Efficient electrothermal actuation of multiple modes of high-frequency nanoelectromechanical resonators

Abstract

The authors observed resonances from multiple vibrational modes of individual silicon-carbide-based nanomechanical resonators, covering a broad frequency range from several megahertz to over a gigahertz. The devices are actuated thermoelastically in vacuum at room temperature using localized Joule heating in a device-integrated metal loop. Their motion is detected piezoresistively using signal downmixing in a similarly integrated metal piezoresistor. The frequencies and amplitudes of the observed resonant peaks are in good agreement with the results from theoretical modeling and finite-element simulations. techniques provide a way to actuate and detect motion simultaneously. There are also stand-alone methods for both actuation, such as thermoelastic 8 and piezoshaker 9,10 actuation; and detection, such as piezoresistive 9-11 and optical, 3,8 as well as detection techniques based on motional changes in the electronic properties of single electron transistors 4,12 and nanotubes.13 Each of these techniques has advantages as well as limitations. For example, the magnetomotive technique typically requires large magnetic fields, whereas optical techniques require careful alignment of optical components.For the experiments reported here, we combine piezoresistive downmixing detection, developed earlier in Ref. 9, with thermoelastic actuation due to localized Joule heating of a metallic resistor. Figure 1͑a͒ shows one of the doubly clamped beam resonators used in the experiments. The beams were made from a single-crystal silicon carbon ͑3C-SiC͒ thin film by multiple aligned steps of e-beam lithography, thin film evaporation, lift-off, and reactive plasma etching.14 They had nominal lengths between 4 and 24 m, a width of 400 nm, and a thickness of 80 nm. Two different thin metal film loops were patterned near the two ends of the beam. The 80-nm-thick, 100-nm-wide loop was patterned from thermally evaporated gold and formed a part of the thermoelastic bilayer actuator ͓right inset of Fig. 1͑a͔͒. The thinner piezoresistor loop was patterned from a 30-nm-thick metal layer created by evaporating a 60%-40% gold palladium alloy ͓left inset of Fig. 1͑a͔͒. It consisted of 250-nm-long, 50-nm-wide legs connected by a larger pad ͓left inset of Fig. 1͑a͔͒. A 2-nm-thick chromium adhesion layer was used in both cases. Typical resistances of metal loops were 30 ⍀ for the actuation loop and 300 ⍀ for the detection loop.Thermoelastic actuation of bilayer structures has long been employed, for example, in thermostats, 15 and relies on the fact that the coefficient of linear thermal expansion varies for different materials. For gold and silicon carbide, ␣ Au Ϸ 12ϫ 10 −6 K −1 and ␣ SiC Ϸ 4.8ϫ 10 −6 K −1 , respectively. Local heating of the gold actuation loop in our devices therefore results in nonuniform expansion and thermal stresses that tend to flex the beam toward the substrate. If the temperature changes periodically at the resonance frequency of one of the mechanical modes of the resonator, the amplitude of deflection will be greatl...

In-plane nanoelectromechanical resonators based on silicon nanowire piezoresistive detection

“…This value is larger than data reported previously (see [1,10] for example). To measure the noise, we followed the technique described in [18]. There was no external drive, and only a bias voltage was applied to the gauges.…”

High-sensitivity linear piezoresistive transduction for nanomechanical beam resonators

“…The small amplitude of the mechanical vibrations, in combination with their very high frequency and the natural tendency of high-aspect ratio beams to operate in a nonlinear regime, represents formidable obstacles for such purpose 11,12 . The application of the most sensitive transduction schemes reported so far for nanomechanical resonators, such as piezoelectric 13 , electrothermal 14 or optomechanical 15 , results either impossible or impractical for simple beams made of silicon with dimensions deep down in the nanoscale and resonant frequencies in the very high-frequency range.…”

Ultimate and practical limits of fluid-based mass detection with suspended microchannel resonators

“…As mentioned, a practical and currently achievable implementation for integrated actuation and transduction can be realized using thin metal film resistors for both thermoelastic actuation 26 and piezoresistive detection. 27 For the latter, we will assume gold film piezoresistors with thickness 50 nm, length 1 m, and width 100 nm are employed.…”

“…As usual, Q represents the device quality factor; ␣ is the thermal coefficient of linear expansion for the metallic ͑gold͒ actuator; ⌬T the temperature rise within the metallic actuator, which has been shown by numerical simulations to be roughly uniform for excitation frequencies below the inverse thermal time constant of the drive loop; 39 E actuator and E device are the Young's moduli for the actuator and device, respectively; and V actuator and V device are the respective volumes. 26 As the actuation efficiency is strongly dependent on the actuator's volume relative to the total device volume, we assume a somewhat thicker ͑80 nm͒ gold film is used compared to that of the piezoresistor. This increased thickness also provides efficient cooling, allowing the device to operate at higher frequencies.…”

“…Such large-scale integration is perhaps most easily achieved by employing integrated, "on-chip" electrical actuation and detection of the device resonant motion. To be concrete in our analyses here, we consider electrothermal actuation 26 and metallic piezoresistive detection, 27 which have been used to realize the first 200-mm-scale "standard NEMS process." 28 The practical limits considered here include, for displacement transduction, the additional electrical-domain Johnson noise arising from the metallic piezoresistor, and, for actuation, the maximum amplitude attainable with electrothermal actuation set by practical constraints, such as the level of steady-state device heating deemed tolerable.…”