Effect of film thickness on the thermal resistance of confined semiconductor thin films

The thermal resistance of semiconductor thin films is predicted using lattice dynamics (LD) calculations and molecular dynamics (MD) simulations. We consider Si and Ge films with thicknesses, L(F), between 0.2 and 30 nm that are confined between larger extents of the other species (i.e., Ge/Si/Ge and Si/Ge/Si structures). The LD predictions are made in the classical limit for comparison to the classical MD simulations, which are performed at a temperature of 500 K. For structures with L(F)< 2 nm, the thin film thermal resistance increases rapidly with increasing film thickness, a trend we attribute to changes in the allowed vibrational states in the film. These changes are found to affect the dependence of the phonon transmission coefficient on incidence angle for the Ge/Si/Ge structures and on frequency for the Si/Ge/Si structures. When L(F)>2 nm, the MD-predicted thermal resistances are independent of the film thickness for the Ge/Si/Ge structures and increase with increasing film thickness for the Si/Ge/Si structures. We attribute these results to phonon transport that is ballistic in the Ge/Si/Ge structures and more diffusive in the Si/Ge/Si structures based on comparisons to the LD predictions, which assume ballistic phonon transport. We find that this difference between the structures cannot be predicted by comparing the mode-averaged phonon mean free path to the film thickness. It can be predicted, however, by considering the frequency dependence of the phonon mean free paths.