Investigating the effects of Silicon etching imperfections on the quadrature error in MEMS gyroscopes

Abstract

Due to the structure symmetry of the architecture of most of the highly sensitive MEMS gyroscopes, their native quadrature error is null. However, with the actual precision limitations of the silicon etching processes, some dispersion in the etching of the flexure springs may results in non-zero coupling stiffness between the X and Y-axis, which leads to a quadrature error. As the stiffness of the flexure springs highly depends on its width, it is necessary to investigate the impact of the local width dispersions on the stiffness coupling. In this paper we report on our approach, which is based on the use of Finite Element Analysis (FEA) to determine the evolution of the stiffness matrix of the springs of our gyroscope regarding the bending beam width imperfections. Based on our results, a statistical analysis is carried out in order to evaluate the mean and the standard deviation of the absolute value of the amplitude of the quadrature signal for a given beam width variation. Then, we compare our model to the actual quadrature error of our gyroscopes, which has been measured with a dedicated bench. It turns out that a bending beam width variation of 0.9% leads to a quadrature error discrepancy with the same order of magnitude that the one measured, emphasizing the importance of the consideration of the bending beams width variation during the dimensioning of MEMS gyroscopes, in order to avoid high quadrature error.