title: Calibration of higher eigenmodes of cantilevers.
abstract: A method is presented for calibrating the higher eigenmodes (resonant modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine a power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonant frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for several cantilever models. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Aleksander
authors.initials: A
authors.lastname: Labuda
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Marta
authors.initials: M
authors.lastname: Kocun
authors.affiliation: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Martin
authors.initials: M
authors.lastname: Lysy
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Tim
authors.initials: T
authors.lastname: Walsh
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Jieh
authors.initials: J
authors.lastname: Meinhold
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Tania
authors.initials: T
authors.lastname: Proksch
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Waiman
authors.initials: W
authors.lastname: Meinhold
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Caleb
authors.initials: C
authors.lastname: Anderson
authors.affiliation: Asylum Research, an Oxford Instruments Company, Santa Barbara, California 93117, USA.
authors.forename: Roger
authors.initials: R
authors.lastname: Proksch