Heat propagation dynamics in thin silicon layers

Nowadays, it is in the main stream of the recent researches that on nanoscale the sample size has an essential contribution to the behavior of the transport processes. In the present paper it is pointed out how to take into account not only the size parameter but the boundary contributions (wall effects from the reflections and scatterings of the phonons). The mathematical calculations are based on the fluctuation dissipation theory for the thermal transport. Calculating the spectra and the related time correlation functions the dynamics of thermal signal propagations are studied via the change of the behavior of the correlation functions in thin (60 and 100 nm) silicon layers. It can be easily recognized from the results of the elaborated calculations how the radical change appears in the signal propagation due to the contribution of the boundary effects. Finally, detailed examples are calculated numerically and analyzed graphically to show how the dynamics of the heat propagation changes depending on the wall effects at nanoscale.