Patent Publication Number: US-2023137130-A1

Title: Phase Analyzer, Sample Analyzer, and Analysis Method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to Japanese Patent Application No. 2021-179615, filed on Nov. 2, 2021, the disclosure of which is hereby incorporated by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a phase analyzer, a sample analyzer, and an analysis method. 
     In a scanning electron microscope equipped with an X-ray detector such as an energy-dispersive X-ray spectrometer (EDS) or a wavelength-dispersive X-ray spectrometer (WDS), spectrum imaging data, in which a position on a sample and an X-ray spectrum are associated with each other, can be obtained. As a technique for determining a distribution of compounds by using spectrum imaging data, phase analysis is known. 
     Description of Related Art 
     For example, JP-A-2018-200270 discloses a phase analyzer in which a graph illustrating an X-ray intensity of each element and a concentration of each element by means of areas is displayed along with a phase map showing a distribution of compounds to facilitate understanding of characteristics of compositions of the compounds. 
     In phase analysis, good phase maps cannot be obtained unless an appropriate number of phases are set. For that reason, it is required to repeatedly perform phase analysis while changing conditions of the number of phases in order to find the appropriate number of phases. 
     SUMMARY OF THE INVENTION 
     A phase analyzer according to a first aspect of the invention includes: 
     a data acquisition unit that acquires spectrum imaging data in which a position on a sample is associated with a spectrum of a signal from the sample; 
     a candidate determination unit that performs multivariate analysis on the spectrum imaging data to determine candidates for the number of phases; 
     a phase analysis unit that creates, for each of the candidates, a phase map group including a number of phase maps corresponding to the number of phases; and 
     a display control unit that causes a display unit to display, for each of the candidates, the phase map group. 
     A sample analyzer according to a second aspect of the invention includes the above phase analyzer. 
     An analysis method according to a third aspect of the invention includes: 
     acquiring spectrum imaging data in which a position on a sample is associated with a spectrum of a signal from the sample; 
     performing multivariate analysis on the spectrum imaging data to determine candidates for the number of phases; 
     creating, for each of the candidates, a phase map group including a number of phase maps corresponding to the number of phases; and 
     causing a display unit to display, for each of the candidates, the phase map group. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram illustrating a configuration of a sample analyzer including a phase analyzer according to an embodiment of the invention. 
         FIG.  2    is a diagram illustrating a configuration of the phase analyzer according to an embodiment of the invention. 
         FIG.  3    is a diagram for describing a hierarchical clustering method. 
         FIG.  4    is a diagram for describing a hierarchical clustering method. 
         FIG.  5    is a graph illustrating a relationship between the number of clusters and linkage criteria. 
         FIG.  6    is a graph illustrating a relationship between the number of clusters and curvatures. 
         FIG.  7    is a table for describing a first database. 
         FIG.  8    is a table for describing a second database. 
         FIG.  9    is a table illustrating an example of a list of names of phases. 
         FIG.  10    is a diagram illustrating an example of a preview screen for displaying phase map group candidates. 
         FIG.  11    is a diagram schematically illustrating a state in which one phase map group is selected on the preview screen. 
         FIG.  12    is a diagram illustrating an example of a GUI screen. 
         FIG.  13    is a flowchart illustrating an example of a process of a phase analyzer according to an embodiment of the invention. 
     
    
    
     DESCRIPTION OF THE DRAWINGS 
     A phase analyzer according to an embodiment of the invention includes: 
     a data acquisition unit that acquires spectrum imaging data in which a position on a sample is associated with a spectrum of a signal from the sample; 
     a candidate determination unit that performs multivariate analysis on the spectrum imaging data to determine candidates for the number of phases; 
     a phase analysis unit that creates, for each of the candidates, a phase map group including a number of phase maps corresponding to the number of phases; and 
     a display control unit that causes a display unit to display, for each of the candidates, the phase map group. 
     In the phase analyzer, since the candidates for the number of phases are determined, and the phase map group including the number of phase maps corresponding to the number of phases is displayed on the display unit for each of the candidates for the number of phases, a user can easily obtain a good phase map group. 
     A sample analyzer according to an embodiment of the invention includes the above phase analyzer. 
     An analysis method according to an embodiment of the invention includes: 
     acquiring spectrum imaging data in which a position on a sample is associated with a spectrum of a signal from the sample; 
     performing multivariate analysis on the spectrum imaging data to determine candidates for the number of phases; 
     creating, for each of the candidates, a phase map group including a number of phase maps corresponding to the number of phases; and 
     causing a display unit to display, for each of the candidates, the phase map group. 
     In the analysis method, since the candidates for the number of phases are determined, and the phase map group including the number of phase maps corresponding to the number of phases is displayed on the display unit for each of the candidates for the number of phases, the user can easily obtain a good phase map group. 
     Preferred embodiments of the invention will be described in detail below with reference to the figures. It is noted that the embodiments described below do not unduly limit the scope of the invention described in the claims. In addition, all of the components described below are not necessarily essential requirements of the invention. 
     1. ANALYZER 
     First, a phase analyzer according to an embodiment of the invention will be described with reference to the figures.  FIG.  1    is a diagram illustrating a configuration of a sample analyzer  100  including a phase analyzer  80  according to an embodiment of the invention. 
     The sample analyzer  100  is a scanning electron microscope equipped with an X-ray detector  70 . In the sample analyzer  100 , by scanning a sample S with an electron probe EP, spectrum imaging data in which a position on the sample S is associated with an X-ray spectrum can be acquired. 
     As illustrated in  FIG.  1   , the sample analyzer  100  includes an electron gun  10 , a condenser lens  20 , a scanning coil  30 , an objective lens  40 , a sample stage  50 , a secondary electron detector  60 , the X-ray detector  70 , and the phase analyzer  80 . 
     The electron gun  10  emits an electron beam. The electron gun  10 , for example, accelerates electrons emitted from a cathode at an anode to emit the electron beam. 
     The condenser lens  20  and the objective lens  40  focus the electron beam emitted from the electron gun  10  to form the electron probe EP. A probe diameter and a probe current thereof can be controlled by the condenser lens  20 . 
     The scanning coil  30  two-dimensionally deflects the electron probe EP. By two-dimensionally deflecting the electron probe EP with the scanning coil  30 , the sample S can be scanned with the electron probe EP. 
     The sample stage  50  can hold the sample S. The sample stage  50  has a moving mechanism for moving the sample S. 
     The secondary electron detector  60  detects secondary electrons emitted from the sample S when the sample S is irradiated with the electron beam. The sample S is scanned by the electron probe EP, and the secondary electrons emitted from the sample S are detected by the secondary electron detector  60 , so that a secondary electron image can be obtained. Also, the sample analyzer  100  may include a backscattered electron detector that detects backscattered electrons emitted from the sample S when the sample S is irradiated with the electron beam. 
     The X-ray detector  70  detects characteristic X-rays emitted from the sample S when the sample S is irradiated with the electron beam. The X-ray detector  70  is, for example, an energy-dispersive X-ray detector. Also, the X-ray detector  70  may be a wavelength-dispersive X-ray spectroscope. Spectrum imaging data can be obtained by scanning the sample S with the electron probe EP and detecting characteristic X-rays emitted from the sample S with the X-ray detector  70 . 
     Spectrum imaging data is data in which positions (coordinates) on a sample and spectra of signals from the sample are associated with each other. In the sample analyzer  100 , data in which positions on the sample S are associated with X-ray spectra can be obtained as the spectrum imaging data. In the sample analyzer  100 , while the sample S is scanned with the electron probe EP, the X-ray spectra are collected for each pixel, and the positions on the sample S (coordinates of pixels) and the X-ray spectra are associated with each other and stored. 
     The phase analyzer (information processing device)  80  performs phase analysis using the spectrum imaging data and displays phase maps. 
       FIG.  2    is a diagram illustrating a configuration of the phase analyzer  80 . 
     As illustrated in  FIG.  2   , the phase analyzer  80  includes a processing unit  800 , an operation unit  810 , a display unit  820 , and a storage unit  830 . 
     The operation unit  810  is used by a user to input operation information and outputs input operation information to the processing unit  800 . Functions of the operation unit  810  can be implemented by input devices such as a keyboard, a mouse, buttons, a touch panel, and a touch pad. 
     The display unit  820  is for displaying images generated by the processing unit  800 , and its functions can be realized by a display such as a liquid crystal display (LCD) or a cathode ray tube (CRT). The display unit  820  displays a graphical user interface (GUI) screen for inputting phase analysis conditions, displaying phase analysis results, and analyzing and editing the phase analysis. 
     The storage unit  830  stores programs and various data for causing a computer to function as each part of the processing unit  800 . In addition, the storage unit  830  also functions as a work area for processing unit  800 . Functions of the storage unit  830  can be realized by a hard disk, a random access memory (RAM), or the like. 
     The processing unit  800  executes the programs stored in the storage unit  830 , and thus functions as a data acquisition unit  802 , a candidate determination unit  804 , a phase analysis unit  806 , and a display control unit  808 , which will be described below. Functions of the processing unit  800  can be realized by executing a program using hardware such as various processors (a CPU, a DSP, etc.) and ASIC (a gate array, etc.). The processing unit  800  includes the data acquisition unit  802 , the candidate determination unit  804 , the phase analysis unit  806 , and the display control unit  808 . 
     The data acquisition unit  802  acquires the spectrum imaging data obtained by analyzing the sample S with the sample analyzer  100 . 
     The candidate determination unit  804  performs multivariate analysis on the spectrum imaging data to determine candidates for the number of phases. The candidate determination unit  804  obtains priority of the number of phases based on results of the multivariate analysis and determines the candidates for the number of phases based on the priority. 
     The phase analysis unit  806  creates phase map groups each including a number of phase maps corresponding to the number of phases for each of the candidates for the number of phases determined by the candidate determination unit  804 . The phase map groups can be created by performing the multivariate analysis on spectrum imaging data. A phase map is an image that shows a distribution of compounds. 
     The display control unit  808  causes the display unit  820  to display the phase map groups for each of the candidates for the number of phases. 
     2. ANALYSIS METHOD 
     2.1. Acquisition of Spectrum Imaging Data 
     The data acquisition unit  802  acquires the spectrum imaging data obtained by analyzing the sample S with the sample analyzer  100 . In the sample analyzer  100 , the sample S is scanned with the electron probe EP to detect the X-rays emitted from the sample S with the X-ray detector  70 , and the X-ray spectrum data is acquired at each detected position. The detected positions (coordinates on the sample S) and the X-ray spectrum data are associated with each other and stored. Thus, the spectrum imaging data can be obtained. 
     2.2. Determination of Candidates for the Number of Phases 
     The candidate determination unit  804  analyzes the spectrum imaging data and extracts coordinate groups (pixel groups) having similar spectra. For example, multivariate analysis is used to analyze the spectrum imaging data. As the multivariate analysis, methods such as self-organizing maps (SOM), a hierarchical clustering method, a K-means method, principal component analysis, singular value decomposition, non-negative matrix decomposition, vertex component analysis, and the like can be exemplified. Also, these techniques may be combined to extract the coordinate groups having similar spectra. 
     The candidate determination unit  804  performs the multivariate analysis to determine the candidates for the number of phases (the number of coordinate groups having similar spectra). 
     The phase analysis unit  806 , for example, performs cluster analysis on the spectrum imaging data to determine candidates for the number of phases. Cluster analysis is a type of multivariate analysis and is unsupervised learning of collecting similar data in data groups and classifying it. Here, as the cluster analysis, a case of determining candidates for the number of phases by combining the self-organizing maps and a hierarchical clustering method will be described. 
     The candidate determination unit  804  first creates the self-organizing maps of the spectrum imaging data. The candidate determination unit  804  learns the self-organizing maps using spectrum data of each pixel constituting the spectrum imaging data as input vectors. This creates a map space that associates the input vectors with each other. In the map space, a degree of similarity of spectrum data is represented by a distance on a map. The candidate determination unit  804  sorts the spectrum data into groups based on the distance on the map space and creates clusters. A cluster is a collection of similar input vectors (spectrum data). 
     The candidate determination unit  804  uses the clusters obtained using the self-organizing maps as minimum unit clusters and merges the minimum unit clusters using a hierarchical clustering method to create new clusters. 
       FIGS.  3  and  4    are diagrams for describing the hierarchical clustering method. 
     As illustrated in  FIGS.  3  and  4   , the candidate determination unit  804  merges the minimum unit clusters C1, C2, C3, C4, C5, C6, C7, C8, C9, and C10 obtained from the self-organizing maps using the hierarchical clustering method to create new clusters. 
     Specifically, the candidate determination unit  804  obtains distances (dissimilarities) between the minimum unit clusters C1, C2, C3, C4, C5, C6, C7, C8, C9, and C10 and merges combinations thereof in descending order of the distance. A process of merging can be represented by a dendrogram. A distance required to merge two clusters is referred to as a linkage criterion. 
     As illustrated in  FIG.  4   , new clusters can be created by cutting the dendrogram at a threshold T. In the hierarchical clustering method, by adjusting the threshold T, any number of clusters can be created. In the illustrated example, by cutting the dendrogram at the threshold T, four clusters are created. 
       FIG.  5    is a graph illustrating a relationship between the number of clusters and linkage criteria. 
     The candidate determination unit  804  obtains the linkage criteria between the minimum unit clusters C1, C2, C3, C4, C5, C6, C7, C8, C9, and C10 and creates the graph (function) indicating the relationship between the number of clusters and the linkage criteria illustrated in  FIG.  5   . 
       FIG.  6    is a graph illustrating a relationship between the number of clusters and curvatures. 
     The candidate determination unit  804  creates the graph indicating the relationship between the number of clusters and the curvatures as illustrated in  FIG.  6    from the graph indicating the relationship between the number of clusters and the linkage criteria as illustrated in  FIG.  5   . Here, the curvature is a curvature at an arbitrary point of the function indicating the relationship between the number of clusters and the linkage criteria. A curvature R at a point (a, f(a)) of y=f(x) can be obtained by the following formula. 
     
       
         
           
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     The candidate determination unit  804  obtains the curvatures for each number of clusters and determines priority based on the curvatures. The priority can be expressed, for example, as a ratio of the largest curvature among the curvatures obtained for each number of clusters as a reference. The greater the curvature, the higher the priority. 
     In the example illustrated in  FIG.  6   , since the curvature is the largest in a case in which the number of clusters is “4,” it has the highest priority and is selected as a candidate 1. Also, since the curvature is the second largest in a case in which the number of clusters is “5,” it has the second highest priority and is selected as a candidate 2. In addition, since the curvature is the third largest in a case in which the number of clusters is “3,” it has the third highest priority and is selected as a candidate 3. 
     From these results, the candidate determination unit  804  determines the case in which the number of phases is 4, the case in which the number of phases is 5, and the case in which the number of phases is 3 as candidates. 
     Here, the candidate determination unit  804  determines only the number of clusters with higher priority than a preset reference value of priority as candidates. For that reason, the case in which the number of clusters is “7” has the fourth largest curvature, but the priority is lower than the preset reference value, and thus it is excluded from the candidates. 
     Also, for example, the candidate determination unit  804  may list a preset number of candidates for the number of phases. That is, in a case in which the number of candidates is set to three in advance, the candidate determination unit  804  lists three candidates for the number of phases in descending order of priority. 
     2.3. Phase Analysis 
     The phase analysis unit  806  creates the phase map groups each including a number of phase maps corresponding to the determined number of phases for each of the candidates for the number of phases determined by the candidate determination unit  804 . 
     In the example illustrated in  FIG.  6   , the candidate determination unit  804  has determined the case in which the number of phases is four, the case in which the number of phases is five, and the case in which the number of phases is three as the candidates. For that reason, the phase analysis unit  806  performs the phase analysis under the condition that the number of phases is four and creates a phase map group including four phase maps. Similarly, the phase analysis unit  806  performs the phase analysis under the condition that the number of phases is five and creates a phase map group including five phase maps. Further, the phase analysis unit  806  performs the phase analysis under the condition that the number of phases is three and creates a phase map group including three phase maps. 
     The phase analysis unit  806  further creates a phase spectrum from each phase map that constitutes the phase map groups. A phase spectrum is a spectrum obtained by averaging (or integrating) spectra of all pixels that constitute a phase map. Further, the phase analysis unit  806  performs a process of naming a phase for each phase map and a process of obtaining an area fraction of each phase (a ratio of an area of each phase to an area of the entire map). 
     A phase name is determined using two databases (a first database and a second database). Here, a case in which a compound name is used as a phase name will be described. 
       FIG.  7    is a table for describing the first database, and  FIG.  8    is a table for describing the second database. 
     In the first database, as illustrated in  FIG.  7   , classification names (compound names), spectrum data, and quantitative results are registered. The first database may be created by registering spectra acquired by the user, or may be a publicly available or commercially available spectrum database. A classification name is a compound name assumed from a quantitative result. Spectrum data is data of a acquired X-ray spectrum. The quantitative result is a result of performing quantitative calculation on the acquired spectrum. For example, in the first database, as data No. 1, SiO 2  is registered as a classification name, SiO 2  spectrum data is registered as data of a spectral shape, and Si: 47.3269% and O: 52.6731% are registered as a quantitative result. 
     In the second database, as illustrated in  FIG.  8   , compound names and composition information are registered. Composition information is calculated from a compound name. For example, in the second database, as data No. 1, SiO 2  is registered as a compound name, and Si: 46.744559% and O: 53.255441% are registered as composition information. 
     The phase analysis unit  806  obtains a correlation coefficient between a phase spectrum obtained from a phase map serving as a naming target and each piece of spectral data registered in the first database. For example, a correlation coefficient between data x and data y can be obtained by the following equations. 
     
       
         
           
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     The phase analysis unit  806  finds spectral data with the largest correlation coefficient from all spectral data registered in the first database. 
     In addition, the phase analysis unit  806  performs quantitative calculation on the phase spectrum obtained from the phase map serving as the naming target and determines a correlation coefficient between the quantitative result and each quantitative result registered in the first database. The phase analysis unit  806  finds a quantitative result with the largest correlation coefficient among all the quantitative results registered in the first database. 
     The phase analysis unit  806  compares the correlation coefficient of the spectrum data with the largest correlation coefficient to the correlation coefficient of the quantitative result with the largest correlation coefficient and adopts the larger correlation coefficient as candidate data in the first database. 
     Also, the phase analysis unit  806  may obtain only the correlation coefficient with the spectrum data and adopt the spectrum data with the largest correlation coefficient as the candidate data in the first database. Similarly, only the correlation coefficients with the quantitative results may be obtained, and the quantitative result with the largest correlation coefficient may be adopted as the candidate data in the first database. In this case, it is assumed that it is set in advance whether to use the spectral data or the quantitative results. 
     The phase analysis unit  806  performs quantitative calculation on a phase spectrum obtained from a phase map serving as the naming target and calculates a correlation coefficient between a quantitative result and each piece of composition information registered in the second database. The phase analysis unit  806  finds the quantitative result with the largest correlation coefficient among all the quantitative results registered in the second database and adopts it as candidate data in the second database. 
     The phase analysis unit  806  compares the correlation coefficient of the candidate data in the first database with the correlation coefficient of the candidate data in the second database and selects the data with the larger correlation coefficient. Then, a compound name registered in the selected data is adopted as a phase name. 
     Also, the candidates in the first database (or the second database) may be adopted as phase names without comparing the candidates in the first database with the candidates in the second database. In this case, it is assumed that the database to be used is set in advance. 
     Also, phase names may be input directly by the user. In addition, as illustrated in  FIG.  9   , the phase analysis unit  806  extracts compound names from the first database and the second database in descending order of correlation coefficient to create a list, and the user may select compound names from this list as phase names. Further, for example, when the user inputs a character string, compound names including the input character string may be extracted from the list in  FIG.  9   . This makes it possible to easily determine the compound names. 
     2.4. Display 
     The display control unit  808  causes the display unit  820  to display the number of phases and the phase map groups for each of the candidates for the number of phases. The display control unit  808  displays the phase map groups in descending order of priority. The display control unit  808  displays, for example, the phase map groups on a preview screen  2  for displaying candidates of the phase map groups. 
       FIG.  10    is a diagram illustrating an example of a preview screen  2  for displaying phase map group candidates. 
     The display control unit  808  displays the phase analysis results performed by the phase analysis unit  806  described above on the preview screen  2  illustrated in  FIG.  10   . 
     The preview screen  2  in  FIG.  10    displays a phase map group in which the number of phases is four, a phase map group in which the number of phases is five, and a phase map group in which the number of phases is three. These three phase map groups are arranged in descending order of priority. 
     In addition, the display control unit  808  displays the compound names (phase names) and each area fraction. As the compound names, compound names determined by the phase analysis unit  806  or compound names input by the user are displayed. Although not shown, the preview screen  2  may display information for the user to select phase map groups, such as phase spectra, a dendrogram, and the like, in addition to the above-described phase names and area fractions. 
       FIG.  11    is a diagram schematically illustrating a state in which one phase map group is selected on the preview screen  2 . 
     On the preview screen  2 , the user can select one phase map group from a plurality of phase map group candidates displayed. For example, in a case in which the display unit  820  includes a touch panel (an example of the operation unit  810 ), the user performs an operation of touching a desired phase map group with a fingertip FG, so that the user can select one phase map group from the plurality of phase map groups displayed on the preview screen  2 . Also, the phase map group may be selected by operating a mouse or keyboard. 
     When the user selects a desired phase map group on the preview screen  2 , the display control unit  808  displays the selected phase map group on the GUI screen. 
       FIG.  12    is a diagram illustrating an example of a GUI screen  4 . 
     On the GUI screen  4 , it is possible to analyze and edit each phase map that constitutes the selected phase map group. The GUI screen  4  displays a plurality of phase maps that constitute the phase map group, names of each phase, area fractions of each phase, and quantitative results thereof. Further, in a region  6  of the GUI screen  4 , an image obtained by combining each phase map and a SEM image is displayed. 
     On the GUI screen  4 , analysis and editing such as qualitative and quantitative analysis of phase spectra, phase combining or uncombining, phase color changes, phase name changes, and the like can be performed. 
     On the GUI screen  4 , the qualitative and quantitative analysis of phase spectra can be performed under various conditions. By performing the qualitative and quantitative analysis of phase spectra, phases can be renamed and compared to other phases. 
     On the GUI screen  4 , a plurality of phase maps can be combined to form one phase map. For example, phase maps with similar distributions can be combined into one phase map, or a plurality of phases with similar compositions can be combined into one phase to create a phase map. In addition, phases (edge phases) that form edges of other phases can be grouped into one phase map. Here, in the phase map, there are cases where two phases cannot be separated at a boundary of the two phases and another phase seems to be present at the boundary between the two phases. Another phase present on the boundary between these two phases is referred to as an edge phase. This edge phase does not actually exist, and thus in a case in which there are a plurality of edge phases, the plurality of edge phases are combined into one. 
     On the GUI screen  4 , colors of phase maps selected by the user can be changed to desired colors. This makes it easier to see the phase maps. 
     Also, on the GUI screen  4 , phase names can be changed. For example, phase names may be changed based on results of the qualitative and quantitative analysis of phase spectra. 
     3. OPERATIONS OF THE PHASE ANALYZER 
       FIG.  13    is a flowchart illustrating an example of a process of the phase analyzer  80 . 
     When the sample analyzer  100  collects signals from the sample S, the data acquisition unit  802  acquires spectrum imaging data (S 10 ). 
     The candidate determination unit  804  performs the multivariate analysis on the spectrum imaging data to determine the candidates for the number of phases (S 20 ). 
     Specifically, first, the candidate determination unit  804  creates self-organizing maps of spectrum imaging data and creates minimum unit clusters. Next, the candidate determination unit  804  creates new clusters by merging the minimum unit clusters using a hierarchical clustering method. In this case, the candidate determination unit  804  determines candidates for the number of clusters, that is, candidate for the number of phases based on the curvatures of the function indicating the relationship between the number of clusters and the linkage criteria as illustrated in  FIG.  6   . 
     The phase analysis unit  806  creates phase map groups including a number of phase maps corresponding to the determined number of phases for each candidate for the number of phases determined by the candidate determination unit  804  (S 30 ). In addition to the phase map groups, the phase analysis unit  806  obtains the compound names (phase names), the area fractions of phases, and the phase spectra. Further, the phase analysis unit  806  performs the qualitative and quantitative analysis on the phase spectra. 
     As illustrated in  FIG.  10   , the display control unit  808  causes the display unit  820  to display the preview screen  2  in which the number of phases and the phase map groups are displayed for each candidate for the number of phases (S 40 ). 
     In a case in which a desired phase map group is selected from a plurality of phase map groups displayed on the preview screen  2  (Yes in S 50 ), the display control unit  808  displays the selected phase map group on the GUI screen  4  (S 60 ). Thus, it is possible to analyze and edit the phase maps. After the selected phase map group is displayed on the GUI screen  4 , the processing unit  800  ends the process of displaying the phase map groups. 
     4. EFFECTS 
     The phase analyzer  80  includes the data acquisition unit  802  that acquires the spectrum imaging data, the candidate determination unit  804  that performs the multivariate analysis on the spectrum imaging data to determine candidates for the number of phases, the phase analysis unit  806  that creates the phase map groups including a number of phase maps corresponding to the number of phases for each of the candidates for the number of phases, and the display control unit  808  that causes the display unit  820  to display the phase map groups for each of the candidates for the number of phases. For that reason, the phase analyzer  80  determines the candidates for the number of phases and causes the display unit  820  to display the phase map groups including a number of phase maps corresponding to the number of phases for each of the candidates for the number of phases, so that the user can easily obtain a good phase map group. For example, in a case in which the user specifies the number of phases and obtains the phase map groups, the user had to repeat an operation to change the number of phases and obtain the phase map groups in order to obtain a good phase map group. On the other hand, since the phase analyzer  80  can display a plurality of phase map groups with mutually different numbers of phases on the display unit  820 , the user can easily obtain a good phase map group simply by selecting one from the plurality of phase map groups. In addition, since the plurality of phase map groups are displayed at the same time, it is easy to compare the phase map groups. 
     Further, in the phase analyzer  80 , the preview screen  2  displaying the plurality of phase map groups displays various information (priority, area fractions, compound names, phase spectra, qualitative and quantitative results, etc.) for determining whether or not the phase map groups are appropriate. For that reason, the user can easily determine whether or not the phase map groups are appropriate. 
     In the phase analyzer  80 , the candidate determination unit  804  obtains the priority of the number of phases based on the results of the multivariate analysis and determines the candidates for the number of phases based on the priority. For that reason, in the phase analyzer  80 , the user can easily specify the number of phases. 
     In the phase analyzer  80 , the phase analysis unit  806  determines the compound names based on each of the phase maps that constitute the phase map groups, and the display control unit  808  causes the display unit  820  to display the compound names. Here, when determining whether or not the phase maps are appropriate, the compound names are important information. Since the compound names are displayed together with the phase maps in the phase analyzer  80 , the user can easily determine whether or not the phase map groups are appropriate. 
     In the phase analyzer  80 , the phase analysis unit  806  obtains the area fraction of each phase based on each of the phase maps that constitute the phase map groups, and the display control unit  808  causes the display unit  820  to display the area fraction of each phase. For that reason, the phase analyzer  80  can obtain information on the area fraction of each phase. 
     Since the sample analyzer  100  includes the phase analyzer  80 , the user can easily obtain good phase maps. 
     5. MODIFIED EXAMPLES 
     5.1. First Modified Example 
     In the above-described embodiment, the candidates for the number of phases have been determined in descending order of the curvatures of the function indicating the relationship between the number of clusters and the linkage criteria. For example, in the example illustrated in  FIG.  6   , the case in which the number of phases is four, the case in which the number of phases is five, and the case in which the number of phases is three have been determined as the candidates in descending order of the curvatures. 
     The method for determining the candidates for the number of phases is not limited to the above embodiment. For example, after the multivariate analysis is performed to determine the number of phases with the highest priority, a number obtained by adding 1 to and subtracting 1 from the number of phases with the highest priority may be used as candidates for the number of phases. In the example illustrated in  FIG.  6   , first, the case in which the number of phases with the largest curvature is four is determined as a candidate, and then the case in which the number of phases is five (4+1) and the number of phases is three (4−1) is determined as a candidate. 
     In addition, when five candidates for the number of phases are listed, a number obtained by adding 2 to and a number obtained by subtracting 2 from the number of phases with the highest priority may be determined as candidates. 
     5.2. Second Modified Example 
     In the above-described embodiment, the case in which the sample analyzer  100  is a scanning electron microscope equipped with the X-ray detector  70  has been described, but the analyzer according to the invention is not limited thereto. For example, the analyzer according to the invention may be any device that can obtain spectra of signals (X-rays, electrons, ions, etc.) from the sample S. The analyzer according to the invention is a transmission electron microscope equipped with an energy-dispersive X-ray spectrometer or a wavelength-dispersive X-ray spectrometer, an electron probe microanalyzer, an Auger microprobe, a photoelectron spectrometer, a focused ion beam device, or the like. 
     Also, the above-described embodiments and modified examples are merely examples, and the invention is not limited thereto. For example, the embodiments and modified examples can be combined as appropriate. 
     The invention is not limited to the above-described embodiments, and various modifications are possible. For example, the invention includes configurations that are substantially the same as the configurations described in the embodiments. Substantially same configurations mean configurations having the same functions, methods and results, or configurations having the same objectives and effects as those of the configurations described in the embodiments, for example. The invention also includes configurations obtained by replacing non-essential elements of the configurations described in the embodiments with other elements. The invention also includes configurations having the same effects as those of the configurations described in the embodiments, or configurations capable of achieving the same objectives as those of the configurations described in the embodiments. The invention further includes configurations obtained by adding known art to the configurations described in the embodiments. 
     As described above, some embodiments of the invention have been described in detail, but a person skilled in the art will readily appreciate that various modifications can be made from the embodiments without materially departing from the novel teachings and effects of the invention. Accordingly, all such modifications are assumed to be included in the scope of the invention.