Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscop
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Muñoz-Saldañaa) and D. Torres-Torres Centro de Investigación y Estudios Avanzados del IPN. Unidad Querétaro, 76001 Querétaro, Qro., México
R. Torres-Martínez Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del IPN. Unidad Querétaro, 76040, Querétaro, Qro., México
G.A. Schneider Hamburg University of Technology, Advanced Ceramics Group, 21073 Hamburg, Germany (Received 14 March 2006; accepted 10 August 2006)
Measurements of vibrational spectra of atomic force microscopy (AFM) microprobes in contact with a sample allow a good correlation between resonance frequencies shifts and the effective elastic modulus of the tip-sample system. In this work we use finite element methods for modeling the AFM microprobe vibration considering actual features of the cantilever geometry. This allowed us to predict the behavior of the cantilevers in contact with any sample for a wide range of effective tip-sample stiffness. Experimental spectra for glass and chromium were well reproduced for the numerical model, and stiffness values were obtained. We present a method to correlate the experimental resonance spectrum to the effective stiffness using realistic geometry of the cantilever to numerically model the vibration of the cantilever in contact with a sample surface. Thus, supported in a reliable finite element method (FEM) model, atomic force acoustic microscopy can be a quantitative technique for elastic-modulus measurements. Considering the possibility of tip-apex wear during atomic force acoustic microscopy measurements, it is necessary to perform a calibration procedure to obtain the tip-sample contact areas before and after each measurement.
I. INTRODUCTION
Atomic force microscopy (AFM) has become in the past years one of the most useful microscopic tools for imaging the surface topography at nanoscale level of several types of materials, whereby it is an essential technique for nanotechnology. AFM is very sensitive for measuring interaction forces between the AFM microprobe and the sample.1–3 The simplest interaction between the AFM microprobe and the sample is the mechanical contact, but it is possible to introduce in a controlled way several additional interaction forces, including electric and magnetic fields. For modulated
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0379 3072 J. Mater. Res., Vol. 21, No. 12, Dec 2006 http://journals.cambridge.org Downloaded: 25 Mar 2015
forces4 acting on the microprobe–sample contact, it is possible to increase the sensitivity of the measurement, including high-frequency excitations. Heterodyne converter procedures combined with lock-in amplifiers allow amplifying very low signals, due to the interaction between AFM microprobe and the sample, for a frequency range from some kHz to several MHz.5 Atomic force acoustic microscopy (AFAM) is a high-frequency force modulation AFM technique that provides stiffness mapping of surfaces. A piezoelectric transducer attached to the AFM microprobe holder or located in the
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