Thermal conductivity of Si nanostructures containing defects: methodology isotope effects, and phonon trapping

A first-principles method to calculate the thermal conductivity in nanostructures that may contain defects or impurities is described in detail. The method mimics the so-called `laser-flash' technique to measure thermal conductivities. It starts with first-principles density-functional theory and involves the {\it preparation\/} of various regions of a supercell at slightly different temperatures. Temperature changes as small as 5K can be monitored without using thermostats. The changes to the phonon density of states and the specific heat induced by several atomic percent of impurities are discussed. The thermal conductivity of Si supercells is calculated as a function of the temperature and of the impurity content. For most impurities, the drop in thermal conductivity is unremarkable. However, there exist narrow ranges of impurity parameters (mass, bond strength, etc.) for which substantial drops in the thermal conductivity are predicted. These drops appear to be related to the vi