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 ($\ell$). 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: $0 \lesssim \Phi_{\mathrm{GB}} \lesssim 0.15$ eV and $\ell \approx 15$--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 $\Phi_{\mathrm{GB}}$ from 0.15 eV to 0.05 eV) and moderate grain growth (increasing $\ell$ 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$^{3/2}$), approaching values achieved in leading chalcogenide thermoelectrics. The model therefore provides a transparent and practical framework for grain-boundary engineering in oxide-based thermoelectrics.