AVS 50th International Symposium
    Nanometer Structures Thursday Sessions
       Session NS-ThM

Paper NS-ThM5
Thermal Approach to Cantilever Calibration over a 200 kHz Bandwidth

Thursday, November 6, 2003, 9:40 am, Room 308

Session: Advances in Scanning Probes
Presenter: N.A. Burnham, Worcester Polytechnic Institute
Authors: G.A. Matei, Wayne State University
E.J. Thoreson, Worcester Polytechnic Institute
N.A. Burnham, Worcester Polytechnic Institute
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A cantilever's stiffness can be determined from an analysis of its thermal distribution spectrum, making use of the equipartition theorem k = k@sub B@T, where k is the cantilever stiffness and k@sub B@T is the thermal energy. We recently showed that it is possible to obtain good values for k, even when the cantilever's resonance is close to the edge of the data acquisition bandwidth, with the formula k = k@sub B@TQ@DELTA@@nu@/(@pi@@nu@@sub k@).@footnote 1@ Here, Q is the quality factor, @DELTA@@nu@ the frequency resolution of the data acquisition, @nu@@sub k@ is the resonant frequency, and is the mean-square amplitude at resonance. The initial work was limited to a 30 kHz bandwidth, that is, to cantilevers of stiffness less than approximately 0.4 N/m. Thermal calibration methods are independent of materials properties, coating thickness, cantilever geometry, and the viscosity of the medium, so there is good motivation to extend the methodology to higher bandwidths and thus stiffer cantilevers. We have now expanded the frequency range to 200 kHz, the bandwidth of the preamplifier of our AFM. By monitoring the raw A-B signal with an oscilloscope, then downloading the signal to a computer in order to manipulate the data, we have determined the stiffness of a 180 kHz cantilever to be 3.9 ± 0.2 N/m. By comparing our results for "force-calibrated" cantilevers with the manufacturer's stiffness calculation, we estimate that the accuracy of our method is 5%. By inverting a coated cantilever and repeating the measurement on the uncoated side, we believe that the precision is a similar value. Moreover, consistent with finite-element analyses, we find that the coating can perturb the stiffness by twenty percent. @FootnoteText@@footnote 1@Comparison of Calibration Methods for Atomic-Force Microscopy Cantilevers," NA Burnham, X Chen, CS Hodges, GA Matei, EJ Thoreson, CJ Roberts, MC Davies, SJB Tendler, Nanotechnology 14 (2003) 1-6.