The search for efficient thermoelectric (TE) materials is crucial due to the energy crisis and environmental concerns. A key parameter in TE performance is the carrier relaxation time, which is challenging to evaluate due to complex scattering mechanisms. While methods like deformation potential (DP) theory and complete electron-phonon coupling (EPC) calculations exist, they are computationally expensive and unsuitable for large systems. This research utilizes a high-throughput approach combined with a compressed sensing method (SISSO) to efficiently predict carrier relaxation time in tetradymite compounds, a family of materials known to include promising TE materials and topological insulators (TIs). The study leverages first-principles calculations of a subset of tetradymites to generate training data for the SISSO model, separating data into topological insulators and normal insulators due to their distinct electronic properties. The goal is to develop a computationally inexpensive descriptor for accurately predicting relaxation time in a vast range of tetradymite compositions.

High-throughput computational methods have significantly advanced materials discovery, particularly in areas like identifying photovoltaic absorbers, predicting compound stability, and screening topological insulators. In the context of thermoelectrics, efforts have focused on predicting low thermal conductivity materials. However, accurately modeling the relaxation time, a critical parameter affecting TE performance, remains challenging. Existing approaches, such as DP theory and EPC calculations, are computationally intensive, limiting their applicability to large systems. This paper addresses this limitation by employing a data-driven approach.

The study begins with first-principles calculations (DFT) using the VASP package to obtain electronic band structures for a set of tetradymites with integer stoichiometry. The DP theory is employed to calculate the relaxation time (τcal) for these compounds, considering electron-acoustic phonon scattering. The calculated relaxation times are divided into two training sets: one for normal insulators (NIs) and one for topological insulators (TIs), reflecting the differences in their electronic band structures. The SISSO (Sure Independence Screening and Sparsifying Operator) method, a compressed sensing technique, is then used to construct descriptors for predicting the relaxation time (τpre) for each set. The descriptors are developed using three elemental properties: atomic mass (m), radius of the p-orbital (r), and Pauling electronegativity (χ). The SISSO algorithm explores various combinations of these properties and their nonlinear transformations to identify optimal descriptors for both NIs and TIs. The virtual crystal approximation is used to extend the model to tetradymites with fractional stoichiometry. The accuracy of the descriptors is assessed by comparing τpre with τcal from first-principles calculations and available experimental data (τexp).

The SISSO method yielded two optimized descriptors, one for NIs and one for TIs, demonstrating strong predictive power with Pearson correlation coefficients exceeding 90% when compared against the first-principles calculations. The NI descriptor emphasizes the average atomic mass as the dominant factor influencing relaxation time, with heavier atoms correlating to longer relaxation times and flatter band structures near the Fermi level. Electronegativity of anions also plays a role, with larger electronegativity leading to shorter relaxation times due to smaller lattice constants and larger effective mass. The TI descriptor highlights the mean square error (mse) of the atomic mass as the most significant feature. The relaxation time in TIs shows an inverse relationship with mse, indicating that larger differences between cation and anion p-orbital radii lead to weaker hybridization, wider band gaps, and longer relaxation times. The descriptors were successfully applied to predict relaxation times for over sixteen million tetradymite compounds with fractional stoichiometry, maintaining good agreement with first-principles calculations. The distribution of predicted relaxation times showed that a significant number of NIs exhibit large relaxation times (>120 fs), while many TIs have ultralow relaxation times (<0.5 fs), potentially valuable for TE applications.

The development of simple, physically interpretable descriptors for predicting carrier relaxation time represents a significant advancement. The accurate predictions for both integer and fractional stoichiometry tetradymites, achieved at negligible computational cost, demonstrate the power of the data-driven SISSO approach. The insights gained from the descriptors, highlighting the roles of atomic mass and electronegativity in NIs and the relationship between p-orbital radii and effective mass in TIs, provide valuable guidance for designing and tuning TE materials. The agreement between the predicted and experimentally measured relaxation times, despite differences in carrier concentration, further validates the model’s reliability. However, the model might not be suitable for heavily doped systems.

This research successfully demonstrates a high-throughput method for predicting carrier relaxation time in tetradymite compounds using a data-driven approach. The derived descriptors offer a computationally efficient and physically interpretable means for exploring a vast chemical space, enabling the identification of promising TE materials. Future work could focus on extending this approach to other TE material families and incorporating additional factors, such as temperature dependence and different scattering mechanisms, to further refine the predictive capability of the model. The ultralow relaxation times identified in TIs warrant further investigation for their potential in enhancing thermoelectric performance.

The study focuses on relaxation time around the band edges, at relatively lower carrier concentrations (10¹⁷-10¹⁸ cm^-3) than those observed in optimized TE materials. This limits the model's applicability to heavily doped systems, where higher carrier concentrations lead to increased scattering and a lower relaxation time. The DP theory used to generate the training data may also introduce approximations. While the model’s accuracy is high, the generalizability to other materials beyond the tetradymite family remains to be tested.