Quantitative analysis of heat dissipation in a micro thermal stage for a broad temperature operation

Abstract

A microscale thermal stage offers precise temperature control by suppressing heat conduction. For its use in a broad range of temperatures, the temperature accuracy has been under debate as both conduction and radiation become important heat paths. In this work, we quantitatively analyze the heat dissipation in a suspended microthermal stage. The stage temperature is electrically heated up to similar to 600 K, showing a nonlinear temperature rise with increasing power. The nonlinearity arises from the interplay between conduction and radiation to the ambient, and the contribution of those pathways varies with the stage temperature. To estimate heat conduction, we model both electronic and phononic heat conduction through a metal. Both the electronic and thermal contributions are estimated using the Wiedemann-Franz Law and the model based on the Boltzmann transport equation. For radiation, the emissivity of the metal-dielectric multilayers is modeled by using the Drude model and Airy's formula over a wavelength range of 1-50 mu m. The size effect on electrical conduction is modeled with the Fuchs-Sondheimer approach. Our model captures the temperature rise of the micro-thermal stage from 300 K to 600 K within-2 % uncertainty. This study presents a framework for a quantitative analysis of complex heat dissipation in micro-electro-mechanical systems.