Materials with ultralow thermal conductivities have a wide range of applications . It is generally accepted that nanocomposite formation can produce very low thermal conductivity, better than the alloy and amorphous limits . In this work we present a detailed analysis of the role of dimensionality in reducing phonon conductivity of ultrathin nanocomposites. Our method uses a recently developed semi-ab-initio technique  based on a combination of density functional peturbation theory , third- and fourth-order elastic anharmonic terms in a crystal Hamiltonian expressed in terms of a temperature-dependent Grüneisen's constant, a quasi-harmonic approximation, and the linearized phonon Boltzmann equation . Our numerical results reproduce the experimentally measured  phonon conductivity results for bulk Si and Ge in the wide temperature range 5-1500 K. Our cross-plane conductivity result for the ultrathin planar superlattice Si(11Å)Ge(11Å) is in good agreement with reported experimental measurements . From our computed results, we draw the conclusion that at and above room temperature the in-plane and cross-plane thermal conductivities in this planar superlattice geometry are, respectively, at least five and ten times lower than the lower of the two bulk conductivities (viz. in bulk Ge). It is also found that the formation of ultrathin nanowire and nanodot superlattice structures (Si inserts in a Ge host) produces conductivity results lower than that obtained for the ultrathin planar superlattice structure. A detailed analysis of these findings will be presented. The role of sample size and doping levels on the reduction of the conductivity will also be discussed.
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