A prediction scheme of the static fracture strength of MEMS structures based on the characterization of damage distribution on a processed surface

Abstract

This paper presents a scheme for predicting the strength of MEMS structures patterned into arbitrary shapes by deep reactive ion etching of a silicon wafer. The scheme is based on the inhomogeneous defect distribution on the etched surfaces. Single-crystal silicon specimens with different shapes were subjected to four-point bending tests with monotonically increasing load. The distributions of the fracture strength were described using two-parameter Weibull statistics, where the two parameters are defined as functions of the etching depth representing the inhomogeneity of the damage on the etched surface in the direction perpendicular to the wafer. In order to estimate the distribution of the local strength determined by the local level of damage, the etched surfaces of specimens without a notch were tested in three different bending directions corresponding to three different stress distributions, and three different strength levels were given due to surface roughness conditions caused by the non-uniformity of the etching process. The estimated values of the parameters were used to estimate the fracture strength of four types of notched specimens with different notch tip radii. The results of comparison between the distributions of predicted strengths and experimental data showed that the fracture strength of arbitrarily shaped structures is predictable on the basis of the information obtained from specimens without notch, by taking into account the characteristics of etched surface, i.e. the inhomogeneous damage.