Radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime

The radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime is investigated based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions prove that there is no thermal rectification. In the ballistic-diffusive regime, the heat flux prefers to flow from the inner boundary to the outer boundary. Furthermore, as the characteristic length (the distance between two circular boundaries) increases from tens of nanometers to tens of microns, the thermal rectification ratio enhances first and then fades away gradually. It attributes to that as the direction of the temperature gradient changes, the average phonon mean free path changes. The difference of the average phonon mean free path finally leads to the change of the heat flux or thermal conductivity. As the temperature decreases, the maximum thermal rectification ratio decreases. In addition, as the radius ratio between the inner and outer boundary increases, the thermal rectification ratio decreases for a given characteristic length.