Thermal conductivity and its relation to atomic structure for symmetrical tilt grain boundaries in silicon.

We perform a systematic study of thermal resistance/conductance of tilt grain boundaries (GBs) in Si using classical molecular dynamics. The GBs studied are naturally divided into three groups according to the structural units forming the GB core. We find that, within each group, the GB thermal conductivity strongly correlates with the excess GB energy. All three groups predict nearly the same GB conductivity extrapolated to the high-energy limit. This limiting value is close to the thermal conductivity of amorphous Si, suggesting similar heat transport mechanisms. While the lattice thermal conductivity decreases with temperature, the GB conductivity slightly increases. However, at high temperatures it turns over and starts decreasing if the GB structure undergoes a premelting transformation. Analysis of vibrational spectra of GBs resolved along different directions sheds light on the mechanisms of their thermal resistance. The existence of alternating tensile and compressive atomic environments in the GB core gives rise to localized vibrational modes, frequency gaps creating acoustic mismatch with lattice phonons, and anharmonic vibrations of loosely-bound atoms residing in open atomic environments.