Monte Carlo simulation of cross-plane thermal conductivity of nanostructured porous silicon films

This paper presents a Monte Carlo (MC) modeling of heat conduction in heavily doped (p(+) and n(+)) porous silicon (PS) films known as mesoporous silicon (meso-PS). A three-dimensional pore network generator is developed to better reproduce the structure of low porosity (f(v)< 50%) meso-PS. The submicron scale heat conduction modeled by the Boltzman transport equation is simulated using the MC method in which the nonlinear phonon dispersion curves of bulk silicon and the phonon lifetime dependent on temperature, frequency, and polarization are taken into account. The proposed method has been applied to predict the effect of the porosity (10%-47%), pore sizes (10-20 nm), pore arrangement (p(+)- and n(+)-type), temperature (50-500 K), and film thickness (50 nm-1 mu m) on the cross-plane thermal conductivity of meso-PS films. Moreover, the simulation results enable to deduce the scattering mean free path (MFP) of phonons in the PS and the scattering MFP due to phonon-pore wall interaction. At room temperature, the thermal conductivity of meso-PS is shown one to two orders of magnitude smaller than that of bulk silicon. A drastic simplification of the phonon dispersion curves and phonon MFP, such as in the Debey approximation, results in an overestimation (by about three times) of the thermal conductivity of meso-PS. The thermal conductivity decreases when the pore size decreases or the porosity increases. For a given porosity and pore size, the thermal conductivity of doped p(+)-type PS is much smaller than that of doped n(+)-type PS. Finally, the simulations of thermal conductivity of doped p(+)-type PS are shown in good agreement with available experimental data which confirms the validity of the current modeling. (C) 2008 American Institute of Physics.