Fundamental band gap and alignment of two-dimensional semiconductors explored by machine learning

Two-dimensional (2D) semiconductors isoelectronic to phosphorene have been drawing much attention recently due to their promising applications for next-generation (opt)electronics. This family of 2D materials contains more than 400 members, including (a) elemental group-V materials, (b) binary III-VII and IV-VI compounds, (c) ternary III-VI-VII and IV-V-VII compounds, making materials design with targeted functionality unprecedentedly rich and extremely challenging. To shed light on rational functionality design with this family of materials, we systemically explore their fundamental band gaps and alignments using hybrid density functional theory (DFT) in combination with machine learning. First, calculations are performed using both the Perdew-Burke-Ernzerhof exchange-correlation functional within the general-gradient-density approximation (GGA-PBE) and Heyd-Scuseria-Ernzerhof hybrid functional (HSE) as a reference. We find this family of materials share similar crystalline structures, but possess largely distributed band-gap values ranging approximately from 0 eV to 8 eV. Then, we apply machine learning methods, including linear regression (LR), random forest regression (RFR), and support vector machine regression (SVR), to build models for the prediction of electronic properties. Among these models, SVR is found to have the best performance, yielding the root mean square error (RMSE) less than 0.15 eV for the predicted band gaps, valence-band maximums (VBMs), and conduction-band minimums (CBMs) when both PBE results and elemental information are used as features. Thus, we demonstrate that the machine learning models are universally suitable for screening 2D isoelectronic systems with targeted functionality, and especially valuable for the design of alloys and heterogeneous systems.