Hierarchical tensile structures with ultralow mechanical dissipation

Abstract

Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitride nanomechanical resonators and realize binary tree-shaped resonators with room temperature quality factors as high as 7.8 × 108 at 107 kHz frequency (1.1 × 109 at T = 6 K). The resonators’ thermal-noise-limited force sensitivities reach 740 zN/Hz1/2 at room temperature and 90 zN/Hz1/2 at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. Moreover, we demonstrate hierarchically structured, ultralow dissipation membranes suitable for interferometric position measurements in Fabry-Pérot cavities. Hierarchical nanomechanical resonators open new avenues in force sensing, signal transduction and quantum optomechanics, where low dissipation is paramount and operation with the fundamental mode is often advantageous.

Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators

“…High-stressed SiN strings can reach exceptionally high Q values, ,, up to 10 9 . ,, This is because in them a great deal more tensile energy is stored in comparison to stressless beams. With the same amount of energy lost per oscillation, high stress resonators thus exhibit very low relative losses, i.e.…”

“…Finally, different deposition parameters may result in different amounts of defects, making a systematic study of the stress dependence of the dissipation challenging. To overcome these limitations, several techniques for stress engineering have been pursued, including bending of the chip, phononic crystal patterning, loss dilution, clamp widening, hierarchical structuring, clamp tapering, or altering the resonator design. , …”

Ultra-coherent nanomechanical resonators based on inverse design

“…First, as a result of the periodic phononic structure, an acoustic bandgap is formed in which phononic modes are trapped and thus unable to radiate into the surrounding environment that otherwise would cause dissipation [4,5,14]. Second, the phononic crystal structure can be also engineered to reduce the phononic mode curvature of the resonator at the clamping points to the substrate [15,16], which will lead to a decrease in the intrinsic dissipation rate for highly stressed systems -a technique that is known as soft-clamping [7][8][9][17][18][19]. Phononic crystal membranes and strings exploiting these effects in harmony have been fabricated, and the membranes have been used in a series of optomechanical experiments [20][21][22].…”

Ultra-high-Q nanomechanical resonators for force sensing

“…In an additional step, phononic crystal engineering allowed researchers to reach the material dissipation limits of nanomechanical resonators by elimination of radiation to the substrate [32,[47][48][49][50][51][52][53][54] and clamping losses [55,56]. Further improvement was made by the realization that the dissipation dilution of a resonator can be increased by appropriate mode-shape engineering, resulting in various geometrical solutions [57][58][59][60][61][62][63][64]. In parallel, experimental demonstrations of the properties of silicon nitride resonators in extreme parameter regimes laid the basis for future applications [65][66][67][68][69][70][71][72][73].…”