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Sensors and Materials, Volume 30, Number 9(2) (2018)
Copyright(C) MYU K.K.
pp. 2101-2124
S&M1663 Research Paper of Special Issue
Published: September 28, 2018

Description of New Piezoresistance Tensor Equation for Cubic Single Crystal and Its Application to Multiaxial Stress [PDF]

Taeko Ando and Toshiyuki Toriyama

(Received April 6, 2018; Accepted August 6, 2018)

Keywords: piezoresistance, cubic single crystal, multiaxial stress, tensor equation

In this paper, we derived a new piezoresistance tensor equation for a cubic single crystal. This equation can be expressed in terms of the three independent principal components of piezoresistance tensors, the isotropic and deviatoric stress tensors, and the fourth-rank coordinate transformation tensor. The piezoresistance tensor equation can be decomposed into a relation between only the hydrostatic part of the stress tensor and the trace of the resistivity change tensor and into a relation between only the deviatoric parts. The hydrostatic part of the piezoresistance tensor equation is invariant with respect to a coordinate transformation. On the other hand, the deviatoric part of the tensor equation is traceless. The proposed piezoresistance tensor decomposition gives a new physical insight into the classical theory of Pfann and Thurston [J. Appl. Phys. 32 (2008) 1961]. It was shown that Pfann and Thurston's theory can be rewritten as a special case of our tensor decomposition. Furthermore, to demonstrate the consistency between the proposed tensor equation and the experimental evidence, some basic experiments on a single-crystal silicon piezoresistive rosette stress gauge subjected to multiaxial stress were carried out.

Corresponding author: Taeko Ando

Cite this article
Taeko Ando and Toshiyuki Toriyama, Description of New Piezoresistance Tensor Equation for Cubic Single Crystal and Its Application to Multiaxial Stress, Sens. Mater., Vol. 30, No. 9, 2018, p. 2101-2124.

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