Thermal wave propagation and reflection modeling in porous silicon membranes

Sensors utilizing thermal phenomena, such as flow sensors or gas sensors, often rely on static heating and temperature measurements. Employing a time-harmonic heat source instead leads to the propagation of a thermal wave in a thermally conductive medium, which is superposed to the static heat flow. This decaying thermal wave is reflected at thermal boundaries between media of different conductivities and behaves similar to, e.g., acoustic shear waves in liquids or the electromagnetic waves in electrically conductive media. We have modeled and investigated reflector designs to optimize the temperature transmission and heat flux of the harmonic thermal wave in miniaturized membrane structures. Our results show that harmonic temperature distribution and heat flow from the heater into the substrate can be reduced by several factors up to an order of magnitude compared to non-reflector designs.