AI-Driven Defect Engineering for Advanced Thermoelectric Materials

Abstract

Thermoelectric materials offer a promising pathway to directly convert waste heat to electricity. However, achieving high performance remains challenging due to intrinsic trade-offs between electrical conductivity, the Seebeck coefficient, and thermal conductivity, which are further complicated by the presence of defects. This review explores how artificial intelligence (AI) and machine learning (ML) are transforming thermoelectric materials design. Advanced ML approaches including deep neural networks, graph-based models, and transformer architectures, integrated with high-throughput simulations and growing databases, effectively capture structure-property relationships in a complex multiscale defect space and overcome the "curse of dimensionality". This review discusses AI-enhanced defect engineering strategies such as composition optimization, entropy and dislocation engineering, and grain boundary design, along with emerging inverse design techniques for generating materials with targeted properties. Finally, it outlines future opportunities in novel physics mechanisms and sustainability, highlighting the critical role of AI in accelerating the discovery of thermoelectric materials.

Keywords: artificial intelligence; defect engineering; machine learning; thermoelectrics.

Figure 1

TE device and performance. a) A schematic of a TE device showing many individual thermocouples that are connected in electrical series. b) Illustration of the variation of Seebeck coefficient S, electrical conductivity σ, total thermal conductivity κ = κ _e + κ _l , where κ _e and κ _l are the electron and lattice thermal conductivities, power factor PF = S ²σ, and figure of merit zT = PF × T/κ as a function of the carrier concentration. c) zT as a function of temperature and year. Adapted with permission.^{[ 74 ]} Copyright 2021, Wiley Online Library.

Figure 2

Development stages of TE materials and the broader energy materials research. a) Evolution of zT value over time in the search for TE materials. Powered by computational methods and advanced AI techniques, the paradigm has shifted from experimental trial and error to high‐throughput calculations and AI‐driven discovery, leading to new TE materials with higher and higher figures of merit zT. Reproduced with permission.^{[ 33} , ³⁵ , ⁷⁸ , ⁷⁹ , ^{80 ]} Copyright 2019, AIP Publishing. Copyright 2019, Elsevier. Copyright 2022, American Association for the Advancement of Science. Copyright 2022, Nature Publishing Group UK London. Copyright 2021, American Association for the Advancement of Science. b) Evolutionary trend of energy materials research since 2015. The publications presented in this figure are retrieved from the Web of Science database with keywords related to automatic energy materials design and discovery. Publications with ML energy materials are filtered based on additional keywords with various AI‐based techniques.

Figure 3

Useful descriptors for materials with defect or disorder. With the Gaussian noise as the local atomic perturbation from the imposed disorder, a) Pair distribution function (PDF) and b) Ewald sum matrix presents a notably sensitive response under two different scenarios: weak disorder and strong disorder, introduced through different levels of local atomic perturbation. c) Sketch for a possible graph representation used in GNN to deal with doping by imposing the doping ratio through the node feature. d) Illustration of e3nn, an implementation of E(3)‐equivariant GNN. Structural information passes within a cutoff radius r _max for a given atom, and the angular information and radial information between two atoms are encoded in spherical harmonics $Y_{lm}({\vec{r}}_{ab})$ and a neural network R(|r _ab |), respectively. Reproduced with permission.^{[ 165 ]} Copyright 2021, Wiley Online Library. e) Persistent homology diagram for amorphous solid. The different colors represent the different dimensional topological features. The location of the data point represents when these topological features appear and disappear with the continuous change of length scale. Reproduced with permission.^{[ 166 ]} Copyright 2020, American Association for the Advancement of Science.

Figure 4

Machine learning (ML) aided defect (doping) engineering for TE. a) Nonlinear behavior of TE‐related transport properties w.r.t. the doped carrier concentration; b) Schematic illustration of ML strategy to emphasize defect information by introducing a separate defect channel with nonlinearity; c) The ML network architecture of DopNet, passing on dopant and host embedding separately before merging them to a dense network. Reproduced with permission.^{[ 200 ]} Copyright 2021, Nature Publishing Group UK London; d) The key ML architecture of CraTENet, improving the expressibility of defect channel using the transformer blocks. Reproduced with permission.^{[ 204 ]} Copyright 2023, IOP Publishing.

Figure 5

ML for the dislocation and the grain boundary. a) The density of geometrically necessary dislocations (left top) and the internal stress field(left down) are taken as the featured descriptor to describe the initial dislocation configuration (right top) and predict the stress‐strain curves for plastic deformation. The neural network is trained to infer the relation between features of the initial dislocation configurations and the ensuing stress‐strain curves. Reproduced with permission.^{[ 210 ]} Copyright 2018, Nature Publishing Group UK London. b) Method for predicting grain boundary thermal conductivities based on local atomic environments. On the left, the SOAP descriptor is utilized for grain boundary structure while r _c is the cutoff radius of the SOAP descriptor. On the right, local distortion factors, Gaussian‐smeared atomic thermal conductivities, and distributions of local atomic environments are groups classified from hierarchical clustering (green: highly under‐coordinated; red: moderately under‐coordinated or strongly strained; grey: moderately strained, weakly strained, or bulk‐like) are presented from top to down to reveal the relation between the grain boundary structure and the thermal transport. Reproduced with permission.^{[ 164 ]} Copyright 2020, Nature Publishing Group UK London.

Figure 6

Entropy engineering for TE materials. a) Phonon mean free path dependence of accumulated lattice thermal conductivity (the red line) and schematic diagram of all‐scale hierarchical structures from the high‐entropy matrix. It schematizes the ability to improve TE performance in all‐scale hierarchical structures through entropy engineering. Reproduced with permission.^{[ 240 ]} Copyright 2021, Nature Publishing Group UK London. b) Explainable machine learning for entropy engineering. The left visualization is a Pearson correlation map for features, where blue and red colors indicate positive and negative correlations. The average impact on model output magnitude and the effect of each feature on the output of the model is presented on the right through the SHAP values. Reproduced with permission.^{[ 258 ]} Copyright 2023, ACS Publications. c) The machine learning (ML) enabled atomic simulation for different local chemical ordering. From top to bottom, thermal conductivities at elevated temperature, spectral thermal conductivity and the cumulative thermal conductively, normalized phonon density of state (DOS) at 300K are presented for random, 800, and 600 K annealed PbSe_0.5Te_0.25S_0.25. Reproduced with permission.^{[ 260 ]} Copyright 2024, AIP Publishing.

Figure 7

Search high zT materials from the topological materials which can be inversely generated with the generative machine learning (ML). a) two transport models indicate that strong band inversion will lead to higher zT performance. M ₀ in the x‐axis is a measure of the energy separation of the band edges at the Γ‐point for the present set of materials, where M ₀ > 0 represents noninverted bands (i.e., normal insulators) and M ₀ < 0represents inverted bands (i.e., topological insulators).^{[ 332 ]} b) The workflow of the generative model for topological materials.^{[ 333 ]} The generative model, CDVAE,^{[ 331 ]} is trained from the topological materials database, while further filter checks the novelty, legitimacy, and topogivity to screen the targeted topological materials. Reproduced with permission.^{[ 332} , ^{333 ]} Copyright 2024, The Royal Society of Chemistry. Copyright 2025, Nature Publishing Group UK London.

Figure 8

Consider sustainability in future TE design. a) Down‐selection and scoring of topological materials. The selection is limited to stable materials (E _hull < 0) characterized by non‐toxic elements, a modest melting temperature T _melt < 2000 K, and low vapor pressure. These materials can then be sorted based on price, net import resilience (NIR), and environmental impact score (Env). When applied to the topological materials database, this process yields roughly 200 materials candidates from a pool of over 16,000. Reproduced with permission.^{[ 18 ]} Copyright 2023, Arxiv. b) The paradigm of inverse design with generative modeling pushes the material space to overcome the performance and sustainability dilemma. Reproduced with permission.^{[ 113 ]} Copyright 2025, Arxiv.