Quantitative Measurement of the Thermal Contact Resistance between a Glass Microsphere and a Plate

Accurate measurements of the thermal resistance between micro-objects made insulating materials are complex because their small size, low conductivity, and presence various ill-defined gaps. We address this issue using a modified scanning microscope operating in vacuum air. The sphere-plate geometry is considered. Under controlled heating power, we measure temperature on top glass microsphere glued to probe as it approaches plate at room with nanometer accuracy. In vacuum, jump observed contact. From modeling sphere, contact ${R}_{K}=(1.4\ifmmode\pm\else\textpm\fi{}0.18)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}\phantom{\rule{0.1em}{0ex}}\mathrm{W}}^{\ensuremath{-}1}$ effective radius $r=36\ifmmode\pm\else\textpm\fi{}4$ nm obtained. air, sphere shows decrease starting from distance $200\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$. A also contact, reduced amplitude. coupling out can be described by shape factor front placed circuit involving series parallel that determined fitting approach curve. air ${R}_{K}^{\ensuremath{\ast}}=(1.2\ifmmode\pm\else\textpm\fi{}0.46)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}\phantom{\rule{0.1em}{0ex}}\mathrm{W}}^{\ensuremath{-}1}$ then estimated jump. method quantitative without requiring any tedious multiple-scale numerical simulation, versatile describe large distances environments.