Calibration of higher eigenmode spring constants of atomic force microscope cantilevers

PACS: 06.20.fb Standards and calibration 07.79.Lh Atomic force microscopesJosé R. Lozano...et al.Standard spring constant calibration methods are compared when applied to higher eigenmodes of cantilevers used in dynamic atomic force microscopy (dAFM). Analysis shows that Sader's original method (Sader et al 1999 Rev. Sci. Instrum. 70 3967–9), which relies on a priori knowledge of the eigenmode shape, is poorly suited for the calibration of higher eigenmodes. On the other hand, the thermal noise method (Hutter and Bechhoefer 1993 Rev. Sci. Instrum. 64 1868–73) does not require knowledge of the eigenmode and remains valid for higher eigenmodes of the dAFM probe. Experimental measurements of thermal vibrations in air for three representative cantilevers are provided to support the theoretical results.er and assistance with data collection from R Wagner. AR gratefully acknowledges financial support from the National Science Foundation via grant CMMI-0927648. JRL acknowledges the hospitality and funding offered to him by A Raman’s group at the Birck Nanotechnology Center, Purdue University, during the completion of this work, as well as financial support from Ministerio de Ciencia e Innovaci´on (Contract No. MAT2009- 08650) and Comunidad de Madrid (Contract No. S2009/MAT- 1467) in Spain.Peer reviewe