title: Radiation and Internal Loss Engineering of High-Stress Silicon Nitride Nanobeams.
abstract: High-stress Si3N4nanoresonators have become an attractive choice for electro- and optomechanical devices. Membrane resonators can achieve quality factor (Q)-frequency (f) products exceeding 1013Hz, enabling (in principle) quantum coherent operation at room temperature. String-like beam resonators possess smaller Q × f products; however, on account of their significantly lower mass and mode density, they remain a canonical choice for precision force, mass, and charge sensing, and have recently enabled Heisenberg-limited position measurements at cryogenic temperatures. Here we explore two techniques to enhance the Q of a nanomechanical beam. The techniques relate to two main loss mechanisms: internal loss, which dominates for high aspect ratios and f ≲ 100 MHz, and radiation loss, which dominates for low aspect ratios and f ≳ 100 MHz. First, we show that by embedding a nanobeam in a 1D phononic crystal (PnC), it is possible to localize its flexural motion and shield it against radiation loss. Using this method, we realize f > 100 MHz modes with Q ≈ 104, consistent with internal loss and contrasting sharply with unshielded beams of similar dimensions. We then study the Q × f product of high-order modes of millimeter-long nanobeams. Taking advantage of the mode-shape dependence of stress-induced "loss dilution", we realize a f ≈ 4 MHz mode with Q × f ≈ 9 × 1012Hz. Our results complement recent work on PnC-based "soft-clamping" of nanomembranes, in which mode localization is used to enhance loss dilution. Combining these strategies should enable ultra-low-mass nanobeam oscillators that operate deep in the quantum coherent regime at room temperature.
authors.affiliation: Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne , Lausanne 1015, Switzerland.
authors.forename: Amir Hossein
authors.initials: AH
authors.lastname: Ghadimi
authors.affiliation: Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne , Lausanne 1015, Switzerland.
authors.forename: Dalziel Joseph
authors.identifier: 0000-0002-0822-9892
authors.initials: DJ
authors.lastname: Wilson
authors.affiliation: Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne , Lausanne 1015, Switzerland.
authors.forename: Tobias J
authors.initials: TJ
authors.lastname: Kippenberg
keywords: acoustic shield; high stress; internal loss; nanomechanics; optomechanics; phononic crystal; radiation loss; silicon nitride