relevance of d33 in resonance enhanced PFM?
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The signal at the resonance (maximal amplitude) is the sum of d33 and electrostatic component. For stiff cantilever and tip and surface potentials approximately equal, it will be d33 Q, where Q is a quality factor. The caveats are:
- generally the Q factor is unknown and is position dependent
- and standard methods (e.g. based on analog phase locked loops) cannot trace the resonance in PFM. AN dresonance frequency is strongly position dependent (resonance frequency can change by 100 kHz for peak wodth of 5 kHz)
The theory of the frequency dependent PFM can be found in
S. JESSE, A.P. BADDORF, and SERGEI V. KALININ, Dynamic Effects in Electromechanical Scanning Probe Microscopies, Nanotechnology 17, 1615 (2006).
This paper also cites several works by C. Harnagea which explore this issue. Also, on Asylum web-ste there is a 24 page support note that discusses this issue (look http://www.asylumresearch.com).
The frequency -tracking methods in PFM can be found in:
S. JESSE, P. MAKSYMOVYCH, and SERGEI V. KALININ, Rapid Multidimensional Data Acquisition in Scanning Probe Microscopy Applied to Local Polarization Dynamics and Voltage Dependent Contact Mechanics, Appl. Phys. Lett. 93, 112903 (2008).
B.J. RODRIGUEZ, C. CALLAHAN, S.V. KALININ, and R. PROKSCH, Dual-Frequency Resonance-Tracking Atomic Force Microscopy, Nanotechnology 18, 475504 (2007).
STEPHEN JESSE, SERGEI V. KALININ, R. PROKSCH, A.P. BADDORF, and B.J. RODRIGUEZ, Energy Dissipation Measurements on the Nanoscale: Band Excitation Method in Scanning Probe Microscopy, Nanotechnology 18, 435503 (2007),
There was also a very nice concept of two-stage cantilevers developed by Veeco and UCSB folks (you can find it by searching for. papers by B. Pittinger in APL)