Integrative Mobility Model For Grain-Boundary-Limited Transport In Thermoelectric Compounds

Grain-boundary-limited charge transport remains a key bottleneck in polycrystalline thermoelectric materials, where reduced carrier mobility degrades electrical conductivity and suppresses the power factor. Here we present a semi-empirical mobility model that integrates three dominant grain-boundary mechanisms: (i) weighted mobility linked to carrier effective mass and concentration, (ii) thermionic emission across grain-boundary barriers, and (iii) geometric suppression arising from a finite mean free path ($\mathrm{\ell }$). The model is validated against a diverse set of polycrystalline thermoelectric materials – including Bi${}_2$Te${}_3$, PbTe, Mg${}_2$Si, and SnSe – showing excellent agreement with experiment ($R^2=0.93$–0.99) and yielding physically consistent parameters: $0\lesssim {\mathrm{\Phi }}_{\mathrm{G}\mathrm{B}}\lesssim 0.15$ eV and $\mathrm{\ell }\approx 15$–60 nm. The model captures the non-monotonic mobility trends produced by the interplay between barrier activation and phonon scattering. We further apply the model to Al-doped ZnO, revealing that combined grain-boundary passivation (reducing ${\mathrm{\Phi }}_{\mathrm{G}\mathrm{B}}$ from 0.15 eV to 0.05 eV) and moderate grain growth (increasing $\mathrm{\ell }$ from 5 nm to 25 nm) can raise the power factor by $\sim 6\times$ (from $\sim 4$ to $\sim 26$ mW,m${}^{-1}$,K${}^{-2}$) and the electronic quality factor $B$ by nearly $7\times$ (from $\sim 0.15$ to $>1.0\times {10}^{-3}$ m${}^2$,V${}^{-1}$,s${}^{-1}$,kg${}^{3\mathrm{/}2}$), approaching values achieved in leading chalcogenide thermoelectrics. The model therefore provides a transparent and practical framework for grain-boundary engineering in oxide-based thermoelectrics.