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Ultrasonic modes in atomic force microscopy

: Kopycinska-Müller, M.; Reinstädtler, M.; Rabe, U.; Caron, A.; Hirsekorn, S.; Arnold, W.

Arnold, W.:
Acoustical Imaging. Vol.27: Proceedings of the 27th International Symposium on Acoustical Imaging : Took place in Saarbrücken from March 24th to March 27th 2003
New York, NY: Kluwer Academic Publishers, 2004 (Acoustical imaging 27)
ISBN: 1-4020-2401-0
International Symposium on Acoustical Imaging <27, 2003, Saarbrücken>
Fraunhofer IZFP ()
atomic force microscopy

Atomic Force Acoustic Microscopy (AFAM) and Lateral Atomic Force Acoustic Microscopy (LAFAM) are dynamic enhancements of the Atomic Force Microscope (AFM). They combine the high lateral resolution of the AFM technique with an excessive sensitivity of a vibrating AFM cantilever to the elastic moduli of an investigated surface. Rectangular-shaped AFM cantilevers behave like a beam clamped from one side. When excited, it can vibrate in a bending or torsional mode. The value of the free resonance frequencies depend on the geometry of the cantilever and its mechanical properties. The AFM cantilever contacting a sample surface via the tip is an equivalent of a beam with two ends clamped. Such a system is stiffer and its "contact" resonance is shifted to higher frequency as compared to the free resonances. The value of the contact resonance frequency depends on the tip-sample forces, like elastic, electrostatic, hydrostatic, and lateral (friction) forces allowing one to deduce information on the surface properties related to these forces. The tip-sample interactions can be described as a set of vertical and lateral springs with dampers. The spring describing vertical forces corresponds to tip-sample vertical contact stiffness which contains both the elastic constants of the tip and the sample, and their contact area. The spring constant of the lateral spring is the lateral tip-sample contact stiffness that contains information about the G modulus. Depending on whether one insonifies either longitudinal or shear waves in the sample, one of the springs can be investigated in detail. The bending modes are excited by out-of-plane oscillations of a sample surface caused by longitudinal waves. A transversal wave with direction of polarization perpendicular to the long axis of the cantilever beam induces torsional vibrations of the cantilever. AFAM and LAFAM techniques can be applied in a spectroscopy and in an imaging mode. In the spectroscopy mode the amplitude of the cantilever vibrations is measured in the function of an applied ultrasound frequency. For small amplitudes of the surface vibrations the value of the contact resonance frequencies can be used to calculate the indentation modulus (bending mode) and shear modulus (torsional mode). When the excitation amplitude increases the measured resonance curves display non-linear behavior. Analysis of such non-linear spectra can provide information about adhesion and friction in the case of the bending and torsional modes, respectively. Usually the amplitude of the cantilever vibration at a frequency close the contact resonance frequency is used for imaging purpose. However, it is also possible to display the contact resonance frequency as an imaging quantity. Examples of spectra in linear and non-linear range, as well as images obtained on various samples with help of AFAM and LAFAM technique will be presented. We will also demonstrate the application of bending and torsional modes of cantilever vibrations for detection of out-of-plane and in-plane oriented ferroelectric domains in the so-called ultrasonic piezo-mode technique.