Unified mobility model for grain‑boundary‑limited transport in polycrystalline thermoelectric materials

Grain-boundary-limited charge transport is a fundamental bottleneck in polycrystalline thermoelectric materials, where reduced carrier mobility degrades electrical conductivity and suppresses power factors. This degradation arises from the interplay of scattering mechanisms: grain-boundary barriers dominate at low temperatures; thermionic activation enables partial barrier crossing at intermediate temperatures; and phonon scattering limits the mean free path at high temperatures. Hence, there remains a need for a physically transparent framework to quantitatively extract these microstructural parameters. In this study, a semi-empirical mobility model that explicitly integrates these grain-boundary mechanisms was developed and validated, expressed as: ${\mu }_{eff}\left(T\right)={\mu }_w\text{exp}\left(-\frac{{\Phi }_{GB}}{k_{B}T}\right)\frac{l\left(T\right)}{l\left(T\right)+w_{GB}}$ where ${\mu }_w$ is the weighted mobility, ${\Phi }_{GB}$ is the grain‑boundary barrier height, $k_B$ is Boltzmann’s constant, $T$ is temperature, $l\left(T\right)$ is the bulk mean free path and $w_{GB}$ is the boundary width. This model was validated for oxide semiconductor, intermetallic, chalcogenide and heuslers polycrystalline materials, achieving excellent agreement with experimental data ($R^2$= 0.97–0.99) and yielding physically consistent parameters: ${\Phi }_{GB}$ ≈ 0–0.056 eV and $l_{300}$ ≈ 6–368 nm. A case study for Ta doped ZnO thermoelectric material shows that barrier passivation (reduction of ${\Phi }_{GB}$ from 0.056 eV to 0.03 eV) combined with modest grain-interior improvement ($l_{300}$→60 nm) can significantly enhance carrier mobility across the entire temperature range. The analysis predicts that, at ∼1000 K, grain engineering could nearly double mobility and electrical conductivity. Consequently, tailoring microstructural features enable a power factor approximately of 7.64x${10}^{-4}$W$m^{-1}{K}^{-2}$ at 1000 K, compared with the reported value of 4x${10}^{-4}$W$m^{-1}{K}^{-2}$. This framework provides concrete, process-addressable targets for grain-boundary engineering and mobility-driven performance gains.