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A Novel Method to Reconstruct the Force Curve by Higher Harmonics of the First Two Flexural Modes in Frequency Modulation Atomic Force Microscope (FM-AFM)

Published online by Cambridge University Press:  04 June 2018

Suoxin Zhang ,
Jianqiang Qian ,
Yingzi Li ,
Yingxu Zhang  and
Zhenyu Wang
Suoxin Zhang
Affiliation:
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
Jianqiang Qian*
Affiliation:
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
Yingzi Li
Affiliation:
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
Yingxu Zhang
Affiliation:
School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China
Zhenyu Wang
Affiliation:
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
*
*Author for correspondence: Jianqiang Qian, E-mail: qianjq@buaa.edu.cn
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Abstract

Atomic force microscope (AFM) is an idealized tool to measure the physical and chemical properties of the sample surfaces by reconstructing the force curve, which is of great significance to materials science, biology, and medicine science. Frequency modulation atomic force microscope (FM-AFM) collects the frequency shift as feedback thus having high force sensitivity and it accomplishes a true noncontact mode, which means great potential in biological sample detection field. However, it is a challenge to establish the relationship between the cantilever properties observed in practice and the tip–sample interaction theoretically. Moreover, there is no existing method to reconstruct the force curve in FM-AFM combining the higher harmonics and the higher flexural modes. This paper proposes a novel method that a full force curve can be reconstructed by any order higher harmonics of the first two flexural modes under any vibration amplitude in FM-AFM. Moreover, in the small amplitude regime, short range forces are reconstructed more accurately by higher harmonics analysis compared with fundamental harmonics using the Sader–Jarvis formula.

Keywords

FM-AFMforce curveflexural modeshigher harmonics
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 24 , Issue 3 , June 2018 , pp. 256 - 263
Copyright
© Microscopy Society of America 2018 

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Footnotes

Cite this article: Zhang S, Qian J, Li Y, Zhang Y, Wang Z (2018) A Novel Method to Reconstruct the Force Curve by Higher Harmonics of the First Two Flexural Modes in Frequency Modulation Atomic Force Microscope (FM-AFM). Microsc Microanal24(3): 256–263. doi: 10.1017/S1431927618000363

References

Binnig, G, Quate, CF and Gerber, C (1986) Atomic force microscope. Phys Rev Lett 56(9), 930.Google Scholar
Chawla, G and Solares, SD (2010) Single-cantilever dual-frequency-modulation atomic force microscopy. Meas Sci Technol 20(1), 015501.Google Scholar
Collins, L, Jesse, S, Balke, N, Rodriguez, BJ, Kalinin, S and Li, Q (2015) Band excitation Kelvin probe force microscopy utilizing photothermal excitation. Appl Phys Lett 106(10), 2921–2923.Google Scholar
Delvallée, A, Feltin, N, Ducourtieux, S, Trabelsi, M and Hochepied, JF (2016) Toward an uncertainty budget for measuring nanoparticles by AFM. Metrologia 53(1), 41–50.CrossRefGoogle Scholar
Dufrêne, YF, Martínezmartín, D, Medalsy, I, Alsteens, D and Müller, DJ (2013) Multiparametric imaging of biological systems by force-distance curve-based AFM. Nat Methods 10(9), 847–854.Google Scholar
Giessibl, FJ (1997) Forces and frequency shifts in atomic-resolution dynamic-force microscopy. Phys Rev B 56(24), 16010–16015.CrossRefGoogle Scholar
Gross, L, Mohn, F, Moll, N, Liljeroth, P and Meyer, G (2009) The chemical structure of a molecule resolved by atomic force microscopy. Science 325(5944), 1110–1114.CrossRefGoogle ScholarPubMed
Hernandopérez, M, Miranda, R, Aznar, M, Carrascosa, JL, Schaap, IA Reguera, D and de Pablo, PJ (2012) Direct measurement of phage phi29 stiffness provides evidence of internal pressure. Small 8(15), 2366–2370.Google Scholar
Herruzo, ET, Asakawa, H, Fukuma, T and Garcia, R (2013) Three-dimensional quantitative force maps in liquid with 10 piconewton, angstrom and sub-minute resolutions. Nanoscale 5(7), 2678–2685.CrossRefGoogle ScholarPubMed
Higgins, MJ, Riener, CK, Uchihashi, T, Sader, JE, Mckendry, R and Jarvis, SP (2005) Frequency modulation atomic force microscopy: A dynamic measurement technique for biological systems. Nanotechnology 16(3), S85–S89.CrossRefGoogle Scholar
Hutter, C, Platz, D, Tholén, EA, Hansson, TH and Haviland, DB (2010) Reconstructing nonlinearities with intermodulation spectroscopy. Phys Rev Lett 104(5), 050801.Google Scholar
Ido, S, Kimura, K, Oyabu, N, Kobayashi, K, Tsukada, M, Matsushige, K and Yamada, H (2013) Beyond the helix pitch: Direct visualization of native DNA in aqueous solution. ACS Nano 7(2), 1817–1822.CrossRefGoogle ScholarPubMed
Kikukawa, A, Hosaka, S and Imura, R (1995) Silicon pn junction imaging and characterizations using sensitivity enhanced Kelvin probe force microscopy. Appl Phys Lett 66(25), 3510–3512.CrossRefGoogle Scholar
Kodera, N, Yamamoto, D, Ishikawa, R and Ando, T (2010) Video imaging of walking myosin v by high-speed atomic force microscopy. Nature 468(7320), 72–76.Google Scholar
Kuchuk, K and Sivan, U (2015) Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM. Beilstein J Nanotechnol 6(1), 149–156.Google Scholar
Li, Y, Qian, JQ and Li, YZ (2010) Theory of higher harmonics imaging in tapping-mode atomic force microscopy. Chin Phys B 19(5), 213–218.Google Scholar
Majzik, Z, Cuenca, AB, Pavliček, N, Miralles, N, Meyer, G, Gross, L and Fernandez, E (2016) Synthesis of a naphthodiazaborinine and its verification by planarization with atomic force microscopy. ACS Nano 10(5), 5340–5345.Google Scholar
Payam, AF, Martinjimenez, D and Garcia, R (2015) Force reconstruction from tapping mode force microscopy experiments. Nanotechnology 26(18), 185706.CrossRefGoogle ScholarPubMed
Pfeiffer, O, Loppacher, C, Wattinger, C, Bammerlin, M, Gysin, U, Guggisberg, M, Rast S, Bennewitz R, Meyer E and Guntherodt HJ (2000) Using higher flexural modes in non-contact force microscopy. Appl Surf Sci 157(4), 337–342.CrossRefGoogle Scholar
Rabe, U, Janser, K and Arnold, W (1996) Vibrations of free and surface‐coupled atomic force microscope cantilevers: Theory and experiment. Rev Sci Instrum 67(9), 3281–3293.Google Scholar
Sader, JE and Jarvis, SP (2004) Accurate formulas for interaction force and energy in frequency modulation force spectroscopy. Appl Phys Lett 84(10), 1801–1803.Google Scholar
Sahin, O, Magonov, S, Su, C, Quate, CF and Solgaard, O (2007) An atomic force microscope tip designed to measure time-varying nanomechanical forces. Nat Nanotechnol 2(8), 507–514.CrossRefGoogle ScholarPubMed
Stark, RW and Heckl, WM (2000) Fourier transformed atomic force microscopy: Tapping mode atomic force microscopy beyond the Hookian approximation. Surf Sci 457(1), 219–228.Google Scholar