JP2019056587A - Measuring method using particle beam and measurement system - Google Patents

Abstract

To provide a measuring method using a particle beam capable of reducing time required for particle beam irradiation in a particle beam experiment.SOLUTION: A measuring method using a particle beam comprises the steps of: irradiating a sample with a particle beam; counting the number of measurement object particles obtained by irradiation; calculating a distribution of the measurement object particles for evaluating the sample by using the distribution of the measurement object particles while assuming that the measurement object particles in a manner of a smooth probability in a density distribution; performing a statistical test on the assumption that the distribution matches a true probability density distribution; and, when the assumption matches, terminating the irradiation of the particle beam.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a measurement method and a measurement system using a particle beam.

  Scattering experiments using particle beams are widely used as a method for measuring or observing the microstructure of materials, mainly in the field of materials science. The particle beam here means proton beam (α beam), electron beam (β beam), muon beam, photon beam (that is, electromagnetic wave, γ beam, X ray, visible light, infrared ray, etc.), neutron beam, neutrino beam, etc. Point. When these particle beams are irradiated onto a sample such as a metal, phenomena such as reflection, transmission, and scattering of the particle beam by the sample can be observed.

  Here, the output of reflected, transmitted or scattered particle beams (hereinafter sometimes referred to as “particles to be measured”. Particles different from the incident particles may be output) may be output electrically, chemically or mechanically. In the particle beam experiment, measurement is performed by a simple detector and the fine structure of the sample is estimated from the distribution shape of the intensity (for example, the number of particles to be measured). As a similar method, the same measurement is performed using an electron beam with a known scanning or transmission electron microscope, and the fine structure of the sample is imaged.

  On the other hand, in recent years, with the development of statistical processing techniques for data analysis, there is an increasing demand for data analysis in materials science. For example, by applying statistical data analysis to the measurement results of particle beam experiments, new discoveries are expected, but in order to do so, a lot of data of at least tens to hundreds of scales must be obtained. However, in the scattering experiment, in order to obtain a clear scattering result image to some extent, the number of detections of the output particles must be sufficiently large, and it is necessary to continue irradiating the particles for a long time. As a result, it takes a very long time to measure to the extent that statistical processing is applied.

  For example, if it is necessary to measure about 20 minutes at a time and 100 types of data are to be acquired, the device must be occupied for about a day and a half. Many experimental devices are expensive, and if they are occupied for a long time, there is a problem that the cost becomes high and the power consumption increases.

International Publication WO2005 / 106440

  In order to obtain data enough to be subjected to statistical data analysis, a long experiment is required. However, considering the cost, it is desirable to minimize the particle beam irradiation time.

  In Patent Document 1, measurement is started after setting measurement conditions for a sample, and the measurement concentration and measurement accuracy of an element contained in the sample are calculated. This measurement accuracy satisfies a predetermined measurement condition. An X-ray irradiation apparatus is disclosed that is configured to end measurement when a value is reached and output the concentration at that time. According to this method, it is possible to avoid taking more measurement time than necessary. However, although depending on the field, the time required for measurement is often empirically known, and it is difficult to expect that the time will be greatly reduced by the termination of Patent Document 1.

  One aspect of the present invention is the probability that a particle to be measured is smooth when the sample is irradiated with a particle beam, the number of particles to be measured obtained by irradiation is counted, and the sample is evaluated using the distribution of the particles to be measured. Obtain the distribution assuming that it appears according to the density distribution, perform a statistical test on the hypothesis that the distribution matches the true probability density distribution, and if the hypothesis matches, terminate the particle beam irradiation. Is a measurement method using a particle beam characterized by Here, “smooth” means that the probability density distribution function is differentiable with respect to the variable and the differential function is continuous.

  Another aspect of the present invention is a measurement system that receives experimental data related to the distribution of particles to be measured obtained by irradiation of a particle beam on a sample and controls irradiation of the particle beam. This system includes a storage device, an experimental data collection unit for storing density distribution data based on experimental data in the storage device in a time series, and estimates a continuous probability density distribution in a time series based on the density distribution data. A continuous distribution estimation unit, a probability density distribution itself, and a statistical test determination unit that evaluates at least one of the physical quantities obtained from the probability density distribution and determines the continuation or termination of particle beam irradiation based on the evaluation result And comprising.

  According to the present invention, the experiment can be completed in a short time, and more experiments can be performed with one experimental facility.

The block diagram which shows the structure outline of Example 1. FIG. 2 is a block diagram illustrating an example of a configuration of physical implementation in the first embodiment. Conceptual diagram showing an example of particle beam scattering experiment Conceptual block diagram of the overall operation of the first embodiment Conceptual diagram of the detection result of the scattering experiment of Example 1 Table showing an example of the data structure of the detection result of the first embodiment Table showing an example of a data structure stored in the experimental data storage unit of the first embodiment FIG. 3 is a flowchart illustrating an example of continuous distribution estimation processing according to the first embodiment. The table figure which shows an example of the data structure which records the result of the continuous distribution estimation process of Example 1 The flowchart which shows an example of the statistical determination procedure of Example 1. The graph figure explaining an example of the meaning of the statistical determination of Example 1 The graph which shows the model example which shows the behavior of the continuous distribution of Example 1. FIG. FIG. 5 is a flowchart showing an example of a statistical determination procedure according to the second embodiment. Conceptual diagram showing an example of physical quantity calculation used in the statistical determination procedure of the second embodiment FIG. 9 is a flowchart showing an example of a statistical determination procedure according to the third embodiment. Conceptual explanatory diagram of an example of continuous distribution estimation processing used in the third embodiment Flow chart showing an example of continuous distribution estimation processing of the fourth embodiment Flow chart showing an example of a statistical determination procedure of the fourth embodiment

  Embodiments will be described in detail with reference to the drawings. However, the present invention is not construed as being limited to the description of the embodiments below. Those skilled in the art will readily understand that the specific configuration can be changed without departing from the spirit or the spirit of the present invention.

  In the structures of the invention described below, the same portions or portions having similar functions are denoted by the same reference numerals in different drawings, and redundant description may be omitted.

  In the case where there are a plurality of elements having the same or similar functions, the same reference numerals may be given with different subscripts. However, when there is no need to distinguish between a plurality of elements, the description may be omitted.

  The position, size, shape, range, and the like of each component illustrated in the drawings and the like may not represent the actual position, size, shape, range, or the like in order to facilitate understanding of the invention. For this reason, the present invention is not necessarily limited to the position, size, shape, range, and the like disclosed in the drawings and the like.

  In an example of the embodiment described in detail below, in an experimental apparatus that irradiates a sample with a particle beam and counts the number of particles scattered by the irradiation, the distribution of the number of scattered particles is assumed to be a smooth distribution. Based on the above, the validity of the estimated distribution is statistically tested. If the test passes, the particle beam irradiation is discontinued. In the statistical test, the validity is determined based on whether or not the estimated distribution can be regarded as substantially equivalent to the true distribution (distribution obtained by an infinite irradiation time). Specifically, changes over time, change rates, variations, etc. of the estimated distribution or parameters derived from the estimated distribution are evaluated. In general, when these values are equal to or less than a predetermined threshold, it can be evaluated that the fluctuations in the distribution converge and approach the true distribution. According to this configuration, in the apparatus for performing the particle beam scattering experiment, the experiment can be completed in a short time, and more experiments can be performed with one experimental facility. Hereinafter, several embodiments including specific variations of the distribution estimation method and the distribution determination method will be described.

  FIG. 1 shows a schematic configuration of a particle beam experiment system according to the first embodiment of the present invention. The particle beam experiment system of the present embodiment is a system including a particle beam experiment apparatus (101) and an experiment result verification apparatus (102).

  The particle beam experimental device (101) is a device that has the function of irradiating a sample with a particle beam and outputting the result of scattering, and the experimental result verification device (102) mainly receives the output of the particle beam experimental device (101). This is a device having a function of performing statistical processing and determining whether or not to continue the experiment.

  The particle beam experiment apparatus (101) includes at least an experiment control unit (111) that controls injection of particle beams, a particle beam experiment unit (112) that actually generates particle beams and detects scattering results, and a particle beam experiment unit (112 ) Is a device having an experimental data processing unit (113) that outputs the detection result as data.

  The experimental result verification device (102) includes an experimental data collection unit (121) that receives the output of the experimental data processing unit (113), a spatially continuous distribution assumed from the result data of the scattering experiment (simply referred to as a continuous distribution). A continuous distribution estimation unit (122) that estimates the statistical distribution of the calculated continuous distribution, and an experimental data storage unit that stores data related to the experiment (123) 124). In this specification and the like, the term “continuous” is used when expressing continuity in the real space and also when expressing continuity in the parameter space.

  FIG. 2 shows an example of a configuration of physical mounting according to the first embodiment. This configuration shows a physical configuration corresponding to the configuration of FIG.

  The particle beam experimental device (101) includes a processor (201) with computing performance, a memory (202) such as DRAM (Dynamic Random Access Memory), which is a volatile temporary storage area that can be read and written at high speed, and an HDD (Hard Disk). Drive) and storage device (203), which is a permanent storage area using flash memory, etc., mouse and keyboard for operation, input device (204) such as control panel, and the results and experimental status A communication interface (206) such as a monitor (205) for showing to the user and a serial port for communicating with the outside. These portions correspond to the experiment control unit 1 (111) and the experiment data processing unit (113) in FIG. 1, but can be configured using a general computer.

  In addition, the particle beam experiment apparatus (101) includes a particle beam generation source (207) for generating particle beams, a sample holder (208) for setting a sample and allowing the particle beam to strike, and particles for detecting scattered results. A line detector (209) is provided. These parts correspond to the particle beam experimental part (112) of FIG.

  In the experimental control unit (111) and the experimental data processing unit (113) of the particle beam experimental apparatus (101) shown in FIG. 1, the processor (201) executes the program recorded in the storage device (203) shown in FIG. Can be realized.

  Further, the particle beam experiment section (112) shown in FIG. 1 makes the particle beam generated by the particle beam generation source (207) shown in FIG. 2 strike the sample set in the sample holder (208), and the scattering result is obtained. It can be implemented by installing the particle beam detector (209) for measurement. As described above, there are various types of particle beams generated from the particle beam generation source (207), such as α rays, β rays, and neutron rays. The particle beam detector (209) may employ various known configurations using electrical, chemical, or mechanical principles as described above.

  Further, this embodiment is an example, and the function of adjusting the focal point of the particle beam as in a known electron microscope or the like, and how to scatter by moving the sample holder (208) or the particle beam generation source (207). It may have a function that can be changed.

  The experimental result verification apparatus (102) can be implemented using a general computer. That is, a processor (211) with computing performance, a memory (212) such as a DRAM that is a volatile temporary storage area that can be read and written at high speed, and a storage device that is a permanent storage area using an HDD, flash memory, etc. (213), an input device (214) such as a mouse and a keyboard for operation, a monitor (215) for indicating the operation to the user, and a communication interface (216) such as a serial port for communicating with the outside It is a device including.

  The experimental data collection unit (121), continuous distribution estimation unit (122), and statistical test determination unit (123) shown in FIG. 1 are stored in the storage device (213) shown in FIG. It can be realized by executing. The experimental data storage unit (124) shown in FIG. 1 can be implemented by the processor (211) executing a program for storing data in the storage device (213).

  FIG. 3 shows a conceptual diagram of the particle beam experiment assumed in the first embodiment. In this figure, the particle beam (302) generated from the radiation source (301) included in the particle beam generation source (207) is irradiated to the sample (303) fixed by the sample holder (208). Yes. As a result, the particle beam that has passed through the sample (303) is detected by a plate-shaped detection device (304) in which a plurality of particle beam detectors (209) are spread in a plane.

  When detected, the particle beam (302) at the time of incidence is scattered by interference with the sample (303), and for example, a circular scattering pattern (305) is formed on the detection device (304). This scattering pattern (305) contains information related to the microstructure of the sample, and post-processing is applied to the scattering pattern (305) to provide physical quantities related to the microstructure of the sample (for example, the distribution of metal atoms in the alloy). Etc.) can be calculated.

  The above measurement technique is known as a particle beam scattering experiment. Various techniques are known. For example, neutrons, which are particles that make up matter, have excellent penetrating power and spin properties, and therefore exert a force on the magnetic field (magnetic moment) created by the nucleus in the center of the atom and the electrons around it. There is an experimental method that uses this property to apply a neutron beam to a substance, measure the scattering method (change in direction, speed, spin direction), and know the arrangement of atoms and magnetic moments in the substance and the state of motion. This is known as a neutron scattering experiment.

  In Example 1, neutron beams are mainly handled as particle beams. However, the irradiated particle beam may be any particle beam such as a photon (γ-ray, X-ray), electron, proton, etc. Even if it has special properties, such as Further, the sample holder (208) may be moved so that a similar pattern can be obtained. In addition, although Example 1 targeted the pattern of the intensity | strength of the scattered particle | grains in the two-dimensional space, the apparatus which performs one-dimensional thru | or three-dimensional pattern measurement may be used, and distribution of energy etc. was added. By preparing a measuring means, it can be extended to an arbitrary dimension.

  FIG. 4 schematically shows the overall operation of the system according to the first embodiment. In this outline, the particle beam experimental device (101) mainly performs the experiment, and the result is received by the experimental result verification device (102) to test the continuous distribution of the scattering pattern and to the particle beam experimental device (101). The procedure is to instruct whether or not to continue the experiment. Hereinafter, specific operations will be described below.

  When the experiment is started, the experiment control unit (111) instructs the particle beam experiment unit (112) to irradiate the particle beam (S401). The particle beam experiment unit (112) receiving it starts particle beam irradiation and particle number counting by the particle beam detector (209) (S402). This experiment is performed in a predetermined sufficiently short time such as 1 minute. The experiment data processing unit (113) converts the measurement result of the detector into data as the experiment time ends (S403).

  FIG. 5 shows a conceptual diagram of measurement results obtained by the particle beam experiment section (112). In the figure, rectangles (501) are arranged in a grid pattern, but these rectangles (501) mean each of the particle beam detectors (209). A detection device (304) is configured by the entire configured grid. The numerical value in the rectangle means the number of particles counted by the particle beam detector (209).

  The scattering pattern (305) looks like this grid-like circle (502), and the count near the center of the circle tends to decrease with increasing number of counts. Since this data is expressed as a kind of image, hereinafter, this count is referred to as an image and is referred to as a luminance value. The experimental data processing unit (113) converts this count number into data that can be output.

  FIG. 6 shows the format of one record of data generated by the experimental data processing unit (113). The experiment ID (601) is an identifier for a case where a plurality of experiments are performed, and is uniquely assigned using the experiment start time and the like. For example, “January 1, 2017 00:00:00”. The experiment period (602) indicates the period during which the experiment was performed, and describes the absolute time obtained using the clock inside the particle beam experiment apparatus (101) and the elapsed time with the experiment start set to zero. For example, “00 minutes 00 seconds to 01 minutes 00 seconds”. Then, the detector ID (603) of the particle beam detector (209) is recorded so as to correspond to the count number (604). Using this data as one record, a set of records related to all particle beam detectors (209) is the result of the experiment.

  The experimental data processing unit (113) outputs the data of FIG. 6 to the outside of the particle beam experimental apparatus (101) through the communication I / F (206). Returning to FIG. 4, the procedure after the output will be described. The output of the experimental data processing unit (113) is received by the experimental data collection unit (121) of the experimental result verification device (102) and stored as experimental data in the experimental data storage unit (124) (S404).

  FIG. 7 shows the configuration of one record of experimental data stored in the experimental data storage unit (124). In the experiment data storage unit (124), the scattering pattern is managed as image-like data. Among the configurations shown in FIG. 6, the experiment ID (601) and the count number (604) are set to the experiment ID (701) and the count number (705). In the experiment period (602), the data ID (702) is an identifier of the image, and the detector ID (603) of the particle beam detector (209) is the X and Y coordinates (703,704) based on the installation coordinates. Is converted to With this data as one record, a set of records related to all particle beam detectors (209) corresponds to one image-like data.

  Returning to FIG. 4 again, the subsequent procedure will be described. When the experimental data collection unit (121) stores the data of FIG. 7 as the measurement result in the experimental data storage unit (124) (S404), the continuous distribution estimation unit (122) is identical to the experimental data storage unit (124). All past data having the experiment ID (701) is acquired, and a continuous distribution estimation process for estimating a continuous distribution is executed based on the acquired past data (S405).

  FIG. 8 shows an outline of the continuous distribution estimation process (S405). In the continuous distribution estimation process (S405), the continuous distribution estimation unit (122) uses the data accumulated in the experimental data accumulation unit (124) to determine the relationship between the X and Y coordinates (703,704) and the count number (705). A process for obtaining a continuous distribution function is performed.

In this process, first, the experiment ID (701) is used as a key, and (x, y) is associated with the count value. At this time, count values may be summed for records having the same (x, y) across a plurality of data IDs (702). That is, for example, according to a table datatable in which the experiment ID (701) is named expid, the data ID (702) is dataid, the X coordinate (703), the Y coordinate (704) are x, y, and the count number (705) is c. Assuming a relational database to be managed, this aggregation is described by the following SQL statement.
select expid, x, y, sum (c) as c from datatable
where expid = [ID of this experiment] group by x, y

  The count number (705) for each data ID (702) is for a predetermined short time, but is converted into data corresponding to the accumulated value of the experiment so far by this calculation. Thereby, the read past data is aggregated so as to be (x, y, luminance) (S801). The luminance corresponds to the count number. Thereby, since the number of data decreases, the time required for calculation is shortened. Here, as the data acquired from the experimental data storage unit (124), the stored output of the previous continuous distribution estimation unit (122) may be acquired and the previous accumulated value may be used. . That is, the amount of calculation may be reduced by adding the latest count value to the previous accumulated value to obtain the latest accumulated value.

  Next, the continuous distribution estimation unit (122) estimates a continuous distribution function (a distribution function continuous at all points in the domain) using the data (S802). That is, the continuous distribution function is estimated on the assumption that the number of scattered particles indicated by the count value as shown in FIG. 5 has a smooth distribution. In this embodiment, a continuous distribution function f with luminance = f (x, y) is obtained by regression analysis.

  In this estimation, a regression analysis method for estimating a known general-purpose non-linear continuous function can be used. Specific examples include Gaussian process regression and support vector regression. Regression analysis uses a method of learning the relationship between explanatory variables and objective variables from examples. For example, assuming a continuous distribution function f with `` objective variable = f (explanatory variable) '' between the explanatory variable and the objective variable, the error `` the objective variable of the actual data-f (explanation of the actual data) The parameter of the continuous distribution function f is determined so that the sum of “variable” ”is minimized.

  In the first embodiment, the distribution can be determined by performing regression analysis using the X coordinate (703) and the Y coordinate (704) as explanatory variables and the count number (705) as an objective variable. At this time, by dividing the function by the total number of counts, the influence of the irradiation time of the particle beam in the experiment, that is, the tendency that the number of detections increases in proportion to the time of the experiment can be offset. In addition, when the fluctuation | variation of probability distribution is estimated, a precision can be improved by using the regression analysis which considered it.

  As a result, the estimation result of the continuous distribution function becomes a set of parameters that determine the continuous distribution. The continuous distribution estimation unit (122) stores this in the experimental data storage unit (124).

  FIG. 9 shows the structure of one record of accumulated data. This data includes the experiment ID (901) inherited from the experiment ID (701) of FIG. 7, the number of data IDs (702) used for estimation of the continuous distribution, that is, the number of distribution calculations (902) representing the measurement time length, parameters A set of name (903) and parameter value (904) is stored. With this data as one record, a set of records related to all parameter names (903) necessary for expressing the continuous distribution corresponds to the continuous distribution.

For example, when using the well-known Gaussian process regression, the continuous distribution function is described as a superposition using the positive definite kernel function k ((x1, y1), (x2, y2)) indicating the correlation between two points. Is done. That means

f (x, y) = ΣG _i × k ((x, y), (x _i , y _i ))

Can be written. Here, Gi is a parameter relating to the i-th coordinate (xi, yi), and (xi, yi) means an explanatory variable of actual data, that is, the position of a grid-like detector. Gi is a numerical value obtained from the measured count, and is a value obtained by the regression analysis. By storing this Gi in the form of parameter name (903) and parameter value (904), the continuous distribution obtained by regression analysis can be reproduced. With the above processing, the scattering particle distribution is estimated on the assumption that the scattering particles to be measured appear according to a smooth probability density distribution.

  Returning to FIG. 4 again, continuous distribution reliability evaluation (S406), which is processing in the next statistical test determination unit (123), will be described. The statistical test / determination unit (123) uses all of the continuous distribution data (FIG. 9) calculated by the continuous distribution estimation unit (122) stored in the experimental data storage unit (124). Determine if the time is sufficient assuming continuous distribution estimation. The determination uses the statistical reliability of the continuous distribution, that is, “the degree to which the continuous distribution obtained in the future can change when the experiment is continued”. In other words, even if the experiment is continued in the future, if the estimated continuous distribution does not change, it can be said that it is not necessary to continue the experiment. The process for performing the evaluation is continuous distribution reliability evaluation (S406). In the continuous distribution reliability evaluation (S406), a statistical test is performed on a hypothesis that the distribution estimated in the continuous distribution estimation process (S405) matches the true probability density distribution.

  The continuous distribution reliability evaluation (S406) will be described with reference to FIG. In the continuous distribution reliability evaluation (S406) of the first embodiment, the validity of the experimental result is determined by evaluating the past estimation result in time series. First, continuous distribution parameters are acquired as a series by acquiring the results of continuous distribution estimation within the same experiment ID from the experimental data storage unit (124), and the continuous distribution is reproduced (S1001).

Next, the similarity between the latest distribution and the distribution is calculated for each reproduced continuous distribution (S1002). This similarity is simply the sum of squares of the grid-point difference,

S = Σ [(f _m (x, y)-f _n (x, y)) ² ÷ σ (x, y) ² ]

Can be used. Note that fm means the continuous distribution to be evaluated, and fn means the latest continuous distribution. In the Gaussian process regression, the variance at each point (x, y), that is, “the expected value of the true value estimated from the current measured value and its statistical fluctuation” can be expressed by a Gaussian distribution. Therefore, a significant difference test in a normal distribution can be performed. In other words, in relation to the above formula, if (fm (x, y) -fn (x, y)) ^ 2 <σ (x, y) ^ 2, it is within the error 1σ range. . Therefore, the statistical validity can be evaluated at a predetermined significance level (depending on the accuracy required by the experiment, for example, 3σ). In addition, any method can be used as long as it is a method that can statistically evaluate the identity between the immediately preceding continuous distribution and the latest continuous distribution, such as using a known amount of information of the Cullback / Librer.

  Next, the degree of change of the similarity S is confirmed (S1003). If there is no change (or the most recent change rate of similarity is below a threshold), it can be said that this experiment has sufficiently converged (S1004). If it still seems to have changed significantly, the experiment has not yet converged (S1005). Therefore, it can be determined whether or not the continuous distribution calculated from the current data can be trusted. In this process, for example, a threshold value is set, and it can be determined whether or not the most recent change rate of similarity is equal to or less than the threshold value (S1003). If the change rate of the threshold is equal to or less than the threshold, the experiment is terminated assuming that the current estimation result is reliable (S1004). If it is not less than the threshold value, the experiment is continued because the current estimation result is not reliable (S1005).

  FIG. 11 shows a schematic diagram thereof. The figure is a graph of the time change regarding the similarity of the continuous distribution. The vertical axis represents the average value of the relative differences in the continuous distribution, and the horizontal axis represents the elapsed time. In the initial period (1101) of the experiment, the result of the experiment is not stable. However, in the section (1102) after sufficient experiment time has passed, the difference in distribution becomes smaller and the change becomes stable. Therefore, the statistical validity can be evaluated by looking at the rate of change in similarity.

  FIG. 12 shows an example of a distribution for explaining the principle of this change. This graph shows the distribution of count numbers, and originally shows a two-dimensional x and y cross section (one dimension) for simplicity. The upper graph (1201) is a graph before sufficient time has passed. Until enough time has passed, the number of particles detected by each detector will be a small number such as 1, 2, 3, etc. Therefore, there are only a few steps in which the relative frequency is extremely large or small. Therefore, the unevenness of the distribution is severe and it is not statistically stable. Even if the continuous distribution is estimated by applying regression analysis to it in the continuous distribution estimation process (S405), the line will be drawn according to the intense unevenness as shown by the broken line in the figure, so it will vary greatly each time the experiment is performed. .

  On the other hand, the graph when sufficient time has elapsed is the graph (1202) below. After a large number of particles are counted, the relative frequency has a sufficiently large number of stages, so that the estimated slope of the continuous distribution is expressed smoothly. In addition, the stability increases statistically, and even if new data is added, it does not change greatly. Specifically, since only the number of current measurements / the total number of measurements so far is increased or decreased, the distribution of relative frequencies does not change as the total number of measurements so far increases. Therefore, the value of the result of taking the difference and taking the sum of squares gradually decreases. Since the distribution is zero when the distributions are exactly the same, the graph is as shown in FIG. 11, and as a result, no change occurs in the estimated continuous distribution in the period (1102) when the slope becomes small. Therefore, since it can be said that the result is not affected even if the experiment is continued further, a signal to end the experiment may be transmitted to the particle beam experiment apparatus (101).

  In the experimental data storage unit (124), the continuous distribution estimated as shown in FIG. 12 by the continuous distribution estimation process (S405) executed by the continuous distribution estimation unit (122) is stored as time-series data. ing. From this data, the distribution corresponding to the cumulative value of the particle beam count at each time point after the start of the experiment can be reproduced. As described in FIG. 10, the statistical determination unit (121) calls the data from the experimental data storage unit (124), calculates and evaluates the similarity between distributions reproduced in time series, and performs an experiment. It is possible to determine whether to end or continue.

  According to the above embodiment, if it is assumed that the continuous distribution is estimated later and the validity thereof is evaluated, the experiment can be terminated early without degrading the accuracy. In this method, the measurement results of the particle beam experiment (for example, the distribution of scattered particles), which is substantially the same as that of the long-time particle beam experiment, can be obtained. The same accuracy can be ensured. As a result, it is possible to conduct experiments with many samples and conditions with high accuracy, and it can be expected to lead to early discovery of new facts.

  In the first embodiment, the similarity of the estimated continuous distribution is evaluated. However, it is also possible to calculate the physical quantity of the sample from the estimated continuous distribution and evaluate the variation of the physical quantity to determine the termination of the experiment.

  As Example 2, an example in which the stability of a physical quantity related to a sample obtained from a continuous distribution is used for the statistical test performed by the statistical test determination unit (123) will be described. The second embodiment is implemented according to the first embodiment, but the main difference is in the content of the continuous distribution reliability evaluation (S406) performed by the statistical test determination unit (123).

  FIG. 13 shows the procedure of continuous distribution reliability evaluation (S406A) in the second embodiment. In the continuous distribution reliability evaluation of the second embodiment, as in the first embodiment, the continuous distribution parameters estimated from the experimental data storage unit (124) are obtained by obtaining the continuous distribution estimation results within the same experiment ID as a series. And reproduce the continuous distribution (S1001). However, unlike Example 1, the reliability is evaluated based on the fact that the fluctuation of the physical quantity related to the sample derived from the continuous distribution, which is the estimation result of the past several times, is reduced. This is based on the viewpoint that even if fluctuations still remain in the continuous distribution itself, it is not necessary to continue the experiment if fluctuations are no longer seen in the physical quantity to be viewed. Compared with the case where the distributions themselves are compared as in the first embodiment, the validity of the physical quantity other than the used physical quantity is not guaranteed, but the effect that the experiment can be terminated earlier can be expected.

  For this reason, in the second embodiment, the physical quantity calculation (S1301) based on the estimated continuous distribution is compared with the threshold value of the calculated physical quantity variation (S1302). If the physical quantity variation is not greater than or equal to the threshold, the estimation result is reliable (S1004), and if the physical quantity variation is greater than or equal to the threshold, the estimation result is not reliable (S1005).

  FIG. 14 shows an example of physical quantity calculation (S1301). This graph shows the probability density distribution along the line (1401) going outward from the center point (1405) on the scattering pattern, with the vertical axis representing the probability density and the horizontal axis representing the distance from the center point (1405). It is expressed by the log-log graph. Actually, a behavior depending on a physical quantity to be seen appears in a section (1402) of an appropriate distance from the vicinity of the center on the scattering pattern. In this example, it is assumed that it appears on the slope a of the tangent line (1403) in the section (1402). Then, the physical quantity can be expressed as a function f (a) of the gradient a. This slope may be obtained by differentiation of the continuous distribution function, or may be calculated by taking a suitable point from the continuous distribution function and using the least square method.

  In the second embodiment, the experimental termination is determined when the value of f (a) converges (the variance is equal to or less than the threshold value). This determination can be implemented by changing the part (vertical axis) using the relative sum of squares in the determination criterion in the first embodiment shown in FIG. 11 to f (a). As described above, the area far from the center (1404) on the scattering pattern has a small number of detected particles, and the method of Example 1 tends to require time until convergence. On the other hand, in the method of the second embodiment, the experiment can be terminated only by the convergence of the range contributing to f (a), and the validity of the necessary f (a) can be ensured.

  As Example 3, an example using a known Bayesian estimation as a statistical test performed by the statistical test determination unit (123) will be described. The third embodiment is an implementation according to the first embodiment. The main difference is that, in the continuous distribution estimation process (S405) performed by the continuous distribution estimation unit (122), the regression analysis (S802) in FIG. 8 is a regression analysis based on Bayesian statistics, and a statistical test determination. As a content of the continuous distribution reliability evaluation (S406) performed by the unit (123), there is a point that the variation of the continuous distribution of the scattering pattern using the Bayesian statistical regression analysis is evaluated.

  FIG. 15 shows the procedure of continuous distribution reliability evaluation (S406B) in the third embodiment. As described above, the continuous distribution estimation in Example 3 uses regression analysis based on Bayesian statistics. Here, regression analysis based on Bayesian statistics assumes a probability distribution with respect to the parameters of the regression curve and corrects the probability distribution based on the observed values to identify the range of the regression curve parameters. Point to.

  FIG. 16 schematically shows an example thereof. In this example, a known B-spline curve is used as the regression curve. In the B-spline curve, the definition area is divided into small sections, and each polynomial (for example, quadratic function) is used in each section. These polynomials obtain a curve with the smallest error on the condition that the boundary becomes continuous and smooth at the boundary of each section.

The B-spline curve uses the coordinates of points called control points as a representation of the parameters of this polynomial. The original polynomial is described with parameters a, b, c, such as ax ² + bx + c, and the error is minimized with the restriction that the polynomials in each section are smoothly connected at the boundary. Although it is necessary to define these parameters, in the B-spline curve, they are derived from the coordinates of the control points, and the calculation method of the derivation comes to naturally connect the partition boundaries smoothly. ing. As a result, a smooth continuous distribution can be created simply by determining the positions of the control points.

  In this embodiment, the scattering pattern is regarded as a three-dimensional space of x-coordinate, y-coordinate, and luminance, and divided into sections (1601) by the x-coordinate and y-coordinate, and control points are arranged at the center of each section. The B-spline curve can be changed by changing the height (luminance direction value) of this control point. For simplicity, 1602 shows a cross-sectional view in the x direction at y. The vertical axis of this graph is the relative frequency (luminance value) of the count number, and the horizontal axis is the x coordinate. The measured data is a histogram (1603) on this graph. On the other hand, the B-spline curve is expressed as a curve such as (1604) (note that it is originally a curved surface including the y direction, but here is a curved line for simplicity). This curve is automatically determined by the control point (1605). If the control point is moved and moved to the position (1606), the curve changes as (1607). Alternatively, when the control point is moved to (1608), the curve changes as shown in (1609). In this way, the curve can be changed by moving the position of the control point, and if it is determined so as to match the histogram (1603), a regression curve can be drawn.

  In Example 3, a probability distribution with respect to parameters is assumed for this regression curve. That is, the probability distribution of the coordinates of the control points is assumed. First, a control point is determined, and when a continuous probability distribution is created therefrom, the probability of obtaining the result of the histogram (1603) can be calculated from the probability distribution. Specifically, if the probability distribution function is integrated in the histogram (1603) section to obtain the selection probability within the histogram frame, it is easy to use a known multinomial distribution (the probability distribution of the histogram when random selection is repeated). Can be calculated.

In Bayesian statistics, this can be calculated in reverse, that is, the probability distribution of the parameter of the multinomial distribution when the observed value of the histogram is given. This probability distribution is generally called a posterior probability distribution. As the posterior probability distribution corresponding to the parameters of the multinomial distribution, generally known Dirichlet distribution (hereinafter Dir ({μ _i }), μ _i is a parameter group of the multinomial distribution) is used.

In Example 3, since the value obtained by integrating the probability distribution obtained using the control points is a parameter of the multinomial distribution, the argument of the Dirichlet distribution is determined by the control points, and the posterior probability distribution = Dir ({μ _i ( Control point coordinates)}). Then, the mode or the expected value of this posterior probability distribution can be used as the estimated value of the continuous distribution function. If the posterior probability is calculated while changing the coordinates of the control points, the variation of the continuous distribution function accompanying the variation of the posterior probability distribution in the latest parameter (that is, the current observation value) can be calculated (S1501). In this calculation, the prediction accuracy can be further improved by using the parameter candidates determined by other experiments or theoretical calculations as the initial prior distribution.

  In the statistical test / determination unit (123) of the third embodiment, after calculating the variation of the continuous distribution function (S1501), the evaluation is performed to obtain an index (S1502). When the index is smaller than a predetermined threshold, the estimation is performed. When the value is reliable, it is output (S1503). As a method for this evaluation, a simple method using the probability value of the most frequent point or a variance of the parameters of the multinomial distribution (obtained by a known method. Posterior probability × square of expected value obtained by integral value of parameter) And an average value or a maximum value of the posterior probability × the difference between the integral value of the square of the parameter and the like.

  According to the method of the third embodiment, the validity of the result can be evaluated without performing time series evaluation. In the time series evaluation, the experiment can be aborted after the change becomes sufficiently small. However, the method of Example 3 is expected to be able to abort the experiment earlier because the experiment can be judged at the same time as the change becomes small. The

  As Example 4, an example in which the cross-validation method is used for the statistical test performed by the statistical test determination unit (123) will be described. The fourth embodiment is also implemented according to the first embodiment, and the main difference is that the continuous distribution estimation process (S405) performed by the continuous distribution estimation unit (122) is the same as the distribution estimation (S802) in FIG. This is the content of continuous distribution reliability evaluation (S406) performed by the test determination unit (123).

  The cross-validation method is a known technique used to evaluate the accuracy of prediction, etc., and randomly divides the given data and uses a part of it for building a prediction model and the rest for accuracy evaluation. This is how to do it. In the fourth embodiment, the accuracy of the continuous distribution of the scattering pattern is evaluated based on the cross-validation method, and a statistical test is performed by evaluating whether the accuracy equal to or higher than a predetermined threshold is obtained.

  FIG. 17 shows a procedure (S802A) for estimating the continuous distribution in the fourth embodiment. Since Example 4 uses cross-validation, each piece of data is evaluated once, with some of the scattering pattern data aggregated at a predetermined interval in the past being used for evaluation data and the rest as data for continuous distribution estimation. Create combinations to be used for Thereby, partial data set combinations A1, A2,... Are comprehensively created for past data (S1701).

  For example, when there are four data for a1, a2, a3, and a4, a1 is for evaluation and a2, a3, and a4 are for estimation, and a2 is for evaluation and a1, a3, and a4 are for estimation There are four combinations: a3 is for evaluation, a1, a2, and a4 are for estimation, a4 is for evaluation, and a1, a2, and a3 are for estimation. In FIG. 17, these combinations are referred to as A1, A2,. In the above example, there are four ways of A1, A2, A3, and A4.

  The number of scattering pattern data used for the evaluation data is such that the calculation time decreases as the number increases, and instead the reliability of the test decreases, and can be determined in advance as a predetermined value from the balance of calculation time and accuracy. it can. For example, if the number of scattering pattern data is 2, there are two combinations, a1 and a2 are for evaluation and a3 and a4 are for estimation, and a3 and a4 are for evaluation and a1 and a2 are for estimation. At this time, since the number of scattering patterns for evaluation is fixed, it is considered that the estimation data increases as the measurement time increases, and the accuracy tends to improve.

  Next, the estimation data is aggregated so as to be (x, y, luminance) for each An of each combination A1, A2,... To form one scattering pattern (S1702). The luminance corresponds to the count number. As this method, the method described in the first embodiment for obtaining the sum of the count numbers for data having the same x and y may be used. Next, a continuous distribution is calculated from the aggregated data (S1703). In the fourth embodiment, in the calculation of continuous distribution, a method is used in which density estimation is performed on each aggregated result to obtain a continuous distribution function f with luminance = f (x, y). The law is used. The kernel density estimation method is a method for estimating an original distribution from a finite sample obtained from a density distribution, and performs a weighted calculation with a predetermined band function.

For example, the density function P (x, y) of a point (x, y)

P (x, y) = Σ v _i × R (d (x, y, x _i , y _i ))

And calculate. Here, the count of the i-th point is written as v _i , the coordinates of the point are written as (x _i , y _i ), and d (x, y, x _i , y _i ) is the coordinates (x, y) and (x _i , y _i ) is a function for obtaining the Euclidean distance. R (r) is a function that attenuates based on the argument distance, and a Gaussian function or the like can be used. This density function P (x, y) is stored as data fn of the continuous distribution function in which the density function P (x, y) is estimated, and stored in the experimental data storage unit (124) in pairs with the data set An (S1704).

  As described above, a continuous spatial distribution of measurement probabilities per unit time of particles estimated at predetermined time intervals can be obtained by a weighted addition operation of surrounding observation values.

  FIG. 18 shows the procedure of continuous distribution reliability evaluation (S406C) using the continuous distribution corresponding to the combinations A1, A2,. First, the latest information of A1, A2,... Among the distribution estimation results within the same experiment ID is acquired (S1801), and the prediction accuracy of the distribution by cross-validation is calculated for each (S1802). The accuracy here is to calculate the difference between the observation probability that can be calculated by dividing the count number of each point by the total number and the value of that point in the continuous distribution P (x, y), and regard the sum of squares as the accuracy. be able to. Thereafter, as in the first embodiment, if the error is larger than the predetermined threshold, the experiment is continued as being unreliable, and if the error is smaller than the predetermined threshold, the experiment is terminated (S1803, S1004, S1005).

  According to this method, although calculation time is required, it is possible to determine whether or not the experiment needs to be continued more precisely. Therefore, when the processor (211) of the experimental result verification apparatus (102) has particularly high performance, the method of the fourth embodiment is considered effective.

  As described above, in the experimental result verification apparatus (102) of each embodiment, the measurement data received by the experimental data related to the distribution of the measurement target particles obtained by the irradiation of the particle beam to the sample is controlled to control the irradiation of the particle beam. The system includes an experimental data collection unit (121) that stores density distribution data based on experimental data in a storage device in time series. Then, the continuous distribution estimation unit (122) estimates a continuous probability density distribution in time series based on the density distribution data. As a method of estimating the probability density distribution, various known methods such as regression analysis for fitting a cumulative value of particle beam counts to a curve or a curved surface can be used. Then, the statistical test / determination unit (123) evaluates the estimated probability density distribution, parameters obtained from the probability density distribution, etc., time-series changes, change rates, variations, and the like, and based on the evaluation results, the particle beam The continuation or end of irradiation is determined.

  As described above, the probability density distribution is estimated under the assumption that the distribution of the scattered particles is smooth, and the particle beam irradiation is terminated based on the statistical test for the probability density distribution. I am doing so.

  The present invention is not limited to the embodiments described above, and includes various modifications. For example, a part of the configuration of one embodiment can be replaced with the configuration of another embodiment, and the configuration of another embodiment can be added to the configuration of one embodiment. Moreover, it is possible to add / delete / replace the configurations of the other embodiments with respect to a part of the configurations of the embodiments.

101 Particle beam experiment equipment
102 Experimental result verification device
122 Continuous distribution estimation unit
123 Statistical test judgment part
S405 Continuous distribution estimation processing
S406 Continuous distribution reliability evaluation

Claims (13)

Irradiate the sample with a particle beam, count the number of particles to be measured obtained by the irradiation,
When evaluating the sample using the distribution of the particles to be measured,
Determining the distribution assuming that the particles to be measured appear according to a smooth probability density distribution,
Perform a statistical test on the hypothesis that the distribution matches the true probability density distribution,
If the hypothesis is a result of fit, the irradiation of the particle beam is terminated.
A measuring method characterized by the above. The measurement method according to claim 1,
As the statistical test, a continuous spatial distribution of the measurement probability per unit time of the measurement target particle is estimated at predetermined time intervals, and the fluctuation of the spatial distribution as a result of the estimation is sufficiently small. Conform
Measuring method. The measurement method according to claim 1,
As the statistical test, a set of counts of the number of particles to be measured obtained at predetermined time intervals is divided into a first group and a second group, and the particles to be measured are measured in the first group. Estimating a continuous spatial distribution of measurement probability per unit time, evaluating the accuracy of the spatial distribution in the second group, and satisfying a predetermined accuracy criterion,
Measuring method. The measurement method according to claim 1,
When obtaining the distribution, the continuous spatial distribution of the measurement probability of the measurement target particle is estimated by regression analysis,
Measuring method. The measurement method according to claim 3,
Obtaining a continuous spatial distribution of the measurement probabilities by weighted addition of surrounding observation values;
Measuring method. The measurement method according to claim 1,
As the statistical test, a continuous spatial distribution of the measurement probability per unit time of the measurement target particle is estimated at predetermined time intervals, and a physical quantity for the sample is calculated from the spatial distribution as a result of the estimation. , When the calculated physical quantity fluctuation is sufficiently small,
A measuring method characterized by the above. The measurement method according to claim 1,
As the statistical test, a probability distribution of a parameter that determines a continuous spatial distribution of measurement probability per unit time of the measurement target particle is estimated, and the expected value of the probability distribution is regarded as the smooth probability density distribution. , When the variation in the probability distribution of the parameter is sufficiently small,
A measuring method characterized by the above. A measurement system that receives experimental data related to the distribution of measurement target particles obtained by irradiation of a particle beam on a sample, and controls irradiation of the particle beam,
A storage device;
An experimental data collection unit for storing density distribution data based on the experimental data in the storage device in time series;
Based on the density distribution data, a continuous distribution estimation unit that estimates a continuous probability density distribution in time series,
A statistical test determination unit that evaluates at least one of the probability density distribution itself and a physical quantity obtained from the probability density distribution, and determines continuation or termination of irradiation of the particle beam based on an evaluation result;
Measuring system. The continuous distribution estimation unit
Aggregating the time-series density distribution data to generate cumulative value data consisting of a set of coordinates and luminance at the coordinates,
Estimating the continuous probability density distribution by regression analysis of the cumulative value data;
The measurement system according to claim 8. The statistical test determination unit
Comparing the probability density distributions estimated in time series, and determining the end of irradiation of the particle beam when at least one of the change, rate of change and variation is smaller than a predetermined threshold,
The measurement system according to claim 8. The statistical test determination unit
From the probability density distribution estimated in time series, calculate physical quantities related to the sample in time series,
Compare the physical quantities calculated in time series, and determine the end of irradiation of the particle beam when the change, rate of change and variation are smaller than a predetermined threshold,
The measurement system according to claim 8. The continuous distribution estimation unit
A regression analysis based on Bayesian statistics is used to estimate a probability distribution for a parameter that determines a continuous spatial distribution of the measurement probability per unit time of the measurement target particle, and with the expected value of the probability distribution, the continuous probability density distribution and Deemed,
The statistical test determination unit
Calculating the variation of the probability density distribution;
An index is obtained from the variation,
Determining the end of irradiation of the particle beam when the index satisfies a predetermined condition;
The measurement system according to claim 8. The continuous distribution estimation unit
For the time-series density distribution data, some are used as evaluation data, the rest are used as continuous distribution estimation data, and combinations are created so that each density distribution data is used once as evaluation data.
Estimating the probability density distribution from the continuous distribution estimation data,
The statistical test determination unit
Calculate the prediction accuracy of the probability density distribution estimated using the evaluation data,
Determining the end of irradiation of the particle beam when the prediction accuracy is greater than a predetermined threshold;
The measurement system according to claim 8.

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