# Analysis of membrane phononic crystals with wide bandgaps and low-mass defects

## TL;DR

This paper develops models and fabrication techniques for membrane phononic crystals with low-mass defects, optimizing for force sensing by balancing acoustic bandgap size and dissipation, and provides design principles for low-dissipation optomechanical systems.

## Contribution

It introduces new modeling and fabrication methods for low-mass defect phononic crystals, analyzing the tradeoffs between mass contrast, bandgap size, and dissipation.

## Key findings

- High mass contrast enhances acoustic isolation.
- Low dissipation defect modes are achievable at low temperatures.
- Design principles for integrating low-mass mechanical modes into optomechanics.

## Abstract

We present techniques to model and design membrane phononic crystals with low-mass defects, optimized for force sensing. Further, we identify the importance of the phononic crystal mass contrast as it pertains to the size of acoustic bandgaps and to the dissipation properties of defect modes. In particular, we quantify the tradeoff between high mass contrast phononic crystals with their associated robust acoustic isolation, and a reduction of soft clamping of the defect mode. We fabricate a set of phononic crystals with a variety of defect geometries out of high stress stoichiometric silicon nitride membranes, and measured at both room temperature and 4 K in order to characterize the dissipative pathways across a variety of geometries. Analysis of these devices highlights a number of design principles integral to the implementation of low-mass, low-dissipation mechanical modes into optomechanical systems.