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This study proposes a new microcantilever design with a rectangular hole at the fixed end of the cantilever that is more sensitive than conventional ones. A commercial finite element analysis software ANSYS is used to analyze it. The Stoney equation is first used to calculate the surface stress induced moment, and then applied to the microcantilever free end to produce deflection. The stress analysis of the proposed and conventional designs is performed, followed by dynamic analysis of the proposed design. We found that the Sader equation is more accurate than Stoney in predicting cantilever deflections, and that for increasing the sensitivity of a microcantilever biosensor increasing the cantilever thickness is more practical.

Biosensors are electronic devices that convert biomolecular interactions into a measurable signal. The purpose of a biosensor is to detect and analyze the unknown biological elements present in a medium. Biosensors have two main elements, a bioreceptor and a transducer. Bioreceptors are target-specific and known biomolecules that combine with the target analyte molecules, and generate a unique signal during the reaction. For sensing purpose one surface of the biosensor is functionalized by depositing a sensing layer of known bioreceptor molecules onto it. This biosensitive layer either contains the bioreceptors or the bioreceptors are covalently bonded to it. The most common types of bioreceptors used in biosensing are based on proteins, antibody/antigen or nucleic acid interactions. The transducer element of the biosensor converts the biomolecular reactions between the target and bioreceptor molecules into a measurable signal. The signals can be measured using appropriate detection techniques like electrochemical, optical or mechanical. In biosensing applications sample preparation and molecular labelling of the target analyte is a basic requirement. Labelling aids in easy detection and monitoring of the biomolecules and bioreactions progress. Radioactive and fluorescent dye based labelling agents are commonly used in biosensors. Labelling is however an expensive and time consuming process. Therefore, label-free detection technique is critical in developing rapid, economic and user-friendly biosensors and bioanalytical kits.

The ability of label-free detection, scalability to allow massive parallelization, and sensitivity of the detection range applicable to

Although generally used in topological investigations of surfaces such as in the atomic force microscopy (AFM), arrays of microcantilevers are attracting much interest as biosensors in label-free, rapid, and realtime assaying of biomolecules. Microcantilevers are being used in a variety of sensing and diagnostic applications. Sander

Cantilever array biosensors use optical detection technique to measure the surface-stress induced deflections in a microcantilever. When the target molecules attach to their functionalized surface, the surface stress distribution on the surface is changed causing deflections in the cantilever (

With the ability of label-free detection and scalability to allow massive parallelization already realized by microcantilever biosensors, the next challenge in cantilever biosensor development lies is achieving the sensitivity in detection range applicable to ^{-4} to 10^{-15} mol/L. The detection of analytes in such large dynamic range requires an extremely sensitive cantilever. This study proposes and analyses a new high sensitive cantilever design that can assay analytes in extremely low concentrations. A commercial finite element analysis software ANSYS is used to analyze and compare the conventional and the proposed microcantilever designs.

The Stoney equation [^{2}, whereas for surface stress it is N/m. For modelling purposes the surface stress induced deflection in a substrate is often compared to a concentrated moment induced deflection in a thin plate.

Applying the Stoney equation assumption that the surface stress bends the plate with uniform curvature, into the concentrated moment induced plate bending the following curvature relation for plate bending can be given as:
_{0}^{3}/12, where

This relation shows that the moment is directly proportional to the induced surface stress and the geometric properties of the plate. Moreover, it does not depend on the material properties of the plate. The governing differential equation for an isotropic, thin plates expressing the bending and twisting moments in terms of the curvature and the deflection is given as [^{3}/12(1^{2}) is the flexural rigidity of the plate. In these equations, the moments are expressed in moment per unit length. Assuming _{x}_{y}_{0}_{xy}

^{-8} Nm/m, calculated from

This study used the microcantilever properties and the experimental data reported in Arntz ^{-1}(∼2.5 μM) myoglobin protein onto the functionalized surface of the silicon microcantilever, which generated a maximum deflection of 0.89 μm at the free end. The cantilever size was 500×100×0.5 μm, and the elastic modulus and Poisson ratio was 130 GPA and 0.28, respectively. The deflections predicted by Stoney equation and the Sader formula can be calculated straightforwardly. In Sader formula (

^{-8} Nm/m applied at the free end of the microcantilever deflections of 0.93 μm and 1.62 μm are produced in the conventional and the proposed designs, respectively. In other words, the deflection in the proposed design is about 75% more than that in the conventional design. Since the sensitivity of a microcantilever biosensor strongly depends on its efficient transformation of biomolecular interactions into the deflection, higher deflection produced in the cantilever indicate higher sensitivity of the biosensor. Based on this comparison we can say that the new design is about 75% more sensitive than the old one. In the figure since the deflection is negligible compared to the overall dimensions of the cantilever, deflection is indistinguishable in the plot. Therefore, for clear representation the deflections shown in

The sharp corners in the proposed microcantilever however can raise the stress concentration factors by many folds. Although in theory the ultimate strength of silicon is very high, but in practice it is of the order of 300 MPa, because of the sharp corners introduced by anisotropic etching [

From the Stoney equation it is clear that for a given surface stress the induced deflection and hence the sensitivity of a cantilever sensor can be increased by either changing the cantilever material or the cantilever geometry. In other words, the equation suggests that by using a cantilever of low elastic modulus material, the deflection can be increased. Since the amount of deflection produced in a microcantilever is linearly proportional to the target analyte solution concentration, higher deflection is an indicator of higher sensitivity. Zhang and Xu [

In biological sensor applications the microcantilevers are usually coated with thin film of gold. The gold film helps formation of monolayer of bioreceptors onto it during functionalization. The film also acts as a reflecting medium during optical readout. Since the thermal conductivity of the gold film is much higher than the silicon or polymer cantilever substrate, thermal stresses are generated which produce bimetallic effects. Investigating the bimetallic effects by depositing a 20 nm thick gold layer on a 1 μm thick silicon substrate cantilever, Ramos

We can also reduce bimetallic effects by increasing the flexural stiffness of the cantilever by increasing its thickness. Owing to its well developed fabrication technologies and excellent structural integrity silicon is the most commonly used material for cantilever biosensors. The sensitivity of silicon cantilever however remains deficient compared to the polymer cantilevers, mainly because of its high stiffness. Therefore, to improve the sensitivity of silicon cantilevers changing the size or shape of the cantilever is another option, and this study investigated both.

The Stoney equation suggests that for a given surface stress the deflection induced in the cantilever is directly proportional to the cantilever length and inversely proportional to its thickness. In other words, by increasing the cantilever length and/or reducing its thickness the deflection can be increased. The advantages of increase in length are two folds. First it helps in inducing higher deflection as suggested by

To perform this exercise a deflection contour based on

From the

The dynamic analysis of microcantilevers used in biosensors is necessary to predict its accurate deflections induced solely by the surface-stress. In practical applications there can by thermal induced, flow-induced excitations that can interfere with and hence produce noise in deflection signals. To prevent noise, a cantilever should have high natural resonance frequency. The fundamental resonance frequency of a rectangular cantilever beam is given as:
_{0, proposed}_{0,conventional}

As suggested by

For

Microcantilever array biosensors are becoming increasingly popular in label-free, realtime and simultaneous detection and monitoring of various chemical and biochemical target analytes. The deflections in microcantilever biosensors lie between few tens to few hundreds of a nanometre, which necessitate sophisticated and expensive readout techniques. The ultimate goal of the microcantilever biosensor design and development is to make them sensitive enough to be used in _{0, proposed}_{0, conventional}

This study was supported by Inha University.

Working principle of a microcantilever biosensor. Functionalization of the biosensor by depositing bioreceptors (left). Surface stress induces deflection (right). Symbols

Modelling the surface stress induced curvature in a microcantilever by equating to a concentrated moment induced curvature. The concentrated moment and the surface stress are related as _{0}

Geometric models of the conventional (upper) and the proposed (lower) microcantilever designs. The material properties and the thickness of them are identical.

Maximum deflections produced in the conventional (upper) and the proposed (lower) designs. The deformed finite element model is shown in blue. For illustration the deflections are displayed scaled up 10-fold.

Von Mises stress distribution in the conventional (upper) and the proposed (lower) designs.

Stoney equation based normalized deflection contour showing relation between the deflection and the length and thickness for a conventional cantilever.

A comparison between old (left) and new (right) microcantilever array biosensors.

Comparison between experimental and analysis results.

0.05 | 0.89 | 0.93 | 0.83 0.86 |