Phonon surface scattering controlled length dependence of thermal conductivity of silicon nanowires

We present a kinetic model to investigate the anomalous thermal conductivity in silicon nanowires (SiNWs) by focusing on the mechanism of phonon-boundary scattering. Our theoretical model takes into account the anharmonic phonon-phonon scattering and the angle-dependent phonon scattering from the SiNWs surface. For SiNWs with diameter of 27.2 nm, it is found that in the case of specular reflection at lateral boundaries, the thermal conductivity increases as the length increases, even when the length is up to 10 mu m, which is considerably longer than the phonon mean free path (MFP). Thus the phonon-phonon scattering alone is not sufficient for obtaining a normal diffusion in nanowires. However, in the case of purely diffuse reflection at lateral boundaries, the phonons diffuse normally and the thermal conductivity converges to a constant when the length of the nanowire is greater than 100 nm. Our model demonstrates that for observing the length dependence of thermal conductivity experimentally, nanowires with smooth and non-contaminated surfaces, and measuring at low temperature, are preferred.