Indentation mapping apparatus and indentation mapping method

Abstract

To provide an indentation mapping device and an indentation mapping method.SOLUTION: An indentation mapping device 100 comprises: an indenter 2 pressed into the surface of a sample 9; a control unit 10 that determines a search point as an indentation position of the indenter 2; a measurement unit 11 that measures a compressive load acting on the indenter 2, and an indentation depth of the indenter 2; and a storage unit 19 that stores mapping data including the search point and the results of measurement by the measurement unit 11. The control unit 10 performs Bayesian optimization based on the mapping data stored in the storage unit 19 to determine a next search point.SELECTED DRAWING: Figure 1

Description

[Technical field]

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

[0002] Patent Document 1 describes a mapping method and a measuring device that performs mapping measurement to measure a certain physical quantity under the condition of each point coordinate in a parameter space consisting of one or more parameters, and obtain the distribution of the physical quantity in the parameter space. In this mapping method and measuring device, a computer is used during the mapping measurement to analyze the coordinates of the points measured so far and the physical quantity to obtain a response surface that approximates the distribution of the physical quantity, and then the coordinates of the points to be measured thereafter are determined so as to improve the approximation accuracy of the response surface, and measurements are performed. 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 an analysis result obtained by an analysis model that analyzes a target event using a plurality of parameters, and a Bayesian optimization method that evaluates combinations of the plurality of parameters when the target event is analyzed by the analysis model based on the analysis results acquired by the acquisition unit, and based on the evaluation results for each combination of the plurality of parameters evaluated, and an optimization processing unit that determines a combination of parameters for the analysis model from among a plurality of parameter combinations.

[0004] Patent Document 3 describes a product design device and a product design method for determining design values ​​of components constituting a product so as to satisfy requirements for the product. For example, this product design device includes a design processing unit that determines multiple design values ​​for multiple components by using Bayesian optimization of a multi-point search with the requirements as objective variables and the components as explanatory variables so as to satisfy multiple requirements, 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 obtained 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] The combinatorial method is a technique in which binary, ternary, and other multi-element 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, which saves the effort of repeating experiments with different compositions. For example, the composition of a multi-element material is continuously changed to form a thin-film or layered sample, and the properties of each part of this sample are evaluated to find the part with the desired properties.

[0007] An example of the combinatorial method is described in Patent Document 4. Patent Document 4 points out that it is often very difficult to predict the physical and chemical properties of a combination of various compounds or materials. In the combinatorial method described in Patent Document 4, a diffusion multi-component having three or more layers made of a metal, a nonmetal, a metal oxide, or an alloy is formed in a single sample, the diffusion multi-component including a plurality of interdiffusion regions at the interface between the different metals, nonmetals, metal oxides, or alloys, and the properties of the diffusion multi-component are evaluated as a function of the composition near the interdiffusion region.

[0008] When evaluating the physical properties of a material, particularly its mechanical properties, a test using a nanoindentation method (hereinafter, sometimes referred to as an indentation test) may be performed. As exemplified in Patent Document 5, the nanoindentation method is a material testing method in which a load is applied to an indenter to press it into a sample, thereby evaluating the mechanical properties or mechanical properties (hereinafter, simply referred to as mechanical properties) of a microscopic region of the sample. The nanoindentation method is a testing method that can directly evaluate materials such as films that require values ​​of local mechanical properties. [Prior art documents] [Patent documents]

[0009] [Patent Document 1] JP 2018-138873 A [Patent Document 2] JP 2019-215750 A [Patent Document 3] JP 2020-052737 A [Patent Document 4] JP 2004-347592 A [Patent Document 5] JP 2012-047625 A Summary of the Invention [Problem to be solved by the invention]

[0010] In the combinatorial method, a combinatorial thin film may be used to grade multiple material compositions in a plane and evaluate the properties of many compositions or material types (hereinafter simply referred to as material types) in one sample. When it is desired to search for a material type having a desired mechanical property using a combinatorial thin film, an indentation test may be 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 an indentation test on various points on the surface of a film-like or plate-like material (hereinafter simply referred to as a film, etc.) and mapping the mechanical properties of the entire film, etc., may be referred to as indentation mapping. When performing this indentation mapping, if an indentation test is performed on the entire surface of the combinatorial thin film (so-called a full-scale test), the test time and number of tests required for mapping will be large. Therefore, it is desired to provide a high-throughput indentation mapping device and indentation mapping method instead of a full-scale test.

[0011] 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 indentation mapping apparatus and an indentation mapping method. [Means for solving the problem]

[0012] 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 a pressing 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 performs Bayesian optimization based on the mapping data stored in the storage unit to determine the next search point.

[0013] The indentation mapping apparatus according to the present invention further comprises: The search points may be selected from cell regions obtained by dividing the sample surface into a plurality of regions.

[0014] The indentation mapping apparatus according to the present invention further comprises: The interval between the cell regions may be larger than the width of a portion where the indenter contacts the sample surface when the indenter is pressed into the sample.

[0015] The indentation mapping apparatus according to the present invention further comprises: The control unit may obtain a prediction function using a Gaussian process based on the mapping data, obtain an acquisition function based on the average and variance of the prediction function, determine a provisional search point where the value of the acquisition function is maximum, and determine the cell area that is closest to the provisional search point, excluding the cell area into which the indenter has already been pressed, as the next search point.

[0016] The indentation mapping apparatus according to the present invention further comprises: The control unit may obtain a prediction function by a Gaussian process based on the mapping data, and output an average of the prediction function as the mapping result.

[0017] In order to achieve the above object, the indentation mapping method according to the present invention comprises the steps of: an indenter pressing step of pressing an indenter into a sample surface; a position determination step of determining a search point of the indenter; A measuring step of measuring a compressive load acting on the indenter and a pressing depth of the indenter, The position determination step determines the next search point by performing Bayesian optimization based on mapping data including the search point and the measurement results measured in the measurement step.

[0018] The indentation mapping method according to the present invention further comprises: The method further includes a dividing step of dividing the sample surface into a plurality of cell regions, The position determining step may include selecting the search point from the cell area.

[0019] The indentation 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 surface.

[0020] The indentation mapping method according to the present invention further comprises: The position determination process may include obtaining a prediction function by a Gaussian process based on the mapping data, obtaining an acquisition function based on the average and variance of the prediction function, determining a provisional search point where the value of the acquisition function is maximum, and determining the cell area that is closest to the provisional search point, excluding the cell area into which the indenter has already been pressed, as the next search point.

[0021] The indentation mapping method according to the present invention further comprises: The method may further include an output step of obtaining a prediction function by a Gaussian process based on the mapping data, and outputting an average of the prediction function as the mapping result. Effect of the Invention

[0022] It is possible to provide a high-throughput indentation mapping apparatus and an indentation mapping method. [Brief description of the drawings]

[0023] [Figure 1] FIG. 2 is an explanatory diagram of a configuration of a mapping device. [Diagram 2] FIG. 2 is a block diagram illustrating the control of the mapping device. [Diagram 3] FIG. 2 is an explanatory diagram of the manner in which the surface of a sample is divided into cell regions and search points. [Figure 4] FIG. 1 is an explanatory diagram of the procedure of an indentation test. [Diagram 5]FIG. 13 is a diagram illustrating an example of a profile. [Figure 6] FIG. 13 is a diagram illustrating the relationship between an indenter and a gap between adjacent cell regions. [Figure 7] FIG. 1 is a flow diagram of indentation mapping. [Figure 8] FIG. 1 is a flow diagram of an indentation test of an initial search point. [Figure 9] FIG. 1 is a flow diagram of obtaining a prediction function based on mapping data. [Figure 10] FIG. 13 is a flow diagram for determining the next search point based on an acquisition function. [Figure 11] FIG. 1 is a flow diagram of an indentation test for the next search point. [Figure 12] FIG. 2 is an explanatory diagram of a sample of Example 1. [Figure 13] FIG. 2 is a diagram for explaining the progress of the indentation test and indentation mapping in Example 1. [Figure 14] FIG. 13 is a diagram for explaining a history of exploration in the first embodiment. [Figure 15] FIG. 1 is a diagram showing a mapping result in Example 1. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] An indentation mapping device and an indentation mapping method according to an embodiment of the present invention will be described with reference to the drawings.

[0025] (Overall configuration) 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 according to this embodiment (hereinafter referred to as mapping method).

[0026] The mapping device 100 includes an indenter 2 to be 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 storage unit 19 that stores mapping data including the search point and the measurement results measured by the measurement unit 11. The control unit 10 performs Bayesian optimization based on the mapping data stored in the storage unit 19 to determine the next search point.

[0027] A sample 9 , which is a plate-like test piece, is placed on the stage 3 with the back surface of the plate aligned along the surface of the stage 3 .

[0028] The mapping method according to this embodiment includes an indenter pressing step of pressing the indenter 2 into the surface of the sample 9, a position determination step of determining a search point as the indentation position of the indenter 2 on the surface of the sample 9, and a measurement step of measuring the compressive load acting on the indenter 2 and the indentation depth of the indenter. The position determination step determines the next search point by performing Bayesian optimization based on mapping data including the search point and the measurement results measured in the measurement step.

[0029] (Detailed explanation) In this embodiment, the indentation method is a material testing method in which a load is applied to the indenter 2 to press it into a predetermined search point on the sample 9, thereby evaluating the mechanical properties or mechanical properties (hereinafter simply referred to as mechanical properties, etc.) of a micro-area of ​​the sample 9. Hereinafter, a material test using the indentation method will be simply referred to as an indentation test. In this embodiment, the indentation mapping refers to performing an indentation test on the surface of the sample 9, and acquiring the mechanical properties, etc. of the entire surface of the sample 9 in a map form based on the results of the test.

[0030] (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. One example of the sample 9 is a combinatorial thin film.

[0031] (Mapping device) As an example, the mapping device 100 includes a base 4, a pillar 5 supported by the base 4, a stage 3 supported by the base 4, an indenter support part 21 supported by the pillar 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.

[0032] 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.

[0033] As an example, the indenter 2 is formed in a cone shape tapering toward one end. Hereinafter, the tapered 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, convex curved). 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 described below 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.

[0034] The indenter support part 21 is a mounting seat for mounting the indenter 2 and lifting 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 lower surface side. One end of the indenter support part 21 is supported by a lifting device 51, which will be described later. The indenter support part 21 is driven to move up and down by the lifting device 51.

[0035] 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 along 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 sliding mechanism 41, which will be described later. In this embodiment, the stage 3 is placed on the sliding mechanism 41.

[0036] The base 4 is a seat of 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 respective screws. The slide mechanism 41 realizes horizontal movement of the stage 3 by arbitrarily rotating the respective screws with the motors to move the stage 3 forward and backward in the axial direction of the respective screws.

[0037] 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 base 4. The support pillar 5 is equipped with a lifting device 51 having a lifting mechanism 52 such as a hydraulic cylinder, a position sensor 53, and a load sensor 54 (see FIG. 2), and the indenter 2 is raised and lowered by raising and lowering the indenter support part 21 connected to the lifting device 51 in the up and down direction (the same as the vertical direction in this embodiment).

[0038] 2, the position sensor 53 is a sensor that detects the pressing depth of the indenter 2 (see FIG. 1). The position sensor 53 may detect the pressing depth of the indenter 2, for example, by detecting the height position of the indenter support portion 21 (see FIG. 1). As the position sensor 53, for example, an optical sensor may be used.

[0039] The load sensor 54 is a sensor that detects a 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.

[0040] 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 operations and acquire information therefrom. The control device 1 may be a personal computer or a PLC having a processor such as a CPU or an MPU and a memory device.

[0041] The storage unit 19 is a storage medium such as a hard disk, a flash memory, etc. As described later, the control unit 10 and the measurement unit 11 may realize these functions by executing a program that realizes a mapping method stored in the storage unit 19.

[0042] The measurement unit 11 is a functional unit that executes a measurement process for measuring 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 function by executing a program that realizes a mapping method stored in the storage unit 19. 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 a change in the indentation depth of the indenter 2 and an associated change in the compressive load acting on the indenter 2. Hereinafter, the change in the indentation depth of the indenter 2 and an associated change in the compressive load acting on the indenter 2 in the indentation test may be simply referred to as a profile. Also, measuring the change in the indentation depth of the indenter 2 and an associated change in the compressive load acting on the indenter 2 in the indentation test may be simply referred to as a profile measurement. Details of the profile measurement will be described later.

[0043] When the measurement unit 11 measures a profile, it stores the measurement result 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 result as mapping data in the storage unit 19, and explanations regarding storage in the storage unit 19 will be omitted as appropriate.

[0044] The control unit 10 is a functional unit that executes an indenter pressing step, a position determining step, a dividing step of dividing the surface of the sample 9 into a plurality of cell regions 91 (see FIG. 3), an indenter pressing step, and an output step of outputting the mapping results. The control unit 10 may realize its functions by executing a program that realizes a mapping method stored in the storage unit 19.

[0045] When performing the indenter pressing step, the control unit 10 controls the lifting device 51 and the slide mechanism 41 to realize an indentation test using the indenter 2 (see FIG. 1).

[0046] When executing the position determination process, if no mapping data is stored in the memory unit 19 (at the start of the indentation test), the control unit 10 determines a random or predetermined search point as the first search point. When executing the position determination process, the control unit 10 performs Bayesian optimization based on the mapping data stored in the memory unit 19 to determine the next search point. When executing the output process, the control unit 10 creates a mapping result based on the mapping data stored in the memory unit 19 and outputs the mapping result.

[0047] The control unit 10 determines a search point, controls the lifting device 51 and the slide mechanism 41 to perform an indentation test on the search point, and causes the measuring unit 11 to acquire a profile, repeating this measurement cycle a predetermined number of times. This improves the accuracy of the mapping result. The improvement in the accuracy of the mapping result will be described later. Hereinafter, the cycle of determining the search point by the control unit 10, performing the indentation test, and acquiring the profile by the measuring unit 11 may be simply referred to as a measurement cycle.

[0048] 3, the control unit 10 selects one of cell regions 91 obtained by dividing the surface of the sample 9 into a plurality of regions as a search point. Then, the control unit 10 selects a search point for the indenter 2 on the sample 9 from the cell region 91. This makes it possible to ensure the intervals between each search point in each indentation test.

[0049] The division of the surface of the sample 9 into cell regions 91, the determination of search points, the indentation test, the acquisition of a profile by the measurement unit 11, the creation of mapping results, and the output of the mapping results by the control unit 10 will be described in detail later.

[0050] (Indentation Test) The indentation test will be described in detail. Fig. 4 shows the steps of the indentation test from state (a) to state (c). The indentation test in this embodiment is a test for evaluating the mechanical properties of a micro-area of ​​the sample 9 by applying a load to the indenter 2 and pressing it into a predetermined cell area 92 of the sample 9.

[0051] In the indentation test, first, a sample 9 is placed on the stage 3 (see FIG. 4(a)).

[0052] Then, the control unit 10 (see FIG. 1) presses the indenter 2 into the determined search point (see FIG. 4(b)). The indenter 2 is pressed until the compressive load (hereinafter simply referred to as 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(b) illustrates a state in which the indenter 2 is pressed to a depth h.

[0053] 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. 4(c)). When the indenter 2 is pressed and then pulled back, an indentation P is formed on the surface portion of the sample 9 where the indenter 2 was pressed.

[0054] FIG. 5 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 in an indentation test. In the process of pressing and pulling back the indenter 2 as shown in FIG. 4 ((a) to (c) in FIG. 4), the compressive load acting on the indenter 2 changes as the indentation depth of the indenter 2 changes, as shown in FIG. 5. FIG. 5 shows a case where the predetermined indentation depth is 20 μm. As the indenter 2 is pressed to a depth of 20 μm, the load acting on the indenter 2 increases. When the indenter 2 is pressed to a depth of 20 μm (depth h=20 μm in FIG. 4(b)), a load of 20 (N) is applied to the indenter 2. When the indenter 2 is pressed to a depth of 20 μm and then pulled back (see FIG. 4(c)), the load acting on the indenter 2 decreases. In the example of Fig. 5, the load acting on the indenter 2 becomes zero when the indenter 2 is pulled back to a pressing depth of 19 µm. This is because an indentation P is formed on the surface of the sample 9 by plastic deformation (see Fig. 4(c)).

[0055] (Indentation Mapping) Indentation mapping will be described in detail. Indentation mapping in this embodiment refers to performing an indentation test on a part of the surface of the sample 9, acquiring a predetermined number of profiles of the part of the surface of the sample 9, and acquiring the mechanical properties and the like of the entire surface of the sample 9 in a map form based on these profiles.

[0056] When performing indentation mapping, the control unit 10 virtually divides the surface of the sample 9 into a plurality of cell regions 91, as shown in FIG.

[0057] The control unit 10 virtually divides the surface of the sample 9 into cell regions 91, for example, as follows. The control unit 10 sets a measurement target region 90 in the center of the surface of the sample 9. The measurement target region 90 may be set as a square region, for example. In the following, it is assumed that the measurement target region 90 is a square region. Next, the measurement target region 90 is divided into n equal parts in a lattice in the x and y directions (where n is an integer of 2 or more). As a result, n 2 cell areas 91 are set. The distance d1 between adjacent cell areas 91, 91 in the x direction is equal to the distance d2 between adjacent cell areas 91, 91 in the y direction. Coordinates (xi, yi) may be assigned to each cell area 91 as necessary. Here, i is an integer between 1 and n.

[0058] As shown in FIG. 6, the interval d between adjacent cell regions 91, 91 should be larger 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 pressing depth h of the indenter 2. This allows the indentation test to be performed without being influenced by the indentation P of the cell region 91a when performing an indentation test on another cell region 91b (the cell region 91 to be subjected to the next indentation test) adjacent to the cell region 91a, which is the cell region 91 on which an indentation test has already been performed. The term "being influenced by the indentation P" means 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 on which an indentation test has already been performed and the region very close thereto, thereby affecting the result of the indentation test on the certain cell region 91b. The interval d should be, for example, 5 times or more the width r. This makes it possible to avoid the influence of an indentation test that has already been performed, which may remain in the vicinity of the outside of the indentation P.

[0059] Indentation mapping is performed by performing an indentation test on each cell region 91 to obtain a profile. It is possible to obtain profiles of all cell regions 91 and perform indentation mapping here, 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, the control unit 10 of the mapping device 100 does not obtain profiles of all cell regions 91 and perform indentation mapping, but obtains profiles of some of the cell regions 91, performs regression calculations using a Gaussian process (Gaussian process regression, Gaussian Processor) based on these profiles, and creates and outputs mapping results.

[0060] 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 region 91 as an output of the mapping result, and outputs the average of this prediction function as the mapping result. The control unit 10 may store this prediction function in the storage unit 19 as an output of the mapping result.

[0061] 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.

[0062] In the Bayesian optimization of this embodiment, a prediction function is acquired, an acquisition function (hereinafter, referred to as acq) is created, and the coordinates in the measurement target region 90 (see FIG. 3) where the value of the acquisition function is maximum are calculated (searched). The prediction function is acquired using mapping data that has already been acquired.

[0063] In order for the control unit 10 to obtain the prediction function, various kernels can be used depending on the purpose of the indentation mapping and the characteristics of the sample 9 (see FIG. 1). In this embodiment, as an example, the Matern kernel (v=2.5) shown in Equation 1 may be used. In the following Equation (1), Γ(ν) is a gamma function, and ν=2.5. Also, d(xi, yi) is the Euclidean distance. Also, K ν is the modified Bessel function of the second kind.

[0064]

number

[0065] An example of the acquisition function created by the control unit 10 is shown in Equation 2. The average in Equation 2 is the average value in the prediction function. The variance is the variance in the prediction function. The constant K is a constant for use in Bayesian optimization and weighting the search, and may be set arbitrarily depending on the purpose of indentation mapping and the characteristics of the sample 9 (see FIG. 1).

[0066]

number

[0067] That is, the control unit 10 acquires the average and variance of the prediction function based on the acquired prediction function, and creates the acquisition function by substituting the average and variance into Equation 2. Note that Equation 2 illustrates a case where the acquisition function in this embodiment is an acquisition function suitable for efficiently finding the part with the highest mechanical strength from the sample 9 (see FIG. 1) and improving the accuracy of the mapping result of the part with the highest mechanical strength, that is, an Upper Confidence Bound. As an example, when it is desired to search for a part predicted to have the highest mechanical strength with a small number of cycles (when priority is given to utilization), the value of the constant K may be set small. Also, when it is desired to improve the accuracy of the mapping result (when priority is given to search), the value of the constant K may be set large. Note that when it is desired to efficiently find the part with the lowest mechanical strength, the acquisition function of the lower confidence bound may be used instead of the acquisition function of the Upper Confidence Bound.

[0068] The calculation (search) of the coordinates where the value of the acquisition function is maximum may be performed using, for example, the known L-BFGS4-B method. The control unit 10 determines the coordinates where the value of the acquisition function is maximum as the next tentative search point.

[0069] Then, the control unit 10 selects, from the cell areas 91 (hereinafter referred to as adjacent cells) adjacent to the tentative search point, the cell area 91 that has already been subjected to indentation testing, and from the remaining adjacent cells, selects the cell area 91 that is closest to the tentative search point, and determines this cell area 91 as the next search point.

[0070] (Indentation mapping flow) Hereinafter, an example of a series of flows of indentation mapping in the mapping method realized by the mapping device 100 will be described based on the flowcharts shown in FIGS. 7 to 11 while also referring to FIGS. 1 to 3 as appropriate.

[0071] First, the overall flow of indentation mapping (steps S1 to S7) will be described based on the flowchart in Fig. 7. When indentation mapping is started, the control unit 10 sets a measurement target region 90 as shown in Fig. 3, and further divides the measurement target region 90 into a plurality of cell regions 91 (step S1).

[0072] Next, the control unit 10 determines three initial search points from among the multiple cell regions 91, and performs an indentation test on these initial search points (step S2). By performing the indentation test, the measurement unit 11 stores the measurement results of the profiles of each search point in the memory unit 19 as mapping data.

[0073] Next, the control unit 10 acquires a prediction function based on the mapping data stored in the storage unit 19 (step S3).

[0074] Next, the control unit 10 determines whether or not a predetermined number of profiles have been acquired (step S4). If a predetermined number of profiles (e.g., 30 points as the predetermined number) have been acquired (YES in step S4), the control unit 10 proceeds to step S7. If a predetermined number of profiles have not been acquired (NO in step S4), the control unit 10 proceeds to step S5. Note that the predetermined number may be a number determined in advance, or may be determined as a number corresponding to a proportion of the total number of grids into which the measurement target region 90 is divided (e.g., a number corresponding to 30%).

[0075] When the process proceeds from step S4 to step S5 (No in step S4), the control unit 10 determines the next search point based on the prediction function and the acquisition function acquired based on the prediction function (step S5).

[0076] Taking the diagram in FIG. 3 as an example, three initial search points Q 1 ,Q 2 ,Q 3 When only the profile of the first search point Q is stored in the storage unit 19 as mapping data, the control unit 10 selects the fourth search point Q as the fourth search point Q. 4That is, the search point Q 1 From Q m-1 When the profile is stored in the storage unit 19 as mapping data, the next search point Q, that is, the m-th search point Q, is m (where m is an integer of 4 or greater).

[0077] Next, an indentation test is performed on the cell region 91 determined as the next search point, and the profile measurement results are stored as mapping data in the storage unit 19 (step S6). When step S6 ends, the process returns to step S3.

[0078] As described above, if a predetermined number of profiles are acquired in step S4 (YES in step S4), the process proceeds from step S4 to step S7. Then, the control unit 10 outputs the prediction function as a mapping result (step S7) and ends the indentation mapping. The control unit 10 stores the prediction function in, for example, the storage unit 19 as an output of the mapping result.

[0079] Step S2 in Fig. 7 will be described in detail with reference to the flowchart in Fig. 8. The contents already described in the explanation of step S2 may be omitted in the following explanation.

[0080] In step S2, the control unit 10 first determines three initial search points from among the multiple cell areas 91 (step S21). The initial search points may be cell areas 91 randomly selected by the control unit 10, or may be cell areas 91 designated in advance. In FIG. 3, the initial search points Q 1 ,Q 2 ,Q 3 In this example, the initial search points are not limited to three points, and four or more points may be selected.

[0081] Next, the control unit 10 causes the slide mechanism 41 to move the stage so that the center of the cell region 91 corresponding to one of the initial search points is located directly under the indenter 2 (step S22). Then, the control unit 10 controls the lifting mechanism 52 of the lifting device 51 to lift and lower the indenter 2 and perform an indentation test (step S23).

[0082] Next, the control unit 10 judges whether the indentation tests of all the initial search points have been completed (step S24), and if the indentation tests of all the initial search points have not been completed, the control unit 10 returns to step S22 (No in step S24). When the control unit 10 has completed the indentation tests of all the initial search points, it ends step S2 (Yes in step S24).

[0083] Step S3 in Fig. 7 will be described in detail with reference to the flowchart in Fig. 9. The contents already described in the explanation of step S3 may be omitted in the following explanation.

[0084] In step S3, the control unit 10 reads and acquires mapping data from the storage unit 19 (step S31). Next, based on the read mapping data, a prediction function is calculated and acquired by Gaussian process regression (step S32), and step S3 ends. In this embodiment, the control unit 10 can store the acquired prediction function in the storage unit 19 and end step S3.

[0085] Step S32 will be further described with reference to the example shown in FIG. 1 ,Q 2 ,Q 3 When only the profile of the initial search point Q is stored in the storage unit 19 as mapping data, the control unit 10 1 ,Q 2 ,Q 3 Obtain a prediction function based on the mapping data corresponding to the profile of the search point Q. 1 From Q m-1 When the profile is stored as mapping data in the storage unit 19, the control unit 10 1From Q m-1 A prediction function is obtained based on the mapping data corresponding to the profile of

[0086] Step S5 in Fig. 7 will be described in detail with reference to the flowchart in Fig. 10. The contents already described in the explanation of step S5 may be omitted in the following explanation.

[0087] In step S5, the control unit 10 first obtains the mean and variance of the prediction function obtained in step S32 (step S51). Next, the control unit 10 creates an acquisition function based on the mean and variance of the prediction function (step S52).

[0088] Next, the control unit 10 calculates the coordinates where the acquisition function is maximum (step S53). Since the prediction function is a function having continuity in the corresponding section within the measurement target region 90, the coordinates where the acquisition function is maximum do not necessarily coincide with the center of each cell region. Therefore, the control unit 10 selects the cell region 91 that is closest to the coordinates where the value of the acquisition function is maximum from among the adjacent cells excluding the cell region 91 that has already been subjected to the indentation test, and determines this cell region 91 as the next search point (step S54), and ends step S5. In this embodiment, the control unit 10 can store the coordinates of the cell region 91 determined as the next search point in the storage unit 19 and end step S5.

[0089] Step 6 in Fig. 7 will be described in detail with reference to the flowchart in Fig. 11. Contents already described in the explanation of step 6 may be omitted in the following explanation.

[0090] In step S6, first, the control unit 10 acquires the coordinates of the cell region 91 determined as the next search point in step S3 (step S61). Next, the control unit 10 causes the slide mechanism 41 to move the stage so that the center of the cell region 91 determined as the next search point is located directly under the indenter 2 (step S62). Then, the control unit 10 controls the lifting mechanism 52 of the lifting device 51 to lift and lower the indenter 2 to perform an indentation test (step S63), and step S6 is completed.

[0091] (Description of the embodiment) An example of indentation mapping performed using the mapping method according to the present embodiment will be described.

[0092] Example 1 Fig. 12 shows sample 9 of Example 1. Sample 9 is a substrate that has been processed by shot peening so that the center portion is harder than the outer periphery, creating a gradation in hardness within the surface of the substrate.

[0093] The substrate of sample 9 is a flat plate of stainless steel (SUS316L). As a pretreatment, the surface of sample 9 is polished to a mirror finish and then subjected to a prescribed heat treatment. The central portion is shot peened to partially harden the surface and form a hardened portion S with high mechanical strength. Sample 9 is a square substrate with a length and width of approximately 34 mm and a thickness of approximately 3 mm. The shot peening was performed under the following conditions: 50 g of copper fine particles with a particle diameter of 70 μm were projected toward the center of the substrate of sample 9 using a suction nozzle with a nozzle diameter of 6 mm at a projection pressure of 0.5 MPa and a nozzle distance of 10 mm for 30 seconds.

[0094] The indentation test and indentation mapping were performed under the following conditions. The indentation test was performed on a square measurement target area 90 of 30 mm length and width in the center of the sample 9, using an indenter 2 (see FIG. 1) with a spherical tip and a radius of curvature of 400 μm, with a predetermined indentation depth set to 21.9 μm. The measurement target area 90 was divided into 50 equal parts lengthwise and widthwise into lattice-shaped cell areas. The indentation mapping was performed with three random initial search points, until the total number of search points reached 200 (an example of a predetermined number).

[0095] FIG. 13 shows the progress of the indentation test and indentation mapping (statuses (a) to (f)). In FIG. 13, the solid black circles indicate initial search points, and the hollow white circles indicate search points determined subsequently. The number of search points increases sequentially from FIG. 13(a) to FIG. 13(f). Note that FIG. 13(a) shows three initial search points, and the total number of search points increases to 34, 67, 100, 134, and 200 from FIG. 13(b) to FIG. 13(f).

[0096] In this embodiment, the acquisition function is set to the Upper Confidence Bound. Therefore, as shown in Fig. 13, in the process of indentation mapping, the positions where the load applied to the indenter 2 is large, that is, the regions of the hardened portion S with high mechanical strength are searched intensively, but the search points are set in a scattered manner throughout the entire measurement target region 90 as a whole. As a result, in the mapping method according to this embodiment, the highest point (or the lowest point) can be automatically and efficiently found for a material such as the sample 9, whose mechanical properties differ within a region of the surface.

[0097] FIG. 14 shows the relationship between the distance between each of the search points where the indentation test was performed and the center of the hardened portion S until the search of the 200 search points was completed, i.e., the search history. The center of the hardened portion S is the position evaluated as having the highest mechanical strength in the mapping results. As shown in FIG. 14, in the search history of this embodiment, the area of ​​the hardened portion S with high mechanical strength is searched most intensively, followed by the area near the outside of the hardened portion S. However, it can be seen that the other parts are also searched appropriately, and the search points are selected (determined) in a variety of ways to prevent oversights in the search.

[0098] FIG. 15 shows a visualization of the mapping result of Example 1. The mapping result is a visualization of a prediction function obtained based on the profile of each search point obtained in an indentation test of 200 points, using a shading display. As shown in FIG. 15, the region Sa corresponding to the hardened portion S (see FIG. 13) is evaluated as a region with high mechanical strength. The region near the outside of the hardened portion S is evaluated as a region in which the mechanical strength increases as it approaches the hardened portion S. The other regions are evaluated as regions with approximately uniform mechanical strength. That is, the mapping result of Example 1 is a result that correctly reflects the mechanical strength of the sample 9, although the indentation test is not performed on the entire surface of the sample 9. In this way, in this embodiment, it is possible to obtain accurate mapping results with high throughput without performing a full test.

[0099] In Example 1, an example of creating a mapping result of sample 9 processed by shot peening so that a gradation in hardness occurs in the plane of the substrate has been described. It is of course possible to create such a mapping result not only for shot peened substrates, but also for combinatorial thin films in which a plurality of material compositions are graded in the plane to evaluate the characteristics of many material types in one sample, and it is considered that the creation of the mapping result allows efficient screening of better material types.

[0100] In this manner, a high-throughput indentation mapping apparatus and an indentation mapping method can be provided.

[0101] [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 caused by pressing the indenter 2 into the surface of the sample 9 and pulling it back, 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.

[0102] (2) In the above embodiment, the sample 9 is described as being a shot-peened substrate or a combinatorial thin film, but the sample 9 from which mapping results can be obtained using the mapping method and mapping device 100 of this embodiment is not limited to these, and any sample 9 may be selected depending on the purpose.

[0103] (3) 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 lattice shape so that the interval d1 between adjacent cell areas 91, 91 in the x direction and the interval d2 between adjacent cell areas 91, 91 in the y direction are as equal as possible.

[0104] (4) In the above embodiment, the case has been described where the spacing d1 between adjacent cell regions 91, 91 in the x direction and the spacing d2 between adjacent cell regions 91, 91 in the y direction are equal. However, the spacing d1d and the spacing d2 only need to be equal to a certain extent, and they are not necessarily the same spacing. For example, a difference between the spacing d1 and the spacing d2 of about plus or minus 30% is fully acceptable. The spacing d1 and the spacing d2 may be set so as to avoid the influence of the indentation P. Also, the spacing d1 and the spacing d2 may be set wide as long as the accuracy of the mapping result is not reduced. If it is desired to increase the accuracy of the mapping result as much as possible, the spacing d1 and the spacing d2 may be set narrow.

[0105] In addition, 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, provided no contradiction arises. Furthermore, the embodiments disclosed in this specification are illustrative, and the embodiments of the present invention are not limited thereto, and can be appropriately modified within the scope that does not deviate from the purpose of the present invention. [Industrial Applicability]

[0106] The present invention can be applied to an indentation mapping apparatus and an indentation mapping method. [Explanation of symbols]

[0107] 1: Control device 2: Indenter 3: Stage 4: Pedestal 5: Prop 6: Step 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 92: Cell area 100: Mapping device (indentation mapping device) K: constant P: Indentation Q: Search point Q 1 :Initial search point (search point) Q 2 :Initial search point (search point) Q 3 :Initial search point (search point) Q 4 :Search point Q m :Search point Q m-1 :Search point S: Hardened part Sa:Area h :Depth d :Spacing d1 : Interval d2: Interval r: width

Claims

1. 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 a pressing 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 performs Bayesian optimization based on the mapping data stored in the memory unit to determine the next search point.

2. The indentation mapping apparatus according to claim 1 , wherein the search points are selected from cell areas obtained by dividing the sample surface into a plurality of areas.

3. 3. The indentation mapping apparatus according to claim 2, wherein the interval between the cell regions is greater than the width of a portion where the indenter contacts the sample surface when the indenter is pressed into the sample surface.

4. 4. The indentation mapping device of claim 3, wherein the control unit obtains a prediction function by a Gaussian process based on the mapping data, obtains an acquisition function based on the average and variance of the prediction function, determines a provisional search point at which the value of the acquisition function is maximum, and determines the cell region that is closest to the provisional search point, excluding the cell region into which the indenter has already been pressed, as the next search point.

5. The indentation mapping device according to claim 1 , wherein the control unit obtains a prediction function by a Gaussian process based on the mapping data, and outputs an average of the prediction function as the mapping result.

6. an indenter pressing step of pressing an indenter into a sample surface; a position determination step of determining a search point as a pressing position of the indenter; A measuring step of measuring a compressive load acting on the indenter and a pressing depth of the indenter, The position determination step is an indentation mapping method in which the next search point is determined by performing Bayesian optimization based on mapping data including the search point and the measurement results measured in the measurement step.

7. The method further includes a dividing step of dividing the sample surface into a plurality of cell regions, The indentation mapping method according to claim 6 , wherein the position determining step selects the search point from the cell region.

8. The indentation mapping method according to claim 7 , wherein the dividing step divides 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 surface.

9. The indentation mapping method of claim 8, wherein the position determination step includes obtaining a prediction function by a Gaussian process based on the mapping data, obtaining an acquisition function based on the average and variance of the prediction function, determining a tentative search point at which the value of the acquisition function is maximum, and determining the cell region that is closest to the tentative search point, excluding the cell region into which the indenter has already been pressed, as the next search point.

10. The indentation mapping method according to claim 6 , further comprising an output step of obtaining a prediction function by a Gaussian process based on the mapping data, and outputting an average of the prediction functions as a mapping result.

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