Percolation of thermal conductivity in amorphous fluorocarbons

We report experimental evidence of the percolation of thermal conductivity in nanometer scale thin films of amorphous fluorocarbon, using time-domain thermoreflectance measurements. According to the theory of Phillips and Thorpe, rigidity percolation in covalent glasses results in a power-law dependence of the elastic modulus on the average coordination number. Our measurements show that thermal conductivity behaves similarly. We derive the relation between thermal conductivity and coordination number from the rigidity percolation model using the theory of minimum thermal conductivity. Experiments verify the individual validity of each of these models in the film samples. This paper elucidates the physics of heat conduction in covalently bonded amorphous solids near the percolation threshold.