Effect of nano-film thickness on thermal resistance at water/silicon interface

Abstract

Parallel to the developments in micro/nano manufacturing techniques, component sizes in micro/nano electro mechanical systems have been decreasing to nanometer scales. Decrease in lengths in heat transfer direction below the heat carrier phonon length scales reduces thermal conduction in semiconductors. This study shows that such altered phonon spectrums with the decrease of size also reduce the heat transfer at the solid/liquid interfaces and can be correlated with the thermal conductivity of the slab. Using Molecular Dynamics (MD), we measured heat transfer between water and silicon of different thickness between 5 nm and 60 nm. Silicon slabs exhibit a linear temperature profile through the bulk where thermal conductivities measured based on Fourier law decreased by the decreasing slab thickness. We applied a semi-theoretical formulism on variation of conductivity by slab thickness. At the interface of these slabs and water, heat passage is disturbed due to the phonon mismatch of dissimilar materials, which is mostly considered as solid/liquid couple interface properties by the earlier literature. Resistance for phonon passage characterized as Kapitza length (LK) is measured for different slab thicknesses at different surface wetting conditions varying between hydrophilic to hydrophobic. Increasing surface wetting decreases the LK while at a certain wetting, decreasing the slab thickness increases the LK. Once the LK of different size slabs normalized by its bulk value (assumed to be the LK of the thickest slab at the corresponding wetting), LK variation by silicon thickness shows a universal behavior independent of surface wetting. A mathematical model describing the exponential increase of LK by decreasing thickness was developed and validated by an earlier model. We further developed a correlation between the corresponding changes of LK and conductivity with respective to their bulk values by analytically combining two models as (LK/LK-Bulk)=exp3.94kBulk-k/(k×kBulk) , using which LK can be predicted from available thermal conductivities of a certain material. Results are crucial for thermal management of current and future electronics.