Surface stress effects on the resonance properties of cantilever sensors

156

153

The authors present a theoretical model to predict the resonance frequency shift due to molecule adsorption on micro-and nanocantilevers. They calculate the frequency shift experienced by cantilevers made of either silicon or the polymer SU-8, when two adsorbates, myosin protein and an alkanethiol, are attached to the cantilever surface. They demonstrate that the effect of the adsorbate stiffness can be comparable or even larger than the mass effect, producing positive frequency shifts. The results provide methods for decoupling both opposite effects and routes for the design of resonators with high sensitivity to molecule adsorption based on either stiffness or mass effects. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2388925͔ Microcantilever resonators have been proposed for highly sensitive label-free detection of organic and biological molecules. [1][2][3] The basic principle is the measurement of the resonance frequency shift due to the added mass of the molecules bound to the cantilever surface. The sensitivity is inversely proportional to the active mass of the resonator. Advances in micro-and nanofabrication techniques have motivated an intense effort for scaling the resonator size down in order to push the detection limits. 2,3 Thus the sensitivity of the technique has rapidly evolved from the picogram to the attogram range, by simply reducing the size of the resonators ͑lengthϫ widthϫ thickness͒ from ͑100-500͒ ϫ ͑20-100͒ ϫ ͑0.5-1͒ to ͑5-20͒ ϫ ͑0.5-2͒ ϫ ͑0.1-0.3͒ m 3 . Consequently, the resonance frequency increases from the kilohertz to the megahertz regime. By further reduction of the size to the nanoscale, the detection limits can achieve unprecedented values. 3 Independently of the cantilever size, the quantification of the adsorbed mass is an issue still not resolved. First, when the molecules are not uniformly adsorbed, the resonance frequency critically depends on the distribution of the molecules on the resonator. 4,5 Second, a discrepancy is, in many cases, found between the added mass calculated by the theory and the mass adsorbed on the cantilever. This discrepancy is generally justified by invoking the effect of the adsorption-induced surface stress on the resonance frequency. 6 In this effect, the surface stress is simplified to an external axial force that creates a shearing moment. Recently, Lu et al. 7 have demonstrated that this model is inadequate to describe the physical system because in the real situation, the cantilever free end allows the deformation to relieve the stress. In their theoretical treatment, a strain-dependent surface stress is necessary to observe some effect on the resonant frequency, and therefore the surface stress effect is expected to be negligible in biomolecular applications.Up to date, the influence of the mechanical properties of the adsorbed molecules on the resonance has been neglected. In this work, we present a theoretical model to study the effect of the stiffness of the molecules bound to a microcantilever on the resonance frequency. We demo...

mentioning

confidence: 99%

Effect of the adsorbate stiffness on the resonance response of microcantilever sensors

Tamayo¹,

Ramos²,

Mertens³

et al. 2006

156

153

“…The total surface stress ͑⌺͒ can be written as a sum of a strain-independent part ͑ ͒ and a strain-dependent part ͑strain ⑀͒, which is related to surface elasticity ͑C s ͒ ⌺ = + C s ⑀. [11][12][13][14][15] In this letter, we study the size-dependency of the Young's modulus in silicon nitride cantilevers when one dimension ͑cantilever thickness͒ is scaled down from 684 to 20 nm. As the SiN x is amorphous, it is difficult to distinguish between the two contributions since parameters ͑e.g., C s ͒ are unknown and difficult to calculate.…”

mentioning

confidence: 99%

Size-dependent effective Young’s modulus of silicon nitride cantilevers

Gavan

Westra

Drift

et al. 2009

131

The effective Young's modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20-684 nm by measuring resonance frequencies from thermal noise spectra. A significant deviation from the bulk value is observed for cantilevers thinner than 150 nm. To explain the observations we have compared the thickness dependence of the effective Young's modulus for the first and second flexural resonance mode and measured the static curvature profiles of the cantilevers. We conclude that surface stress cannot explain the observed behavior. A surface elasticity model fits the experimental data consistently. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3152772͔ Micro-and nanoelectromechanical systems are widely studied for their application in sensing and actuation devices. 1 Down-scaling of such devices improves their sensitivity however at the same time mechanical properties may start to deviate from the bulk behavior. The finite-size effects have been the subject of theoretical studies for the past years. [2][3][4][5][6][7][8] In experimental work on single-crystalline Si cantilevers it has been shown that the Young's modulus strongly depends on the thickness. 9 This behavior has also been observed for suspended crystalline silver nanowires. 10 In describing the properties of nanoscale devices, the bulk Young's modulus ͑E͒ is generally replaced by the effective Young's modulus ͑E eff ͒ to account for size-dependent effects, including surface stress. The total surface stress ͑⌺͒ can be written as a sum of a strain-independent part ͑ ͒ and a strain-dependent part ͑strain ⑀͒, which is related to surface elasticity ͑C s ͒ ⌺ = + C s ⑀. [11][12][13][14][15] In this letter, we study the size-dependency of the Young's modulus in silicon nitride cantilevers when one dimension ͑cantilever thickness͒ is scaled down from 684 to 20 nm. As the SiN x is amorphous, it is difficult to distinguish between the two contributions since parameters ͑e.g., C s ͒ are unknown and difficult to calculate. However, by comparing the experimental data for the first and second mode to theory, we show that the straindependent part of the total surface stress is responsible for the size-dependency.Cantilevers are fabricated from low-pressure chemical vapor deposited ͑LPCVD͒ silicon nitride ͑SiN x ͒ on Si͑100͒ substrates and are patterned with an electron-beam pattern generator. After resist development we use reactive ion etching in a CHF 3 / O 2 ͑20:1͒ plasma to transfer the pattern to the SiN x layer. After this step cantilevers are released using a KOH etch process ͑15 min etching time at 85°C; Si etch rate about 1 m / min͒, yielding facetting along the ͑111͒ planes, as shown in Fig. 1͑a͒. This process introduces a negligible undercut, so that length corrections can be disregarded. 16 Cantilevers are fabricated with the following dimensions: lengths ͑L͒ from 8 to 100 m, widths ͑w͒ 8, 12, or 17 m, and thicknesses ͑h͒ ranging from 20 to 684 nm.The thickness was measured using an ellipsometer ͑Leitz SP͒ with an accuracy of ...

“…5,13 Using Eqs. ͑1͒-͑7͒, tangential stress resultants and tangential stress couples, which are energetically conjugate to ␥ and ͓see Eq.…”

Section: ͑6͒mentioning

confidence: 99%

“…Due to their small size and thus the large surface-to-volume ratio, the surface stress effects have been suggested as the explanation for the size effects. 8 As a consequence, the majority of research concerning the elastic response of nanostructures have focused on surface stress [9][10][11] and surface elasticity 5,12,13 effects. Miller and Shenoy 5 developed a simple model to incorporate surface elasticity in an effective elastic modulus for plates and rods.…”

mentioning

confidence: 99%

Surface stress-induced change in overall elastic behavior and self-bending of ultrathin cantilever plates

Sadeghian

Goosen

Bossche

et al. 2009

In this letter, the dominant role of surface stress and surface elasticity on the overall elastic behavior of ultrathin cantilever plates is studied. A general framework based on two-dimensional plane-stress analysis is presented. Because of either surface reconstruction or molecular adsorption, there exists a surface stress and a surface elasticity imbalance between top and bottom surface of the cantilever. The surface elasticity imbalance creates an extra bending-extensional coupling which has not been taken into account previously. This leads to a modified extensional stiffness, bending stiffness and bending-extensional coupling stiffness. Due to the surface stress imbalance, an extended Stoney's formula for self-bending of ultrathin cantilevers is derived.