Polar distortion in ultrathin ${\text{BaTiO}}_3$ films studied by in situ LEED $I\text{−}V$

Phase stability in nanoscale ferroelectrics is governed by the interplay of electrostatic depolarization energy, domain formation, adsorption, and surface band bending. Using in situ low-energy electron-diffraction intensity versus voltage (LEED $I\text{−}V$ $$), we have characterized 4 and 10 ML ${\text{BaTiO}}_3$ films, grown using pulsed laser deposition with fully compressive strain on a ${\text{SrRuO}}_3/{\text{SrTiO}}_3$ substrate. LEED $I\text{−}V$ reveals a single surface dead layer and a monodomain vertically polarized state below. The single orientation is attributed to the intrinsic imprint asymmetry and the stability of a polarized phase to compensation of depolarizing charges by dipoles induced by surface stress.

Figure 1

(Color online) 10 ML thick ${\text{BaTiO}}_3$ films grown on ${\text{SrRuO}}_3/{\text{SrTiO}}_3$: (a) in situ RHEED oscillation during deposition and RHEED pattern, (b) ex situ AFM topography, (c) cross-sectional $Z$ contrast STEM image, and (d) in situ $\left(1\times 1\right)$ LEED pattern after deposition.

Figure 2

(Color online) Pendry $R$ factor as a function of $\mathit{a}$ and $\mathit{c}$ lattice parameters for the 10 ML system. Six different situations have been explored: (a) no polarization and no surface structure optimization, (b) no polarization with surface structure optimization, (c) upward polarization without surface structure optimization, (d) upward polarization with surface structure optimization, (e) downward polarization without surface structure optimization, and (f) downward polarization with surface structure optimization.

Figure 3

Pendry $R$ factor as a function of the number of ${\text{BaTiO}}_3$ unit cells assumed with upward and downward polarization. The Pendry $R$ factor as a function of the number of upward polarized unit cells is also presented without the presence of the top Ba-O dead layer, for comparison.

Figure 4

Pendry $R$ factor as a function of the top oxygen layer occupancy, as obtained for the 4 ML LEED data set.

Figure 5

Calculated LEED $I\text{−}V$ curves for cubic ${\text{BaTiO}}_3\left(001\right)$ in five distinct situations: Ti centered (no displacement), Ti displaced up $\left(0.06\text{Å}\right)$, Ti displaced down $\left(0.06\text{Å}\right)$, a combination of Ti displacement up and down in domains ($0.06\text{Å}$, 50%, and 50%), and a $\left(2\times 2\right)$ structure with up and down Ti displacements $\left(0.06\text{Å}\right)$.

Figure 6

Comparison between several experimental measurements (thick) and calculated intensities (thin) for the best-fit structure found for the 4 and 10 ML systems.

Figure 7

(Color online) Best-fit surface structure obtained for the 4 and 10 ML ${\text{BaTiO}}_3$ thin films. The internal rumple in first and second Ba-O ($\Delta Z_{\text{BaO-}1}$ and $\Delta Z_{\text{BaO-}2}$) and ${\text{Ti-O}}_2$ ($\Delta Z_{\text{TiO-}1}$ and $\Delta Z_{\text{TiO-}2}$) layers, as well as the interlayer distances $\left(d_1,d_2.d_3\right)$, are schematically presented. The interlayer distances are defined as the distance between the midpoint of one layer to the midpoint of the next consecutive layer.