Lumped Microhotplate Model

In the previous paragraph, the basic considerations of FEM modelling have been laid out. The outcome of a static thermal simulation based on this model is a 3-d temperature field T x,y,z). In this section it is discussed, how the characteristic figures, such as thermal resistance and thermal time constant of the membrane, can be deduced. 

The temperature sensor on the hotplate measures the membrane temperature, Tm, at a certain location, Xg, such as the membrane center  

On the other hand, the total heating power can be calculated as the product of heating voltage, Vheat. and heating current, 4eaf For a heater occupying an area, Aheat. in the geometric model, the power density can be calculated to  

A characteristic measurement includes the determination of the microhotplate temperature as a function of its power consumption. The curves can be fitted by a second-order polynomial using the coefficients tjo and t]i. 

The reference temperature. To, refers to ambient temperature, i.e., the membrane temperature before applying any heating power. The thermal resistance, t], can be generally defined as  

---

The coefficients of thermal resistance can either be measured for existing devices or be calculated with the thermal microhotplate model presented in Chap. 3. In analogy to resistor-heated membranes, the model can be used for evaluation and optimization of new designs. A combination of the presented transistor model equations with the lumped microhotplate model in Sect. 3.4 would allow to also derive an AHDL model for coupled-system simulations. 

The suggested procedure to arrive at this goal is presented in Fig. 3.1. It starts with the transfer of a certain microhotplate layout into a geometry model for a complex FEM simulation. This step is shown in Fig. 3.2 and will be explained in more detail in one of the next sections. A complex 3-d FEM simulation is then performed. The results of this simulation are used to produce a lumped-element model. This model is translated into a hardware description language (HDL). Using the resistances of the device elements such as the heater resistance, Rheat> and the resistance of the temperature sensor, Rx. co-simulations with the circuitry can be performed. 

---