Compact thermoelectric coupled models of micromachined thermal sensors using trajectory piecewise-linear model order reduction

Numerical simulation has become an effective way to design and optimize micromachined thermal sensors. To improve the speed of development process, fast simulation is indispensable. This paper investigates compact models, which are accurate low order representations of high order finite element models, for micromachined thermal sensors. Because the thermal field and the electric field act on and influence each other, the compact models should be established from the thermoelectric coupled full models. Thermoelectric coupling and temperature dependent resistivity make the problems strong nonlinearity. Therefore a powerful nonlinear model order reduction method, named trajectory piecewise-linear (TPWL) method, is employed. Its core idea is approximating the nonlinear model piecewise-linearly along a training trajectory. The performance of the TPWL method and fast TPWL method are compared. And the effects of linearization point number and local reduced basis order on accuracy, efficiency and size of the TPWL compact models are studied. Moreover, the expandability of the TPWL compact models is also discussed. Results show that the TPWL compact models are suitable for the design and optimization of micromachined thermal sensors.