Design of Micro-heaters Inspired by Space Filling Fractal Curves

Micro-heating capabilities are important in applications such as thermotherapy, drug delivery, gas sensing and so on. Micro-heaters need to be designed such that they provide uniform temperature across a given surface with minimum metal consumption. In case of Joule heating based micro-heaters, the metal coil design plays an important role in determining its heating characteristics. This paper presents multiple designs of space filling curves that can be used as metal coils in micro-heaters to achieve uniform temperature distribution. We have modelled three types of fractal geometries of different orders - Peano, Hilbert and Moore. In order to compare the performance of these geometries with a typical double spiral heat-pad, we kept a fixed area of 30 mm × 30 mm and input power of 1 W. We have used PDMS (poly-dimethylsiloxane) of thickness 200 μm as a base for the heat-pad and copper is used for the geometries. Further, we maintained constant metal width and thickness of 0.375 mm and 100 μm respectively, across all geometries. Our finite element analysis (FEA) suggests that Peano order-2 & 3, Moore order-3 & 4, Hilbert order-3 & 4 outperformed the double spiral heat-pad in terms of temperature uniformity. The average temperature of all these micro-heaters are around 370 K for 1 W input power. Overall, Peano order -2 curve performed better compared to all geometries in terms of the metal coil length and temperature uniformity trade-off.