Micro-hot-plates without simply connected hot-spots and with almost-circular temperature distribution

We have recently shown that the temperature distribution in micro-hot-plates with perfectly circular geometry can be accurately expressed in terms of modified Bessel functions. However, the geometry of practical micro-hot-plates cannot be perfectly circular due to several issues, including the presence of the electrical contacts; in fact, a typical manifestation of poor circular-symmetry is the occurrence of simply-connected hot-spots. Here we systematically investigate all these issues and describe strategies for designing micro-hot-plates without simply-connected hot-spots and with an almost circular temperature distribution. FEM simulations consistently confirm that our methodology reduces the temperature deviations from ideal circular symmetry down to levels which are unimportant for most applications (e.g. less than 2.5°C for a micro-hot-plate operating at 800°C). As a result of the excellent circular symmetry, the temperature distribution in the proposed micro-hot-plates, unlike previously reported devices, can be accurately expressed in terms of the modified Bessel functions, which is a key step toward the design of micro-hot-plates with unprecedented temperature uniformity or with desired temperature profiles.