Method and equipment for generating strain-energy curve of material

Abstract

The invention provides a method and equipment for generating a strain-energy curve of a material. The method is applied to material science and engineering fields. The method comprises the following steps: acquiring an original structure of a to-be-processed material; performing mechanical matrix solution on the original structure to obtain Poisson ratios in multiple strain directions; determining a balance structure in each strain direction, continuously increasing the strain by taking the original structure as a starting point for each strain direction, determining a unit cell parameter according to a Poisson's ratio and a current strain value, and determining a balance structure under the current strain until the current strain reaches a preset maximum strain corresponding to the strain direction; obtaining a balance structure under the preset maximum strain in the current strain direction; and acquiring energy under each strain corresponding to each balance structure in each strain direction, and generating a strain-energy curve C1 of the to-be-processed material under the condition of increasing the strain. According to the method, the calculation power consumption is reduced, and the calculation result can be ensured to be a global minimum value without falling into a local minimum value.

Description

Technical Field

[0001] This invention relates to the field of materials science and engineering, and specifically to a method and apparatus for generating strain-energy curves of materials. Background Technology

[0002] In the field of materials science and engineering, a deep understanding of the physical and chemical properties of crystalline substances is crucial for the research, development, application, and performance optimization of materials. However, studying these properties often relies on complex physical and chemical experiments. Such experiments are not only time-consuming, labor-intensive, and costly, but also extremely difficult to perform for certain substances that are difficult to purify or unstable.

[0003] With the development of computational chemistry, methods such as density functional theory have provided new and effective approaches to exploring the physical and chemical properties of crystalline materials. These methods can obtain the physical and chemical properties of crystalline materials with good accuracy without the need for complex experiments. In practical production and daily life, the mechanical properties of materials, such as Young's modulus, shear modulus, and Poisson's ratio, are key parameters for material selection and design. Computational chemistry methods can accurately calculate these mechanical properties without being affected by defects or impurities in the material. Therefore, existing technologies can use the method of constructing strain-energy curves of materials to achieve precise exploration of the physicochemical properties of crystalline materials. Among these, strain-energy curves can be applied to wafer manufacturing, directly serving as a scientific guide for subsequent process steps to precisely control the selection of processing parameters and processing accuracy.

[0004] However, existing computational chemistry methods often get stuck in local optima rather than global optima when determining strain-energy curves of materials, resulting in inaccurate calculation results and high computational cost. Figure 1 This paper demonstrates the time complexity of traditional methods for calculating the equilibrium structure of crystalline materials under different strain conditions. This method involves geometric optimization of atomic positions while maintaining fixed unit cell parameters. The area of ​​each bar in the graph represents the required time complexity, clearly showing that traditional methods require significantly more time and consume more computational resources. Summary of the Invention

[0005] In view of this, the first aspect of the present invention provides a method for generating strain-energy curves of materials, comprising: Obtain the original structure of the material to be processed; The mechanical matrix of the original structure is solved, and the Poisson's ratio in multiple strain directions is obtained from the mechanical matrix. Determine the equilibrium structure under each strain direction. For each strain direction, starting from the original structure, the strain is continuously increased according to the required strain resolution. Starting from the set initial strain, the cell parameters are determined according to the Poisson's ratio and the current strain value, and the equilibrium structure under the current strain is determined until the current strain reaches the preset maximum strain corresponding to the strain direction, and the equilibrium structure under the preset maximum strain of the current strain direction is obtained. The energy at each strain corresponding to each equilibrium structure under each strain direction is obtained, and the strain-energy curve C1 of the material to be treated under increased strain conditions is generated.

[0006] Optionally, the method for generating a strain-energy curve of a material provided by the present invention further includes: Obtain the location and strain direction of the phase transition in the strain-energy curve C1; Starting from the strain at the phase transition position, the starting strain is continuously reduced according to the required strain resolution, and the unit cell parameters are updated according to the reduced strain and the Poisson's ratio in the corresponding strain direction. The equilibrium structure under different reduced strains is determined according to the updated unit cell parameters, and the energy corresponding to each equilibrium structure is recorded. Based on the reduced strains and the energy of the corresponding equilibrium structure, strain-energy curve C2 is generated; Based on the strain direction where the phase transition occurs, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 in the corresponding strain direction until the strain-energy curve C2 intersects with the strain-energy curve C1 in the corresponding strain direction, and then stop reducing the strain. The strain point with the minimum energy at the corresponding strain is selected from the intersecting strain-energy curves C1 and C2, and the strain-energy curve C3 of the material to be treated is generated under various strain conditions.

[0007] Alternatively, the equilibrium structure under each strain direction can be determined as follows: For one strain direction, a first strain d1 is set, and a first cell parameter is determined based on the Poisson's ratio of the current strain direction and the first strain d1. The equilibrium structure s1 under the first strain d1 is determined based on the first cell parameter. Using the equilibrium structure s1 as the initial structure, the first strain d1 is increased according to the required strain resolution to obtain the second strain d2. The second cell parameters are determined according to the Poisson's ratio in the current strain direction and the second strain d2. The equilibrium structure s2 under the second strain d2 is determined according to the second cell parameters. The strain in the current strain direction is continuously increased and the cell parameters are updated according to the required strain resolution until the strain in the current strain direction reaches the preset maximum strain dn, and the equilibrium structure sn under the preset maximum strain dn in the current strain direction is obtained.

[0008] Optionally, before solving the mechanical matrix of the original structure and obtaining the Poisson's ratio in multiple strain directions based on the mechanical matrix, the method further includes: performing geometric optimization on the original structure to obtain an optimized structure.

[0009] A second aspect of the present invention provides a method for generating strain-energy curves of a material, comprising: Obtain the original structure of the material to be processed; The mechanical matrix of the original structure is solved, and the Poisson's ratio in multiple strain directions is obtained from the mechanical matrix. For each strain direction, based on the required strain resolution, preset number of nodes, and maximum strain Dmax, a minimum strain step size D1 and a maximum strain step size D2 are set, wherein the maximum strain Dmax and the maximum strain step size D2 satisfy an integer ratio, and the maximum strain step size D2 and the minimum strain step size D1 satisfy an integer ratio. The first fixed cell parameter is set according to the Poisson's ratio of the current strain direction and the maximum strain step size D2. The equilibrium structure s1m of multiple strains under the maximum strain step size D2 is determined simultaneously using the preset number of nodes and the first fixed cell parameter. The equilibrium structure s1m of each strain is taken as the initial structure. The second fixed cell parameter is set according to the Poisson's ratio of the current strain direction and the minimum strain step size D1. The strain is increased based on the strain corresponding to the initial structure according to the minimum strain step size D1 to obtain multiple strains under the minimum strain step size D1. The equilibrium structure s2n of multiple strains under the minimum strain step size D1 is determined simultaneously using the preset number of nodes according to the second fixed cell parameter. Obtain the energy at each strain corresponding to each equilibrium structure s1m and equilibrium structure s2n in each strain direction, and generate the strain-energy curve C1 of the material to be treated under increased strain conditions in each strain direction.

[0010] Optionally, the method for generating a strain-energy curve of a material provided by the present invention further includes: Obtain the location and strain direction of the phase transition in the strain-energy curve C1; Starting from the strain at the phase transition position, the starting strain is continuously reduced according to the required strain resolution, and the unit cell parameters are updated according to the reduced strain and the Poisson's ratio in the corresponding strain direction. The equilibrium structure under different reduced strains is determined according to the updated unit cell parameters, and the energy corresponding to each equilibrium structure is recorded. Based on the reduced strains and the energy of the corresponding equilibrium structure, strain-energy curve C2 is generated; Based on the strain direction where the phase transition occurs, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 in the corresponding strain direction until the strain-energy curve C2 intersects with the strain-energy curve C1 in the corresponding strain direction, and then stop reducing the strain. The strain point with the minimum energy at the corresponding strain is selected from the intersecting strain-energy curves C1 and C2, and the strain-energy curve C3 of the material to be treated is generated under various strain conditions.

[0011] Optionally, the number of strain equilibrium structures s1m at the maximum strain step size D2 is determined as follows: , Where m represents the number of equilibrium structures s1m.

[0012] Optionally, the strain is increased based on the strain corresponding to the initial structure according to the minimum strain step D1, including: The strain is increased for each strain under the maximum strain step size D2 according to the minimum strain step size D1; Wherein, the number of times each strain increases under the maximum strain step size D2 is: , Where q represents the number of times each strain increases.

[0013] Optionally, the number of strain equilibrium structures s2n at the minimum strain step size D1 is determined as follows: , Where n represents the number of equilibrium structures s2n.

[0014] Optionally, before solving the mechanical matrix of the original structure and obtaining the Poisson's ratio in multiple strain directions based on the mechanical matrix, the method further includes: performing geometric optimization on the original structure to obtain an optimized structure.

[0015] A third aspect of the present invention provides a strain-energy curve generation device for a material, the device comprising: a processor and a memory connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to cause the processor to perform the strain-energy curve generation method for the material described above.

[0016] In Embodiment 1 of this invention, a small first strain d1 is set based on the required strain resolution. The first unit cell parameters are determined by combining the Poisson's ratio of the current strain direction to obtain the corresponding equilibrium structure s1. Then, using the equilibrium structure of the previous strain point as the initial structure, the strain is continuously increased and the unit cell parameters are updated until a preset maximum strain dn is reached, obtaining a complete strain-equilibrium structure data set for that strain direction. This progressively increasing calculation method, using the previous equilibrium structure as the initial point, effectively reduces the difference between the initial and final equilibrium structures in each calculation, reduces the time consumed by calculation steps, lowers computational power consumption, and improves calculation speed. Simultaneously, it avoids unstable structures during equilibrium optimization that could lead to energy calculation errors, ensuring that the calculation results are closer to the global minimum.

[0017] In Embodiment 2 of this invention, a predetermined number of nodes are used to implement parallel task processing. First, the equilibrium structure s1m under multiple strains at the maximum strain step size is calculated based on the original structure. Then, these equilibrium structures are used as the initial structure to calculate the equilibrium structure s2n under multiple strains at the minimum strain step size. Finally, the energy at the corresponding strain for each equilibrium structure is obtained, and a strain-energy curve C1 is generated. This method of first calculating the initial structure at a large strain step size and then iterating the results at a small strain step size based on the equilibrium results can divide the task into several parts, making full use of the computing power of parallel nodes. While ensuring that the time complexity (CPU time) is not increased excessively, the total time consumption is effectively reduced and the computational efficiency is improved. Moreover, iterating at a small strain step size under a large strain step size divides the strain into very small blocks, effectively reducing the difference between the initial structure and the final equilibrium structure in each calculation. This avoids unstable structures during the equilibrium optimization process, which could lead to energy calculation errors and ensure that the calculation results are closer to the global minimum.

[0018] This invention also performs strain-energy analysis on the test material undergoing phase transition. By generating a curve in reverse and comparing it with the strain-energy curve C1 corresponding to the strain direction, the strain point with the minimum energy in the intersecting curves is selected to generate curve C3. By selecting the point with the minimum energy between the two curves, the state with the lowest energy is screened out, thereby further eliminating the influence of metastable phases. The strain-energy curve C3 generated in this way only contains the information of the most stable state of the material under different strain conditions, avoiding curve fluctuations caused by metastable phases, and obtaining a smooth phase transition potential energy curve, making the energy change law during the material phase transition process clearer and more intuitive. Attached Figure Description

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram illustrating the time complexity of the conventional method in this embodiment of the invention; Figure 2 This is a flowchart of the strain-energy curve generation method for the first material in this embodiment of the invention; Figure 3 This is a time complexity diagram of Embodiment 1 in the present invention; Figure 4 This is a flowchart of the method for generating the strain-energy curve of the second material in this embodiment of the invention; Figure 5 This is a time complexity diagram of Embodiment 2 in this invention. Figure 6 This is the strain-energy curve C1 diagram under the conventional method in this embodiment of the invention; Figure 7 This is Figure C1, showing the strain-energy curve of Embodiment 2 in this invention. Detailed Implementation

[0021] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0023] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can also refer to the internal connection of two components; and they can refer to a wireless connection or a wired connection. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0024] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. Example 1

[0025] like Figure 2 As shown, this embodiment of the invention provides a method for generating strain-energy curves of materials. This method is executed by an electronic device such as a computer or server, and specifically includes: S11, Obtain the original structure of the material to be processed. The material to be processed can be any crystalline material used for wafer fabrication, or it can be an amorphous material. The original structure refers to the equilibrium configuration of the material to be processed under stress-free conditions.

[0026] S12, solve the mechanical matrix of the original structure, and obtain the Poisson's ratio in multiple strain directions based on the mechanical matrix.

[0027] Choose an appropriate calculation method based on the material type to calculate the Poisson's ratio for different strain directions from the mechanical matrix of the original structure. It is worth noting that if high computational accuracy is not required, the Poisson's ratio for each crystal plane under zero strain conditions can be directly calculated from the mechanical matrix. Although this method is essentially based on a first-order linear approximation, it is more accurate than directly using literature values. This is because the Poisson's ratios given in the literature are usually coarse approximations under the assumption of isotropy, completely ignoring the differences in atomic arrangement and interactions between different crystal planes, while calculations based on the mechanical matrix retain the intrinsic information specific to the crystal planes.

[0028] To further improve computational accuracy, a three-dimensional strain-Poisson's ratio-energy curve scanning method can be used to obtain an accurate Poisson's ratio fitting function. Using strain and Poisson's ratio as independent input variables, a three-dimensional surface of strain-Poisson's ratio-energy is constructed. After obtaining the three-dimensional energy surface in the strain and Poisson's ratio parameter space through scanning, the Poisson's ratio corresponding to the minimum energy at each strain can be accurately located. A high-order Poisson's ratio fitting function is then constructed through high-order polynomial fitting. Compared to traditional linear approximation, this function can fully capture the nonlinear mechanical behavior of materials under large strains, thereby achieving accurate prediction of the Poisson's ratio in multiple strain directions and significantly improving the reliability and accuracy of subsequent calculations.

[0029] S13, determine the equilibrium structure under each strain direction. For each strain direction, starting from the original structure, the strain is continuously increased according to the required strain resolution. Starting from the set initial strain, the cell parameters are determined according to Poisson's ratio and the current strain value, and the equilibrium structure under the current strain is determined until the current strain reaches the preset maximum strain corresponding to the strain direction, and the equilibrium structure under the preset maximum strain of the current strain direction is obtained.

[0030] Specifically, the required strain resolution and initial strain should be as small as possible to ensure that the change in the equilibrium structure at each strain is not too large; for example, a strain resolution of 0.01 or 0.001. The strain applied in each strain direction is... Figure 3 The increment method shown ( Figure 3 The horizontal axis represents strain, and the vertical axis represents the calculation time per unit strain. Iterative calculations are achieved through segmentation. Specifically, the task is performed on a single node. Starting from an initial strain, strain is applied to the original structure according to the required strain resolution to find the equilibrium structure at that strain. Then, the strain is continuously increased, and the equilibrium structure at the corresponding strain is found sequentially until the preset maximum strain in that strain direction is reached, at which point the calculation stops.

[0031] When calculating the equilibrium structure under each strain, under the condition of structural relaxation calculation, the structure will be optimized to the minimum value under the constraints, but not necessarily the minimum value. If the optimization result is the minimum value, then this structure is an equilibrium structure under strain.

[0032] S14, obtain the energy of each equilibrium structure under each strain direction, and generate the strain-energy curve C1 of the material to be treated under increased strain conditions.

[0033] The strain-energy curve C1 is a curve with strain as the independent variable and energy as the dependent variable; the strain-energy curve C1 corresponding to multiple strain directions is calculated by iterative calculation.

[0034] according to Figure 3 As shown, Figure 3 The horizontal axis represents strain, and the vertical axis represents the calculation time per unit strain. The area of ​​the bar chart for each strain node represents the required time complexity (CPU time). Traditional methods calculate the changes in unit cell parameters under different compressive-tensile strains based on Poisson's ratio. Using fixed unit cell parameters, they geometrically optimize the atomic positions to obtain equilibrium structures under different strain conditions, calculate the energy of the equilibrium structure, and generate a strain-energy curve C1 with strain as the independent variable and energy as the dependent variable. The strain-energy curve C1 is shown below. Figure 6 As shown (the horizontal axis represents the strain between compression and tension, with negative values ​​for compression and positive values ​​for tension, in angstroms; the vertical axis represents the equilibrium structural energy, in volts), its time complexity is as follows: Figure 1 ( Figure 1 The horizontal axis represents strain, and the vertical axis represents the calculation time per unit strain. By comparison... Figure 3 and Figure 1 It can be seen that this method greatly reduces the time for each strain node and reduces the total time consumption.

[0035] This embodiment iteratively calculates the equilibrium structure under strain, ensuring that the difference between the equilibrium structure under strain and the original structure is sufficiently small in each calculation. Each time, only a tiny deformation is added to the equilibrium structure of the previous step, greatly reducing the degree of structural change each time. This method improves the calculation speed and significantly reduces the consumption of computing power. The method also effectively avoids the occurrence of unstable structures during the calculation of the equilibrium structure, which would lead to inaccurate energy under strain. In other words, it can ensure that the calculation result is a global minimum and will not get stuck in a local minimum.

[0036] The strain-energy curve C1 can be applied to wafer manufacturing. Using the strain-energy curve C1 as a key guide for subsequent process steps allows for precise control of process parameter selection and processing accuracy. Specifically, in thin film deposition, by analyzing the energy change trend of the current wafer material under different strains (such as the critical energy threshold between the elastic energy storage region and the plastic deformation region), deposition rate, temperature, and stress matching parameters can be precisely set to avoid film cracking or interface peeling due to strain accumulation exceeding the material's energy carrying capacity. In etching, based on the nonlinear response characteristics of energy with strain in the strain-energy curve (such as the energy peak corresponding to fracture strain), it is possible to... Dynamically adjusting the etching depth prevents over-etching from causing wafer structural damage or sidewall stress concentration. In the chemical mechanical polishing (CMP) process, the stress-energy coupling relationship of the curve is used to optimize polishing pressure and rotation speed. By controlling the energy accumulation rate of surface strain, wafer warpage or surface defects caused by excessive local stress during polishing are reduced. Furthermore, in subsequent epitaxial growth or heterogeneous integration processes, this curve can serve as a quantitative benchmark for residual strain from previous processes. By matching the strain-energy curve characteristics (such as elastic modulus and hardening index) of the preceding and following processes, substrate selection and process compatibility design are guided, ensuring the interfacial bonding strength and long-term reliability of multi-material stacks. In short, the strain-energy curve C1 provides a full-link quantitative basis for wafer processing, from the intrinsic mechanical properties of materials to the control of process parameters, significantly reducing process trial-and-error costs and improving product yield.

[0037] Specifically, step S13, which involves determining the equilibrium structure under each strain direction, includes: S131, for one of the strain directions, set a first strain d1, and determine the first cell parameter according to the Poisson's ratio of the current strain direction and the first strain d1, and determine the equilibrium structure s1 under the first strain d1 according to the first cell parameter.

[0038] The cell parameters are the side length and included angle of each cell in the material, and the first strain d1 should be set to a relatively small strain.

[0039] S132, taking the equilibrium structure s1 as the initial structure, the first strain d1 is increased according to the required strain resolution to obtain the second strain d2. The second cell parameters are determined according to the Poisson's ratio in the current strain direction and the second strain d2. The equilibrium structure s2 under the second strain d2 is determined according to the second cell parameters. The strain in the current strain direction is continuously increased and the cell parameters are updated according to the required strain resolution until the strain in the current strain direction reaches the preset maximum strain dn, and the equilibrium structure sn under the preset maximum strain dn in the current strain direction is obtained.

[0040] Each time the strain is increased, the strain is increased starting from the previously calculated strain point, and the equilibrium structure corresponding to the previous strain point is used as the initial structure to calculate the equilibrium structure for the current strain. This process continues until the preset maximum strain dn is reached, resulting in a strain-equilibrium structure (d1, s1), (d2, s2), (d3, s3)...(dn, sn) in the strain direction, where d1 < d2 < s3... < d3. Then, steps S131-S132 are repeated until strain-equilibrium structures in all strain directions are obtained.

[0041] Then, step S14 will obtain the strain and energy in different strain directions based on the energy of each strain corresponding to each equilibrium structure, and generate the strain-energy curve C1 based on the energy corresponding to each strain.

[0042] In this embodiment, a small first strain d1 is set based on the required strain resolution. The first unit cell parameters are calculated using the Poisson's ratio in the current strain direction to obtain the corresponding equilibrium structure s1. Then, using the equilibrium structure of the previous strain point as the initial structure, the strain is continuously increased and the unit cell parameters are updated until the preset maximum strain dn is reached, obtaining a complete strain-equilibrium structure data set for that strain direction. This step-by-step increasing calculation method, using the previous equilibrium structure as the initial point, effectively reduces the difference between the initial and final equilibrium structures in each calculation, reduces the time consumed by calculation steps, reduces computational power consumption, and improves calculation speed. Simultaneously, it avoids unstable structures during equilibrium optimization that could lead to energy calculation errors, ensuring that the calculation results are closer to the global minimum.

[0043] Furthermore, after obtaining the strain-energy curve C1, the following is also included: S15, obtain the location of the phase transition and the strain direction in the strain-energy curve C1.

[0044] Find the strain point in each strain-energy curve C1 where an energy abrupt change occurs between adjacent strain points and the energy change exceeds a preset threshold. This strain point is the point where a phase transition has occurred. Obtain the points where phase transitions occur in the material to be treated under different strain conditions, including the corresponding strain and strain direction.

[0045] S16, starting from the strain at the phase transition position, continuously reduce the starting strain according to the required strain resolution, and update the unit cell parameters according to the reduced strain and the Poisson's ratio in the corresponding strain direction. Determine the equilibrium structure under different reduced strains according to the updated unit cell parameters, and record the energy corresponding to each equilibrium structure.

[0046] This step determines whether to perform operations S16-S19 based on the continuity of the phase transition. Specifically, for phase transitions in the same strain direction, if it is a discontinuous phase transition, it indicates that the structure has fractured and is irreversible, so there is no need to calculate the energy curve at reduced strain. If it is a continuous phase transition, then each strain point is continuously reduced according to the required strain resolution, and the equilibrium structure and energy at that strain are calculated. For example, metallic materials undergo continuous phase transitions. The first strain point where a phase transition occurs or the energy change is the largest can be used as the starting point, and the strain point is reduced according to the required strain resolution, and the corresponding equilibrium structure and energy are calculated.

[0047] S17, based on the reduced strains and the energy of the corresponding equilibrium structure, generate strain-energy curves C2.

[0048] Based on the initial strain point and the energy of the equilibrium structure corresponding to the reduced strain, a strain-energy curve C2 is generated. If continuous phase transitions occur in multiple strain directions, multiple strain-energy curves C2 will be generated.

[0049] S18. Based on the strain direction of the phase transition, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 of the corresponding strain direction until the strain-energy curve C2 intersects with the strain-energy curve C1 of the corresponding strain direction, and stop reducing the strain.

[0050] The strain-energy curve C2 and the strain-energy curve C1 under the same strain direction are continuously compared until the two curves intersect. Then, the strain is reduced and no further strain-energy curves are generated.

[0051] S19, take the strain point with the minimum energy at the corresponding strain from the intersecting strain-energy curves C1 and C2, and generate the strain-energy curve C3 of the material to be treated under various strain conditions.

[0052] By taking min(C1,C2), the strain-energy curve C3 can be obtained.

[0053] This embodiment performs strain-energy analysis on the test material undergoing a phase transition. A curve is generated in reverse and compared with the corresponding strain-energy curve C1. The strain point with the lowest energy in the intersecting curves is used to generate curve C3. By selecting the point with the lowest energy between the two curves, the lowest and most stable state is identified, further eliminating the influence of metastable phases. The resulting strain-energy curve C3 contains only the information of the most stable state of the material under different strain conditions, avoiding curve fluctuations caused by metastable phases. This yields a smooth phase transition potential energy curve, making the energy change pattern during the material's phase transition process clearer and more intuitive.

[0054] The strain-energy curve C3 is used to study the conditions under which the material to be processed undergoes phase transformation or irreversible structural transformation, and to provide boundary condition guidance for the wafer processing process.

[0055] In one embodiment, before step S12 solves the mechanical matrix of the original structure and obtains the Poisson's ratio for multiple strain directions based on the mechanical matrix, the method further includes: performing geometric optimization on the original structure to obtain an optimized structure.

[0056] By calculating the interatomic forces, the positions of atoms in the original structure are continuously moved until they reach their lowest energy equilibrium positions. Then, Poisson's ratio is calculated based on the optimized structure. This optimized structure fully reflects the differences in atomic arrangement and interactions across different crystal planes. Furthermore, by using the mechanical matrix to solve for Poisson's ratio or calculating higher-order Poisson's ratios based on the optimized structure, the calculation becomes more accurate. A more accurate Poisson's ratio results in a more precise reflection of strain under real-world conditions. Applying uniaxial strain directly while keeping other orthogonal axes unchanged (i.e., a 0 Poisson's ratio) yields lower accuracy. Similarly, directly using the Poisson's ratio reported in the literature, which fails to consider higher-order variations (i.e., only the constant term), also results in lower accuracy.

[0057] This embodiment calculates the interatomic forces and continuously moves the atoms in the original structure to their lowest energy equilibrium positions, thus achieving a more stable structure. This lays a solid foundation for solving the subsequent mechanical matrices. Because the optimized structure is closer to the true stable state, the Poisson's ratios calculated based on this will be more accurate and reliable in multiple strain directions. Accurate Poisson's ratios are crucial for in-depth research into the mechanical properties of materials, providing more precise data support for further analysis of material behavior under different strain conditions.

[0058] Specifically, taking cristobalite crystal as an example, strain-energy calculations for compression-tension deformation are performed along the strain direction of the crystal's z-axis. According to Example 1, only the strain-energy curve under tension is analyzed, with a required resolution of 0.01. The first strain d1 = 0.01, thus obtaining strains at various points d2 = 0.02, d3 = 0.03, and so on until the maximum strain is reached. Based on each strain and Poisson's ratio pr1, the corresponding cell parameters are calculated, and then the corresponding equilibrium mechanism and energy are calculated, generating the strain-energy curve C1.

[0059] Example 2 like Figure 4 As shown, this embodiment of the invention provides a method for generating strain-energy curves of materials. This method is executed by an electronic device such as a computer or server, and specifically includes: S21, Obtain the original structure of the material to be processed.

[0060] The material to be processed can be any crystalline material used in wafer fabrication, or it can be an amorphous material. The original structure refers to the equilibrium configuration of the material to be processed under stress-free conditions.

[0061] S22, solve the mechanical matrix of the original structure, and obtain the Poisson's ratio in multiple strain directions based on the mechanical matrix.

[0062] Choose an appropriate calculation method based on the material type to calculate the Poisson's ratio for different strain directions from the mechanical matrix of the original structure. It is worth noting that if high computational accuracy is not required, the Poisson's ratio for each crystal plane under zero strain conditions can be directly calculated from the mechanical matrix. Although this method is essentially based on a first-order linear approximation, it is more accurate than directly using literature values. This is because the Poisson's ratios given in the literature are usually coarse approximations under the assumption of isotropy, completely ignoring the differences in atomic arrangement and interactions between different crystal planes, while calculations based on the mechanical matrix retain the intrinsic information specific to the crystal planes.

[0063] To further improve computational accuracy, a three-dimensional strain-Poisson's ratio-energy curve scanning method can be used to obtain an accurate Poisson's ratio fitting function. Using strain and Poisson's ratio as independent input variables, a three-dimensional surface of strain-Poisson's ratio-energy is constructed. After obtaining the three-dimensional energy surface in the strain and Poisson's ratio parameter space through scanning, the Poisson's ratio corresponding to the minimum energy at each strain can be accurately located. A high-order Poisson's ratio fitting function is then constructed through high-order polynomial fitting. Compared to traditional linear approximation, this function can fully capture the nonlinear mechanical behavior of materials under large strains, thereby achieving accurate prediction of the Poisson's ratio in multiple strain directions and significantly improving the reliability and accuracy of subsequent calculations.

[0064] S23, for each strain direction, set the minimum strain step size D1 and the maximum strain step size D2 according to the required strain resolution, the preset number of nodes and the maximum strain Dmax. The maximum strain Dmax and the maximum strain step size D2 satisfy an integer ratio, and the maximum strain step size D2 and the minimum strain step size D1 satisfy an integer ratio.

[0065] A preset number of nodes is used to calculate the strain equilibrium structure under different strain step sizes.

[0066] S24, set the first fixed cell parameter according to the Poisson's ratio of the current strain direction and the maximum strain step size D2, and use the preset number of nodes to determine the equilibrium structure s1m of multiple strains under the maximum strain step size D2 according to the first fixed cell parameter.

[0067] Using a preset number of nodes, the equilibrium structure s1m under multiple strain conditions with the maximum strain step size D2 is calculated based on the original structure.

[0068] Several strains are calculated based on the maximum strain Dmax and the maximum strain step size D2, and the corresponding equilibrium structures (d11, s11), (d12, s12), (d13, s13) ... (d1m, s1m) are calculated based on the first fixed cell parameters and each strain, where d11 < d12 < d13 < ... < d1m.

[0069] S25, take the equilibrium structure s1m of each strain as the initial structure, set the second fixed cell parameters according to the Poisson's ratio of the current strain direction and the minimum strain step D1, and increase the strain based on the strain corresponding to the initial structure according to the minimum strain step D1 to obtain multiple strains under the minimum strain step D1. Use the preset number of nodes to simultaneously determine the equilibrium structure s2n of multiple strains under the minimum strain step D1 according to the second fixed cell parameters.

[0070] Then, using a preset number of nodes as a basis, the equilibrium structures s1m obtained with large step size are calculated under multiple strain conditions at the minimum strain step size D1, and the equilibrium structures s2n are calculated.

[0071] Taking the equilibrium structure s11 as the initial structure, add multiple minimum strain step sizes D1 to the base of d11. This means that the strain between each large strain step is further divided into multiple small strain steps, and so on, to obtain multiple strains between each strain of d12, d13...d1m and the equilibrium structure (d21, s21), (d22, s22)...(d2n, s2n).

[0072] S26, obtain the energy of each equilibrium structure s1m and equilibrium structure s2n under each strain direction, and generate the strain-energy curve C1 of the material to be treated under increased strain conditions in each strain direction.

[0073] Based on the above steps, we can obtain (d11, s11), (d21, s21), (d22, s22)...(d2i, s2i), (d12, s12)...(d1m, s1m)...(d2n, s2n) under one strain direction, where i=1,2,3...n. Calculate the energy of the corresponding equilibrium structure based on the strain, and generate the strain-energy curve C1 under that strain direction. Repeat steps S23-S26 to obtain the strain-energy curve C1 of the material to be treated under increased strain conditions for each strain direction, as shown below. Figure 7 As shown (the horizontal axis represents the strain of compression versus tension, with negative values ​​for compression and positive values ​​for tension, in angstroms; the vertical axis represents the equilibrium structural energy, in volts). Figure 7 Compared with traditional methods Figure 6 In contrast, we can see that the points on the two curves that do not coincide and are above the point in this scheme are local minima rather than global minima of the traditional method. That is, the traditional method is that the point in the strain range of -5 to 4 is the optimal solution, and the other points are not the optimal solution, thus getting stuck in a local optimum. However, the energy of all strain points obtained by this scheme is closest to the minimum value, which is the global optimum.

[0074] like Figure 5 As shown ( Figure 5 The horizontal axis represents strain, and the vertical axis represents the calculation time per unit strain. This is the time complexity graph used in Example 2. It shows that the large-step strain (blue bars on the horizontal axis) is divided into multiple small-step strains (red bars on the horizontal axis). The area of ​​each strain node in the bar graph represents the required time complexity (CPU time). By comparison... Figure 5 and Figure 1 It can be seen that this method particularly reduces the strain time for small steps, thus reducing the total time consumption.

[0075] This embodiment utilizes a preset number of nodes to achieve parallel task processing. First, based on the original structure, it calculates equilibrium structures s1m for multiple strains at the maximum strain step size. Then, using these equilibrium structures as initial structures, it calculates equilibrium structures s2n for multiple strains at the minimum strain step size. Finally, it obtains the energy at the corresponding strain for each equilibrium structure and generates a strain-energy curve C1. This method of first calculating the initial structure at a large strain step size and then iterating the results at a small strain step size based on the equilibrium results can divide the task into several parts, fully utilizing the computing power of parallel nodes. While ensuring that the time complexity (CPU time) is not excessively increased, it effectively reduces the total time consumption and improves computational efficiency. Moreover, iterating at a small strain step size under a large strain step size divides the strain into very small blocks, effectively reducing the difference between the initial structure and the final equilibrium structure in each calculation. This avoids unstable structures during the equilibrium optimization process, which could lead to energy calculation errors and ensure that the calculation results are closer to the global minimum.

[0076] The strain-energy curve C1 generated in this embodiment is also used in wafer manufacturing. For specific applications, please refer to the use of strain-energy curve C1 in Embodiment 1, which will not be repeated here.

[0077] Furthermore, after obtaining the strain-energy curve C1, the following is also included: S27, obtain the location of the phase transition and the strain direction in the strain-energy curve C1.

[0078] Find the strain point in each strain-energy curve C1 where an energy abrupt change occurs between adjacent strain points and the energy change exceeds a preset threshold. This strain point is the point where a phase transition has occurred. Obtain the points where phase transitions occur in the material to be treated under different strain conditions, including the corresponding strain and strain direction.

[0079] S28, starting from the strain at the phase transition position, continuously reduces the starting strain according to the required strain resolution, and updates the unit cell parameters according to the reduced strain and the Poisson's ratio in the corresponding strain direction. Based on the updated unit cell parameters, the equilibrium structure under different reduced strains is determined, and the energy corresponding to each equilibrium structure is recorded.

[0080] This step determines whether to perform operations S16-S19 based on the continuity of the phase transition. Specifically, for phase transitions in the same strain direction, if it is a discontinuous phase transition, it indicates that the structure has fractured and is irreversible, so there is no need to calculate the energy curve at reduced strain. If it is a continuous phase transition, then each strain point is continuously reduced according to the required strain resolution, and the equilibrium structure and energy at that strain are calculated. For example, metallic materials undergo continuous phase transitions. The first strain point where a phase transition occurs or the energy change is the largest can be used as the starting point, and the strain point is reduced according to the required strain resolution, and the corresponding equilibrium structure and energy are calculated.

[0081] S29, based on the reduced strains and the energy of the corresponding equilibrium structure, generate strain-energy curves C2.

[0082] Based on the initial strain point and the energy of the equilibrium structure corresponding to the reduced strain, a strain-energy curve C2 is generated. If continuous phase transitions occur in multiple strain directions, multiple strain-energy curves C2 will be generated.

[0083] S30, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 of the corresponding strain direction according to the strain direction of the phase transition, until the strain-energy curve C2 intersects with the strain-energy curve C1 of the corresponding strain direction, and stop reducing the strain.

[0084] The strain-energy curve C2 and the strain-energy curve C1 under the same strain direction are continuously compared until the two curves intersect. Then, the strain is reduced and no further strain-energy curves are generated.

[0085] S31, take the strain point with the minimum energy at the corresponding strain from the intersecting strain-energy curves C1 and C2, and generate the strain-energy curve C3 of the material to be treated under various strain conditions.

[0086] By taking min(C1,C2), the strain-energy curve C3 can be obtained.

[0087] This embodiment performs strain-energy analysis on the test material undergoing a phase transition. A curve is generated in reverse and compared with the corresponding strain-energy curve C1. The strain point with the lowest energy in the intersecting curves is used to generate curve C3. By selecting the point with the lowest energy between the two curves, the lowest and most stable state is identified, further eliminating the influence of metastable phases. The resulting strain-energy curve C3 contains only the information of the most stable state of the material under different strain conditions, avoiding curve fluctuations caused by metastable phases. This yields a smooth phase transition potential energy curve, making the energy change pattern during the material's phase transition process clearer and more intuitive.

[0088] The strain-energy curve C3 generated in this embodiment is used to study the conditions under which the material to be processed undergoes phase transformation or irreversible structural transformation, and to provide boundary condition guidance for the wafer processing process.

[0089] In one embodiment, the number of strain equilibrium structures s1m determined in step S24 under the maximum strain step size D2 is: , Where m represents the number of equilibrium structures s1m.

[0090] In one embodiment, step S25, which involves increasing the strain based on the strain corresponding to the initial structure according to the minimum strain step size D1, includes: The strain is increased for each strain under the maximum strain step size D2 based on the minimum strain step size D1; Wherein, the number of times each strain increases under the maximum strain step size D2 is: , Where q represents the number of times each strain increases.

[0091] In one embodiment, the number of strain equilibrium structures s2n determined in step S25 under the minimum strain step size D1 is: , Where n represents the number of equilibrium structures s2n.

[0092] In one embodiment, before solving the mechanical matrix of the original structure in step S22 and obtaining the Poisson's ratio of multiple strain directions based on the mechanical matrix, the method further includes: performing geometric optimization on the original structure to obtain an optimized structure.

[0093] Calculating Poisson's ratio based on optimized structures offers several advantages. First, optimized structures fully reflect the differences in atomic arrangement and interactions across different crystal planes. Second, the calculation of Poisson's ratio using mechanical matrices or higher-order Poisson's ratios based on optimized structures leads to more accurate calculations. The strain calculated using the correct Poisson's ratio obtained from optimized structures more accurately reflects the strain under real-world conditions. In contrast, directly applying uniaxial strain while keeping other orthogonal axes unchanged (i.e., a 0 Poisson's ratio) results in lower accuracy. Similarly, directly using Poisson's ratios reported in the literature, which fail to consider higher-order variations (i.e., only the constant term), also results in lower accuracy.

[0094] This embodiment calculates the interatomic forces and continuously moves the atoms in the original structure to their lowest energy equilibrium positions, thus achieving a more stable structure. This lays a solid foundation for solving the subsequent mechanical matrices. Because the optimized structure is closer to the true stable state, the Poisson's ratios calculated based on this will be more accurate and reliable in multiple strain directions. Accurate Poisson's ratios are crucial for in-depth research into the mechanical properties of materials, providing more precise data support for further analysis of material behavior under different strain conditions.

[0095] Specifically, taking cristobalite crystal as an example, strain-energy calculations for compressive-tensile deformation are performed along the strain direction of the crystal's z-axis. According to Example 2, only the strain-energy curve under tensile conditions is analyzed. Assuming the maximum strain Dmax = 0.1, the minimum strain step size D1 = 0.005, and the maximum strain step size D2 = 0.02, the number of strains under the large strain step size is m = Dmax / D2 = 5. Therefore, we can obtain: When m1=0.02, the original structure (or optimized structure) is used as the initial structure, and strain m1 is applied to calculate the equilibrium structure s11; When m2=0.04, the equilibrium structure s12 is calculated by applying strain m2 with the original structure (or optimized structure) as the initial structure. When m3=0.06, the equilibrium structure s13 is calculated by applying strain m3 with the original structure (or optimized structure) as the initial structure. When m4=0.08, the equilibrium structure s14 is calculated by applying strain m4 with the original structure (or optimized structure) as the initial structure. When m5=0.1, the original structure (or optimized structure) is used as the initial structure, and strain m5 is applied to calculate the equilibrium structure s15.

[0096] Under small strain steps, the strain is increased based on strains m1, m2, m3, m4, and m5, with each strain increase being q = D2 / D1 - 1 = 3. Therefore, the final number of equilibrium structures under small strain steps is n = Dmax / D1 - Dmax / D2 = 15, as detailed below: For strain m1, there will be 3 small strains: The first small strain m11 = 0.02 + 0.005 = 0.025. Taking the equilibrium structure s11 as the initial structure, the strain m11 is applied, and the equilibrium structure s21 is calculated. The second small strain m12 = 0.02 + 2 × 0.005 = 0.03. Taking the equilibrium structure s11 as the initial structure, the strain m12 is applied to calculate the equilibrium structure s22. The third small strain m13 = 0.02 + 3 × 0.005 = 0.035. Taking the equilibrium structure s11 as the initial structure, the strain m13 is applied to calculate the equilibrium structure s23. For strain m2, there will be 3 smaller strains: The first small strain m21 = 0.04 + 0.005 = 0.045. Taking the equilibrium structure s12 as the initial structure, the strain m21 is applied, and the equilibrium structure s24 is calculated. The second small strain m22 = 0.04 + 2 × 0.005 = 0.05. Taking the equilibrium structure s12 as the initial structure, the strain m22 is applied to calculate the equilibrium structure s25. The third small strain m23 = 0.04 + 3 × 0.005 = 0.055. Taking the equilibrium structure s12 as the initial structure, the strain m23 is applied to calculate the equilibrium structure s26. For strain m3, there will be 3 smaller strains: The first small strain m31 = 0.06 + 0.005 = 0.065. Taking the equilibrium structure s13 as the initial structure, the strain m31 is applied, and the equilibrium structure s27 is calculated. The second small strain m32 = 0.06 + 2 × 0.005 = 0.07. Taking the equilibrium structure s13 as the initial structure, the strain m32 is applied to calculate the equilibrium structure s28. The third small strain m33 = 0.06 + 3 × 0.005 = 0.075. Taking the equilibrium structure s13 as the initial structure, the strain m33 is applied to calculate the equilibrium structure s29. For strain m4, there will be 3 smaller strains: The first small strain m41 = 0.08 + 0.005 = 0.085. Taking the equilibrium structure s14 as the initial structure, the strain m41 is applied, and the equilibrium structure s210 is calculated. The second small strain m42 = 0.08 + 2 × 0.005 = 0.09. Taking the equilibrium structure s14 as the initial structure, the strain m42 is applied to calculate the equilibrium structure s211. The third small strain m43 = 0.08 + 3 × 0.005 = 0.095. Taking the equilibrium structure s14 as the initial structure, the strain m43 is applied to calculate the equilibrium structure s212. For strain m5, there will be 3 smaller strains: The first small strain m51 = 0.1 + 0.005 = 0.105. Taking the equilibrium structure s15 as the initial structure, the strain m51 is applied, and the equilibrium structure s213 is calculated. The second small strain m52 = 0.1 + 2 × 0.005 = 0.11. Taking the equilibrium structure s15 as the initial structure, the strain m52 is applied to calculate the equilibrium structure s214. The third small strain m53 = 0.1 + 3 × 0.005 = 0.115. Taking the equilibrium structure s15 as the initial structure, the strain m53 is applied to calculate the equilibrium structure s215.

[0097] Based on the strain under the large step length and the strain under the small step length, the energy of the corresponding equilibrium structure is calculated, and the strain-energy curve of the cristobalite crystal under tensile deformation along the strain direction of the z-axis is generated.

[0098] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for generating strain-energy curves of a material, characterized in that, include: Obtain the original structure of the material to be processed; The mechanical matrix of the original structure is solved, and the Poisson's ratio in multiple strain directions is obtained from the mechanical matrix. Determine the equilibrium structure under each strain direction. For each strain direction, starting from the original structure, the strain is continuously increased according to the required strain resolution. Starting from the set initial strain, the cell parameters are determined according to the Poisson's ratio and the current strain value, and the equilibrium structure under the current strain is determined until the current strain reaches the preset maximum strain corresponding to the strain direction, and the equilibrium structure under the preset maximum strain of the current strain direction is obtained. The energy at each strain corresponding to each equilibrium structure under each strain direction is obtained, and the strain-energy curve C1 of the material to be treated under increased strain conditions is generated.

2. The method according to claim 1, characterized in that, Also includes: Obtain the location and strain direction of the phase transition in the strain-energy curve C1; Starting from the strain at the phase transition position, the starting strain is continuously reduced according to the required strain resolution, and the unit cell parameters are updated according to the reduced strain and the Poisson's ratio in the corresponding strain direction. The equilibrium structure under different reduced strains is determined according to the updated unit cell parameters, and the energy corresponding to each equilibrium structure is recorded. Based on the reduced strains and the energy of the corresponding equilibrium structure, strain-energy curve C2 is generated; Based on the strain direction where the phase transition occurs, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 in the corresponding strain direction until the strain-energy curve C2 intersects with the strain-energy curve C1 in the corresponding strain direction, and then stop reducing the strain. The strain point with the minimum energy at the corresponding strain is selected from the intersecting strain-energy curves C1 and C2, and the strain-energy curve C3 of the material to be treated is generated under various strain conditions.

3. The method according to claim 1, characterized in that, The equilibrium structure under each strain direction is determined as follows: For one strain direction, a first strain d1 is set, and a first cell parameter is determined based on the Poisson's ratio of the current strain direction and the first strain d1. The equilibrium structure s1 under the first strain d1 is determined based on the first cell parameter. Using the equilibrium structure s1 as the initial structure, the first strain d1 is increased according to the required strain resolution to obtain the second strain d2. The second cell parameters are determined according to the Poisson's ratio in the current strain direction and the second strain d2. The equilibrium structure s2 under the second strain d2 is determined according to the second cell parameters. The strain in the current strain direction is continuously increased and the cell parameters are updated according to the required strain resolution until the strain in the current strain direction reaches the preset maximum strain dn, and the equilibrium structure sn under the preset maximum strain dn in the current strain direction is obtained.

4. A method for generating strain-energy curves of a material, characterized in that, include: Obtain the original structure of the material to be processed; The mechanical matrix of the original structure is solved, and the Poisson's ratio in multiple strain directions is obtained from the mechanical matrix. For each strain direction, based on the required strain resolution, preset number of nodes, and maximum strain Dmax, a minimum strain step size D1 and a maximum strain step size D2 are set, wherein the maximum strain Dmax and the maximum strain step size D2 satisfy an integer ratio, and the maximum strain step size D2 and the minimum strain step size D1 satisfy an integer ratio. The first fixed cell parameter is set according to the Poisson's ratio of the current strain direction and the maximum strain step size D2. The equilibrium structure s1m of multiple strains under the maximum strain step size D2 is determined simultaneously using the preset number of nodes and the first fixed cell parameter. The equilibrium structure s1m of each strain is taken as the initial structure. The second fixed cell parameter is set according to the Poisson's ratio of the current strain direction and the minimum strain step size D1. The strain is increased based on the strain corresponding to the initial structure according to the minimum strain step size D1 to obtain multiple strains under the minimum strain step size D1. The equilibrium structure s2n of multiple strains under the minimum strain step size D1 is determined simultaneously using the preset number of nodes according to the second fixed cell parameter. Obtain the energy at each strain corresponding to each equilibrium structure s1m and equilibrium structure s2n in each strain direction, and generate the strain-energy curve C1 of the material to be treated under increased strain conditions in each strain direction.

5. The method according to claim 4, characterized in that, Also includes: Obtain the location and strain direction of the phase transition in the strain-energy curve C1; Starting from the strain at the phase transition position, the starting strain is continuously reduced according to the required strain resolution, and the unit cell parameters are updated according to the reduced strain and the Poisson's ratio in the corresponding strain direction. The equilibrium structure under different reduced strains is determined according to the updated unit cell parameters, and the energy corresponding to each equilibrium structure is recorded. Based on the reduced strains and the energy of the corresponding equilibrium structure, strain-energy curve C2 is generated; Based on the strain direction where the phase transition occurs, compare the energy generation strain-energy curve C2 with the strain-energy curve C1 in the corresponding strain direction until the strain-energy curve C2 intersects with the strain-energy curve C1 in the corresponding strain direction, and then stop reducing the strain. The strain point with the minimum energy at the corresponding strain is selected from the intersecting strain-energy curves C1 and C2, and the strain-energy curve C3 of the material to be treated is generated under various strain conditions.

6. The method according to claim 4, characterized in that, The number of strain equilibrium structures s1m at the maximum strain step size D2 is determined as follows: ， Where m represents the number of equilibrium structures s1m.

7. The method according to claim 4, characterized in that, Based on the minimum strain step D1, the strain is increased from the strain corresponding to the initial structure, including: The strain is increased for each strain under the maximum strain step size D2 according to the minimum strain step size D1; Wherein, the number of times each strain increases under the maximum strain step size D2 is: ， Where q represents the number of times each strain increases.

8. The method according to claim 6, characterized in that, The number of strain equilibrium structures s2n at the minimum strain step size D1 is determined as follows: ， Where n represents the number of equilibrium structures s2n.

9. A strain-energy curve generation device for a material, characterized in that, include: A processor and a memory connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to cause the processor to perform the strain-energy curve generation method for a material as described in any one of claims 1-8.

Images