Low-energy electron diffraction from ferroelectric surfaces: Dead layers and surface dipoles in clean Pb(Zr,Ti)O3(001)

The positions of the low energy electron diffraction (LEED) spots from ferroelectric single crystal films depend on its polarization state, due to electric fields generated outside of the sample. One may derive the surface potential energy, yielding the depth where the mobile charge carriers compensating the depolarization field are located ($\ensuremath{\delta}$). On ferroelectric $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_{3}$(001) samples, surface potential energies are between 6.7 and 10.6 eV, and $\ensuremath{\delta}$ values are unusually low, in the range of $1.8\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.16em}{0ex}}\AA{}$. When $\ensuremath{\delta}$ is introduced in the values of the band bending inside the ferroelectric, a considerably lower value of the dielectric constant and/or of the polarization near the surface than their bulk values is obtained, evidencing either that the intrinsic `dielectric constant' of the material has this lower value or the existence of a `dead layer' at the free surface of clean ferroelectric films. The inwards polarization of these films is explained in the framework of the present considerations by the formation of an electron sheet on the surface. Possible explanations are suggested for discrepancies between the values found for surface potential energies from LEED experiments and those derived from the transition between mirror electron microscopy and low energy electron microscopy.