Si-Ge crystal direct band gap prediction network structure based on a graph neural network

Abstract

The application discloses a Si-Ge crystal direct band gap prediction network structure based on a graph neural network, and belongs to the field of computer algorithms.The graph neural network structure is a special code for Si-Ge crystal direct band gap prediction, and specifically comprises distance embedding, angle embedding, an embedding layer, an interaction layer and a classification layer; the classification layer further comprises a category weight balance coefficient.The network model composed of the five modules of distance embedding, angle embedding, the embedding layer, the interaction layer and the classification layer is used to realize feature extraction of Si-Ge crystals to final classification, all direct band gap samples can be accurately identified, and misclassification as indirect band gap is reduced; the Si-Ge crystals of any layer can be accurately predicted, so that the universality of the model is improved.

Description

Technical Field

[0001] This invention belongs to the field of computer algorithms and relates to a direct bandgap prediction network structure for Si-Ge crystals based on graph neural networks. Background Technology

[0002] The Materials Genome Initiative aims to halve the R&D cycle and costs of new materials through the organic integration of experimentation, computation, and theory, thereby accelerating progress in areas such as clean energy, national security, and human welfare. Semiconductor science and technology play a crucial role in the current development of human society. Advances in semiconductor science and technology have brought about the widespread adoption of the internet and the development of the information industry, transforming human life and production. Semiconductor science and technology are also continuously fostering emerging industries, such as new energy, solid-state lighting, mobile internet, the Internet of Things, big data, cloud computing, and smart home appliances. Semiconductor science and technology continues to flourish, with new materials, ideas, and technologies constantly emerging. For example, the emergence of novel two-dimensional materials may bring us higher-performance devices and new application technologies, and the development of semiconductor spintronics may be applied to novel spin devices. Si and Ge are both indirect bandgap semiconductor materials. The radiative recombination of electrons and holes in Si and Ge does not conform to the momentum conservation law required for optical transitions; an additional auxiliary phonon is needed to satisfy the momentum conservation law and achieve optical transitions.

[0003] Strained Si6 / Ge4 superlattices can achieve luminescence through band folding within their small Brillouin zones, creating a direct bandgap. The Si / Ge interface induces a change in crystal potential, causing the superlattice wavefunction to expand to a certain extent in the Si (unit cell) reciprocal lattice space. This results in partial overlap of the valence and conduction band edge wavefunctions in the reciprocal lattice space, leading to luminescence. However, the quasi-direct bandgap optical transition matrix of strained Si6 / Ge4 superlattices remains very small, making it impossible to overcome the theoretical limit and achieve efficient luminescence of Si6 / Ge4 superlattices by improving the quality of epitaxially grown crystals. Traditional trial-and-error experimental methods are very costly and can only be applied to small quantities of Si. n / Ge m The study focuses on superlattices. In fact, for a given Si / Ge superlattice with N atomic layers, it has approximately 2... NDifferent Si and Ge compositions are considered. The search space includes both direct and indirect bandgap materials. To better distinguish all materials, electronic bandgap calculations are needed. Density functional theory (DFT) is the most commonly used tool for bandgap calculations. However, its calculations are relatively time-consuming and cannot be performed on all candidate materials in the entire search space. Therefore, a fast and efficient screening tool is urgently needed. Graph neural networks have recently been widely used in molecular biology; therefore, a direct bandgap prediction network structure for Si-Ge crystals based on graph neural networks is proposed. Summary of the Invention

[0004] Objective of the Invention: The objective of this invention is to provide a graph neural network-based direct bandgap prediction network structure for Si-Ge crystals, which offers advantages such as fast prediction speed and high accuracy. This solves the problem of lengthy simulation calculations using density functional theory, which often hinders the rapid development of direct bandgap prediction for Si-Ge crystals and impacts the discovery of new silicon-based materials.

[0005] Technical solution: The present invention provides a graph neural network-based direct bandgap prediction network structure for Si-Ge crystals. The graph neural network structure is a dedicated code for predicting the direct bandgap of Si-Ge crystals, which specifically includes interconnected distance embedding, angle embedding, embedding layer, interaction layer and classification layer.

[0006] The classification layer includes a category weight balancing coefficient.

[0007] Furthermore, the distance embedding input receives the atomic spatial coordinates and atomic number of the Si-Ge crystal, which is one of the first layer structure inputs in the network and is used to calculate the interatomic distance of the input crystal structure.

[0008] The angle-embedded input terminal receives the atomic spatial coordinates and atomic numbers of the Si-Ge crystal.

[0009] It is one of the first-layer input terminals in the network, used to calculate the interatomic angles of the input crystal structure.

[0010] Furthermore, the outputs of the distance embedding and angle embedding are respectively connected to the input of the embedding layer.

[0011] The embedding layer is the second layer of the network structure, used to fuse the distance embedding and angle embedding in the first layer, and output the distance and angle feature embeddings.

[0012] Furthermore, the output of the embedding layer is connected to the input of the interaction layer.

[0013] The interaction layer is the third layer of the network, used to exchange information between the embedded features of the second layer and update the model parameters.

[0014] Furthermore, the output of the interaction layer is connected to the input of the classification layer.

[0015] The classification layer is the fourth layer of the network, used to classify the output information of the third layer to determine whether the input Si-Ge crystal has a direct bandgap or an indirect bandgap.

[0016] Furthermore, the category weight balance coefficient is an internal structure in the fourth classification layer, used to balance the direct bandgap and introductory bandgap categories to achieve correct classification of all direct bandgap categories and reduce misclassification.

[0017] Beneficial effects: Compared with the prior art, the features of this invention are: 1) It can train a network model specifically for predicting the direct bandgap of Si-Ge crystals using existing data; by using a network model composed of five modules, namely distance embedding, angle embedding, embedding layer, interaction layer and classification layer, the feature extraction and final classification of Si-Ge crystals are realized; the prediction accuracy of the test set is expected to reach more than 95%, and all direct bandgap samples can be accurately identified, reducing misclassification as indirect bandgap; 2) It can achieve accurate prediction for Si-Ge crystals of any layer, not limited to the 16-layer structure of existing data, thereby improving the universality of the model. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the structure of the present invention;

[0019] Figure 2 This is the accuracy recall curve of the present invention;

[0020] Figure 3 This is a graph showing the change in the predictive performance of the present invention on the test set;

[0021] Figure 4 This is a bar chart of the test set accuracy under different sample sizes in the training set according to the present invention;

[0022] Figure 5 This is a bar chart comparing the accuracy of the model of this invention with the category balance weight coefficient removed and the complete model of this invention;

[0023] Wherein, 1 is distance embedding, 2 is angle embedding, 3 is embedding layer, 4 is interaction layer, 5 is classification layer, and 6 is category weight balance coefficient. Detailed Implementation

[0024] To more clearly illustrate the technical solution of the present invention, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0025] like Figure 1 As shown, the present invention discloses a graph neural network-based direct bandgap prediction network structure for Si-Ge crystals. The graph neural network structure is dedicated code for direct bandgap prediction of Si-Ge crystals. Its network structure includes distance embedding 1, angle embedding 2, embedding layer 3, interaction layer 4, and classification layer 5. The classification layer 5 includes a class weight balancing coefficient 6, which is added to the loss calculation.

[0026] Furthermore, the distance embedding 1 is used to calculate the interatomic distance of the input crystal structure.

[0027] Furthermore, the angle embedding 2 is used to calculate the interatomic angles of the input crystal structure.

[0028] Furthermore, the embedding layer 3 is used to embed the input distance and angle into features.

[0029] Furthermore, the interaction layer 4 is used to realize information interaction between embedded features and update model parameters.

[0030] Furthermore, the classification layer 5 is used to classify the input Si-Ge crystal based on the features output by the network, determining whether the input Si-Ge crystal has a direct bandgap or an indirect bandgap.

[0031] Furthermore, the category weight balance coefficient 6 is used to balance the direct bandgap and introductory bandgap categories to achieve correct classification of all direct bandgap categories and reduce misclassification.

[0032] Example 1

[0033] The present invention discloses a direct bandgap prediction network structure for Si-Ge crystals based on graph neural networks, the structure of which includes distance embedding 1, angle embedding 2, embedding layer 3, interaction layer 4, and classification layer 5.

[0034] The input data to the network uses a crystal structure composed of 16 layers of Si-Ge crystals stacked in any combination. Whether it has a direct bandgap is obtained by calculating the band curve using density functional theory. The complete dataset consists of 3813 crystal samples. The training set uses 3700 samples for training, including 1533 samples with direct bandgap and 2167 samples with indirect bandgap. The test set uses 113 samples for testing, including 41 samples with direct bandgap and 72 samples with indirect bandgap.

[0035] To verify the effectiveness of the graph neural network-based Si-Ge crystal direct bandgap prediction network for predicting the direct bandgap of Si-Ge crystals, combined with... Figure 1-3 The present invention will be further described below.

[0036] Figure 1 This is a diagram of the direct bandgap prediction network structure for Si-Ge crystals based on graph neural networks. The structure includes distance embedding 1, angle embedding 2, embedding layer 3, interaction layer 4, and classification layer 5. Figure 2 The precision-recall curve is the most commonly used graph neural network (GNN) to demonstrate the performance of network models in the field of machine learning. This curve can be used to intuitively evaluate the performance of the designed graph neural network-based Si-Ge crystal direct bandgap prediction network. As can be seen from the figure, the test set accuracy reached 99.12%, with all 41 direct bandgap samples correctly predicted and all 71 indirect bandgap samples correctly predicted. From the results, we can conclude that the graph neural network-based Si-Ge crystal direct bandgap prediction network can fully meet the target requirements. It can be trained with existing Si-Ge crystal data and can correctly predict the direct bandgap of unknown samples, while ensuring that indirect bandgap is not misidentified as direct bandgap. Figure 3 The graph shows the change in prediction performance on the test set as the number of iterations increases, with the horizontal axis representing the number of iterations and the vertical axis representing accuracy. The graph shows that in the first 100 iterations of training, the classification performance on the test set did not meet expectations. When the number of iterations increased from 100 to 200, the performance began to gradually increase, and when the number of iterations reached 200, the performance essentially achieved the ideal classification accuracy. When the number of iterations increased again, the classification accuracy began to stabilize. At this point, the model had learned the optimal parameters and could perfectly predict the direct bandgap of Si-Ge crystals.

[0037] Example 2

[0038] To evaluate the impact of training a graph neural network-based Si-Ge crystal direct bandgap prediction network structure on test set performance with different training set sample sizes, this embodiment gradually reduced the number of training set samples by 50 samples each time, and simultaneously added these 50 samples to the test set. A total of 5 reductions in the training set sample size and 5 increases in the test set sample size were performed, and the performance changes were observed. The results of this embodiment are as follows: Figure 4 As shown in the figure, it can be seen that each reduction in the number of training set samples reduces the accuracy of the test set. When the number of training set samples is 3450 and the number of test set samples is 363, the accuracy of the test set can still be maintained at around 94%, which is in line with the original intention of the network structure design.

[0039] Example 3

[0040] The present invention adds a class balancing weight coefficient to the Si-Ge crystal direct bandgap prediction network structure based on graph neural networks. The goal is to balance the weights of the direct bandgap class and the indirect bandgap class, giving the direct bandgap class a larger weight coefficient and preventing more direct bandgap samples from being mispredicted as indirect bandgap, thus avoiding the omission of potentially important Si-Ge crystal structures. To verify the effect of the added weight coefficient, this embodiment compares the accuracy of the model without the class balancing weight coefficient and the complete model of this invention on the test set. The results of the embodiment are as follows: Figure 5 As shown in the figure, the accuracy of the model without the class balance weight coefficient is lower than that of the complete model described in this invention. The results of this embodiment demonstrate that using the class balance weight coefficient has a crucial impact on the prediction accuracy of the test set, avoiding the omission of potentially important Si-Ge crystal structure band gaps.

[0041] Example 4

[0042] This invention proposes a graph neural network-based direct bandgap prediction network for Si-Ge crystals. The training data uses Si-Ge crystal structures with arbitrary combinations of 16 layers, and their direct bandgap is calculated using density functional theory. To verify the predictive ability of the proposed network structure for Si-Ge structures with arbitrary layers, this embodiment uses more data for testing. By taking several common Si-Ge crystal structures and determining whether they have direct bandgap characteristics, the network structure is input and the prediction results are output. The results show that it can accurately predict these common Si-Ge crystal structures, which fully demonstrates that the graph neural network-based direct bandgap prediction network for Si-Ge crystals of this invention has universality for Si-Ge crystal structures with arbitrary layers, and can provide a solid foundation for the future development of more Si-Ge crystal materials.

[0043] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A graph neural network-based direct bandgap prediction network structure for Si-Ge crystals, characterized in that, The graph neural network structure is a dedicated code for direct bandgap prediction of Si-Ge crystals. Specifically, it includes interconnected distance embedding (1), angle embedding (2), embedding layer (3), interaction layer (4) and classification layer (5). The classification layer (5) includes a category weight balance coefficient (6). The input terminal of the distance embedding (1) receives the atomic spatial coordinates and atomic number of the Si-Ge crystal, which is the first input terminal of the first layer structure in the network; the distance is calculated for the input crystal structure; The input terminal of the angle embedding (2) receives the atomic spatial coordinates and atomic number of the Si-Ge crystal. It is the second input terminal of the first layer structure in the network, which calculates the interatomic angles of the input crystal structure; The outputs of the distance embedding (1) and the angle embedding (2) are respectively connected to the input of the embedding layer (3). The embedding layer (3) is the second layer structure of the network, which fuses the distance embedding (1) and angle embedding (2) in the first layer and embeds the output distance and angle features; The output of the embedded layer (3) is connected to the input of the interaction layer (4). The interaction layer (4) is the third layer of the network, which performs information interaction on the embedded features of the second layer and updates the model parameters. The output of the interaction layer (4) is connected to the input of the classification layer (5). The classification layer (5) is the fourth layer of the network, which performs feature classification on the output information of the third layer to determine whether the input Si-Ge crystal has a direct bandgap or an indirect bandgap. The category weight balance coefficient (6) is the internal structure of the fourth classification layer (5). It balances the direct bandgap and indirect bandgap categories to achieve correct classification of all direct bandgap categories and reduce misclassification.

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