The Role of Convection and Size Effects in Microhotplate Heat Exchange: Semiconductor and Thermomagnetic Gas Sensors

The analysis of the influence of microhotplate size on the convective heat exchange of gas sensors is presented. Usually, the role of convection in the heat exchange of gas sensors is not considered in thermal simulation models because of the complexity of the convection process. As a result, the contribution of this process to the overall heat loss of sensors remains without detailed analysis. We analyzed convection issues in two groups of gas sensors: semiconductor and thermocatalytic (calorimetric) sensors and, on the other hand, in the oxygen sensors of the thermomagnetic type. It is demonstrated that there is a critical size leading to the formation of convective heat exchange flow. Below this critical value, only thermal conductivity of ambient air, IR (infrared) radiation from the heated microhotplate surface, and thermal conductivity of the microhotplate-supporting elements should be considered as channels for heat dissipation by the microhotplate, and the contribution of free convection can be neglected. The expression for the critical size contains only fundamental constants of air, d_cr~4·ν·Dg3, where ν is the kinematic viscosity of air, D is the diffusion coefficient, and g is the acceleration of free fall, d_cr~0.5 cm. Therefore, if the size of the microhotplate d <<d_cr, the influence of convection heat exchange can be neglected. Similar results were obtained in the analysis of the behavior of thermal magnetic sensors of oxygen, which use paramagnetic properties of molecular oxygen for the determination of O₂ concentration. In this case, the critical size of the sensor is also of significance; if the size of the magnetic sensor is much below this value, the oxygen concentration value measured with such a device is independent of the orientation of the sensor element. The results of the simulation were compared with the measurement of heat loss in micromachined gas sensors. The optimal dimensions of the sensor microhotplate are given as a result of these simulations and measurements.