Despite the fact that a number of technical devices, such as piezoresistive sensors or Hall sensors, rely on anisotropic conductivity phenomena, the techniques for modeling anisotropy of conduction are still limited. Usually, those devices are simulated using very specific solutions which are not easily shared between different applications. We have developed a general method for consistent Finite Element Analysis (FEA) modeling based on the diagonalization of the resistivity matrix by main axis transformation. The new method has been successfully applied to simulate piezoresistive four-terminal-transducers such as those used in pressure sensors. In this particular case, the results obtained from the simulation of the mechanical system can be applied to the subnet of the transducer region in a second load step to calculate the electric field distribution. For each finite element, an orthotropic resistivity matrix and the appropriate coordinate system are obtained by diagonalization of the anisotropic matrix, which is calculated from the mechanical stress distribution using the piezoresistive equations. Our new method does not rely on simplifying assumptions concerning the boundary conditions, nor does it neglect parts of the mechanical stress tensors. Based on comparison with theoretical solutions for simple structures and on experimental investigation, matrix diagonalization was found to be a powerful tool for solving problems related to anisotropic conductivity using standard FEA packages.
To date, the usefulness of piezoresistive pressure sensors is still limited by their instability and inaccuracy. Therefore, the physical protection of the sensor elements and the robustness of the output signals with respect to environmental disturbances are important issues in the design and manufacturing of piezoresistive sensors. One approach to the encapsulation of small piezoresistive sensors is to adapt the passivation techniques commonly used in microelectronic
manufacturing. An ideal passivation system is one that eliminates cross- sensitivities while not affecting the transfer behavior of the sensor. In reality, however, the same physical mechanisms that prevent cross-sensitivities will generally also modify the sensor's transfer function. The paper describes how accuracy and stability of non-encapsulated silicon pressure sensors can be optimized under consideration of mechanisms connected to environmental conditions like temperature and humidity. The performance of pressure sensors as a function of passivation layer properties and climatic conditions was experimentally studied. Valuation criteria were stochastic shares of the output voltage (noise). It was found that fast changes in the ambient climate induce significant measurement errors. Experimental results will be given that suggest new conclusions regarding the physics behind instabilities in piezoresistive sensors and yield approaches for improved sensor design.
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