Optimal Thin-Film Topology Design for Specified Temperature Profiles in Resistive Heaters

In this paper, we optimized the topology of a thin-film resistive heater as well as the electrical potential of the electrodes on the boundaries. The objective was to minimize the difference between the actual and prescribed temperature profiles. The thin-film thickness was represented by 100 design variables, and the electrical potential at each electrode were also design variables. The topology optimization problem (inverse problem) has been solved with two methods, i.e., with a genetic algorithm (GA) and with a conjugate gradient method using adjoint and sensitivity problems (CGA). The genetic algorithm used here was modified in order to prevent nonconvergence due to the nonuniqueness of topology representation. The conjugate gradient method used in inverse conduction was extended to cope with our electrothermal problem. The GA and CGA methods started with random topologies and random electrical potential values at electrodes. Both the CGA and GA succeeded in finding optimal thin-film thickness distributions and electrode potential values, even with 100 topology design variables. For most cases, the maximum discrepancy between the optimized and prescribed temperature profiles was under $0.5°C$⁠, relative to temperature profiles of the order of $70°C$⁠. The CGA method was faster to converge, but was more complex to implement and sometimes led to local minima. The GA was easier to implement and was more unlikely to lead to a local minimum, but was much slower to converge.