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Thermoelectric materials can be used to construct devices which recycle waste heat into electricity. However, the best known thermoelectrics are based on rare, expensive or even toxic elements, which limits their widespread adoption. To enable deployment on global scales, new classes of effective thermoelectrics are thus required. $\textit{Ab initio}$ models of transport properties can help in the design of new thermoelectrics, but they are still too computationally expensive to be solely relied upon for high-throughput screening in the vast chemical space of all possible candidates. Here, we use models constructed with modern machine learning techniques to scan very large areas of inorganic materials space for novel thermoelectrics, using composition as an input. We employ an attention-based deep learning model, trained on data derived from $\textit{ab initio}$ calculations, to predict a material's Seebeck coefficient, electrical conductivity, and power factor over a range of temperatures and $\textit{n}$- or $\textit{p}$-type doping levels, with surprisingly good performance given the simplicity of the input, and with significantly lower computational cost. The results of applying the model to a space of known and hypothetical binary and ternary selenides reveal several materials that may represent promising thermoelectrics. Our study establishes a protocol for composition-based prediction of thermoelectric behaviour that can be easily enhanced as more accurate theoretical or experimental databases become available.