Investigation of local stress fields: Finite element modelling and High Resolution X-Ray Diffraction

Abstract

The influence of local stress fields on the electrical properties of Si-based nanostructures is of increasing concern. The experimental evaluation of stresses at the required scale (few nanometres) remains, however, a very challenging task. We propose a non destructive X-ray diffraction technique for local strain measurements using a laboratory radiation source. This technique provides an alternative route to micro diffraction experiments. High resolution X-ray diffraction is used to analyse the diffraction from the periodic strain field induced in silicon by a periodic array. We analyzed arrays of Si₃N₄ lines (thickness: 149 nm, width: 145 nm, pitch: 169 nm) on silicon, and arrays of single crystal Si lines (period: 0.6 micrometers, width: period/2, thickness: 50 nm) etched in SOI (Silicon On Insulator) and capped with SiO₂ and Si₃N₄. Reciprocal space maps were performed around the Si substrate diffraction lines. A Bartels 4 reflections Ge 220 monochromator was used in combination with a 3 reflections Ge 220 analyser. X ray diffraction rocking curves performed on Si 004 and Si 224 reveal distinct superlattice peaks whose spacing is related to the in-plane periodicity. Reciprocal space maps reveal particular intensity distributions caused by the stress gradient in the transverse and perpendicular directions of the lines. Reciprocal space maps obtained by High Resolution X-Ray Diffraction are compared with maps calculated from displacement fields derived from finite element modeling. Very clear superlattice peaks are, however, observed around the bulk Silicon substrate reciprocal lattice nodes, which indicates a great sensitivity of this method to elastic stresses. The influence of the lines aspect ratio on the reciprocal space maps has been studied both experimentally and through modelling.