Conditioning of Piezoresistance Coefficient Extraction

TL;DR

This paper analyzes the conditions for accurately extracting piezoresistance coefficients, demonstrating that a well-designed test structure yields a well-conditioned matrix, leading to reliable coefficient estimation with minimal error propagation.

Contribution

It provides a mathematical framework for testing structure design, ensuring well-conditioned matrices for precise piezoresistance coefficient extraction.

Findings

The test structure produces a well-conditioned matrix A.

The extraction error is less than 8% for typical input errors.

Numerical estimation confirms the robustness of the method.

Abstract

The necessary and sufficient condition for the piezoresistance coefficient extraction and conditioning of the extraction problem are considered as a problem of the certain matrix A. This matrix is implied by the stress distribution on the certain test structure. For the given test structure matrix A was calculated and the condition number was estimated. Obtained value of condition number shows that proposed test structure gives well-conditioned matrix A. Both the geometrical analysis and numerical estimation of condition number shows that the problem of extraction is well-conditioned and the test structure is properly designed. For the given condition number the error propagation of the input data was considered. For assumed levels of the input data errors, the relative error of piezoresistance coefficient is less than 8%.