Systematic design of micro-resistors for temperature control by quasi-simultaneous heating and temperature sensing

A single resistor can be used for quasi-simultaneously heating and temperature sensing. For instance, in microsystems this strategy is often employed for temperature control, flow sensors, gas sensors, material characterization, hot-wire anemometers, bio-MEMS and more. However, the design of such integrated resistors is complex due to both many design parameters and several conflicting specifications so that until now there is no method for predicting, based on a given set of specifications, if a solution exists and, eventually, for systematic design of optimal devices. Here we determine a complete set of relations which allows to easily find if, for given specifications, a solution is possible and, if not, to identify which specifications must be relaxed. Moreover, even with very severe specifications, our relations offer insight for systematic design of optimal resistors for quasi-simultaneous heating and temperature sensing; illustrative design cases are reported.