The piezoresponse force microscopy of surface layers and thin films: Effective response and resolution function

Signal formation mechanism in piezoresponse force microscopy (PFM) of piezoelectric surface layers and thin films on rigid and elastically matched substrates with different dielectric properties is analyzed and compared. This analysis provides the extension of recent studies of clamping effects in thin films in uniform fields [K. Lefki and G. J. M. Dormans, J. Appl. Phys. 76, 1764 (1994); L. Chen et al., J. Mater. Res. 19, 2853 (2004)] and in PFM in uniform materials [S. V. Kalinin et al., Phys. Rev. B 70, 184101 (2004); A. N. Morozovska et al., Phys. Rev. B 75, 174109 (2007)] to the case of PFM of thin films. Thickness dependence of effective piezoelectric response, object transfer function components, and Rayleigh two-point resolution are derived. Obtained exact series and simple Pade approximations can be applied for the effective piezoresponse analytical calculations in the case of films capped on various substrates. The effective piezoresponse is thickness dependent for films on substrates with low dielectric permittivity (extrinsic size effect), whereas the thickness dependence is essentially suppressed for giant permittivity or metallic substrates. The implications of analysis for ferroelectric data storage and device applications are discussed.