JPH06302665A - Defective position analysis method - Google Patents

Abstract

PURPOSE:To speedily judge the defective position inside million particles by performing calculation for the number of cells nearly corresponding to the number of particles so that the amount of calculation is approprimately directly proportional to the number of particle rather than its square. CONSTITUTION:The position of each kind of defect is automatically specified and displayed from the layout of a given atom. Namely, a processor is provided with the data of an input value 1, a program 2 for executing the processing details shown in figure, and a memory for storing the data of an output value 3 which is the result of processing. Then, the space where particles exist is divided into fine cells by a space division 103 rather than paying attention to the particles themselves, thus calculating how close each cell is located to a close particle. Then, the position of defect is judged from the density information of atoms in each space by such processing as the allocation of atoms and discrimination 104 of impurity atoms or a region of several hundreds of atoms where defects are assumed to exist is specified, only that region is displayed graphically, and then the position of defects is specified visually.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a simulation method for quantifying a physical phenomenon and reproducing it as a behavior of a particle by simulation, and in particular, regarding an atom, a molecule, or an ion as a particle, It relates to a method of analyzing a position.

[0002]

2. Description of the Related Art A method of analyzing the position of a defect in a material is to detect the occurrence and diffusion of vacancy defects, interstitial atomic defects, or impurity defects in the material, which are observed in the process steps of LSI fabrication, at the atomic level using a computer. This is the method used for analysis.

When performing the defect diffusion analysis at the atomic level dynamically, a physical phenomenon is often treated as the behavior of particles like molecular dynamics. As a method for searching the position of defects in a substance when treating a substance composed of atoms, molecules, or ions as a set of particles, in the past, the information on the arrangement of atoms and the bond information between atoms was visualized and the analyst's own The position of the defect was judged by the eyes. In the conventional calculation function and calculation algorithm, the number of particles that can be handled in the simulation is from several hundred particles to several thousand at most. Therefore, it was possible to easily specify the position of the defect while changing the viewpoint three-dimensionally by displaying the atomic arrangement and the bond bond information in a graphic form using a workstation (WS) or the like. .

Further, the existence state of particles around each particle has been examined to determine whether or not particles are missing or abundant from the dense and dense state of particle density.

[0005]

The conventional method of visually identifying the defect position using the graphics display cannot cope with the simulation of millions of atoms which will be more widely performed in the future. In fact, it is a typical graphics display with millions of atoms at the same time 19
When it is displayed on a screen of 21 inches, the size of each atom is about 2 millimeters. Moreover, since 100 or more atoms are arranged in the depth direction and overlap each other, it is extremely difficult to visually identify the defect position. It is conceivable to take out hundreds of millions of atoms and display them for visual identification.
It would be a very time consuming task, as it would create a screen close to a million different types. In such a situation, it has become very important to determine the defect position of particles in a shorter time.

An object of the present invention is to provide a method for promptly using a computer to detect the positions of a large number of defects obtained by a simulation method in which a physical phenomenon is simulated as the behavior of particles.

[0007]

In order to achieve the object of the present invention, the positions of various defects may be automatically specified and displayed from a given arrangement of atoms. As a means to do this, instead of focusing on the particles themselves, the space in which the particles exist is divided into minute cells, and how close each cell is to the nearby particles is calculated. The position of the defect is determined from. Alternatively, after specifying a region of hundreds of atoms which is considered to have a defect, only that region is graphically displayed and the defect position is visually specified. At that time, the number of screens to be displayed can be suppressed to about 100 even in a system of several million atoms by automatically searching for a candidate for a region where a defect exists.

Further, when the defect automatic retrieval processing is performed on millions of atoms, a large amount of time is spent on the defect analysis which requires a calculation proportional to the square of the number of particles. Should be controlled so as to be proportional to the number of particles. Therefore, instead of focusing on the particles, the space in which the particles exist is divided into minute cells, and by calculating how close each cell is to nearby particles, and determining the position of the defect, The time can be reduced.

[0009]

In the defect position analyzing method of the present invention, the calculation is performed for the number of cells substantially corresponding to the number of particles, and the calculation amount is made to be proportional to about the square of the number of particles, not to the square. It becomes possible to determine the defect position in the particle at high speed.

[0010]

EXAMPLE An example of the present invention will be described below. The input values are the number of atoms, the name (type) and coordinates of each atom, and the boundary condition of the space in which the atom exists. From this information, the number of impurity defects, the names of impurity atoms and their coordinates, the number and coordinates of interstitial atoms, and the number and coordinates of vacancy defects are output.

FIG. 1 shows a processing procedure of the defect analysis method according to the present invention. FIG. 26 shows the configuration of a computer system for carrying out the present invention shown in FIG. The processing device 260 has data of an input value of 1, a program 2 for executing the processing content shown in FIG. 1, and a memory 261 for storing the data of an output value of 3 which is a processing result. An input device 262 having a device and a keyboard and an output device 263 for displaying a processing result in a graph are connected. In the processing procedure shown in FIG. 1, first, the number and positions of impurity defects, vacancy defects, and interstitial atomic defects are analyzed.
The input value 1 specifying the type of atom, the coordinates of each atom, the size of the space in which the atom exists, and the boundary conditions is the input device 262.
Input from. This input value 1 is the information 101 of the space including the size of the space to be analyzed and the boundary conditions, and the information 102 of the atom that specifies the number of atoms in the space, the type of atoms, and the coordinates of each atom. Consists of. As these input values 1, it is also possible to use the result of a simulation in which a physical phenomenon is digitized and simulated as the behavior of particles. The defect position is analyzed by the process 2 based on these pieces of information. In the space division processing 103, the analysis space is divided into cells, and in the processing 104, atoms are assigned to the divided cells and at the same time impurity atoms are discriminated. afterwards,
In the process 105, the divided cells are classified into the following three by a method of analyzing the density state of the divided cells from the relationship between the divided cells and each atom to find the vacancy position and interstitial atom position. . There are three areas: 1) the area of normal spatial density, 2) the area of vacancy with low spatial density, and 3) the area of interstitial atoms with high spatial density. In process 106, the vacancy position and interstitial atom position are specified based on the classification result of process 105. After the above processing 2 is performed, the number of impurity defects and coordinates 107, the number of vacancy defects and coordinates 10
8 and the number of interstitial atoms and the coordinate 109 are output to the output device 263 as the output value 3.

First, the information that is input to this system will be described in detail. The input value 1 of the present system is roughly classified into information 101 of the space to be analyzed and information 102 of atoms existing in the space. Usually, the space to be analyzed is three-dimensional, but this method can be applied to any dimension.
The space information 101 includes the number of dimensions and space range information. The atom information 102 includes the number of atoms, types of atoms,
And the coordinates of each atom are included.

FIG. 2 shows one specific example of the input value 1. The space information 101 includes a space dimension number 201, each dimension interval region 202, and a flag 203 indicating whether or not a periodic boundary condition is applied in each dimension direction. In this specific example, only a space having a rectangular parallelepiped shape can be designated. The atom information 102 is the number of atoms 204, the type name of each atom 20
5 and coordinates 206 of each atom.

FIG. 3 shows the state of the space and the atom described by the specific example of the input value shown in FIG. In this specific example, the number of atoms is as small as 36, but vacancy defects 301, interstitial atoms 3
02 and impurity defect 303 exist in one place each. The other atoms show a normal periodic crystal arrangement. However, the vacancies and the atoms around the interstitial atoms are present at positions slightly deviated from the periodic crystal arrangement in order to alleviate the strain associated with defects.

Next, the analysis processing 2 which is the center of this system
The contents of will be described in detail. In analysis process 2, the space to be analyzed is divided into a plurality of cells, and the divided cells are divided into 1) regions of normal spatial density and 2) holes with low spatial density based on the relative positional relationship between the divided cells and each atom. Is classified into three regions, that is, the region where 3) exists and 3) the region where interstitial atoms with high spatial density exist. The vacancy position is extracted from the connection state of the region where the vacancy exists, and the interstitial atom position is extracted from the connection state of the region where the interstitial atom exists.

As shown in FIG. 1, process 2 is divided into four sub-processes. Each process will be described in detail. FIG. 4 shows a processing flow of the space division processing 103. First, processing 401
Then, the volume of the analysis space is calculated from the information of the analysis space region read from the space information 101. In process 402, the number density of atoms is calculated using the number of atoms of the atom information 102 that has already been obtained. Since the average volume occupied by one atom can be known from this atomic number density, process 4
In 03, the average interatomic distance is evaluated. In this embodiment, the space is divided into cells with a size that divides this average interatomic distance by 6 to 10 so that each cell contains 0 or 1 atom. In process 404, the number of cell divisions in each space dimension is determined based on the value obtained by equally dividing the average interatomic distance and the size of the space. Since the number of cells is arranged in an integer number in each dimension, the size of one cell is slightly different depending on the dimension. Finally, in process 405, a list that associates the serial numbers of the divided cells with the spatial coordinates is created, and the space division process 103 ends. FIG. 5 shows a processing flow of allocation processing of atoms to each divided cell and discrimination processing 104 of impurity atoms. In process 501, the appearance frequency of each atomic species is calculated based on the atomic type obtained from the atomic information 102. From the information on the appearance frequency, in the process 502, atomic species having a low abundance ratio with respect to the total number of atoms are identified as defects due to impurity atoms. Subsequently, in process 503, each atom is assigned to a divided cell. In this process, the cell number corresponding to each atom is calculated, and the atom number corresponding to the cell is recorded. This information is used later in the divided cell classification process 105.

Next, the division cell classification processing 105 will be described in detail. There are several possible methods for classifying divided cells. Hereinafter, the five methods will be described in detail. (1) Method for obtaining density distribution by expanding atomic radius In this method, starting from the corresponding cell of each atom, the information of the existence of the atom is propagated in the direction of each spatial dimension, and the information from the atom is transmitted to each cell. Record the distance. When the existence information of different atomic comrades is sufficiently contacted, the information propagation is terminated. When attention is paid to one cell, if there are many atoms in the vicinity of that cell, the amount of the presence information will be correspondingly large, and the value of the presence information in that cell will be large. Also, since the value of existence information is larger for cells closer to the atom, depending on the value of existence information of each cell,
The degree of atom concentration near each cell can be known. As a result, interstitial atomic defects exist in areas where cells close to the atoms are dense, and vacancy defects exist in areas where cells far from the atoms are dense. I understand.

FIG. 6 shows a processing flow of the above method. In process 601, a list for referring to cell numbers adjacent to each cell is created as a preliminary preparation. In the initial value setting process 602, the value 1 is set in each cell in which an atom exists. After that, the existence information of the atoms is propagated to the surrounding cells, and the following work is repeated until the existence information from the atoms in the vicinity are sufficiently in contact with each other (603). The repetitive work is performed on all cells (604). Processing 60
At 5, for each cell, the value of that cell is added to the cell adjacent to it, the value of that cell is doubled, and then the original value from the adjacent cell is added to that cell. This process requires retaining the previous value and setting the new value simultaneously for all applicable cells. By this repetitive work, the value in the cell gradually increases, but by dividing by the value of (2 + 2d) ^ k, the sum of the cell values can be normalized by the number of atoms. here,
(2 + 2d) ^ k represents the (2 + 2d) th power of k, d is the number of spatial dimensions, and k is the number of iterations. The 2 in the first term in () means to double its own value, and the 2d in the second term means to be added from the most adjacent cells in 2d directions. The cell value set in this way is
The cell in which the atom was present is the largest, and the value becomes smaller as the cell moves away from the atom. The abundance density of atoms in each spatial region can be known from the value set in each cell.

A method of propagating the atomic existence information will be specifically described with reference to FIG. The existence information 701 shown in FIG. 7 shows a part of the distribution of the cell values immediately after assigning each atom to the cell, the atom exists in the center cell, has the value 1, and the values of other cells are All are 0. The cell value is propagated from each cell to four adjacent directions 705. In the existence information 702 after propagating the cell value once, the value of the cell in which the atom existed is 2 and the value of the adjacent cell is 1. After that, the propagation is repeated, and the values of the cells after the second and third times become the presence information 703 and 704. As can be seen from the state 704 after three times, the cells having the same value are present at approximately the same distance from the central cell where the atom was present. The presence information (i,
If the value of the cell located at j) is a (k: i, j), the value of the cell after the (k + 1) th propagation is the recurrence formula of the following (Equation 1) according to the value setting method already described. Given in. a (k + 1: i, j) = 2a (k: i, j) + [a (k: i + 1, j) + a (k: i, j + 1) + a (k: i-
1, j) + a (k: i, j-1)] (Equation 1) Factor 2 in the first term on the right-hand side is a value for emphasizing the presence or absence of atoms, and may be a value of 2 or more. The expression in [] of the second term on the right side is the sum of the values added from the cells adjacent to the cell (i, j) of interest, and the expression differs depending on the cell division method.

With respect to the specific example shown in FIG. 3, the cell value after dividing the space by dividing the average interatomic distance into eight equal to one side of the cell and repeating the atom existence information four times The state is shown in FIGS. Since the cell value becomes smaller when the whole is shown in one figure, the part was cut out and displayed. FIG. 8 shows a crystal arrangement, that is, a state around the atoms in a state close to a regular arrangement is cut out, and the vicinity of four atoms in the center of FIG. 3 is shown. Since the propagation was repeated four times, the value of the cell 802 in which the atom existed is 148, which is the largest value. The value of the cell becomes smaller as the distance from the cell in which the atom was present decreases, and 4 is the smallest in the intermediate region 801 between the atoms. On the other hand, FIG. 9 shows the state of the cell value in the region in which vacancies such as the vacancies 301 in FIG. 3 exist. Cell 90 in the region where the vacancy exists, even if it has a value in the normal interatomic region
The value of 1 continues to have 0. Further, FIG. 10 shows a state of cell values in a region where interstitial atoms such as the interstitial atom 302 in FIG. 3 exist. In FIG. 10, the value of the cell 1001 in which the interstitial atoms were present reaches a large value 152, which is a value 148 corresponding to the atoms in the regular array. In some cells 1002 in which atoms around interstitial atoms existed, the cell 1002 also had a value larger than 148. As mentioned above,
By propagating the atomic existence information to the adjacent cells, the atomic density at each spatial position can be easily known.

(2) Method for Obtaining Density Distribution by Atomic Occupied Region Represented by Voronoi Polyhedron In this method, the space to be analyzed is the occupied region of each atom,
That is, it is divided into Voronoi polyhedra. When attention is paid to one of a plurality of points distributed in space, the Voronoi polyhedron is the one having the smallest area among the polyhedrons formed by the perpendicular bisectors of the point of interest and the points in the vicinity thereof. In particular, in the case of two dimensions, the Voronoi polygon has the smallest area among the polygons formed by the perpendicular bisectors of the point of interest and the points in the vicinity thereof. Since the analysis space is divided into cells in advance as in (1) above, this Voronoi polyhedron is also represented by discrete cells. The shape of this Voronoi polyhedron has almost the same shape and size in a regular crystal arrangement, but the shape and size are different near the defect. The present method is a method of searching the existing position of a defect using this property.

11 and 12 show the processing flow of this method. FIG. 11 is the first half of the divided cell classification process, which is a process of distributing the analysis target space to the occupied area of each atom. 12
Is the latter half of the divided cell classification process, at the same time we obtain Voronoi cells of each atom, and at the same time obtain the average value of Voronoi cells,
This is a process of identifying the position of a vacancy or interstitial atom from the difference from the average Voronoi cell value. In Figure 11 in the first half,
First, in process 1101, a list of cells to be searched in the occupied area is created in order to create a Voronoi polyhedron cell. 8 to 1 in each dimension from the cell where the atom exists
0 cell areas are listed. This number is changed depending on how many average interatomic distances are divided when the space is divided into cells. In process 1102, the occupied atomic number and the distance value stored as the value of each cell are cleared. Then, the following processing is performed on all atoms and all cells to be searched (1103, 1104). In process 1105, the distance from the atom position to the center of the cell to be searched is calculated. If the occupied atomic number is already recorded in the cell to be searched (1106), the smaller atomic number and distance between the recorded distance and the distance calculated this time are recorded again (1107), and if not recorded, Record the calculated distance and atomic number as the cell value (11
08). By the above process, the atom closest to the cell and its distance are recorded for all the divided cells. As a result, cells belonging to the Voronoi polyhedron corresponding to each atom are determined.

In the latter half of FIG. 12, as shown in FIG. 27, a table including an atomic number 270, a Voronoi volume 271, and a Voronoi cell 272 composed of a plurality of cells is provided for each atom, and each atom is provided. An average Voronoi volume 275 storing the average value of these values and an average Voronoi cell 276 composed of a plurality of cells are provided. The Voronoi cell 272 and the average Voronoi cell 276 are configured by the number of cells including any Voronoi polyhedron obtained in FIG. 11. Cells with atoms 274a, 274b
Is located in the center of each cell group, and the cell 274a or 274
cell 273a or 27 located at the same relative position from b
3b is the corresponding cell. The range indicated by the thick line in FIG. 12 is the Voronoi polyhedron (polygon) for the atoms contained in the cell 274a, which is obtained in FIG.

First, in process 1201, the cell values of the Voronoi volume 271 and Voronoi cell 272 for each atom, and the average Voronoi volume 275 and the average Voronoi cell 276 for all atoms are cleared. In order to obtain Voronoi information and average value information of each atom, the following processing 1203 is performed on all cells (12
02). In process 1203, 1 is added to the Voronoi volume 271 of the atomic number 270 recorded in each cell, 1 is set to the position of the Voronoi cell of the corresponding atom, and at the same time, 1 is added to the corresponding position of the average Voronoi cell 276. It After the processing is completed for all cells, the processing 120
In 4, each cell value of the average Voronoi cell 276 and the average Voronoi volume 275 are divided by the number of particles, and each average value is obtained. As a result, the average shape and volume of the Voronoi polyhedron for each atom in the entire space can be obtained.

Next, in order to compare the Voronoi information of each atom with the average value, the following processing 120 is performed on all the atoms.
6, 1207, and 1208 are executed (120
5). In the process 1206, the sum of squares of the difference between each cell value of the Voronoi cell of each atom and each cell value of the average Voronoi cell is calculated, and the value obtained by dividing the square root by the average Voronoi volume 275 is taken as the displacement of the Voronoi cell of that atom. The value of this displacement is large for atoms displaced from the regular arrangement and for atoms in the vicinity thereof. In process 1207, atoms having a Voronoi volume equal to or larger than the average value and having large displacement are recognized as atoms in the vicinity of the vacancy. In process 1208, atoms having a Voronoi volume below the average and large displacement are recognized as interstitial atoms and atoms in the vicinity thereof. In the processes 1207 and 1208, the vacancy or the interstitial atom can be recognized by using the deviations of the Voronoi volume and the displacement with respect to all the atoms as a reference. After performing these processes for all the atoms, in process 1209, the center of the group of atoms recognized as the vicinity of the vacancy is set as the vacancy defect position.
Further, in the process 1210, the atom located at the center of the group of atoms recognized as the interstitial atom and the atoms in the vicinity thereof is set as the position of the interstitial atom. Through the above processing, the positions of vacancy defects and interstitial atom defects that utilize the shape of the Voronoi polyhedron can be specified.

Results obtained by applying the present method to the specific example shown in FIG. 3 will be described with reference to FIGS. 14 and 15 show the correspondence between Voronoi polyhedra obtained from the atomic arrangement shown in FIG. 3 and Voronoi cells. FIG. 13 shows the value of each cell of the average Voronoi cell 1301. When an atom is arranged at the center of a 13 × 13 cell, the average value of the cells occupied by the atom is given. The area around the center is definitely occupied,
The value decreases toward the periphery and reaches 0. The shape of the average Voronoi polyhedron of this system is 90 square.
It turns out that it is almost equal to the rotated form. FIG. 14 shows the values of the Voronoi cell 1401 of atoms having a regular arrangement and the values of the Voronoi cell 1402 of atoms near the vacancy defect.
Voronoi cell 1401 of atoms in a regularly arranged region
Is almost the same as the shape of the average Voronoi cell, and is almost a shape obtained by rotating a square by 90 degrees. A Voronoi cell 1402 of an atom near a vacancy defect has a shape close to a pentagon with one of its corners directed to the lower right, and shows a shape different from that of the Voronoi cell 1401 which is a region including regularly arranged atoms. This atom is located at the upper left of the vacancy defect 301 in FIG. The Voronoi volume of this atom is larger than the average Voronoi volume, and the displacement with respect to the average Voronoi polyhedron is also large. FIG. 15 shows values of the Voronoi cell 1501 of an atom near the interstitial atom and the Voronoi cell 1502 of an interstitial atom. A Voronoi cell 1501 of an atom in the vicinity of the interstitial atom 302 of FIG. 3 has a shape obtained by cutting off a part of a corner of the Voronoi cell of an atom of a region having a regular arrangement. This atom is located to the left of the interstitial atom. The Voronoi volume of this atom is smaller than the average Voronoi volume, and the displacement with respect to the average Voronoi polyhedron is also large. Voronoi cell 1502 of interstitial atom 302 of FIG.
Is completely different from the Voronoi cells of the atoms in the regularly arranged region, has a shape close to a square, has a small Voronoi volume, and has a large displacement.

As described above, the atoms closest to the cells obtained by dividing the analysis space are associated with each other to obtain the Voronoi polyhedron of each atom, and the position of the vacancy defect and the interstitial atom defect is determined from the volume and shape thereof. Can be specified.

(3) Method of expanding the atomic occupied area according to the shape of the average Voronoi polyhedron to obtain the density distribution In the present method, the method of "starting from the cell corresponding to each atom, In the method, the information of the existence of atoms is propagated in the direction of each spatial dimension, and the distance from the atom is recorded in each cell. ” It is not a method of transmitting information but a method of propagating along a shape similar to the shape of the average Voronoi polyhedron obtained in (2). According to this method, the existence information of atoms is propagated only to the cells in the region having a shape similar to the average Voronoi polyhedron, so that the number of cells subject to the information propagation processing is smaller than that of the method (1). .

(4) Method for more accurately calculating the shape and volume of the Voronoi polyhedron The accuracy of the Voronoi polyhedron acquisition method used in the above methods (2) and (3) may be insufficient. In fact, as shown in FIG. 17, when there is a cell 1703 at approximately the same distance from two atoms 1701 and 1702, it is the cell 1 that acquires the cell, even if the difference in distance is extremely small.
There was only one atom 1702 near 703. The point on the line 1705 that bisects the line 1704 connecting the two atoms vertically is located at the same distance from the two atoms, but the cell 17
The center point 1706 of 03 is slightly displaced from the vertical bisector. Therefore, the value indicated by the atom 1701 at this cell position was 0, and the value indicated by the atom 1702 at this cell position was 1. When comparing with the average Voronoi polyhedron,
The Voronoi cell value is either 0 or 1, and even a slight difference in distance may cause a large error.

In this method, the value of each atom with respect to the Voronoi cell is not limited to an integer value of 0 and 1, but the volume value 1 of one cell is distributed according to the distance from both atoms, Each atom is given a given real value. In the example shown in FIG. 17, the equidistant line 1705 from two atoms is the cell 1703.
Since the ratio of dividing the area of the is 3: 7,
A value of 1 is 0.3 at this cell position, and a value of atom 1702 is 0.7 at this cell position. This makes it possible to reduce the variance of the average Voronoi shape and more clearly specify the difference in shape. FIG. 17
In the case of 2D, the case of 3D is shown, but in the case of 3D, one cell is divided by the perpendicular bisector of two atoms.

Further, when calculating the average Voronoi cell value, as described above, the position of the atom in the cell is ignored, and only the centers of the cells in which the atoms were present are made coincident and the average is not calculated. , By calculating after shifting the position of the cell value so that the atom is located at the center of the cell, it is possible to obtain a more accurate average Voronoi shape. That is, the above operation is equivalent to changing the division of the cell so that the atom is located at the center of the cell, and with the change of the division, the original cell value is distributed to some new cells. It The vector corresponding to the above shift operation is 1
Contained within one cell. In this way, the method of shifting the cell value so that the atoms are located at the center can be used when comparing the Voronoi cell values of the respective atoms, so that the comparison can be performed with higher accuracy.

(5) Method of calculating a plurality of average Voronoi cell values Depending on the system to be analyzed, there may be a plurality of types of Voronoi cell shapes with respect to the atomic arrangement of the crystal structure. In order to analyze such a system with high accuracy, it is necessary to calculate the average Voronoi cell value for each of a plurality of types of shapes.

The simplest specific example described above is a compound system as shown in FIG. Fig. 18 shows atomic species 18
This is a system in which the atomic species 1802 indicated by 01 and white circles are regularly arranged. FIG. 18 is described in a two-dimensional space to simplify the description. In the case of two dimensions, the Voronoi polyhedron is a polygon, but the name is polyhedron. Atomic species 18
The Voronoi polyhedron 1803 of 01 has a shape close to a square. On the other hand, the Voronoi polyhedron of the atomic species 1802 takes a shape close to a hexagon, but there are vertically long ones 1804 and horizontally long ones 1805 depending on the arrangement relationship with the atomic species 1801. Therefore, it is natural to calculate the average Voronoi cell value according to the atomic species, but even if the same atomic species are compared and the Voronoi cell shapes differ greatly, it is determined that the shapes are different and multiple types of shapes are determined. An average value needs to be calculated for. That is, in this method,
The data storage area shown in is provided for each shape of the Voronoi cell. The Voronoi shape of the atoms around the defect is also calculated as an average Voronoi cell value of another type, but the appearance frequency is smaller than the average Voronoi cell value of atoms having a regular crystal arrangement, so that it can be easily distinguished.

Even in a system having one kind of atomic species, the Voronoi cell may have different shapes. The crystal structure of silicon is a diamond structure, and the arrangement relationships of each atom in the crystal structure are all equivalent. However, in the three-dimensional space in which the silicon crystal exists, two types of Voronoi polyhedron appear when the direction of the dimension is specified. FIG. 19 shows the arrangement relationship of each atom and the shape of the Voronoi polyhedron at that time. The shape of the Voronoi polyhedron of each silicon atom is such that two side surfaces of two triangular prisms having different shapes are rotated by 90 degrees and bonded to each other to combine them. However, depending on the directions of the four bonds of the silicon atom, the Voronoi polyhedron appears in two different directions. In FIG. 19, the atom 1901
The Voronoi polyhedron 1903 possessed by and the Voronoi polyhedron 1904 possessed by the atom 1902 have the same shape but only different directions. However, it is better to calculate the average values separately assuming that both shapes are different. Can be applied as is and analysis is easy.

In order to deal with such a crystal structure, it is necessary to calculate a plurality of average Voronoi cell values. In a system containing defects in a silicon crystal, two types of Voronoi polyhedra that are oriented in different directions and have almost the same volume are obtained, and at the same time, some deformed Voronoi polyhedra are obtained.

Several examples of the method of classifying the divided cells have been shown. In each case, the number of vacancy defects, interstitial atom defects, or impurity defects and the number thereof are determined by the calculation amount which is almost proportional to the number of atoms. The coordinates can be specified. Since the space is discretely divided by cells and the calculation is done by focusing on the divided cells, it is not necessary to calculate the combination of atoms, so the calculation amount is smaller than the calculation amount proportional to the square of the number of atoms. You can analyze with.

Next, the information that is output from this system will be described in detail. The output value 3 of the present system shown in FIG. 1 comprises information 107 on the number and coordinates of impurity defects, information 108 on the number and coordinates of vacancy defects, and information 109 on the number and coordinates of interstitial atomic defects. Number of impurity defects and coordinate information 107
Recognizes impurities by examining the abundance ratio of atom types, and can extract the number and coordinates from the atom information indicated by the input value 1. By classifying the divided cells, information 108 and 109 on the number and coordinates of vacancy defects and interstitial atom defects can be easily obtained.

One specific example of the output value 3 is shown in FIG.
FIG. 16 shows the result of the defect analysis performed on the specific example of the input value 1 shown in FIG. The input information 1601 shows an outline of the space information and the atom information described by the input value 1. In the impurity defect information 107, the impurity defect is 1
That is, the atom is a carbon atom, and its specific position coordinates are shown. The vacancy defect information 108 indicates that there is one vacancy defect and its specific position coordinates. The interstitial atom defect information 109 indicates that there is one interstitial atom defect and its specific position coordinates. All of this information is output as the output value 3.

In the above embodiments, as the shape of the cells obtained by dividing the space, the cells are equally divided in the case of one-dimensional, rectangular in the case of two-dimensional, and rectangular parallelepiped in the case of three-dimensional. In the case of one-dimensional, the cell division method of equal division is considered to be most effective, but in the case of two-dimensional or three-dimensional, triangulation or tetrahedral division is performed depending on the periodic structure of the crystal. It may be more effective to adopt.

The existence probability of defects is generally extremely small.
Therefore, this method realizes high-speed analysis by omitting the regions of regularly arranged structures that occupy the majority of the system from the analysis target in advance. Therefore, the space to be analyzed is divided through a plurality of stages. First, the space is divided into large cells, the regions in which atoms are regularly arranged are extracted and excluded, and in the next stage, regions in which defects are likely to exist are extracted from other regions, and this is extracted. After dividing into smaller cells, the highly accurate evaluation as described above is performed. With such a hierarchical evaluation method, highly accurate analysis can be performed in a short calculation time. Next, another embodiment of the output method of the output value of the present system will be described below. In particle simulations involving the present invention, not only the states of atoms are captured as simple numerical values, but the simulation results are often grasped by three-dimensional visualization. But,
In the case of a simulation that handles a large number of atoms ranging from thousands to millions such that the present invention is effectively used, the position coordinates and bonding states of the atoms which have been conventionally used are ball-and-ball-shaped.
It is difficult to read information from a visualized image even when using a stick display method. When displaying one million atoms on a screen of 19 to 21 inches, which is the size of a typical visualization display, the size of one atom is about 2 millimeters, and the atomic coordinate position is slightly small due to the presence of defects. Even if it changes, it is difficult to recognize the difference from the screen.

In the present invention, the defect information obtained by the analysis is mainly displayed to facilitate the recognition of the defect distribution status and the mutual positional relationship of the defects. The feature of the display according to the present invention is that among the atoms of the basic atomic species, those that have a regular arrangement, that is, the atoms that do not largely deviate from the crystal arrangement are displayed in a transparent or semitransparent state, and other impurity atoms and vacancies are displayed. This is to display only the atoms that are out of the regular arrangement of crystals such as defects or interstitial atom defects in an opaque color. In particular, by changing the display color depending on the defect state, it becomes extremely easy to recognize the analysis result.

FIG. 25 shows an example in which the output of the defect analysis is displayed using the graphics display 2501 of the output device 263 of FIG. In the case of FIG. 25, regularly arranged atoms are transparent and excluded from the display. Only the impurity atom 2503, the vacancy defect 2504, and the interstitial atom defect 2505 are displayed in an opaque color. The areas of these defects are displayed in the defined space area 2502. A legend 2506 showing the meaning of each color is also displayed in the display. Furthermore, it is important to make it easy to recognize the defect position by using the device 2507 that can change the viewpoint position of the three-dimensionally displayed image on the display with a dial or the like.

Before specifying the position of the defect for each atom, after roughly specifying the defect region of several hundreds of atoms and its position, the arrangement of atoms existing in the region and the bond bond information are graphically displayed. By displaying, the defect position can be easily specified visually. FIG. 24 shows an example in which the atomic arrangement of the limited area and the bond bond information are displayed.

Next, another embodiment of the present invention will be described.
The input values are the number of atoms, the name (type) of each atom, the coordinates, and the boundary condition of the space in which the atom exists, as in the above-described embodiment. From this information, the number of impurity defects, the names of impurity atoms and their coordinates, the number and coordinates of interstitial atoms, and the number and coordinates of vacancy defects are output. The function of this embodiment is the same as that of the above embodiment, but the processing contents are slightly different. That is, in the present embodiment, by comparing the input atomic position with the reference atomic position of the system to be analyzed, the information on the atomic arrangement defect is generated.

FIG. 20 shows a processing procedure of the defect analysis method according to the present invention. The input value 1 and the output value 3 are the same as in the case of the defect analysis method of FIG. In process content 2, first, a process 2001 for creating a reference atom position of a system to be analyzed is performed, a process 2002 for comparing the created reference atom position with an input atom position is performed, and a process 2003 performs atom Are classified into three: 1) impurity atoms, 2) vacancy defect atoms, and 3) interstitial atoms. Finally, various defect positions are extracted by the process 2004.

FIG. 21 shows a processing flow of the reference atom position creation processing 2001. In process 2101, the impurity atom is specified by calculating the existence ratio of each atomic species. Further, in the process 2102, the basic compound that constitutes the system is specified based on the analysis result. In process 2103, the basis vector that is the basic structure factor of the crystal is calculated. Finally, in process 2104, based on the calculated defined vector, the corresponding reference atom position is searched from the database that stores data relating to the crystal structures of various basic compounds. Reference atom position creation processing 2001 shown in FIG.
Can be used when it is easy to identify the crystal system. For a more general structure, it is necessary to use the processing flow of another embodiment shown in FIG.

Reference atom position creation processing 20 shown in FIG.
In 01, the entire analysis space is divided into minute cells by the space division processing 103 shown in FIG. Then, the process 220
In 1, the Voronoi polyhedron represented by the combination of a plurality of cells is calculated for each atom, and the basic Voronoi polyhedron in the analysis space is obtained. In this case, as described above, a plurality of types of Voronoi polyhedrons basically exist even in one structural system, so it is necessary to calculate the average value for each of the plurality of types of polyhedrons. In process 2202, a basis vector that gives an atomic position in the structure is generated from the obtained average Voronoi polyhedron. This vector gives the position to the adjacent atom if the atoms are regularly arranged. Finally, processing 2203
By this, a reference atom position is generated from the obtained basis vector.

Subsequently, a process 2002 for comparing the position of the reference atom with the position of the atom in the analysis object, an atom classification process 20.
03 and defect position extraction processing 2004 will be described with reference to FIG. In the process shown in FIG. 23, the position coordinates of the reference atom and the atom of the analysis target given in the same region are compared (2002), and the impurity atom, the vacancy defect atom, or the lattice is compared based on the comparison result. Atoms are classified into three interatomic atoms (2003), and defect positions are calculated (200
4).

First, in process 2301, a space division process for dividing the analysis space into minute cells and a process for assigning reference atoms to the cells are performed. If the space division has already been performed at the stage of generating the reference atom, the processing 2301 is omitted. In process 2302, atoms in the analysis target are assigned to the divided cells. In process 2303, the position coordinates of the reference atom and the analysis target atom assigned to the divided cells are compared. In this process, first, all cells are searched, and each cell has both the reference atom and the analysis target atom in the same cell, the cell containing only the reference atom, and the cell containing only the analysis target atom. , It is classified as a cell that contains neither. Atoms contained in the same cell exist in the region where the atom to be analyzed and the reference atom are almost the same. If only one atom is contained in the cell, it may be divided into adjacent cells depending on how to divide the cells, so pay attention to the cell containing only one reference atom,
It is checked whether or not only one atom to be analyzed exists in the cell adjacent to this. As a result, the atoms associated with the adjacent cells are recognized as regularly arranged atoms. In the atom associated with each cell, when the reference atom and the analysis target atom have different atom types, the analysis target atom is recognized as an impurity atom defect.

Next, atom classification processing 2003 is performed. First, in process 2304, if there is an analysis target atom that does not correspond to the reference atom by the above-mentioned atomic position comparison, this atom is extracted as a residual atom and further classified as a candidate for an atom near the defect. Also, processing 2304
Then, by the atomic position comparison in the process 2002, the reference atom and the analysis target atom which are left without being able to correspond to each other are extracted as the remaining atoms. In process 2305, atoms adjacent to these remaining atoms are searched for using the divided cells. In the residual atom classification processing 2306, the following processing is performed. When all the atoms adjacent to the reference atom have a pair, it is recognized that a defect exists at the position corresponding to the reference atom. When all the atoms adjacent to the analysis target atom have a pair, the analysis target atom is recognized as an interstitial atom defect.

In the process 2307, the defect position is calculated for each of the various defects recognized by the above process. By the series of these processes, the number and position of various defects can be analyzed by comparing the reference atom and the atom to be analyzed.

[0052]

According to the present invention, the amount of calculation for calculating the position of an impurity defect, a vacancy defect, or an interstitial atomic defect existing in a system containing millions of atoms is the same as that of the conventional number of atoms. Two
Since the amount is proportional to about the first power instead of the power, the calculation time can be significantly reduced, and the defect analysis simulation can be easily performed.

[Brief description of drawings]

FIG. 1 shows a procedure of a defect analysis method showing an embodiment of the present invention.

FIG. 2 is a specific example of input values of a defect analysis method.

FIG. 3 is a schematic diagram of a space and an atom showing a specific example of an input value.

FIG. 4 is a processing flowchart of space division processing.

FIG. 5 is a processing flow chart of atom allocation and impurity atom discrimination processing.

FIG. 6 is an example of a process flow diagram of a classification process of divided cells.

FIG. 7 is a diagram showing a method of transmitting atom presence information.

FIG. 8 shows a state of a regular atomic arrangement region by the atomic radius expansion method.

FIG. 9 is a state in the vicinity of a vacancy defect by the atomic radius expansion method.

FIG. 10 shows a state in the vicinity of an interstitial atomic defect by the atomic radius expansion method.

FIG. 11 is the first half of another example of the processing flow chart of the classification processing of divided cells.

FIG. 12 is the latter half of another embodiment of the processing flow diagram of the classification processing of divided cells.

FIG. 13 is a diagram of average Voronoi cell values.

FIG. 14 shows Voronoi cell values of regularly arranged atoms and atoms in the vicinity of vacancy defects.

FIG. 15 shows Voronoi cell values of atoms in the vicinity of interstitial atom defects and interstitial atoms.

FIG. 16 is a specific example of output values of defect analysis.

FIG. 17 is a diagram illustrating a method for improving accuracy when a boundary between two Voronoi polyhedra divides a cell.

FIG. 18 is a diagram showing that in the case of a compound having a plurality of atomic species, a plurality of Voronoi polyhedron shapes are present even if they are regularly arranged.

FIG. 19 is a diagram showing that there are a plurality of Voronoi polyhedron shapes even when a single atomic species has a regular arrangement.

FIG. 20 is a configuration diagram of a defect analysis method showing another embodiment of the present invention.

FIG. 21 is a diagram showing a flow of reference atom position creation.

FIG. 22 is a diagram showing another flow of creating reference atom positions.

FIG. 23 is a diagram showing a flow of processing for comparing the positions of a reference atom and an atom to be analyzed, classifying the atom, and extracting a defect position.

FIG. 24 is a display example of atomic arrangement and bond information in a limited area where a defect exists.

FIG. 25 is a display example of a defect on a graphics display.

FIG. 26 shows the configuration of a computer system that implements the present invention.

FIG. 27 shows the data of Voronoi cell and average Voronoi cell.
Data structure.

[Explanation of symbols]

1 ... input value, 2 ... defect analysis processing, 3 ... output value, 101 ...
Analysis target space information, 102 ... Atom information, 103 ... Spatial cell division processing, 104 ... Atom assignment and ratification object atom discrimination processing, 105 ... Division cell division processing, 106 ... Defect position extraction processing, 107 ... Information on the number and coordinates of impurity defects,
108 ... Information on the number and coordinates of vacancy defects, 109 ... Information on the number and coordinates of interstitial atomic defects, 301 ... Vacancy defects, 302 ...
Interstitial atomic defects, 303 ... Impurity atomic defects

Claims (10)

[Claims] 1. When analyzing the arrangement of particles that are atoms, molecules, or ions that constitute a substance using a computer having a storage device and a display device, a) the number and types of the particles to be analyzed, And inputting information of atoms relating to respective coordinates of the particles and information of space relating to the space where the particles are present, b) dividing the space into minute cells based on the information of the space, c) based on the information of the atoms, determining the impurity atoms while allocating the particles to the divided cells, and d) placing each of the cells in the vicinity of a vacancy defect and between the lattices of the particles. A cell near an atom and a cell near a regular arrangement of the particles, e) extracting the position of each defect from the classified cell, and f) the position of the analyzed defect. Display on the display Defect location analysis method characterized by. 2. In the step d), the presence information of the particles is propagated in each direction defined by the spatial dimension starting from the cell corresponding to each of the particles, and is determined by the propagated presence information. 2. The defect position analyzing method according to claim 1, wherein each cell is classified based on a density state of a value of a reach distance from each particle. 3. The defect position according to claim 1, wherein in the step d), each cell is classified by determining the particle density and the defect by using a Voronoi polyhedron representing a region occupied by the particle. analysis method. 4. The presence information is propagated according to the shape of an average Voronoi polyhedron.
The described defect position analysis method. 5. The defect position analyzing method according to claim 3, wherein the Voronoi polyhedron is expressed by connecting a plurality of discrete cells. 6. When constructing a Voronoi polyhedron using the discrete cells, if the cell includes a boundary of the Voronoi polyhedron, the weight of the cell with respect to the Voronoi polyhedron is included in the Voronoi polyhedron of the cells. The defect position analysis method according to claim 5, wherein the defect position analysis method is represented by a real number proportional to the volume ratio of the region. 7. The defect position analysis according to claim 4, wherein a space to be analyzed is constituted by a plurality of different Voronoi polyhedron shapes, and an average value of the existence information is obtained for each of a plurality of shapes. Method. 8. When analyzing the arrangement of particles that are atoms, molecules, or ions constituting a substance using a computer having a storage device and a display device, a) the number and types of the particles to be analyzed, And inputting information of atoms relating to respective coordinates of the particles and information of space relating to the space where the particles are present, b) generating information indicating a reference particle position based on the information of the space And c) comparing the reference particle position with the input particle position based on the information of the atom, classifying each particle into an impurity defect atom, a vacancy defect atom, or an interstitial atom defect, and , D) A defect position analysis method, wherein the position of the extracted defect is displayed on the display device. 9. In step f) of claim 1 or step d) of claim 8, the regularly arranged particles are displayed transparently or semi-transparently, and the positions of the defects including vacancy defects are made opaque. A defect location analysis method characterized by displaying. 10. An atom constituting a substance using a computer,
Molecules, or when analyzing the arrangement of particles that are ions, divide the space into a plurality of cells based on the information of the space to be analyzed and the particles present therein, the particles in each of the cells It is determined whether or not the particles are impurity atoms by allocating, and each of the cells is classified into atoms with regular arrangement, atoms in the vicinity of vacancy defects, or atoms in the vicinity of interstitial atom defects, and defect positions are A method for analyzing a defect position characterized by specifying.