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Volume 2 , Issue 1 , June 2016 , Pages: 8 - 29
Quantitative Normal Force Measurements by Means of Atomic Force Microscopy Towards the Accurate and Easy Spring Constant Determination
Andrzej Sikora, Electrotechnical Institute, Division of Electrotechnology and Materials Science, M. Skłodowskiej-Curie Wrocław, Poland
Received: Sep. 7, 2015;       Accepted: Oct. 6, 2015;       Published: Oct. 14, 2015
DOI: 10.11648/j.nsnm.20160201.12        View        Downloads  
Due to its rapid popularity increase within last three decades, with particular focus on submicrometer quantitative surface’s properties imaging, atomic force microscopy (AFM) is still a subject of development and research in terms of both better understanding and efficient utilization of various measurement techniques. Quantitative and comparable measurements at nanoscale are a significant issue, as both: science and industry desire reliable results, allowing to perform repetitive experiments at any time and location. Therefore a numerous analysis and research projects were carried out to provide metrological approach for those techniques in terms of providing the traceability and the uncertainty estimation. In this paper an overview of various methods and approaches towards quantitative determination of the normal spring constant of the AFM probes is presented.
Atomic Force Microscopy, Scanning Probe, Spring Constant, Calibration, Normal Force Measurement, Force Spectroscopy
To cite this article
Andrzej Sikora, Quantitative Normal Force Measurements by Means of Atomic Force Microscopy Towards the Accurate and Easy Spring Constant Determination, Nanoscience and Nanometrology. Vol. 2, No. 1, 2016, pp. 8-29. doi: 10.11648/j.nsnm.20160201.12
[ 1 ]
G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett., vol. 56, pp. 930–933, 1986.
[ 2 ]
S. Morita, Roadmap of Scanning Probe Microscopy. Springer Berlin Heidelberg, 2007.
[ 3 ]
H. K. Wickramasinghe, “Progress in scanning probe microscopy,” Acta Mater., vol. 48, no. 1, pp. 347–358, Jan. 2000.
[ 4 ]
B. Bhushan, Springer Handbook of Nanotechnology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010.
[ 5 ]
S. P. Jarvis and S. Yamamoto, “Tip-surface interactions studied using a force controlled atomic force microscope in ultrahigh vacuum,” Physics (College. Park. Md)., vol. 70, no. April, pp. 2238–2240, 1997.
[ 6 ]
E. Radlein, R. Ambos, and G. H. Frischat, “Atomic force microscopy of coated glasses,” J. Anal. Chem., vol. 353, pp. 413–418, 1995.
[ 7 ]
S. Lesko, E. Lesniewska, A. Nonat, J. C. Mutin, and J. P. Goudonnet, “Investigation by atomic force microscopy of forces at the origin of cement cohesion.,” Ultramicroscopy, vol. 86, no. 1–2, pp. 11–21, Jan. 2001.
[ 8 ]
R. Giles, J. P. Cleveland, S. Manne, P. K. Hansma, B. Drake, P. Maivald, C. Boles, J. Gurley, and V. Elings, “Noncontact force microscopy in liquids,” Appl. Phys. Lett., vol. 63, no. 5, p. 617, 1993.
[ 9 ]
A. Altes, R. Heiderhoff, and L. J. Balk, “Quantitative dynamic near-field microscopy of thermal conductivity,” J. Phys. D. Appl. Phys., vol. 37, no. 6, pp. 952–963, Mar. 2004.
[ 10 ]
G. Bernhard, M. Fiege, A. Altes, and R. Heiderhoff, “Quantitative thermal conductivity measurements with nanometre resolution,” J. Phys. D Appl. Phys., vol. 32, pp. L13–L17, 1999.
[ 11 ]
V. V. Zavyalov, J. S. McMurray, and C. C. Williams, “Scanning capacitance microscope methodology for quantitative analysis of p - n junctions,” J. Appl. Phys., vol. 85, no. 11, pp. 7774–7783, 1999.
[ 12 ]
B.-F. Ju, Y. Ju, and M. Saka, “Quantitative measurement of submicrometre electrical conductivity,” J. Phys. D. Appl. Phys., vol. 40, no. 23, pp. 7467–7470, Dec. 2007.
[ 13 ]
U. Weißker, S. Philippi, A. Leonhardt, P. Banerjee, A. Reed, F. Wolny, Y. Obukhov, T. M, G. Xiang, R. Adur, I. Lee, A. J. Hauser, F. Y. Yang, D. V Pelekhov, B. Büchner, and P. C. Hammel, “Ultramicroscopy Quantitative magnetic force microscopy on permalloy dots using an iron filled carbon nanotube probe,” Ultramicroscopy, vol. 2, pp. 1–6, 2011.
[ 14 ]
S. Jeffery, A. Oral, and J. B. Pethica, “Quantitative electrostatic force measurement in AFM,” Appl. Surf. Sci., pp. 280–284, 2000.
[ 15 ]
A. Gigler, C. Gnahm, O. Marti, T. Schimmel, and S. Walheim, “Towards quantitative materials characterization with Digital Pulsed Force Mode imaging,” J. Phys. Conf. Ser., vol. 61, pp. 346–351, Mar. 2007.
[ 16 ]
A. Cuenat, A. Muñiz-Piniella, M. Muñoz-Rojo, W. C. Tsoi, and C. E. Murphy, “Quantitative nanoscale surface voltage measurement on organic semiconductor blends.,” Nanotechnology, vol. 23, no. 4, p. 045703, Feb. 2012.
[ 17 ]
B. Cappella and G. Dietler, “Force-distance curves by atomic force microscopy,” Surf. Sci. Rep., vol. 34, no. 1–3, pp. 1–104, 1999.
[ 18 ]
M. Brogly, H. Awada, and O. Noel, “4 Contact Atomic Force Microscopy: A Powerful Tool in Adhesion Science,” in Applied Scanning Probe Methods XI, B. Bhushan and H. Fuchs, Eds. Springer-Verlag Berlin Heidelberg, 2009, pp. 73–95.
[ 19 ]
A. Ptak, H. Gojzewski, M. Kappl, and H.-J. Butt, “Influence of humidity on the nanoadhesion between a hydrophobic and a hydrophilic surface,” Chem. Phys. Lett., vol. 503, no. 1–3, pp. 66–70, Feb. 2011.
[ 20 ]
C. Gu, C. Ray, S. Guo, and B. B. Akhremitchev, “Single-Molecule Force Spectroscopy Measurements of Interactions between C 60 Fullerene Molecules,” pp. 12898–12905, 2007.
[ 21 ]
C. C. Wu, H. W. Su, C. C. Lee, M. J. Tang, and F. C. Su, “Quantitative measurement of changes in adhesion force involving focal adhesion kinase during cell attachment, spread, and migration,” Biochem. Biophys. Res. Commun., vol. 329, no. 1, pp. 256–265, 2005.
[ 22 ]
D. Craig, A. Krammer, K. Schulten, and V. Vogel, “Comparison of the early stages of forced unfolding for fibronectin type III modules.,” Proc. Natl. Acad. Sci. U. S. A., vol. 98, no. 10, pp. 5590–5, May 2001.
[ 23 ]
A. Sikora and A. Iwan, “AFM study of the mechanical wear phenomena of the polyazomethine with thiophene rings: Tapping mode, phase imaging mode and force spectroscopy,” High Performance Polymers, vol. 24, no. 3. pp. 218–228, 2012.
[ 24 ]
F. Spectroscopy, W. Shi, Y. Zhang, C. Liu, Z. Wang, and X. Zhang, “Interaction between Dendrons Directly Studied by Single-Molecule,” Synthesis (Stuttg)., no. 29, pp. 1318–1323, 2008.
[ 25 ]
J. J. Roa, G. Oncins, F. T. Dias, V. N. Vieira, J. Schaf, and M. Segarra, “AFM as an alternative for Young’s modulus determination in ceramic materials in elastic deformation regime,” Phys. C Supercond. its Appl., vol. 471, no. 17–18, pp. 544–548, 2011.
[ 26 ]
E. Canetta and A. K. Adya, “Atomic force microscopic investigation of commercial pressure sensitive adhesives for forensic analysis.,” Forensic Sci. Int., vol. 210, no. 1–3, pp. 16–25, Jul. 2011.
[ 27 ]
S. Strasser, A. Zink, G. Kada, P. Hinterdorfer, O. Peschel, W. M. Heckl, A. G. Nerlich, and S. Thalhammer, “Age determination of blood spots in forensic medicine by force spectroscopy.,” Forensic Sci. Int., vol. 170, no. 1, pp. 8–14, Jul. 2007.
[ 28 ]
B. Bhushan, “Nanotribology and nanomechanics,” Wear, vol. 259, no. 7–12, pp. 1507–1531, Jul. 2005.
[ 29 ]
D. B. Serrell, J. Law, A. J. Slifka, R. L. Mahajan, and D. S. Finch, “A uniaxial bioMEMS device for imaging single cell response during quantitative force-displacement measurements,” Biomed. Microdevices, vol. 10, no. 6, pp. 883–889, 2008.
[ 30 ]
“NT-MDT company webpage/ Etalon probes information,” 2009. [Online]. Available: [Accessed: 07-Jul-2015].
[ 31 ]
F. J. Giessibl, “Atomic resolution on Si(111)-(7×7) by noncontact atomic force microscopy with a force sensor based on a quartz tuning fork,” Appl. Phys. Lett., vol. 76, no. 11, p. 1470, 2000.
[ 32 ]
F. J. Giessibl, “Subatomic Features on the Silicon (111)-(7x7) Surface Observed by Atomic Force Microscopy,” Science, vol. 289, no. 5478. pp. 422–425, 2000.
[ 33 ]
“Micro Star Technologies company webpage,” 2012. [Online]. Available: [Accessed: 07-Jul-2015].
[ 34 ]
G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett., vol. 53, no. 12, pp. 1045–1047, 1988.
[ 35 ]
H. Xie, J. Vitard, D. S. Haliyo, and S. Régnier, “Enhanced accuracy of force application for AFM nanomanipulation using nonlinear calibration of optical levers,” IEEE Sens. J., vol. 8, no. 8, pp. 1478–1485, 2008.
[ 36 ]
K. Nieradka, G. Jóźwiak, D. Kopiec, P. Grabiec, P. Janus, A. Sierakowski, and T. Gotszalk, “A method for linearization of split photodiode position detectors response,” Procedia Eng., vol. 25, pp. 358–361, 2011.
[ 37 ]
K. Nieradka, G. Małozięć, D. Kopiec, P. Grabiec, P. Janus, a Sierakowski, and T. Gotszalk, “Expanded beam deflection method for simultaneous measurement of displacement and vibrations of multiple microcantilevers.,” Rev. Sci. Instrum., vol. 82, no. 10, p. 105112, Oct. 2011.
[ 38 ]
D. Georgakaki, S. Mitridis, A. A. Sapalidis, E. Mathioulakis, and H. M. Polatoglou, “Calibration of tapping AFM cantilevers and uncertainty estimation: Comparison between different methods,” Meas. J. Int. Meas. Confed., vol. 46, no. 10, pp. 4274–4281, 2013.
[ 39 ]
J. E. Sader, I. Larson, P. Mulvaney, and L. R. White, “Method for the calibration of atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 66, no. 7, pp. 3789–3798, 1995.
[ 40 ]
C. T. Gibson, B. L. Weeks, C. Abell, T. Rayment, and S. Myhra, “Calibration of AFM cantilever spring constants,” Ultramicroscopy, vol. 97, no. 1–4, pp. 113–118, 2003.
[ 41 ]
“AIST-NT webpage.” [Online]. Available: [Accessed: 07-Jul-2015].
[ 42 ]
S. Rode, R. Stark, J. Lübbe, L. Tröger, J. Schütte, K. Umeda, K. Kobayashi, H. Yamada, and A. Kühnle, “Modification of a commercial atomic force microscopy for low-noise, high-resolution frequency-modulation imaging in liquid environment,” Rev. Sci. Instrum., vol. 82, no. 7, p. 073703, 2011.
[ 43 ]
D. Rugar, H. J. J. Mamin, and P. Guethner, “Improved fiber-optic interferometer for atomic force microscopy,” Appl. Phys. Lett., vol. 55, no. 25, pp. 2588–2590, 1989.
[ 44 ]
J. Chu, T. Itoh, C. Lee, T. Suga, and K. Watanabe, “Novel high vacuum scanning force microscope using a piezoelectric cantilever and the phase detection method,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct., vol. 15, no. 4, pp. 1551–1555, 1997.
[ 45 ]
T. Gotszalk, P. Grabiec, E. Tomerov, and I. W. Rangelow, “Thermally driven micromechanical beam with piezoresistive deflection readout,” Microelectron. Eng., vol. 68, pp. 550–556, 2003.
[ 46 ]
E. M. Chow, G. G. Yaralioglu, C. F. Quate, and T. W. Kenny, “Characterization of a two-dimensional cantilever array with through-wafer electrical interconnects,” Appl. Phys. Lett., vol. 80, no. 4, pp. 664–666, 2002.
[ 47 ]
I. W. Rangelow, T. Ivanov, K. Ivanova, B. E. Volland, P. Grabiec, Y. Sarov, A. Persaud, T. Gotszalk, P. Zawierucha, M. Zielony, D. Dontzov, B. Schmidt, M. Zier, N. Nikolov, I. Kostic, W. Engl, T. Sulzbach, J. Mielczarski, S. Kolb, D. P. Latimier, R. Pedreau, V. Djakov, S. E. Huq, K. Edinger, O. Fortagne, A. Almansa, and H. O. Blom, “Piezoresistive and self-actuated 128-cantilever arrays for nanotechnology applications,” Microelectron. Eng., vol. 84, no. 5–8, pp. 1260–1264, May 2007.
[ 48 ]
A. Schneider, R. H. Ibbotson, R. J. Dunn, V. Djakov, E. Huq, and T. Gotszalk, “Parallel Imaging with Arrays of SU-8 Microcantilevers,” no. September, 2010.
[ 49 ]
J. M. Łysko, P. Dumania, P. Janus, M. Grodner, H. Kłos, K. Skwara, and Grab, “Nanosensitive Silicon Microprobes for Mechanical Detection and Measurements,” Mater. Sci. Appl., vol. 02, no. 06, pp. 582–591, 2011.
[ 50 ]
D. Kopiec, P. Pałetko, K. Nieradka, W. Majstrzyk, P. Kunicki, A. Sierakowski, G. Jóźwiak, and T. Gotszalk, “Closed-loop surface stress compensation with an electromagnetically actuated microcantilever,” Sensors Actuators B Chem., vol. 213, pp. 566–573, 2015.
[ 51 ]
T. Göddenhenrich, H. Lemke, U. Hartmann, and C. Heiden, “Force microscope with capacitive displacement detection,” J. Vac. Sci. Technol. A, vol. 8, pp. 383–387, 1990.
[ 52 ]
G. Binnig, C. Gerber, E. Stoll, T. R. Albrecht, and C. F. Quate, “Atomic Resolution with Atomic Force Microscope,” Europhys. Lett., vol. 3, no. 12, pp. 1281–1286, Jun. 1987.
[ 53 ]
R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology, vol. 12, p. R1, 2001.
[ 54 ]
J. Hrabina, J. Lazar, P. Klapetek, and O. Číp, “Multidimensional interferometric tool for the local probe microscopy nanometrology,” Meas. Sci. Technol., vol. 22, no. 9, p. 94030, 2011.
[ 55 ]
M. Xu, T. Dziomba, G. Dai, and L. Koenders, “Self-calibration of scanning probe microscope: mapping the errors of the instrument,” Meas. Sci. Technol., vol. 19, no. 2, p. 025105, Feb. 2008.
[ 56 ]
S. Strube, G. Molnar, and H.-U. Danzebrink, “Compact field programmable gate array (FPGA)-based multi-axial interferometer for simultaneous tilt and distance measurement in the sub-nanometre range,” Meas. Sci. Technol., vol. 22, no. 9, p. 94026, Sep. 2011.
[ 57 ]
M. Zielony and T. Gotszalk, “Digital setting of scanning field in scanning probe microscopy,” Prz. Elektrotechniczny, vol. 86, no. 11A, pp. 180–183, 2010.
[ 58 ]
D. Nečas and P. Klapetek, “Gwyddion: an open-source software for SPM data analysis,” Cent. Eur. J. Phys., vol. 10, no. 1, pp. 181–188, Nov. 2011.
[ 59 ]
“SPIP online manual.” [Online]. Available: [Accessed: 07-Jul-2015].
[ 60 ]
I. Horcas, R. Fernández, J. M. Gómez-Rodríguez, J. Colchero, J. Gómez-Herrero, and a M. Baro, “WSXM: a software for scanning probe microscopy and a tool for nanotechnology.,” Rev. Sci. Instrum., vol. 78, no. 1, p. 13705, Jan. 2007.
[ 61 ]
J. M. Skwierczynski, G. Maloziec, D. Kopiec, K. Nieradka, J. Radojewski, and T. P. Gotzszalk, “Radio frequency modulation of semiconductor laser as an improvement method of noise performance of scanning probe microscopy position sensitive detectors,” Opt. Appl., vol. 41, no. 2, pp. 323–331, 2011.
[ 62 ]
A. Ptak, M. Kappl, and H. J. Butt, “Modified atomic force microscope for high-rate dynamic force spectroscopy,” Appl. Phys. Lett., vol. 88, no. 26, p. 263109, 2006.
[ 63 ]
W. F. Heinz and J. H. Hoh, “Spatially resolved force spectroscopy of biological surfaces using the atomic force microscope.,” Trends Biotechnol., vol. 17, no. 4, pp. 143–150, 1999.
[ 64 ]
C. Reynaud, F. Sommer, C. Quet, N. El Bounia, T. M. Duc, and N. El Bounia, “Quantitative determination of Young’s modulus on a biphase polymer system using atomic force microscopy,” Surf. Interface Anal., vol. 189, no. 30, pp. 185–189, Aug. 2000.
[ 65 ]
P. J. de Pablo, J. Colchero, J. Gómez-Herrero, A. M. Baró, P. J. De Pablo, and J. Gomez-Herrero, “Jumping mode scanning force microscopy,” Appl. Phys. Lett., vol. 73, no. 22, pp. 3300–3302, 1998.
[ 66 ]
F. Moreno-Herrero, J. Colchero, J. Gómez-Herrero, A. M. Baró, and J. Ávila, “Jumping mode atomic force microscopy obtains reproducible images of Alzheimer paired helical filaments in liquids,” Eur. Polym. J., vol. 40, no. 5, pp. 927–932, 2004.
[ 67 ]
E. Weilandt, S. Hild, O. Marti, and A. Rosa-Zeiser, “The simultaneous measurement of elastic, electrostatic and adhesive properties by scanning force microscopy: pulsed-force mode operation,” Meas. Sci. Technol., vol. 8, pp. 1333–1338, 1997.
[ 68 ]
J. Legleiter, M. Park, B. Cusick, and T. Kowalewski, “Scanning probe acceleration microscopy (SPAM) in fluids: mapping mechanical properties of surfaces at the nanoscale.,” Proc. Natl. Acad. Sci. U. S. A., vol. 103, no. 13, pp. 4813–8, Mar. 2006.
[ 69 ]
D. M. Panaitescu, A. N. Frone, M. Ghiurea, and I. Chiulan, “Influence of storage conditions on starch/PVA films containing cellulose nanofibers,” Ind. Crops Prod., vol. 70, pp. 170–177, 2015.
[ 70 ]
L. Chopinet, C. Formosa, M. P. Rols, R. E. Duval, and E. Dague, “Imaging living cells surface and quantifying its properties at high resolution using AFM in QITM mode.,” Micron, vol. 48, pp. 26–33, 2013.
[ 71 ]
O. Sahin, “Harnessing bifurcations in tapping-mode atomic force microscopy to calibrate time-varying tip-sample force measurements,” Rev. Sci. Instrum., vol. 78, no. 103707, pp. 1–4, 2007.
[ 72 ]
O. Sahin, S. Magonov, C. Su, C. F. Quate, and O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol., vol. 2, no. 8, pp. 507–514, 2007.
[ 73 ]
A. Sikora and L. Bednarz, “Mapping of the surface’s mechanical properties due to analysis of torsional cantilever bending in dynamic force microcopy,” in Scanning Probe Acoustic Techniques, F. Marinello, D. Passeri, and E. Savio, Eds. Springer Berlin Heidelberg, 2012, p. w druku.
[ 74 ]
A. Sikora, M. Woszczyna, M. Friedemann, F. J. Ahlers, and M. Kalbac, “AFM diagnostics of graphene-based quantum Hall devices.,” Micron, vol. 43, no. 2–3, pp. 479–86, Feb. 2012.
[ 75 ]
M. G. Reitsma, R. S. Gates, and R. F. Cook, “Torsional spring constant measurement of a T-shaped atomic force microscope cantilever Materials Science and Engineering Laboratory,” Exp. Mech., 2009.
[ 76 ]
J. A. Greenwood and K. L. Johnson, “Mechanics of adhesion of viscoelastic solids,” Philos. Mag. A Phys. Condens. Matter, Struct. Defects Mech. Prop., vol. 43, no. 3, pp. 697–711, 1981.
[ 77 ]
B. V Derjaguin, V. M. Muller, and Y. U. P. Toporov, “Effect of contact deformations on the adhesion of particles,” J. Colloid Interface Sci., vol. 53, pp. 314–326, 1975.
[ 78 ]
J. K. Kim, D. E. Lee, W. Il Lee, and K. Y. Suh, “Measurement of pull-off force on imprinted nanopatterns in an inert liquid.,” Nanotechnology, vol. 21, no. 29, p. 295306, Jul. 2010.
[ 79 ]
D. Xu and K. M. Liechti, “On the modified Tabor parameter for the JKR – DMT transition in the presence of a liquid meniscus,” vol. 315, pp. 772–785, 2007.
[ 80 ]
E. Boer-Duchemin, E. Tranvouez, and G. Dujardin, “The interaction of an atomic force microscope tip with a nano-object: a model for determining the lateral force.,” Nanotechnology, vol. 21, no. 45, p. 455704, Nov. 2010.
[ 81 ]
J. Drelich, G. W. Tormoen, and E. R. Beach, “Determination of solid surface tension from particle-substrate pull-off forces measured with the atomic force microscope.,” J. Colloid Interface Sci., vol. 280, no. 2, pp. 484–97, Dec. 2004.
[ 82 ]
C. Clifford and M. P. Seah, “Improved methods and uncertainty analysis in the calibration of the spring constant of an atomic force microscope cantilever using static experimental methods,” Meas. Sci. Technol., vol. 20, no. 12, p. 125501, Dec. 2009.
[ 83 ]
G. A. Matei, E. J. Thoreson, J. R. Pratt, D. Newell, and N. A. Burnham, “Precision and accuracy of thermal calibration of atomic force microscopy cantilevers,” Rev. Sci. Instrum., vol. 77, no. 8, p. 083703, 2006.
[ 84 ]
C. T. Gibson, D. Alastair Smith, and C. J. Roberts, “Calibration of silicon atomic force microscope cantilevers.,” Nanotechnology, vol. 16, no. 2, pp. 234–238, 2005.
[ 85 ]
“ISO 27911:2011, Surface chemical analysis -- Scanning-probe microscopy -- Definition and calibration of the lateral resolution of a near-field optical microscope.”
[ 86 ]
“ISO 11039:2012, Surface chemical analysis -- Scanning-probe microscopy -- Measurement of drift rate.”
[ 87 ]
“ISO 11952:2014, Surface chemical analysis -- Scanning-probe microscopy -- Determination of geometric quantities using SPM: Calibration of measuring systems.”
[ 88 ]
“ISO 13095:2014, Surface Chemical Analysis -- Atomic force microscopy -- Procedure for in situ characterization of AFM probe shank profile used for nanostructure measurement.”
[ 89 ]
“ISO/DIS 11775, Surface chemical analysis -- Scanning-probe microscopy -- Determination of cantilever normal spring constants.”
[ 90 ]
T. R. Albrecht, S. Akamine, T. E. Carver, C. F. Quate, and E. L. Ginzton, “Microfabrication of cantilever styli for the atomic force microscope,” J. Vac. Sci. Technol. A Vacuum, Surfaces, Film., vol. 94305, no. January, pp. 3386–3396, 1990.
[ 91 ]
H.-J. Butt, P. Siedle, K. Seifert, K. Fendler, T. Seeger, E. Bamberg, A. L. Weisenhorn, K. Goldie, and A. Engel, “Scan Speed Limit In Atomic Force Microscopy,” J. Microsc., vol. 169, no. 1, pp. 75–84, Jan. 1993.
[ 92 ]
J. E. Sader, “Parallel beam approximation for V-shaped atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 66, no. 9, pp. 4583–4587, 1995.
[ 93 ]
J. E. Sader, J. W. M. Chon, and P. Mulvaney, “Calibration of rectangular atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 70, no. 10, pp. 3967–3969, 1999.
[ 94 ]
J. W. M. Chon, P. Mulvaney, and J. E. Sader, “Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids,” J. Appl. Phys., vol. 87, no. 8, pp. 3978–3988, 2000.
[ 95 ]
H. Frentrup and M. S. Allen, “Error in dynamic spring constant calibration of atomic force microscope probes due to nonuniform cantilevers.,” Nanotechnology, vol. 22, no. 29, p. 295703, Jul. 2011.
[ 96 ]
J. Bowen, D. Cheneler, D. Walliman, S. G. Arkless, Z. Zhang, M. C. L. Ward, and M. J. Adams, “On the calibration of rectangular atomic force microscope cantilevers modified by particle attachment and lamination,” Meas. Sci. Technol., vol. 21, no. 11, p. 115106, Nov. 2010.
[ 97 ]
J. M. Neumeister and W. A. Ducker, “Lateral, normal, and longitudinal spring constants of atomic force microscopy cantilevers,” Rev. Sci. Instrum., vol. 65, no. 8, pp. 2527–2531, 1994.
[ 98 ]
C. A. Clifford and M. P. Seah, “The determination of atomic force microscope cantilever spring constants via dimensional methods for nanomechanical analysis,” Nanotechnology, vol. 16, no. 9. pp. 1666–1680, 2005.
[ 99 ]
B. Y. Chen, M. K. Yeh, and N. H. Tai, “Accuracy of the spring constant of atomic force microscopy cantilevers by finite element method,” Anal. Chem., vol. 79, no. 4, pp. 1333–1338, 2007.
[ 100 ]
J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma, “A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy,” vol. 403, no. 1993, 2012.
[ 101 ]
T. Gotszalk, P. B. Grabiec, and I. W. Rangelow, “A novel piezoresistive microprobe for atomic and lateral force microscopy,” Sensors Actuators A Phys., vol. 123–124, pp. 370–378, Sep. 2005.
[ 102 ]
F. Loizeau, T. Akiyama, S. Gautsch, A. Meister, P. Vettiger, and N. De Rooij, “2D cantilever array with fixed geometries and varying spring constants for life science applications,” Procedia Eng., vol. 25, pp. 669–672, 2011.
[ 103 ]
J. L. Hutter and J. Bechhoefer, “Calibration of atomic-force microscope tips,” Rev. Sci. Instrum., vol. 64, no. 7, pp. 1868–1873, 1993.
[ 104 ]
M. Jaschke, “Calculation of thermal noise,” Energy, vol. 6, pp. 1–7, 1995.
[ 105 ]
R. Levy and M. Maaloum, “Measuring the spring constant of atomic force microscope cantilevers: thermal fluctuations and other methods,” Nanotechnology, vol. 13, p. 33, 2002.
[ 106 ]
M. S. Allen, H. Sumali, and P. C. Penegor, “Effect of Tip Mass on Atomic Force Microscope Calibration by Thermal Method,” in Conference: 2009 IMAC-XXVII: Conference & Exposition on Structural Dynamics, 2009, pp. 1–9.
[ 107 ]
R. Proksch, T. E. Schäffer, J. P. Cleveland, R. C. Callahan, and M. B. Viani, “Finite optical spot size and position corrections in thermal spring constant calibration,” Nanotechnology, vol. 15, no. 9. pp. 1344–1350, 2004.
[ 108 ]
“Online ODB sensitivity calculator,” 2015. [Online]. Available:
[ 109 ]
L. O. Heim, T. S. Rodrigues, and E. Bonaccurso, “Direct thermal noise calibration of colloidal probe cantilevers,” Colloids Surfaces A Physicochem. Eng. Asp., vol. 443, pp. 377–383, 2014.
[ 110 ]
M. Boudaoud, Y. Haddab, Y. Le Gorrec, and P. Lutz, “Study of thermal and acoustic noise interferences in low stiffness atomic force microscope cantilevers and characterization of their dynamic properties,” Review of Scientific Instruments, vol. 83, no. 1. 2012.
[ 111 ]
S. F. Nørrelykke and H. Flyvbjerg, “Power spectrum analysis with least-squares fitting: Amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 81, no. 7, pp. 1–16, 2010.
[ 112 ]
E. Bonaccurso and H. J. Butt, “Microdrops on atomic force microscope cantilevers: Evaporation of water and spring constant calibration,” J. Phys. Chem. B, vol. 109, no. 1, pp. 253–263, 2005.
[ 113 ]
J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma, “A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy,” Rev. Sci. Instrum., vol. 64, no. 2, p. 403, 1993.
[ 114 ]
Y. M. Tseytlin, “Kinetostatic model of spring constant ratios for an AFM cantilever with end extended mass,” Ultramicroscopy, vol. 110, no. 2, pp. 126–129, 2010.
[ 115 ]
G. Jóźwiak, D. Kopiec, P. Zawierucha, T. Gotszalk, P. Janus, P. Grabiec, and I. W. Rangelow, “The spring constant calibration of the piezoresistive cantilever based biosensor,” Sensors Actuators, B Chem., vol. 170, pp. 201–206, 2012.
[ 116 ]
D. Kopiec, “PhD thesis: The properties and utilization of the micro- and nanomechanical tools for nanoforces measurements.,” Wrocław University of Technology, 2015.
[ 117 ]
M. Woszczyna, P. Zawierucha, M. Świątkowski, T. Gotszalk, P. Grabiec, N. Nikolov, J. Mielczarski, E. Mielczarska, N. Glezos, T. Ivanow, K. Ivanowa, Y. Sarov, and I. W. Rangelow, “Quantitative force and mass measurements using the cantilever with integrated actuator and deflection detector,” Microelectron. Eng., vol. 86, no. 4–6, pp. 1043–1045, Apr. 2009.
[ 118 ]
J. Singh and J. E. Whitten, “Forces between Polymer Surfaces and Self-Assembled Monolayers,” J. Macromol. Sci. Part A, vol. 45, no. 11, pp. 884–891, Sep. 2008.
[ 119 ]
J. Melcher, C. Carrasco, X. Xu, J. L. Carrascosa, J. Gómez-Herrero, P. José de Pablo, A. Raman, J. Melchera, C. Carrascob, X. Xua, J. L. Carrascosad, J. Gomez-Herrerob, P. J. de Pablob, and A. Ramana, “Origins of phase contrast in the atomic force microscope in liquids.,” Proc. Natl. Acad. Sci. U. S. A., vol. 106, no. 33, pp. 13655–13660, Aug. 2009.
[ 120 ]
J. te Riet, A. J. Katan, C. Rankl, S. W. Stahl, A. M. van Buul, I. Y. Phang, A. Gomez-Casado, P. Schön, J. W. Gerritsen, A. Cambi, A. E. Rowan, G. J. Vancso, P. Jonkheijm, J. Huskens, T. H. Oosterkamp, H. Gaub, P. Hinterdorfer, C. G. Figdor, and S. Speller, “Interlaboratory round robin on cantilever calibration for AFM force spectroscopy,” Ultramicroscopy, vol. 111, no. 12, pp. 1659–1669, 2011.
[ 121 ]
B. Ohler, “Cantilever spring constant calibration using laser Doppler vibrometry,” Rev. Sci. Instrum., vol. 78, no. 6, pp. 10–15, 2007.
[ 122 ]
D.-A. Mendels, M. Lowe, A. Cuenat, M. G. Cain, E. Vallejo, D. Ellis, and F. Mendels, “Dynamic properties of AFM cantilevers and the calibration of their spring constants,” J. Micromechanics Microengineering, vol. 16, no. 8, pp. 1720–1733, 2006.
[ 123 ]
J. D. Holbery, V. L. Eden, M. Sarikaya, and R. M. Fisher, “Experimental determination of scanning probe microscope cantilever spring constants utilizing a nanoindentation apparatus,” Rev. Sci. Instrum., vol. 71, no. 10, pp. 3769–3776, 2000.
[ 124 ]
J. D. Holbery and V. L. Eden, “A comparison of scanning microscopy cantilever force constants determined using a nanoindentation testing apparatus,” J. Micromechanics, vol. 10, no. 2000, pp. 85–92, 2000.
[ 125 ]
M.-S. Kim, J.-H. Choi, Y.-K. Park, and J.-H. Kim, “Atomic force microscope cantilever calibration device for quantified force metrology at micro- or nano-scale regime: the nano force calibrator (NFC),” Metrologia, vol. 43, no. 5, pp. 389–395, 2006.
[ 126 ]
M. S. Kim, I. M. Choi, Y. K. Park, and D. I. Kang, “Atomic force microscope probe calibration by use of a commercial precision balance,” Meas. J. Int. Meas. Confed., vol. 40, no. 7–8, pp. 756–760, 2007.
[ 127 ]
C. T. Gibson, G. S. Watson, and S. Myhra, “Determination of the spring constants of probes for force microscopy/spectroscopy,” Nanotechnology, vol. 7, no. 3. pp. 259–262, 1999.
[ 128 ]
R. S. Gates and J. R. Pratt, “Prototype cantilevers for SI-traceable nanonewton force calibration,” Meas. Sci. Technol., vol. 17, no. 10, pp. 2852–2860, 2006.
[ 129 ]
M. G. Reitsma and R. S. Gates, “A New High Precision Procedure for AFM Probe Spring Constant Measurement using a Microfabricated Calibrated Reference Cantilever Array (CRCA),” NSTI-Nanotech 2006, vol. 1, pp. 785–788, 2006.
[ 130 ]
A. D. Slattery, A. J. Blanch, J. S. Quinton, and C. T. Gibson, “Accurate measurement of Atomic Force Microscope cantilever deflection excluding tip-surface contact with application to force calibration,” Ultramicroscopy, vol. 131, pp. 46–55, 2013.
[ 131 ]
G. A. Shaw, J. Kramar, and J. Pratt, “SI-traceable spring constant calibration of microfabricated cantilevers for small force measurement,” Exp. Mech., vol. 47, no. 1, pp. 143–151, 2007.
[ 132 ]
E. D. Langlois, G. A. Shaw, J. A. Kramar, J. R. Pratt, and D. C. Hurley, “Spring constant calibration of atomic force microscopy cantilevers with a piezosensor transfer standard,” Rev. Sci. Instrum., vol. 78, no. 9, 2007.
[ 133 ]
P. J. Cumpson, C. A. Clifford, and J. Hedley, “Quantitative analytical atomic force microscopy: a cantilever reference device for easy and accurate AFM spring-constant calibration,” Meas. Sci. Technol., vol. 15, no. 7, pp. 1337–1346, Jul. 2004.
[ 134 ]
C. J. Tourek and S. Sundararajan, “An alternative method to determining optical lever sensitivity in atomic force microscopy without tip-sample contact,” Rev. Sci. Instrum., vol. 81, no. 7, 2010.
[ 135 ]
P. J. Cumpson and J. Hedley, “Accurate analytical measurements in the atomic force microscope: a microfabricated spring constant standard potentially traceable to the SI.” Nanotechnology, vol. 14, no. 12, pp. 1279–1288, 2003.
[ 136 ]
P. J. P. J. Cumpson, P. Zhdan, and J. Hedley, “Calibration of AFM cantilever stiffness: A microfabricated array of reflective springs,” Ultramicroscopy, vol. 100, no. 3–4, pp. 241–251, Aug. 2004.
[ 137 ]
P. J. Cumpson, J. Hedley, C. A. Clifford, X. Chen, and S. Allen, “Microelectromechanical system device for calibration of atomic force microscope cantilever spring constants between 0.01 and 4 N/m,” J. Vac. Sci. Technol. A Vacuum, Surfaces, Film., vol. 22, no. 4, p. 1444, 2004.
[ 138 ]
R. Wagner, J. P. Killgore, R. C. Tung, A. Raman, and D. C. Hurley, “Vibrational shape tracking of atomic force microscopy cantilevers for improved sensitivity and accuracy of nanomechanical measurements,” Nanotechnology, vol. 26, no. 4, p. 045701, 2015.
[ 139 ]
M. Ekwińska, G. Ekwiński, and Z. Rymuza, “Calibration of normal force in atomic force microscope,” in Recent Advantages in Mechatronics, Springer Berlin Heidelberg, 2007, pp. 505–510.
[ 140 ]
M. Ekwińska and Z. Rymuza, “Normal Force Calibration Method Used for Calibration of Atomic Force Microscope,” vol. 116, pp. 78–81, 2009.
[ 141 ]
“Nanoidea webpage.” [Online]. Available: [Accessed: 14-Jun-2013].
[ 142 ]
A. Sikora, L. Bednarz, G. Ekwiński, and M. Ekwińska, “The determination of the spring constant of T-shaped cantilevers using calibration structures,” Meas. Sci. Technol., vol. 25, no. 4, p. 044015, Apr. 2014.
[ 143 ]
X. Li, D. Su, and Z. Zhang, “A novel technique of microforce sensing and loading,” Sensors Actuators, A Phys., vol. 153, no. 1, pp. 13–23, 2009.
[ 144 ]
B. Liu, Y. Yu, D. K. Yao, and J. Y. Shao, “A direct micropipette-based calibration method for atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 80, no. 6, pp. 1–9, 2009.
[ 145 ]
S. M. Notley, S. Biggs, and V. S. J. Craig, “Calibration of colloid probe cantilevers using the dynamic viscous response of a confined liquid,” Rev. Sci. Instrum., vol. 74, no. 9, pp. 4026–4032, 2003.
[ 146 ]
V. Kelley and R. Wishengrad, “PeakForce QNM User Guide 004-1036-000,” 2011.
[ 147 ]
C. T. Gibson, D. J. Johnson, C. Anderson, C. Abell, and T. Rayment, “Method to determine the spring constant of atomic force microscope cantilevers,” Rev. Sci. Instrum., vol. 75, no. 2, pp. 565–567, 2004.
[ 148 ]
G. B. Webber, G. W. Stevens, F. Grieser, R. R. Dagastine, and D. Y. C. Chan, “Variations in properties of atomic force microscope cantilevers fashioned from the same wafer.,” Nanotechnology, vol. 19, no. 10, p. 105709, 2008.
[ 149 ]
S. A. Edwards, W. A. Ducker, and J. E. Sader, “Influence of atomic force microscope cantilever tilt and induced torque on force measurements,” J. Appl. Phys., vol. 103, no. 6, 2008.
[ 150 ]
J. L. Hutter, “Comment on Tilt of Atomic Force Microscopy Cantilevers,” Langmuir, vol. 21, pp. 2630–2632, 2005.
[ 151 ]
R. S. Gates and J. R. Pratt, “Accurate and precise calibration of AFM cantilever spring constants using laser Doppler vibrometry,” Nanotechnology, vol. 23, no. 37. p. 375702, 2012.
[ 152 ]
M.-S. Kim, J.-H. Choi, J.-H. Kim, and Y.-K. Park, “Accurate determination of spring constant of atomic force microscope cantilevers and comparison with other methods,” Measurement, vol. 43, no. 4, pp. 520–526, May 2010.
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