Ballistic Thermal Transfer in Nanosystems

Abstract

This work is concerned with analysis of cross-plane thermal transfer in nanofilms.The paper presents a developed general model of phonon radiation transfer (EPRT) based on the Boltzmann transport equation. The EPRT model assumes that the thermal transfer inside a dielectric or metal medium between two metal walls is maintained at different temperatures. These walls are like heat reservoirs; their surfaces are blackbodies. The paper first presents a model of the phonon radiation transfer of the absolute blackbodies in a wide range of temperatures where a model of the ballistic thermal transfer is applicable. It conducts a comparative analysis between phonon radiation transfer and electromagnetic radiation.The basic equation is a formula to calculate a phonon radiation intensity of the absolute blackbody depending on the temperature. Therefore, the formula for the total intensity of phonons is similar to the Stefan-Boltzmann law. The main difference of phonon radiation transfer is that a value of the phonon Stefan-Boltzmann constant is affected by temperature and properties of materials (average acoustic waves in solid bodies and Debye temperature). This can be seen from the curves for Si, Ge, and Diamond.The paper presents a received analytical equation for effective thermal conductivity using a heat flux in a cross-plane direction. The results obtained show the size and temperature dependences of the effective thermal conductivity of silicon, germanium and diamond nanofilms for the ballistic transport in the cross-plane direction. Finally, the paper compares the calculated results with those of available models of different foreign authors, which are in good compliance.

Keywords

• ballistic thermal transfer
• phonon radiative transfer (EPRT)
• cross-plane thermal transport
• phonons
• thermal conductivity of nanofilms