On-the-fly machine learning potential accelerated accurate prediction of lattice thermal conductivity of metastable silicon crystals

In this paper, we propose a convenient strategy to accelerate the evaluation of lattice thermal conductivity through combining phonon Boltzmann transport equation (PBTE) and on-the-fly machine learning potential (FMLP). The thermal conductivity of diamond silicon ($d\text{\ensuremath{-}}\mathrm{Si}$) is evaluated firstly by density functional theory (DFT), FMLP, and empirical potential with PBTE, respectively. The results demonstrate the proposed strategy integrates the prediction accuracy of DFT and computational speed of empirical potential, breaking the dilemma of traditional thermal conductivity assessment schemes. Based on this, the efficient strategy is applied to predict thermal conductivity of 102 low-energy metastable silicon crystals with energies between $d\text{\ensuremath{-}}\mathrm{Si}$ and experimentally ${\mathrm{Si}}_{24}$. Among them, the $Cmcm\text{\ensuremath{-}}{\mathrm{Si}}_{16}, P6/mmm\text{\ensuremath{-}}{\mathrm{Si}}_{36}$-2, $Pnma\text{\ensuremath{-}}{\mathrm{Si}}_{32}$-2 are predicted to host lowest lattice thermal conductivity in $xx$ (8.213 ${\mathrm{Wm}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$), $yy$ (10.917 ${\mathrm{Wm}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$), and $zz$ (11.807 ${\mathrm{Wm}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$) directions, respectively. Such low lattice thermal conductivity benefits from the combined effect of low phonon group velocity and intense phonon scattering caused by distorted $s{p}^{3}$ hybrid states in these metastable silicon crystals. The findings presented in this work provide new candidates and insights of silicon-based materials with ultra-low thermal conductivity, which will greatly expand the applications in thermoelectric and thermal insulation fields.