JP7744009B2 - Mapping method and indentation mapping device - Google Patents

Description

The present invention relates to a mapping method and an indentation mapping device.

Patent Document 1 describes a mapping method and measurement device that measures a physical quantity under the conditions of each point coordinate in a parameter space consisting of one or more parameters, and performs mapping measurement to obtain the distribution of that physical quantity in the parameter space. This mapping method and measurement device uses a computer to analyze the coordinates of points measured up to that point and the physical quantity during the mapping measurement to obtain a response surface that approximates the distribution of that physical quantity, and then determines the coordinates of points to be measured subsequently to further improve the approximation accuracy of the response surface. Polynomial approximation, radial basis function method, spline interpolation, Gaussian process regression, Kriging method, and logistic regression can be used to obtain the response surface.

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

Patent Document 3 describes a product design device and a product design method that determine design values for components that make up a product so that the product meets its requirements. For example, this product design device includes a design processing unit that determines multiple design values for multiple components to meet multiple requirements by using Bayesian optimization in a multi-point search with the requirements as the objective variable and the components as the explanatory variables, and an output unit that outputs the multiple design values determined by the design processing unit.

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 found sequentially during the optimization process using Gaussian process regression. As described in Patent Document 1, Gaussian process regression is also known as a method for approximating distributions.

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 reduces the scanning interval between the previous measurement position and the next measurement position when the measured magnetic field is near its maximum value, minimum value, or pole, and increases the scanning interval between the previous measurement position and the next measurement position in other locations. Whether or not the measurement is near a maximum value or the like is determined based on an approximate curve predicted using the least squares method or the like based on multiple measurement values already obtained, and a determination is made based on this approximate curve. This measurement position control device and method makes it possible to automatically shorten the measurement time for the electric or magnetic field distribution.

The combinatorial method is a technique in which multi-component materials, such as binary and ternary systems, 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 then evaluating the properties of each part of this sample to find the part with the desired properties.

Patent Document 5 describes an example of a combinatorial method. Patent Document 4 points out that predicting the physical and chemical properties of combinations of various compounds or materials is often extremely difficult. The combinatorial method described in Patent Document 5 forms a diffusion multicomponent of three or more layers consisting of metals, nonmetals, metal oxides, or alloys in a single sample, the diffusion multicomponent including multiple interdiffusion regions at the interfaces between the different metals, nonmetals, metal oxides, or alloys, and evaluates the properties of the diffusion multicomponent as a function of composition near the interdiffusion regions.

When evaluating the physical properties of materials, particularly their mechanical or 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 the sample, to evaluate the mechanical 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, where local mechanical property values are required.

Non-Patent Document 1 describes a method for adaptively selecting the undetermined parameters of the acquisition function for 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.

JP 2018-138873 A Japanese Patent Application Laid-Open No. 2019-215750 Japanese Patent Application Laid-Open No. 2020-052737 Japanese Patent Application Laid-Open No. 2006-003229 Japanese Patent Application Laid-Open No. 2004-347592 JP 2012-047625 A

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>

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 using combinatorial thin films 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, and the mechanical properties of the entire combinatorial thin film are mapped. 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.

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 in that the testing time and number of tests required for mapping are significant. In particular, when trying to identify a region with specified properties (the so-called optimal solution), there is a need to reduce the testing time and number of tests required for mapping. Therefore, there is a need to provide a high-throughput mapping method.

However, with methods such as those described in Patent Document 4, which change the scanning interval between the previous and next measurement positions based on a predicted approximation curve, although some improvement in throughput can be expected, a sufficient improvement in throughput cannot be expected. Furthermore, methods such as those described in Patent Document 4 are not suitable for the purpose of identifying areas with specified characteristics in a short test time and with a small number of tests. Therefore, there is a need for mapping methods that can further increase throughput in identifying areas with specified characteristics.

The present invention was made in light of these circumstances, and its purpose is to provide a high-throughput mapping method and indentation mapping device for identifying regions with specified characteristics.

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.

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.

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.

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.

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.

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.

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;
The pre-termination measurement step may be executed when it is determined in the termination determination step that the mapping termination condition is not satisfied.

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.

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.

The mapping method according to the present invention further comprises:
The position determination process may determine the position where the value of the acquisition function is maximum as a tentative search point, and determine 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.

The 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 expected value of the prediction function as a mapping result.

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.

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 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.

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.

This provides a high-throughput mapping method for identifying sites with specific characteristics.

FIG. 1 is an explanatory diagram of a configuration of a mapping device. FIG. 2 is a functional block diagram of a mapping device. FIG. 1 is an explanatory diagram of the procedure of an indentation test. FIG. 1 is an explanatory diagram of the procedure of an indentation test. FIG. 1 is an explanatory diagram of the procedure of an indentation test. FIG. 10 is a diagram illustrating an example of a profile. 1A and 1B are explanatory diagrams of the manner in which the surface of a sample is divided into cell regions and search points. FIG. 10 is a diagram illustrating the relationship between an indenter and the spacing between adjacent cell regions. FIG. 10 is a diagram illustrating updating of a measurement target area. FIG. 10 is a diagram illustrating updating of a measurement target area and updating of a cell. FIG. 10 is a diagram illustrating updating of a measurement target area and updating of a cell. FIG. 1 is a flow diagram of mapping. FIG. 10 is a flow diagram of step S2. FIG. 10 is a flow diagram of step S7.

Based on the drawings, a mapping method and indentation mapping device according to an embodiment of the present invention will be described.

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

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.

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

The update process is executed when it is determined in the area update determination process that the update conditions are met. In the update process, a new measurement target area is set that is an area included in the current measurement target area, includes a cell area containing a position where the expected value (hereinafter sometimes simply referred to as the expected value) of a prediction function for a specified characteristic derived in the immediately preceding Bayesian optimization is predicted to be maximum or minimum, and is smaller than the current measurement target area.

The mapping method according to this embodiment can achieve high throughput in identifying regions with specific characteristics.

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

The mapping device 100 includes an indenter 2 that is pressed into the surface of the 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.

The control unit 10 executes at least the division process, update process, position determination process, and area update determination process described above in order 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 process.

A plate-shaped test piece, sample 9, is placed on stage 3.

(Detailed explanation)
In this embodiment, the indentation method is a material testing method in which a load is applied to an indenter 2 to press the indenter 2 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.

(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.

(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.

The indenter 2 is a tip-shaped member used to perform an indentation test on the sample 9 placed on the 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.

As an example, the indenter 2 is formed in a cone shape that tapers toward one end. Hereinafter, the narrowing end of the indenter 2 will be referred to simply 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 as desired 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 bottom end when attached to the indenter support part 21.

The indenter support part 21 is a mounting seat for attaching the indenter 2 and 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 the lifting device 51, which will be described later. The indenter support part 21 is driven to rise and fall by the lifting device 51.

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

The base 4 is the 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 screws. The slide mechanism 41 realizes horizontal movement of the stage 3 by arbitrarily rotating the screws using the motors to move the stage 3 forward and backward in the axial direction of the screws.

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 an elevator device 51 (see Figure 2) that has an elevator mechanism 52 such as a hydraulic cylinder, a position sensor 53, and a load sensor 54. The indenter 2 is raised and lowered by raising and lowering the indenter support part 21 connected to the elevator device 51 in the up and down direction (the same as the vertical direction in this embodiment).

Figure 2 shows a functional block diagram of the mapping device 100. As shown in Figure 2, the position sensor 53 is a sensor that detects the indentation depth of the indenter 2 (see Figure 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 portion 21 (see Figure 1). An optical sensor, for example, may be used as the position sensor 53.

The load sensor 54 is a sensor that detects the compressive load acting on the indenter 2 (see Figure 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 Figure 1) downward. The load sensor 54 may be, for example, a pressure sensor equipped with a piezoelectric element.

The control device 1 includes a control unit 10, a measurement unit 11, and a memory 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 PLC having a processor such as a CPU or MPU and a memory device.

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

The measurement unit 11 is a functional unit that executes an indentation test process, which measures the compressive load acting on the indenter 2 (see Figure 1) and the indentation depth of the indenter as a measurement process. The measurement unit 11 may realize its functions by executing a program that implements a mapping method stored in the memory unit 19.

During 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 using its position sensor 53 and load sensor 54. In this embodiment, as an example, the measurement unit 11 measures changes in the indentation depth of the indenter 2 and the associated changes in the compressive load acting on the indenter 2. Hereinafter, changes in the indentation depth of the indenter 2 and the associated changes in the compressive load acting on the indenter 2 during an indentation test may be simply referred to as a profile. Furthermore, measuring changes in the indentation depth of the indenter 2 and the associated changes in the compressive load acting on the indenter 2 during an indentation test may be simply referred to as measuring a profile. Details of profile measurement will be provided below.

When the measurement unit 11 measures a profile, it stores the measurement results as mapping data in the memory unit 19. In the following explanation, we will assume that when the measurement unit 11 measures a profile, it always stores the measurement results as mapping data in the memory unit 19, and will omit appropriate explanations regarding storage in the memory unit 19.

The control unit 10 is a functional unit that executes the division process, update process, position determination process, measurement process, and area update determination process in the mapping method. In addition to the division process, the control unit 10 also executes the initial position determination process, cell update determination process, termination determination process, pre-termination measurement process, and output process, which will be described later. Details of each process executed by the control unit 10 will be described later. The control unit 10 may realize the function of executing these processes by executing a program that implements the mapping method stored in the memory unit 19.

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 Figure 1) to perform the indentation test.

(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.

In an indentation test, first, the sample 9 is placed on the stage 3 (see Figure 3).

Then, the control unit 10 (see Figure 1) presses the indenter 2 into the cell region 91 determined as the search point (see Figure 4). The indenter 2 continues to be 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). Figure 4 illustrates a state in which the indenter 2 has been pressed to a depth h.

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 Figure 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.

Figure 6 shows an example of a profile, i.e., 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 pressing depth of the indenter 2 changes, as shown in Figure 6. Figure 6 shows the case where the specified pressing depth is 20 μm. As the indenter 2 is pressed to a pressing depth of 20 μm, the load acting on the indenter 2 increases. When the indenter 2 is pressed to a pressing depth of 20 μm (when depth h = 20 μm in Figure 4), a load of 20 (N) is applied to the indenter 2. After the indenter 2 is pressed 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 has been formed on the surface of the sample 9 due to plastic deformation (see Figure 5).

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

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 Figure 7, and divides the measurement target area 90 into multiple cell areas 91 at intervals d.

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. As an example, the measurement target area 90 may be set as a square area. The following explanation will be given assuming that the measurement target area 90 is a square area.

Next, the measurement target area 90 is divided into n equal parts in a grid in the x and y directions (where n is an integer greater than or equal to 2). This results in ⁿ² cell areas 91 being 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, where i is an integer greater than or equal to 1 and less than or equal to n. In this embodiment, the distance on the coordinate system between the centers of adjacent cell areas 91 is 1.

As shown in Figure 8, the distance d between adjacent cell regions 91, 91 should be 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 for an indentation test to be performed on another cell region 91b (a cell region 91 that may be the target of the next indentation test) adjacent to a cell region 91a where an indentation test has already been performed, without being affected by the indentation P of the cell region 91a. "Being affected by the indentation P" means that when performing an indentation test on a certain cell region 91b, the indenter 2 will press into the area overlapping with and immediately adjacent to the area of the indentation P of the cell region 91a where an indentation test has already been performed, 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 avoids the effects of previous indentation tests that may remain near the outside of the indentation mark P.

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

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 using a predetermined procedure described below, controls the measurement unit 11, lifting device 51, and 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 in the memory unit 19 as mapping data. 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 it in the memory unit 19 as mapping data may be simply referred to as a measurement cycle.

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, including the testing 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.

That is, the control unit 10 acquires (calculates) a prediction function (hereinafter sometimes simply referred to as a prediction function) using 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 the mapping result (an example of an output process). The control unit 10 may store this prediction function in the memory unit 19 as an output of the mapping result.

Improvement of the accuracy of the mapping results 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 that includes a position determination process in which Bayesian optimization is performed to determine the next search point.

In this embodiment, Bayesian optimization involves obtaining a prediction function for a specified characteristic using Gaussian process regression, creating an acquisition function that represents the likelihood of improving on the previous optimal value (the coordinate in the measurement area 90 that is currently predicted to be the best for the specified characteristic), and determining the coordinate (an example of a position) in the measurement area 90 where the value of the acquisition function is maximized, i.e., a tentative search point.

Prediction functions are obtained using previously acquired mapping data. Various kernels can be used to obtain prediction functions using the control unit 10, depending on the purpose of the indentation mapping and the characteristics of the sample 9 (see Figure 1).

The coordinates at which the value of the acquisition function to be used as a temporary search point is maximized may be determined using the GP-UCB algorithm, for example, using the following formula:

Here, _xt is the coordinate (temporary search point) where the value of the acquisition function is maximized, and is not necessarily an integer coordinate. _μt-1 is an expected value, and its value increases in locations close to the provisional optimal solution (maximum or minimum value for a specified characteristic). σt _-1 is the standard deviation, and its value increases in locations where profile acquisition is insufficient. _βt is a parameter that determines the trade-off between exploration and exploitation, and is preferably set to a value between 2 and 6.

The control unit 10 then excludes cell areas 91 (hereinafter referred to as adjacent cells) that contain or are adjacent to the tentative search point from those that have already undergone indentation testing, selects the cell area 91 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 contains the tentative search point as the next search point, but if the cell area 91 that contains 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 has not undergone indentation testing as the next search point.

Here, it is possible to initially subdivide the measurement target area 90 to define cell areas 91, and then sequentially acquire profiles for each subdivided cell area 91 to perform indentation mapping. However, subdividing the cell area 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 on positions away from the area with the specified characteristics does not lead to the identification of the area with 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 area into cell areas 91 from the beginning and performing indentation mapping, the control unit 10 performs rough mapping to identify areas where areas with the specified characteristics are likely to exist, and then sequentially narrows down the measurement target area 90.

First, as shown in FIG. 9, the control unit 10 defines a measurement target area 90A (e.g., 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 multiple cell areas 91A are indicated by dashed lines.

Next, the measurement target area 90A is mapped by repeating a number of measurement cycles to identify an area (hereinafter referred to as the candidate area) where a portion with the specified characteristics is likely to exist. In Figure 9, the candidate area is indicated by a dashed line. The control unit 10 then updates (reduces) the current measurement target area 90 to the new measurement target area 90 by defining an area that includes the candidate area but is smaller than the measurement target area 90A as the new measurement target area 90B (see Figures 9 and 10). 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 Figures 9 and 10, open circles indicate the centers of cell areas 91 for which profiles have already been acquired, i.e., cell areas 91 that have been determined as search points and have undergone indentation testing (hereinafter referred to as searched cells). In this embodiment, for example, an area where the most recently searched cells are adjacent (e.g., 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). Measurement target area 90B may have an area that is, for example, one-third to one-fifth the area of 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 mapping throughput.

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 control unit 10 updates (reduces) the cell area 91 (cell area 91A) to a cell area 91 (cell area 91B) smaller than the current area. For example, the cell area 91B may have an area equal to an integer fraction of the cell area 91A; FIG. 10 shows a case where the cell area 91B is one-fourth the current area. Hereinafter, updating the cell area 91 to a cell area 91 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. Furthermore, some of the cell areas 91A among the multiple cell areas 91A are indicated by dashed lines. Also, some of the multiple cell areas 91B are indicated by dashed lines. When updating a cell, it is recommended that the center of the cell area 91 before the update overlaps with the center of the cell area 91 after the update.

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 the cell area 91 of measurement target area 90C, is narrower than cell area 91B. As mentioned above, cell area 91B is narrower than cell area 91A.

Note that Figure 11 shows only a portion of cell areas 91A, 91B, and 91C for the purpose of explanation. Also, in Figure 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.

Note that the cell renewal is performed while maintaining the relationship that the distance d between the renewed cell regions 91, 91 is greater than the maximum width r of the portion where the indenter 2 contacts the surface of the sample 9, as shown in Figure 8.

When updating the cell, in order to maintain the relationship that the distance d between the updated cell areas 91, 91 is greater than the maximum width r of the portion where the indenter 2 contacts the surface of the sample 9, it is advisable to determine the end point of the cell update in advance.

As the end point for cell updates, it is advisable to predetermine, for example, the size of the smallest cell area 91 after cell updates or the range of the size of the smallest cell area 91 after cell updates (an example of a predetermine size; hereinafter, the size of the smallest cell area 91 and the range of the smallest cell area 91 sizes are collectively referred to as the minimum cell size). Then, updates to the measurement target area and cells can be allowed until the updated cell area 91 reaches the minimum cell size. In other words, updates are allowed if the current cell area 91 exceeds the minimum cell size, and are not allowed if the current cell area 91 is the minimum cell size. In Figure 11, each intersection of the thin-line grid shown in the measurement target area 90A indicates the center of area 91X when the measurement target area 90A is divided into the smallest cell areas 91 after cell updates. In the example shown in Figure 11, area 91X is the same size as cell area 91C, and no further updates to the measurement target area or cells can be performed for measurement target area 90C and cell area 91C.

(Indentation mapping flow)
Below, 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.

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 executes a division process to divide the measurement target area 90 into multiple cell areas 91, and then proceeds to step S2.

In step S2, the control unit 10 executes a position determination process to determine cell areas 91 to be used as search points from among the multiple cell areas 91. In step S2, as shown in FIG. 13, if no mapping data exists in the memory unit 19 (step 21, No), an initial position determination process is executed to determine three or more predetermined cell areas 91 (e.g., five) from among the multiple cell areas 91 as initial search points (step 22), and step S2 is terminated. Note that 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.

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.

7 as an example, when only the profiles of three cells _Q1 , _Q2 , and _Q3 as a cell region 91 are stored as mapping data in the memory unit 19, and when a provisional search point _q4 is determined as the coordinate at which the value of the acquisition function by Bayesian optimization is maximized based on this mapping data, the control unit 10 determines cell _Q4 as a cell region 91 including provisional search point _q4 as the next search point. When the profiles of cells _Q1 to Qm _-1 are stored as mapping data in the memory unit 19, and when a provisional search point _qm is determined as the coordinate at which the value of the acquisition function by Bayesian optimization is maximized based on this mapping data, the control unit 10 selects cell Qm as the next search point from the remaining adjacent cells, excluding cell _Q2 for _which an indentation test has already been performed, and determines this _{cell Qm} as the next search point (where m is an integer of 4 or greater). The distance between the provisional search point qm and the cell area 91 is the straight-line distance between the provisional 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.

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

Once step S2 is completed, proceed to step S3.

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 4.

In step S4, the control unit 10 executes a region update determination process to determine whether the update conditions for the measurement target region 90 are met. In the region update determination process, 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 processes (step S2) are adjacent or overlapping, it is determined that the update conditions are met (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 processes (step S2) are not adjacent, it is determined that the update conditions are not met, and the process returns to step S2 (step S4, No).

Here, a cell region 91 is adjacent to another cell region 91 when the other cell region 91 is one of the eight cells surrounding the cell region 91. Furthermore, when cell regions 91 containing positions predicted to have the maximum or minimum expected value derived in each of the most recent two or more Gaussian process regressions overlap, this 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.

In step S4, the prerequisite for determining that the update conditions for the measurement target area 90 are met may be that step S2 has been performed a predetermined number of times (e.g., 10 times) for the current measurement target area 90. This may improve the accuracy of the mapping.

In step S5, the control unit 10 executes a cell update determination process to determine whether the cell area 91 has reached the minimum cell size. If the cell area 91 has not reached the minimum cell size, i.e., if the cell area 91 exceeds the minimum cell size (step S5, No), the process proceeds to step S6. If the cell area 91 has reached the minimum cell size (step S5, Yes), the process proceeds to step S7.

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

In step S7, the control unit 10 executes a termination determination step to determine whether the mapping termination condition is met. If it is determined that the mapping termination condition is met (step S7, YES), the control unit 10 terminates the mapping. If it is determined that the mapping termination condition is not met (step S7, NO), the control unit 10 proceeds to step S8.

In this embodiment, an example of the condition for terminating the mapping in step 7 is when cell areas 91 containing 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 process) overlap. In other words, the control unit 10 may determine that the condition for terminating the mapping is met when cell areas 91 containing 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 process) overlap.

In step S7, the termination condition for mapping may be whether step S8, described below, has been performed at least once. In this case, the termination condition for mapping may also be whether the cell regions 91 containing 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.

That is, as shown in FIG. 14, in step S7, it is first determined whether step S8 has been executed at least once (step S71). 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).

If step S8 has been executed at least once (step S71, YES), proceed to step S73.

In step S73, it is determined whether the cell areas 91 containing the positions predicted to have the maximum or minimum expected values derived in each of the three most recent Gaussian 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, terminating the mapping (see Figure 12). If they do not overlap (step S73, No), the process proceeds to step S72.

In step S7, the prerequisite for determining that the mapping termination condition is met may be that 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 area 90. This may improve the accuracy of the mapping.

In addition, in step S7, the control unit 10 may determine that the mapping termination condition is met not only when cell areas 91 containing 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 process) overlap, but also when the termination determination process (step S7) has already been performed three times, i.e., when the pre-termination measurement process (step S8) has already been performed three times. In this way, it is possible to avoid unnecessarily increasing the measurement cycle during mapping.

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 a pre-termination 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 2.

The cell area 91 selected in step S8 may be selected from the cell areas 91 adjacent to the cell area 91 that was set as the search point in the immediately preceding step 2. In this case, searched cells are excluded from the cell areas 91 selected in step S8. The cell area 91 adjacent to 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 the mapping.

By using the mapping method described above, the number of measurement cycles required to identify regions with specified characteristics can be significantly reduced (for example, to one-hundredth of the number required) compared to conventional methods (full-scale testing). 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 specified characteristics can be reduced by approximately half. In other words, updating (reducing) the measurement target region takes advantage of the comprehensive search performance 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 rough mapping to get a rough idea), and then enables highly accurate search of regions where regions with specified characteristics are likely to exist, thereby improving mapping accuracy. These improvements enable high throughput while improving mapping accuracy.

In this way, a high-throughput indentation mapping device and mapping method can be provided.

[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 pressed into and pulled back from the surface of the sample 9,
Although the case where the indenter 2 is pressed to a predetermined depth has been described as an example, the profile can also be obtained when the indenter 2 is pressed until the load acting on the indenter 2 reaches a predetermined magnitude.

(2) In the above embodiment, the measurement target area 90 is described as being a square area, but the measurement target area 90 may also 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.

(3) In the above embodiment, the case was described 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. However, distance d1 and distance d2 only need to 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 distance d1 and distance d2 is fully acceptable. Distances d1 and d2 should be set so as to avoid the influence of indentation P. They may also be set wide enough as long as the accuracy of the mapping results is not reduced. If you want to maximize the accuracy of the mapping results, you should set them narrower.

(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.

For example, in the above embodiment, the region update determination process describes a case in which the update condition is determined to be satisfied when cell regions 91 containing positions predicted to have the maximum or minimum expected value derived in each of the three Gaussian process regressions in the current, previous, and second-to-last position determination processes are adjacent to or overlapping each other. However, the conditions for determining that the update condition is satisfied are not limited to this. For example, the conditions may be defined such that, for positions predicted to have the maximum or minimum expected value derived in each of the Gaussian process regressions, the update condition is determined to be satisfied when the coordinate distance between the current and previous positions is within √2 and the coordinate distance between the previous and previous-previous positions is within √2. In other words, the update condition in the region update determination process may be determined based on the positional relationship in the coordinates, or may be determined based on the positional relationship between the cell regions 91.

In the above embodiment, an example of a condition for terminating mapping in the termination determination step is described as a case where cell areas 91 containing 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, a condition for terminating mapping can 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 in the coordinate system, or based on the positional relationship between cell areas 91.

(5) In the above embodiment, the control unit 10 excludes cell areas 91 that have already undergone indentation testing from 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 a cell area 91 that has already undergone indentation testing, the measurement process may be omitted.

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 that no contradictions arise. Furthermore, the embodiments disclosed in this specification are merely examples, and the present invention is not limited to these embodiments. They can be modified as appropriate within the scope of the purpose of the present invention.

The present invention can be applied to mapping methods and indentation mapping devices.

DESCRIPTION OF SYMBOLS 1: Control device 2: Indenter 3: Stage 4: Base 5: Support 9: Sample 10: Control unit 11: Measurement unit 19: Memory unit 21: Indenter support unit 41: Slide mechanism 51: Elevating device 52: Elevating mechanism 53: Position sensor 54: Load sensor 90: Measurement target 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 _Qm : Cell Qm _-1 : Cell h: Depth d: Spacing d1: Spacing d2: Spacing q4: Temporary search point qm: Temporary search point r: Width

Claims (14)

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. The mapping method described in 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. The mapping method described in claim 1 or 2 further includes 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. 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. 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. The mapping method described in claim 5, wherein the termination determination step determines that the termination condition for mapping is met if the positions at which the expected value is maximized or minimized, derived in each of the most recent two or more Bayesian optimizations performed in the position determination step, are adjacent or overlapping. 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. The mapping method described in any one of claims 1 to 7, wherein the measurement step includes an indentation test step of performing an indentation test in which an indenter is pressed into the sample surface to measure the compressive load acting on the indenter and the indentation depth of the indenter as the information. The mapping method described in claim 8, wherein the dividing step divides the cell regions so that the spacing between the cell regions is greater than the width of the portion where the indenter contacts the sample surface when the indenter is pressed. 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. 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. 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. 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. 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.