Phonon Wave Heat Conduction in Thin Films and Superlattices

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Abstract
Heat conduction in thin films and superlattices is important for many engineering applications such as thin-film based microelectronic, photonic, thermoelectric, and thermionic devices. Past modeling efforts on the thermal conductivity of thin films were based on solving the Boltzmann transport equation that treats phonons as particles. The effects of phonon interference and tunneling on the heat conduction and the thermal conductivity of thin films and superlattices remain to be explored. In this work, the wave effects on the heat conduction in thin films and superlattices are studied based on the consideration of the acoustic wave propagation in thin film structures and neglecting the internal scattering. A transfer matrix method is used to calculate the phonon transmission and heat conduction through these structures. The effects considered in this work include the phonon interference, tunneling, and confinement. The phonon dispersion is considered by introducing frequency-dependent Lamb constants. A ray-tracing method that treats phonons as particles is also developed for comparison. Sample calculations are performed on double heterojunction structures resembling Ge/Si/Ge and n-period superlattices similar to Ge/Si/n(Si/Ge)/Ge, It is found that phonon confinements caused by the phonon spectra mismatch and by the total internal reflection create a dramatic decrease of the overall thermal conductance of thin films. The phonon interference in a single layer does not have a strong effect on its thermal conductance but for superlattice structures, the stop bands created by the interference effects can further reduce the thermal conductance. Tunneling of phonon waves occurs when the constituent layers are 1–3 monolayer thick and causes a slight recovery in the thermal conductance when compared to thicker layers. The thermal conductance obtained from the ray tracing and the wave methods approaches the same results for a single layer. For superlattices, however, the wave method leads to a finite thermal conductance even for infinitely thick superlattices while the ray tracing method gives a thermal conductance that decreases with increasing number of layers. Implications of these results on explaining the recent thermal conductivity data of superlattices are explored.