Scholarly article on topic 'Cross talk between bending, twisting, and buckling modes of three types of microcantilever sensors'

Cross talk between bending, twisting, and buckling modes of three types of microcantilever sensors Academic research paper on "Materials engineering"

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Academic research paper on topic "Cross talk between bending, twisting, and buckling modes of three types of microcantilever sensors"

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Scientific Instruments

Cross talk between bending, twisting, and buckling modes of three types of microcantilever sensors

Sangmin Jeon, Yehuda Braiman, and Thomas Thundat

Citation: Review of Scientific Instruments 75, 4841 (2004); doi: 10.1063/1.1809259 View online: http://dx.doi.org/10.1063/1.1809259

View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/75/11?ver=pdfcov Published by the AIP Publishing

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REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 75, NUMBER 11 NOVEMBER 2004

Cross talk between bending, twisting, and buckling modes of three types of microcantilever sensors

Sangmin Jeona)

Life Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

Yehuda Braiman

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

Thomas Thundat

Life Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

(Received 7 April 2004; accepted 27 August 2004; published 1 November 2004)

Microcantilevers generally deflect in three ways: bending, twisting, and buckling. Among these, the accurate measurement of bending is essential for atomic force microscopy imaging and sensing applications. However, it was found that the bending of certain cantilevers can be coupled with twisting and buckling of the cantilever. In this article, cross talk between bending and twisting modes of microcantilevers of three different designs such as rectangular, triangular, and piezoresistive cantilevers is described. For the experiments, a thermal stress was applied to the rectangular and triangular cantilevers, and a Lorentz force was exerted on the triangular and the piezoresistive cantilevers. While the bending of the rectangular cantilever induced a negligible amount of twisting when heated, the triangular cantilevers showed nonlinear twisting responses during bending. This nonlinear response of the triangular cantilever was attributed to the variations in the spring constants between the two legs. When a Lorentz force was exerted on the triangular cantilevers, coupling of the bending and twisting modes depended on the direction of a magnetic field. For the piezoresistive cantilevers, a Lorentz force induced the in-phase buckling which accompanied both the bending and twisting modes. © 2004 American Institute of Physics. [DOI: 10.1063/1.1809259]

I. INTRODUCTION

Microcantilevers have attracted much attention recently, not only because of the popularity of atomic force microscopy (AFM), but also because of the potential for use as extremely sensitive sensor platforms for chemical and biological detection.1-5 A microcantilever is generally deflected in three ways: bending, twisting, and buckling. Of these three modes, bending of the cantilever is used for both imaging and sensing applications. The bending of a cantilever is usually monitored by an optical beam deflection method that measures the curvature of the cantilever. AFM images are obtained by maintaining a constant bending (curvature) of the cantilever during imaging while sensing applications are carried out by monitoring the bending of the cantilever due to adsorption-induced changes in surface stress. On the contrary, a friction force image is obtained by measuring the twisting of the cantilever during the scanning of the substrate, and the local slope of the surface affects the amount of twists of the cantilever. While the cross talk between the bending and twisting was already known from friction force measurements using AFM,6-8 the effect of the cross talk in sensor applications has not been studied to the best of our knowledge.

Here we describe the cross talk between cantilever bend-

a) Author to whom correspondence should be addressed; electronic mail: s59@ornl.gov

ing and twisting due to application of a thermal stress and a Lorentz force. Figure 1 shows the various shapes of commercial cantilevers and the corresponding deflection modes that are measured in this article. The vertical bending of a rectangular silicon cantilever in Fig. 1(a) is generally used for sensor applications. Greater bending implies larger adsorption-induced stress (in most cases more molecule adsorption) on the cantilever. In bimaterial cantilevers, greater bending corresponds to larger temperature changes. However, the different shaped cantilevers in Figs. 1 (b) and 1 (c), which have two legs, are very often twisted or buckled by thermal stress or magnetic force variations. Such twisting and buckling results in a nonlinear bending signal.

II. EXPERIMENTAL DETAILS

Rectangular silicon cantilevers were purchased from MikroMasch (Oregon), and triangular and piezoresistive silicon cantilevers were purchased from Park Scientific (Sunnyvale, CA). The dimensions of the rectangular, triangular, and piezoresistive cantilevers are 350 X 35 X 1, 180 X 38 X 1, and 305 X 50 X 3 ¡m (length, width, thickness), respectively. Cantilever optical deflection measurements were conducted using a four-quadrant AFM head with an integrated laser and position-sensitive detector (Digital Instruments, Santa Barbara, CA). The signal from each quadrant of the position sensitive detector was obtained by a home built electronic circuit.

0034-6748/2004/75(11 )/4841/4/$22.00

© 2004 American Institute of Physics

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FIG. 1. Various shapes and deflection modes of the cantilevers tested. (a) A rectangular silicon cantilever bends downwards due to temperature or surface stress changes. (b) A triangular silicon cantilever is coated with gold through a mask to form a circuit and positioned between two permanent magnets. A Lorentz force twists cantilever laterally as alternating voltage is applied by a function generator. (c) A silicon piezoresistive cantilever is buckled in phase as an alternating voltage is applied.

To ascertain the thermal responses of the cantilever, the rectangular and triangular cantilevers were sequentially coated with a 2.5 nm thickness of chromium and a 25 nm thickness of gold. In order to apply a Lorentz force to the triangular cantilever, one side of the silicon cantilever was coated with gold in a pattern which allowed current to flow through the cantilever when connected to a function generator [see Fig. 1(b)]. Since the cantilever was positioned between two strong permanent magnets (Delta Magnet DE32, Schiltigheim, France), passage of current through the cantilever caused a Lorentz force normal to the plane of the cantilever. The Lorentz force direction was opposite in each leg since the direction of the current flow was opposite in each leg.

The Lorentz force can be applied to the triangular and piezoresistive cantilever without the magnets. A current-carrying wire produces the magnetic field around the wire. When there are two wires carrying currents, they will exert forces on each other. One wire sets up a magnetic field that influences the other wire, and vice versa. If the currents go opposite ways, the force is repulsive. Since gold (or boron) is deposited on one side of the surface of the triangular (or piezoresistive) cantilever, the repulsive force acts as a torque to deform the cantilever out of plane.

III. RESULTS AND DISCUSSIONS A. Cross talk by thermal stress

A thermal stress was applied to the rectangular and triangular cantilevers, and the cross talk between bending and twisting modes was studied. The upper panel of Fig. 2 shows the change in temperature due to heating from 22 to 33 ° C. Temperature was increased by a heater and measured by a thermocouple located very near the cantilever. The middle panel shows the raw signals from A, B, C, and D that represent each quadrant of the position sensitive detector (PSD). Upon heating the cantilever, the rectangular cantilever starts to bend due to the difference in the thermal expansion coefficient of the gold film versus the underlying silicon, and the position of the reflected laser beam moves vertically on the PSD. The slightly larger changes of A and D compared to B and C imply that the cantilever is undergoing twisting as well as bending. The changes in bending and twisting, calculated

FIG. 2. The upper panel shows the change of temperature. The middle panel shows the responses of each section of the quadrant photodiode detector as temperature increases. A, B, C, and D represent the positions of each section in the quadrant photodiode detector. The lower panel shows the calculated vertical bending and lateral twisting.

by (A-C) + (B-D) and (A-B) + (C-D), respectively, are shown in the lower panel of Fig. 2, and the twisting response of the rectangular cantilever is seen to be very small compared to the bending response.

On the contrary, the response of the triangular cantilever is nonlinear as shown in Fig. 3. Again, the upper and middle panels represent the temperature and the raw signals from the detector quadrants. The bending response is similar to that of

Î Bending

Twisting

0 5 10 15

Time (min)

FIG. 3. The upper and middle panels show the temperature and the signals from each section of the quadrant photodiode detector. A, B, C, and D represent the positions of each section in the quadrant photodiode detector, and the response seen is very nonlinear due to temperature changes. The lower panel shows that the twisting exceeds the bending as temperature is further increased.

Rev. Sci. Instrum., Vol. 75, No. 11, November 2004

Cross talk between cantilever modes

FIG. 4. The upper panel shows the signals from each section of the quadrant photodiode detector as a sinusoidal current (1 V, 0.1 Hz) passes through the triangular cantilever with an external magnetic field. The cantilever is positioned between two permanent magnets. The lower panel shows the calculated vertical bending and lateral twisting. A cartoon above the figure shows the direction of a magnetic field (dotted arrow) and an induced magnetic force (®: outwards from the paper, ©: inwards to the paper).

a rectangular cantilever in the initial heating stages, and the bending reaches a maximum at 25 ° C. With further heating of the cantilever, the increased twisting alters the bending response significantly. This nonlinear response may be due to the asymmetric nature of the cantilever legs [e.g., varying thickness (including coating) or defect density between legs]. The asymmetric triangular cantilever with different spring constants, widths, thicknesses, or even defect densities for each leg should be avoided for sensor applications where temperature regimes are required.

B. Cross talk by a Lorentz force

The coupling of the bending and twisting modes of the cantilever was also investigated by applying a Lorentz force to the triangular and piezoresistive cantilevers. This method had been developed to measure the torsional spring constant of the microcantilever for friction force experiments,9 but was found to also be useful to measure the coupling due to misalignment of the cantilever and detector. When a cantilever is mounted on a holder with an angle of inclination, the trajectory of the reflected laser beam from the cantilever does not move horizontally on the detector if the cantilever is twisting.

The upper panel of Fig. 4 shows the raw signals from the detector as an electric field was applied to the triangular cantilever between two magnets [see Fig. 1(b)] with an amplitude of 1 V and a frequency of 0.1 Hz. The signals from A and C change in the same direction, but signals from B and D vary in the opposite direction to that of A and C. This implies that a Lorentz force twists the cantilever laterally. The relatively larger changes of A and B compared to C and D can be easily equalized by adjusting the position of the detector and the cantilever. When the four detector signals vary with the same amplitude and phase, the alignment of the

FIG. 5. The upper panel shows the signals from each section of the quadrant photodiode detector as a sinusoidal current (3 V, 0.1 Hz) passes through the triangular cantilever without an external magnetic field. The lower panel shows the calculated vertical bending and lateral twisting. Arrow in the cartoon above the figure shows the direction of an induced magnetic force.

cantilever and detector is complete. If this cannot be done, the cantilever may have different spring constants for the legs and should be discarded. Although this is a simple test, it is useful to confirm the alignment of the cantilever and detector, and to ensure that measurements taken with the cantilever will be reproducible.

A similar experiment was performed on the triangular cantilever without the magnets. The upper panel of Fig. 5 shows the raw signals from the detector as an electrical voltage was applied to the triangular cantilever with the amplitude of 3 V and a frequency of 0.1 Hz. Since the Lorentz force is weaker without an external magnetic field, a higher voltage is applied. The lower panel of Fig. 5 shows the calculated bending and twisting motion. While the Lorentz force induced a twisting of the cantilever with an external magnetic field as seen in Fig. 4, it induced mainly a bending of the cantilever without the external magnetic field. This difference comes from the different directions of the magnetic field and the induced force as shown in Figs. 4 and 5. The unusual responses from the triangular cantilever may be due to the nonparallel legs.

Compared with the triangular cantilever that has two nonparallel legs, the piezoresistive cantilever has two parallel legs. The piezoresistive cantilevers were designed to measure the bending of the cantilever electrically. However, some piezoresistive cantilever sensing applications, such as detection of explosive molecules using deflagration, adopt the optical beam deflection technique for monitoring cantilever bending.10 Most of the commercial piezoresistive cantilevers have rectangular shapes, but they have two legs to pass the current through the cantilever [see Fig. 1(c)]. Piezoresistive cantilevers are made of silicon and doped with boron to a depth of 100 nm. Its electrical resistance is about 2 КЛ. If a current is applied to the cantilever, the boron doped silicon portion is heated but the temperature does not greatly affect the deflection of the cantilever because it is not

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Jeon, Braiman, and Thundat

FIG. 6. The upper panel shows the signals from each section of the quadrant photodiode detector as a sinusoidal current (1 V, 0.1 Hz) passes through the piezoresistive cantilever. The lower panel shows the calculated vertical bending and lateral twisting. Arrows in the cartoon above the figure show the direction an induced magnetic force.

both bending and twisting signal due to the buckling shown in the lower panel of Fig. 6 suggests that the influence of cross talk in the cantilever deflection response should be considered when a piezoresistive cantilever is used for sensor applications.

In summary, we have measured the cross talk between the bending and the twisting modes during the deflection of silicon microcantilevers of various shapes. The observed cantilever deflection is influenced significantly by the cross talk. This effect can be minimized by using rectangular cantilevers for sensor applications. However, the secondary resonance frequencies generated by cantilever twisting and buckling can be useful when using the triangular and pi-ezoresistive cantilevers in specific applications, such as quantification of adsorbed mass.

ACKNOWLEDGMENTS

This research was supported by the DOE Office of Biological and Environmental Research (OBER) and DOE-Environmental Science Management Program (EMSP), and the DOE Division of Materials Sciences and Engineering. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Dept. of Energy under Contract No. DE-AC05-00OR22725.

bimetallic. In order to avoid a possible electrical short circuit, the piezoresistive cantilever is not coated with gold. On the contrary, the Lorentz force between two parallel current-carrying wires in opposite direction induces the torque that curves cantilever.

The upper panel of Fig. 6 shows the raw signals from the detector as an electrical voltage was applied to the piezore-sistive cantilever with an amplitude of 1 V and a frequency of 0.1 Hz. Interestingly, A, B, C, and D change in the same direction, and the change is always negative compared to the base line. Furthermore, the frequency of the change is twice than that of the applied electrical voltage. This is caused by the buckling of the cantilever. Since the buckling of the cantilever makes the reflected beam larger than the size of the detector, the individual and total signal from the detector decreases as depicted in the figure. The large variation in

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