Analysis of thermal conductance of ballistic point contacts

Substantial reduction of thermal conductance (K-ph) was recently reported for air gap heterostructures (AGHs) in which two bulk layers were connected by low-density nanopillars. We analyze K-ph using a full phonon dispersion and including important phonon scattering. We find a transition from ballistic at low temperatures to quasi-ballistic transport near room temperature and explain the slow roll-off in K-ph that occurs near room temperature. We show that the density of nanopillars deduced from the analysis depends strongly on the phonon dispersion assumed. Our model provides a good agreement with experiment that will be necessary to design AGHs for thermoelectric applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4726111]