Analytical heat-transfer modeling of multilayered microdevices

Abstract

In this paper, we present a general analytical modeling of the steady-state temperature distribution within a two-dimensional multilayered structure heated by arbitrary multi-heaters. Possible heat flux distributions on the heater–layer interface are discussed in detail. For a double-layer device, the selection of these distributions shows negligible influence on the total energy consumption and the average temperature across each heater–layer interface. The effects of the heat conduction inside the heaters are investigated according to the heater–layer thermal conductivity contrast and the thickness-to-width aspect ratio of heaters. Based on this model, we have developed a new method that can directly compute the electricity input powers to maintain required temperatures in specified regions. The cross talk within the heater array can be easily evaluated with this method. Moreover, its application in the thermal design of microfluidic devices is demonstrated by analyzing the experimental results in [2]. The linear relationship between the temperatures of the microchannel and corresponding heater is proven with our analytical model. The solution is also extended to structures with arbitrary embedded thin-film heaters and utilized to evaluate the surface temperature linearity of a microdevice with thin-film heaters that are covered with an insulating SiO2 layer.