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