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+title: "DeePTB-E3 Selected as an ICLR 2025 Spotlight: A New Chapter in the Series of Works - DeePTB-NEGF Empowers Quantum Transport"
+date: 2025-02-12
+categories:
+- DeePTB
+---
+
+Since the release of the DeePTB v1 version[1], which supports the prediction of Slater-Koster tight-binding (TB) parameters, in Nature Communications in 2023, the DeePTB project has achieved a series of breakthroughs. Subsequently, the DeePTB team introduced the E3 equivariant version[2]. Its core method, the E3 equivariant representation based on Strictly Localized Equivariant Message-passing (SLEM), has made a breakthrough in the processing of quantum operator matrices, enabling more accurate and efficient representation of key quantum operators such as the Kohn-Sham (KS) Hamiltonian, density matrix, and overlap integral. The related research has been accepted as a Spotlight article at the ICLR 2025 conference. On this basis, the team further combined the DeePTB method with the Non-equilibrium Green's Function (NEGF) method to introduce the AI-accelerated quantum transport simulation framework DeePTB-NEGF[3]. This framework significantly improves the computational efficiency of quantum transport simulations. It has been successfully applied to transport calculations in high-throughput and large-scale scenarios, providing a new and efficient tool for quantum transport theoretical research and semiconductor device simulations.
+
+<!-- more -->
+
+## The DeePTB Method with a Strictly Localized Equivariant Network Accepted by ICLR 2025
+The core method of the DeePTB E3 version - the E3 equivariant representation based on **SLEM**(**S**trictly **L**ocalized **E**quivariant **M**essage-passing), including quantum operator matrices such as the KS Hamiltonian, density matrix, and overlap integral, has been successfully accepted by the ICLR 2025 conference. It received high scores of 8, 8, and 6 from reviewers and was successfully shortlisted as a Spotlight article.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic1.png pic_center width="60%" height="60%" /></center>
+
+###### A comparison illustration between the design of SLEM and traditional Message Passing Neural Networks (MPNN) on one-dimensional graphs. (a) MPNN message passing. (b) SLEM message passing. Spheres and sticks represent nodes and edges respectively; arrows indicate the direction of message passing. rcut: predefined cutoff radius; reff: effective cutoff radius after two hidden layer updates. L is the index of the layer.
+
+SLEM addresses the issues of high computational costs and difficult parallelization in the equivariant representation of quantum operators in the LCAO basis set by adopting a scheme of SO2-accelerated tensor product operations and designing a strictly local message-passing model. This design greatly enhances the model's transferability and enables parallel inference for large systems in equivariant operator prediction tasks. For the Overlap matrix required for property calculations, the SLEM model uses the special properties of two-center integrals and invariant parameterization, reducing the fitting accuracy and cost of Overlap to only 3% of that of an E3 network of the same scale. For systems such as molecules, the team also provides the Localized Equivariant Message-passing (LEM) model, which can more accurately describe the non-locality of charges in non-periodic systems and offer better accuracy. This has been verified in the QH9 dataset:
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic2.png pic_center width="60%" height="60%" /></center>
+
+###### Test results of the LEM model on the QH-9 large molecular Hamiltonian dataset
+
+Currently, all data involved in SLEM work has been publicly sourced at *https://www.aissquare.com/datasets/detail?pageType=datasets&name=Quantum_Operator_Dataset&id=286*. 
+
+The functions are integrated into the DeePTB project repository. You are welcome to test and use them!
+
+## Release of the DeePTB-NEGF Framework: AI-Accelerated Electronic Transport Simulation
+During the review and publication of the DeePTB E3 version paper, the DeePTB project team did not stop making progress. Through the joint efforts of team members and collaborators, the DeePTB method was successfully extended to the field of quantum transport, and the DeePTB-NEGF framework was formed. This framework provides new ideas for the property prediction and performance optimization of nanoelectronic devices. The related work has been compiled into a preprint paper and released (https://arxiv.org/abs/2411.08800).
+
+Currently, DeePTB has implemented two Hamiltonian prediction schemes, DeePTB-SK[1] and DeePTB-E3[2], which are used to predict tight-binding models and DFT KS Hamiltonians, respectively. Based on the DeePTB method, the team independently developed a Non-equilibrium Green's Function (NEGF) calculation module for transport calculations of electronic devices, forming a highly integrated first-principles quantum transport simulation framework, DeePTB-NEGF. The NEGF module has now achieved: (1) Acceleration of matrix block tridiagonalization; (2) Acceleration of electrode self-energy calculations based on the Bloch theorem; (3) NEGF-Poisson self-consistency based on the tight-binding Hamiltonian to meet the simulation requirements of gated devices. The overall process of the DeePTB-NEGF framework is shown in Figure 1.
+
+The release of the DeePTB-NEGF framework marks the development of an integrated AI-accelerated electronic transport simulation tool based on the universal first-principles calculation acceleration framework of DeePTB. To verify the effectiveness of this framework, the team conducted research in two fields: molecular electronics and carbon-based electronics, taking break junctions and carbon nanotube field-effect transistors as research objects, and obtained results that are highly consistent with experimental measurements.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic3.png pic_center width="60%" height="60%" /></center>
+
+###### Figure 1. Flowchart of the DeePTB-NEGF framework
+
+### Break Junctions
+The break junction experiment is an effective platform for studying quantum transport processes at the atomic scale and is the main experimental method for forming molecular junctions. This process starts with a metal nanowire, which is stretched to form an atomic chain until it breaks. Subsequently, molecules in the solution connect to the broken ends to form a molecular junction, which is further stretched until the molecular junction breaks. Experimentally, through the statistical analysis of the conductance of a large number of stretching processes, extensive research has been carried out on the quantum transport characteristics of the metallic atomic contact stage and the molecular junction stage during this process[4]. However, traditional first-principles calculation methods (such as DFT-NEGF) are limited by high computational costs and cannot meet the needs of large-scale conductance statistical analysis. Therefore, current theoretical calculation research mainly focuses on the conductance analysis of specific structures and cannot be directly compared with experimental results.
+
+The DeePTB team closely collaborated with the team of Professor Hou Shimin from Peking University to conduct in-depth research on the two stages of the gold electrode break junction experiment commonly used in experiments - the gold atomic contact (as shown in Figures 2(a) and (b)) and the molecular junction (as shown in Figure 3(a)). Through molecular dynamics simulations, a large number of gold atomic contact and molecular junction configurations were generated by multiple stretchings, and random sampling was performed to obtain training set configurations. Based on the DeePTB-E3 scheme, 122 frames of gold atomic contact configurations and 268 frames of molecular structures were used as the training set to obtain high-precision gold atomic contact Hamiltonian models and molecular junction Hamiltonian models, respectively. Through the DeePTB-NEGF framework, the DFT-NEGF self-consistent process can be skipped, and the transmission spectra corresponding to the configurations at each moment during the stretching process can be efficiently calculated. The zero-bias conductance of a large number (tens of thousands of frames of structures) can be statistically analyzed to obtain a conductance statistical histogram. For the gold atomic contact system (as shown in Figure 2e), the conductance histogram obtained by simulating nearly ten thousand frames of structures is basically consistent with the experimental results, successfully reproducing the positions of the two characteristic peaks between 1G₀ and 2G₀. For the molecular junction system, this framework accurately predicted the transmission spectra at each moment during the stretching process (as shown in Figure 3b), and the main peak position of the conductance histogram (as shown in the lower right inset of Figure 3c) obtained through statistics is 10⁻³˙³G₀, which is very close to the experimental conductance peak position of 10⁻³˙⁶G₀.
+
+The above results show that the DeePTB-NEGF framework can efficiently and accurately calculate transport properties in complex systems, greatly reducing the computational cost of high-throughput quantum transport simulations with first-principles accuracy and providing new ideas for theoretical research in the field of quantum transport.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic4.png
+ pic_center width="60%" height="60%" /></center>
+
+###### Figure 2. Simulation results of DeePTB-NEGF on gold atomic contacts. (a) Structure of the gold atomic contact. It includes the semi-infinite structures at both ends used for transport calculations and the periodic structure used for model training. (b) Three moments during the stretching process of the gold atomic contact break junction. (c) Comparison of the zero-bias transmission between DFT-NEGF and DeePTB-NEGF under different stretching speeds of the break junction. (d) Comparison of the zero-bias conductance (RMSE and MAE) between DFT-NEGF and DeePTB-NEGF under different stretching speeds of the break junction. (e) Comparison between the conductance histogram calculated by DeePTB-NEGF and the experimental results under different stretching speeds of the break junction.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic5.png
+ pic_center width="60%" height="60%" /></center>
+
+ ###### Figure 3. Simulation results of DeePTB-NEGF on molecular junctions. (a) Three moments during the stretching process of the molecular junction. (b) Transmission spectra of DeePTB-NEGF and DFT-NEGF, corresponding to the three moments in (a). (c) Comparison of the similarity between the transmission spectra predicted by DeePTB-NEGF and those calculated by DFT-NEGF under different training set sizes using the Spearman coefficient. Inset in the upper left: The molecular structure used in this simulation; Inset in the lower right: Conductance histogram of the molecular junction.
+
+### Carbon Nanotube Field-Effect Transistors
+Since the invention of carbon nanotube field-effect transistors (CNT FETs)[5][6], they have attracted much attention due to their excellent device properties and have important applications in digital circuits, radio frequency electronics, sensing and detection, etc[7]. Although there have been a large number of theoretical studies on CNT-FETs, most of them rely on semi-empirical methods or only perform first-principles calculations on small-scale systems (such as CNTs with small gate lengths and small diameters), and cannot perform quantum transport simulations on devices of the same size as experiments. This greatly limits the guiding role of simulation research in experimental research.
+
+The DeePTB-NEGF framework makes it possible to perform quantum transport calculations on large-scale systems. Based on the DeePTB-SK scheme, the team simulated the transport properties of local bottom gate (LBG) CNT FETs through the DeePTB-NEGF framework. The device structure is shown in Figure 4(a). By using the energy bands of CNTs with small diameters and lengths as training labels, the team obtained a locally environment-corrected Slater-Koster tight-binding Hamiltonian model, which can effectively predict the electronic structures of CNTs of the same size as experiments. The tight-binding Hamiltonian, with its sparse matrix, small size, and orthogonality characteristics, is more suitable for quantum transport problems in large-scale systems compared to the DFT Hamiltonian. At the same time, the DeePTB-NEGF framework incorporates the electrostatic effect of the gate into the transport calculation through the NEGF-Poisson self-consistent iteration method (as shown in Figure 1), thereby obtaining properties such as the source-drain current and local density of states under different gate voltages, and further drawing the transfer characteristic curves.
+
+To compare the influence of different tube diameters on the transfer characteristic curves, the team simulated the transfer characteristic curves of CNTs with different tube diameters (0.79nm - 1.35nm) and compared them with experimental results[8]. Experimentally, the observed tube diameter is approximately 1.3nm, which is between CNT(16,0) (tube diameter 1.27nm) and CNT(17,0) (tube diameter 1.35nm). The calculation results are shown in Figure 4b. Different tube diameters of CNTs have a significant impact on the off-state performance of the device. The results of CNT(16,0) and CNT(17,0) are the closest to the experimental results, consistent with the experimental observation of the tube diameter. Through the analysis of the local density of states, it was revealed that the different off-state barrier heights of devices with different tube diameters are the reason for the different off-state performances of the devices. Furthermore, the team studied the influence of different channel lengths on the transfer characteristic curves when the tube diameter is fixed (CNT(16,0)). As shown in Figure 4(c), when the channel length is reduced from 9nm to 4nm, the short-channel effect of the device becomes more and more obvious, and the off-state current and subthreshold swing increase continuously as the channel length decreases. This indicates that without optimizing the device structure, the size reduction potential of LBG CNT FETs is very limited.
+
+The above results not only verify the effectiveness of the DeePTB-NEGF framework in performing electronic transport calculations under non-equilibrium conditions but also illustrate the importance of using device structures of the same size as experiments for transport simulations.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/DeePTB-E3_12_02_2025/pic6.png
+ pic_center width="60%" height="60%" /></center>
+
+ ###### Figure 4. Simulation results of DeePTB-NEGF on CNT FETs. (a) Structure of the Local Bottom Gate (LBG) CNT FET. (b) Transfer characteristic curves of LBG CNT FETs with different tube diameters and comparison with experimental results. (c) Transfer characteristic curves of LBG CNT FETs with different channel lengths. The carbon nanotube used is CNT(16,0). (d) Local density of states along the transport direction under different gate voltages (-0.8V, -0.4V, 0.0V). The carbon nanotube used is CNT(17,0).
+
+## The Future of DeePTB: Collaborate and Create Together
+Finally, as an open-source project, the DeePTB team sincerely invites all interested colleagues to join. Whether you provide valuable data resources, participate in model or software development, or offer improvement suggestions, every contribution will help DeePTB move towards higher goals. All forms of cooperation are welcome, including but not limited to internships, visits, doctoral and postdoctoral research collaborations. We also encourage everyone to communicate and discuss with the DeePTB team through GitHub Issues, email, or other means.
+
+## References
+[1] Gu Q, Zhouyin Z, Pandey S K, et al. Deep learning tight-binding approach for large-scale electronic simulations at finite temperatures with ab initio accuracy[J]. Nature Communications, 2024, 15(1): 6772.
+
+[2] Zhouyin Z, Gan Z, Pandey S K, et al. Learning local equivariant representations for quantum operators[J]. arXiv preprint arXiv:2407.06053, 2024.
+
+[3] Zou J, Zhouyin Z, Lin D, et al. Deep Learning Accelerated Quantum Transport Simulations in Nanoelectronics: From Break Junctions to Field-Effect Transistors[J]. arXiv preprint arXiv:2411.08800, 2024.
+
+[4] Gehring P, Thijssen J M, van der Zant H S J. Single-molecule quantum-transport phenomena in break junctions[J]. Nature Reviews Physics, 2019, 1(6): 381-396.
+
+[5] Tans S J, Verschueren A R M, Dekker C. Room-temperature transistor based on a single carbon nanotube[J]. Nature, 1998, 393(6680): 49-52.
+
+[6] Martel R, Schmidt T, Shea H R, et al. Single-and multi-wall carbon nanotube field-effect transistors[J]. Applied Physics Letters, 1998, 73(17): 2447-2449.
+
+[7] Liu Y F, Zhang Z Y. Carbon based electronic technology in post-Moore era: progress, applications and challenges br[J]. Acta Physica Sinica, 2022, 71(6).
+
+[8] Franklin A D, Luisier M, Han S J, et al. Sub-10 nm carbon nanotube transistor[J]. Nano Letters, 2012, 12(2): 758-762.