Vacancy formation energy and its connection with bonding environment in solid: A high-throughput calculation and machine learning study

The generation of the vacancy involving the bond breaking/re-formation occurs naturally in the material. Here, we present a framework for automatically computing the vacancy-formation energy (E-f) and for analyzing the bonding environment concealed in the E-f by using an artificial neural network (ANN). The 'effective' bonding that determines the energy of the system and the E-f will be clarified. The phase-change memory material GeTe is used as a case study. Firstly, 791 Ge-vacancy containing GeTe structures are studied and a large data set of the formation energy of the Ge-vacancy is obtained, which is helpful to understand the vacancy-induced issue of the amorphous GeTe including the resistance drift, etc. By using the ANN fitting based on the large energy data set, a bonding picture that is applicable to both the crystalline and the amorphous state of GeTe is predicted. In terms of the contribution to the formation energy of the vacancy, the weight ratio of the bond with length of 3.0-3.6 angstrom and 3.6-4.5 angstrom can be approximated as 6:1. The bonding information is further confirmed by using the first-principles electronic structure analysis on the randomly chosen samples. The bonding analysis using the ANN method based on a large vacancy-formation-energy data set is demonstrated to be a novel alternative technique to understand the bonding in the material. The proposed framework can be applied to a wide range of materials.