Novel approach for the 3D modeling of electrical conduction phenomena in highly anisotropic materials

Reinhard Buchhold; Ralf Gollee; Arne Nakladal; Gerald Gerlach

doi:10.1117/12.360476

3 September 1999 Novel approach for the 3D modeling of electrical conduction phenomena in highly anisotropic materials

Reinhard Buchhold, Ralf Gollee, Arne Nakladal, Gerald Gerlach

Proceedings Volume 3875, Materials and Device Characterization in Micromachining II; (1999) https://doi.org/10.1117/12.360476
Event: Symposium on Micromachining and Microfabrication, 1999, Santa Clara, CA, United States

Abstract

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.

Citation Download Citation

Reinhard Buchhold, Ralf Gollee, Arne Nakladal, and Gerald Gerlach "Novel approach for the 3D modeling of electrical conduction phenomena in highly anisotropic materials", Proc. SPIE 3875, Materials and Device Characterization in Micromachining II, (3 September 1999); https://doi.org/10.1117/12.360476

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