Physics-Inspired Augmentation of Equivariant Graph Neural Networks for Modeling Quantum Confinement

Modern nanoelectronic devices are complex, multiphasic heterostructures characterized by the central role that atomic-scale interactions and quantum mechanics play in determining their electronic properties. Notably, next-generation transistors such as gate-all-around devices contain nanosheets that display nontrivial electronic behavior due to quantum confinement and interfacial effects, significantly impacting device performance. However, simulation methodologies that can accurately reproduce these effects such as density functional theory are computationally intractable for simulation of real-world transistors due to the cubic complexity of diagonalization of the quantum Hamiltonian. To address this scaling limitation, machine learning approaches have been proposed for electronic and material property prediction. Graph neural networks (GNNs) in particular have shown near ab-initio accuracy while preserving linear scaling [1, 2, 3, 4] in molecules and bulk material systems dominated by local interactions. In this work, we propose novel physics-inspired architectural augmentations to equivariant graph neural-network architectures to address the nonlocal confinement effects present in nanosheets -- a task that state-of-the-art GNNs fail at -- while maintaining favorable scaling in system size. These augmentations include expanding atomic positions in sinusoidal basis mirroring the eigenfunctions of confined material systems and adding global nodes that transmit boundary condition information throughout the structure. We focus on predicting electronic density of states (DOS) and current density of states (cDOS) [5] of thin and ultra-thin strained silicon nanosheets similar to those in modern transistor gate stacks. Our proposed neural network architecture demonstrates up to 65% improvement over the state-of-the-art in DOS predictions and 20% for cDOS predictions, achieving an overall 0.18% and 8% error in each property, respectively. Furthermore, our model shows improvements in generalizability, with high extrapolation performance on nanosheets with thicknesses beyond the training set, thereby enabling simulations of devices at scales unattainable by ab initio methods. This work paves the way for data-efficient, accurate, and scalable electronic structure prediction for a wide variety of transistor geometries and gate materials for the rapid design and iteration of next-generation transistors.


[1] K.T. Schütt. et al. (2017) Advances in Neural Information Processing Systems 30, pp. 992-1002
[2] Batzner, et al. (2022). Nat Commun 13, 2453
[3] Victor Fung, et al. (2022). Chemistry of Materials 34 (11), 4848-4855
[4] Ilyes Batatia et al.(2022). Advances in Neural Information Processing Systems.
[5] Rahman, et al. (2003). IEEE Transactions on Electron Devices, 50(9), 1853–1864.