Steady-state 1D electrothermal modeling of an electrothermal transducer

Electrothermal models that describe the steady-state electrothermal behavior of a general electrothermal transducer have been developed using the one-dimensional heat transport equation. Compared to previously reported electrothermal transducer models, these models produce simpler equations for the temperature change versus an electrical input. Models of the transducer temperature distribution are derived using various thermal conditions such as surface convection and temperature-dependent electrical resistivity. The models are made for a general electrothermal transducer by assuming that the transducer is attached to arbitrary thermal resistances at its boundaries. Critical thermal parameters of the transducer - such as the position of maximum temperature, maximum temperature change and average temperature change - are derived from the models. It is shown that the average temperature change versus applied power and voltage relationships of the simpler models always agree with the more accurate model within factors of 12/π² and respectively. It is also shown that the temperature change of an electrothermal transducer is approximately linear with respect to applied voltage when actuated in a certain voltage range. The models are compared to FEM simulations and experimental results of an electrothermal micromirror.