Numerical simulation of transient phonon heat transfer in silicon nanowires and nanofilms

Abstract

This work proposes a numerical simulation of heat conduction in silicon nanowires and nanofilms. Boltzmann equation for phonons is solved in the relaxation time approximation. The equation is integrated in an axisymmetric cylindrical two dimensional geometry. Solid angle integration is done by means of Discrete Ordinate Method. Moreover, in contrast to other models published in literature, spectral dependency of relaxation times and acoustic wave dispersion are taken into account in this numerical resolution. Consequently, thermal profiles are obtained for silicon nanowires and nanofilms in steady state allowing computation of thermal conductivity and/or thermal conductance. Besides, we solve the unsteady Boltzmann equation in order to obtain nanosystems temporal evolution. The results obtained with this code match nanofilms and nanowires already predicted thermal profiles in steady state. In unsteady condition, diffusive state (Fourier) is discussed for nanowires and nanofilms. At low temperatures, ballistic phenomenons are seen in nanofilms, whereas, in nanowires, due to boundary scattering, diffusion regime is observed.