Lattice Boltzmann Modeling of Phonon Heat Conduction in Superlattice Structures

The results of temperature prediction and determination of effective thermal conductivity in periodic Si-Ge superlattice in one dimension, at length scale comparable to the mean free path are presented. Classical heat transfer models such as Fourier’s law do not represent what actually happens within electronic devices at these length scales. Phonon-border and phonon-interface scattering effects provide discontinuous jumps in temperature distribution when the mean free path is comparable with the device’s characteristic length, a relation given by the Knudsen number (Kn). For predicting the temperature within the periodic Si-Ge superlattice use is made of the lattice Boltzmann method in one dimension, using Debye’s model in the phonon dispersion relation. The predictions show that as Kn increases, so do the jumps at the borders, the same as at the interfaces. The prediction also shows that the effective conductivity of the Si-Ge superlattice decreases as Kn and the number of layers of material increase, and that k_eff decreases as the magnitude of p increases, a factor that allows heat flow between one layer and another. Use of gray LBM leads to good approximations of the actual temperature field and thermal conductivity values for the superlattice materials model when the physics of phonons established by Debye’s model is used.