Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics

Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics

Christoph Reinhardt, Tina Müller, Alexandre Bourassa, Jack C. Sankey Department of Physics, McGill University, Montréal, Québec, H3A 2T8, Canada jack.sankey@mcgill.ca

In force sensing, optomechanics, and quantum motion experiments, it is typically advantageous to create lightweight, compliant mechanical elements with the lowest possible force noise. Here we report wafer-scale batch fabrication and characterization of high-aspect-ratio, nanogram-scale SiN  “trampolines” having quality factors above and ringdown times exceeding five minutes ( mHz linewidth). We measure a thermally limited force noise sensitivity of 16.20.8 aN/Hz at room temperature, with a spring constant (1 N/m) 2-5 orders of magnitude larger than those of competing technologies. We also characterize the suitability of these devices for high-finesse cavity readout and optomechanics applications, finding no evidence of surface or bulk optical losses from the processed nitride in a cavity achieving finesse 40,000. These parameters provide access to a single-photon cooperativity in the resolved-sideband limit, wherein a variety of outstanding optomechanics goals become feasible.

Advances in nanofabrication over the past decades have enabled the growth and patterning of pristine materials, and the creation of mechanical sensors of extraordinary quality Poot2012Mechanical. Cantilevers sensitive to attonewton forces at room temperature have been fabricated from silicon (e.g.  aN/Hz Yasumura2000Quality) and diamond ( aN/Hz Tao2014Single) using “top-down” techniques, while “bottom-up” fabricated devices can in principle achieve below 10 aN/Hz at room temperature (e.g. approaching 5 aN/Hz for silicon nanowires Nichol2008Displacement or carbon nanotubes Jensen2008An), and  zN/Hz at low temperatures (nanotubes Moser2014Nanotube). These complementary approaches carry with them an important trade-off: on one hand, bottom-up techniques can assemble fewer atoms into smaller, more sensitive structures, but the technology is comparatively young, and it is more difficult to incorporate additional structures and/or probes. These low-mass objects also tend to have very low spring constants (i.e. below 10 mN/m), making them highly susceptible to van der Waals “sticking” forces at short distances. On the other hand, top-down devices are currently not as sensitive at low temperature (e.g.  zN/Hz for diamond at 93 mK Tao2014Single), but are reliably fabricated, are compatible with a wide variety of probes, and naturally integrate with other on-chip systems. Some of their remarkable achievements to date include detection of a single electron spin Rugar2004Single, nanoscale clusters of nuclei Degen2009Nanoscale, persistent currents in normal metal rings Castellanos2013Measurement, and the force noise associated with the quantized nature of light Purdy2013Observation. Further, integrating with quantum electronics and / or optical resonators has provided (among other things) access to a regime in which quantum effects play a central role in the mechanical element’s motion OConnell2010Quantum; Teufel2011Sideband; Chan2011Laser; Safavi2012Observation; Purdy2015Optomechanical; Underwood2015Measurement; Meenehan2015Pulsed.

The intrinsic force noise of a mechanical system is ultimately determined by its dissipative coupling to the environment Saulson1990Thermal. In equilibrium, assuming the average energy flow to and from the environment balances such that the equipartition theorem is satisfied, the force noise density experienced by the mechanical system is


where is the temperature of the environment, is the participating (effective) mass of the resonator, is its amplitude ringdown time, and is the Boltzmann constant. Written this way, it is immediately evident that the fundamental thermal noise floor of a mechanical sensor benefits from a small mass and a long ringdown time.

Here we report wafer-scale batch fabrication of high-aspect-ratio, nanogram-scale SiN “trampoline” resonators with ringdown times approaching 6 minutes (1 mHz linewidth) at room temperature. This class of devices, together with Ref. Norte2016Mechanical (submitted simultaneously), consistently achieve an intrinsic force noise below  aN/Hz at room temperature (293 K), and our measured value =16.20.8 aN/Hz is similar to what is in principle possible using a single layer of graphene Kumar2015Ultrasensitive. Furthermore, this low noise is accompanied by spring constants  N/m that are - orders of magnitude higher than those of competing devices Poot2012Mechanical; Yasumura2000Quality; Nichol2008Displacement; Tao2014Single; Jensen2008An; Kumar2015Ultrasensitive, and the 100100 surface area is compatible with the incorporation of additional structures Norte2016Mechanical. We also demonstrate their suitability for sensitive interferometric readout and optomechanics applications by positioning an extended membrane (fabricated by the same means) within an optical cavity of finesse , finding no evidence of additional bulk or surface optical losses from the processed nitride at telecom wavelengths (1550 nm), consistent with literature Wilson2009Cavity; Sankey2010Strong. In fact, for certain membrane positions, the cavity finesse is increased to , as expected for a lossless dielectric slab in a single-port cavity. Finally, to set an approximate upper bound on the size of the cavity field required for high-finesse applications, we position a trampoline in a cavity field wide enough that of the light falls outside the structure. Consistent with recent simulations Chang2012Ultrahigh, we find that the majority of this “clipped” light is in many cases recovered by the cavity.

I Mechanical Properties

Figure 1: Fabricated SiN “trampoline” resonators. (a) Optical image of the released structure with a window size of  mm (upper) and a schematic of its KOH-etched cross-section (lower). Right-hand images show (i) an optical image of the -wide central pad, (ii) a scanning electron microscope (SEM) image of the --wide tether (near the pad), and (iii) an SEM image of the 4.6--wide overhanging nitride. Left from the overhang is the angled, KOH-etched silicon substrate showing typical roughness and residues. (b) Optical image of devices inside the ultrahigh vacuum (UHV) fiber interferometer.

Drawing inspiration from similar structures having embedded Bragg mirrors Groblacher2009Demonstration; Kleckner2011Optomechanical and high- nitride strings Verbridge2006High, we pattern single-layer resonators suitable for a “membrane-in-the-middle” Thompson2008Strong optomechanical geometry. Figure 1(a) shows a typical structure, comprising (i) an 80-nm-thick, 100--wide central pad suspended by (ii) 2.1--wide tethers. These devices are suspended from a 675--thick, (single-side-polished) silicon wafer, upon which 100 nm of stoichiometric SiN was commercially deposited via low-pressure chemical vapor deposition.111Note SiN -coated wafers purchased from University Wafer and Addison Engineering produce similar results. Nitride on silicon appears blue, and suspended nitride appears yellow. The filleted shapes Verbridge2006High of the central nitride pad and corner clamping points ensure that all suspended structures are held flat by the nitride’s internal stress (nominally GPa), and that regions of concentrated strain in the structure’s normal modes are minimized. The fillets are nominally circular; on the central pad their radius defines the pad diameter and the corner fillets are defined to have a quarter of this radius, to reduce their relative mass. The tethers are long ( mm) to simultaneously increase the mechanical quality factor Schmid2011Damping and decrease the mechanical frequency , thereby maximizing without contributing too much mass. The cross section of the wafer (lower image of Fig. 1(a), also faintly visible from above) results from the minimum anisotropic KOH etch required to cut a clear-shot window through the silicon. This choice minimizes the region of overhanging nitride (iii), a known source of mechanical dissipation Ni2012Enhancement; Schmid2011Damping. The angle of the undercut silicon associated with this etch technique also serves to further increase the rigidity of the supporting frame at the clamping points. Additional fabrication details can be found in Appendix I.

We characterize the structure’s mechanical resonances using a fiber interferometer at a vacuum below torr (see Fig. 1(b)). Laser light is directed along a fiber toward a cleaved tip (positioned within 100 of the trampoline), and the interference between reflections from the cleave and trampoline records the instantaneous displacement. A piezo actuator attached to the stage is used to exert an oscillatory mechanical drive.

Figure 2: Mechanical modes of a trampoline having lateral dimensions of Fig. 1 and thickness 80 nm, measured with a fiber interferometer operating at wavelength 1550 nm and power 220 . (a) Approximate response to piezo drive, showing first nine resonances (thin blue line). Pink line shows the response of the Si frame. Simulated resonance frequencies (dashed gray lines) agree to within of measured values with SiN parameters density 2700 kg/m, Young’s modulus 250 GPa, Poisson ratio 0.23, and internal stress GPa. Inset shows a “typical” ringdown for the fundamental (“symmetric” ) mode with fit (red curve) having functional form , where , , and are allowed to float. Black line shows the ringdown extrapolated from the early data, and gray dashed line shows (run-to-run variation by a factor of ). The ringdown time s (error represents statistical fluctuations of multiple measurements) corresponds to a room temperature force noise aN/Hz. (b) Simulated displacement profiles for the “symmetric” (), “torsional” () and “antisymmetric” () modes labeled in (a). (c) Measured frequency (kHz), simulated frequency (kHz), ringdown time (s), quality factor , mass (ng), spring constant (N/m) and force noise (aN/Hz) for the first 9 modes. The mass has a 10% systematic error due to uncertainty in the thickness and density of the nitride.

Figure 2(a) shows the amplitude of driven oscillations as a function of frequency for the fiber positioned over the nitride pad (blue) and silicon frame (pink). Both curves contain many peaks, and several very strong resonances (labeled) emerge whenever the tip is positioned over the pad. There are a few ways to convincingly identify these as trampoline modes, aside from noting their large response. First, they uniformly exhibit significantly larger quality factors (measured by ringdown; see below), whereas supporting frame resonances exhibit low-amplitude peaks of . Second, we compare the observed frequencies with those predicted by a finite-element simulation (COMSOL) of our geometry. We simulate the volume of the released nitride in the thin membrane limit, and apply perfectly-clamped boundary conditions along the outer edges of the overhanging nitride. The nitride itself is modeled using the material parameters listed in the caption, and we set its internal stress to

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