Large-scale supercell tight constraint model scaling method based on feature screening

Abstract

The invention relates to the technical field of quantum transport simulation, and discloses a large-scale supercell tight constraint model scaling method based on feature screening. In order to solve the problems that the quantum transport calculation cost of an unbalanced Green function is too high and a large number of orbits have no substantial contribution to transport due to the fact that the Hamiltonian matrix dimension in a large-scale super-cell tight constraint model is sharply increased along with the size, a three-layer technical scheme is provided, and a node / edge mask mechanism is introduced in a graph neural network prediction stage; selectively shielding irrelevant items according to atomic transport importance; the full-atom Hamiltonian is scaled to an effective subspace, and only a track which is close to a Fermi surface and contributes to an energy band structure remarkably is reserved; and efficient model scaling is realized in a controllable range of key transport parameter errors such as band gaps and effective quality. According to the method, the calculation cost of quantum transport simulation can be remarkably reduced, the bottleneck of large-scale defect supercell chain simulation is broken through, and an efficient and feasible scheme is provided for large-size complex system quantum transport research.

Description

Technical Field

[0001] This invention relates to the fields of computational materials science, quantum transport simulation, and semiconductor device design. Specifically, it relates to a large-scale supercell tight-binding (TB) model scaling method based on feature selection, which is particularly suitable for quantum transport simulation of defective and amorphous semiconductor systems (such as amorphous oxide and silicon carbide). It can be combined with multilayer graph neural networks (GNN) containing symmetric graph attention mechanisms, density functional theory (DFT), and non-equilibrium Green's function (NEGF) methods to achieve efficient and accurate simulation of large-scale, defective, aperiodic supercell chains. Background Technology

[0002] As the feature size of semiconductor devices continues to shrink to the nanometer or even atomic scale, quantum effects (such as carrier tunneling and quantum confinement) and defect effects (such as oxygen vacancies and interstitial atoms) have become the core factors determining the electrical performance of devices. Traditional drift-diffusion models can no longer accurately describe carrier transport behavior, and there is an urgent need for transport simulation tools based on quantum mechanics to support the design of next-generation semiconductor devices.

[0003] The TB model, as the core framework for quantum transport simulation, combined with NEGF, can describe carrier transport in materials with different electronic structures at a reasonable computational cost, serving as a crucial bridge between first-principles calculations and device-level modeling. However, existing methods for constructing and scaling TB models suffer from significant technical bottlenecks:

[0004] Large-scale supercell computation is costly: As the size of the supercell increases (such as a defective kiloatomic supercell), the size of the Hamiltonian matrix of the TB model increases quadratically, which leads to a sharp increase in the computational cost of subsequent NEGF quantum transport simulations, even exceeding the current computing power capacity, making it impossible to simulate large-scale defective supercell chains.

[0005] Existing models lack efficient feature selection mechanisms: In actual quantum transport processes, a large number of atomic orbitals in the supercell do not make substantial contributions to the band structure and transport properties. However, existing TB model construction methods, such as empirical parameter fitting and Wannier transformation, all require the retention of all atomic orbitals. They have not established a selective selection mechanism based on atomic importance, such as the contributions of defects and band edge states, resulting in a large amount of redundant information in the matrix.

[0006] Periodicity dependence and poor adaptability to defective systems: The TB model construction method based on Wannier transform depends on the periodicity of crystals and is difficult to apply to non-periodic systems such as those with defects or amorphous structures; while empirical fitting methods lack transferability and cannot flexibly adjust the model size to balance accuracy and efficiency, which further limits their application in industrial semiconductor devices (such as thin-film transistors and power devices).

[0007] The computational complexity is mismatched with the system size: the computational complexity of existing methods increases superlinearly with the number of atoms (e.g., the computational complexity of the Vannier transform is close to O(N³)), while the demand for simulation of large-scale defective supercells (with more than 1000 atoms) in semiconductor device design is becoming increasingly urgent. The contradiction between the two has become the core obstacle restricting the industrial application of quantum transport simulation.

[0008] Therefore, developing a method that can efficiently screen core orbitals, scale TB models, and adapt to non-periodic defect systems while ensuring the accuracy of key transport parameters is of great significance for breaking through the bottleneck of large-scale quantum transport simulation and promoting the precision and efficiency of semiconductor device design. Summary of the Invention

[0009] To address the technical bottlenecks of existing large-scale defective supercell (TB) models, such as the excessively large Hamiltonian matrix dimension leading to extremely high computational costs for NEGF quantum transport and the lack of substantial contribution of many deep orbitals to transport properties, this invention proposes a feature-based scaling method for large-scale supercell tight-binding models. The core concept of this invention is to break away from the traditional modeling paradigm of full-atom, full-band fitting. First, based on first-principles state density and band structure characteristics, a physical masking mechanism is introduced to accurately screen and retain key atomic orbitals that significantly contribute to band-edge states and defect states near the band gap, while selectively masking irrelevant atoms that do not substantially contribute to transport. Second, the orbital matrix elements of these key atoms are extracted to construct an effective subspace, achieving physical dimensionality reduction and scaling of the large-scale Hamiltonian matrix. Finally, the dimensionality-reduced core atomic structure is mapped as graph features and input into a Geometric Array Neural Network (GNN) for targeted training, and the GNN fits and outputs the scaled tight-binding parameters. This invention, while strictly ensuring the accuracy of key transport parameters such as band gap and effective mass, minimizes the computational cost of quantum transport simulation and successfully overcomes the simulation scale limitations of large-scale defective supercell chains.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A method for scaling large-scale hypercell tight-binding models based on feature selection includes the following steps:

[0012] Step S1, Obtain target system data: Collect basic data for DFT calculation of semiconductor supercell systems with defects and corresponding defect-free systems. The basic data includes the band structure, density of states, supercell atomic coordinates and interatomic bonding information of the system.

[0013] Step S2 introduces a physical masking mechanism for nodes and edges: based on the density of states analysis results obtained from DFT calculation, the transport importance of atoms in the supercell is evaluated, and irrelevant atomic nodes and their associated chemical bond edges that do not contribute substantially to quantum transport properties are selectively masked.

[0014] Step S3, constructing an effective subspace: Based on the retained key atomic orbitals that were not masked in step S2, the large-scale all-atom Hamiltonian matrix is ​​screened and dimension-reduced, and the matrix rows and columns corresponding to the retained atomic orbitals are extracted to construct the scaled effective subspace Hamiltonian matrix.

[0015] Step S4, train the output scaled TB model: construct a GNN architecture, map the selected supercell atomic structure into graph features and input them into the network, use the DFT band structure near the Fermi surface as the learning target for fitting training, and output the scaled tight-binding model parameters under the premise that the errors of the key transport parameters meet the preset conditions.

[0016] Step S5, Large-scale quantum transport simulation application: Substitute the Hamiltonian matrix constructed from the scaled tight-binding model parameters into the NEGF equation to perform quantum transport simulation calculations for a large-scale supercell system with point defects.

[0017] Furthermore, in steps S2 and S3, the specific process of the physical masking mechanism and the construction of the effective subspace is as follows:

[0018] The orbital energy screening threshold was set to Fermi level ±3 eV. Based on DFT density of states analysis, only high-importance atomic orbitals that significantly contribute to band-edge states and defect states within this energy range were retained, while high-energy redundant orbitals were removed. A low-dimensional Hamiltonian matrix was constructed based on the retained orbitals after screening, and its size was scaled from the full atomic scale to less than 30% of the original scale, while ensuring that the sparsity of the matrix was greater than 55%.

[0019] Furthermore, in step S4, the GNN architecture includes a feature encoder, a symmetric graph attention convolutional layer, and an output module:

[0020] The feature encoder projects the 6-dimensional descriptor, 4-dimensional bond attributes, and supercell volume information of atoms into a unified-dimensional latent representation feature through layer normalization (LayerNorm) and the nonlinear activation function (LeakyReLU).

[0021] The symmetric graph attention convolutional layer adopts a multi-layer multi-head structure, which fuses node and edge features through a symmetric message passing mechanism. When calculating the attention coefficient, the node feature averaging and edge feature concatenation are used to ensure the symmetry of physical interactions.

[0022] The output module maps high-dimensional features to TB model parameters through a multilayer perceptron, where self-loop edges output the potential energy parameters and non-self-loop edges output the transition integral parameters.

[0023] Furthermore, when outputting the transition integral parameters, the graph neural network imposes a physical space truncation constraint on them, ensuring that they satisfy a formula that decays exponentially with distance:

[0024]

[0025] In the formula, t ij For the effective transition integral of the output, t ij ' Let r be the initial transition integral predicted by the graph neural network. ij r is the spatial distance between atom i and atom j. cut The cutoff radius is 2 to 4 Å.

[0026] Furthermore, in step S4, the preset condition for the key transport parameter error is: the band gap deviation of the band structure generated by the output tight-binding model compared with the DFT calculation result is less than 0.02 eV, and the effective mass error is less than 10%.

[0027] Compared with the prior art, the beneficial effects of the present invention include:

[0028] (1) Significantly improved computational efficiency. It breaks through the limitations of traditional all-atom solutions, constructs an effective subspace through physical masking, and enables the TB matrix to be scaled up to 90%, thereby increasing the computational speed of subsequent NEGF quantum transport by thousands of times and successfully breaking through the bottleneck of fast simulation of supercells with defects at the thousand-atom level.

[0029] (2) Strict physical accuracy is guaranteed. The masking mechanism of this invention specifically preserves the key orbital and core band features near the Fermi surface, so that the errors of key transport parameters such as band gap and effective mass are strictly controlled within an extremely low threshold, achieving a high degree of consistency between the simulation accuracy after dimensionality reduction and scaling and the full atom model.

[0030] (3) Strong adaptability to non-periodic systems. The graph structure of the graph neural network is naturally adapted to non-periodic systems with defects and amorphous structures. The feature selection and masking mechanism does not depend on the spatial periodicity of the crystal, which effectively solves the bottleneck of existing traditional methods (such as the maximum localization Wannier function method) in modeling large-scale isolated defect systems.

[0031] (4) Excellent physical interpretability. The TB model parameters (in-situ energy, transition integral) extracted in this invention are subject to strict physical formula constraints and fully conform to the physical laws of atomic bonding and electron interaction; moreover, the matrix sparsity and orbital localization characteristics after dimensionality reduction are better, which greatly facilitates the analysis of the underlying physical mechanism of semiconductor devices. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the 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 based on these drawings without creative effort.

[0033] Figure 1 The flowcharts for the feature-based TB model scaling method and the flowcharts for constructing a multi-layer GNN architecture including a symmetric graph attention mechanism are shown below.

[0034] Figure 2 This is a comparison diagram of the structure of the entire atom and the subspace of this invention.

[0035] Figure 3 This is a comparison diagram showing the bandgap fitting effect after applying the side masking mechanism to SiC according to the present invention.

[0036] The left side shows the band structure fitted with all atoms, while the right side shows the band structure fitted using a side masking mechanism.

[0037] Figure 4 This is a comparison chart of the TB matrix size and value before and after scaling in this invention.

[0038] The left side is the TB matrix of all atoms, and the right side is the TB matrix scaled using the edge masking mechanism. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below in conjunction with specific embodiments and accompanying drawings. Those skilled in the art should understand that the embodiments described are only helpful in understanding this invention and are not limited to the following embodiments.

[0040] This embodiment uses a 96-atom silicon carbide (SiC) supercell as the target system to achieve scale-up of the TB model, which is ultimately used for quantum transport simulation of this defective supercell chain. This system is a typical large-scale aperiodic system with a large number of atoms and low symmetry. Existing methods are computationally expensive, which perfectly suits the technical advantages of this invention.

[0041] Example:

[0042] Constructing a physics-aware GNN prediction model:

[0043] like Figure 1 As shown, the model architecture of this invention includes three feature encoders, three GNN layers, and a TB parameter output module. The feature encoders refer to atomic feature encoders that project 6-dimensional atomic descriptors into 128-dimensional embeddings, and bond feature encoders that process 4-dimensional bond attributes. Both employ a "double-layer projection + LayerNorm + LeakyReLU" structure. The GNN layers have four attention heads and 128 hidden layer dimensions, using a symmetric message passing mechanism to ensure the symmetry of atomic interactions. The output module includes two perceptron layers (512-dimensional → 128-dimensional → 1-dimensional), outputting the in-situ energy and transition integral.

[0044] The training is set to a batch size of 8 and an initial learning rate of 10. -4 The ReduceLROnPlateau scheduler (patience value 10, decay factor 0.99) is used, with 10 training steps. 4 The loss function is the Fermi-Dirac weight multiplied by the absolute error of the energy eigenvalues:

[0045]

[0046] In the formula, E is the band eigenvalue and α is the attenuation coefficient.

[0047] Node / edge masking mechanism for filtering critical tracks:

[0048] like Figure 2 As shown, the determination of highly important atoms is based on DOS analysis using DFT, which screens out atoms in the 4H-SiC supercell whose contribution to the band edge states is greater than 5%.

[0049] Masking is performed by embedding a mask layer in the output layer of the GNN, which automatically masks 78 low-importance atoms (with edge state contributions of less than 5%) and their associated edges. The resulting graph structure retains only 18 nodes and their corresponding chemical bond edges.

[0050] Constructing an effective subspace:

[0051] like Figure 3 and 4 As shown, the energy screening threshold is set to Fermi level ±3 eV, retaining only atomic orbitals within this range. The subspace Hamiltonian matrix is ​​constructed based on the screened orbitals, using the in-situ energy predicted by GNN and the transition integral to construct an 18×18 TB matrix with a sparsity of 56% (the proportion of non-zero elements), which is 96% smaller than the original 96×96 matrix.

[0052] Adaptive scaling and accuracy verification:

[0053] As shown in Table 1, the error thresholds were set to a bandgap error of less than 0.02 eV and an effective mass error of less than 10%. However, due to GPU bandwidth limitations, the speed advantage was not fully realized. Scaling optimization involved adjusting the orbital filtering threshold (from ±2.5 eV to ±3.0 eV at the Fermi surface), ultimately determining the optimal scaling ratio to be 96%. At this point, the bandgap error was 0.0026 eV (the DFT bandgap was 1.9113 eV, and the scaled TB model bandgap was 1.9067 eV); the effective mass error was 0.0077 m0 (the effective mass was 0.1529 m0, and the scaled TB model effective mass was 0.1452 m0). Both met the above requirements.

[0054] Before scaling After scaling Calculation speed <![CDATA[0.915 hours / 10 4 steps]]> <![CDATA[0.458 hours / 10 4 steps]]> Matrix size 96 × 96 18 × 18 sparsity 56% 61% Bandwidth deviation 0.0046 eV (0.24%) 0.0026 eV (0.13%) Effective quality deviation <![CDATA[0.0077 m0]]> <![CDATA[0.0019 m0]]>

[0055] Table 1.

Claims

1. A method for scaling large-scale hypercell tight-binding models based on feature selection, characterized in that, The method steps are as follows: Step S1: Obtain the basic data for first-principles calculations of the target semiconductor large-scale supercell system. The basic data includes the band structure, density of states, atomic coordinates, and interatomic bonding information of defective and defect-free supercells. Step S2: Introduce a node and edge masking mechanism. Based on the density of states and band characteristics calculated using first principles, evaluate the transport importance of atoms in the supercell and selectively mask irrelevant atomic nodes and their associated chemical bond edges that do not substantially contribute to quantum transport properties. Step S3: Based on the unmasked retained atomic nodes in step S2, scale the large-scale all-atom Hamiltonian matrix, extract the matrix rows and columns corresponding to the retained atomic orbitals, and construct an effective subspace Hamiltonian matrix containing some atoms. Step S4: Input the shielded supercell atomic structure features into the graph neural network, and perform fitting training with the first-principles band structure in step S1 as the target. Within the preset band gap and effective mass error threshold range, output the scaled tight-binding model parameters, and use these parameters for non-equilibrium Green's function quantum transport calculation.

2. The method according to claim 1, characterized in that, The process of evaluating the transport importance of atoms within the supercell and selectively shielding them as described in step S2 is as follows: Based on the density of states analysis results obtained from first-principles calculations, atomic orbitals that make significant contributions to band edge states and defect states near the band gap were selected. The maximum matrix dimension that the preset unbalanced Green's function solver can handle is calculated, and the atomic orbitals are sorted according to their contribution to determine the final set of highly important atoms to be retained. The remaining atoms outside this set are then masked.

3. The method according to claim 1, characterized in that, The specific process for constructing the effective subspace Hamiltonian matrix containing a subset of atoms in step S3 is as follows: Based on the order of the unmasked retained atomic orbitals in step S2, a global index mapping table is established for the large-scale all-atom Hamiltonian matrix; Based on the global index mapping table, only the matrix blocks formed by the intersection of rows and columns corresponding to the index are extracted from the all-atom Hamiltonian matrix to form a dimensionality-reduced scaling matrix as the effective subspace.

4. The method according to claim 1, characterized in that, The graph neural network described in step S4 includes a symmetric graph attention mechanism, which maps atoms in the supercell to nodes and chemical bonds between atoms to edges, and fuses node features, edge features and global volume features of the supercell through a symmetric message passing mechanism.

5. The method according to claim 4, characterized in that, The node features include at least the electronegativity, number of valence electrons, covalent radius, and ionic charge of the atom; the edge features include at least the bond vector and the bond type classified according to the two atoms connected.

6. The method according to claim 1, characterized in that, The tight-binding model parameters output by the graph neural network in step S4 include potential energy parameters and transition integral parameters; during the prediction phase of the graph neural network, a physical space truncation constraint is applied to the transition integral parameters to satisfy a formula that decays exponentially with interatomic distance: In the formula, t ij For the effective transition integral of the output, t ij ' Let r be the initial transition integral predicted by the graph neural network. ij r is the spatial distance between atom i and atom j. cut The set cutoff radius.

7. The method according to claim 1, characterized in that, In the fitting training process of the graph neural network described in step S4, the full band of energy is not fully fitted. Instead, the band edge states and defect states near the band gap are extracted using the energy window as the core training target.

8. The method according to claim 7, characterized in that, The loss function of the graph neural network includes penalty terms for bandgap error and effective quality error. By iteratively optimizing the network weights, the error between the output tight-binding model's band structure near the Fermi surface and the first-principles calculation results is controlled within a preset threshold.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the large-scale supercell tight-binding model scaling method based on feature screening as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the large-scale supercell tight-binding model scaling method based on feature screening as described in any one of claims 1 to 8.

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