A measurement technique of quasi-ballistic thermal transport in tens of nanometers has been developed by using time-domain thermoreflectance of gold nano-islands. The suppressed apparent thermal conductivity of transparent substrates (fused quartz, crystal quartz, and sapphire) due to quasi-ballistic thermal transport is obtained through the transient temperature change of the gold nano-islands formed on the substrate surface, and the size effect of thermal conductivity in the range of tens of nanometers is quantified by varying the gold nano-island sizes. Furthermore, characteristic phonon mean free paths of the substrates were obtained by fitting the measured size effect with a solution of a Boltzmann transport equation. The results identify that the size-effect of amorphous fused quartz at room temperature becomes significant when the size is reduced below 60 nm.

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