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Research Papers

Identification and Analysis of Artifacts in Amplitude Modulated Atomic Force Microscopy Array Operation

[+] Author and Article Information
Samuel Jackson

Department of Mechanical Engineering,
University of Canterbury,
Christchurch 8041, New Zealand
e-mail: samuel.jackson@pg.canterbury.ac.nz

Stefanie Gutschmidt

Department of Mechanical Engineering,
University of Canterbury,
Christchurch 8041, New Zealand
e-mail: stefanie.gutschmidt@canterbury.ac.nz

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 6, 2016; final manuscript received April 11, 2017; published online May 17, 2017. Assoc. Editor: Anindya Chatterjee.

J. Comput. Nonlinear Dynam 12(5), 051018 (May 17, 2017) (7 pages) Paper No: CND-16-1539; doi: 10.1115/1.4036520 History: Received November 06, 2016; Revised April 11, 2017

To increase measurement throughput of atomic force microscopy (AFM), multiple cantilevers can be placed in close proximity to form an array for parallel throughput. In this paper, we have measured the relationship between amplitude and tip-sample separation distance for an array of AFM cantilevers on a shared base actuated at a constant frequency and amplitude. The data show that discontinuous jumps in output amplitude occur within the response of individual beams. This is a phenomenon that does not occur for a standard, single beam system. To gain a better understanding of the coupled array response, a macroscale experiment and mathematical model are used to determine how parameter space alters the measured amplitude. The results demonstrate that a cusp catastrophe bifurcation occurs due to changes in individual beam resonant frequency, as well as significant zero-frequency coupling at the point of jump-to-contact. Both of these phenomena are shown to account for the amplitude jumps observed in the AFM array.

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References

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Polesel-Maris, J. , Aeschimann, L. , Meister, A. , Ischer, R. , Bernard, E. , Akiyama, T. , Giazzon, M. , Niedermann, P. , Staufer, U. , Pugin, R. , Rooij, N. , Vettiger, P. , and Heinzelmann, H. , 2007, “ Piezoresistive Cantilever Array for Life Sciences Applications,” J. Phys.: Conf. Ser., 61, pp. 955–959.
Seong, M. , Somnath, S. , Kim, H. J. , and King, W. P. , 2014, “ Parallel Nanoimaging Using an Array of 30 Heated Microcantilevers,” RSC Adv., 4(47), pp. 24747–24754. [CrossRef]
Loizeau, F. , and Favre, M. , 2013, “ 2D Cantilever Array With Spherical Tips for Parallel Force Spectroscopy on Cancerous Cells,” 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS), Barcelona, Spain, June 16–20, pp. 1186–1189.
Schneider, A. , Ibbotson, R. , Dunn, R. , and Huq, S. , 2011, “ Arrays of SU-8 Microcantilevers With Integrated Piezoresistive Sensors for Parallel AFM Applications,” Microelectron. Eng., 88(8), pp. 2390–2393. [CrossRef]
Sarov, Y. , Ivanov, T. , Frank, A. , and Rangelow, I. W. , 2011, “ Thermally Driven Multi-Layer Actuator for 2D Cantilever Arrays,” Appl. Phys. A, 102(1), pp. 61–68. [CrossRef]
Zhao, X. , and Dankowicz, H. , 2006, “ Characterization of Intermittent Contact in Tapping-Mode Atomic Force Microscopy,” ASME J. Comput. Nonlinear Dyn., 1(2), p. 109. [CrossRef]
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Jackson, S. , Gutschmidt, S. , Roeser, D. , and Sattel, T. , 2016, “ Development of a Mathematical Model and Analytical Solution of a Coupled Two-Beam Array With Nonlinear Tip Forces for Application to AFM,” Nonlinear Dyn., 87(2), pp. 775–787. [CrossRef]
Dankowicz, H. , and Schilder, F. , 2013, Recipes for Continuation, SIAM, Philadelphia, PA.

Figures

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Fig. 1

The four-beam array used to obtain the amplitude approach curves. Each beam has an inbuilt bimorph heater actuator and piezoresistive bridge sensor. The bridge sensors were not used for this investigation due to a low signal-to-noise ratio (SNR). Each beam is 350 μm long and 40 μm wide. The gap between each beam is 5 μm.

Grahic Jump Location
Fig. 2

Experimental amplitude approach curve of a four-beam microarray. Each beam is actuated in turn with a constant amplitude at its resonant frequency. The resonant frequencies are 37.75 kHz for beam 1, 36.62 kHz for beam 2, 36.76 kHz for beam 3, and 37.28 kHz for beam 4. The region containing dynamic phenomena of interest is circled. Blue—beam 1, red—beam 2, green—beam 3, and black—beam 4 (see figure online for color).

Grahic Jump Location
Fig. 3

Experimental amplitude approach curve of a microsingle beam. The beam is actuated with a constant amplitude at its resonant frequency. The resonant frequency is 99.79 kHz.

Grahic Jump Location
Fig. 4

Equivalent macroscale experimental setup: (a) macroscale test rig to simulate AM-AFM of a two beam array and (b) aluminum strips are added between beams as a method of varying the coupling strength. Lb is the length of shared base material, which can be varied by swapping out coupling pieces.

Grahic Jump Location
Fig. 5

Amplitude approach curves of a macroscale two beam array. Only beam 1 is actuated in all cases. Blue—beam 1 and red—beam 2: (a) frequencies close together (47.50 Hz and 48.51 Hz), 6 mm of coupling material, (b) frequencies far apart (41.85 Hz and 48.56 Hz), 6 mm of coupling material, (c) frequencies close together (47.50 Hz and 48.51 Hz), 12 mm of coupling material, and (d) frequencies far apart (41.85 Hz and 48.56 Hz), 12 mm of coupling material (see figure online for color).

Grahic Jump Location
Fig. 6

Deflection approach curves of a macroscale two beam array. Only beam 1 is actuated in all cases. A positive deflection represents deflection toward the surface. Blue—beam 1 and red—beam 2: (a) frequencies close together (47.50 Hz and 48.51 Hz), 6 mm of coupled material, (b) frequencies far apart (41.85 Hz and 48.56 Hz), 6 mm of coupled material, (c) frequencies close together (47.50 Hz and 48.51 Hz), 12 mm of coupled material, and (d) frequencies far apart (41.85 Hz and 48.56 Hz), 12 mm of coupled material (see figure online for color).

Grahic Jump Location
Fig. 7

Simulation of the approach to surface curve of a two beam array in the range of frequency crossing. Discontinuous jumps between the solution branches account for the observed experimental results (Fig. 5(d)). The simulation was performed with 8.7 mm of shared base material. Blue—beam 1 and red—beam 2 (see figure online for color).

Grahic Jump Location
Fig. 8

Simulated deflection curves corresponding to Fig. 7. Multiple solution branches are again observed. The simulation was performed with 8.7 mm of shared base material. A positive deflection represents deflection toward the surface. Blue—beam 1 and red—beam 2 (see figure online for color).

Grahic Jump Location
Fig. 9

Surface plot of beam 1 amplitude in a two beam array in relation to tip-sample separation and coupling strength

Grahic Jump Location
Fig. 10

Surface plot of beam 2 amplitude in a two beam array in relation to tip-sample separation and coupling strength

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