Signal interpretation in DFRT PFM
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Hello,
In attempting DFRT PFM of nanoscale ferroelectrics, how is one supposed to interpret the collected signals of multiple amplitude and phase channels (more specifically phase)? Is it correct to assume that the average of Amp1 and Amp2 will yield the magnitude of the response?
As far as phase goes, in published data it has been represented from -100 to 100 in a range representing the domain state orientation, however my collected signal (for both channels) can range from 0-180, 180-270, 270-360, which makes interpretation of these phase signals and the qualitative orientation of the domains unclear. I would greatly appreciate any clarification of these issues. -
In DRFT, two things are true if peak is single-harmonic oscillator like:
- the resonance frequency is tarcked correctly
- the sum of amplitudes is proportional to maximal response
If the width of the peak is (a) known and (b) is position independent, both the dissipation and absolute response can be ascertained.
Experience with band excitation (which can be interpreted as N-frequency version of DRFT) suggests that
- for decent samples (single crystals, films) peak is well behaved -> DRFT should work
- for nanopparticles, nanowires, etc. there are very large changes in peak shape - > DRFT not guaranteed to work.
However, in any case it will work much better then single-frequency PFM -
So is that to say that in the case of a nanoparticle or nanowire, the large changes in peak shape result in artifacts within the phase signals? Would there be any post processing required to see negative phase values? As it is collected on the Asylum, the phase only is collected from a 0-360 range.
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There are three answers:
- the next person to ask is Roger Proksch (roger@asylumresearch.com), who have started the whole DRFT business
- band excitation and its equivalents are the only fully reliable way to do these measurements (equivalents inclusing full amplitude-frequency sweeps by Kos and Hurley, and many single-frequency maps by Huey)
- better somehting then nothing -
tak emaps at each frequency (say, from 100 kHz to 200 kHz with 2 kHz step), you will be able to align them (e.g. using imge toolbox in MatLab) and recover resoances. It is not the most easy approach - can be done once, but probably not most productive in long run.
Importantly, very often resoannce frequency changes during spectroscopic experiment (i.e. hysteresis loop acquisitions), and there image alighning approach does not work at all. -
No. Taking several cantilever tunes at "suspect" locations may help.
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Snnnn, a couple of things regarding your questions...
Since the phase it typicaly 90 degrees at resonance, we have adjusted the phase range to be between -90 and +270 degrees. If it goes outside of this, we wrap it back into that range. It is perfectly possible to access the unwrapped data, contact me offline if you would like t play with that.
The original idea behind DFRT was to make use of the contact resonance for better SNR while avoiding crosstalk between changes in the contact resonance due to topography. This ends up making nice images at a good SNR. Since then, we've realized that since we have A1, A2, phi1 and phi2 we have enough information to quantify other things. Within the framework of a simple harmonic oscillator, we can get the drive amplitude (proportional to d33), drive phase (polarization direction), resonant frequency (stiffness) and Q (dissipation). One recent nice observation is that solving the transcendental equations to et these quantities also does not converge when the interactions are non-linear. This is a nice safety/reality check on the measurments.
Hope this helps,
Roger