Investigation of the natural convection boundary condition in microfabricated structures

Heat loss through surrounding air has an important thermal effect on microfabricated structures. This effect is generally modeled as a natural convection boundary condition. However, the correct procedure for the determination of the convective coefficient (h) at microscales continues to be debated. In this paper, a microheater is fabricated on a suspended thin film membrane. The natural convection on the microheater is investigated using 3-omega measurements and complex analytical modeling. It is found that the value of h that fits experimental data should have an apparently larger value than that at larger scales; however, it is also shown that the increased h is actually contributed by heat conduction instead of heat convection. A method of determining the correct h that can be used for microfabricated structures is proposed by using the heat conduction shape factor.