Nanometer Scale Assessment of Mechanical Strain Induced in Silicon by a Periodic Line Array

Measuring stress and strain, induced by nanostructures, at the nanometer scale is still a challenge. In this work, we investigate the strain induced by sub-micrometric periodic line arrays deposited on single crystal (001) Si substrate. We study the influence of the lines width and the spacing between the lines for two sets of samples: a silicon nitride lines array and a poly-silicon line array capped with a Si₃N₄ stressor layer. The periodic strain field in mono-crystalline silicon is investigated by High Resolution X-ray Diffraction which is very sensitive to local strain (<10⁻⁴), has the required resolution, and is non-destructive. X-ray reciprocal space maps (RSM) are measured on a 4 circles goniometer with a laboratory source. The line arrays induce a periodic strain field in silicon, which gives rise to distinct satellites in reciprocal space. The intensity envelope of these satellites is related to the strain field in one cell. In order to assess this strain field in silicon, mechanical modeling is necessary. Elastic calculations are performed with a Finite Element Modeling (FEM) code in order to extract the displacement field that is used for structure factor calculations within kinematical approximation. The calculated reciprocal space map is compared to the experimental results in order to validate the strain field. We show that for capped poly arrays, the diffracted intensity envelope is influenced by the spacing between the lines. This area is filled with silicon nitride which induces a noticeable change in displacement and strain field. While for bare stressor arrays the nitride line width is responsible of change in displacement field and thus on the RSM intensity envelope.