problem, it is possible to determine the height profile of the sample at multiple locations within the area, and in some embodiments, a complete height profile is obtained for the area.

[0080] An optimization problem as formulated in Equation 1 takes as input the second location of the second image and determines the height value (and the first location) of the first image. This is not limiting and the optimization problem can be formulated in reverse (the first location is the input and together with the second location the height value is determined).

[0081] According to some embodiments, the optimization problem can be modified to take into account various constraints or corrections.

[0082] According to some embodiments, the determination of the height profile takes into account a first estimate of the height profile. The first estimate can be based, for example, on design data used to produce the sample. Hence, the design data can be used to provide the first estimate of the height profile. The first estimate of the height profile can be used as a starting point for determining height values ​​and then improved when attempting to solve the optimization problem.

[0083] According to some embodiments, the optimization problem includes a constraint C(h) that links some or all of the height values ​​in the area. A non-limiting example of a modified optimization problem is provided below.

[0084]

number

[0085] As shown in Equation 2, the optimization problem is a minimization problem involving multiple functions (in addition to the constraint C(h)). As in Equation 1, each function is a function of the gray level intensity ("g(x i )" and the gray level intensity of the first location.

[0086]

number

[0087]

number

[0088]

number

[0089] An example of a constraint C(h) may include the expected variation of the height profile (e.g., a constraint on the derivative of the height profile). If a height value can be determined at a location, the determination of the height value is constrained by the expected variation of the height profile in a region that includes this location. This example is not limiting and other constraints may be taken into account. According to some embodiments, one or more constraints may be formulated in the optimization problem, for example based on a priori knowledge of the sample (e.g., provided by the manufacturer of the sample) and / or based on measurements performed on the sample (e.g., 2D CD measurements).

[0090] Because the determination of height values ​​relies on minimizing the difference between pixel intensities in the first image and the second image (as described above), this determination may be more difficult in regions of the sample where the height profile tends to be "flat" (see, for example, region 400 in FIG. 4, which shows a first estimate of the height profile 410 along axis "X" 420). Indeed, corresponding pixel intensities in the first and second images also tend to have "flat" profiles. In some embodiments, the use of a term C(x) that constrains the derivative of the height profile makes the optimization problem easier to solve even in these "flat" regions of the height profile.

[0091] According to some embodiments, C(x) provides a constraint that links some or all of the height values ​​in the area (e.g., in Equation 2, a constraint is imposed on the derivatives of the height profile, which therefore links together the height values ​​to be determined). Since the height values ​​are interrelated by this constraint, the optimization problem needs to be solved simultaneously for multiple height values ​​at multiple different locations. In other words, the output of the optimization problem includes as a solution multiple different interrelated height values ​​obtained for different locations in the area. This is different from Equation 1, where it is possible to determine each height value as a solution of an independent optimization problem.

[0092] It was noted above that the formulation of the optimization problem may rely on the assumption that the gray level intensity of a given point of the sample is independent of the illumination angle. According to some embodiments, this assumption may be relaxed when solving the optimization problem. In some embodiments, a correction term G(x) is introduced into the optimization problem to take into account possible variations in the gray level intensity based on the illumination angle.

[0093] The modified optimization problem is provided below. Equation 3 is not limiting (in this equation, G α\β (x) corresponds to the correction term. In addition, in some embodiments, Equation 3 can further include a constraint C(h) on multiple height values, as described above in Equation 2. h=argmin|g(x)-G α\β (x)f(xh x (tan α-tan β))| 2 formula 3

[0094] The correction term G(x) can be determined, in some embodiments, based on specific data extracted from a sample (similar to the sample to be tested). For example, the method as described above can be performed on the sample. The sample can then be cut and examined using an atomic force microscope to determine the true height profile. The difference between the height profile determined by solving the optimization problem and the true height profile provides the correction term G(x).

[0095] In some embodiments, the correction term G(x) can be determined based on a model of the sample.

[0096] In some embodiments, the correction term G(x) can be set as a parameter to be solved in an optimization problem.

[0097] In some embodiments, various different illumination angles (α1, ..., α N It is possible to acquire a set of multiple images of a given area of ​​the sample at different illumination angles α. The optimization problem is to find the optimal set of multiple image pairs of this set (for each pair, the images are illuminated at different illumination angles αi and α j where i ≠ j), can be formulated as described in the various embodiments above.

[0098] In some embodiments, multiple areas of the specimen are acquired at a first illumination angle by the electron beam testing tool scanning the specimen, and then multiple areas of the specimen are acquired at a second illumination angle by the electron beam testing tool scanning the specimen. For a given area of ​​the specimen, a spatial offset may be introduced between the first and second acquisitions (e.g., due to a relative error in positioning of the electron beam testing tool between the first and second acquisitions).

[0099] In light of the above, according to some embodiments the spatial alignment process may be performed based on data providing information on grey level intensities of the first image and / or data providing information on grey level intensities of the second image.

[0100] According to some embodiments, the spatial alignment process may rely on a first estimate of the height profile and an image of the area acquired with an illumination angle equal to zero.

[0101] A non-limiting example of the spatial registration process is provided in FIG.

[0102] Assume that a first estimate h0 of the height profile within an area of ​​the specimen is obtained (see operations 500, 510, and 520) and assume that an image of the area is acquired by an electron beam testing tool with an illumination angle equal to zero. The corresponding gray level intensity is denoted as f0. Assume that an image of the area is acquired by an electron beam testing tool with an illumination angle α (the corresponding gray level intensity is f α , and images of the area are acquired by an electron beam testing tool at illumination angles β different from α (with corresponding gray level intensities f β Let us assume that the

[0103] The method can include performing a spatial alignment (operation 530) between f0 and a height profile of the sample (which in a first iteration of the method corresponds to h0). In some embodiments, this can include aligning an axis of symmetry of f0 with an axis of symmetry of h0 (assuming that f0 and h0 are each symmetric).

[0104] This method uses the gray level intensity f α This can further include correcting the spatial distribution of f0 onto the angle α based on h (h=h0 in the first iteration of this method), (f' α (operation 540) to obtain. Indeed, it was mentioned above that data providing information of the gray level intensity of a first image of the area acquired with a first illumination angle is linked to data providing information of the gray level intensity of a second image of the area acquired with a second illumination angle based on the height profile, the first illumination angle, and the second illumination angle. In particular, the following (non-limiting) relationship can be used to project f0 onto the angle α: f0(x)=f' α (xh(tan α-tan β)) Equation 4

[0105] f' α and f α and the resulting offset between the two images, Δ α Then, f α is this offset Δ α Based on the

[0106]

number

[0107] Gray level intensity f β The same procedure can be applied to correct the spatial distribution of f0, which is projected onto the angle β (f') based on h (h=h0 in the first iteration of this method).β In particular, to project f onto the angle β, the following (non-limiting) relationship can be used: f0(x)=f' β (xh(tan α-tan β)) Equation 5

[0108] f' β and f β and the resulting offset between the two images, Δ β Then, f β is this offset Δ β Based on the

[0109]

number

[0110] Then, for example, using the method of FIG.

[0111]

number

[0112]

number

[0113] In some embodiments, in operation 550, the method further comprises: α and f' α and a correction term (G, as described above) that takes into account the dependence of the gray level intensity on the illumination angle. α\β This allows one to determine the

[0114] As a new estimate of the height profile h is determined, the method may in some embodiments be repeated, for example by returning to operation 530 (and repeating operations 540 to 580) until a convergence criterion (e.g. defining that the difference between the height profiles obtained in two successive iterations is less than a threshold) is met.

[0115] The various embodiments described above can be performed on different slices of the sample (along the "Y" axis, see reference 251 in FIG. 2A) to obtain height profiles h(x) of different slices of the sample along the "Y" axis.

[0116] It is to be understood that the invention is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings.

[0117] It will also be appreciated that the system according to the invention may be implemented, at least in part, in a suitably programmed computer. Likewise, the invention contemplates a computer program readable by a computer for carrying out the method of the invention. The invention further contemplates a non-transitory computer readable memory tangibly embodying a program of instructions executable by a computer for carrying out the method of the invention.

[0118] The present invention is capable of other embodiments and of being practiced and carried out in various ways. It is therefore 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 appreciate that the conception on which the present disclosure is based may be readily 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.

[0119] Those skilled in the art will readily appreciate that various modifications and changes may be made to the embodiments of the invention as described above without departing from the scope thereof as defined in and by the appended claims. [Explanation of symbols]

[0120] 100 Test Systems 101 Low Resolution Tester, Low Resolution Test Tool 102 High-resolution machine, high-resolution test tool 103 Computer-Based Systems, Operating Systems 104 Processor and Memory Circuit (PMC) 105 Hardware-based input interface 106 Hardware-based output interface 107 Storage Systems 108 Computer-Based Graphical User Interfaces (GUIs) 109 Data Repository 110 CAD Server 121 Low-resolution image data 122 High-resolution image data 123 Instruction related data 124 Instruction related data 250 X axis 251 Y axis 252 Z axis 268 Distance between the first and second locations 270 first location of first image, first position of first image 271 second location of second image, second position of second image 279 A given portion of a sample 280 First Lighting Angle 281 Second Lighting Angle 282 Vertical axis or plane 283 Samples 285 focal plane 290 Sample height profile 291 Height value of a given part 295 Image Location 296 axes (gray level intensity) 297 Gray Level Intensity 298 Gray Level Intensity 400 areas 410 Height Profile 420 Axis “X”

Claims

1. 1. A system for testing a semiconductor specimen, the system including a processor and memory circuit (PMC), the processor and memory circuit (PMC) comprising: a first image associated with a first gray level intensity profile of an area of ​​a given semiconductor specimen acquired by an electron beam testing tool at a first illumination angle; a second image associated with a second gray level intensity profile of the area acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle; and Get Using the first gray level intensity profile and the second gray level intensity profile, solving an optimization problem that allows determining a plurality of height values ​​that provide information about a height profile of the given semiconductor sample within the area. It is configured as follows: Solving the optimization problem for a first location in the first image having a first grey level intensity and for a second location determined in the second image having a second grey level intensity and in dependence on at least one given height value of the plurality of height values; (i) said second grey level intensity or data providing information thereof corresponds to said first grey level intensity or data providing information thereof according to an optimization criterion; and (ii) the relationship between the second location and the first location is fitted to a model that models the expected position of a given point in the second image for a given point of the sample placed at a given location in the first image as a function of at least the first illumination angle, the second illumination angle, and the height profile of the sample; determining said given height value such that Including, The system, wherein solving the optimization problem includes using a correction term in the optimization problem that takes into account a dependence of gray level intensity on illumination angle, and all images, including the first image and the second image, of an area of ​​the given semiconductor specimen acquired by the electron beam testing tool and used in solving the optimization problem to determine a plurality of different height values ​​that provide information about the height profile of the given semiconductor specimen were acquired by the electron beam testing tool using the same given focal plane.

2. The system of claim 1 , wherein the system is configured to determine the given elevation value at a location within the area that is dependent on the first location or the second location.

3. The system further comprises:

2. The system of claim 1, configured to determine the given height value at a location dependent on the first location, the height value, and the first illumination angle or the second location, the height value, and the second illumination angle.

4. The system of claim 1 , wherein the optimization problem includes a constraint linking some or all of the plurality of height values ​​within the area.

5. The system of claim 1 , wherein multiple height values ​​are determined simultaneously as a solution to the optimization problem.

6. The system of claim 1 , configured to take into account a first estimate of the height profile for determining the plurality of height values.

7. 2. The system of claim 1, configured to determine a height value at a given location within the area that fits an expected variation of the height profile of the sample in a region that includes the given location.

8. (i) the correction terms are determined using ground truth data of a sample; (ii) the correction terms are determined using a model of the sample; or (iii) The system of claim 1 , wherein at least one of the following is satisfied: the correction term is determined in solving the optimization problem.

9. The system of claim 1 , configured to perform a spatial alignment process of at least one of the data providing information on grey level intensities of the first image and the data providing information on grey level intensities of the second image.

10. 2. The system of claim 1, wherein the first location and the second location are linked by a relationship that is dependent on the given height value of the specimen at the location where the given height value was determined, the first illumination angle, and the second illumination angle.

11. 1. A method for testing a semiconductor specimen, the method comprising: a first image associated with a first gray level intensity profile of an area of ​​a given semiconductor specimen acquired by an electron beam testing tool at a first illumination angle; a second image associated with a second gray level intensity profile of the area acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle; and and solving an optimization problem using the first gray level intensity profile and the second gray level intensity profile to determine a plurality of height values ​​providing information of a height profile of the given semiconductor sample within the area; Including, Solving the optimization problem for a first location in the first image having a first grey level intensity and for a second location determined in the second image having a second grey level intensity and in dependence on at least one given height value of the plurality of height values; (i) said second grey level intensity or data providing information thereof corresponds to said first grey level intensity or data providing information thereof according to an optimization criterion; and (ii) the relationship between the second location and the first location is fitted to a model that models the expected position of a given point in the second image for a given point of the sample placed at a given location in the first image as a function of at least the first illumination angle, the second illumination angle, and the height profile of the sample; determining said given height value such that Including, The method, wherein solving the optimization problem includes using a correction term in the optimization problem that takes into account a dependence of gray level intensity on illumination angle, and all images, including the first image and the second image, of an area of ​​the given semiconductor specimen acquired by the electron beam testing tool and used in solving the optimization problem to determine a plurality of different height values ​​that provide information about the height profile of the given semiconductor specimen were acquired by the electron beam testing tool using the same given focal plane.

12. 12. The method of claim 11, comprising determining the given height value at a location dependent on the first location, the given height value, and the first illumination angle, or the second location, the given height value, and the second illumination angle.

13. The method of claim 11 , wherein the optimization problem includes constraints linking some or all of the plurality of height values ​​within the area.

14. The method of claim 11 , wherein multiple height values ​​are determined simultaneously as a solution to the optimization problem.

15. 12. The method of claim 11 , comprising using at least one of a priori knowledge of the specimen and two-dimensional critical dimension measurements of the specimen in the optimization problem to determine the plurality of height values.

16. 12. The method of claim 11, comprising determining a height value at the given location within the area that fits an expected variation of the height profile of the sample in a region that includes the given location.

17. (i) the correction terms are determined using ground truth data of a sample; (ii) the correction terms are determined using a model of the sample; or (iii) The method of claim 11 , wherein at least one of the following is satisfied: the correction term is determined in solving the optimization problem.

18. 12. The method of claim 11, comprising performing a spatial alignment process of at least one of the data providing information on grey level intensities of the first image and the data providing information on grey level intensities of the second image.

19. 12. The method of claim 11 , wherein the first location and the second location are linked by a relationship that depends on the given height value of the specimen at the location where the given height value was determined, the first illumination angle, and the second illumination angle.

20. A non-transitory computer-readable medium containing instructions that, when executed by a processor, cause the processor to perform operations, the operations including: a first image associated with a first gray level intensity profile of an area of ​​a given semiconductor specimen acquired by an electron beam testing tool at a first illumination angle; a second image associated with a second gray level intensity profile of the area acquired by the electron beam testing tool at a second illumination angle different from the first illumination angle; and and solving an optimization problem using the first gray level intensity profile and the second gray level intensity profile to determine a plurality of height values ​​providing information of a height profile of the given semiconductor sample within the area; Including, Solving the optimization problem for a first location in the first image having a first grey level intensity and for a second location determined in the second image having a second grey level intensity and in dependence on at least one given height value of the plurality of height values; (i) said second grey level intensity or data providing information thereof corresponds to said first grey level intensity or data providing information thereof according to an optimization criterion; and (ii) the relationship between the second location and the first location is fitted to a model that models the expected position of a given point in the second image for a given point of the sample placed at a given location in the first image as a function of at least the first illumination angle, the second illumination angle, and the height profile of the sample; determining said given height value such that Including, A non-transitory computer-readable medium, wherein solving the optimization problem includes using a correction term that takes into account a dependence of gray level intensity on illumination angle, and all images, including the first image and the second image, of an area of ​​the given semiconductor specimen acquired by the electron beam testing tool and used in solving the optimization problem to determine a plurality of different height values ​​that provide information about the height profile of the given semiconductor specimen were acquired by the electron beam testing tool using the same given focal plane.

Images