Electro-Thermal-Mechanical Modeling of Gas Sensor Hotplates

Thermo-Electro-Mechanical Simulation of Semiconductor Metal Oxide Gas Sensors

“…After the electrical behavior is modeled, the resistance is found with R=Aj→V0.222222em0.222222em, where A is the cross-sectional area of the film. The relationship between the resistance and the applied voltage is plotted in Figure 7, where the described model reproduces the measured data very well [92].…”

“…One simple example of a suspended membrane SMO sensor and micro-heater is shown in Figure 5 and Figure 6. In Figure 6 we also see the presence of a heat spreading plate which is commonly used in order to improve the temperature uniformity across the active region of the sensor [92]. The electrodes for gas sensing are placed on top of the membrane above the heat spreading plate.…”

“…This method is effective when all stacked layers have the same lateral dimensions, but the sweep function becomes very complex when the layers have different shapes. An alternative is drawing the thin layers as two-dimensional objects and modeling them as shell elements, meaning that the vertical dimension is not explicitly simulated, but rather a linear extrapolation is used [92]. This solution simplifies the geometry and may result in some errors.…”

“…When assigning material properties for the simulation, it is essential that these are calibrated to the fabrication process. Published values for many parameters can vary significantly, since they depend considerably on the fabrication process [92]. An example is the thermal conductivity which is strongly influenced by the quality of the crystal structure in the layer, which is in-turn defined by the fabrication process and post-fabrication annealing.…”

“…First the electric behavior is described with ∇·truej→=Qj,v0.222222em0.222222em, truej→=σtrueE→0.222222em0.222222em, and trueE→=−ΔV0.222222em0.222222em, where j→ is the current density, Qj,v is the current source, σ is the electrical conductivity, E→ is the electric field, and V is the applied potential. When shell elements are used for approximation, the equations must be modified in order to make use of the tangential gradient operator which removes the normal component of the applied potential [92]. After the electrical behavior is modeled, the resistance is found with R=Aj→V0.222222em0.222222em, where A is the cross-sectional area of the film.…”