We realise a circular gray-field polariscope to image stress-induced birefringence in thin (sub-micron thick) silicon nitride membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling. Furthermore, using a sample with a well-known stress anisotropy, we extract a value for the photoelastic (Brewster) coefficient of silicon nitride, C ≈ (3.4 ± 0.1) × 10−6 MPa−1. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal patterns.
References
This measurement was conducted on a separate sample with a 238.6-nm thick SiN layer grown in the same conditions as the ribbon. We take the typical deviation of measured stress in x and y directions as combined measurement error and film inhomogeneity of 2%.
The transmittance of a membrane of thickness d and refractive index n is given by .
