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 P_z, deposited charge density σ, surface dielectric constant ε_surface, its voltage dependence ε_surface(U), as well as the built-in electric bias voltage U_int 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 P_z and σ contribute additively in PFS, while they are subtractive in PFM, hence allowing the two contributions to be separated. ε_surface 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, U_int and ε_surface(U) are derived by an absolute matching of the P_z 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.