Analysis of thermal conductance of ballistic point contacts

Substantial reduction of thermal conductance (Kph) was recently reported for air gap heterostructures (AGHs) in which two bulk layers were connected by low-density nanopillars. We analyze Kph 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 Kph 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 application