# Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

## TL;DR

This paper introduces a polarimetric imaging technique to map stress-induced birefringence in silicon nitride resonators, providing quantitative stress analysis and a new photoelastic coefficient measurement, with potential for quality control.

## Contribution

The study presents a novel polarimetric method for stress analysis in silicon nitride membranes, including a new measurement of the material's photoelastic coefficient.

## Key findings

- Quantitative stress mapping aligns with finite element models.
- New value for silicon nitride's photoelastic coefficient: approximately 3.4×10^{-6} MPa^{-1}.
- Method applicable for quality control of stressed membranes with phononic patterns.

## Abstract

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (submicron thick) silicon nitride (SiN) 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 (FEM). Furthermore, using a sample with a well known stress anisotropy, we extract a new value for the photoelastic (Brewster) coefficient of silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal patterns