Signal-to-noise ratio of resonant microcantilever type chemical sensors as a function of resonant frequency and quality factor

Fadel, Ludivine; Dufour, Isabelle; Lochon, Frdédéric; Français, Olivier

doi:10.1016/j.snb.2003.10.016

Cited by 32 publications

(25 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, for a given amplifier, the frequency noise is essentially due to the variation of the amplifier phase . According to the Barkhausen condition, which is satisfied in all oscillators, the frequency noise, , can be expressed with a first-order limited development (small phase variations) (18) The expression of the phase of the micromechanical resonator near the resonant frequency allows one to obtain the expression of the oscillator stability, , as a function of the resonant frequency and quality factor [25] ( 19) As in the case of intrinsic noise, the frequency fluctuation can be used to relate the LOD to : Expression (20) may be used to determine the optimum sensitive coating thickness for minimum LOD. The case of a PIB coating on a silicon microcantilever m m m is presented in Fig.…”

Section: Oscillator Configurationmentioning

confidence: 99%

Effect of Coating Viscoelasticity on Quality Factor and Limit of Detection of Microcantilever Chemical Sensors

et al. 2007

Self Cite

View full text Add to dashboard Cite

Abstract-Microcantilevers with polymer coatings hold great promise as resonant chemical sensors. It is known that the sensitivity of the coated cantilever increases with coating thickness; however, increasing this thickness also results in an increase of the frequency noise due to a decrease of the quality factor. By taking into account only the losses associated with the silicon beam and the surrounding medium, the decrease of the quality factor cannot be explained. In this paper, an analytical expression is obtained for the quality factor, which accounts for viscoelastic losses in the coating. This expression explains the observed decrease of the quality factor with increasing polymer thickness. This result is then used to demonstrate that an optimum coating thickness exists that will maximize the signal-to-noise ratio and, thus, minimize the sensor limit of detection.

show abstract

Section: Oscillator Configurationmentioning

confidence: 99%

Effect of Coating Viscoelasticity on Quality Factor and Limit of Detection of Microcantilever Chemical Sensors

et al. 2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…1). Chemical detection using microcantilever-based sensors is based on the measurement of the resonant frequency shift Δf, which is induced by the mass increase of the vibrating microstructure during sorption of the target species into the sensitive coating [6]:…”

Section: Introductionmentioning

confidence: 99%

“…According to the partition coefficient (K) of the analyte/sensitive coating pair [6], which is defined as the ratio of the concentration of the analyte in the coating and the ambient concentration, CA, of the analyte in the surrounding medium, the mass variation Δm is proportional to the concentration CA. Thus, the sensitivity of the chemical sensor, S, is proportional to the resonant frequency of the microcantilever in the surrounding medium (gas or liquid) [6]:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of hydrodynamic force on microcantilever vibrations: Applications to liquid-phase chemical sensing

Dufour

Lemaire

Caillard

et al. 2014

Sensors and Actuators B: Chemical

View full text Add to dashboard Cite

Abstract:At the microscale, cantilever vibrations depend not only on the microstructure's properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever's vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include inplane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no insitu measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range.

show abstract

“…This decrease in the quality factor increases the frequency noise (which is proportional to f res /Q when operating in an oscillator configuration 40,67,68 ), thus increasing the limit of detection (LOD) in biochemical sensing applications. The quality factor is defined as 2p times the ratio of the maximum energy stored in a resonating system to the amount of energy dissipated in one cycle.…”

Section: Quality Factormentioning

confidence: 99%

Characteristics of laterally vibrating resonant microcantilevers in viscous liquid media

Cox

Josse

Heinrich

et al. 2012

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

The characteristics of microcantilevers vibrating laterally in viscous liquid media are investigated and compared to those of similar microcantilevers vibrating in the out-of-plane direction. The hydrodynamic loading on the vibrating beam is first determined using a numerical model. A semi-analytical expression for the hydrodynamic forces in terms of the Reynolds number and the aspect ratio (beam thickness over beam width) is obtained by introducing a correction factor to Stokes' solution for a vibrating plate of infinite area to account for the effects of the thickness. The results enable the effects of fluid damping and effective fluid mass on the resonant frequency and the quality factor (Q) to be investigated as a function of both the beam's geometry and liquid medium's properties and compared to experimentally determined values given in the literature. The resonant frequency and Q are found to be higher for laterally vibrating microcantilevers compared to those of similar geometry experiencing transverse (out-of-plane) vibration. Compared to transversely vibrating beams, the resonant frequency of laterally vibrating beams is shown to decrease at a slower rate (with respect to changes in viscosity) in media having higher viscosities than water. The theoretical results are compared to experimental data obtained for cantilevers completely immersed in solutions of varying aqueous percent glycerol. The increases in resonant frequency and Q are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.

show abstract

Signal-to-noise ratio of resonant microcantilever type chemical sensors as a function of resonant frequency and quality factor

Cited by 32 publications

References 24 publications

Effect of Coating Viscoelasticity on Quality Factor and Limit of Detection of Microcantilever Chemical Sensors

Effect of Coating Viscoelasticity on Quality Factor and Limit of Detection of Microcantilever Chemical Sensors

Effect of hydrodynamic force on microcantilever vibrations: Applications to liquid-phase chemical sensing

Characteristics of laterally vibrating resonant microcantilevers in viscous liquid media

Contact Info

Product

Resources

About