Monte Carlo transient phonon transport in silicon and germanium at nanoscales

David Lacroix (1, 2) , Karl Joulain (1) , Denis Lemonnier (1)

1 LET - Laboratoire d'études thermiques
2 LEMTA - Laboratoire d'Energétique et Mécanique Théorique et Appliquée

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 this 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 stimulate conductivity thermal dependence on heat exchange at nanoscales. Finally, size effects and validity of heat conduction law are investigated for several slab thicknesses.

Domaines: Thermique [physics.class-ph]

David Lacroix, Karl Joulain, Denis Lemonnier. Monte Carlo transient phonon transport in silicon and germanium at nanoscales. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2005, 72 (6), pp.064305-1-064305-11. ⟨10.1103/physRevB.72.064305⟩. ⟨hal-00017489⟩