Stress measurements in silicon devices through Raman spectroscopy: Bridging the gap between theory and experiment

The different steps that have to be taken in order to derive information about local mechanical stress in silicon using micro-Raman spectroscopy experiments, including theoretical and experimental aspects, are discussed. It is shown that the calculations are in general less complicated when they are done in the axes system of the sample. For that purpose, the secular equation is calculated in the axes system [110], [−110], [001], which is important for microelectronics structures. The theory relating Raman mode shift with stress tensor components is applied using two analytical stress models: uniaxial stress and planar stress. The results of these models are fitted to data from micro-Raman spectroscopy experiments on Si3N4/poly-Si lines on silicon substrate. In this fit procedure, the dimensions of the laser spot and its penetration depth in the substrate are also taken into account.