Heat transport at nanoscales in semiconductors is investigated with a statistical method. The Boltzmann transport equation (BTE), which characterizes phonon motion and interaction within the crystal lattice, has been simulated with a Monte Carlo technique. Our model takes into account media frequency properties through the dispersion curves for longitudinal and transverse acoustic branches. The BTE collisional term involving phonon scattering processes is simulated with the relaxation times approximation theory. A new distribution function accounting for the collisional processes has been developed in order to respect energy conservation during phonons scattering events. This nondeterministic approach provides satisfactory results in what concerns phonon transport in both ballistic and diffusion regimes. The simulation code has been tested with silicon and germanium thin films; temperature propagation within samples is presented and compared to analytical solutions (in the diffusion regime). The two-material bulk thermal conductivity is retrieved for temperature ranging between 100 K and 500 K. Heat transfer within a plane wall with a large thermal gradient (250 K to 500 K) is proposed in order to expose the model ability to simulate conductivity thermal dependence on heat exchange at nanoscales. Finally, size effects and validity of heat conduction law are investigated for several slab thicknesses.

The authors study the thermal conductivity of silicon nanowires by simulation of phonon motion and interactions through a dedicated Monte Carlo model. This model solves the Boltzmann transport equation, taking into account silicon acoustic mode dispersion curves and three phonon interactions (the normal and umklapp processes). The confinement, which limits the thermal conductivity in such structures, is described by diffuse reflection at lateral boundaries of the nanowire without any adjustment by a boundary collision time, which depends on a specularity factor. They compare simulation results to experimental measurements on similar nanostructures. A good agreement is achieved for almost all the considered diameters.