Relation between Raman frequency and triaxial stress in Si for surface and cross-sectional experiments in microelectronics components

Abstract

This paper provides a detailed description explaining how to calculate the relation between the silicon Raman frequency and local stress or strain in the silicon, applied to stress measurements in microelectronics. This relation is well known for measurements from the (100) surface of silicon. However, it is often used in the wrong way, neglecting non-zero stress tensor elements. Especially, in current 3D microelectronics technology, where the stress caused by through Si vias or micro-bumps is of large importance, the vertical stress component, which highly affects the measured Raman frequency shift, is often erroneously neglected. In addition, the equations for the (100) surface are also often used incorrectly for cross-sectional measurements from a (110) surface. In this paper, different ways to calculate the relation between Raman frequency and triaxial stress, and the related Raman peak intensities, are discussed in detail.