Tightly bound model correction method based on hybrid functional and defect calibration

Abstract

The invention discloses a tight constraint model correction method based on hybrid functional and defect calibration. According to the method, an initial energy band of a defect-containing supercell is obtained based on a standard PBE functional, and energy band correction is carried out by utilizing a band gap difference value of a defect-free reference unit cell between the PBE functional and an HSE functional. In combination with charge transition energy level and energy window constraint of HSE functional calculation, an extrinsic defect energy band is analyzed and deentangled through wave function locality or projection energy band, the extrinsic defect energy band is integrally translated to transition energy level alignment, and a high-precision calibration energy band is obtained. The initial energy band and the calibration energy band are sequentially put into a graph neural network for preliminary training and continuous training so as to accurately extract tightly bound model parameters. And constructing a device channel Hamiltonian by means of the parameter, and executing quantum transport simulation in cooperation with a non-equilibrium Green Function (NEGF). According to the method, synchronous high-precision correction of the band gap and the defect energy level is realized with relatively low calculation cost, and a reliable scheme is provided for device-level quantum transport simulation of a defect-containing semiconductor system.

Description

Tight-Bound Model Correction Method Based on Hybrid Functional Analysis and Defect Calibration Technical Field

[0001] This invention belongs to the field of semiconductor materials and device simulation technology, specifically relating to an automatic correction method for tight-binding models that achieves high-precision bandgap correction based on hybrid functionals and simultaneously incorporates charge transition energy level defect calibration, and its application in quantum transport simulation. Background Technology

[0002] The electrical properties of semiconductor devices are related to the band structure of the materials (especially the band gap E). g The energy levels of defects are closely related to the energy levels of these defects. As device sizes become smaller and applications become more complex, problems such as defect-induced carrier trapping and transport degradation are becoming increasingly prominent. It is urgent to reveal their microscopic mechanisms through accurate quantum transport simulations to provide theoretical support for device structure optimization.

[0003] Tight-binding (TB) models have become a core tool for simulating transport in defective semiconductor devices due to their balance between computational efficiency and quantum mechanical accuracy. However, existing TB model construction and correction methods have significant drawbacks: Standard Density Functional Theory (DFT) generally underestimates the bandgap due to the Generalized Gradient Approximation (GGA) exchange-correlated functionals, and defect energy level localization is significantly inaccurate; although accurate descriptions can be achieved through charge transition levels (CTLs), existing TB models lack a systematic calibration mechanism. For complex material systems with severe band entanglement in their electronic structure, traditional correction methods struggle to accurately extract characteristic energy levels, leading to TB parameter fitting biases and inaccurate defect energy level localization after CTL calibration. Meanwhile, although hybrid functionals can significantly improve bandgap accuracy (far superior to GGA), the computational cost increases superlinearly with the system size, making them unsuitable for device simulation of large atomic systems. Existing TB model corrections are mostly limited to simple bandgap scaling, lacking directional CTL calibration of defect energy levels, and have not established a hybrid accuracy fusion framework of "low-cost DFT + a small amount of high-precision HSE data", resulting in the model being unable to reproduce experimentally consistent high-precision bandgap characteristics, and exhibiting poor parameter stability and transferability.

[0004] Therefore, developing an automatic correction method for tight-binding models based on hybrid functionals to achieve high-precision bandgap correction and coordinated CTL defect energy level calibration is of great significance for overcoming the contradiction between computational accuracy and efficiency and promoting the precision of quantum transport simulation of semiconductor devices. Summary of the Invention

[0005] To address the problems of underestimation of the standard DFT bandgap, inaccurate defect level localization, and excessively high computational cost of hybrid functionals in semiconductor electronic structure simulations, which makes it difficult to directly apply to large-scale defective systems, this invention proposes a tight-binding model correction method based on hybrid functionals and defect calibration. This method aims to obtain physically meaningful and highly accurate TB model parameters at a lower computational cost, thereby improving the accuracy of quantum transport simulations in defective semiconductor systems.

[0006] The first aspect of this invention is to provide a tight-binding model correction method based on hybrid functionals and defect calibration. The method includes: performing structural optimization and stress relief on a defective supercell, and obtaining the initial band structure data of the defective supercell based on standard functional calculations; selecting a defect-free single-cell system corresponding to the defective supercell, calculating the band structure based on standard functionals and hybrid functionals respectively, obtaining the energy shifts between the conduction band and the valence band, and using the energy shifts to correct the band gap of the initial band structure data of the defective supercell based on standard functionals; further calculating the charge transition energy levels of the defective supercell using hybrid functionals, and adjusting the position of the defect energy levels after band gap correction according to the charge transition energy levels to obtain a calibrated high-precision band structure.

[0007] The initial band structure data is input into the machine learning model for preliminary training to establish a mapping relationship between atomic structure and band topology. The machine learning model is then further trained or fine-tuned based on the high-precision band structure to obtain the TB model parameters.

[0008] According to one aspect of the above technical solution, the standard functional is the Perdew-Burke-Ernzerhof (PBE) functional, and the hybrid functional is the Heyd-Scuseria-Ernzerhof (HSE) functional; the defect-free supercell reference system obtains a band gap E under the PBE functional and the HSE functional, respectively. g PBE and E g HSE The difference between the two is used to characterize the bandgap correction amount:

[0009]

[0010] Based on the bandgap correction, the initial bandgap of the defective supercell calculated by the PBE functional is edited so that the corrected bandgap matches the high-precision hybrid functional results.

[0011] According to one aspect of the above technical solution, the method of bandgap correction for the PBE band uses a scissor operator to perform a rigid translation operation on the defective supercell bandgap data. The energy levels in the conduction band region are shifted upwards by the conduction band offset, and the energy levels in the valence band region are shifted downwards by the valence band offset. This stretches the bandgap of the defective supercell to be consistent with the hybrid functional calculation result, and the corrected energy satisfies:

[0012]

[0013]

[0014] Among them, E c and E v These are the conduction band and valence band energy levels before correction, E c ' and E v ' These are the corrected conduction band and valence band energy levels, ΔE. c and ΔE v These are the conduction band shift and valence band shift obtained by comparing the defect-free unit cell system under hybrid and standard functionals, respectively, and satisfying the following:

[0015]

[0016] According to one aspect of the above technical solution, the formation of the defect-free and defective supercells can satisfy:

[0017]

[0018] Among them, E defect (q) represents the total energy of the system when the defect is in charge state q, E defect_free Let n be the total energy of the defect-free system. i μ represents the number of atoms added or removed from the i-th component. i E represents the chemical potential of the corresponding element. f For the Fermi level, E corr This is a charge correction term; by comparing the defect formation energies under different charge states, the charge transition energy levels can be obtained, and these charge transition energy levels satisfy:

[0019]

[0020] Wherein, ε(q1 / q2) is the charge transition energy level of the defect between charge states q1 and q2, and VBM is the valence band top; the charge transition energy level is used to characterize the actual energy level position of the defect in the band gap.

[0021] According to one aspect of the above technical solution, the defect energy level position calibration includes: setting an energy window constraint in the bandgap-corrected band structure, identifying and unentangled non-intrinsic defect bands from the defective supercell band data after bandgap correction through wavefunction locality analysis or projected band analysis; and calculating the initial energy center E of the defect band. d The eigenvalue defect band is then shifted as a whole, aligning its energy center with the CTL position, while keeping the conduction and valence band positions unchanged. This results in the corrected defect level center E. d ' satisfy:

[0022]

[0023] Where, ΔE d The correction amount used to align the energy center of the defect-related state with the charge transition energy level.

[0024] According to one aspect of the above technical solution, the machine learning model is a Graph Neural Network (GNN) with physical perception. Its input features include using atoms in a defective supercell structure as nodes of the graph, chemical bonds between atoms or interactions within the cutoff radius as edges of the graph, and the features of the nodes include atom type and coordinate information, while the features of the edges include distance and relative vector information between atoms.

[0025] According to one aspect of the above technical solution, the TB model is characterized by a Hamiltonian matrix, which includes potential energy and transition integrals, and its expression in wave vector k-space is:

[0026]

[0027] Among them, t ij R represents the in-situ energy in the case of the transition integral or self-loop between orbits i and j. ij denoted by , hc represents the Hermitian conjugate term; by solving the eigenvalue problem of the Hamiltonian, the predicted band structure corresponding to the TB model is obtained.

[0028] According to one aspect of the above technical solution, the training of the GNN includes a preliminary training phase and a continued training phase. In the preliminary training phase, the initial PBE band structure data containing defective supercells is input into the graph neural network for iterative optimization, enabling the network to learn the fundamental physical mapping between atomic structure and band topology, thus locking most of the network's weights. In the continued training phase, high-precision band structure data, after calibration of both the band gap and defect energy levels, is input into the network that has completed the preliminary training. A smaller learning rate is used to update the network's weights, ensuring that the band structure predicted by the TB model parameters output by the network can accurately fit the band gap and defect energy level positions of the calibrated defective supercell band structure.

[0029] According to one aspect of the above technical solution, the loss function for model training is constructed based on the difference between the high-precision band eigenvalues ​​and the predicted band eigenvalues, and adopts a weighted error form, with the weight function satisfying:

[0030]

[0031] Wherein, α corresponds to the eigenvalue energy, and is the weight control parameter; through the weight function, the fitting accuracy of the model to key energy levels near the valence band top and conduction band bottom is improved.

[0032] According to one aspect of the above technical solution, the TB model parameters are used to construct the Hamiltonian of the semiconductor device channel, and combined with the non-equilibrium Green's function (NEGF) method for device quantum transport simulation.

[0033] According to one aspect of the above technical solution, the method is applicable to wide bandgap semiconductors or low-dimensional semiconductor systems, and is particularly applicable to defective systems containing interstitial atoms, substitutional defects, or interface defects.

[0034] A second aspect of the present invention is to provide an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the tight-binding model correction method based on hybrid functionals and defect calibration as described in the first aspect above.

[0035] A third aspect of the present invention is to provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the tight-binding model correction method based on hybrid functionals and defect calibration as described in the first aspect above.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] This invention achieves simultaneous high-precision correction of band gap and defect levels without significantly increasing computational costs by constructing a hybrid precision framework of "low-cost standard functional calculation + high-precision calibration of a small number of hybrid functionals." The resulting TB model significantly improves the accuracy of bandgap description while maintaining physical interpretability, accurately reflecting defect-induced local electronic states and their impact on carrier transport. This method is applicable to large-scale semiconductor systems, possesses good versatility and scalability, and can be widely applied to quantum transport simulation and device performance prediction. Attached Figure Description

[0038] 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.

[0039] Figure 1 is an overall flowchart of the tight-binding model correction method based on hybrid functionals and defect calibration provided in an embodiment of the present invention.

[0040] Figure 2 is a flowchart of the bandgap correction process using the difference between PBE and HSE bandgap provided in an embodiment of the present invention.

[0041] Figure 3 shows the PBE and HSE bands of a 16-atom defect-free 4H-SiC unit cell provided in the embodiment of the present invention, and the C-containing band structure. i A schematic diagram of the calculated charge transition energy levels of the defective 4H-SiC supercell.

[0042] Figure 4 is a flowchart of the preliminary training and continued training process based on graph neural networks provided in an embodiment of the present invention.

[0043] Figure 5 shows a C-containing embodiment of the present invention. i A schematic diagram showing the GNN fitting results of the band structure of the defective 4H-SiC supercell and the quantum transport simulation results of the channel of the defective device. Detailed Implementation

[0044] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention. For those skilled in the art, any equivalent substitutions or modifications made to this invention without departing from the concept of this invention should fall within the scope of protection of this invention.

[0045] This embodiment uses carbon-containing interstitials (C) iTaking a 4H-SiC supercell system with defects as an example, this paper illustrates the specific implementation process of the tight-binding model correction method based on hybrid functionals and defect calibration described in this invention. 4H-SiC is a typical wide-bandgap semiconductor material with wide applications in power devices, but its large bandgap and complex interface and bulk defect states, especially C... i Defects can easily introduce localized trap levels within the bandgap, leading to carrier trapping, threshold drift, and degradation of device switching performance. Therefore, using C-containing... i Using the defective 4H-SiC system as the implementation object, the technical effects of this invention in bandgap correction, defect energy level calibration and quantum transport modeling can be effectively verified.

[0046] Figure 1 shows a flowchart of the tight-binding model correction method based on hybrid functionals and defect calibration, including the following steps:

[0047] Step 1: Perform structural optimization and stress relief on the defective supercell, and obtain the initial DFT band data based on the PBE standard functional;

[0048] Step 2: Calculate the bandgap data of the corresponding defect-free unit cell under the HSE hybrid functional and the PBE standard functional, obtain the bandgap correction amount, and perform bandgap correction on the PBE bandgap of the supercell.

[0049] Step 3: Calculate the charge transition energy levels of the defective supercell using HSE hybrid functionals, and calibrate the defect energy level positions accordingly to obtain a high-precision energy band.

[0050] Step 4: Perform preliminary GNN training on the initial PBE band containing defects to establish a physically meaningful basic model, and then continue to train the basic model separately using the calibrated high-precision band.

[0051] Step 5: Obtain the tight-binding model parameters that have both physical meaning and high accuracy, and combine them with the NEGF method to simulate device quantum transport.

[0052] In step 1, the implementation process includes:

[0053] In this embodiment, defect-free 4H-SiC single cells, supercells, and C-containing cells are first constructed. i Defective supercell. Based on a 16-atom 4H-SiC unit cell, a 96-atom supercell is formed by extending along the lattice direction. An interstitial carbon atom is introduced into this supercell, resulting in a C-containing supercell. i The defective 4H-SiC supercell structure was then subjected to geometric optimization and stress release to eliminate local high stress and unreasonable bond lengths, allowing the system to reach a stable relaxation state.

[0054] Preferably, the structure optimization and standard density functional calculations are implemented using Quantum ESPRESSO software, the exchange-correlation functional is the Perdew-Burke-Ernzerhof (PBE) functional, the plane wave cutoff energy ecutwfc can be set to 30 Ry, and the charge density cutoff energy ecutrho can be set to 240 Ry. For the ground state solution of the 96-atom 4H-SiC supercell, the Γ-point calculation is preferred, and the structure optimization convergence condition can be set to a total energy convergence threshold of 10. -4 Ry, atomic force convergence threshold 10 -4 Ry / bohr. The relaxed C-containing solution is obtained through the above processing. i The defective 4H-SiC supercell structure was determined, and its initial PBE band structure was further calculated.

[0055] After the above processing, we obtain the relaxed C-containing... i Initial PBE band structure data for defective 4H-SiC supercells. As shown in Figure 2, in step 2, the standard PBE functional for C-containing cells is corrected. i The systematic underestimation of the band gap in defective 4H-SiC was investigated. A 16-atom 4H-SiC unit cell was selected, and its band structure was calculated using PBE and HSE hybrid functionals, as shown in Figures 3(a) and 3(b). The comparison reveals that, near the band gap, the HSE hybrid functional significantly increases the band gap E without substantially altering the band dispersion relation. g This provides a basis for direct bandgap correction based on PBE results and demonstrates the rationality of using bandgap editing to correct the PBE bandgap underestimation. Furthermore, the bandgap values ​​of the 4H-SiC unit cell under the PBE functional and the HSE hybrid functional are E0, respectively. g PBE and E g HSE The difference between the two is defined as the bandgap correction, i.e.:

[0056]

[0057] In this embodiment, the band gap of the 4H-SiC unit cell under the PBE functional can be 2.20 eV, and the band gap under the HSE hybrid functional can be 3.23 eV, from which the band gap correction ΔE is obtained. g The value is 1.03 eV. Based on the bandgap correction, the C-containing bandgap obtained in step 1 is... i The band gap is corrected in the initial PBE band structure of the defective supercell.

[0058] The bandgap correction employs a scissor operator to rigidly shift the initial defective supercell bandgap data, shifting the energy levels in the conduction band region upwards by a conduction band offset ΔE. cThe energy levels located in the valence band region are shifted downwards by a valence band offset ΔE. v This ensures that the modified bandgap is consistent with the HSE hybrid functional results. The modified energy satisfies:

[0059]

[0060]

[0061] Among them, E c and E v These are the conduction band and valence band energy levels before correction, E c ' and E v ' These are the corrected conduction band and valence band energy levels, ΔE. c and ΔE v These are the conduction band shift and valence band shift obtained from the 4H-SiC unit cell system under hybrid and standard functionals, respectively, and they satisfy the following:

[0062]

[0063] In this embodiment, a correction method primarily involving an overall upward shift of the conduction band is preferred, thereby maintaining the relative stability of the localized distribution of defects in the valence band region to a greater extent. After bandgap correction, the C-containing... i The band gap width of the defective 4H-SiC supercell was stretched to be consistent with the HSE results.

[0064] After completing the bandgap correction, further calibration of C is required. i The true energy level positions of defects within the band gap were determined using HSE hybrid functionals to calculate the formation energies of the defect-free and defect-containing 4H-SiC supercells. The defect formation energies satisfy the following:

[0065]

[0066] Among them, E defect (q) represents the total energy of the system when the defect is in charge state q, E defect_free Let n be the total energy of the defect-free system. i μ represents the number of atoms added or removed from the i-th component. i E represents the chemical potential of the corresponding element. f For the Fermi level, E corr This is a charge correction term; by comparing the formation energies under different charge states, the charge transition energy levels of the defect can be obtained, which satisfy:

[0067]

[0068] Wherein, ε(q1 / q2) is the charge transition energy level of the defect between charge states q1 and q2, and VBM is the valence band top; the charge transition energy level is used to characterize the actual energy level position of the defect in the band gap.

[0069] In this embodiment, the PBE functional and the HSE hybrid functional are used to respectively address the C-containing... i The formation energies of defective 4H-SiC supercells under different charge states were calculated, and the charge transition energy levels were obtained accordingly. As shown in Figures 3(c) and 3(d), Figure 3(c) shows the formation energies of C-containing supercells calculated based on PBE functionals. i CTL results for defective 4H-SiC supercells, Figure 3(d) shows the C-containing supercells calculated based on HSE hybrid functionals. i CTL results for defective 4H-SiC supercells. By comparing Figure 3(c) and Figure 3(d), it can be seen that there are significant differences in the defect charge transition energy level positions obtained by using different functionals. Among them, the CTL results obtained by the HSE hybrid functional are more suitable as the basis for calibrating the true energy level positions of defects.

[0070] Therefore, in the defective supercell band structure after bandgap correction, an energy window constraint is set, and the entanglement with C is identified and unentangled through wavefunction locality analysis or projected band analysis. i Defect-related intriguing defect bands, calculate the initial energy center E of the defect bands. d Based on the CTL position results under the HSE hybrid functional shown in Figure 3(d), the entire intrinsic defect band is directionally shifted so that the modified defect level center satisfies:

[0071]

[0072] Where, ΔE d The correction amount is used to align the energy center of the defect-related state with the charge transition energy level; without destroying the completed bandgap correction results and without changing the relative positions of the main conduction band and valence band, the defect energy level position is aligned with the high-precision HSE-CTL result, thereby obtaining the target band that simultaneously meets the requirements of high-precision bandgap and high-precision defect energy level.

[0073] In step 4, as shown in Figure 4, the training of the graph neural network includes an initial training phase and a continued training phase. In the initial training phase, a large amount of low-cost initial PBE bandgap data containing defective supercells is input into the GNN for iterative optimization. The GNN uses C... iThe graph representation of the defective 4H-SiC supercell structure is used as the input training data, where atoms are the nodes of the graph, and the chemical bonds or interactions within the cutoff radius between atoms are the edges of the graph. The features of the nodes include the atom type and coordinate information, and the features of the edges include the distance and relative vector information between atoms. This allows the network to learn the basic physical mapping relationship between the atomic structure and the low-cost band topology, and obtain a basic model that locks most of the network weights and has physical meaning.

[0074] In the continued training phase, the high-precision supercell band structure with defects, after bandgap correction and defect energy level calibration, is input into the pre-trained GNN model. A smaller learning rate is used to update some weights, enabling the network's output predicted band structure to more accurately fit the calibrated bandgap and defect energy level positions. The training loss function adopts a weighted error form, and the weight function satisfies:

[0075]

[0076] Where E is the corresponding eigenvalue energy, and α is the weight control parameter; the weight function improves the model's fitting accuracy to key energy levels near the valence band top and conduction band bottom.

[0077] After the above two-stage training, the graph neural network outputs physically meaningful and highly accurate tight-binding model parameters. These parameters include potential energy and interatomic transition integrals, and are used to construct the Hamiltonian of the semiconductor device channel, which can be expressed in wave vector k-space as:

[0078]

[0079] Among them, t ij Let represent the in-situ energy of the transition integral or self-loop case between orbits i and j, Rij represent the corresponding lattice vector, and hc represent the Hermitian conjugate term; the TB model parameters are obtained by solving the eigenvalue problem of the Hamiltonian. Figure 5(a) shows the TB model containing C. i The band structure of the defective 4H-SiC supercell is corrected, and the band fitting results are obtained after GNN training. The left figure shows the band structure based on PBE functional calculation and CTL calibration, and the right figure shows the band structure based on HSE functional calculation and CTL calibration. As shown in Figure 5(a), after band gap correction, defect energy level calibration, and further training of GNN, the band structure generated by the obtained TB model can more accurately fit the high-precision target band, especially in terms of band gap width and defect energy level position, which is consistent with the HSE and CTL calibration results.

[0080] To further verify the effectiveness of the method of the present invention, in step 5, the modified TB model is combined with the non-equilibrium Green's function method to construct the Hamiltonian of the 4H-SiC MOSFET device channel and perform quantum transport simulation. In the device model, the gate dielectric thickness can be set to 30 nm SiO2, the energy integration step size is preferably 5 meV, and the potential self-consistent convergence threshold is preferably 10. -3 V. Simulation results show that, compared with the PBE-TB model without HSE hybrid functional bandgap correction and CTL defect level calibration, the modified TB model obtained in this invention can more accurately reflect C. i The effect of defects on device transport behavior is shown in Figure 5(b). The device transfer characteristics are manifested by the turn-off current (I0). off The reduction in conduction current is significantly lower, and the suppression of conduction current is more consistent with high-precision results. Figures 5(c) and 5(d) show the results at V... G Under 0V conditions, the local density of states (LDOS) and transmittance distribution of a 4H-SiC defect channel before and after band structure editing are shown. Comparison of Figures 5(c) and 5(d) reveals that after band structure editing, the band gap and defect-related local state locations within the channel are consistent with the calibration target. Furthermore, the transmittance distribution near the band gap is more reasonable, indicating that the modified TB model obtained in this invention can more accurately reflect the C... i The impact of defects on device transport behavior.

[0081] By combining the transfer characteristics, local density of states, and transmission spectrum distribution of defective and defect-free channels, it can be verified that the method of the present invention achieves simultaneous and accurate correction of the bandgap and defect energy levels of wide-bandgap defective semiconductor systems under low cost. The resulting tight-binding model is suitable for subsequent device-level quantum transport simulation, avoiding computationally expensive functional calculations and significantly improving the accuracy of quantum transport simulation of semiconductor devices.

[0082] It should be noted that the 4H-SiC supercell size and C used in this embodiment are different. i The defect configuration, PBE and HSE calculation parameters, graph neural network structure, and device simulation conditions can all be adjusted according to actual application requirements, but this does not affect the core technical idea of ​​this invention based on "low-cost standard functional bandgap calibration + hybrid functional bandgap calibration + CTL defect level calibration + graph neural network training".

Claims

1. A method for correcting a tightly bound model based on hybrid functionals and defect calibration, characterized in that, The method steps are as follows: Step S1: Perform structural optimization and stress relief on the defective supercell, and obtain the initial band structure data of the defective supercell based on the standard PBE functional calculation; Step S2: Calculate the band structure data of the defect-free unit cell corresponding to the defective supercell under the HSE hybrid functional and the PBE functional, compare the calculation results to obtain the conduction band and valence band offsets of the hybrid functional relative to the standard functional, and use the offsets to correct the band gap of the initial defective supercell band structure data in Step S1; Step S3: Calculate the electrical conductivity of the defective supercell using the HSE functional. Charge transition levels (CTLs) are calculated based on the defect level positions. The defect level positions in the defective supercell bandgap data after bandgap correction in step S2 are shifted and adjusted to obtain a high-precision calibrated defective supercell bandgap. Step S4: The initial defective supercell bandgap data described in step S1 is input into a graph neural network for preliminary training to establish a physically meaningful basic model. Subsequently, the calibrated defective supercell bandgap data described in step S3 is input into this basic model for separate further training to extract tightly bound model parameters that have both physical meaning and high precision.

2. The method according to claim 1, characterized in that, The CTL mentioned in step S3 is calculated using the following formula: In the formula, ε(q1 / q2) is the charge transition energy level of the defect between charge states q1 and q2, q1 and q2 are two different charge states of the defect, and E formation (q1;E f =VBM) is the Fermi level E f Defect formation energy E in charge state q1 at the top of the valence band VBM formation (q2;E f =VBM) is the Fermi level E f Defect formation energy at charge state q2 when located at the top of the valence band VBM.

3. The method according to claim 1, characterized in that, The bandgap correction of the initial defective supercell bandgap data using the conduction band offset and valence band offset in step S2 is specifically performed as follows: a scissor operator is used to perform a rigid translation operation on the initial defective supercell bandgap data, shifting the energy levels in the conduction band region upward by the conduction band offset, and shifting the energy levels in the valence band region downward by the valence band offset, thereby stretching the bandgap of the defective supercell to be consistent with the hybrid functional calculation result.

4. The method according to claim 1, characterized in that, The process of shifting and adjusting the defect energy level positions in the defective supercell bandgap data described in step S3 includes: setting an energy window constraint; identifying and untangling the eigenvalue defect bands from the defective supercell bandgap data after bandgap correction in step S2 through wavefunction locality analysis or projected bandgap analysis; calculating the initial energy center of the defect bands; and translating the eigenvalue defect bands as a whole so that their energy centers are aligned with the CTL position results, while keeping the conduction band and valence band positions unchanged.

5. The method according to claim 1, characterized in that, The tight-binding model parameters mentioned in step S4 specifically include Hamiltonian matrix elements used to describe the electronic structure of a semiconductor, wherein the Hamiltonian matrix elements are composed of in-situ energy and transition integrals between atoms.

6. The method according to claim 5, characterized in that, The input data of the graph neural network includes a crystal structure diagram representation containing defective supercells. The crystal structure diagram representation uses atoms as nodes of the graph and chemical bonds or interactions within the cutoff radius between atoms as edges of the graph. The features of the nodes include the type of atoms and coordinate information, and the features of the edges include the distance between atoms and relative vector information.

7. The method according to claim 1 or 6, characterized in that, The initial training and separate continued training mentioned in step S4 adopt transfer learning or fine-tuning strategies. The specific process is as follows: In the initial training stage, a large amount of low-cost initial defective supercell band data is input into the graph neural network for iterative optimization. The mean square error or mean absolute error is used as the loss function, so that the network learns the basic physical mapping relationship between atomic structure and band topology, and locks most of the network weights. During the continued training phase, the high-precision calibrated defective supercell band structure is input into the network that has completed the initial training. The network weights are updated using a small learning rate, so that the band structure generated by the tightly bound model parameters output by the network can accurately fit the band gap and defect energy level positions of the calibrated defective supercell band structure.

8. The method according to claim 1, characterized in that, The standard functional mentioned in step S1 is the PBE functional, and the hybrid functional mentioned in steps S2 and S3 is the HSE functional. The semiconductor system covers wide bandgap semiconductor materials or low-dimensional semiconductor materials.

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 tight-binding model correction method based on hybrid functionals and defect calibration 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 tight-binding model correction method based on hybrid functionals and defect calibration as described in any one of claims 1 to 8.

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