Two-dimensional silicon phononic crystals have attracted extensive research interest for thermoelectric applications due to their reproducible low thermal conductivity and sufficiently good electrical properties. For thermoelectric devices in high-temperature environment, the coherent phonon interference is strongly suppressed; therefore phonon transport in the incoherent regime is critically important for manipulating their thermal conductivity. On the basis of perturbation theory, we present herein a novel phonon scattering process from the perspective of bond order imperfections in the surface skin of nanostructures. We incorporate this strongly frequency-dependent scattering rate into the phonon Boltzmann transport equation and reproduce the ultra low thermal conductivity of holey silicon nanostructures. We reveal that the remarkable reduction of thermal conductivity originates not only from the impediment of low-frequency phonons by normal boundary scattering, but also from the severe suppression of high-frequency phonons by surface bond order imperfections scattering. Our theory not only reveals the role of the holey surface on the phonon transport, but also provide a computation tool for thermal conductivity modification in nanostructures through surface engineering.

二维硅声子晶体因其可再现的低导热性和足够好的电性能而吸引了热电应用的广泛研究兴趣。对于高温环境下的热电设备，相干声子干扰会被强烈抑制；因此，声子在非相干状态下的输运对于操纵其热导率至关重要。基于微扰理论，我们从纳米结构表面皮肤中键序缺陷的角度提出了一种新颖的声子散射过程。我们将这种与频率密切相关的散射速率纳入声子玻耳兹曼输运方程，并重现了多孔硅纳米结构的超低热导率。我们发现，热导率的显着降低不仅源自正常边界散射对低频声子的阻碍，而且还归因于表面键合阶次缺陷散射对高频声子的严重抑制。我们的理论不仅揭示了多孔表面在声子传输中的作用，而且还提供了通过表面工程对纳米结构中的导热系数进行修改的计算工具。