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

Abstract

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

Transition from Phononic to Geometrical Mie Modes Measured in Single Subwavelength Polar Dielectric Spheres

“…20,21,24,25 This normalization procedure is based on the assumption that the sphere and substrate are thermalized to the hot plate temperature (440 K). Due to the inherently small contact area between the sphere and substrate, 26 we have assessed the possibility of a thermal gradient arising within the sphere as a consequence of conductive cooling through air and the sphere (see Supporting Information, subsection 1.2.2). We find that the sphere temperature deviates by less than 1 K from the substrate temperature, thus validating our assumption.…”

Quantitative Measurement of Thermal Conductivity by SThM Technique: Measurements, Calibration Protocols and Uncertainty Evaluation

“…Among these measurement methods, the Scanning Thermal Microscopy (SThM) [2,3] is the most used technique as it enables to reach a lateral resolution less than 100 nm with appropriate probes [4,5], whereas optical approaches such as photothermal radiometry [6], thermo-reflectance [7], and photo-reflectance [8] are limited by light diffraction and have thus higher lateral spatial resolution. Based on conventional atomic force microscopy (AFM) equipped with a miniaturised thermal sensor, SThM devices have been developed actively since the 1990s in order to operate either in passive mode for surface temperature measurements [9] or in active mode for phase transition detection [10], thermal contact resistance [11], and thermal conductivity contrast imaging [12][13][14].…”