Mapping method and indentation mapping device

Abstract

To provide a mapping method and an indentation mapping device that have high throughput regarding identifying a portion with predetermined characteristics.SOLUTION: A mapping method includes: a division step of determining a measurement target region 90 on a sample surface and dividing the measurement target region 90 into a plurality of cell regions 91; an update step of updating the current measurement target region 90 to a new measurement target region 90 and updating the cell regions 91 to regions 91 smaller than the current region; a position determination step of determining a cell region 91 to be a search point from among the plurality of cell regions 91; a measuring step of measuring information on the cell region 91 of the search point when the search point is determined; and a region update determination step of determining whether update conditions for the measurement target region 90 are satisfied.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a mapping method and an indentation mapping device. [Background technology]

[0002] Patent Document 1 describes a mapping method and a measurement device that performs mapping measurement by measuring a certain physical quantity under the conditions of each point coordinate in a parameter space consisting of one or more parameters, and obtaining the distribution of the physical quantity in the parameter space. In this mapping method and measurement device, a computer is used during the mapping measurement to analyze the coordinates of the points measured up to that point and the physical quantity to obtain a response surface that approximates the distribution of the physical quantity, and then coordinates of points to be measured subsequently are determined so as to improve the approximation accuracy of the response surface, and measurements are performed accordingly. Polynomial approximation, radial basis function method, spline interpolation, Gaussian process regression, Kriging method, and logistic regression can be used to obtain the response surface.

[0003] Patent Document 2 describes an analysis device etc. The analysis device includes an acquisition unit that acquires analysis results obtained by an analysis model that analyzes a target phenomenon using multiple parameters, and an optimization processing unit that uses a Bayesian optimization method to evaluate combinations of the multiple parameters when the target phenomenon is analyzed by the analysis model based on the analysis results acquired by the acquisition unit, and determines a parameter combination of the analysis model from among the multiple parameter combinations based on the evaluation results for each evaluated combination of the multiple parameters.

[0004] Patent Document 3 describes a product design device and a product design method for determining design values ​​of components that make up a product so as to satisfy requirements imposed on the product. For example, this product design device includes a design processing unit that determines multiple design values ​​for multiple components so as to satisfy multiple requirements by using Bayesian optimization of a multi-point search with the requirements as objective variables and the components as explanatory variables, and an output unit that outputs the multiple design values ​​determined by the design processing unit.

[0005] As described in Patent Documents 2 and 3, Bayesian optimization is known as a so-called optimization technique (see Patent Documents 2 and 3). In Bayesian optimization, a response surface is sequentially determined by Gaussian process regression during the optimization process. As described in Patent Document 1, Gaussian process regression is also known as a distribution approximation method.

[0006] Patent Document 4 describes a measurement position control device and method for controlling the measurement position when measuring the reception strength distribution of an electric or magnetic field radiated from an antenna. This measurement position control device and method shortens the scanning interval between the previous measurement position and the next measurement position near the maximum, minimum, or pole of the measured magnetic field, and lengthens the scanning interval between the previous measurement position and the next measurement position in other locations. Whether or not a measurement is near a maximum value or the like is determined by predicting an approximate curve using the least squares method or the like based on multiple measured values ​​already obtained, and determining based on this approximate curve. This measurement position control device and method is capable of automatically shortening the measurement time for the electric or magnetic field distribution.

[0007] The combinatorial method is a technique in which multi-component materials, such as binary and ternary materials, are mixed in various compositions, evaluated, and then the composition with the desired properties is identified. The combinatorial method allows many compositions to be tested at once, eliminating the need to repeatedly change the composition and repeat experiments. For example, the combinatorial method involves continuously changing the composition of a multi-component material to form a thin film or layered sample, and evaluating the properties of each part of this sample to find the part with the desired properties.

[0008] An example of a combinatorial method is described in Patent Document 5. Patent Document 4 points out that it is often extremely difficult to predict the physical and chemical properties of combinations of various compounds or materials. In the combinatorial method described in Patent Document 5, a diffusion multicomponent having three or more layers made of a metal, nonmetal, metal oxide, or alloy is formed in a single sample, the diffusion multicomponent including multiple interdiffusion regions at the interface between the different metals, nonmetals, metal oxides, or alloys, and the properties of the diffusion multicomponent are evaluated as a function of composition near the interdiffusion regions.

[0009] When evaluating the physical properties of a material, particularly its mechanical properties, nanoindentation testing (hereinafter sometimes referred to as indentation testing) may be performed. As exemplified in Patent Document 6, nanoindentation is a materials testing method in which a load is applied to an indenter, forcing it into a sample, to evaluate the mechanical properties or mechanical properties (hereinafter simply referred to as mechanical properties) of a microscopic region of the sample. Nanoindentation is a testing method that can directly evaluate materials such as films that require local mechanical property values.

[0010] Non-Patent Document 1 describes a method for adaptively selecting undetermined parameters of an acquisition function of GP-UCB using the gradient of the evaluation point in order to easily and appropriately set the undetermined parameters of the acquisition function in Bayesian optimization. [Prior art documents] [Patent documents]

[0011] [Patent Document 1] Japanese Patent Application Publication No. 2018-138873 [Patent Document 2] Japanese Patent Application Publication No. 2019-215750 [Patent Document 3] Japanese Patent Publication No. 2020-052737 [Patent Document 4] Japanese Patent Application Laid-Open No. 2006-003229 [Patent Document 5] Japanese Patent Application Laid-Open No. 2004-347592 [Patent Document 6] Japanese Patent Application Laid-Open No. 2012-047625 [Non-patent literature]

[0012] [Non-Patent Document 1] Adaptive Selection of Hyperparameters of Acquisition Functions Based on Evaluation Point Gradient, Proceedings of the 33rd Annual Conference of the Japanese Society for Artificial Intelligence (2019), Hasebe et al., [Retrieved November 8, 2021], Internet<https: / / www.jstage.jst.go.jp / article / pjsai / JSAI2019 / 0 / JSAI2019_4I3J201 / _pdf / -char / ja> Summary of the Invention [Problem to be solved by the invention]

[0013] In combinatorial methods, combinatorial thin films are sometimes used to grade multiple material compositions within a plane and evaluate the properties of many compositions or material types (hereinafter simply referred to as material types) in a single sample. When combinatorial thin films are used to search for material types with desired mechanical properties, indentation tests are sometimes performed on various points on the surface of the combinatorial thin film to map the mechanical properties of the entire combinatorial thin film. Hereinafter, performing indentation tests on various points on the surface of a film- or plate-shaped material (hereinafter simply referred to as a film, etc.) and mapping the overall mechanical properties of the film, etc., may be referred to as indentation mapping.

[0014] When performing mapping such as this indentation mapping, if a so-called full test is performed (in the case of indentation mapping, the entire surface of a combinatorial thin film is divided equally and subjected to indentation testing), there is a problem that the testing time and number of tests required for mapping are large and laborious. In particular, when it is desired to identify a portion having a predetermined characteristic (a so-called optimal solution), there is a need to reduce the testing time and number of tests required for mapping. Therefore, it is desirable to provide a high-throughput mapping method.

[0015] However, with a method such as that described in Patent Document 4, in which the scanning interval between the previous measurement position and the next measurement position is changed based on a predicted approximation curve, although a certain degree of improvement in throughput can be expected, a sufficient improvement in throughput cannot be expected. Furthermore, a method such as that described in Patent Document 4 is not suitable for the purpose of identifying a region having a predetermined characteristic in a short test time and with a small number of tests. Therefore, a mapping method that can further increase the throughput in identifying a region having a predetermined characteristic is desired.

[0016] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a high-throughput mapping method and indentation mapping apparatus for identifying a portion having a predetermined characteristic. [Means for solving the problem]

[0017] In order to achieve the above object, a mapping method according to the present invention comprises: a dividing step of determining a measurement target area on the sample surface and dividing the measurement target area into a plurality of cell areas; an updating step of updating the current measurement target area to a new measurement target area and updating the cell area to an area smaller than the current area; a position determination step of determining a cell area to be a search point from among the plurality of cell areas; a measurement step of measuring information of the cell area of ​​the search point when the search point is determined; an area update determination step of determining whether an update condition for the measurement target area is satisfied; The position determination step performs Bayesian optimization based on mapping data including the measurement results obtained in the measurement step, and determines the cell area to be the next search point based on the position where the value of the acquisition function is maximized; the updating step is executed when it is determined in the area update determination step that an update condition is satisfied; In the update process, a new measurement target area is set that is an area included in the current measurement target area, includes the cell area containing the position where the expected value for a specified characteristic derived in the previous Bayesian optimization is predicted to be maximum or minimum, and is narrower than the current measurement target area.

[0018] The mapping method according to the present invention further comprises: In the area update determination step, it may be determined that the update condition is satisfied when the cell areas determined as the search points in the most recent two or more position determination steps are adjacent to each other.

[0019] The mapping method according to the present invention further comprises: The method may further include an initial position determination step of determining three or more predetermined cell areas as the search points at the start of mapping in the measurement step.

[0020] The mapping method according to the present invention further comprises: The method further includes a cell update determination step of determining whether the cell area has reached a predetermined size, The update process may be performed when it is determined in the area update determination process that the update conditions are met and when it is determined in the cell update determination process that the cell area has not reached a predetermined size.

[0021] The mapping method according to the present invention further comprises: further including a termination determination step of determining whether a termination condition for the mapping is satisfied; The termination determination process may be executed when it is determined in the area update determination process that an update condition is satisfied and when it is determined in the cell update determination process that the cell area has reached a predetermined size.

[0022] The mapping method according to the present invention further comprises: The termination determination step may determine that the termination condition for mapping is met if the positions predicted to have the maximum or minimum expected values ​​derived in each of the most recent two or more Bayesian optimizations performed in the position determination step are adjacent or overlapping.

[0023] The mapping method according to the present invention further comprises: The method further includes a pre-termination measurement step of selecting one or more of the unsearched cell areas in the measurement target area and measuring information of the selected cell areas; Pre-termination measurements The step may be executed when it is determined in the termination determination step that the termination condition of the mapping is not satisfied.

[0024] The mapping method according to the present invention further comprises: The measuring step may include an indentation test step of performing an indentation test in which an indenter is pressed into the surface of the sample to measure the compressive load acting on the indenter and the indentation depth of the indenter as the information.

[0025] The mapping method according to the present invention further comprises: The dividing step may divide the cell regions so that the intervals between the cell regions are larger than the width of a portion where the indenter contacts the sample surface when the indenter is pressed into the sample.

[0026] The mapping method according to the present invention further comprises: The position determination step is The value is The position where the maximum value is reached may be determined as a tentative search point, and the cell area closest to the tentative search point, excluding the cell areas where the indentation test has already been performed, may be determined as the next search point.

[0027] The mapping method according to the present invention further comprises: Based on the mapping data, a Gaussian process I think The method may further include an output step of acquiring a prediction function and outputting an expected value of the prediction function as a mapping result.

[0028] The mapping method according to the present invention further comprises: The position determining step includes: The next search point may be determined based on the mapping data including the measurement results of the cell area obtained before the update process and the measurement results of the cell area obtained after the update process.

[0029] The mapping method according to the present invention further comprises: The position determining step includes: The next search point may be determined based on the mapping data, which was obtained before the update process and includes measurement results of the cell area included in the measurement target area after the update process, and measurement results of the cell area obtained after the update process.

[0030] In order to achieve the above object, an indentation mapping apparatus according to the present invention comprises: an indenter that is pressed into the sample surface; a control unit that determines a search point as a pressing position of the indenter; a measuring unit for measuring a compressive load acting on the indenter and an indentation depth of the indenter; a storage unit that stores mapping data including the search points and the measurement results measured by the measurement unit, The control unit a dividing step of setting a measurement target area on the sample surface and dividing the measurement target area into a plurality of cell areas; an updating step of updating the current measurement target area to a new measurement target area and updating the cell area to an area smaller than the current area; a position determination step of determining a cell area to be a search point from among the plurality of cell areas; an area update determination step of determining whether or not an update condition for the measurement target area is satisfied; In the position determination step, Bayesian optimization is performed based on the mapping data, and the cell area to be the next search point is determined based on the position where a value of an acquisition function related to a predetermined characteristic is maximized; When it is determined that the update condition is satisfied in the area update determination step, the update step is executed; As the new measurement target area, an area that is included in the current measurement target area and includes the cell area that includes the position where the expected value derived in the immediately preceding Bayesian optimization is predicted to be maximum or minimum is set, and is narrower than the current measurement target area. [Effects of the Invention]

[0031] It is possible to provide a high-throughput mapping method for identifying sites with predetermined properties. [Brief explanation of the drawings]

[0032] [Figure 1] FIG. 1 is an explanatory diagram of a configuration of a mapping device. [Figure 2] FIG. 2 is a functional block diagram of a mapping device. [Figure 3] FIG. 1 is an explanatory diagram of the procedure of an indentation test. [Figure 4] FIG. 1 is an explanatory diagram of the procedure of an indentation test. [Figure 5] FIG. 1 is an explanatory diagram of the procedure of an indentation test. [Figure 6] FIG. 10 is a diagram illustrating an example of a profile. [Figure 7] 1A and 1B are explanatory diagrams of the manner in which the surface of a sample is divided into cell regions and search points. [Figure 8] FIG. 10 is a diagram illustrating the relationship between an indenter and the spacing between adjacent cell regions. [Figure 9] FIG. 10 is a diagram illustrating updating of a measurement target area. [Figure 10] FIG. 10 is a diagram illustrating updating of a measurement target area and updating of a cell. [Figure 11] FIG. 10 is a diagram illustrating updating of a measurement target area and updating of a cell. [Figure 12] FIG. 1 is a flow diagram of mapping. [Figure 13] FIG. 10 is a flow diagram of step S2. [Figure 14] FIG. 10 is a flow diagram of step S7. DETAILED DESCRIPTION OF THE INVENTION

[0033] A mapping method and an indentation mapping apparatus according to an embodiment of the present invention will be described with reference to the drawings.

[0034] (Summary) In the following, indentation mapping will be described as an example of a mapping method.

[0035] The mapping method according to this embodiment includes the following steps: The method includes a division process for determining a measurement target area on the sample surface and dividing the measurement target area into a plurality of cell areas; an update process for updating the current measurement target area to a new measurement target area and updating the cell area to a smaller area than the current area; a position determination process for determining a cell area to be used as a search point from among the plurality of cell areas; a measurement process for measuring information about the cell area of ​​the search point when the search point has been determined; and an area update determination process for determining whether the update conditions for the measurement target area are met.

[0036] The position determination step performs Bayesian optimization based on mapping data including the measurement results obtained in the measurement step, and determines the cell area at the position where the value of the acquisition function is maximized as the next search point.

[0037] The update process is executed when it is determined in the region update determination process that the update condition is satisfied. In the update process, a new measurement region is set that is included in the current measurement region, includes a cell region including a position where the expected value (hereinafter, sometimes simply referred to as the expected value) of a prediction function for a predetermined characteristic derived in the immediately preceding Bayesian optimization is predicted to be maximum or minimum, and is smaller than the current measurement region.

[0038] The mapping method according to this embodiment can achieve high throughput in identifying regions having predetermined characteristics.

[0039] As shown in FIG. 1, an indentation mapping device 100 according to this embodiment (hereinafter referred to as mapping device 100) realizes an indentation mapping method using the mapping method according to this embodiment.

[0040] The mapping device 100 includes an indenter 2 that is pressed into the surface of a sample 9, a control unit 10 that determines a search point as the indentation position of the indenter 2 on the surface of the sample 9, a measurement unit 11 that measures the compressive load acting on the indenter 2 and the indentation depth of the indenter 2, and a memory unit 19 that stores mapping data including the search point and the measurement results measured by the measurement unit 11.

[0041] The control unit 10 executes at least the above-described division step, update step, position determination step, and region update determination step to realize the mapping method according to this embodiment in the mapping device 100. The control unit 10 also causes the measurement unit 11 to execute the measurement step.

[0042] A sample 9, which is a plate-shaped test piece, is placed on the stage 3.

[0043] (Detailed explanation) In this embodiment, the indentation method is a material testing method in which a load is applied to an indenter 2 and the indenter 2 is pressed into a predetermined search point on a sample 9, thereby evaluating the mechanical properties or properties (hereinafter simply referred to as mechanical properties, etc.) of a microscopic region of the sample 9. Hereinafter, a material test using the indentation method will be simply referred to as an indentation test. In this embodiment, indentation mapping refers to performing an indentation test on the surface of the sample 9 and obtaining a map of the mechanical properties, etc. of the entire surface of the sample 9 based on the results of the test.

[0044] (sample) The sample 9 is a test piece to be evaluated for mechanical properties. The sample 9 is formed, for example, in the shape of a flat plate or a thin film. An example of the sample 9 is a combinatorial thin film.

[0045] (mapping device) As an example, the mapping device 100 includes a base 4, a support 5 supported by the base 4, a stage 3 supported by the base 4, an indenter support part 21 supported by the support 5, an indenter 2 supported by the indenter support part 21 and hanging down with its tip facing the stage 3, and a control device 1 such as a personal computer.

[0046] The indenter 2 is a tip-shaped member for performing an indentation test on a sample 9 placed on a stage 3. As described above, the indenter 2 is pressed into a predetermined search point on the surface of the sample 9. The indentation test will be described later.

[0047] As an example, the indenter 2 is formed in a cone shape that tapers toward one end. Hereinafter, the taper side of the indenter 2 will be simply referred to as the tip. The tip of the indenter 2 may be angular (for example, pointed) or rounded (for example, curved and convex downward). The shape of the indenter 2 may be set arbitrarily depending on the purpose of the indentation test. The indenter 2 is attached to the indenter support part 21, which will be described later, with the tip side facing the stage 3. In other words, the tip of the indenter 2 refers to the lower end when attached to the indenter support part 21.

[0048] The indenter support part 21 is a mounting seat for attaching the indenter 2 and for raising and lowering the indenter 2. The indenter support part 21 is formed, for example, in the shape of a thick plate. The indenter support part 21 fixes the indenter 2 to its underside. One end of the indenter support part 21 is supported by an elevating device 51, which will be described later. The indenter support part 21 is driven to rise and fall by the elevating device 51.

[0049] The stage 3 is a support seat for placing the sample 9. A flat area is formed on the upper surface of the stage 3, and the sample 9 can be placed with its plate surface aligned with the upper surface of the stage 3. For example, the entire upper surface of the stage 3 is formed flat and horizontal. The stage 3 can be moved in the horizontal direction by a slide mechanism 41, which will be described later. In this embodiment, the stage 3 is placed on the slide mechanism 41.

[0050] The base 4 is a seat for the mapping device 100. The base 4 has a slide mechanism 41 on its upper surface. The slide mechanism 41 may include, for example, a pair of intersecting (for example, perpendicular) screws and a pair of motors that rotate the screws. The slide mechanism 41 moves the stage 3 horizontally by arbitrarily rotating the screws with the motors to move the stage 3 forward and backward in the axial direction of the screws.

[0051] The support pillar 5 is a support member that supports the indenter 2 so that it can be raised and lowered. In this embodiment, the lower end of the support pillar 5 is supported by the pedestal 4. The support pillar 5 is equipped with an elevating device 51 (see FIG. 2 ) that has an elevating mechanism 52 such as a hydraulic cylinder, a position sensor 53, and a load sensor 54, and the indenter 2 is raised and lowered by raising and lowering the indenter support part 21 connected to the elevating device 51 in the up and down direction (the same as the vertical direction in this embodiment).

[0052] Fig. 2 shows a functional block diagram of the mapping device 100. As shown in Fig. 2, the position sensor 53 is a sensor that detects the indentation depth of the indenter 2 (see Fig. 1). The position sensor 53 may detect the indentation depth of the indenter 2, for example, by detecting the height position of the indenter support part 21 (see Fig. 1). The position sensor 53 may be, for example, an optical sensor.

[0053] The load sensor 54 is a sensor that detects the compressive load acting on the indenter 2 (see FIG. 1). The load sensor 54 may detect the compressive load acting on the indenter 2, for example, by detecting the force with which the lifting mechanism 52 presses the indenter support portion 21 (see FIG. 1) downward. As the load sensor 54, for example, a pressure sensor equipped with a piezoelectric element may be used.

[0054] The control device 1 includes a control unit 10, a measurement unit 11, and a storage unit 19. The control device 1 communicates with the slide mechanism 41 and the lifting device 51 to control their operation and acquire information from them. The control device 1 may be a personal computer or a PLC having a processor such as a CPU or MPU and a memory device.

[0055] The storage unit 19 is a storage medium such as a hard disk or a flash memory. In this embodiment, the storage unit 19 stores programs for implementing a mapping method, including a division step, an update step, a position determination step, a measurement step, an area update determination step, an initial position determination step, a cell update determination step, an end determination step, a pre-end measurement step, and an output step. Each of these steps will be described later. In this embodiment, the storage unit 19 is also capable of storing mapping data, which will be described later.

[0056] The measurement unit 11 is a functional unit that executes an indentation test process, which is a measurement process that performs an indentation test to measure the compressive load acting on the indenter 2 (see FIG. 1) and the indentation depth of the indenter. The measurement unit 11 may realize its functions by executing a program that realizes a mapping method stored in the storage unit 19.

[0057] In an indentation test, the measurement unit 11 communicates with the lifting device 51 and measures the compressive load acting on the indenter 2 and the indentation depth of the indenter 2 from its position sensor 53 and load sensor 54. In the present embodiment, as an example, the measurement unit 11 measures changes in the indentation depth of the indenter 2 and the accompanying changes in the compressive load acting on the indenter 2. Hereinafter, the changes in the indentation depth of the indenter 2 and the accompanying changes in the compressive load acting on the indenter 2 in an indentation test may be simply referred to as a profile. Furthermore, measuring changes in the indentation depth of the indenter 2 and the accompanying changes in the compressive load acting on the indenter 2 in an indentation test may be simply referred to as measuring a profile. Details of profile measurement will be described later.

[0058] When the measurement unit 11 measures a profile, it stores the measurement results as mapping data in the storage unit 19. In the following explanation, it is assumed that when the measurement unit 11 measures a profile, it always stores the measurement results as mapping data in the storage unit 19, and explanations regarding storage in the storage unit 19 will be omitted as appropriate.

[0059] The control unit 10 is a functional unit that executes the above-mentioned division step, update step, position determination step, measurement step, and area update determination step in the mapping method. In addition to the above-mentioned division step, the control unit 10 also executes an initial position determination step, a cell update determination step, an end determination step, a pre-end measurement step, and an output step, which will be described later. Details of each step executed by the control unit 10 will be described later. The control unit 10 may realize the function of executing these steps by executing a program that realizes the mapping method, stored in the storage unit 19.

[0060] When performing the indentation test process, the control unit 10 controls the lifting device 51 and the slide mechanism 41 to enable the measurement unit 11 (see FIG. 1) to perform the indentation test.

[0061] (Indentation test) The indentation test will be described in detail. Figures 3 to 5 show the procedure of the indentation test. The indentation test in this embodiment is a test in which a load is applied to the indenter 2 to press it into a predetermined position on the surface of the sample 9 (in this embodiment, a cell region 91 determined as a search point), thereby evaluating the mechanical properties and the like of a minute region of the sample 9. The cell region 91 is a region obtained by partitioning a part of the surface of the sample 9. The cell region 91 will be described later.

[0062] In the indentation test, first, a sample 9 is placed on a stage 3 (see FIG. 3).

[0063] Then, the control unit 10 (see FIG. 1) presses the indenter 2 into the cell region 91 as the determined search point (see FIG. 4). The indenter 2 is pressed until the compressive load (hereinafter simply referred to as the load) acting on the indenter 2 reaches a predetermined value, or until the indenter 2 is pressed to a predetermined pressing depth (predetermined pressing depth). FIG. 4 illustrates a state in which the indenter 2 is pressed to a depth h.

[0064] When the load acting on the indenter 2 reaches a predetermined value, or when the indenter 2 is pressed to a predetermined depth, the indenter 2 is pulled back (see FIG. 5). When the indenter 2 is pressed and then pulled back, an indentation P may be formed on the surface of the sample 9 where the indenter 2 was pressed.

[0065] Figure 6 shows an example of a profile of the change in the load acting on the indenter 2 as the indenter 2 is pressed into and pulled back from the surface of the sample 9 during an indentation test. During the process of pressing and pulling back the indenter 2, as shown in Figures 3 to 5, the compressive load acting on the indenter 2 changes as the indenter 2 presses down to a depth of 20 μm, as shown in Figure 6. Figure 6 shows a case where the specified indentation depth is 20 μm. As the indenter 2 is pressed down to a depth of 20 μm, the load acting on the indenter 2 increases. When the indenter 2 is pressed down to a depth of 20 μm (when the depth h = 20 μm in Figure 4), a load of 20 N is applied to the indenter 2. After pressing down to 20 μm, when the indenter 2 is pulled back (see Figure 5), the load acting on the indenter 2 decreases. In the example of Figure 6, the load acting on the indenter 2 becomes zero when the indenter 2 is pulled back to a depth of 19 μm. This is because an indentation P is formed on the surface of the sample 9 due to plastic deformation (see FIG. 5).

[0066] (indentation mapping) Indentation mapping will now be described. Indentation mapping in this embodiment refers to performing an indentation test at a plurality of different positions on the surface of sample 9, obtaining a predetermined number of profiles of a portion of the surface of sample 9, and obtaining a map of the mechanical properties and the like of the entire surface of sample 9 based on these profiles.

[0067] When performing indentation mapping, the control unit 10 defines a measurement target area 90 (an example of a measurement target area) on the surface of the sample 9, as shown in FIG. 7, and divides the measurement target area 90 into a plurality of cell areas 91 at intervals d.

[0068] The control unit 10 virtually divides the measurement target area 90 into cell areas 91 as follows, for example. The control unit 10 first sets the measurement target area 90 in the center of the surface of the sample 9. The measurement target area 90 may be set as a square area, for example. The following description will be given assuming that the measurement target area 90 is a square area.

[0069] Next, the measurement target area 90 is divided into n equal parts in the x and y directions in a grid pattern (where n is an integer of 2 or more). 2 cell areas 91 are set. The distance d1 between adjacent cell areas 91 in the x direction is equal to the distance d2 between adjacent cell areas 91 in the y direction. Each cell area 91 may be assigned a coordinate (xi, yi) indicating its position as necessary. Note that i is an integer between 1 and n. Note that in this embodiment, the distance on the coordinate system between the centers of adjacent cell areas 91 is 1.

[0070] As shown in FIG. 8 , the distance d between adjacent cell regions 91, 91 is preferably greater than the maximum width r of the portion where the indenter 2 contacts the surface of the sample 9 when the indenter 2 is pressed. The width r may be calculated based on the shape of the indenter 2 and the indentation depth h of the indenter 2. This allows the indentation test to be performed without being affected by the indentation P of the cell region 91a when performing an indentation test on another cell region 91b (a cell region 91 that may be the target of the next indentation test) adjacent to the cell region 91a where an indentation test has already been performed. The phrase "being affected by the indentation P" refers to the fact that, when performing an indentation test on a certain cell region 91b, the indenter 2 is pressed into the region overlapping with the region of the indentation P of the cell region 91a where an indentation test has already been performed and the region immediately adjacent thereto, thereby affecting the results of the indentation test on the certain cell region 91b. The distance d should be at least three times, preferably five times, the width r. This makes it possible to avoid the influence of the indentation test that has already been performed, which may remain in the vicinity of the outside of the indentation P.

[0071] Indentation mapping is performed by performing an indentation test on the center of each cell region 91 to obtain a profile, and storing the obtained profile in the storage unit 19 as mapping data.

[0072] The control unit 10 determines one cell area 91 to be used as a search point from among the cell areas 91 within the measurement target area 90 in a predetermined procedure described below, controls the measurement unit 11, the lifting device 51, and the slide mechanism 41 to perform an indentation test on this search point, causes the measurement unit 11 to acquire a profile, and stores the acquired profile as mapping data in the memory unit 19. This measurement cycle is repeated a predetermined number of times. This improves the accuracy of the mapping results. The improvement in the accuracy of the mapping results will be described later. Below, the cycle of determining the search point by the control unit 10, performing the indentation test, acquiring the profile by the measurement unit 11, and storing the profile as mapping data in the memory unit 19 may be simply referred to as a measurement cycle.

[0073] Here, it is possible to acquire profiles of all cell regions 91 and perform indentation mapping, but performing such a full test would increase the amount of work required for mapping, such as the test time and number of tests. Therefore, rather than acquiring profiles of all cell regions 91 and performing indentation mapping, the control unit 10 of the mapping device 100 acquires profiles of some of the cell regions 91, performs regression calculations using a Gaussian process (Gaussian Process Regression) based on these profiles, and creates and outputs mapping results.

[0074] That is, the control unit 10 acquires (calculates) a prediction function (hereinafter may be simply referred to as a prediction function) by a Gaussian process based on the profile of the acquired cell area 91 as an output of the mapping result, and outputs the expected value of this prediction function as a mapping result (an example of an output step). The control unit 10 may store this prediction function in the storage unit 19 as an output of the mapping result.

[0075] Improving the accuracy of the mapping result will now be described in detail. As described above, in order to improve the accuracy of the prediction function, the control unit 10 repeats a measurement cycle including a position determination step of performing Bayesian optimization to determine the next search point.

[0076] In the Bayesian optimization of this embodiment, a prediction function for a specified characteristic is obtained by Gaussian process regression, an acquisition function is created that represents the degree of possibility of improving over the previous optimal value (the coordinate in the measurement target area 90 that is predicted to be the best for the specified characteristic at this time), and the coordinate (an example of a position) in the measurement target area 90 where the value of the acquisition function is maximum, i.e., a tentative search point, is determined.

[0077] The prediction function is obtained using already acquired mapping data. The control unit 10 can use various kernels to obtain the prediction function depending on the purpose of indentation mapping and the characteristics of the sample 9 (see FIG. 1).

[0078] The coordinates at which the value of the acquisition function becomes maximum as a provisional search point may be determined using the GP-UCB algorithm, for example, according to the following equation.

[0079]

number

[0080] where x t is the coordinate (temporary search point) where the value of the acquisition function is maximized, and is not necessarily an integer coordinate. t-1 is the expected value, and its value increases near the provisional optimum (maximum or minimum value for a given characteristic). t-1 is the standard deviation, and its value increases in areas where profile acquisition is weak. t is a parameter that determines the trade-off between exploration and exploitation, and it is preferable to set a value between 2 and 6.

[0081] Then, the control unit 10 excludes the cell area 91 that has already undergone indentation testing from the cell area 91 (hereinafter referred to as adjacent cells) that includes or is adjacent to the tentative search point, and selects the cell area 91 that is closest to the tentative search point from the remaining adjacent cells, and determines this cell area 91 as the next search point. In other words, the control unit 10 generally determines the cell area 91 that includes the tentative search point as the next search point, but if the cell area 91 that includes this tentative search point has already had a profile acquired (has undergone indentation testing), it determines the cell area 91 that is closest to this tentative search point and that has not undergone indentation testing as the next search point.

[0082] Here, it is possible to initially subdivide the measurement target area 90 to define cell areas 91, and then sequentially acquire profiles for each of the subdivided cell areas 91 to perform indentation mapping. However, subdividing the cell areas 91 from the beginning increases the amount of work required for mapping, such as the test time and number of tests. Furthermore, repeating indentation tests at positions away from the portion having the specified characteristics does not lead to the identification of the portion having the specified characteristics, and increases the amount of work required for mapping, such as the test time and number of tests. Therefore, rather than repeating measurement cycles for the initially defined measurement target area 90, or subdividing the cell areas 91 from the beginning to perform indentation mapping, the control unit 10 performs a rough mapping to estimate the area where the portion having the specified characteristics is likely to exist, and then sequentially narrows down the measurement target area 90.

[0083] First, as shown in Fig. 9, the control unit 10 defines a measurement target area 90A (for example, the first measurement target area 90) on the surface of the sample 9. Then, the measurement target area 90A is divided into cell areas 91A of relatively large area. Note that in Fig. 9, each intersection of the grid shown in the measurement target area 90A represents the center of the cell area 91A. Also, in Fig. 9, some of the cell areas 91A among the multiple cell areas 91A are indicated by dashed lines.

[0084] Next, the measurement target area 90A is mapped by repeating a number of measurement cycles to determine an area (hereinafter referred to as a candidate area) where a portion having a predetermined characteristic is likely to exist. In FIG. 9, the candidate area is indicated by a dashed line. The control unit 10 then determines an area that includes the candidate area and is smaller than the measurement target area 90A as a new measurement target area 90B (see FIGS. 9 and 10), thereby updating (reducing) the current measurement target area 90 to the new measurement target area 90. Note that the measurement target area 90B is naturally included in the measurement target area 90A. Hereinafter, updating the current measurement target area 90 to the new measurement target area 90 will simply be referred to as updating the measurement target area. In FIGS. 9 and 10, an open circle indicates the center position of a cell area 91 for which a profile has already been acquired, i.e., a cell area 91 that has been determined as a search point and has been subjected to an indentation test (hereinafter, sometimes referred to as a searched cell). In this embodiment, for example, an area where the most recently searched cells are adjacent (for example, three adjacent cells searched in the last three searches) is selected as a candidate area, and this candidate area is designated as the new measurement target area 90 (measurement target area 90B). The measurement target area 90B may have an area that is, for example, one-third to one-fifth of the area of ​​the measurement target area 90A. When selecting a candidate area of ​​the same area, it is advisable to select an area that includes at least the position predicted to have the maximum or minimum expected value derived in the Gaussian process regression in the most recent position determination step, and that includes as many searched cells as possible. In other words, the candidate area selected includes an area that can be predicted to be optimal or best at the current time. This may improve the throughput of mapping.

[0085] Furthermore, as shown in FIG. 10, the control unit 10 divides the measurement target area 90B into cell areas 91B each having an area smaller than the cell area 91A. That is, the cell area 91 (cell area 91A) is updated (reduced) to a cell area 91 (cell area 91B) having an area smaller than the current area. The cell area 91B may have an area that is, for example, an integer fraction of the area of ​​the cell area 91A, and FIG. 10 shows a case where the cell area 91B is one-fourth the area of ​​the cell area 91A. Hereinafter, updating the cell area 91 to a cell area 91 having an area smaller than the current area will be simply referred to as cell updating. Note that in FIG. 10, each intersection of the thin-line grid shown in the measurement target area 90B represents the center of the cell area 91B. Also, each intersection of the thin-line grid shown in the measurement target area 90B represents the center of the area that was formerly the cell area 91A. Also, some of the cell areas 91A among the areas that were formerly the multiple cell areas 91A are indicated by two-dot chain lines. Also, some of the multiple cell areas 91B are indicated by dashed lines. When updating a cell, it is advisable to make the center of the cell area 91 before the update overlap with the center of the cell area 91 after the update.

[0086] The measurement target area update and cell update may be repeated two or more times. Figure 11 shows a case where measurement target area 90A is updated to measurement target area 90B, which is included in but smaller than measurement target area 90A, and measurement target area 90B is then updated to measurement target area 90C, which is included in but smaller than measurement target area 90A. Cell area 91C, which is cell area 91 of measurement target area 90C, is narrower than cell area 91B. As described above, cell area 91B is narrower than cell area 91A.

[0087] 11, only a portion of cell areas 91A, 91B, and 91C is shown for the purpose of explanation. Also, in FIG. 11, the center of cell area 91A is indicated by a black-filled rectangle, the center of cell area 91B by a black-filled triangle, and the center of cell area 91C by a black-filled circle. Here, the center of cell area 91B and the center of cell area 91A, or the center of cell area 91C and the center of cell area 91A, are shown as the centers of cell area 91A. Also, the center of cell area 91C and the center of cell area 91B are shown as the centers of cell area 91B.

[0088] The cell renewal is performed while maintaining the relationship that the distance d between the renewed cell regions 91, 91 is larger than the maximum width r of the portion where the indenter 2 contacts the surface of the sample 9, as shown in FIG.

[0089] In order to maintain the relationship that the spacing d between the cell areas 91, 91 after the update is greater than the maximum width r of the part where the indenter 2 contacts the surface of the sample 9 when updating the cell, it is advisable to determine the end point of the cell update in advance.

[0090] As the end point of the cell update, for example, the size of the smallest cell area 91 after the cell update or the range of the size of the smallest cell area 91 after the cell update may be predetermined (an example of a predetermined size; hereinafter, the size of the smallest cell area 91 and the range of the size of the smallest cell area 91 are collectively referred to as the minimum cell size). Then, the update of the measurement target area and the cell update may be permitted until the updated cell area 91 reaches the smallest cell size. That is, the update may be permitted if the current cell area 91 exceeds the smallest cell size, but may not be permitted if the current cell area 91 is the smallest cell size. In FIG. 11, each intersection of the thin-line grid shown in the measurement target area 90A indicates the center of an area 91X when the measurement target area 90A is divided into the smallest cell areas 91 after the cell update. In the example shown in FIG. 11, the area 91X is the same size as the cell area 91C, and no further update of the measurement target area or cell updates may be performed for the measurement target area 90C and the cell area 91C.

[0091] (Indentation mapping flow) Hereinafter, an example of a series of indentation mapping steps in the mapping method implemented by the mapping device 100 will be described based on the flowcharts shown in FIGS. 12 to 14, with appropriate reference to FIGS. 1, 2, and 7.

[0092] As shown in Figure 12, when indentation mapping begins, in step S1, the control unit 10 sets a measurement target area 90 on the surface of the sample 9, as shown in Figures 7 and 11, and performs a division process to divide the measurement target area 90 into multiple cell areas 91, and then proceeds to step S2.

[0093] In step S2, the control unit 10 executes a position determination process to determine cell regions 91 to be used as search points from among the multiple cell regions 91. In step S2, as shown in FIG. 13, if there is no mapping data in the storage unit 19 (step 21, No), an initial position determination process is executed to determine three or more predetermined cell regions 91 (e.g., five) from among the multiple cell regions 91 as initial search points (step 22), and step S2 is terminated. The number of initial search points may be increased or decreased depending on the expected complexity of the distribution of the sample 9. For example, if the mapping result is expected to have a multi-modal distribution, it is recommended to set a larger number of initial search points (e.g., five or six). This prevents the local optimum from being derived instead of the global optimum, thereby improving the accuracy of the mapping.

[0094] If mapping data exists in the memory unit 19 (step 21, Yes), Bayesian optimization is performed based on the mapping data, and the cell area 91 to be used as the next search point is determined based on the coordinates where the value of the acquisition function is maximized, and step S2 is terminated.

[0095] 7 as an example, only the profiles of three cells Q1, Q2, and Q3 as a cell region 91 are stored as mapping data in the storage unit 19. When a provisional search point q4 is determined as the coordinate where the value of the acquisition function by Bayesian optimization is maximized based on this mapping data, the control unit 10 determines the cell Q4 as a cell region 91 including the provisional search point q4 as the next search point. m-1 When the profile is stored in the storage unit 19 as mapping data, a provisional search point q is determined as the coordinate at which the value of the acquisition function by Bayesian optimization is maximized based on this mapping data. m When the cell Q2 has been determined, the control unit 10 selects a tentative search point q from the remaining adjacent cells, excluding the cell Q2 for which the indentation test has already been performed, as the next search point. m The cell Q is the closest cell area 91 to m Select this cell Q mis determined as the next search point (where m is an integer equal to or greater than 4). The distance between the temporary search point qm and the cell area 91 is the straight-line distance between the temporary search point qm and the center of the cell area 91. In other words, since the prediction function by Gaussian process regression is a function that has continuity in the section corresponding to the measurement target area 90, the coordinates at which the acquired function is maximized do not necessarily coincide with the center of each cell area. Therefore, the control unit 10 selects the cell area 91 that is closest to the coordinates at which the value of the acquired function is maximized from among the adjacent cells excluding the cell area 91 for which the indentation test has already been performed, and determines this cell area 91 as the next search point.

[0096] In step 21, the next search point may be determined based on mapping data including the measurement results of the cell area 91 acquired before performing step S6, which will be described later, and the measurement results of the cell area 91 acquired after performing step S6. In this case, the next search point may be determined based on mapping data including the measurement results of the cell area 91 acquired before performing step S6 and included in the measurement target area 90 after performing step S6, and the measurement results of the cell area 91 acquired after performing step S6. Doing so may improve the throughput of mapping.

[0097] When step S2 is completed, the process proceeds to step S3.

[0098] In step S3, an indentation test is performed on the cell area 91 determined as the search point (an example of an indentation test process), and a measurement process is executed in which the profile measurement results are stored in the memory unit 19 as mapping data, and then the process proceeds to step S4.

[0099] In step S4, the control unit 10 executes a region update determination step to determine whether an update condition for the measurement region 90 is satisfied. In the region update determination step, if the cell regions 91 containing positions predicted to have the maximum or minimum expected values ​​derived in each of the most recent two or more (e.g., three times: the current, previous, and the time before last) position determination steps (step S2) are adjacent to or overlap with each other, it is determined that the update condition is satisfied (step S4, Yes), and the process proceeds to step S5. In step S4, if the cell regions 91 containing positions predicted to have the maximum or minimum expected values ​​in the most recent two or more position determination steps (step S2) are not adjacent to each other, it is determined that the update condition is not satisfied, and the process returns to step S2 (step S4, No).

[0100] Here, a cell region 91 being adjacent to another cell region 91 means that the other cell region 91 is one of the eight cells surrounding the cell region 91. Furthermore, a case where cell regions 91 including positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more Gaussian process regressions overlap means that the positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more Bayesian optimizations are all within the same cell region 91.

[0101] In step S4, the fact that step S2 has been executed a predetermined number of times (for example, 10 times) or more for the current measurement target area 90 may be set as a precondition for determining that the update condition for the measurement target area 90 is met. By doing so, the accuracy of mapping may be improved.

[0102] In step S5, the control unit 10 executes a cell update determination step of determining whether the cell area 91 has reached the minimum cell size. If the cell area 91 has not reached the minimum cell size, that is, if the cell area 91 exceeds the minimum cell size (step S5, No), the control unit 10 proceeds to step S6. If the cell area 91 has reached the minimum cell size (step S5, YES), the control unit 10 proceeds to step S7.

[0103] In step S6, the control unit 10 updates the current measurement target area 90 to a new measurement target area 90, updates the cell area 91 to a cell area 91 that is narrower than the current area, and returns to step S2.

[0104] In step S7, the control unit 10 executes an end determination step of determining whether or not the mapping end condition is satisfied. If it is determined that the mapping end condition is satisfied (step S7, YES), the control unit 10 ends the mapping. If it is determined that the mapping end condition is not satisfied (step S7, NO), the control unit 10 proceeds to step S8.

[0105] In this embodiment, an example of the condition for terminating the mapping in step 7 can be when cell areas 91 including positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more (e.g., most recent three) Gaussian process regressions performed in step 2 (position determination step) overlap. That is, the control unit 10 may determine that the condition for terminating the mapping is satisfied when cell areas 91 including positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more (e.g., most recent three) Bayesian optimizations performed in step 2 (position determination step) overlap.

[0106] Furthermore, in step S7, the condition for terminating the mapping may be whether or not step S8, which will be described later, has been executed at least once. In this case, the condition for terminating the mapping may also be whether or not the cell regions 91 including the positions predicted to have the maximum or minimum expected values, derived in each of the most recent two or more Bayesian optimizations performed in step 2 (position determination process), overlap.

[0107] That is, as shown in FIG. 14, in step S7, first, it is determined whether step S8 has been executed at least once (step S71), and if step S8 has not been executed even once (step S71, NO), it is determined that the mapping termination condition is not met (step S72), step S7 is terminated, and the process proceeds to step S8 (see FIG. 12).

[0108] If step S8 has been executed at least once (step S71, YES), the process proceeds to step S73.

[0109] In step S73, it is determined whether the cell areas 91 including the positions predicted to have the maximum or minimum expected values ​​derived in each of the most recent three Gaussian assumption regressions performed in step 2 (position determination process) overlap. If they overlap (step S73, Yes), it is determined that the mapping termination condition is met (step S74), and step S7 is terminated, thereby terminating mapping (see FIG. 12). If they do not overlap (step S73, No), the process proceeds to step S72.

[0110] In step S7, the mapping termination condition may be determined to be satisfied if step S6 has been executed at least once and step S2 has been executed a predetermined number of times (e.g., six times) or more for the current measurement target region 90. This may improve the accuracy of mapping.

[0111] Furthermore, in step S7, the control unit 10 may determine that the mapping termination condition is satisfied not only when the cell areas 91 including the positions predicted to have the maximum or minimum expected values ​​derived in each of the most recent two or more (e.g., most recent three) Bayesian optimizations performed in step 2 (position determination step) overlap, but also when the termination determination step (step S7) has already been performed three times, i.e., when the pre-termination measurement step (step S8) has already been performed three times. In this way, it is possible to avoid needlessly increasing the measurement cycle during mapping.

[0112] In step S8, one or more (e.g., three) unsearched cell areas 91 in the current measurement target area 90 are selected, an indentation test is performed on the selected cell areas 91, and the profile measurement results are stored in the memory unit 19 as mapping data. A pre-termination measurement process is then executed, and the process proceeds to step 2.

[0113] The cell area 91 selected in step S8 may be selected from the cell areas 91 in the vicinity of the cell area 91 that was set as the search point in the immediately preceding step 2. At this time, searched cells are excluded from the cell areas 91 selected in step S8. The cell area 91 in the vicinity of the cell area 91 that was set as the search point in the immediately preceding step 2 may be, for example, any of the 24 cell areas 91 (8 on the inside and 16 on the outside) that surround the cell area 91 that was set as the search point in the immediately preceding step 2. Doing so may improve the accuracy of mapping.

[0114] The mapping method described above significantly reduces the number of measurement cycles required to identify regions with desired characteristics compared to conventional methods (full-scale testing) (for example, to one-hundredth of the number). Furthermore, compared to mapping methods using Bayesian optimization that do not update the measurement target region or cells, the number of measurement cycles required to identify regions with desired characteristics can be reduced by approximately half. Specifically, updating (reducing) the measurement target region leverages the exhaustive search capabilities of the variance-weighted acquisition function while enabling focused search on regions with high expected values ​​as the search progresses, thereby improving mapping accuracy. Furthermore, updating cells (reducing the cell region) initially roughly estimates the distribution to speed up search convergence (performing a rough mapping to get a rough idea), and then enables highly accurate search for regions where regions with desired characteristics are likely to exist, thereby improving mapping accuracy. These improvements enable high throughput while improving mapping accuracy.

[0115] In this way, a high-throughput indentation mapping apparatus and mapping method can be provided.

[0116] [Another embodiment] (1) In the above embodiment, when the mapping device 100 acquires a profile that is a change in the load acting on the indenter 2 as the indenter 2 is pushed into and pulled back from the surface of the sample 9, The case where the indenter 2 is pressed to a predetermined depth has been described as an example, but the profile can also be acquired when the indenter 2 is pressed until the load acting on the indenter 2 reaches a predetermined magnitude.

[0117] (2) In the above embodiment, the measurement target area 90 is assumed to be a square area, but the measurement target area 90 may be rectangular. Even if the measurement target area 90 is rectangular, it is preferable to divide the measurement target area 90 into a grid so that the distance d1 between adjacent cell areas 91, 91 in the x direction and the distance d2 between adjacent cell areas 91, 91 in the y direction are as equal as possible.

[0118] (3) In the above embodiment, the case where the distance d1 between adjacent cell regions 91, 91 in the x direction and the distance d2 between adjacent cell regions 91, 91 in the y direction are equal has been described. However, the distance d1 and the distance d2 need only be equal to a certain extent, and they do not necessarily have to be the same distance. For example, a difference of about plus or minus 30% between the distances d1 and d2 is fully acceptable. The distances d1 and d2 may be set so as to avoid the influence of the indentation P. Furthermore, they may be set wide enough as long as the accuracy of the mapping results is not reduced. If the accuracy of the mapping results needs to be maximized, the distances d1 and d2 may be set narrower.

[0119] (4) The mapping termination condition in step S7 described in the above embodiment is not limited to the example given in the above embodiment, and may be changed as appropriate depending on the purpose of mapping and the accuracy required for mapping. Similarly, the update condition in step S4 and the setting of the minimum cell size in step S5 may also be changed as appropriate depending on the purpose of mapping and the accuracy required for mapping.

[0120] For example, in the above embodiment, the region update determination step determines that the update condition is satisfied when the cell regions 91 including the positions predicted to have the maximum or minimum expected value derived from the Gaussian process regressions in the current, previous, and two-previous position determination steps are adjacent to or overlap with each other. However, the condition for determining that the update condition is satisfied is not limited to this. For example, the condition may be determined such that, for the positions predicted to have the maximum or minimum expected value derived from each Gaussian process regression, the distance on the coordinates between the current and previous positions is within √2 and the distance on the coordinates between the previous and previous-previous positions is within √2. That is, the update condition in the region update determination step may be determined based on the positional relationship on the coordinates or the positional relationship between the cell regions 91.

[0121] Furthermore, in the above embodiment, an example of the condition for terminating mapping in the termination determination step has been described as a case where cell areas 91 including positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more Gaussian assumption regressions performed in the position determination step overlap. However, the condition for terminating mapping is not limited to this. For example, the condition for terminating mapping can also be a case where the coordinate distance between positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more Gaussian assumption regressions is within √2. In other words, the condition for terminating mapping in the termination determination step may be determined based on the positional relationship on the coordinates or the positional relationship between the cell areas 91.

[0122] (5) In the above embodiment, the control unit 10 excludes the cell area 91 that has already undergone indentation testing from the adjacent cells that are cell areas 91 that include or are adjacent to the tentative search point, selects the cell area 91 that is closest to the tentative search point from the remaining adjacent cells, and determines this cell area 91 as the next search point. However, in the position determination process after the pre-termination measurement process has been performed at least once, the control unit 10 may simply determine the cell area 91 that includes the tentative search point as the next search point, and if the cell area 91 that includes this tentative search point overlaps with the cell area 91 that has already undergone indentation testing, the measurement process may be omitted.

[0123] The configurations disclosed in the above embodiments (including other embodiments, the same applies below) can be applied in combination with configurations disclosed in other embodiments, as long as no contradiction arises. Furthermore, the embodiments disclosed in this specification are examples, and the embodiments of the present invention are not limited to these, and can be modified as appropriate within the scope that does not deviate from the purpose of the present invention. [Industrial Applicability]

[0124] The present invention is applicable to a mapping method and an indentation mapping apparatus. [Explanation of symbols]

[0125] 1: Control device 2: Indenter 3: Stage 4: Base 5: Prop 9: Sample 10: Control section 11: Measuring part 19: Storage section 21:Indenter support part 41: Slide mechanism 51: Lifting device 52: Lifting mechanism 53: Position sensor 54: Load sensor 90: Measurement area 91: Cell area 91A: Cell area 91B: Cell area 91C: Cell area 91C: Cell area 91X :Area 91a: Cell area 91b: Cell area 100: Mapping device (indentation mapping device) K: constant P: Indentation Q1: Cell Q2: Cell Q3: Cell Q4: Cell Q m :cell Q m-1 :cell h: depth d: spacing d1: Interval d2: Interval q4: Temporary search point qm: temporary search point r: width

Claims

1. a dividing step of determining a measurement target area on the sample surface and dividing the measurement target area into a plurality of cell areas; an updating step of updating the current measurement target area to a new measurement target area and updating the cell area to an area smaller than the current area; a position determination step of determining a cell area to be a search point from among the plurality of cell areas; a measurement step of measuring information of the cell area of ​​the search point when the search point is determined; an area update determination step of determining whether an update condition for the measurement target area is satisfied; The position determination step performs Bayesian optimization based on mapping data including the measurement results obtained in the measurement step, and determines the cell area to be the next search point based on the position where the value of the acquisition function is maximized; the updating step is executed when it is determined in the area update determination step that an update condition is satisfied; In the update process, a mapping method is provided in which a new measurement target area is set as an area that is included in the current measurement target area, includes the cell area that includes the position where the expected value for a specified characteristic derived in the previous Bayesian optimization is predicted to be maximum or minimum, and is smaller than the current measurement target area.

2. The mapping method according to claim 1, wherein the area update determination step determines that the update condition is satisfied if the cell areas determined as the search points in the most recent two or more position determination steps are adjacent to each other.

3. 3. The mapping method according to claim 1, further comprising an initial position determination step of determining three or more predetermined cell areas as the search points at the start of mapping in the measurement step.

4. The method further includes a cell update determination step of determining whether the cell area has reached a predetermined size, 4. A mapping method according to claim 1, wherein the update process is performed when the area update determination process determines that the update condition is met and the cell update determination process determines that the cell area does not have a predetermined size.

5. further including a termination determination step of determining whether a termination condition for the mapping is satisfied; 5. The mapping method according to claim 4, wherein the termination determination step is executed when it is determined in the area update determination step that an update condition is satisfied and when it is determined in the cell update determination step that the cell area has reached a predetermined size.

6. 6. The mapping method according to claim 5, wherein the termination determination step determines that the termination condition for mapping is met if the positions at which the expected values ​​are maximum or minimum, derived in each of the most recent two or more Bayesian optimizations performed in the position determination step, are adjacent or overlapping.

7. The method further includes a pre-termination measurement step of selecting one or more of the unsearched cell areas in the measurement target area and measuring information of the selected cell areas; The mapping method according to claim 6 , wherein the pre-termination measurement step is executed when it is determined in the termination determination step that the termination condition for mapping is not satisfied.

8. 8. The mapping method according to claim 1, wherein the measurement step includes an indentation test step of performing an indentation test in which an indenter is pressed into a surface of a sample to measure the compressive load acting on the indenter and the indentation depth of the indenter as the information.

9. 9. The mapping method according to claim 8, wherein the dividing step divides the cell regions so that the intervals between the cell regions are larger than the width of the portion where the indenter contacts the sample surface when the indenter is pressed into the sample.

10. The mapping method described in claim 8 or 9, wherein the position determination process determines the position where the value of the acquisition function is maximum as a tentative search point, and determines the cell area among the cell areas that is closest to the tentative search point as the next search point, excluding the cell areas where the indentation test has already been performed.

11. The mapping method according to claim 1 , further comprising an output step of obtaining a prediction function by a Gaussian process based on the mapping data, and outputting an expected value of the prediction function as a mapping result.

12. The position determining step includes: A mapping method according to any one of claims 1 to 11, wherein the next search point is determined based on the mapping data including measurement results of the cell area obtained before the update process and measurement results of the cell area obtained after the update process.

13. The position determining step includes: A mapping method according to any one of claims 1 to 11, wherein the next search point is determined based on the mapping data, which was acquired before the update process and includes measurement results of the cell area included in the measurement target area after the update process, and measurement results of the cell area acquired after the update process.

14. an indenter that is pressed into the sample surface; a control unit that determines a search point as a pressing position of the indenter; a measuring unit for measuring a compressive load acting on the indenter and an indentation depth of the indenter; a storage unit that stores mapping data including the search points and the measurement results measured by the measurement unit, The control unit a dividing step of setting a measurement target area on the sample surface and dividing the measurement target area into a plurality of cell areas; an updating step of updating the current measurement target area to a new measurement target area and updating the cell area to an area smaller than the current area; a position determination step of determining a cell area to be a search point from among the plurality of cell areas; an area update determination step of determining whether or not an update condition for the measurement target area is satisfied; In the position determination step, Bayesian optimization is performed based on the mapping data, and the cell area to be the next search point is determined based on the position where a value of an acquisition function related to a predetermined characteristic is maximized; When it is determined that the update condition is satisfied in the area update determination step, the update step is executed; An indentation mapping device that sets a new measurement target area as an area that is included in the current measurement target area, and includes the cell area that includes the position where the expected value derived in the previous Bayesian optimization is predicted to be maximum or minimum, and is narrower than the current measurement target area.

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