Nanomechanical resonators can now be realized that achieve fundamental resonance frequencies exceeding 1 GHz, with quality factors ͑Q͒ in the range 10 3 рQр10 5 . The minuscule active masses of these devices, in conjunction with their high Qs, translate into unprecedented inertial mass sensitivities. This makes them natural candidates for a variety of mass sensing applications. Here we evaluate the ultimate mass sensitivity limits for nanomechanical resonators operating in vacuo that are imposed by a number of fundamental physical noise processes. Our analyses indicate that nanomechanical resonators offer immense potential for mass sensing-ultimately with resolution at the level of individual molecules.
Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.
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We describe a broadband radio frequency balanced bridge technique for electronic detection of displacement in nanoelectromechanical systems ͑NEMS͒. With its two-port actuation-detection configuration, this approach generates a background-nulled electromotive force in a dc magnetic field that is proportional to the displacement of the NEMS resonator. We demonstrate the effectiveness of the technique by detecting small impedance changes originating from NEMS electromechanical resonances that are accompanied by large static background impedances at very high frequencies. This technique allows the study of important experimental systems such as doped semiconductor NEMS and may provide benefits to other high frequency displacement transduction circuits. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1507833͔The recent efforts to scale microelectromechanical systems ͑MEMS͒ down to the submicron domain 1 have opened up an active research field. The resulting nanoelectromechanical systems ͑NEMS͒ with fundamental mechanical resonance frequencies reaching into the microwave bands are suitable for a number of important technological applications. Experimentally, they offer potential for accessing interesting phonon mediated processes and the quantum behavior of mesoscopic mechanical systems. Among the most needed elements for developing NEMS based technologies-as well as for accessing interesting experimental regimes-are broadband, on-chip transduction methods sensitive to subnanometer displacements. While displacement detection at the scale of MEMS has been successfully realized using magnetic, 2 electrostatic 3,4 and piezoresistive 5 transducers through electronic coupling, most of these techniques become insensitive at the submicron scales. Moreover, the attractive electronic two-port actuation-detection configuration of most MEMS devices becomes hard to realize at the scale of NEMS, due to the unavoidable stray couplings encountered with the reduced dimensions of NEMS. An on-chip displacement transduction scheme that scales well into the NEMS domain and offers direct electronic coupling to the NEMS displacement is magnetomotive detection. 6,7 Magnetomotive reflection measurements as shown schematically 8 in Fig. 1͑a͒ have been used extensively. 6,7,9 Here, the NEMS resonator is modeled as a parallel RLC network with a mechanical impedance, Z m (), a two-terminal dc coupling resistance, R e , and mechanical resonance frequency, 0 . When driven at by a source with impedance R s , the voltage on the load, R L , can be approximated asHere, R L ϭR S ϭ50 ⍀. We have made the approximation that R e ӷ͉Z m ()͉, as is the case in most experimental systems. Apparently, the measured electromotive force ͑EMF͒ due to the NEMS displacement proportional to Z m () is embedded in a background close to the drive voltage amplitude, ͉V o ͉ ϳ͉V in ͉Ϫ20 log R e /(R L ϩR e ) dB. 10 This facilitates the definition of a useful parameter at ϭ 0 , the detection efficiency, S/B, as the ratio of the signal voltage to the background. For the r...
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