Determination of the nanoscale dielectric properties in ferroelectric lead zirconate titanate (PZT) thin films

We report on nanoscale experiments with <100 nm lateral resolution being able to differentiate the effective dielectric polarisation Pz, deposited charge density σ, surface dielectric constant εsurface, its voltage dependence εsurface(U), as well as the built-in electric bias voltage Uint in ferroelectric lead zirconate titanate (PZT) thin films. This is possible by combining piezoresponse force microscopy (PFM) and pull-off force spectroscopy (PFS), both methods based on scanning force microscopy (SFM). The differentiation becomes possible since both Pz and σ contribute additively in PFS, while they are subtractive in PFM, hence allowing the two contributions to be separated. εsurface can be quantified by means of the experimental PFS data and the calculated effective penetration depth of PFM developed in a finite element modelling. Finally, Uint and εsurface(U) are derived by an absolute matching of the Pz values measured by PFM and PFS.Our nanoscale results obtained on PZT thin films reveal values for the above specified quantities that have the same order of magnitude as those obtained from macroscopic measurements reflecting the integral response using large electrode areas. However, we stress that the data reported here reveal physical properties deduced on the nanometer scale. Furthermore, they are recorded during one single experimental investigation, using one single set-up only.