I have read some articles about calculation piezoelectric properties by AFM, especially contact mode. Could you bring any resources, data, experience, and thoughts about that?
I suggest you to have a look at the following papers:
-Investigations into local piezoelectric properties by atomic force microscopy
C. Durkan, D. P. Chu, P. Migliorato, and M. E. Welland
Applied Physics Letters 76(3):366-368 (2000)
Available on RG at: https://www.researchgate.net/publication/234884976_Investigations_into_local_piezoelectric_properties_by_atomic_force_microscopy
-Piezoelectric and Semiconducting Coupled Power Generating Process of a Single ZnO Belt/Wire. A Technology for Harvesting Electricity from theEnvironment
Jinhui Song, Jun Zhou, and Zhong Lin Wang
Nano Letters, Vol.6 (8) 1656-1662 (2006)
Available at: http://nanoscience.gatech.edu/zlwang/paper/2006/06_NL_5.pdf
-Piezoresponse force microscopy of ferroelectric thin films
In University of Groningen research database by A. Morelli (2009)
Available at: https://www.rug.nl/research/portal/files/2657210/02_c2.pdf
I suggest to check publications about Piezoresponse Force Microscopy (PFM). As far as I know, Neus Domingo is a well-known researcher in that field, you should have a look at her publications:
In an ideal AFM piezoelectric measurement, an electric field is applied to a piezoelectric material, and the tip accurately follows the piezoelectric motion. However, a significant challenge of AFM piezoelectric measurements is that the tip motion can be due to a combination of piezoelectricity, electrostriction, and electrostatic interactions between the tip and electric field present.10 If the piezoelectric is driven by a voltage at a frequency f, the piezoelectric motion will also be of frequency f, since the piezoelectric constant represents the linear relation between the strain and applied field. The higher-order electrostrictive term depends upon the square of the applied field, and would, therefore, be at a frequency 2f. The displacement of the tip due to its interaction with the electric field also exhibits an f component. So a measurement of the f component of the tip deflection is a superposition of piezoelectric motion and motion due to the electrostatic interaction. In order to accurately measure the magnitude of the piezoelectric constant, the interaction between the tip and electric field must be minimized. The need to reduce this tip-field interaction determines the type of tips that can be used in piezoelectric measurements.
Article Electric field induced nanoscale polarization switching and ...
In terms of AFM measurement, you will typically obtain both the amplitude and phase measurements. For Bruker AFM's, the default unit for amplitude is in voltage, thus it is crucial to change the unit to metric scale (nm) in order to use the amplitude data for calculations such as piezoelectric coefficient (d33). In terms of phase measurement, the default unit is typically in degrees and it indicates the dipole moments on the sample surface.
In terms of sample preparation, for bulk piezoelectric sample, you would need to ensure electrical contact on the bottom or top of the sample. For thin film piezoelectric sample, you would need to ensure electrical contact on the top of the sample.
I hope this helps. Don't hesitate to message me if you have any questions regarding PFM.