In this paper we present a comparison of three different methods that can be used for estimating the stiffness of qPlus sensors. The first method is based on continuum theory of elasticity. The second (Cleveland's method) uses the change in the eigenfrequency that is induced by the loading of small masses. Finally, the stiffness is obtained by analysis of the thermal noise spectrum. We show that all three methods give very similar results. Surprisingly, neither the gold wire nor the gluing give rise to significant changes of the stiffness in the case of our home-built sensors. Furthermore we describe a fast and cost-effective way to perform Cleveland's method. This method is based on gluing small pieces of a tungsten wire; the mass is obtained from the volume of the wire, which is measured by optical microscopy. To facilitate detection of oscillation eigenfrequencies under ambient conditions, we designed and built a device for testing qPlus sensors.

Institute of Physics Academy of Sciences of the Czech Republic Cukrovarnicka 10 162 53 Prague Czech Republic

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Binnig G, Rohrer H, Gerber C, Weibel E. Phys Rev Lett. 1982;49:57–61. doi: 10.1103/PhysRevLett.49.57. DOI

Binnig G, Quate C F, Gerber C. Phys Rev Lett. 1986;56:930–933. doi: 10.1103/PhysRevLett.56.930. PubMed DOI

Albrecht T R, Grütter P, Horne D, Rugar D. J Appl Phys. 1991;69:668–673. doi: 10.1063/1.347347. DOI

Giessibl F J. Science. 1995;267:68–71. doi: 10.1126/science.267.5194.68. PubMed DOI

Barth C, Reichling M. Nature. 2001;414:54–57. doi: 10.1038/35102031. PubMed DOI

Sugimoto Y, Pou P, Abe M, Jelinek P, Pérez R, Morita S, Custance Ó. Nature. 2007;446:64–67. doi: 10.1038/nature05530. PubMed DOI

Setvín M, Mutombo P, Ondráček M, Majzik Z, Śvec M, Cháb V, Ošt’ádal I, Sobotik P, Jélinek P. ACS Nano. 2012;6:6969. doi: 10.1021/nn301996k. PubMed DOI

Teobaldi G, Lämmle K, Trevethan T, Watkins M, Schwarz A, Wiesendanger R, Shluger A L. Phys Rev Lett. 2011;106:216102. doi: 10.1103/PhysRevLett.106.216102. PubMed DOI

Ternes M, Lutz C P, Hirjibehedin C F, Giessibl F J, Heinrich A J. Science. 2008;319:1066–1069. doi: 10.1126/science.1150288. PubMed DOI

Sugimoto Y, Pou P, Custance O, Jelinek P, Abe M, Perez R, Morita S. Science. 2008;322:413–417. doi: 10.1126/science.1160601. PubMed DOI

Hirth S, Ostendorf F, Reichling M. Nanotechnology. 2006;17:148–154. doi: 10.1088/0957-4484/17/7/S08. PubMed DOI

Dürig U, Gimzewski J K, Pohl D W. Phys Rev Lett. 1986;57:2403–2406. doi: 10.1103/PhysRevLett.57.2403. PubMed DOI

Howald L, Meyer E, Lüthi R, Haefke H, Overney R, Rudin H, Güntherodt H-J. Appl Phys Lett. 1993;63:117–120. doi: 10.1063/1.109732. DOI

Loppacher C, Bammerlin M, Guggisberg M, Schär S, Bennewitz A, Baratoff A, Meyer E, Güntherodt H-J. Phys Rev B. 2000;62:16944. doi: 10.1103/PhysRevB.62.16944. DOI

Giessibl F J. Appl Phys Lett. 2000;76:1470–1472. doi: 10.1063/1.126067. DOI

Ternes M, González C, Lutz C P, Hapala P, Giessibl F J, Jelínek P, Heinrich A J. Phys Rev Lett. 2011;106:016802. doi: 10.1103/PhysRevLett.106.016802. PubMed DOI

König T, Simon G H, Rust H-P, Heyde M. Appl Phys Lett. 2009;95:083116. doi: 10.1063/1.3189282. DOI

Fournier N, Wagner C, Weiss C, Temirov C, Tautz F S. Phys Rev B. 2011;84:035435. doi: 10.1103/PhysRevB.84.035435. DOI

Sun Y, Mortensen H, Schär S, Lucier A-S, Miyahara Y, Grütter P, Hofer W. Phys Rev B. 2005;71:193407. doi: 10.1103/PhysRevB.71.193407. DOI

Majzik Z, Setvín M, Bettac A, Feltz A, Cháb V, Jelínek P. Beilstein J Nanotechnol. 2012;3:249–259. doi: 10.3762/bjnano.3.28. PubMed DOI PMC

Hembacher S, Giessibl F J, Mannhart J, Quate C F. Phys Rev Lett. 2005;94:056101. doi: 10.1103/PhysRevLett.94.056101. PubMed DOI

Sweetman A, Jarvis S, Danza R, Bamidele J, Gangopadhyay S, Shaw G A, Kantorovich L, Moriarty P. Phys Rev Lett. 2011;106:136101. doi: 10.1103/PhysRevLett.106.136101. PubMed DOI

Shaw G A, Pratt J R, Kubarych Z J. Small mass measurements for tuning fork-based force microscope cantilever spring constant calibration; Proceedings of the Society for Experimental Mechanics; 2011. NIST.

Kennedy S J, Cole D G, Clark R L. Rev Sci Instrum. 2009;80:125103. doi: 10.1063/1.3263907. PubMed DOI

Cleveland J P, Manne S, Bocek D, Hansma P K. Rev Sci Instrum. 1993;64:403. doi: 10.1063/1.1144209. DOI

Gao S, Zhang Z, Wu Y, Herrmann K. Meas Sci Technol. 2009;21:015103. doi: 10.1088/0957-0233/21/1/015103. DOI

Cole D G. Meas Sci Technol. 2008;19:125101. doi: 10.1088/0957-0233/19/12/125101. DOI

Lübbe J, Doering L, Reichling M. Meas Sci Technol. 2012;23:045401. doi: 10.1088/0957-0233/23/4/045401. DOI

Wutscher E, Giessibl F J. Rev Sci Instrum. 2011;82:093703. doi: 10.1063/1.3633950. PubMed DOI

Morita S, Giessibl F J, Wiesendanger R. Noncontact Atomic Force Microscopy. Springer; 2009.

Chen C J. Introduction to Scanning Tunneling Microscopy. Oxford University Press; 1993.

Golovko D S, Haschke T, Wiechert W, Bonaccurso E. Rev Sci Instrum. 2007;78:043705. doi: 10.1063/1.2720727. PubMed DOI

Gibson C T, Weeks B L, Abell C, Rayment T, Myhra S. Ultramicroscopy. 2003;97:113–118. doi: 10.1016/S0304-3991(03)00035-4. PubMed DOI

Welker J, de Faria Elsner F, Giessibl F J. Appl Phys Lett. 2011;99:084102. doi: 10.1063/1.3627184. DOI

Sader J E, Jarvis S P. Appl Phys Lett. 2004;84:1801. doi: 10.1063/1.1667267. DOI

Graphene on SiC(0001) inspected by dynamic atomic force microscopy at room temperature