Responsivity

Abstract

A change of mass or temperature, or an applied force causes a response of a mechanical resonator. The response can, e.g., be a change in frequency or vibrational amplitude. The responsivity of a mechanical resonator is the linear slope of the response to a particular stimulant. In case of a sensor application, the responsivity to the input parameter to be measured should be maximal. However, the responsivity to other inputs, such as a change in ambient temperature, should be minimal in order not to cause an unwanted cross-response. In this chapter, the responsivities of micro and nanomechanical resonators to mass (distributed and point masses), forces, and temperature are discussed.

Transduction of Single Nanomechanical Pillar Resonators by Scattering of Surface Acoustic Waves

“…This suggests that we measured the compression mode of both pillars, since the eigenfrequency of compression modes is mainly a function of the height of a pillar and not its diameter. 45 These results are in agreement with the FEM simulations discussed above.…”

“…It can be seen from eq that the transmission scattering parameter of the pillar S P includes the normalized frequency response of a single, weakly damped resonator. The maximum absolute value of | S P | is at the pillar’s resonance frequency f res and consequently proportional to | S P ( f res ) | ∝ Q 0 Q rad It becomes clear from eq that the pillar scatters the most when its damping is dominated by radiation losses, as expected. If this is already the case, | S P | and the overall signal strength cannot be further maximized by improving Q rad .…”

Nanoelectromechanical Infrared Spectroscopy with In Situ Separation by Thermal Desorption: NEMS-IR-TD

“…37 It is estimated that the LoD can be improved by at least 1 to 2 orders of magnitude by (i) reducing the tensile stress of the silicon nitride resonators from 100 MPa down to 1 MPa 37,38 and (ii) by implementing a different readout method that does not require metal electrodes that pass over the resonator, which deteriorate the photothermal responsivity. 34 Desorption Dynamics. The dynamic of the desorption process is studied with NEMS-IR-TD by isothermal and dynamic thermogravimetric analysis (TGA) as presented in Figure 4.…”

“…The NEMS-IR-TD setup allows for the simultaneous monitoring of the process by a combination of photothermal IR spectroscopy, shown in Figure 3 (a,b), and thermogravimetric analysis, shown in Figure 3 (c,d). Assuming an approximately homogeneous mass distribution on the resonator surface, the additional loaded mass of caffeine and theobromine can be calculated from the recorded resonance frequency 34 ( eq 1 ). Due to the chip being cooled below room temperature for the caffeine measurements, residual contaminants present in the measurement chamber start to adsorb on the resonators’ surface while caffeine is desorbing.…”

“…386529) following a protocol from Szkop et al 33 Sample Mass Calculation. For small changes, the response to mass can be linearized by a first-order Taylor expansion, given by R = −1/(2m_r), 34 where m_r corresponds to the resonator mass. However, in this work several nanograms of analyte were sampled, which is within the range of the resonator mass itself.…”