Double-Side-Coated Nanomechanical Membrane ... - ACS Publications

Jun 6, 2013 - World Premier International (WPI) Research Center, International Center for Materials ... Copyright © 2013 American Chemical Society. *...
0 downloads 0 Views 2MB Size
Article pubs.acs.org/Langmuir

Double-Side-Coated Nanomechanical Membrane-Type Surface Stress Sensor (MSS) for One-Chip−One-Channel Setup Genki Yoshikawa,*,† Frederic Loizeau,‡ Cory J. Y. Lee,†,§ Terunobu Akiyama,‡ Kota Shiba,† Sebastian Gautsch,‡ Tomonobu Nakayama,† Peter Vettiger,‡ Nico F. de Rooij,‡ and Masakazu Aono† †

World Premier International (WPI) Research Center, International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ‡ Institute of Microengineering (IMT), Ecole Polytechnique Fédérale de Lausanne (EPFL), Jaquet-Droz 1, Neuchâtel CH-2002, Switzerland § University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada ABSTRACT: With their capability for real-time and label-free detection of targets ranging from gases to biological molecules, nanomechanical sensors are expected to contribute to various fields, such as medicine, security, and environmental science. For practical applications, one of the major issues of nanomechanical sensors is the difficulty of coating receptor layers on their surfaces to which target molecules adsorb or react. To have measurable deflection, a single-side coating is commonly applied to cantilever-type geometry, and it requires specific methods or protocols, such as inkjet spotting or gold− thiol chemistry. If we can apply a double-side coating to nanomechanical sensors, it allows almost any kind of coating technique including dip coating methods, making nanomechanical sensors more useful with better user experiences. Here we address the feasibility of the double-side coating on nanomechanical sensors demonstrated by a membrane-type surface stress sensor (MSS) and verify its working principle by both finite element analysis (FEA) and experiments. In addition, simple hand-operated dip coating is demonstrated as a proof of concept, achieving practical receptor layers without any complex instrumentation. Because the double-side coating is compatible with batch protocols such as dip coating, double-side-coated MSS represents a new paradigm of one-chip−one-channel (channels on a chip are all coated with the same receptor layers) shifting from the conventional one-chip−multiple-channel (channels on a chip are coated with different receptor layers) paradigm.



INTRODUCTION Nanomechanical sensors1−3 can detect almost any kind of molecule ranging from gases to biological molecules because their transduction mechanisms basically rely on the fundamental properties of molecules, such as volume and mass in socalled static and dynamic modes, respectively. With their capability of real-time and label-free measurements, they are expected to contribute to various fields such as medicine, security, and environmental science.4−10 Toward practical applications, one of the major issues with nanomechanical sensors is the difficulty in coating receptor layers on their surfaces where target molecules adsorb or react. In the case of static mode operation based on the analyteinduced surface stress, a single-side coating is commonly applied to cantilever-type geometry to produce deflection, which is measured by either optical or electrical methods as the signal from the sensors. In this case, however, the coating methods and protocols are restricted to a few specific ones, such as inkjet spotting11 or thiol chemistry with a single-sidecoated gold layer.12 With such specific methods or protocols, most of the standard coating procedures cannot be applied because those procedures usually include the incubation of the © XXXX American Chemical Society

substrate in a solution for several hours. In addition, the singleside coating also requires the passivation of the opposite surface to avoid nonspecific binding, which results in difficulties in analyzing the observed deflection signal. Double-side coating is a simple method to circumvent these problems. Although the double-side coating can be effectively utilized in the case of dynamic mode operation,13 it is difficult to read out in the case of the static mode by the common optical (laser) method because the double-side coating leads to an in-plane elongation as illustrated in Figure 1. Alternatively, piezoresistive read-out is an effective method for the measurement of in-plane elongation, more specifically, in-plane stress induced by the surface stresses on both the top and bottom sides of a sensing structure. A few studies reported that piezoresistive cantilevers with specific structures and piezoresistors can achieve better sensitivity via the double-side Special Issue: Interfacial Nanoarchitectonics Received: November 24, 2012 Revised: May 31, 2013

A

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX

Langmuir

Article

Figure 1. Schematic side views of (a, b) optical and (c, d) piezoresistive cantilevers and (e, f) an MSS with single- and double-side coatings, respectively. The top view of MSS is shown in Figure 2. (Dark- and light-gray parts) Bulk and thin silicon parts, respectively. (Yellow parts) Constricted bridges that suspend the center membrane in MSS. (Red parts) Piezoresistors integrated into the piezoresistive cantilevers and constricted bridges of MSS. (Green layers, circles, and arrows) Receptor layers, analytes adsorbed on the surfaces, and the surface stresses induced by the analytes, respectively, where detectable analytes are colored with red lines around the green circles. (Red arrows) Measurable signals: (a) deflection, (c) local bending/in-plane stresses, (d) local in-plane stress, (e) amplified total bending/in-plane stresses, and (f) amplified total in-plane stress. Note that piezoresistive signals depend on various factors including the crystal orientation, type of dopants, and direction of current flow. In the case of MSS, p-type Si(100) is used as a piezoresistor with current flowing in the [110] direction. Note that the dimensions and deformations of each part are exaggerated.

Figure 2. FEA of the distribution of ΔR/R in the middle plane (150 nm below the top surface) of the piezoresistors, which have a doping depth of 300 nm from the top surface. A surface stress of −3.0 N/m is applied uniformly on (a) the top surface and (b) on both the top and bottom surfaces of the center circular membranes. The dimensions of each part in direction x × y × z are as follows: center membrane, (ϕ500) × 2.5 μm3; sensing beams for R1 and R3, 10 × 16 × 2.5 μm3; and sensing beams for R2 and R4: 26 × 10 × 2.5 μm3. All of the sensing beams are covered with passivation layers: SiO2 (80 nm) and Si3N4 (80 nm).17

coating.14,15 In the case of cantilever geometry, however, a piezoresistor can detect only a local stress that is induced at the place where the piezoresistor is located as shown in Figure 1c,d. Another problem arises for measuring isotropic surface stress with a piezoresistive cantilever made of commonly used p-type single-crystal silicon with the (100) surface because its relative resistance change is proportional to the difference between the stresses in the [110] and [11̅0] directions, resulting in virtually zero signal except for the limited area close to the clamped end.16,17 One can design a larger piezoresistor by means of ntype doping along the entire cantilever to integrate the whole induced stress,18,19 whereas it requires larger passivation or stress compensation layers that reduce the sensitivity in addition to the optimization of thermal issues for actual measurements.19 In contrast, a membrane-type surface stress sensor (MSS), which we recently developed,16,17 can efficiently detect the whole surface stress induced on the center membrane even in the case of the double-side coating as shown in Figure 1e,f. Another important difference between MSS and a piezoresistive cantilever is the use of a stress concentration/localization mechanism. The isotropic deformation induced on the membrane by a given surface stress is accumulated at the periphery of the membrane and efficiently transduced to the four constricted sensing beams as an

amplified uniaxial stress. The stress enhancement mechanism was analytically and experimentally demonstrated16,17,20 and is also shown in Figure 2. The unique structure of MSS without a free end allows for stable operation, and its full Wheatstone bridge configuration provides additional stability for electrical measurements. In the present study, we investigate the feasibility of a double-side coating on nanomechanical sensors by means of MSS and verify its working principle by finite element analysis (FEA) and experiments. We also perform detailed analyses of the difference between single- and double-side coatings to gain insight into double-side coatings on piezoresistive nanomechanical sensors and provide some design guidelines for further optimization. Double-side coating works with almost any kind of coating method, including dip coating, for immobilizing various receptor layers, providing an interface between nanomechanical sensors and a large variety of coating materials/methods/ protocols for various applications. As a proof of concept, gas detection with double-side-coated MSS prepared by a simple hand-operated dip coating method has been demonstrated, showing consistent signals. The double-side coating approach leads to a new paradigm of one-chip−one-channel (channels on a chip are coated with the same receptor layers) shifting from B

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX

Langmuir

Article

Figure 3. (a) FEA of ΔR/R of the MSS yielded with the piezoresistors at the various planes along the z axis of the constricted beams. (Inset) Side view of a constricted bridge of MSS with the z axis and the positions of each plane simulated. The ratio of applied surface stress on the top and bottom surfaces of the center membrane of MSS is varied while keeping the total surface stress constant (−3.0 N/m). “Top surface stress ratio 1.0” indicates that the surface stress of −3.0 N/m is applied only on the top surface, and “top surface stress ratio 0.5” indicates that a surface stress of −1.5 N/m is applied equally on both the top and bottom surfaces. The dimensions of each part in direction x × y × z are as follows: center membrane, (ϕ500) × 2.5 μm3; sensing beams for R1 and R3, 10 × 16 × 2.5 μm3; and sensing beams for for R2 and R4, 26 × 10 × 2.5 μm3. For simplicity, no passivation layers are included in this calculation. (b) Thickness dependence of ΔR/R yielded with the ideal piezoresistors at the top surface planes of the constricted beams. For the black and gray lines, a surface stress of −3.0 N/m is applied only on the top surface and on both the top and bottom surfaces of the center membrane of MSS, respectively. Note that the total surface stress in the case of the gray line is −6.0 N/m. The thicknesses of all components of the MSS are varied at the same time while keeping all other dimensions the same as those of the MSS simulated in panel a. As for the demonstration of the merit of the double-side coating approach, the membrane was coated with a simple hand-operated dip coating method. In the present demonstration, the MSS chip was attached to a glass slide with double-sided adhesive tape and was dipped in an ethanol solution of poly(vinylpyrrolidone) (PVP) with a concentration of 5 g/L and then slowly withdrawn from the solution. Because the water solution of PSS used for the inkjet spotting has the high surface tension we used an ethanol solution of PVP that is more suitable for the dip coating because of the lower surface tension and better wettability of ethanol. Note that the entire procedure was operated all by hands without any device and completed in less than a minute. In this case, all of the membranes on the MSS chip are coated with the same polymer layers. Although the absolute thickness of the coating layers cannot be precisely controlled with such a handoperated dip coating method, the obtained coating layers were found to yield large consistent signals, working as a practical receptor layer as shown later. Gas Measurements. The polymer-coated MSS chip was mounted in a closed chamber and was exposed to 20% water vapor in pure nitrogen carrier gas at a flow rate of 100 mL/min for 3 min, followed by nitrogen purging for 3 min. The signals were measured with the same electrical setup with a bias voltage of −1.5 V in all cases.

the conventional one-chip-multiple-channel (channels on a chip are coated with different receptor layers) paradigm.



METHODS

Finite Element Analysis (FEA). For the quantitative verification of double-side-coated MSS, FEA was performed using COMSOL Multiphysics 3.5a with the Structural Mechanics module. Each structure was meshed with 10 000−20 000 elements, which give sufficient resolution for the present simulations. On the basis of the analytically verified simulations, the surface stress (s, N/m) can be described using a thin film on the surface with a minute thickness (tsurf m) that simulates 2D plane and a 3D bulk stress (σbulk, N/m2) applied in the thin film: s = σbulktsurf.16,17,21 In the present study, surface stress of −3.0 N/m was simulated by applying an initial bulk stress of 3.0 × 108 N/m2 on a thin film with a thickness of 1 × 10−8 m. The surface stress is applied on the top surface (for single-side coating) or on both top and bottom surfaces (for double-side coating) of the center membrane of the MSS. The matrix of the anisotropic Young’s modulus22 is applied to single-crystal Si(100). The Young’s modulus and Poisson’s ratio of other materials were set as follows: SiO2 (70 GPa, 0.17) and Si3N4 (250 GPa, 0.23). Note that the distribution of ΔR/R presented in Figure 2 is simulated by assuming that the current flows in the [110] direction. These relative resistance changes are valid only for the piezoresistors, whereas the nondoped regions do not have such resistance changes. MSS Chips. The MSS chips with sensing elements arranged in a 2D array were used for the experiments.17 They were fabricated from 4 in. silicon-on-insulator (SOI) wafers with an n-type device layer (∼4 μm thick, ∼10 Ω·cm). The detailed fabrication process and the measurement setup are available in ref 17. The dimensions of each part are described in the caption of Figure 2. Deposition of Polymer Layers. For the comparison of the singleand double-side coatings, the center membrane of MSS was coated with poly(sodium 4-styrenesulfonate) (PSS) layers using a customized inkjet spotting system (Microjet Co. Ltd., model LaboJet-500SP). A PSS solution with a concentration of 5 g/L was deposited to form a 1μm-thick PSS layer either on the top or on both the top and bottom surfaces. Although it is rather difficult to obtain consistent morphology via inkjet spotting, it is possible to control the amount of polymer with a calibrated volume of droplets ejected from the inkjet nozzle. Because we applied exactly the same condition in successive inkjet spotting, the polymer layers on the surfaces of each membrane have reasonably similar properties within ∼10% error in the output signals.



RESULTS AND DISCUSSION Figure 2 shows the results of FEA for the single- and doubleside-coated MSS. The distribution of the relative resistance change (ΔR/R) is plotted as a color gradient. Because the four resistors (R1−R4) comprise a full Wheatstone bridge in MSS, the total output (Vout) is approximately given by the following equation Vout =

ΔR3 ΔR 4 ⎞ VB ⎛ ΔR1 ΔR 2 − + − ⎜ ⎟ 4 ⎝ R1 R2 R3 R4 ⎠

(1)

where VB is the bias voltage applied to the bridge. Thus, the mutually positive and negative relative resistance changes in the R1, R3 and R2, R4 pairs lead to the maximum output. Although larger relative resistance changes are observed in single-sidecoated MSS, a number of relative resistance changes are also confirmed in the case of double-side-coated MSS. In terms of the relative resistance change value averaged on the C

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX

Langmuir

Article

piezoresistive sensing beams, double-side-coated MSS can yield ∼37% of the signal observed for single-side-coated MSS. In the case of solid coatings such as polymers with uniform expansion or shrinkage of the whole coating film, this value varies depending on the material properties of the coating films.23 In any case, the double-side-coated MSS is confirmed to yield a finite amount of signal. These results can be explained by the structure of MSS in which the constricted sensing beams (R1− R4) are confined between the center membrane and the thick bulk silicon part that is basically immovable. Thus, as the center membrane expands or shrinks because of the in-plane tensile or compressive stress induced by the adsorption of analytes on the top and bottom surfaces of the membrane, the sensing beams are compressed or elongated, resulting in a considerable amount of stress on the piezoresistors integrated into the sensing beams as shown in Figures 1 and 2. To understand the difference between single- and doubleside coatings quantitatively, we investigated the position dependence of a piezoresistor along the z axis, which is parallel to the thickness direction of the beam. According to basic mechanics,24 the stress (σ) induced in a bending beam is given as follows

σ=

E z R

Figure 4. Obtained output signals (Vout) from the MSS coated with PSS only on the top surface (---) and on both top and bottom surfaces ().

and 1.0−1.5 μV for piezoresistive sensing, including MSS)16 with a bandwidth of ∼3 Hz. On the basis of this definition, we can evaluate the practical limit of detection, in other words, the minimum detectable surface stress, which is estimated to be 0.15−0.90 mN/m for optical read-out cantilevers and 0.077− 0.11 mN/m for the latest version of single-side-coated MSS.17 Thus, the minimum detectable surface stress of double-sidecoated MSS is in the range of 0.20−0.30 mN/m, which is still comparable to that of optical read-out cantilevers.2,4−7,10−12 To demonstrate the convenience of the double-side coating method, we deposited polymer layers on the MSS surfaces by a simple hand-operated dip coating method as shown in Figure 5a. Figure 5b shows the results obtained with the double-sidecoated MSS chip prepared by the hand-operated dip coating method. It is found that, even with this simple method, the MSS chip can yield consistent signals from the different channels on the same MSS chip. As described in the previous section and shown in Figure 5a, anyone can perform this procedure without any complex instrumentation. The chip can also be immersed in any solution as long as the solution does not break the passivation layers or aluminum electrodes. Therefore, one can apply almost any kind of standard procedure or protocol developed so far for the coating of silicon substrates, such as silane chemistry, which usually requires at least 1 or 2 h of incubation in a solution, which is difficult to perform by the inkjet spotting method. In the case of double-side coating methods, all channels on a chip will be coated with the same receptor layer. Whereas a chip with multiple membranes can record iterative data that are important in assessing the reproducibility of the measurement, each chip will work basically as one channel. To measure multiple samples, one can prepare multiple chips coated with different receptors instead of having one chip coated with different types of receptors on the same chip, which is rather difficult to prepare in most cases because of technical problems such as cross-contamination, drying out while coating different channels, and so forth. This one-chip−one-channel approach will be also helpful in realizing standard chips by batch fabrication for mass production with acceptable lot-to-lot variation.

(2)

where R is the radius of bending, E is the Young’s modulus of the beam, and z is the distance from the neutral axis, along which there is no compression or dilation, thereby defined as z = 0. In the case of constant bending, the stress is proportional to the distance z from the neutral axis and reaches a maximum at the surface of the beam. This z dependence is clearly observed in Figure 3a. It should be noted that there are stress ratio values that result in zero output, indicating that some specific anisotropy in the coating layers on top and bottom surfaces can lead to very low sensitivity. Another important feature of the results in Figure 3a is the constant output from the piezoresistors located at the neutral axis. Because there is no contribution of the bending motion at the neutral axis,25 this constant output value can be regarded as the contribution of “pure” in-plane stress. In this case, the output signal will never cross the zero point. Thus, if one can fabricate the MSS structure with piezoresistors embedded in the neutral axis plane, then it will not suffer from the zero signal issue although the absolute signal by this pure in-plane stress is not as high as that by the bending stress. To enhance the absolute signal, one can make a thinner geometry as shown in Figure 3b. It is worth noting that the signal from double-side-coated MSS can exceed that from the single-side-coated one by making a 2 to 3 times thinner geometry. For actual fabrication, however, several practical issues have to be taken into account, such as the thickness of piezoresistors that can be as thick as the whole thickness,26 fragility, and intrinsic 1/f noise,27 which increases as the number of carriers is decreased.17 The basic feature of the double-side coating obtained by FEA (Figure 2) is experimentally verified as shown in Figure 4. Although the signal of the double-side-coated MSS is about 30−40% of that of the single-side-coated MSS, the double-sidecoated MSS still yields a considerable amount of signal. To assess the sensitivity of double-side-coated MSS quantitatively, we performed a practical comparison in terms of the experimental signal-to-noise ratio based on experimentally observed noise (0.5−3.0 nm for an optical read-out cantilever with commonly used dimensions (500 × 100 × 1 μm3)4,28−30



CONCLUSIONS We have demonstrated an effective solution to the coating of nanomechanical sensors by means of the double-side coating. It has been verified by both FEA and experiments that the MSS can yield reasonable signals even with the double-side coating. D

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX

Langmuir

Article

cible preparation of multiple chips, which will be helpful in most cases.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +81(0)29-8604749. Fax: +81(0)29-860-4706. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS We express our appreciation to Dr. Heinrich Rohrer for his initial investigations and discussions on piezoresistive surface stress sensing, which led to the invention and development of the MSS concept and technology. We acknowledge the technical support by the clean room staffs of CSEM’s Microsystems Technology Division. This research was supported by the World Premier International Research Center (WPI) Initiative on Materials Nanoarchitectonics (MANA); a Grant-in-Aid for Young Scientists (A) 23685017 (2011), MEXT, Japan; a Nakatani Foundation research grant; and the Japan Science and Technology Agency (JST).



REFERENCES

(1) Barnes, J. R.; Stephenson, R. J.; Welland, M. E.; Gerber, C.; Gimzewski, J. K. Photothermal spectroscopy with femtojoule sensitivity using a micromechanical device. Nature 1994, 372, 79−81. (2) Gimzewski, J. K.; Gerber, C.; Meyer, E.; Schlittler, R. R. Observation of a chemical-reaction using a micromechanical sensor. Chem. Phys. Lett. 1994, 217, 589−594. (3) Thundat, T.; Warmack, R. J.; Chen, G. Y.; Allison, D. P. Thermal and ambient-induced deflections of scanning force microscope cantilevers. Appl. Phys. Lett. 1994, 64, 2894−2896. (4) Huber, F.; Lang, H. P.; Backmann, N.; Rimoldi, D.; Gerber, C. Direct detection of a braf mutation in total rna from melanoma cells using cantilever arrays. Nat. Nanotechnol. 2013, 8, 125. (5) Zhang, J. Y.; Lang, H. P.; Yoshikawa, G.; Gerber, C. Optimization of DNA hybridization efficiency by ph-driven nanomechanical bending. Langmuir 2012, 28, 6494−6501. (6) Buchapudi, K. R.; Huang, X.; Yang, X.; Ji, H. F.; Thundat, T. Microcantilever biosensors for chemicals and bioorganisms. Analyst 2011, 136, 1539−1556. (7) Yoshikawa, G.; Lang, H. P.; Akiyama, T.; Aeschimann, L.; Staufer, U.; Vettiger, P.; Aono, M.; Sakurai, T.; Gerber, C. Sub-ppm detection of vapors using piezoresistive microcantilever array sensors. Nanotechnology 2009, 20, 015501. (8) Boisen, A.; Thundat, T. Design & fabrication of cantilever array biosensors. Mater. Today 2009, 12, 32−38. (9) Raorane, D. A.; Lim, M. D.; Chen, F. F.; Craik, C. S.; Majumdar, A. Quantitative and label-free technique for measuring protease activity and inhibition using a microfluidic cantilever array. Nano Lett. 2008, 8, 2968−2974. (10) Pera, I.; Fritz, J. Sensing lipid bilayer formation and expansion with a microfabricated cantilever array. Langmuir 2007, 23, 1543− 1547. (11) Bietsch, A.; Zhang, J. Y.; Hegner, M.; Lang, H. P.; Gerber, C. Rapid functionalization of cantilever array sensors by inkjet printing. Nanotechnology 2004, 15, 873−880. (12) McKendry, R.; Zhang, J. Y.; Arntz, Y.; Strunz, T.; Hegner, M.; Lang, H. P.; Baller, M. K.; Certa, U.; Meyer, E.; Güntherodt, H. J.; Gerber, C. Multiple label-free biodetection and quantitative DNAbinding assays on a nanomechanical cantilever array. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 9783−9788. (13) Henriksson, J.; Villanueva, L. G.; Brugger, J. Ultra-low power hydrogen sensing based on a palladium-coated nanomechanical beam resonator. Nanoscale 2012, 4, 5059−5064.

Figure 5. (a) Photograph of the hand-operated dip coating setup for creating double-sided coatings for the MSS chip. Observe that the setup is very simple and practical and can be used for various coating solutions. (b) Obtained output signals (Vout) for three MSS membranes on the same double-side-coated chip. This MSS chip was coated with PVP using hand-operated dip coating. Note that the three output signals (solid red, black, and blue lines) are almost completely overlapped and appear as almost a single line, demonstrating a high degree of consistency in the coating.

Although the double-side coating sacrifices some sensitivity compared to a single-side coating, the double-side coating provides wider opportunities for various materials with easier coating methods. We have also investigated the difference between single- and double-side coatings and have provided some guidelines for the optimization of the geometry for double-side coatings. The MSS with piezoresistors embedded at the neutral axis plane is an example of the optimized structures for the double-side coating because it is almost insensitive to the anisotropic coatings on both surfaces without suffering from the zero output issue. The double-side coating approach allows almost any kind of procedure/protocol for silicon coatings, including dip coating, silane chemistry, and gold−thiol chemistry. The simple proof-of-concept measurement by the MSS chip prepared by hand-operated dip coating without any complex instrumentation demonstrated the convenience of the double-side coating approach. Another important aspect of the present study is a new paradigm of one-chip−one-channel shifting from the conventional one-chip−multiple-channel paradigm. Whereas the one-chip−multiple-channel strategy would be better suited for some applications, the one-chip− one-channel approach provides a more feasible and reproduE

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX

Langmuir

Article

(14) Rasmussen, P. A.; Grigorov, A. V.; Boisen, A. Double sided surface stress cantilever sensor. J. Micromech. Microeng. 2005, 15, 1088−1091. (15) Choudhury, A.; Hesketh, P. J.; Thundat, T. G.; Hu, Z.; Vujanic, R. Design and Testing of Single and Double Sided Cantilevers for Chemical Sensing. IEEE Sensors; IEEE: New York, 2007; Vols. 1−3, pp 1432−1435. (16) Yoshikawa, G.; Akiyama, T.; Gautsch, S.; Vettiger, P.; Rohrer, H. Nanomechanical membrane-type surface stress sensor. Nano Lett. 2011, 11, 1044−1048. (17) Yoshikawa, G.; Akiyama, T.; Loizeau, F.; Shiba, K.; Gautsch, S.; Nakayama, T.; Vettiger, P.; Rooij, N. F. d.; Aono, M. Two dimensional array of piezoresistive nanomechanical membrane-type surface stress sensor (MSS) with improved sensitivity. Sensors 2012, 12, 15873− 15887. (18) Rasmussen, P. A.; Hansen, O.; Boisen, A. Cantilever surface stress sensors with single-crystalline silicon piezoresistors. Appl. Phys. Lett. 2005, 86, 203502. (19) Choudhury, A.; Hesketh, P. J.; Thundat, T.; Hu, Z. Y. A piezoresistive microcantilever array for surface stress measurement: curvature model and fabrication. J. Micromech. Microeng. 2007, 17, 2065−2076. (20) Yoshikawa, G.; Rohrer, H. Strain Amplification Schemes for Piezoresistive Cantilevers.7th International Workshop on Nanomechanical Cantilever Sensors, Banff, 2010. (21) Ricci, A.; Giuri, E.; Ricciardi, C. Simulation of Surface Stress Effect on Mechanical Behaviour of Silicon Microcantilevers. COMSOL Users Conference 2006 Milano, Milano, 2006. (22) Hopcroft, M. A.; Nix, W. D.; Kenny, T. W. What is the Young’s modulus of silicon? J. Microelectromech. Syst. 2010, 19, 229−238. (23) Yoshikawa, G. Mechanical analysis and optimization of a microcantilever sensor coated with a solid receptor film. Appl. Phys. Lett. 2011, 98, 173502. (24) Sarid, D. Scanning Force Microscopy; Oxford University Press: New York, 1994. (25) Note that the “neutral axis” referred to here expands or contracts by the in-plane deformation. Thus, to be more precise, the “neutral axis” here should read the “neutral axis for bending motion” because the definition of the “neutral axis” indicates that there is neither expansion nor contriction. (26) Chen, Y.; Xu, P. C.; Li, X. X. Axial-stressed piezoresistive nanobeam for ultrahigh chemomechanical sensitivity to molecular adsorption. Anal. Chem. 2012, 84, 8184−8189. (27) Hooge, F. N. 1/f noise is no surface effect. Phys. Lett. A 1969, 29, 139−140. (28) Watari, M.; Galbraith, J.; Lang, H. P.; Sousa, M.; Hegner, M.; Gerber, C.; Horton, M. A.; McKendry, R. A. Investigating the molecular mechanisms of in-plane mechanochemistry on cantilever arrays. J. Am. Chem. Soc. 2007, 129, 601−609. (29) Zhang, J.; Lang, H. P.; Huber, F.; Bietsch, A.; Grange, W.; Certa, U.; McKendry, R.; Güntherodt, H.-J.; Hegner, M.; Gerber, C. Rapid and label-free nanomechanical detection of biomarker transcripts in human rna. Nat. Nanotechnol. 2006, 1, 214−220. (30) Ndieyira, J. W.; Watari, M.; Barrera, A. D.; Zhou, D.; Vogtli, M.; Batchelor, M.; Cooper, M. A.; Strunz, T.; Horton, M. A.; Abell, C.; Rayment, T.; Aeppli, G.; McKendry, R. A. Nanomechanical detection of antibiotic mucopeptide binding in a model for superbug drug resistance. Nat. Nanotechnol. 2008, 3, 691−696.

F

dx.doi.org/10.1021/la3046719 | Langmuir XXXX, XXX, XXX−XXX