JP2006172406A - Method for creating interface structure data and system for supporting creation of interface structure data - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for creating interface structure data and surface structure data satisfying periodic boundary conditions in the direction in parallel with interface or surface. <P>SOLUTION: A surface periodic slab model is created by creating surface unit lattice satisfying the periodic boundary conditions and using a predetermined surface direction as a boundary surface from unit lattice of crystal structure and adding a vacuum layer to an object formed by arranging some surface unit lattice. In addition, the interface periodic slab model is created by adding the vacuum layer after joining two different surface unit lattice. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a system that supports creation of interface structure data used as input data when executing a simulation for obtaining an electronic state of a substance at an interface and a surface.

  In recent years, computer simulation is taking on an important position in material development as the speed of computers increases, the capacity of usable memory increases, and the development of simulation algorithms. In particular, there is an increasing demand for precise analysis at the atomic level of nanometer-sized structures.

  Examples of widely used atomic level simulation software include VASP, CASTEP, and Gaussian. However, these softwares have strong research colors and do not take into account the convenience of those who do not specialize in simulation. In order to execute the simulation, an input file in which details of the calculation contents are described is required, but in order to create this, a certain degree of expertise is required. In particular, it takes a lot of time to input the atomic arrangement, which is troublesome for those who have specialized knowledge. Therefore, in order to make the simulation software easily available to many people, it is important to develop an input support system. An example of such a support system is “MedeA” of Materials Design (http://www.materialsdesign.com/). Although this system uses VASP or the like for the simulation engine unit, the user interface has been improved to greatly reduce the labor of creating an input file, and it is easy to use for those who do not have specialized knowledge. In particular, regarding atomic arrangement, in addition to being able to read data from a commercial crystal structure database and use it for simulation input, operations such as replacing, moving, adding, and deleting atoms can be easily performed. Therefore, it is easy to create an atomic arrangement of the target crystal structure and execute a simulation.

  On the other hand, in order to investigate the catalytic reaction, it is important to simulate the surface and the interface during device design. Naturally, in order to execute the simulation of the interface or the surface, an input file corresponding to the simulation is required.

  In VASP and CASTEP, focusing on the fact that the crystal has a three-dimensional periodic structure, an infinitely large system can be simulated by expanding the electron wave function with a plane wave. On the other hand, Gaussian is suitable for finite system simulation because the electron wave function is expanded by a local function such as a Gaussian function. However, the interface has a periodic structure in a two-dimensional direction parallel to the interface, but does not have periodicity in a direction perpendicular to the interface. That is, strictly speaking, the interface structure cannot be simulated by the software.

  Therefore, a periodic slab model is used to treat the interface or surface as a three-dimensional periodic structure without impairing the essence of the simulation. Examples of its use are disclosed in Non-Patent Documents 1 and 2. A unit structure of the periodic slab model is schematically shown in FIG. FIG. 2A shows a surface periodic slab model. Atoms exist only in the slab 2 part, and a vacuum layer 1 in which no atoms exist is added above and below the slab 2 part. Considering a model in which this structure is arranged three-dimensionally, periodic boundary conditions similar to those of crystals are imposed in the a-axis and b-axis directions, and periodic boundary conditions are imposed in the c-axis direction across a vacuum layer. Has been. Here, if the thickness d of the slab is large, the influence of the back surface of the slab hardly appears on the surface of the slab. That is, it is almost equivalent to a state where d is infinite, and the actual surface state is well reproduced. In practice, d is often about 10 atomic layers. Further, the vacuum layers provided above and below the slab are thickened so that the interaction between the slabs through this layer can be ignored. Thereby, the periodicity in the c-axis direction can be ignored, and an isolated surface state can be reproduced. The thickness of the vacuum layer may be about 5 angstroms or more.

Yamamoto, Iwata, Yamazaki, Okamoto, Ohno, Uda, “Introduction to First Principles Simulator”, Advance Software Co., Ltd., July 10, 2004, p. 50

  In FIG. 2B, the vacuum layer 1 is added only to the upper part of the slab 2. Since the periodic boundary condition is imposed also in the c-axis direction, the two models in FIGS. 2A and 2B are equivalent. Choose the one that is easy to use according to the situation.

  FIG. 2C shows a periodic slab model of the interface structure. An interface slab is realized by providing two unit cells and closely arranging the surface slab 3 made from the first unit cell and the surface slab 4 made from the second unit cell.

  Since the periodic slab model satisfies a three-dimensional periodic boundary condition, it can be handled by the simulation software.

  Conventionally, however, there is no general-purpose system to support the creation of periodic slab models, and researchers have built and used systems specialized for individual objects. For this reason, it is difficult for a person who does not have specialized knowledge to execute the simulation of the interface and the surface state. Also, researchers with specialized knowledge needed to build different systems for each target structure.

  By providing a general-purpose system for supporting the creation of the periodic slab model, the creation of the interface structure data and the surface structure data describing the atomic arrangement necessary for performing the simulation of the interface and the surface structure is supported.

  A surface unit cell that satisfies the periodic boundary condition is created from the crystal unit cell. If a surface unit cell having an arbitrary plane orientation that satisfies the periodic boundary condition in the surface horizontal direction is created, the surface unit cell may become infinitely large. Such a surface unit cell contains an infinite number of atoms, but since there is an upper limit on the number of atoms that can be handled in the simulation, a large surface unit cell is not suitable. Therefore, in the present invention, only the plane orientation specified by the Miller index is considered. Since the plane orientation used in the experiment is almost always expressed by a simple Miller index, there is no practical problem.

  A modified extended grid is created by expanding the unit grid and changing the boundary surface. A deformed extended lattice having a plane specified by the Miller index as a boundary is a surface unit lattice. A surface slab is created by arranging a finite number of the surface unit cells. Furthermore, a surface periodic slab model is created by adding a vacuum layer to the surface slab.

  Also, an interface slab is created by joining the two surface slabs. In order to satisfy the periodic boundary conditions even after joining, the joining surface shapes of the two surface slabs need to match. Therefore, a surface slab is created after shaping processing such as expansion, rotation, compression, and expansion of each surface unit lattice so that the joint surface shapes match. At the same time, consideration is given so that the dangling bonds present on the joint surface of the two surface slabs are bonded as smoothly as possible. Further, the atomic positions in the two surface slabs are relatively moved to smooth the interatomic bond at the joint surface.

  Join two shaped surface slabs to create an interface slab. An interface periodic slab model is created by adding a vacuum layer to the interface slab.

  Further, dangling bonds remaining at the interface between the slab and the vacuum layer are terminated with hydrogen atoms or the like. By this process, a slab model having a stable atomic arrangement can be obtained.

  By preparing an input file creation support system corresponding to the interface and surface structure, material design by simulation can be easily performed.

A method for creating a surface periodic slab model according to the best mode for carrying out the present invention will be described with reference to the flowchart of FIG. First, a unit cell that forms a crystal structure that is the basis of the surface unit cell is prepared (step S1). The data may be obtained from experiments such as X-ray structure analysis, or may be obtained from a database in which experimental data is accumulated. It may be the result of simulation by the classical molecular dynamics method. Further, it may be processed by adding atoms to these unit cells. FIG. 3 schematically shows the unit cell. The unit cell 30 is a parallelepiped, and its shape is characterized by three lattice vectors a, b, and c constituting the sides. The magnitudes of these vectors are a, b, c, respectively, the angle between vectors a and b is γ, the angle between a and c is β, and the angle between b and c is α. The crystal structure is obtained by moving the unit cell by the translation vector R represented by Formula 1 and superimposing them on all the integers n ₁ , n ₂ , and n ₃ .

Number 1

R = n ₁ a + n ₂ b + n ₃ c (1)

で表される時、これを内部座標表現と呼ぶ。結晶構造では格子の境界にある原子は、隣接する格子との間で共有されている。例えば、（００１）面上の原子は、ｃ軸方向に±ｃだけずれた格子との間で共有されており、格子の角にある原子は隣接する八個の格子の間で共有されている。そこで、式２の内部座標表現では、ｘ，ｙ，ｚは全て０以上かつ１未満とすることにより、格子境界にある原子が複数の格子に含まれることを避けている。以下の説明では内部座標表現を用いるが、それ以外の表現を用いた場合にも、本実施の形態は適用可能である。例えば、直交座標系での各原子位置の座標を保持しても良い。The atomic arrangement within the unit cell characterizes the atomic arrangement of the entire crystal structure. Atomic position (x, y, z) is

This is called the internal coordinate representation. In the crystal structure, atoms at lattice boundaries are shared between adjacent lattices. For example, atoms on the (001) plane are shared between lattices shifted by ± c in the c-axis direction, and atoms at the corners of the lattice are shared between eight adjacent lattices. . Therefore, in the internal coordinate expression of Expression 2, x, y, and z are all set to 0 or more and less than 1, thereby avoiding atoms at lattice boundaries being included in a plurality of lattices. In the following description, the internal coordinate expression is used, but the present embodiment can be applied even when other expressions are used. For example, the coordinates of each atomic position in the orthogonal coordinate system may be held.

  Normally, the Bravey lattice is used as a reference when designating the plane orientation. Therefore, when a basic unit lattice is given, it is good to extend it to a Bravay lattice and then perform the following processing. The conversion from the basic unit cell to the Bravay cell is not difficult for those skilled in the art. Although it is possible to apply the following processing to the basic unit cell, it should be noted that it does not match the normal plane orientation.

  A point to be noted when creating a surface periodic slab model from a unit cell is that a periodic boundary condition is imposed in a direction parallel to the surface. That is, the target periodic simulation result cannot be obtained unless the surface periodic slab model is composed of a surface slab having an atomic arrangement that is smoothly connected at the boundary.

  Considering a surface slab having an arbitrary plane orientation, an infinitely large surface unit cell may be required to satisfy the periodic boundary condition. However, since the number of atoms that can be handled at one time in the simulation is limited, the size of the surface slab is limited. Therefore, in the present embodiment, a surface unit cell having a plane orientation specified by the Miller index (h k l) is created. When the number of atoms contained in the unit cell is n, the number N of atoms contained in the surface unit cell represented by the Miller index (h k l) is approximately expressed by Equation 3.

Number 3

N = n × h × k × l (3)
However, when any of h, k, and l is 0, the value is calculated as 1. It should be noted that N does not contain atoms such as hydrogen for treating dangling bonds, which will be described later, and that the number of atoms also increases due to a rotation operation when creating an interface structure, which will be described later. . Since there is an upper limit on the number of atoms contained in the surface unit cell, the plane orientation that can be created is limited.

  Alternatively, it may have a function of designating the surface orientation with another numerical value such as an angle and outputting a plurality of candidates for the surface orientation mirror index having an angle close to that. In that case, the structure to be actually used is designated by external input from among the plurality of candidates.

理では（１１０）面として扱われる。なお、ｈ＋ｋ＝−ｉが常に成立している。In the hexagonal system, the plane orientation is expressed using four indices (h k i l), and (h k l) and

In theory, it is treated as the (110) plane. Note that h + k = −i is always established.

ただし、ｈ，ｋ，ｌのいずれかが０の場合には、その方向には格子の拡張を行わずに単位格子を保持する。例えば、ｈ＝０の場合には、ａ′＝ａ，ｘ′＝ｘである。Next, the unit cell of the crystal is expanded (step S2). A new lattice is formed by closely arranging unit lattices of h in the a-axis direction, k in the b-axis direction, and l in the c-axis direction so as to satisfy the translation vector R and form a parallelepiped. Create Hereinafter, the new lattice created in this way is referred to as an extended lattice. FIG. 4 shows an example of an extended grid. (231) In order to create a surface unit cell, two unit cells 30 are arranged in close contact with each other, two in the a-axis direction, three in the b-axis direction, and one in the c-axis direction. Let the lattice vectors characterizing the parallelepiped of the extended lattice be a ′, b ′, c ′. Further, when the internal coordinate expression is changed in accordance with the change of the lattice vector, the crystal structure generated from the unit cell 30 and the crystal structure generated from the extended lattice match.

However, when any one of h, k, and l is 0, the unit cell is held without extending the cell in that direction. For example, when h = 0, a ′ = a and x ′ = x.

  The (111) plane of the extended lattice is equivalent to the (h k l) plane of the unit lattice. For example, the (111) plane of the extended grid shown in FIG. 4 is equivalent to the (231) plane of the unit grid 30. Similarly, the (110) plane, (101) plane, and (011) plane of the extended grid are equivalent to the (h k 0) plane, (h 0 l) plane, and (0 k l) plane of the unit grid, respectively. . The (110) plane of the extended grid shown in FIG. 4 is equivalent to the (230) plane of the unit grid 30.

原子位置の内部座標は次式で変換される。

成した結晶構造も、単位格子３０から生成される結晶構造と一致する。また、五面体５１をｃ′移動させても同一の結果が得られることは明らかであるし、五面体５２を−ａ′、もしくは五面体５１をａ′移動させ、拡張格子の（１００）面同士が接するようにつなぎ合わせても、同様の結果を得ることができる。さらに、同様の方法で境界面を（０１１）面もしくは（１１０）面に変更できることは明らかである。もしくは、拡張格子を回転させてから境界を（１０１）面に変更しても、同様の結果を得ることができる。以下では、このように境界面を変更した拡張格子を、変形拡張格子Ａと呼ぶ。In step S3, the boundary surface of the extended lattice is changed. If the specified Miller indices (h k l) are not all zero, the boundary surface is changed to the (111) surface. When only one is 0, for example, when only h is 0, the boundary surface is the (011) plane. Similarly, the boundary is the (101) plane when only k is 0, and the (110) plane when l is 0. FIG. 5 shows how the boundary surface is changed to the (101) surface. First, the extended lattice is divided into two pentahedrons 51 and 52 with the (101) plane as a boundary (FIG. 5A). The two divided pentahedrons are separated and shown in FIG. Next, either pentahedron is moved in the c′-axis direction by the lattice vector. Here, the pentahedron 52 is moved by −c ′. FIG. 5C shows the two pentahedrons after the movement separated from each other, but actually the two pentahedrons are in contact with the (001) plane of the extended lattice, and the arrangement of FIG. It becomes. That is, the two pentahedrons after moving again form a parallelepiped. At this time, the lattice vector is converted as follows.

The internal coordinates of the atomic position are converted by the following formula.

The formed crystal structure also matches the crystal structure generated from the unit cell 30. It is clear that the same result can be obtained even if the pentahedron 51 is moved by c ′, and the pentahedron 52 is moved by −a ′ or the pentahedron 51 is moved by a ′, and the (100) plane of the extended lattice is obtained. Similar results can be obtained even if they are joined together. Further, it is obvious that the boundary surface can be changed to the (011) plane or the (110) plane by the same method. Alternatively, the same result can be obtained even if the boundary is changed to the (101) plane after the extended lattice is rotated. Hereinafter, the extended lattice with the boundary surface changed in this way is referred to as a modified extended lattice A.

原子位置の内部座標は次式で変換される。

変形拡張格子Ｂとする。変形拡張格子Ｂの（００１）面は、変形拡張格子Ａの（０１１）面であり、すなわち、拡張格子の（１１１）面であり、さらに、単位格子の（ｈ ｋ ｌ）面と等価である。In order to change the boundary surface of the extended lattice to the (111) plane, the boundary surface of the modified extended lattice A may be further changed. FIG. 6 is a schematic diagram showing how the boundary surface of the modified extended lattice A is further changed to the (011) plane. The deformation extended lattice A is divided by the (011) plane (FIG. 6A), and one pentahedron is moved along the c ″ axis. When the arrangement is made such that the (001) planes are in contact with each other, a parallelepiped having a set of boundary planes as the (011) plane of the modified extended lattice A is formed (FIG. 6B). The crystal structure generated from this parallelepiped also coincides with the crystal structure generated from the unit cell. By this modification, the lattice vector is converted as follows.

The internal coordinates of the atomic position are converted by the following formula.

Let it be a deformation extended lattice B. The (001) plane of the modified extended lattice B is the (011) plane of the modified extended lattice A, that is, the (111) surface of the extended lattice, and is equivalent to the (h k l) surface of the unit lattice. .

  With the above operation, a modified extended lattice can be created that has an arbitrary surface specified by the Miller index (h k l) of the unit lattice as a boundary and satisfies the periodic boundary condition. This deformation extended lattice becomes a surface unit lattice for creating a surface slab.

With the surface unit cell, the surface structure can be easily made. In the following description, it is assumed that the desired plane orientation of the unit cell is modified so as to be the (001) plane of the surface unit cell. The lattice vectors characterizing the surface unit lattice are rewritten as a, b, and c. When this surface unit cell is moved by the translation vector R represented by Equation 1 and they are superposed on every R, a crystal structure is formed. Here, when the range of n ₃ is limited to a non-negative integer, a semi-infinite surface structure with the (001) plane as the surface is formed. When applied to the surface unit cell shown in FIG. 6B, a semi-infinite surface structure with the (h k l) plane of the unit cell as the surface is formed. Furthermore, by providing an upper limit for n ₃ , it is possible to create a slab that extends infinitely in the surface parallel direction. The infinitely extending slab is equivalent to a surface slab obtained by extending a surface unit cell in the c-axis direction and a periodic boundary condition in the surface parallel direction is imposed. By changing the upper limit of the n _3, the thickness of the surface slab is changed. Therefore, in step S6, the thickness of the surface slab is secured so that the influence of the back surface of the slab does not appear on the slab surface, and the thickness of the surface slab does not exceed the maximum number of atoms that can be simulated. It is better to specify by external input. also the range of n ₃ is a negative integer, it can of course be created similar surface slab.

  Vacuum layers are generated above and below the surface slab (step S7). When the length of the c-axis is multiplied by q and the internal coordinates of the atoms in the c-axis direction are divided by q, a vacuum layer in which no atoms are present is generated, and the surface periodic slab model shown in FIG. Further, when all atoms are moved by a predetermined distance in the c-axis direction, the surface periodic slab model shown in FIG. 2A is completed. The larger the vacuum layer, the smaller the interaction through the vacuum layer and the more accurate the simulation, but the longer the simulation takes. Usually, it may be about 5 angstroms.

  At the interface between the surface slab and the vacuum layer, there is a dangling bond resulting from cutting the crystal at a finite position, and the structure is unstable. Therefore, in step S8, it is preferable to terminate the dangling bonds with hydrogen atoms or the like to create a stable electronic state.

  Since the bond cut when the crystal is cut becomes a dangling bond, it is easy to know its position and angle. Therefore, a hydrogen atom or the like is added so as to maintain the position and angle of the bond. The bond length may be changed. If you know the atomic species, you can know the approximate bond length, so it is better to add atoms at the corresponding positions. For example, it is widely known that the bond distance between a hydrogen atom and a silicon atom is about 1.5 angstroms, and the bond distance between a hydrogen atom and a carbon atom is about 1 angstrom.

  If the simulation software has an atom position optimization function, optimization may be performed to move the added atom to a stable position (step S9). Furthermore, it is even more preferable to optimize the position including several layers of atoms from the slab surface.

  By the above procedure, a surface periodic slab model satisfying the periodic boundary condition in the surface direction can be created from the unit cell forming the crystal structure. After performing conversion according to the input format of the simulation software, it may be output to the outside or used as input to the simulation software via an internal storage device such as a memory.

  The surface is an interface between the slab and the vacuum, and in this sense, the surface periodic slab model can also be called an interface periodic slab model.

  In order to create a periodic slab model of an interface structure, it is preferable to create two surface unit lattices by the method disclosed as the best mode for carrying out the present invention and to join them on a predesignated surface. . At that time, in order to satisfy the periodic boundary condition in the interface, that is, the bonding surface direction, the shape of the bonding surface of each surface unit cell must be the same. However, even in the case of a surface unit lattice created from different unit lattices or a surface unit lattice created from the same unit lattice, the shape of the joining surface is almost inconsistent when the plane orientations are different. Furthermore, even if the shape of the bonding surface is the same, a stable structure cannot be realized unless the bonds between the atoms via the bonding surface are combined smoothly, so it is inappropriate as an interface structure used for simulation. . Therefore, the interface periodic slab model creation method according to the second embodiment of the present invention performs the joining process after deforming the joining surface according to the procedure disclosed below.

  The surface shapes of the two surface unit cells are shown in FIG. FIG. 8A shows the bonding surface of the first surface unit cell, and FIG. 8B shows the bonding surface of the second surface unit cell. Both are views seen from the c-axis positive direction, the first surface unit cell has a slab in the c-axis positive direction from the bonding surface, and the second surface unit cell has a slab in the c-axis negative direction from the bonding surface. It is formed.

The joint surface is a parallelogram, and its shape is characterized by the length of two non-parallel sides and the angle between them. The fact that the shapes of the joint surfaces are the same means that the two parallelograms are congruent. That is, it is sufficient if the following expression is satisfied.

格子を大きく拡張すればするほど、その大きさの差の割合を小さくすることが可能であるが、表面拡張格子に含まれる原子数が増大するので、シミュレーションを実行することが可能な最大原子数を超えないように注意する。As mentioned above, Equation 10 is usually not satisfied. Therefore, the joint surface is deformed to satisfy Equation (10). In step S21, the surface unit cell is expanded. For example, if a ₂ is close to twice a ₁ , create a surface extended lattice in which two first surface unit lattices are arranged in the a-axis direction,

The larger the lattice, the smaller the percentage difference in size can be reduced, but the number of atoms contained in the surface extended lattice increases, so the maximum number of atoms that can be simulated Be careful not to exceed.

Further, step S21 includes a process of rotating the surface expansion grating about an axis perpendicular to the joint surface. By this deformation, γ ₁ and γ ₂ can be changed. If rotation at an arbitrary angle is allowed, an infinitely large surface expansion grating is required to satisfy the periodic boundary condition in the surface direction, so the Miller index is also considered here. FIG. 7 shows how the surface extended grating is rotated. The boundary surface is changed to (i j 0), and one of the changed axes is defined as the a ′ axis. It can be seen that when the coordinate axis is rotated so that the a-axis before the change coincides with the a′-axis, the atoms in the surface extended lattice rotate. Thus, the rotation operation can be processed as a boundary surface change of the surface expansion grid. As described in the first embodiment, it is needless to say that the change of the boundary surface is accompanied by the further extension of the surface expansion grating, and the angle γ between the b axis and the axis is also changed.

  The order of the expansion and rotation of the surface lattice may be switched or repeated. It is preferable to make the joining surface shapes of the two surface extended gratings as close as possible.

  In step S21, the deformation is focused on only the shape of the joint surface. However, even if the joining surface shapes of the two surface-extended lattices coincide with each other, after joining them, bonds between atoms via the joining surfaces, that is, interfaces, are not always combined smoothly. A non-smooth interface is not stable and does not reflect the actual interface structure. Therefore, a plurality of surface lattice pairs are created as interface slab candidates in step S21, and after joining in step S22 described later, a slab most suitable as an interface is selected.

  After the joining surface shapes of the two surface extended lattices are substantially the same, the surface extended lattice is compressed or expanded, that is, by changing only the lattice vector while maintaining the internal coordinates of the atoms of the surface extended lattice, The joint surface shapes of the two surface extended gratings are matched (step S22). In the present embodiment, since the joint surface is the (001) plane, the magnitude a of the vector a, the magnitude b of the vector b, and the angle γ between the vectors a and b are changed. If the deformation here is large, the properties of the target system may change greatly. Therefore, it is important to reduce the shape difference of the joint surfaces as much as possible in step S21.

In order to make the two joint surface shapes shown in FIGS. 8A and 8B coincide, when a, b, and γ are made to coincide with arbitrary values a _M , b _M , and γ _M , respectively. good. a _M value of between _{a 1} and _{a 2, b M} are values between _{b 1} and _{b 2,} γ _M is preferably a value between gamma ₁ and gamma _2. For example, a _M may be an average value of a ₁ and a ₂ .

ｂ_Ｍについても同様に最適値を決定することができる。When the Young's modulus of the crystal structure that is the basis of the two surface extended lattices is known, the surface extended lattice may be deformed in consideration of the value. The Young's modulus of the first crystal structure is E ₁ , and the Young's modulus of the second crystal structure is E ₂ . Further, the length of one side of the joint surface of the first surface extended grating is a ₁ , and the length of the corresponding side of the joint surface of the second surface extended grating is a ₂ . In the case of a ₁ > a ₂ , when the length a _M of the one side is set to an arbitrary value between a ₁ and a ₂ , a force for expanding the joint surface in the first surface structure, A force to narrow the joint surface acts on the second surface structure. _Assuming that the magnitude of the force is the same as in the case of the crystal structure underlying the surface-extended lattice, E ₁ (a ₁ -a _M ) and E ₂ (a _M -a ₂ ) are used using the Young's modulus. It is expressed. Assuming that these forces are balanced in the optimum state, the optimum a _M can be obtained from Equation 11.

You can be determined similarly optimum value also b _M.

前記第二の表面拡張格子についても同様に、表面に垂直な方向の大きさを変化させると良い。When the shape of the joint surface of the surface expansion lattice is changed, it is preferable that the size in the direction perpendicular to the joint surface is also changed. For example, the volume before deformation and the volume after deformation may be the same. Alternatively, when the Poisson's ratio σ is known, it may be deformed according to the value. That is, as a result of the deformation of the surface expansion grating, when the area of the joint surface portion of the first surface expansion grating changes from S to S ′, the length c of the c-axis is expressed by Expression 12. Change to c '.

Similarly, the size of the second surface extended grating may be changed in the direction perpendicular to the surface.

  As the Young's modulus and Poisson's ratio, experimentally obtained values may be used, or values obtained by crystal structure simulation may be used. More generally, the same deformation may be performed using an elastic compliance tensor.

  In step S22, a set of surface expansion gratings 71 and 72 having the same joining surface shape are joined. FIG. 9 is a schematic view of the state of joining as seen from a direction perpendicular to the a-axis and parallel to the joining surface 70. The surface expansion gratings 71 and 72 are in contact with each other at their joint surfaces, and their a-axis and b-axis coincide with each other. However, the directions of vectors indicating the c-axis of the first surface extended grating 71 and the second surface extended grating 72 generally do not match.

失わない。一方、ｚ′は１以上になっても良いし、負になることもあり得る。第二の表面拡張格子７２に含まれる原子の内部座標を変化させても同様の効果が得られるし、二つの表面拡張格子に含まれる原子の内部座標を、それぞれ異なる量だけ平行移動させても良い。ステップＳ２１において接合面形状が一致した、複数組の表面拡張格子を作成した場合には、ステップＳ２２でも全ての表面拡張格子対について同様の処理を行い、その中から、界面を介した原子間結合が、滑らかになるものを選び出す。Step S <b> 22 includes translation of the internal coordinates of the atoms included in the first surface extended lattice 71. When two individually created surface extended lattices are arranged so as to be in contact with each other at the joint surface, that is, at the interface (see FIG. 9), they are included in the first surface extended lattice 71 and the second surface extended lattice 72. Bonds through the interface between atoms are not smoothly connected. Therefore, in order to make the coupling smooth, the internal coordinates of each atom included in the first surface extended lattice 71 are moved by the vector (Δx, Δy, Δz) input from the outside.

I will not lose. On the other hand, z ′ may be 1 or more and may be negative. The same effect can be obtained by changing the internal coordinates of the atoms included in the second surface extended lattice 72, and the internal coordinates of the atoms included in the two surface extended lattices can be translated by different amounts. good. When a plurality of sets of surface extended lattices having the same bonding surface shape are created in step S21, the same processing is performed for all the surface extended lattice pairs in step S22, and the interatomic bond via the interface is performed from among them. But pick out the smooth one.

  In the processing so far, the two surface-extended gratings have a structure that satisfies the boundary condition including the c-axis direction. Since the process of increasing the thickness of the slab is easy for a lattice that satisfies the periodic boundary condition in the c-axis direction, the thickness of the slab is set here (step S6). When the lattice vector in the c-axis direction is changed in the next step S7, the periodic boundary in the meaning of Expression 1 is not satisfied. The example of FIG. 9 shows a case where the surface expansion grating is sufficiently thick, and step S6 is omitted.

  After bonding, the lattice vector in the c-axis direction is unified to handle it as an interface slab. If the vacuum layer added in step S7 is sufficiently thick, the periodic boundary condition in the c-axis direction can be ignored. Therefore, the lattice vector in the c-axis direction may be in any direction as long as it is not parallel to the interface. Therefore, in this embodiment, the lattice vector in the c-axis direction is set perpendicular to the interface.

  When the lattice vector in the c-axis direction of the first surface extended grating 71 is perpendicular to the interface, the slab 3 is formed, and when the lattice vector in the c-axis direction of the second surface extended grating 72 is perpendicular to the interface, the slab 4 is formed. An interface slab can be formed by converting the internal coordinate expression so that the atomic position does not change according to the addition of the two lattice vectors.

  As in the first embodiment, in step S7, a vacuum layer is added to the interface slab. Thereby, an interface period slab model is made.

  Since dangling bonds remain at the boundary between the interface slab and the vacuum layer, termination treatment is performed with hydrogen atoms or the like (step S8).

  In step S9, the structure of the atoms near the vacuum layer of the interface slab is relaxed. Furthermore, it is preferable to optimize the position of the constituent atoms of the second surface slab with respect to the constituent atoms of the first surface slab because the joining becomes smoother. When structure optimization is performed by applying constraint conditions to the atomic arrangement within each surface structure, the time required for optimization can be greatly reduced as compared to the case where there are no constraint conditions. It is even more preferable if no constraint is imposed on several layers of atoms near the interface.

  Although the embodiments of the present invention have been described above, the present invention is not limited to these embodiments.

  For example, a laminated structure may be created without generating a vacuum layer. The stacked structure is useful for quantum well simulation and the like. Two or more kinds of crystal structures may be stacked. When a vacuum layer is generated after lamination, a film structure on the surface can be realized. Furthermore, a superlattice can also be created by creating a further laminated structure using the laminated structure as a basic lattice.

  At any stage during the creation of the interface structure, substitution, movement, addition, or deletion of atoms may be performed. It is also possible to create a periodic slab model that realizes the structure of molecules adsorbed on the surface by adding arbitrary molecules to the surface after creating the surface structure.

It is a schematic flowchart which shows the flow of the process which produces an interface and a surface structure. It is a schematic diagram which shows the periodic slab model of (a), (b) surface structure. (C) It is a schematic diagram which shows the periodic slab model of an interface structure. It is a schematic diagram which shows a unit cell. It is a schematic diagram which shows a mode that a unit lattice is expanded and an extended lattice is produced. It is a schematic diagram which shows a mode that the boundary surface of an extended grating | lattice is changed to (101) plane. It is a schematic diagram which shows a mode that the boundary surface of a correction | amendment extended grating | lattice is changed to (011) plane. It is a schematic diagram for demonstrating a surface unit lattice being rotated within the surface perpendicular | vertical to the surface. It is a schematic diagram which shows the joint surface of two surface unit lattices. It is the schematic diagram which looked at a mode that two surface unit lattices were joined from a direction perpendicular to a axis and parallel to a joined surface.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Vacuum layer 2 Slab 3 Surface slab created from the 1st unit cell 4 Surface slab 30 created from the 2nd unit cell 30 Unit cell 51 The pentahedron 52 extended lattice produced when dividing an extended lattice by (101) plane The pentahedron 70 generated when dividing by the (101) plane The joint surface 71 of the surface expansion lattice First surface expansion lattice 72 Second surface expansion lattice

Claims (7)

An extended lattice is created by expanding a unit lattice formed from outside to form a crystal structure so as to be an integral multiple in the crystal axis direction, and the boundary surface of the expanded lattice is defined as a (111) plane, ( 110) plane, (101) plane, (011) plane is changed to any one of the surface unit grids specified by an arbitrary Miller index and satisfying the periodic boundary condition in the surface direction. A method for creating surface structure data, characterized in that the surface structure data is created by arranging a plurality of samples. The surface data creation method according to claim 1, wherein the surface structure data is a surface periodic slab model. An interface structure data creation method comprising creating interface structure data by joining two different surface unit lattices created by the method according to claim 1 at a predetermined joining surface. 4. The interface structure data creation method according to claim 3, wherein when the shapes of the joint surfaces of the two surface unit lattices are different, the two surface unit lattices are joined after matching the shapes of the joint surfaces. 5. . The interface structure data creation method according to claim 3, wherein the interface structure data is an interface periodic slab model. An extended lattice is created by expanding a unit lattice formed from outside to form a crystal structure so as to be an integral multiple in the crystal axis direction, and the boundary surface of the expanded lattice is defined as a (111) plane, ( 110) plane, (101) plane, (011) plane is changed to any one of the surface unit grids specified by an arbitrary Miller index and satisfying the periodic boundary condition in the surface direction. Surface structure data creation support system, characterized in that surface structure data is created by arranging several of them. An interface structure data creation support system for creating interface structure data by joining two different surface unit lattices created by the system according to claim 6 at a predetermined joining surface.

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