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High-Q, in-plane modes of nanomechanical resonators operated in air

Philip S. Waggoner, Christine P. Tan, Leon M. Bellan, and Harold G. Craighead


We have fabricated 90 nm thick mechanical resonators, studied the resonance spectrum as a function of pressure, and found that some higher order resonant modes feature quality factors on the order of 2000 at atmospheric pressure, namely two symmetric, in-plane resonant modes. Even after deposition of a relatively thick polymer layer, the quality factor of the in plane mode in air only decreased slightly, suggesting that functional sensing layers can be used with devices operated in air. These encouraging results open the door for resonant micro- and nanoelectromechanical systems to biosensor and chemical sensor applications at atmospheric pressure.

Research Summary

Figure 1: SEM micrograph of the trampoline resonators, with 10 μm scale bar.

Viscous damping is perhaps the greatest limitation on the applicability of nanomechanical resonant sensors, typically reducing device quality factors by several orders of magnitude when operated in air or liquid as compared to vacuum [1]. In addition to degraded sensitivity due to lower quality factors, the viscous media also effectively adds mass to the sensors, shifting the resonant frequency and further decreasing sensitivity to added mass. In order to achieve real-time, ambient sensing of biological and chemical analytes, a solution to these problems must be achieved.

Device fabrication and experimental methods are described elsewhere [2]. Briefly, the resonators were made from a 90 nm thick film of low stress silicon nitride that was deposited on a thermally oxidized silicon wafer, with an oxide thickness of ~1.8 μm. The trampoline-shaped resonators were defined using photolithography and an anisotropic CF4 plasma etch. Devices were released from the substrate using a timed etch in hydrofluoric acid to remove the sacrificial layer of SiO2. An SEM micrograph of an array of resonators is shown in Fig. 1. Device resonances were excited using an external piezoelectric element and detected interferometrically.

Figure 2: In-plane resonant modes excited locally with a modulated laser focused on each support arm, demonstrating that these peaks correspond to side-to-side resonance.

Finite element analysis predicted two symmetric in-plane modes for these resonators to occur at 41.5 MHz, but experimentally these modes were found at 35 and 35.5 MHz, with splitting likely due to fabrication variability that breaks the degeneracy. In order to confirm that these resonances corresponded to the in-plane mode, a second, modulated laser was used to excite resonance locally using each support arm of the trampoline through thermal expansion stresses. As shown in Fig. 2, exciting the top and bottom or the left and right arms produced one of the two peaks, proving that these two resonances were in fact the in-plane modes because of the directional dependence of the excitation.

The quality factors of several modes were monitored as a function of pressure, and are shown in Fig. 3. While all modes decrease as atmospheric pressure is approached, the in-plane modes have the highest Q in air, roughly 2200. In order to test the ability of these devices to be used as sensors at high pressures, a 9 nm thick model sensing layer, 4-tert-butyl-calix(6)arene, was thermally evaporated on the resonators. Even after deposition, the quality factor of the in-plane modes remained on the order of 2000 at 30 Torr, as shown in Fig. 4.

These results are promising for biological and chemical sensing applications in air, and suggest that these and similar devices operated in an in-plane mode of resonance would be ideal for retaining high Q and high sensitivity outside of vacuum.

Figure 3: Quality factor of several resonant modes shown as a function of pressure. f(00) is the fundamental, out-of-plane resonant mode.

Figure 4: Quality factor comparisons for the fundamental (out-of-plane) and in-plane modes before and after deposition of a relatively thick (~10% of the resonator) polymer sensing layer.


  1. “Micro- and nanomechanical sensors for environmental, chemical, and biological detection,” Waggoner, PS and Craighead, HG, Lab Chip 7, 1238 (2007).  Abstract
  2. “High-Q, in-plane modes of nanomechanical resonators operated in air,” Waggoner, PS, Tan, CP, Bellan, LM, and Craighead, HG, J. Appl. Phys. 105 (2009) 094315.  Abstract