Gas-Phase Heat Transfer From a Heated Microcantilever Inside a Vacuum Enclosure Available to Purchase

The modeling of heat transfer inside a vacuum packaged MEMS devices has been performed by several researchers mostly through Monte Carlo simulations. In this work, we employ an analytical approach to study the heat transport of gas inside a high vacuum enclosure. In this pressure range, the interaction between gas molecules is negligible compared to their interaction with the walls, and hence the gas is treated as the free-molecule gas. The heated cantilever is modeled as a uniform beam with a rectangular cross section located at a certain distance away from the bottom wall which could represent a substrate in the real device. To account for various situations, the temperatures of the surrounding walls are allowed to be different from each other and different from that of the beam and the substrate. The temperature contour and the heat flux are obtained from the analytical approach. A molecular simulation code based on the direct simulation Monte Carlo (DSMC) has been developed and employed to validate the analytical results and excellent agreements have been obtained. The effects of incomplete thermal accommodation are also investigated. It is anticipated that the developed analytical solutions would be very valuable to the design of Pirani sensors and other MEMS devices utilizing micro heaters, for example, the thermal sensing atomic force microscope.