Intricate short-range order in GeSn alloys revealed by atomistic simulations with highly accurate and efficient machine-learning potentials

GeSn alloys hold promise for silicon-compatible integrated applications in electronics, photonics, and topological quantum devices. However, understanding their intricate structures using density functional theory (DFT) calculations is hindered by spatiotemporal constraints. To overcome this limitation, we develop highly accurate and efficient machine-learning interatomic potentials based on a neuroevolution potential approach with farthest point sampling on a comprehensive DFT data set. The application of the developed machine-learning potential in large-scale atomistic simulations bridges the spatiotemporal gap between modeling and advanced characterizations, and facilitates the discovery of structural intricacies in GeSn alloys. Through extensive statistical sampling, we identify a type of short-range order (SRO) that is distinguished by both its structural signature and electronic band gap from the SRO structure previously predicted. Modeling based on a large simulation cell reveals the coexistence of nano SRO domains with various degrees of ordering, demonstrating a complex spatial heterogeneity of SRO structure. Our study not only reinforces the significance of fine-level structural information in alloys, but it also constitutes an effective framework for exploring SRO in a broad range of complex alloys based on highly accurate and effective machine-learning potentials.