Thermal conductivity of amorphous carbon thin films

Thermal conductivities $\Lambda$ of amorphous carbon thin films are measured in the temperatures range 80--400 K using the $3\omega$ method. Sample films range from soft a-C:H prepared by remote-plasma deposition ($\Lambda = 0.20$ W m$^{-1}$ K$^{-1}$ at room temperature) to amorphous diamond with a large fraction of $sp^3$ bonded carbon deposited from a filtered-arc source ($\Lambda = 2.2$ W m$^{-1}$ K$^{-1}$). Effective-medium theory provides a phenomenological description of the variation of conductivity with mass density. The thermal conductivities are in good agreement with the minimum thermal conductivity calculated from the measured atomic density and longitudinal speed of sound.