Computational approaches have become indispensable for predicting the thermoelectric performance of nanostructured materials, particularly through the calculation of the dimensionless figure of merit (ZT). The thermoelectric efficiency of a material is governed by ZT, defined as (S²σT)/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity. Accurate prediction of ZT requires a detailed understanding of electronic and phononic transport, which can be addressed using density functional theory (DFT) coupled with Boltzmann transport theory.
Electronic contributions to ZT are primarily determined by the Seebeck coefficient, electrical conductivity, and electronic thermal conductivity. DFT provides a robust framework for calculating electronic band structures, density of states, and carrier effective masses, which directly influence these parameters. For nanostructured materials, quantum confinement effects modify the electronic density of states near the Fermi level, leading to enhanced Seebeck coefficients. For instance, in quantum dot superlattices, sharp peaks in the density of states can increase the power factor (S²σ) by restricting carrier energy distribution.
Boltzmann transport theory, when applied within the relaxation time approximation, enables the calculation of electronic transport coefficients. The relaxation time, often derived from first-principles scattering calculations or empirical models, plays a critical role in determining σ and the electronic component of κ. In nanostructured materials, boundary scattering becomes significant, reducing carrier mobility compared to bulk counterparts. However, energy filtering effects—where low-energy carriers are selectively scattered—can enhance S without severely degrading σ.
Phononic contributions to ZT arise from lattice thermal conductivity (κ_l), which is often the dominant factor limiting thermoelectric efficiency. DFT-based lattice dynamics calculations, combined with solutions to the phonon Boltzmann transport equation, allow for the prediction of κ_l. In nanostructured materials, phonon scattering at interfaces, grain boundaries, and defects substantially reduces κ_l. For example, silicon nanowires with rough surfaces exhibit κ_l reductions of up to two orders of magnitude compared to bulk silicon due to enhanced boundary scattering.
Band engineering strategies are critical for optimizing ZT in nanostructured thermoelectrics. DFT simulations enable the exploration of doping effects, alloying, and strain engineering to tailor electronic band structures. For instance, resonant doping—where impurity states hybridize with host bands—can enhance the Seebeck coefficient by introducing sharp features near the Fermi level. Similarly, band convergence, achieved through alloying or strain, increases the number of contributing energy valleys, improving the power factor.
Quantum confinement effects are particularly pronounced in low-dimensional thermoelectric materials. In quantum wells and nanowires, carrier confinement leads to discrete energy levels, altering both electronic and thermal transport. DFT simulations of confined systems reveal that reduced dimensionality can decouple electronic and phononic transport, allowing for high S while maintaining low κ_l. For example, bismuth telluride (Bi₂Te₃) thin films exhibit enhanced ZT due to quantum confinement-induced modifications in the density of states.
The interplay between electronic and phononic transport necessitates multiscale modeling approaches. While DFT provides accurate electronic structure information, molecular dynamics or lattice dynamics simulations are required to capture phonon-phonon interactions and boundary scattering effects. Coupling these methods with Boltzmann transport theory enables a comprehensive prediction of ZT across different length scales.
Challenges remain in accurately predicting ZT due to approximations in computational methods. The relaxation time approximation, for instance, may not fully capture energy-dependent scattering mechanisms. Advanced methods, such as the iterative solution of the Boltzmann equation or machine learning-assisted force constants, are being developed to improve accuracy. Additionally, anharmonic effects in phonon transport, which are significant in many thermoelectric materials, require careful treatment beyond harmonic approximations.
Despite these challenges, computational models have successfully guided the discovery of high-ZT nanostructured materials. For example, simulations predicted that silicon-germanium (SiGe) nanocomposites would exhibit low κ_l due to phonon scattering at interfaces, a result later confirmed experimentally. Similarly, DFT-based screening identified half-Heusler compounds as promising thermoelectrics due to their favorable band structures.
In summary, computational modeling of thermoelectric properties in nanostructured materials relies on a synergistic combination of DFT and Boltzmann transport theory. By accounting for electronic band structure, phonon scattering, and quantum confinement effects, these models provide valuable insights for designing high-performance thermoelectric materials. Continued advancements in computational techniques will further enhance predictive accuracy, accelerating the development of next-generation thermoelectrics.