Thermal Spreading Resistance of Near Surface Localized Heating-Induced Size Effects in Semiconductors

Abstract

Abstract Localized heating is encountered in various scenarios, including the operation of transistors, light-emitting diodes, and some thermal spectroscopy techniques. When localized heating occurs on a scale comparable to the mean free path of the dominant energy carriers, additional thermal resistance is observed due to ballistic effects. The main objective of this study is to find a relation between this resistance, problem geometry, and material thermal properties in situations involving localized heating. Models based on the solution of the Fourier heat diffusion equation and the gray phonon Boltzmann Transport Equation are solved simultaneously to calculate the additional thermal resistances that arise from localized heating. Subsequently, the results are analyzed to derive the desired relationship. It is noted that in the context of localized heating resistance, the effects of geometrical variables are non-linear and substantial, particularly when the Knudsen numbers for the boundary and heat source exceed certain thresholds. Specifically, when the Knudsen number for the heat source becomes comparable to 1 localized heating resistance is observed. However, when the Knudsen number based on heat source height and width surpasses 8 and 20, respectively the heat source behaves akin to a point source, no longer significantly affecting the localized heating resistance. At this juncture, the maximum resistance limit is reached.