Modeling the Thermal Conductivity of Si Nanowires with Surface Roughness

Good thermoelectric devices with a high value of figure of merit are required to convert back waste heat into useful energy. One way to achieve this goal is to engineer the surface of nanostructures by introducing roughness, thus leading to a significant reduction of their thermal conductivity. We formulate here new theoretical descriptions of phonon interface roughness scattering in Si nanowires with a surface distributed either according to a Gaussian or exponential correlation function. Our calculations of the thermal conductivity of Si nanowires show an excellent agreement with experimental data. It is further demonstrated that the distribution of the nanowire surface (Gaussian or exponential) has almost no influence on the thermal conductivity. We finally predict that the thermal conductivity depends on the nanowire crystal orientation with a lower value along the (100) rather than the (111) direction. The developed scheme can now be used to model the thermal conductivity of other materials as well.