# Probing the Surface Polarization of Ferroelectric Thin Films by X-ray
Standing Waves

###### Abstract

Understanding the mechanisms underlying a stable polarization at the surface
of ferroelectric thin films is of particular importance both from a
fundamental point of view and to achieve control of the surface polarization
itself. In this study, it is demonstrated that the X-ray standing wave
technique allows the polarization near the surface of a ferroelectric thin
film to be probed directly. The X-ray standing wave technique is employed to
determine, with picometer accuracy, Ti and Ba atomic positions near the
surface of three differently strained $\mathrm{BaTiO_{3}}$ thin films grown on
scandate substrates, with a $\mathrm{SrRuO_{3}}$ film as bottom electrode.
This technique gives direct access to atomic positions, and thus to the local
ferroelectric polarization, within the first 3 unit cells below the surface.
By employing X-ray photoelectron spectroscopy, a detailed overview of the
oxygen-containing species adsorbed on the surface, upon exposure to ambient
conditions, is obtained. The combination of structural and spectroscopic
information allows us to conclude on the most plausible mechanisms that
stabilize the surface polarization in the three samples under study. The
different amplitude and orientation of the local ferroelectric polarizations
are associated with surface charges attributed to the type, amount and spatial
distribution of the oxygen-containing adsorbates.

###### keywords:

Ferroelectric polarization, X-ray standing wave, X-ray photoelectron
spectroscopy

Le Phuong Hoang, Irena Spasojevic, Tien-Lin Lee, David Pesquera, Kai
Rossnagel, Jörg Zegenhagen, Gustau Catalan, Ivan A. Vartanyants, Andreas
Scherz, and Giuseppe Mercurio*

Le Phuong Hoang
European XFEL, 22869 Schenefeld, Germany
Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg,
Germany
Institute of Experimental and Applied Physics, Kiel University, 24098 Kiel,
Germany
Irena Spasojevic
Department de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra,
Spain
Tien-Lin Lee, Jörg Zegenhagen
Diamond Light Source Ltd., Didcot, OX110DE Oxfordshire, United Kingdom
David Pesquera
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST,
Campus UAB, Bellaterra, 08193 Barcelona, Spain
Kai Rossnagel
Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, 22607
Hamburg, Germany
Institute of Experimental and Applied Physics, Kiel University, 24098 Kiel,
Germany
Gustau Catalan
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST,
Campus UAB, Bellaterra, 08193 Barcelona, Spain
Institucio Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona,
Catalonia
Ivan A. Vartanyants
Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
Andreas Scherz, Giuseppe Mercurio
European XFEL, 22869 Schenefeld, Germany
Email<EMAIL_ADDRESS>

##  1 Introduction

Ferroelectric thin films have attracted great scientific interest due to their
properties, such as switchable polarization, ferroelasticity,
piezoelectricity, and pyroelectricity, which are crucial for technological
applications.[1, 2, 3, 4] Displacive ferroelectrics, such as BaTiO3 (BTO),
exhibit an intrinsic spontaneous polarization associated with the relative
displacement of cations and anions within the unit cell.[5] This polarization
can be manipulated by varying the lattice parameters of the ferroelectrics.[6,
7] To this end, ferroelectric thin films have been grown on substrates with
different lattice constants. The lattice mismatch can induce uniform strain or
strain gradients in the thin films.[8] Suitable substrates and bottom
electrodes have been employed to tune the ferroelectric polarization, which is
typically measured by piezoresponse force microscopy (PFM), a technique that
is sensitive to the average polarization of the entire film, for thicknesses
of a few tens of nanometer.[9, 10] The distribution of the ferroelectric
polarization at the surface, which can differ from that of the bulk, has been
investigated theoretically as a function of various parameters, such as
surface termination and adsorbates.[11, 12] However, an experimental method
that can simultaneously probe the surface ferroelectric polarization and the
chemical composition of the adsorbates is still lacking.

The determination of the surface polarization has a two-fold relevance. First,
from a fundamental point of view, uncompensated charges at the surface of a
ferroelectric thin film can be screened, among several mechanisms, by external
charges provided by adsorbates[13, 14, 15, 16] or can lead to a reconstruction
of the top unit cells to minimize the surface energy.[17, 18, 19] This, in
turn, can influence the polarization of deeper layers and for very thin films
affect the polarization of the entire sample.[20] Therefore, in order to
control the ferroelectric polarization of a thin film, probing it and
understanding its stabilization mechanisms near the surface are of particular
importance. Second, from the point of view of promising applications,
ferrolectrics have been proposed as catalysts with chemical activity that is
switchable between reducing and oxidizing surfaces depending on the
polarization direction.[21, 22, 23, 24, 25, 26] In this context, determining
the surface polarization is the first step towards the development of
efficient ferroelectric catalysts.

Among non-destructive techniques employed to determine atomic positions at
(and near) the surface, and thus the microscopic origin of ferroelectric
polarization, crystal truncation rod (CTR) scattering and low-energy electron
diffraction (LEED-IV) have been successfully employed to reveal atomic
structures with approximately $\pm 10\text{\,}\mathrm{pm}$ accuracy.[13, 14,
15, 17, 27, 28] However, neither of the above methods provides spectroscopic
information on atoms in ferroelectric thin films and adsorbate species. This
could be achieved by X-ray photoelectron diffraction, however, at the expense
of rather complex multiple-scattering simulations.[29, 30, 31, 32, 33]

In this work we employ the X-ray standing wave (XSW) technique, a combination
of X-ray diffraction (XRD) and X-ray spectroscopy, to determine atomic
positions with picometer (pm) accuracy and chemical specificity. The
structural accuracy of this technique for determining atomic positions in
single crystals and adsorbates on crystal surfaces has been demonstrated
extensively.[34, 35, 36, 37, 38] Furthermore, the XSW technique proved to be
successful in determining the polarity of non-centrosymmetric single
crystals[39] and thin films,[40, 41] as well as ferroelectric thin films.[42,
43] In the latter experiments, the average polarity of the thin films was
determined by combining XSW and X-ray fluorescence spectroscopy (XFS). Here,
we apply the XSW technique, in combination with X-ray photoelectron
spectroscopy (XPS), a more surface sensitive technique than XFS, to measure
the displacement of Ti atoms from the center of the unit cell in differently
strained BTO thin films, and thereby deduce the ferroelectric polarization at
different depths near the surface. These data are interpreted in the context
of the average film polarization measured by PFM, as well as the type, content
and spatial distribution of adsorbates on the sample surface. This combination
of the structural sensitivity of XSW with the chemical specificity and depth
selectivity of XPS, provides a detailed insight into the near-surface
polarization distribution and its interplay with adsorbates and the bulk
ferroelectric polarization.

##  2 X-ray standing waves generated in thin films

The XSW technique is particularly useful for determining atomic positions in
crystals, surfaces, and their adsorbates.[34, 35, 36, 37, 38] The interference
between incoming and Bragg-diffracted X-ray plane waves in a perfect crystal
results in an X-ray standing wave field with the following sinusoidal
modulation of the X-ray intensity $I_{\mathrm{XSW}}$ (Figure 1a,b):

$I_{\mathrm{XSW}}\left(E_{\nu}\right)\propto
1+\left|\frac{\mathcal{E}_{\mathrm{H}}}{\mathcal{E}_{\mathrm{0}}}\right|^{2}+2\left|\frac{\mathcal{E}_{\mathrm{H}}}{\mathcal{E}_{\mathrm{0}}}\right|\cos\left(\alpha(E_{\nu})+\boldsymbol{h}\boldsymbol{r}\right),$
(1)

where $\boldsymbol{h}=2\pi\boldsymbol{H}$, and $\boldsymbol{H}$ is the
reciprocal lattice vector. In Equation (1), the three terms represent the
incident, Bragg-diffracted, and interference X-ray wave, respectively. As the
incident photon energy $E_{\nu}$ varies through the (hkl) Bragg reflection,
the phase $\alpha(E_{\nu})$ between the Bragg-diffracted
$\mathcal{E}_{\mathrm{H}}$ and incident $\mathcal{E}_{0}$ electric field
amplitudes changes by $\pi$. This leads to a shift of the XSW field along
$\boldsymbol{H}$ by $d_{\mathrm{hkl}}/2$, where
$d_{\mathrm{hkl}}=\lvert\boldsymbol{H}\rvert^{-1}$ is the spacing between two
consecutive (hkl) atomic planes (Figure 1b). Atoms at different positions in
the unit cell experience different X-ray absorption and hence give rise to
different photoelectron (PE) yield as a function of the photon energy
$E_{\nu}$. As a result, the atomic positions can be determined with pm spatial
resolution by monitoring the corresponding PE yield (Section 3.5).

In a typical ferroelectric thin film grown on a substrate, the lattice
mismatch may lead to strain gradients inside the epitaxial layers.[8]
Therefore, thin films are generally characterized by a deformation field
$\boldsymbol{u}\left(z\right)$, which defines the actual displacement of atoms
from the corresponding position in a perfect crystal, and the static Debye-
Waller factor $\mathrm{e}^{-W(z)}$, which accounts for random displacement of
atoms from their average position along the $z$ direction (Figure 1a). In
contrast to the perfect crystal case above, the XSW generated in a thin film
is modified by the deformation phase
$\varphi\left(z\right)=\boldsymbol{h}\cdot\boldsymbol{u}\left(z\right)$ due to
the crystal deformation field. Based on the dynamical theory of diffraction,
the Takagi-Taupin equations[44, 45, 46] describe the propagation of X-rays in
a deformed crystal, and thus give the following XSW intensity generated in a
typical ferroelectric thin film:

$I_{\mathrm{XSW}}\left(E_{\nu},z\right)=1+R\left(E_{\nu},z\right)+2C\sqrt{R\left(E_{\nu},z\right)}\mathrm{e}^{-W\left(z\right)}\cos\left(\alpha(E_{\nu},z)+\varphi\left(z\right)+2\pi
z/d_{\mathrm{hkl}}\right),$ (2)

where $R_{0}(E_{\nu})=R(E_{\nu},0)$ indicates the observable X-ray diffracted
intensity at the sample surface ($z=0$), and the parameter $C$ depends on the
X-ray polarization[47] (Section B.9, Supporting Information). Based on the XSW
generated in a ferroelectric thin film, from the PE yield curve

$\begin{split}\kappa^{s}_{\gamma}(E_{\nu})=I_{0}^{-1}\int_{0}^{t_{L_{0}}}dz\rho_{\mathrm{yi}}\left(E_{\nu},z,\gamma\right)|T\left(E_{\nu},z\right)|^{2}\Big{[}1+R\left(E_{\nu},z\right)+2C\sqrt{R\left(E_{\nu},z\right)}\mathrm{e}^{-W_{0}}F^{s}_{c,\gamma}\\\
\cos\left(\alpha(E_{\nu},z)+\varphi_{0}+2\pi
P^{s}_{c,\gamma}\right)\Big{]},\end{split}$ (3)

we can determine the average position and distribution of atoms $s$, which are
defined as the coherent position $P^{s}_{c,\gamma}$ and coherent fraction
$F^{s}_{c,\gamma}$, respectively. These parameters are equivalent to the phase
and amplitude of the structure factor
$\boldsymbol{S}^{s}_{\boldsymbol{h}}=\sum_{j}\exp(\mathrm{i}\boldsymbol{h}\boldsymbol{r}_{j}^{s})=\left|\boldsymbol{S}^{s}_{\boldsymbol{h}}\right|\exp(\mathrm{i}\varphi^{s}_{\boldsymbol{h},\gamma})$,
with atoms at positions $\boldsymbol{r}_{j}^{s}$. More specifically,
$P^{s}_{c,\gamma}=\varphi^{s}_{\boldsymbol{h},\gamma}/(2\pi)$ and
$F^{s}_{c,\gamma}=|\boldsymbol{S}^{s}_{\boldsymbol{h}}|\mathrm{e}^{-W_{s}}$,
where $\mathrm{e}^{-W_{s}}$ is the Debye-Waller factor accounting for thermal
and static atomic displacements. Therefore, the absolute average position of
atoms $s$ within the unit cell along $\boldsymbol{H}$ is given by
$z^{s}_{\gamma}=P^{s}_{c,\gamma}d_{\mathrm{hkl}}$, and their spatial
distribution is characterized by $F^{s}_{c,\gamma}$, with
$0<P^{s}_{c,\gamma}<1$ and $0<F^{s}_{c,\gamma}<1$. In particular,
$F^{s}_{c,\gamma}=1$ refers to all atoms at the same $z$, while
$F^{s}_{c,\gamma}=0$ corresponds to a uniform distribution of two or more
atomic positions across the unit cell.

In Equation (3), the PE yield function $\kappa^{s}_{\gamma}(E_{\nu})$ is the
sum of yield contributions from atoms in the top layer $L_{0}$ at positions
$0<z<t_{L_{0}}$, weighted by $\rho_{\mathrm{yi}}(E_{\nu},z,\gamma)$, with XSW
transmission $T\left(E_{\nu},z\right)$, and normalization factor
$I_{0}=\int_{0}^{t_{L_{0}}}dz\rho_{\mathrm{yi}}(E_{\nu},z,\gamma)$. The
function
$\rho_{\mathrm{yi}}(E_{\nu},z,\gamma)=\exp\left(-z/\lambda_{l,\gamma}\right)$,
where $\lambda_{l,\gamma}=\lambda_{l}(E_{\nu})\sin\gamma$, gives the
probability of detecting a photoelectron from the atomic core level $l$ at
depth $z$, with exit angle $\gamma$ from the sample surface (Figure 1c). The
parameter $\lambda_{l}\left(E_{\nu}\right)$ indicates the inelastic mean free
path (IMFP), or more correctly the effective attenuation length (EAL) that
includes elastic scattering effects.[48] Tuning $\gamma$ allows the surface
sensitivity to be varied and provides average atomic positions over different
depths from the surface. To determine the average distribution of atoms $s$ at
a given exit angle $\gamma$, the measured PE yield curve is fitted with
Equation (3) using $P^{s}_{c,\gamma}$ and $F^{s}_{c,\gamma}$ as fit
parameters. In fact, all other quantities in Equation (3) can be calculated
from known sample properties (Section B.9, Supporting Information), or derived
from the fit of Bragg reflectivity data, e.g., the average amorphization
$\mathrm{e}^{-W_{0}}$ of layer $L_{0}$ and the corresponding deformation phase
$\varphi_{0}$ (Section 3.3).

##  3 Results and Discussion

###  3.1 Sample characterization

The samples investigated in this work are BTO ferroelectric thin films grown
on three different substrates DyScO3 (DSO), GdScO3 (GSO), and SmScO3 (SSO)
with a SrRuO3 (SRO) thin film in between serving as the bottom electrode.
Sample growth was performed by means of pulsed laser deposition (Section A.1,
Supporting Information) on substrates with (001) orientation according to the
pseudocubic notation.[49] The thickness of the BTO and SRO thin films was
determined by grazing X-ray reflectivity (Section A.2, Supporting
Information). The SRO layers have thicknesses in the range of
$20-$$26\text{\,}\mathrm{nm}$, while the BTO layers are
$20\text{\,}\mathrm{nm}$, $37\text{\,}\mathrm{nm}$ and
$35.5\text{\,}\mathrm{nm}$ thick on DSO, GSO and SSO, respectively (Table 1).
To determine the average in-plane strain of the thin films, X-ray reciprocal
space maps (RSM) around the (-103) substrate Bragg peak were measured (Section
A.3, Supporting Information). Results reported in Figure 7 (Supporting
Information) show that all BTO and SRO thin films are coherently strained to
their underlying substrates, without any relaxation of the in-plane lattice
parameter. The in-plane strain applied by a substrate to the BTO thin film is
calculated as
$\epsilon^{a}_{\mathrm{BTO}}=\left(a_{\mathrm{BTO}}-a_{\mathrm{b,BTO}}\right)/a_{\mathrm{b,BTO}}$,
by comparing the measured in-plane lattice parameter of the thin film
$a_{\mathrm{BTO}}$ (Section A.3, Supporting Information) with the respective
bulk value $a_{b,\mathrm{BTO}}=$ $3.992\text{\,}\mathrm{\text{Å}}$.[5] As a
result, the in-plane compressive strain in the BTO thin film is smallest on
the SSO substrate ($-0.38\%$, $a_{b,\mathrm{SSO}}=$
$3.977\text{\,}\mathrm{\text{Å}}$[50]), it increases on GSO ($-0.63\%$,
$a_{b,\mathrm{GSO}}=$ $3.967\text{\,}\mathrm{\text{Å}}$[50]), and is largest
on DSO ($-1.23\%$, $a_{b,\mathrm{DSO}}=$
$3.943\text{\,}\mathrm{\text{Å}}$[50]) (Table 1). The in-plane compressive
strain in BTO thin films induces an out-of-plane spontaneous ferroelectric
polarization.[6] To determine the average polarization orientation of the as-
grown BTO thin films, and to verify that all samples can be electrically
switched, piezoresponse force microscopy (PFM) was employed. PFM data (Section
A.4, Supporting Information) show that the average BTO polarization of
BTO/SRO/DSO is down ($\mathrm{P}^{\downarrow}$), while in the other two
samples it is up ($\mathrm{P}^{\uparrow}$), i.e., with the Ti atom below
($\mathrm{P}^{\downarrow}$) or above ($\mathrm{P}^{\uparrow}$) the center of
the oxygen octahedra (Figure 1b). The different average polarization direction
of the three BTO samples may be related to the chemistry and electrostatic
potential at the interface between SRO and BTO thin films.[11, 51, 52]
Finally, both the absence of side peaks in RSM data and the presence of a
homogeneous as-grown phase measured by PFM support the presence of a single
domain in our samples. This ensures that atomic positions of the same
structural phase are measured by XSW measurements.

Table 1: BTO and SRO layer thicknesses, $t_{\mathrm{BTO}}$ and $t_{\mathrm{SRO}}$, resulting from grazing X-ray reflectivity (Section A.2, Supporting Information). All substrates are $0.5\text{\,}\mathrm{mm}$ thick. Compressive in-plane strain in BTO ($\epsilon^{a}_{\mathrm{BTO}}$) thin films, measured by X-ray reciprocal space maps (Section A.3, Supporting Information). Orientation of the average BTO polarization $\mathrm{P}$ measured by PFM (Section A.4, Supporting Information). Acronym | Sample |  $t_{\mathrm{BTO}}$ (nm) |  $t_{\mathrm{SRO}}$ (nm) |  $\epsilon^{a}_{\mathrm{BTO}}$ (%) | $\mathrm{P}$
---|---|---|---|---|---
BTO/SRO/DSO | BaTiO3/SrRuO3/DyScO3 | 20 | 26 | -1.23 | $\downarrow$
BTO/SRO/GSO | BaTiO3/SrRuO3/GdScO3 | 37 | 24 | -0.63 | $\uparrow$
BTO/SRO/SSO | BaTiO3/SrRuO3/SmScO3 | 35.5 | 20 | -0.38 | $\uparrow$

###  3.2 X-ray standing wave setup

XSW experiments were performed at the I09 beamline of Diamond Light
Source.[53] The soft X-ray branch of I09, equipped with a plane grating
monochromator, delivered an X-ray beam of approximately
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ $\times$
$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ full width at half maximum (FWHM)
at the sample. Each XSW measurement consists of recording Bragg reflections
and simultaneously photoelectron spectra of the sample. The Bragg reflections
were measured by scanning the photon energy $E_{\nu}$ with the incoming X-ray
beam impinging on the sample at a fixed angle of incidence
$\mathrm{\theta}=87\degree$ (Figure 1c). The intensity of the diffracted X-ray
beam was measured by a Si photodiode with a central through hole for the
incident beam to pass (Figure 1c). With this experimental geometry, the (001)
Bragg reflections of the BTO and SRO films and the substrates were recorded
within the range of photon energy $E_{\nu}$ from $1400\text{\,}\mathrm{eV}$ to
$1700\text{\,}\mathrm{eV}$. Simultaneously, XPS spectra were measured by a
Scienta EW4000 electron analyzer, with the detection system consisting of a
microchannel plate (MCP) followed by a charge-coupled device (CCD). The wide
acceptance angle of the electron analyzer enabled parallel measurements of
spectra over three different exit angle ranges: $\gamma_{1}$ ($7.8\degree\pm
5.4\degree$), $\gamma_{2}$ ($18.5\degree\pm 5.4\degree$) and $\gamma_{3}$
($27.4\degree\pm 3.6\degree$). This provides the chemical and structural
information of the BTO films with increasing depth sensitivity from
$\gamma_{1}$ to $\gamma_{3}$. The overall spectral energy resolution, limited
by the X-ray bandwidth, was approximately $400\text{\,}\mathrm{meV}$. The
(001) Bragg reflections, XPS and XSW experimental results are reported in the
following Sections 3.3, 3.4, and 3.5, respectively.

###  3.3 (001) Bragg reflections

To determine the atomic positions at the BTO surface along the out-of-plane
polarization direction, the (001) Bragg reflection was chosen for the XSW
experiments. Figure 2a shows the reflectivity curves around the (001)
reflections of the BTO, SRO, and substrates. The reflections of the substrate
are more than two orders of magnitude stronger and much narrower compared to
those of the thin layers. The low intensity and the broadening of the thin
film Bragg peaks results from two factors: the finite film thickness and the
inhomogeneous strain. More specifically, the reflectivity of BTO [SRO] films
lies in the range of $0.03\%-0.05\%$ [$0.01\%-0.02\%$], whereas the substrate
reflectivity is of the order of $10\%$ for all samples. Going from SSO, to
GSO, and then to DSO, the substrate Bragg peak gradually shifts to higher
photon energies, as expected from the decreasing trend of the bulk out-of-
plane lattice parameters of the substrates (Figure 7, Supporting Information).
This trend suggests that the in-plane strain in the films becomes more
compressive in BTO and less tensile in SRO (Section B.3, Supporting
Information) in the same substrate order. As a result, the average $c$
parameters of BTO (Section B.1, Supporting Information) increase from the SSO
to the DSO sample: $\overline{c}_{\mathrm{BTO}}=$
$4.055(22)\text{\,}\mathrm{\text{Å}}$, $4.063(23)\text{\,}\mathrm{\text{Å}}$,
$4.070(45)\text{\,}\mathrm{\text{Å}}$, respectively. For the BTO thin films,
the measured $\overline{c}_{\mathrm{BTO}}$ parameters correspond to an average
out-of-plane strain
$\overline{\epsilon}^{c}_{\mathrm{BTO}}=\left(\overline{c}_{\mathrm{BTO}}-c_{b,\mathrm{BTO}}\right)/c_{b,\mathrm{BTO}}$
of $0.48\%$, $0.68\%$ and $0.84\%$ for SSO, GSO and DSO, respectively, with
the bulk out-of-plane lattice parameter $c_{b,\mathrm{BTO}}=$
$4.036\text{\,}\mathrm{\text{Å}}$.[5]

As anticipated in Section 2, an epitaxial thin film may be characterized by an
inhomogeneous out-of-plane strain. According to the general strain profile
model discussed in Refs.[8, 54], the strain gradient is expected to be
proportional to the strain, ${\partial\epsilon}^{c}/{\partial
z}\propto\epsilon^{c}$, independently of the actual relaxation mechanism. As a
result, the out-of-plane parameter $c$ follows an exponential dependence on
$z$:

$c(z)=c_{b}\left(1+\epsilon_{\mathrm{int}}^{c}\mathrm{e}^{-(t-z)/\delta}\right),$
(4)

where $\epsilon_{\mathrm{int}}^{c}=(c_{\mathrm{int}}-c_{b})/c_{b}$ is the
strain at the interface with the underlying layer (or substrate), and $\delta$
is the penetration depth of strain that is inversely proportional to the
strain gradient. This model has been successfully applied to ferroelectric
thin films of several 100s $\text{\,}\mathrm{nm}$.[8, 54] In a recent
work,[55, 56] it was also found that $50\text{\,}\mathrm{nm}$ thick
$\mathrm{PbTiO_{3}}$ films, displaying high crystalline quality and no
indication of in-plane relaxation, could be well described by an exponential
profile of $c$ parameters, as further confirmed by TEM images. In this
case,[56] the strain gradient was assigned to a compositional gradient of lead
oxide dipolar vacancies. A similar distribution of vacancies or defects could
be present also in our samples and may underlay the presence of strain
gradients. In fact, in our work modeling BTO and SRO thin films with a
constant $\overline{c}$ leads to unsatisfactory fit results. To fit the
experimental reflectivity curves in Figure 2, BTO and SRO layers are divided
into $n$ sublayers $L_{i}$ (with $i=0,...,n-1$) of equal thickness $t_{i}$
with an out-of-plane lattice parameter $c_{i}$ varying exponentially with $i$
as described by Equation (4), Debye-Waller factor $\mathrm{e}^{-W_{i}}$, and
deformation phase $\varphi_{i}=2\pi(c_{i}-\overline{c})t_{i}/\overline{c}^{2}$
(Section B.10, Supporting Information). In our samples, the minimum common
number of sublayers necessary to accurately describe them is $n=5$. Increasing
the number of sublayers $n$ does not improve the fit. Experimental data in
Figure 2a are fitted with the reflectivity $R_{0}(E_{\nu})$ using the fitting
parameters $\mathrm{e}^{-W_{i}}$ ($i=0,...,4$), $\epsilon_{\mathrm{int}}^{c}$
and $\delta$ for the BTO and SRO layer (Section 2 and Section B.9, Supporting
Information).

The best fits to the reflectivity curves shown in Figure 2a reproduce
reasonably well the main features of the experimental data. This validates the
strain gradient theory used to model these samples. The resulting out-of-plane
parameters $c_{i}$ are shown in Figure 2b and in Figure 9 (Supporting
Information). The Debye-Waller factors $\mathrm{e}^{-W_{i}}$ in BTO sublayers
are mostly $\geq 0.9$ with lower values at the interface to SRO (Table 3,
Supporting Information). A similar observation of larger structural disorder
at the interface to the layer below has been revealed by other transmission
electron microscopy (TEM) studies.[57, 58, 59] The fit parameters
$\epsilon_{\mathrm{int}}^{c}$ and $\delta$ of BTO show a direct and inverse
proportionality to the in-plane compressive strain
$\epsilon^{a}_{\mathrm{BTO}}$, respectively (Table 4, Supporting Information).
In fact, a larger in-plane compressive strain $\epsilon^{a}_{\mathrm{BTO}}$
leads to larger average out-of-plane strain
$\overline{\epsilon}^{c}_{\mathrm{BTO}}$ and therefore, a larger strain
gradient up to ${\partial\epsilon^{c}}/{\partial z}=$
$1.7\text{\times}{10}^{-3}\text{\,}{\mathrm{nm}}^{-1}$ in BTO/SRO/DSO. Similar
and even larger strain gradients have been previously observed by TEM and CTR
scattering measurements on BTO thin films[15, 59] and other
ferroelectrics.[56, 57, 58] Interestingly, despite the different in-plane
compressive strains in the three samples (Table 1), the strain gradients lead
to similar out-of-plane lattice parameters $c_{0}$ at the top sublayer
$L_{0}$: $4.038\text{\,}\mathrm{\text{Å}}$, $4.046\text{\,}\mathrm{\text{Å}}$,
$4.045\text{\,}\mathrm{\text{Å}}$. Subsequently, the fitting of the
experimental reflectivity curves in Figure 2a provides the necessary
structural data to calculate the PE yield fit function
$\kappa^{s}_{\gamma}(E_{\nu})$ in Equation (3). We turn now to the
determination of the experimental PE yield from XPS spectra.

###  3.4 Ba and Ti XPS

The photoelectron yield $\kappa^{s}_{\gamma}(E_{\nu})$ of atomic species $s$,
measured at exit angle range $\gamma$ and photon energy $E_{\nu}$, is defined
as the corresponding PE peak integral after background subtraction. To
determine the PE yield of Ba and Ti atoms in the BTO thin films, Ba 4d and Ti
2p PE spectra were measured over the three exit angle ranges ($\gamma_{1}$,
$\gamma_{2}$, $\gamma_{3}$), and the results are reported in Figure 3. The Ti
spectra in Figure 3a show the 2p doublet at $458.8$ and
$464.5\text{\,}\mathrm{eV}$. Spectra measured at different exit angles show
the same spectral shape. This indicates that Ti atoms at different depths from
the BTO surface experience the same chemical environment for the formation of
the nominal Ti4+ state. In particular, the absence of a peak at
$1.7\text{\,}\mathrm{eV}$ below the main Ti 2p3/2 peak provides evidence for
the absence of oxygen vacancies leading to Ti3+ near the BTO surface.[14] In
contrast, Ba 4d spectra, displayed in Figure 3b, show at least two kind of
atomic species. The spin-orbit split levels Ba 4d5/2 and Ba 4d3/2 at
$88.8\text{\,}\mathrm{eV}$ and at $91.4\text{\,}\mathrm{eV}$ originate from
the Ba atoms below the surface and are hence referred to as the bulk component
($\mathrm{Ba_{bulk}}$). On the other hand, the $\mathrm{Ba_{surf}}$ peaks
exhibit a binding energy shift $\Delta\mathrm{BE}=+$$1.2\text{\,}\mathrm{eV}$
and twice the FWHM compared to the bulk component. The enhancement of
$\mathrm{Ba_{surf}}$ in the most surface sensitive spectrum (Ba($\gamma_{1}$))
clearly indicates its correspondence to Ba atoms at the BTO surface. The
assignment of the BE-shifted Ba components is still controversial, with some
studies attributing them to BaCO3 or $\mathrm{Ba(OH)_{2}}$,[28, 60, 61] and
others to BaO2 species.[62, 63] Regardless of the chemical binding of Ba
atoms, a recent X-ray photoelectron diffraction study revealed that these Ba
atoms are only located at the topmost BaO plane.[64] Our data confirm the
surface origin of the BE-shifted Ba 4d component, and the larger FWHM is
consistent with multiple chemical environments surrounding the surface Ba
atoms observed in previous work. As a result, the PE yield of the surface unit
cell ($\gamma_{1}$) is given by the sum of the two components
($\mathrm{Ba_{surf}}+\mathrm{Ba_{bulk}}$) in order to include both Ba atoms at
the surface and just below it, while the Ba PE yield of the deeper unit cells
(at $\gamma_{2}$ and $\gamma_{3}$) is given only by the $\mathrm{Ba_{bulk}}$
component. On the other hand, the Ti PE yield is given by the total area of
the Ti doublet for all exit angle ranges. As shown above, the possibility
provided by XPS to distinguish between atoms in different chemical
environments enables the XSW technique to selectively determine the positions
of different chemical species of the same element.

###  3.5 Ba and Ti XSW

Figure 4 shows the normalized PE yields of Ti and Ba,
$\kappa^{\mathrm{Ti}}_{\gamma}(E_{\nu})$ and
$\kappa^{\mathrm{Ba}}_{\gamma}(E_{\nu})$, measured over the exit angle ranges
$\gamma_{1}$, $\gamma_{2}$, and $\gamma_{3}$ around the BTO (001) Bragg peak
of the three samples under study. Each $\kappa^{s}_{\gamma}(E_{\nu})$ and
corresponding error bar $\sigma_{\kappa}$ result from the average and standard
deviation of $N$ photoelectron yield profiles ($5<N<10$) measured under the
same conditions. Each PE yield curve shown in Figure 4 is normalized by the
intensity of the incoming X-ray beam and by the respective photoionization
cross-section over the measured photon energy range (Section B.8, Supporting
Information). In correspondence to the BTO reflectivity maxima
$\kappa^{\mathrm{Ti}}_{\gamma}(E_{\nu})$ curves show a peak-like shape, while
$\kappa^{\mathrm{Ba}}_{\gamma}(E_{\nu})$ profiles display a dip. This can be
explained as follows. For the BTO (001) reflection, the Bragg diffraction
planes are near the Ba atomic planes[65, 66] (dashed lines in Figure 1b). When
the incoming X-ray photon energy reaches the Bragg condition ($E_{\nu}\approx
E_{B}$) from the low-energy side, the XSW forms with a sinusoidal modulation
of the X-ray intensity $I_{\mathrm{XSW}}$ and period $d_{001}$ along
$\boldsymbol{H}$. At this point, the standing wave antinodes and nodes are
between and at the diffraction planes, respectively (Figure 1a,b). Therefore,
Ti atoms, which are nearly half way between two adjacent diffraction planes
and hence more aligned with the antinodes, show an increase in the PE yield,
while Ba atoms (near the diffraction planes and aligned with the nodes)
experience a decrease in $I_{\mathrm{XSW}}$ and consequently have smaller
$\kappa^{\mathrm{Ba}}_{\gamma}(E_{\nu})$. As the photon energy is varied
through the Bragg condition ($E_{\nu}>E_{B}$), the nodes and antinodes move by
$d_{001}/2$ along $\boldsymbol{H}$ and the XSW intensity modulation fades
away. Because of the weak diffraction of the incoming X-ray wave from the thin
film, the reflectivity maxima of our samples range from $0.02\%$ to $0.05\%$.
Therefore, the interference between the incoming and Bragg-diffracted X-ray
waves results in a weak XSW intensity modulation with an amplitude, which is
proportional to $2\sqrt{R_{0}(E_{\nu})}$, of less than $4\%$. Nevertheless, as
shown below, this is sufficient to determine, from the information encoded in
the PE yield profiles, the average atomic distribution within the unit cell
with pm spatial accuracy.

Table 2: Coherent position $P_{c,\gamma}^{s}$ and coherent fraction $F_{c,\gamma}^{s}$ of Ba and Ti PE yield fits (Figure 4) at the exit angle ranges $\gamma_{1}$, $\gamma_{2}$, and $\gamma_{3}$, in the three samples under study. Coherent position offset of Ti atoms from the center of the unit cell defined by Ba atoms, $\Delta P^{\mathrm{Ti}}_{c,\gamma}=P^{\mathrm{Ti}}_{c,\gamma}-\left(P^{\mathrm{Ba}}_{c,\gamma}-0.5\right)$, and absolute off-center displacement of Ti atoms, $\Delta z^{\mathrm{Ti}}_{\gamma}=c_{0}\Delta P^{\mathrm{Ti}}_{c,\gamma}$, expressed in pm. Sample | Angle range | $P_{c,\gamma}^{\mathrm{Ba}}$ | $F_{c,\gamma}^{\mathrm{Ba}}$ | $P_{c,\gamma}^{\mathrm{Ti}}$ | $F_{c,\gamma}^{\mathrm{Ti}}$ | $\Delta P^{\mathrm{Ti}}_{c,\gamma}$ |  $\Delta z^{\mathrm{Ti}}_{\gamma}$ (pm)
---|---|---|---|---|---|---|---
| $\gamma_{1}$ | 0.99(1) | 0.47(4) | 0.54(3) | 0.34(7) | 0.05(5) | 20
BTO/SRO/DSO | $\gamma_{2}$ | 1.00(1) | 0.81(5) | 0.54(1) | 0.55(6) | 0.04(2) | 16
| $\gamma_{3}$ | 1.00(1) | 0.82(5) | 0.52(3) | 0.46(8) | 0.02(4) | 8
| $\gamma_{1}$ | 1.05(1) | 0.46(4) | 0.54(3) | 0.29(6) | -0.01(4) | -4
BTO/SRO/GSO | $\gamma_{2}$ | 1.06(1) | 0.88(3) | 0.55(2) | 0.32(5) | -0.01(3) | -4
| $\gamma_{3}$ | 1.04(1) | 0.78(3) | 0.56(1) | 0.54(5) | 0.02(2) | 8
| $\gamma_{1}$ | 1.08(2) | 0.42(7) | 0.63(6) | 0.44(19) | 0.05(8) | 20
BTO/SRO/SSO | $\gamma_{2}$ | 1.02(1) | 1.00(3) | 0.55(4) | 0.41(12) | 0.03(5) | 12
| $\gamma_{3}$ | 1.02(1) | 1.00(7) | 0.56(2) | 0.59(9) | 0.04(3) | 16

The XSW analysis presented here is based on the calculation of the
reflectivity $R_{0}(E_{\nu})$ which assumes either upward or downward average
polarization of the BTO film, as it results from PFM data (Table 1). The
respective positions of Ba, Ti and O atoms in the unit cell for the
reflectivity calculations come from known BTO bulk values.[5] The model
employed is validated by the reasonably good fit of both reflectivity and
yield data. In fact, the experimental PE yields shown in Figure 4 are well
fitted by Equation (3) with the fitting results, $P^{s}_{c,\gamma}$ and
$F^{s}_{c,\gamma}$, summarized in Table 2. As expected from the atomic
coordinates used to construct the structural model in the XSW analysis, Ba
atoms have $P^{\mathrm{Ba}}_{c,\gamma}\approx 1$, while Ti atoms have
$P^{\mathrm{Ti}}_{c,\gamma}\approx 0.5$. Their exact atomic positions vary
with sample and depth by up to few tens of pm with an error bar (averaged over
$\gamma$) of $4\text{\,}\mathrm{pm}$ for Ba and $12\text{\,}\mathrm{pm}$ for
Ti (Section B.11, Supporting Information). In the context of a displacive
ferroelectric like BTO,[67] the relevant physical quantity is the displacement
of Ti atoms from the center of the unit cell (defined by
$P^{\mathrm{Ba}}_{c,\gamma}$), which directly relates to the ferroelectric
polarization.[68] Therefore, we calculate $\Delta
P^{\mathrm{Ti}}_{c,\gamma}=P^{\mathrm{Ti}}_{c,\gamma}-\left(P^{\mathrm{Ba}}_{c,\gamma}-0.5\right)$
and the corresponding absolute off-center displacement (in pm) of Ti atoms
$\Delta z^{\mathrm{Ti}}_{\gamma}=c_{0}\Delta P^{\mathrm{Ti}}_{c,\gamma}$. XSW
data at different exit angle ranges $\gamma$ provide Ti atomic displacements
at different depths $z$ from the BTO surface. For Ba 4d [Ti 2p] photoelectrons
at the (001) BTO Bragg energy $E_{B}$, the IMFPs are $\lambda_{l,\gamma}=$
$3.4\text{\,}\mathrm{\text{Å}}$, $8.0\text{\,}\mathrm{\text{Å}}$,
$11.6\text{\,}\mathrm{\text{Å}}$ [$2.7\text{\,}\mathrm{\text{Å}}$,
$6.4\text{\,}\mathrm{\text{Å}}$, $9.2\text{\,}\mathrm{\text{Å}}$] for
$\gamma_{1}$, $\gamma_{2}$ and $\gamma_{3}$, respectively. The corresponding
probability yield functions $\rho_{\mathrm{yi}}(z)$, reported in Figure 5a,
indicate that $\Delta z^{\mathrm{Ti}}_{\gamma_{1}}$ relates mostly ($\approx
70\%$) to atoms within the first unit cell, while $\Delta
z^{\mathrm{Ti}}_{\gamma_{2}}$ [$\Delta z^{\mathrm{Ti}}_{\gamma_{3}}$] results
primarily from a $\rho_{\mathrm{yi}}(z)$-weighted average of atomic positions
within the top 2 [3] unit cells. Ti atomic displacements in the top three BTO
unit cells resulting from the respective $\Delta z^{\mathrm{Ti}}_{\gamma}$ are
displayed in Figure 5b-d (Table 2). In particular, the XSW fit results of the
BTO/SRO/DSO sample reveal positive $\Delta z^{\mathrm{Ti}}_{\gamma}$ values
which decrease as $\gamma$ increases. This corresponds to an upward
ferroelectric polarization $\mathrm{P}^{\uparrow}$ with decreasing amplitude
from the surface to the bulk. In contrast, the BTO/SRO/GSO sample shows a
minor offset $\Delta z^{\mathrm{Ti}}_{\gamma}<0$ for $\gamma_{1}$ and
$\gamma_{2}$, while $\Delta z^{\mathrm{Ti}}_{\gamma_{3}}>0$. This indicates an
upward polarization $\mathrm{P}^{\uparrow}$ at larger depths that nearly
vanishes with a minor reversal just below the surface. Finally, in the
BTO/SRO/SSO sample, $\Delta z^{\mathrm{Ti}}_{\gamma}>0$, i.e., an upward
polarization ($\mathrm{P}^{\uparrow}$), is observed for all $\gamma$.

We now move to discussing the atomic coherent fractions. For Ba at the exit
angle ranges $\gamma_{2}$ and $\gamma_{3}$ the coherent fraction is relatively
high in all samples ($F^{\mathrm{Ba}}_{c,\gamma}>0.8$), indicating high
structural order. In particular, in BTO/SRO/SSO, where no reversal of
ferroelectric polarization with depth is observed,
$F^{\mathrm{Ba}}_{c,\gamma_{2}}$ and $F^{\mathrm{Ba}}_{c,\gamma_{3}}$ are
equal to $1$. The latter values are an overestimation because at room
temperature atomic vibrations lead to $F_{c}<1$, even in a perfectly ordered
atomic layer. The overestimation of $F_{c}$ is due to two possible reasons.
First, our XSW analysis does not include non-dipolar parameters, which are
currently not available for p, d, and f initial states,[69] and thus, higher
$F_{c}$ are expected without correcting for non-dipole effects. Second, the
nonlinear behaviour of the MCP may lead to an overestimation of the count
rate, consequently of the XSW modulation amplitude, and thus of $F_{c}$.
Conversely, in BTO/SRO/DSO and BTO/SRO/GSO, $F^{\mathrm{Ba}}_{c,\gamma_{2}}$
and $F^{\mathrm{Ba}}_{c,\gamma_{3}}$ values are $12\%$ to $22\%$ lower,
depending on sample and $\gamma$. This is attributed to the averaging over
atoms in unit cells with different polarizations, which also contribute to the
generally lower coherent fraction of Ti atoms in the range of $0.3-0.6$. On
the other hand, for the most surface sensitive measurements at $\gamma_{1}$,
both Ba and Ti atoms have a lower coherent fraction of $0.3$ to $0.5$. The
generally lower $F^{s}_{c,\gamma}$ at the surface can be attributed to the
larger structural disorder induced by the interactions of the atoms at the
topmost oxide plane with adsorbates.

###  3.6 Discussion

XSW data reveal that the absolute displacements of Ti atoms from the center of
the unit cell ($\Delta z^{\mathrm{Ti}}_{\gamma_{i}}$) decrease from
BTO/SRO/SSO, through BTO/SRO/DSO, to BTO/SRO/GSO. This trend is not correlated
with the in-plane compressive strain $\epsilon^{a}_{\mathrm{BTO}}$, as it
could have been expected. Instead, we explain the measured off-center
displacements of Ti atoms in light of oxygen-containing adsorbates at the
surface, as detailed below. Upon exposure to ambient conditions water adsorbs
on the BTO surface and dissociates into OH- and H+. While OH- chemisorbs on
top of cations (Ba or Ti) or at O vacancies, H+ binds to a lattice oxygen atom
($\mathrm{O_{L}}$) at or below the surface to form $\mathrm{O_{L}H^{-}}$.[14,
15, 70] Our depth-dependent O1s XPS spectra (Section B.5, Supporting
Information) reveal the presence of: (i) negatively charged chemisorbed O
species, i.e., $\mathrm{OH}^{-}$ (hydroxyl groups) or $\mathrm{O_{2}}^{-}$
(peroxo groups), modeled by the component $\mathrm{O(4)}$, and (ii)
$\mathrm{O_{L}H^{-}}$ species, resulting from a $\mathrm{H^{+}}$ ion bound to
an $\mathrm{O_{L}}$, or a hydroxyl group adsorbed at a oxygen-vacancy site,
modeled by the component $\mathrm{O(2)}$. Negatively charged $\mathrm{OH}^{-}$
or $\mathrm{O_{2}}^{-}$ molecules favor the upward polarization
$\mathrm{P}^{\uparrow}$,[11] while positively charged $\mathrm{H^{+}}$ atoms
of $\mathrm{O_{L}H^{-}}$ species favor the downward polarization
$\mathrm{P}^{\downarrow}$.[13]

In the BTO/SRO/DSO sample, the BTO film has downward average polarization
$\mathrm{P}^{\downarrow}$ (Table 1) with upward polarization
$\mathrm{P}^{\uparrow}$ in the topmost unit cells (Figure 5b). The latter is
favored by negatively charged $\mathrm{OH}^{-}$ or $\mathrm{O_{2}}^{-}$
molecules adsorbed on the surface, represented by component $\mathrm{O(4)}$ in
Figure 11a (Supporting Information). In particular, the off-center
displacement of Ti atoms decreases from the surface towards the bulk. This
trend is consistent with a reversal of the ferroelectric polarization below
the top three unit cells, which however is beyond our XSW depth sensitivity.
For this configuration to be stable, a concentration of positive charges at
the polarization flip interface is required. Importantly, the depth dependence
of component $\mathrm{O(2)}$ in this sample is consistent with a distribution
of $\mathrm{O_{L}H^{-}}$ species over about $4$ unit cells ($\approx$
$15\text{\,}\mathrm{\text{Å}}$) below the surface (Figure 11d, Supporting
Information), and thus indicates the accumulation of $\mathrm{H}^{+}$ atoms as
a possible charge compensation mechanism for the polarization reversal below
the surface (Figure 5b). A similar scenario has been suggested by Lee and
coworkers.[15] In their study, atomic positions across the BTO thin film were
derived from CTR scattering experiments, while the increase in component
$\mathrm{O(2)}$ upon water adsorption was assigned to the presence of
$\mathrm{H}^{+}$ or defects. In our study, the combination of depth-dependent
XSW and XPS, and PFM provides further experimental evidence that suggests the
presence of a $\mathrm{H}^{+}$-mediated polarization reversal below the BTO
surface.

In the BTO/SRO/GSO sample, the BTO film has an upward average polarization
$\mathrm{P}^{\uparrow}$ (Table 1) in agreement with a positive displacement of
Ti atoms in the most bulk-sensitive data ($\Delta
z^{\mathrm{Ti}}_{\gamma_{3}}>0$). In contrast, the more surface-sensitive data
show a small negative displacement of Ti atomic positions (Figure 5c), which
indicates a minor polarization reversal at the top unit cells. The
polarization reversal at the surface of a $\mathrm{P}^{\uparrow}$-polarized
BTO thin film, upon hydroxylation of a BaO-terminated surface with
$\mathrm{O_{L}H^{-}}$, has been predicted by DFT calculations and supported by
LEED-IV data.[13] In the present work, we go one step further and
simultaneously provide structural and the following chemical evidence in
support of this predicted behaviour. In fact, in this sample, contrary to the
one above, O1s XPS data show that $\mathrm{O_{L}H^{-}}$ species are confined
at the surface with concentration similar to $\mathrm{OH}^{-}$ or
$\mathrm{O_{2}}^{-}$ species (Figure 11b,d, Supporting Information). The minor
displacement of Ti atoms from the center of the unit cells near the surface,
resulting into a vanishing net polarization, is attributed to the competition
between positively charged $\mathrm{H^{+}}$ atoms of $\mathrm{O_{L}H^{-}}$
species that favor downward polarization $\mathrm{P}^{\downarrow}$ and
negatively charged $\mathrm{OH^{-}}$ or $\mathrm{O_{2}}^{-}$ molecules that
favor upward polarization $\mathrm{P}^{\uparrow}$.[11]

In the BTO/SRO/SSO sample, the BTO film has an upward average polarization
$\mathrm{P}^{\uparrow}$ (Table 1), and a positive off-center displacement of
Ti atoms throughout the top BTO unit cells is observed (Figure 5d). This
scenario implies upward polarization $\mathrm{P}^{\uparrow}$ with accumulation
of positive bound charge at the surface. To stabilize this configuration, a
compensating negative screening charge at the surface is required. O 1s XPS
spectra (Figure 11c, Supporting Information) show a large concentration of
negatively charged O species (OH- and/or $\mathrm{O_{2}}^{-}$). In this
context, the larger displacement of Ti atoms at the surface
($20\text{\,}\mathrm{pm}$), as compared to deeper unit cells, can be
understood as a direct influence of dissociated water molecules on BTO surface
atoms. A recent DFT study[12] predicted that in TiO2-terminated samples OH-
binds to Ti atoms at the surface, thereby inducing a larger offset of Ti atoms
in the topmost atomic plane. Our XSW data provide direct experimental evidence
for this predicted behavior. Moreover, further oxidation of the hydroxyl group
Ti-OH leads to the formation of different peroxide species (e.g.,
$\mathrm{Ti-O^{-}}$, $\mathrm{Ti=O_{2}^{-}}$)[71] with negatively charged O
atoms that contribute to the component $\mathrm{O(4)}$ and favor
$\mathrm{P}^{\uparrow}$ polarization,[11, 12] as shown by our experimental
data.

In single-domain BTO bulk crystals at room temperature with upward
$\mathrm{P}^{\uparrow}$ [downward $\mathrm{P}^{\downarrow}$] polarization,
neutron diffraction analysis revealed that the displacement of Ti atoms is
$5\text{\,}\mathrm{pm}$ above [below] the center of the unit cell.[5] In
comparison, the most bulk-sensitive XSW data $\Delta
z^{\mathrm{Ti}}_{\gamma_{3}}$ show larger Ti atomic displacements. This can be
explained by the residual strain at the top sublayer, leading to out-of-plane
lattice parameters $c_{0}$ larger than the bulk value $c_{b,\mathrm{BTO}}$,
and consequently larger atomic displacements. Moreover, as shown above, atomic
positions near the surface are influenced by adsorbates, which may lead to
smaller (BTO/SRO/GSO) or larger (BTO/SRO/DSO and BTO/SRO/SSO) atomic
displacements depending on their type and content.

In summary, the three samples under study have different in-plane compressive
strain and thickness (Table 1), however the corresponding strain gradients
lead to a similar average out-of-plane lattice parameter $c_{0}$ in the top
sublayer of the BTO/SRO/GSO and BTO/SRO/SSO samples and a slightly smaller one
in the BTO/SRO/DSO sample. Upon exposure to ambient conditions each sample
displays a different distribution of the ferroelectric polarization near the
surface with the common result of screening the bulk polarization and
stabilizing the ferroelectric thin film surface. The available data show that
there is a correlation between the local polarization at the top unit cells
and the type and content of adsorbates on the surface. The interplay of
available adsorbates and bulk ferroelectric polarization leads to the
resulting distribution of local polarization near the surface. Further studies
are required to elucidate to which extent the adsorption of external species
influence or are influenced by the polarization below the surface.

##  4 Conclusions

In this work, the XSW technique is successfully employed to BTO thin films to
determine the displacement of Ti atoms from the center of the unit cell,
defined by Ba atomic positions. In previous studies, the XSW technique in
combination with XFS has been employed to determine the polarization
orientation of the entire film ($\mathrm{P}^{\uparrow}$ or
$\mathrm{P}^{\downarrow}$).[40, 41, 43, 65, 72, 73, 74, 75] Here, we have
measured the photoelectron yield to determine the near-surface displacement of
Ti atoms independently from the polarization in the bulk of the thin film.
First, modeling X-ray diffraction data has provided the distribution of out-
of-plane lattice parameters resulting from the epitaxial strain in our thin
films. Second, the structural sensitivity of the X-ray standing wave combined
with the chemical specificity, surface sensitivity and depth selectivity of
X-ray photoelectron spectroscopy has provided Ti and Ba atomic positions at
different depths with pm spatial resolution. Since the Ba position defines the
center of the unit cell, the measure of the Ti position gives direct access to
the local ferroelectric polarization at (and near) the surface. The
ferroelectric polarization in the top unit cells of the BTO samples under
study has been interpreted with the help of depth-dependent O 1s XPS spectra.
A detailed analysis of oxygen species adsorbed on the surface has suggested
the possible charge compensation mechanisms that are consistent with the
distribution of ferroelectric polarizations derived from XSW data. In
particular, we have identified three different scenarios: (i) a polarization
reversal from downward $\mathrm{P}^{\downarrow}$ to upward
$\mathrm{P}^{\uparrow}$ polarization leading to a tail-to-tail polarization
configuration near the third unit cell that could be stabilized by
$\mathrm{H^{+}}$ atoms diffused below the surface (Figure 5b); (ii) a minor
polarization reversal from upward $\mathrm{P}^{\uparrow}$ to downward
$\mathrm{P}^{\downarrow}$ polarization above the third unit cell leading to a
vanishing polarization, as a result of the competing presence of
$\mathrm{O_{L}H^{-}}$ which favors downward polarization
$\mathrm{P}^{\downarrow}$ and $\mathrm{OH^{-}}$ or $\mathrm{O^{2-}}$ which
favor upward polarization $\mathrm{P}^{\uparrow}$ (Figure 5c); (iii) a uniform
upward polarization $\mathrm{P}^{\uparrow}$ in the BTO film up to the surface
accompanied by a large concentration of compensating negatively charged
chemisorbed oxygen species (Figure 5d).

The variety of the observed ferroelectric configurations demonstrates the
complexity of these systems and underscores the importance of investigating
them from different perspectives to gain a better understanding of the
mechanisms that determine the ferroelectric polarization at the surface. The
novelty of this work lies in the combination of structural and spectroscopic
information, offered by the XSW technique, to provide at once a comprehensive
picture of the ferroelectric polarization at (and near) the surface. This type
of study can be applied to other interesting oxides and can be extended to a
broader class of other technologically relevant materials, such as
multiferroics.[76] Moreover, in the context of catalytic reactions at
ferroelectric surfaces the determination and control of surface polarization
and the interplay with adsorbates is crucial. To this end, in operando XSW
investigations can guide material engineering towards more efficient
catalysts.[22, 23] Importantly, the few pm structural accuracy of XSW provides
a rigorous test for bechmarking different theoretical models and thereby
improving their predictive power.[11, 12] Finally, we anticipate that the XSW
technique can be employed to investigate the dynamics of ferroelectric
polarization switching, specifically to simultaneously track structural and
electronic changes of atoms in real time and corresponding measurements at
X-ray free-electron laser facilities are in preparation.

Acknowledgements

We acknowledge the Diamond Light Source Ltd. for beamtime at the I09 beamline
under the SI27468-1 proposal and thank the staff for their assistance during
our experiments. D.P acknowledges funding from ‘la Caixa’ Foundation
fellowship (ID 100010434). I.S. and D.P. acknowledge financial support from
the Spanish Ministerio de Ciencia e Innovacion (MICINN), grant No.
PID2019-109931GB-I00. The ICN2 is funded by the CERCA programme / Generalitat
de Catalunya and by the Severo Ochoa Centres of Excellence Programme, funded
by the Spanish Research Agency (AEI, CEX2021-001214-S).

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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Figure 1: (a) XSW intensity of BTO (001) Bragg reflection and $z$ axis
orientation, with $z=0$ at the sample surface. (b) Side view of the top two
BTO unit cells with ferroelectric polarization $\mathrm{P}^{\uparrow}$ and
$\mathrm{P}^{\downarrow}$, and Bragg spacing $d_{001}$. (c) Sketch of the
experimental setup (top view) used at the beamline I09 of the Diamond Light
Source, including sample, electron analyzer, and photodiode. The photodiode
was located $10\text{\,}\mathrm{mm}$ away from the sample and was equipped
with an Al mask in front to minimize the fluorescence background. The Bragg
angle $\theta$ and the photoelectron exit angle $\gamma$ are shown, together
with photoelectron exit angle ranges $\gamma_{1}$, $\gamma_{2}$ and
$\gamma_{3}$, incident $\boldsymbol{k}_{0}$ and Bragg-diffracted
$\boldsymbol{k}_{\boldsymbol{H}}=\boldsymbol{k}_{0}+\boldsymbol{H}$ X-ray
wavevectors.

Figure 2: (a) (001) Bragg reflectivity $R_{0}(E_{\nu})$ (points) and
corresponding fit curves (solid lines) of samples BTO/SRO/DSO (pink),
BTO/SRO/GSO (cyan) and BTO/SRO/SSO (green). (b) BTO out-of-plane lattice
parameter $c_{i}$ (solid lines) in sublayers $L_{i}$ and $c(z)$ (dotted lines)
based on Equation (4). The average BTO out-of-plane lattice parameters
$\overline{c}_{\mathrm{BTO}}$ are marked by black stars.

Figure 3: PE spectra of Ti 2p (a) and Ba 4d (b) core levels measured with
$E_{\nu}=$ $1420\text{\,}\mathrm{eV}$ at the exit angle ranges $\gamma_{1}$,
$\gamma_{2}$, and $\gamma_{3}$, on the BTO/SRO/DSO sample. Each spectrum is
normalized to the respective PE intensity maximum. Shaded component areas
refer to spectra measured at the exit angle range $\gamma_{1}$. The
$\mathrm{Ba_{surf}}$ [$\mathrm{Ba_{bulk}}$] component refers to Ba atoms at
[below] the top BaO atomic plane. Similar PE spectra measured on the
BTO/SRO/GSO and BTO/SRO/SSO samples are reported in Figure 10 (Supporting
Information).

Figure 4: Ti and Ba PE yield data (green and blue points) measured with
$E_{\nu}=$ $1420\text{\,}\mathrm{eV}$ at the exit angle ranges $\gamma_{1}$,
$\gamma_{2}$, and $\gamma_{3}$ on BTO/SRO/DSO (a), BTO/SRO/GSO (b), and
BTO/SRO/SSO (c), and corresponding fit curves (solid lines). Reflectivity
$R_{0}(E\nu)$ data (gray points) and fit curves (solid gray lines) around the
(001) BTO Bragg energies $E_{B}=$ $1524\text{\,}\mathrm{eV}$ (a),
$1527.2\text{\,}\mathrm{eV}$ (b), $1530.4\text{\,}\mathrm{eV}$ (c) (marked by
vertical dashed lines). For clarity,
$\kappa^{\mathrm{Ti}}_{\gamma_{1}}(E_{\nu})$ of BTO/SRO/SSO is shown with only
one error bar, which corresponds to the average error bar of all
$\kappa^{\mathrm{Ti}}_{\gamma_{1}}(E_{\nu})$ data points. All PE yield curves
are normalized (Section B.8, Supporting Information) and, for clarity, the
curves above $\mathrm{Ba}(\gamma_{3})$ are vertically shifted by $0.08$ from
the one below.

Figure 5: (a) Probability yield functions $\rho_{\mathrm{yi}}(z)$ of Ba 4d and
Ti 2p photoelectrons at $E_{B}=$ $1525\text{\,}\mathrm{eV}$ integrated over
the three exit angle ranges $\gamma_{1}$, $\gamma_{2}$ and $\gamma_{3}$.
Sketch of Ba and Ti atoms in the top three unit cells of BTO/SRO/DSO (b),
BTO/SRO/GSO (c), and BTO/SRO/SSO (d). For a better visualization, Ti atomic
displacements $\Delta z^{\mathrm{Ti}}_{\gamma}$ are twice larger than values
in Table 2. The length of polarization vectors (solid arrows) is proportional
to the corresponding $\Delta z^{\mathrm{Ti}}_{\gamma}$. The direction of the
average ferroelectric polarization in BTO films measured by PFM is marked by
dashed arrows below the third unit cell. For clarity, only $\mathrm{OH^{-}}$
and $\mathrm{O_{L}H^{-}}$ species are sketched, while $\mathrm{O_{2}^{-}}$
species and $\mathrm{O_{L}}$ atoms are omitted.

Supporting Information

##  Appendix A Sample growth and characterization

###  A.1 Sample growth

Epitaxial bilayers BTO/SRO are grown on DSO, GSO, SSO substrates using pulsed
laser deposition. The ceramic targets of SRO and BTO were 8 cm away from the
substrates and ablated using a KrF excimer laser ($\lambda$ =
$248\text{\,}\mathrm{nm}$, fluence
$5.4\text{\,}\mathrm{J}\text{\,}{\mathrm{cm}}^{-2}$, $2\text{\,}\mathrm{Hz}$
repetition rate). The deposition of SRO and BTO layer is conducted in O2
atmosphere with pressure pO2 = 100 mTorr and deposition temperature of
$908\text{\,}\mathrm{K}$ and $973\text{\,}\mathrm{K}$, respectively. Sample
cooling with the rate of $3\text{\,}\mathrm{K}\text{\,}{\mathrm{min}}^{-1}$ is
conducted in the environment of saturated O2 (pO2 = $10^{4}$ mTorr) to prevent
the formation of oxygen vacancies.

###  A.2 Grazing X-ray reflectivity

Figure 6: Grazing X-ray reflectivity data of as-grown samples used to
determine the thickness of the BTO and SRO thin films (Table 1).

Grazing X-ray reflectivity data of as-grown samples, measured by a PANalytical
X’Pert Pro diffractometer, are shown in Figure 6. The measured reflectivity
$R_{g}(q)$ can be expressed as

$R_{g}(q)=R_{F}(q)\Big{|}\frac{1}{\rho_{s}}\int_{-\infty}^{\infty}\frac{d\rho_{e}(z)}{dz}\exp{(-\mathrm{i}qz)dz}\Big{|}^{2},$
(5)

where $R_{F}$ and $\rho_{s}$ are the Fresnel reflectivity and the electron
density of the substrate, respectively [77]. In Equation (5) $R_{g}$ is
expressed as a function of the wavevector transfer
$q=(4\pi\sin{\theta})/\lambda$ , where $\theta$ is the incident angle of X-ray
and $\lambda=$ $1.54\text{\,}\mathrm{\text{Å}}$ is the wavelength of Cu
K$\alpha$ incident radiation. In practice, thin film thicknesses are
determined as follows. First, $R_{F}$ is calculated using the Parratt
formalism [78]. Second, the Fourier inversion of $R_{g}/R_{F}$ provides the
autocorrelation of the derivative of the electron density $\rho^{\prime}_{e}$
as a function of $z$. This function displays peaks in correspondence of the
interfaces, where $\rho^{\prime}_{e}$ is largest, thereby providing the
thicknesses of layers above the substrate.

###  A.3 X-ray reciprocal lattice map

Figure 7: Reciprocal space maps around (-103) substrate Bragg peak of the
BTO/SRO/DSO (a), BTO/SRO/GSO (b) and BTO/SRO/SSO (c) samples. The gray
vertical dashed lines indicate the reciprocal lattice parameter
$Q_{\mathrm{x}}$ shared by the substrate, the BTO, and SRO thin films in each
sample.

Figure 7 shows X-ray reciprocal lattice maps of the three samples around
(-103) substrate Bragg peak, measured by a PANalytical X’Pert Pro
diffractometer. The diffraction peaks of the substrates have very narrow
intensity distribution, while the intensity distribution of BTO and SRO layers
are weaker and broader. Reciprocal lattice parameters $Q_{\mathrm{x}}$ and
$Q_{\mathrm{z}}$ of intensity peaks are related to the real space in-plane and
out-of-plane lattice parameters, $a$ and $c$, by the following relations:
$a=-\lambda/(2Q_{\mathrm{x}})$ and $c=(3\lambda)/(2Q_{\mathrm{z}})$ [79]. The
values $Q_{\mathrm{x}}$ and $Q_{\mathrm{z}}$ of each diffraction peak are
obtained by fitting the intensity distribution with a pseudo-Voigt function
[80].

###  A.4 Piezoresponse force microscopy

Figure 8: PFM phase image of the BTO/SRO/DSO (a), BTO/SRO/GSO (b), and
BTO/SRO/SSO (c) samples. The sign of the applied tip voltage ($\pm\mathrm{V}$)
within the gray boxes and the resulting average polarization direction
$\mathrm{P}^{\uparrow}$ or $\mathrm{P}^{\downarrow}$ in the probed areas are
marked on each panel. The PFM phase beyond the gray boxes indicates the
average polarization direction of as-grown samples. (d) The corresponding
hysteresis loops.

Piezoresponse force microscopy in Dual AC Resonance Tracking (DART) mode [81]
was used to probe the polarization of as-grown samples and to prove that
ferroelectric polarization can be switched by the application of positive or
negative voltage between the PFM tip and the SRO electrode. Figure 8a-c show
the PFM phase image of each sample after the application of a voltage to
switch the polarization inside the marked gray boxes. A positive [negative]
voltage of sufficient amplitude forces the polarization to be
$\mathrm{P}^{\downarrow}$ [$\mathrm{P}^{\uparrow}$], with the corresponding
PFM phase $0\degree$ [$180\degree$]. The PFM phase outside the gray boxes
indicates the polarization of the as-grown sample. Therefore, Figure 8a shows
an average downward polarization $\mathrm{P}^{\downarrow}$ in the BTO/SRO/DSO
sample, while an average upward polarization $\mathrm{P}^{\uparrow}$ in the
BTO/SRO/GSO and BTO/SRO/SSO samples. Note also that PFM phase images show no
indication of multiple domains in any of the as-grown sample. Furthermore,
switching spectroscopy PFM (SS-PFM) was employed to measure hysteresis loops
on each sample. From these data, reported in Figure 8d, we measure in the
BTO/SRO/DSO sample a coercive voltage of $V_{c}=$ $1.1\text{\,}\mathrm{V}$
with a negative bias $V_{b}=$ $-0.9\text{\,}\mathrm{V}$. In contrast, the
BTO/SRO/GSO sample shows $V_{c}=$ $1.6\text{\,}\mathrm{V}$ with a positive
bias $V_{b}=$ $0.7\text{\,}\mathrm{V}$. Finally, the BTO/SRO/SSO sample has an
unbiased hysteresis loop with a coercive voltage $V_{c}=$
$1.1\text{\,}\mathrm{V}$.

##  Appendix B Data analysis

###  B.1 Average out-of-plane lattice parameter $\overline{c}$

BTO and SRO average out-of-plane parameters $\overline{c}$ are calculated from
the corresponding (001) Bragg peaks using the Bragg condition
$\overline{c}=($12\,400\text{\,}\mathrm{eV}\text{\,}\mathrm{\text{Å}}$)/(2\overline{E}_{\nu}\sin\theta_{B})$.
$\overline{E}_{\nu}$ is the average of energy values $E_{\nu}$ around the
Bragg peaks, weighted with reflectivity $R_{0}(E_{\nu})$. The energy ranges
for calculating $\overline{E}_{\nu}$ of BTO and SRO are respectively $1510$
$\text{\,}\mathrm{eV}$ \- $1547.5$ $\text{\,}\mathrm{eV}$ and $1587$
$\text{\,}\mathrm{eV}$ \- $1624$ $\text{\,}\mathrm{eV}$, where the
$R_{0}(E_{\nu})$ has finite values.

###  B.2 Reflectivity fit results

Table 3 and Table 4 report the results of reflectivity fit shown in Figure 2a.

Table 3:  BTO and SRO Debye-Waller factors $\mathrm{e}^{-W_{i}}$ of sublayers $L_{i}$ ($i=0,...,4$) resulting from the fits of (001) Bragg reflection data in the three samples under study (Figure 2). Layer | sublayer | fit parameters | BTO/SRO/DSO | BTO/SRO/GSO | BTO/SRO/SSO
---|---|---|---|---|---
| $L_{0}$ | $\mathrm{e}^{-W_{0}}$ | 1 | 0.9 | 1
| $L_{1}$ | $\mathrm{e}^{-W_{1}}$ | 1 | 1 | 1
BTO | $L_{2}$ | $\mathrm{e}^{-W_{2}}$ | 1 | 1 | 0.8
| $L_{3}$ | $\mathrm{e}^{-W_{3}}$ | 1 | 1 | 1
| $L_{4}$ | $\mathrm{e}^{-W_{4}}$ | 1 | 0.1 | 0.5
| $L_{0}$ | $\mathrm{e}^{-W_{0}}$ | 0.4 | 0.7 | 0.9
| $L_{1}$ | $\mathrm{e}^{-W_{1}}$ | 0.9 | 0.6 | 1
SRO | $L_{2}$ | $\mathrm{e}^{-W_{2}}$ | 1 | 0.9 | 0.6
| $L_{3}$ | $\mathrm{e}^{-W_{3}}$ | 0.4 | 1 | 0.5
| $L_{4}$ | $\mathrm{e}^{-W_{4}}$ | 0.04 | 0 | 0.8
Table 4:  BTO and SRO interface strain $\epsilon_{\mathrm{int}}$ and penetration depth of strain $\delta$ resulting from the fits of (001) Bragg reflection data in the three samples under study (Figure 2). Layer | fit parameters | BTO/SRO/DSO | BTO/SRO/GSO | BTO/SRO/SSO
---|---|---|---|---
BTO | $\epsilon_{\mathrm{int}}$ | 0.06 | 0.03 | 0.01
| $\delta$ | 36 | 136 | 233
SRO | $\epsilon_{\mathrm{int}}$ | -0.01 | -0.05 | -0.04
| $\delta$ | 589 | 56 | 71

###  B.3 SRO structural properties

Figure 9: SRO out-of-plane lattice parameters $c_{i}$ (solid lines) in
sublayers $L_{i}$ and $c(z)$ (dotted lines) according to Equation (4).

The in-plane strain applied by a substrate to the BTO thin film is calculated
as
$\epsilon^{a}_{\mathrm{SRO}}=\left(a_{\mathrm{SRO}}-a_{\mathrm{b,SRO}}\right)/a_{\mathrm{b,SRO}}$,
by comparing the measured in-plane lattice parameter of the thin film
$a_{\mathrm{SRO}}$ (Section A.3) with the respective bulk value of the
pseudocubic cell with parameter $a_{\mathrm{b,SRO}}\approx
c_{\mathrm{b,SRO}}=$ $3.923\text{\,}\mathrm{\text{Å}}$ [82]. As a result, the
DSO, GSO, and SSO substrates impose an in-plane tensile strain on the SRO
films of $0.51\%$, $1.12\%$, and $1.38\%$, respectively. This leads to a
decreasing average out-of-plane lattice parameter in SRO following the same
substrate order: $\overline{c}_{\mathrm{SRO}}=$
$3.885(19)\text{\,}\mathrm{\text{Å}}$, $3.876(24)\text{\,}\mathrm{\text{Å}}$,
$3.866(23)\text{\,}\mathrm{\text{Å}}$. These measured $\overline{c}$
parameters correspond to an average out-of-plane tensile strain
$\overline{\epsilon}^{c}_{\mathrm{SRO}}=\left(\overline{c}_{\mathrm{SRO}}-c_{b,\mathrm{SRO}}\right)/c_{b,\mathrm{SRO}}$
of $-0.96\%$, $-1.20\%$, and $-1.45\%$, respectively. Figure 9 shows the
exponential distribution of SRO out-plane lattice parameters $c_{i}$ (Equation
4 in the article) in different sublayers $L_{i}$, resulting from the (001)
Bragg reflections fits shown in Figure 2a.

###  B.4 Ti 2p, Ba 4d and C 1s XPS

Figure 10: Ti 2p, Ba 4d and C 1s PE spectra of the BTO/SRO/GSO sample (a, b,
c) and the BTO/SRO/SSO sample (d, e, f), respectively. Ti 2p and Ba 4d spectra
are shown at the exit angle ranges $\gamma_{1}$, $\gamma_{2}$, and
$\gamma_{3}$, while panels c and f show the sum of C 1s spectra over all
measured exit angle ranges. Note that both C 1s spectra are normalized to the
peak intensity of C 1s spectrum in panel (f) to underscore the different
content of carbon species in the two samples.

Figure 10 shows typical PE spectra Ti 2p, Ba 4d, and C 1s core levels of the
BTO/SRO/GSO and BTO/SRO/SSO samples. Ti and Ba PE spectra show similar
features as the spectra in Figure 3 discussed in Section 3.4. The larger noise
of PE spectra in Figure 10d-e result from the lower PE intensity due to the
larger amount of C and O species on the BTO/SRO/SSO surface. In fact, the
corresponding C 1s spectrum (Figure 10f) has an area approximately three times
larger than of the one of the BTO/SRO/GSO sample (Figure 10c). In particular,
component $\mathrm{C(1)}$ at $284.6\text{\,}\mathrm{eV}$ is assigned to
adventitious carbon, resulting from hydrocarbons adsorbed on the sample
surface, upon exposure to ambient environment, while component $\mathrm{C(2)}$
with a BE shift of $1.4\text{\,}\mathrm{eV}$ refers to $\mathrm{CO}$ species
[63]. The C1s spectrum of the BTO/SRO/DSO sample (not shown) is similar to the
one of the BTO/SRO/GSO sample (Figure 10c).

###  B.5 O 1s XPS

O 1s XPS spectra measured at different exit angle range $\gamma$ (Figure
11a-c) provide a detailed picture of oxygen-related species at the BTO
surface. Let us focus first on the most bulk sensitive
$\mathrm{O}(\gamma_{3})$ spectra. Here, the most prominent peak
$\mathrm{O(1)}$ at $529.8\text{\,}\mathrm{eV}$ refers to O atoms in BTO
lattice ($\mathrm{O_{L}}$). The other O components result from H2O
dissociation ($\mathrm{O(2)}$ and $\mathrm{O(4)}$) and $\mathrm{CO_{x}}$
species ($\mathrm{O(3)}$). In general, adsorption of $\mathrm{H_{2}O}$ on BTO
may lead to molecular physisorption with $\mathrm{\Delta BE}\approx$
$3.9\text{\,}\mathrm{eV}$ [71, 63]. O 1s spectra in Figure 11a-c show evidence
of molecular physisorbed water only at the exit angle ranges $\gamma_{1}$ and
$\gamma_{2}$ and with minor contributions to the total spectral area smaller
than $3\%$. This suggests that the surface favors water dissociation into OH-
and H+, which is typical of BaO-terminated surfaces [83, 13] but is also
present on $\mathrm{TiO_{2}}$-terminated surfaces [71]. While OH- chemisorbs
on top of cations (Ba or Ti) or at O vacancies, H+ binds to $\mathrm{O_{L}}$
at the BTO surface or diffuses inside the film to form $\mathrm{O_{L}H^{-}}$
[14, 15, 70], assigned to component $\mathrm{O(2)}$. The latter has a smaller
binding energy shift $\mathrm{\Delta BE}=$ $1\text{\,}\mathrm{eV}$ [84], given
the chemical environment much closer to $\mathrm{O_{L}}$, as compared to
chemisorbed OH-. In contrast, OH- is assigned to component $\mathrm{O(4)}$
with a larger binding energy shift $\mathrm{\Delta BE}=$
$2.7\text{\,}\mathrm{eV}$ [28, 15]. In addition, other species, resulting from
$\mathrm{O_{2}}$ adsorption such as peroxo complexes (e.g. BaO2, Ti-O-O-Ti,
Ti=O${}_{2}^{-}$), can contribute to component $\mathrm{O(4)}$ [71]. In this
case, oxidation of BaO-terminated surfaces or Ti-OH leads to the presence of
O${}_{2}^{-}$ at the surface. Finally, component $\mathrm{O(3)}$ at
$\mathrm{\Delta BE}=$ $1.8\text{\,}\mathrm{eV}$ is assigned to COx species,
such as carbonates $\mathrm{CO_{3}^{2-}}$, $\mathrm{C=O}$ bonds, ester
(C-(C=O)-OR) or carboxylic acid (C-(C=O)-OH) compounds [85, 63]. In the
BTO/SRO/DSO, BTO/SRO/GSO, and BTO/SRO/SSO samples, the contribution of
component $\mathrm{O(3)}$ to the $\gamma$-integrated spectral area is $\approx
0\%$, $3\%$, and $6\%$, respectively. Following the same substrate order,
component $\mathrm{O(2)}$ [$\mathrm{O(4)}$] represents $15\%$ [$32\%$], $19\%$
[$30\%$], and $13\%$ [$53\%$] of the $\gamma$-integrated spectral area.

Figure 11: O 1s PE spectra $\mathrm{O}(\gamma_{1})$, $\mathrm{O}(\gamma_{2})$
and $\mathrm{O}(\gamma_{3})$ integrated over the respective exit angle ranges
in the BTO/SRO/DSO (a), BTO/SRO/GSO (b), and BTO/SRO/SSO (c) samples. Each
spectrum is normalized to the respective maximum PE intensity. Shaded
component areas $\mathrm{O(1)}$, $\mathrm{O(2)}$, $\mathrm{O(3)}$, and
$\mathrm{O(4)}$ refer to $\mathrm{O}(\gamma_{3})$ spectra. Components
$\mathrm{O(1)}$, $\mathrm{O(2)}$, $\mathrm{O(3)}$, and $\mathrm{O(4)}$
originate from O atoms in the lattice ($\mathrm{O_{L}}$),
$\mathrm{O_{L}H^{-}}$ species, $\mathrm{CO_{x}}$ species, and
$\mathrm{OH^{-}}$ and/or $\mathrm{O_{2}^{-}}$ species, respectively. The ratio
of component $\mathrm{O(2)}$ [$\mathrm{O(4)}$] over component $\mathrm{O(1)}$
as a function of exit angle range $\gamma$ is displayed in panel (d) [(e)] for
the three samples under study.

To gain information on the depth distribution of the different oxygen species,
a quantitative analysis of $\mathrm{O(2)}$ and $\mathrm{O(4)}$ relative
spectral area as a function of exit angle range $\gamma$ was performed. The
ratio of spectral areas between component $\mathrm{O(2)}$ [$\mathrm{O(4)}$]
and $\mathrm{O(1)}$ measured at exit angle range $\gamma_{j}$ ($j=1,2,3$) is
calculated as
$R_{2}=A_{\mathrm{O(2)}}^{\gamma_{j}}/A_{\mathrm{O(1)}}^{\gamma_{j}}$
[$R_{4}=A_{\mathrm{O(4)}}^{\gamma_{j}}/A_{\mathrm{O(1)}}^{\gamma_{j}}$].
Figure 11d,e shows $R_{2}$ and $R_{4}$ at the different $\gamma_{j}$ together
with the corresponding fit functions. The model employed to fit these data
[86] assumes that adsorbates form a patched overlayer of thickness
$t_{\mathrm{O(k)}}$ ($k=2,4$) and coverage $\Gamma$ ($0<\Gamma<1$), which
indicates the fraction of surface covered by the overlayer. $R_{2}$ and
$R_{4}$ data in Figure 11d,e are fitted with the fitting parameter $\Gamma$,
while $t_{\mathrm{O(k)}}$ is varied in $1\text{\,}\mathrm{\text{Å}}$ steps to
obtain the best fit with $R^{2}\approx 1$. On all samples, the adsorbates
represented by component $\mathrm{O(4)}$ form a superficial layer of thickness
$\approx$ $4\text{\,}\mathrm{\text{Å}}$, corresponding to 1 monolayer [71]. In
contrast, in the BTO/SRO/DSO sample, component $\mathrm{O(2)}$ is distributed
below the BTO surface with thickness $\approx$ $15\text{\,}\mathrm{\text{Å}}$,
while in the BTO/SRO/GSO and BTO/SRO/SSO samples, component $\mathrm{O(2)}$ is
concentrated near the surface with thickness $\approx$
$6\text{\,}\mathrm{\text{Å}}$. The larger thickness $t_{\mathrm{O(2)}}$ in the
BTO/SRO/DSO sample cannot be explained by a thicker overlayer of
$\mathrm{O_{L}H^{-}}$ species above the BTO surface because the molecules in
the overlayer would be in a different chemical environment and thus appear at
a different binding energy. Instead, our experimental data suggest a scenario
where $\mathrm{H^{+}}$ atoms are distributed below the BTO surface to form
$\mathrm{O_{L}H^{-}}$ species (Figure 5b), as already proposed in other works
[70, 15].

In summary, in the BTO/SRO/DSO sample, $\mathrm{O_{L}H^{-}}$ species have the
largest distribution below the BTO surface and $\mathrm{H^{+}}$ atoms serve as
charge compensation mechanism of the tail-to-tail polarization configuration
revealed by XSW and PFM measurements. In the BTO/SRO/GSO sample, the
comparable amount of $\mathrm{OH^{-}}$ and $\mathrm{O_{L}H^{-}}$ species near
the surface favor a ferroelectric polarization with opposite orientation,
resulting into a vanishing net polarization amplitude just below the BTO
surface. Finally, in the BTO/SRO/SSO sample, the ferroelectric polarization is
pointing upward in the unit cells near the surface with overall the largest
amplitude among the samples under study. This is consistent with the largest
amount of negatively charged hydroxyl or $\mathrm{O_{2}^{-}}$ molecules
concentrated near the surface, as shown by component $\mathrm{O(4)}$ in Figure
11c.

###  B.6 XPS fit results

PE spectra were measured using a fixed mode of the electron analyzer with a
pass energy of $200\text{\,}\mathrm{eV}$ [$100\text{\,}\mathrm{eV}$] for Ba
4d, Ti 2p, C 1s [O 1s] core-level emission lines. In general, all PE spectra
in this work were fitted using the software CasaXPS with Shirley background
subtraction and a combination of Gaussian/Lorentzian functions with the best
fit provided by ratio $70/30$ (for Ba 4d, O 1s, C 1s) and $40/60$ (for Ti 2p).
A summary of the resulting BE shifts and FWHM of each component is reported in
Table 5.

Table 5: FWHM of each fit component and BE shift of components $\mathrm{P(m)}$ ($\mathrm{m=2,3,4,5}$) from $\mathrm{P(1)}$ in Ba 4d, Ti 2p, O1s and C1s PE spectra. | Ba 4d | Ti 2p | O 1s | C 1s
---|---|---|---|---
|  BE shift (eV) |  FWHM (eV) |  BE shift (eV) |  FWHM (eV) |  BE shift (eV) |  FWHM (eV) |  BE shift (eV) |  FWHM (eV)
$\mathrm{P(1)}$ |  – |  0.83 |  – |  1.02 |  – |  1.14 |  – |  1.37
$\mathrm{P(2)}$ |  2.58 |  0.83 |  5.72 |  2.04 |  1 |  1.36 |  1.4 |  1.75
$\mathrm{P(3)}$ |  1.21 |  1.65 |  |  |  2 |  1.32 |  |
$\mathrm{P(4)}$ |  3.80 |  1.65 |  |  |  2.7 |  1.54 |  |
$\mathrm{P(5)}$ |  |  |  |  |  3.85 |  1.45 |  |

###  B.7 Inelastic mean free path

The inelastic mean free path $\lambda_{l}(E_{\nu})$ is defined, according to
Ref. [87], as:

$\lambda_{l}(E_{\nu})=\frac{\mathcal{A}(E)(E_{\nu}-\mathrm{BE})}{E_{p}^{2}\bigl{\\{}\mathcal{B}\left[ln(\mathcal{Y}\mathcal{A}(E_{\nu})(E_{\nu}-\mathrm{BE}))\right]-\mathcal{C}/(E_{\nu}-\mathrm{BE})+\mathcal{D}/(E_{\nu}-\mathrm{BE})^{2}\bigr{\\}}}.$
(6)

In Equation (6):
$\mathcal{A}(E_{\nu})=\left[1+(E_{\nu}-\mathrm{BE})/(2m_{e}c^{2})\right]/\left[1+(E_{\nu}-\mathrm{BE})/(m_{e}c^{2})\right]^{2}$,
$\mathcal{B}=-1.0+9.44/(E_{p}^{2}+E_{g}^{2})^{0.5}+0.69\rho^{0.1}$,
$\mathcal{C}=19.7-9.1\mathcal{U}$, $\mathcal{D}=534-208\mathcal{U}$,
$\mathcal{Y}=0.191\rho^{-0.5}$, and $\mathcal{U}=N_{v}\rho/M$. In these
equations: $\mathrm{BE}$ is the binding energy of photoelectrons from core
level $l$, $m_{e}$ is the rest mass of electron, $c$ is the speed of light,
$N_{v}$ is the total number of valence electrons per molecule, $\rho$ is bulk
density, $M$ is the molecular weight, $E_{p}=28.816(N_{v}.\rho/M)^{0.5}$ is
the free-electron plasmon energy and $E_{g}$ is the band gap energy in eV. In
the case of BTO: $N_{v}=24$, $M=$
$233.19\text{\,}\mathrm{g}\text{\,}{\mathrm{mol}}^{-1}$ [88], $\rho=$
$6.02\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}$ [88] and $E_{g}=$
$3.76\text{\,}\mathrm{eV}$ [89].

###  B.8 Photoelectron yield normalization

The PE yield undergoes two normalization steps: (i) by the incident X-ray
intensity, and (ii) by the photoionization cross-section. First, the X-ray
intensity $I_{0}$ is measured as the drain current from the last mirror before
the sample. The incident X-ray intensity $I_{0}$ decreases by approximately
$10\%$ in the energy range from $1400$ to $1700\text{\,}\mathrm{eV}$ (Figure
12b). This is due to the decreasing monochromator grating efficiency.
Furthermore, the $I_{0}$ sawtooth profile in the region from $1480$ to
$1620\text{\,}\mathrm{eV}$ results from the top-up electron injection at the
Diamond Light Source. PE yield data normalized by $I_{0}$ are shown in Figure
12c. Here, the decrease in PE yield by a factor $\approx 1.8$ over the whole
photon energy range follows from the varying photoionization cross-section
[90, 91]. The second normalization step consists in dividing PE yield data by
a second order polynomial resulting from the fit of $7$ points at each end of
a yield curve in Figure 12c, where no XSW effect is observed. An example of
fitting curve is shown in Figure 12c (blue solid line), while the normalized
PE yield curves are reported in Figure 12d. Finally, at each photon energy
$E_{\nu}$, average and standard deviation of PE yield data (measured under the
same conditions) are calculated to determine the PE yield values and error
bars reported in Figure 4.

Figure 12: (a) Ba 4d PE yield raw data of the BTO/SRO/DSO sample measured in
$5$ consecutive photon energy scan (run). (b) Incident X-ray beam intensity
$I_{0}$. (c) PE yield raw data normalized by $I_{0}$. (d) PE yield raw data
normalized by $I_{0}$ and photoionization cross-section.

###  B.9 Reflection and transmission calculation

The X-ray diffracted intensity from the sublayer $L_{i}$ with thickness
$t_{i}$ at photon energy $E_{\nu}$ and $z_{i}<z<z_{i}+t_{i}$ is calculated as
[47]:

$R(E_{\nu},z)=\beta|Y|^{2}|r(E_{\nu},z)|^{2}=\beta|Y|^{2}\Bigg{|}\frac{x_{1}-x_{2}x_{3}\exp(-\sigma\Delta
z_{i})}{1-x_{3}\exp(-\sigma\Delta z_{i})}\Bigg{|}^{2},$ (7)

where $x_{1}=-\Big{(}b+\sqrt{b^{2}-C_{1}^{2}}\Big{)}/C_{1}$,
$x_{2}=-\Big{(}b-\sqrt{b^{2}-C_{1}^{2}}\Big{)}/C_{1}$, and
$x_{3}=(x_{1}-r_{t_{i}})\exp(\sigma t_{i})/(x_{2}-r_{t_{i}})$,
$\sigma=2\mathrm{i}\sqrt{b^{2}-C_{1}^{2}}/L_{ex}$, and $\Delta z_{i}=z-z_{i}$.
The reflection amplitude at the bottom [top] of $L_{i}$ is defined as
$r_{t_{i}}=r(E_{\nu},\Delta z_{i}=t_{i})$ [$r(E_{\nu},\Delta z_{i}=0)$], and
$r$ at the top of $L_{i}$ is then treated as the reflection at the bottom of
layer $L_{i-1}$. Starting from the boundary condition of $r(E_{\nu},z)=0$ at
the bottom of the substrate, Equation (7) is employed recursively to calculate
the diffracted intensity at the top of $L_{0}$, i.e. $R(E_{\nu},0)$ (Section
2).

Parameters appearing in Equation (7) are summarized in the following. In
particular, $b$ is defined as $b=-y(E_{\nu})-\mathrm{i}y_{0}+y_{\varphi}(z)$
where
$y(E_{\nu})=2\sqrt{\beta}(\sin^{2}{\theta_{B}})(E_{\nu}-E_{B})/(E_{B}X_{\mathrm{r}})+\chi_{0\mathrm{r}}(1+\beta)/(2\sqrt{\beta}X_{\mathrm{r}})$,
$y_{0}=(\chi_{0\mathrm{i}}(1+\beta))/(2\sqrt{\beta}X_{\mathrm{r}})$,
$y_{\varphi}(z)=(L_{ex}/2)d\varphi(z)/dz$. Here, $y(E_{\nu})$ is a
dimensionless parameter that indicates the energy deviation from the exact
Bragg energy $E_{B}$ during incident photon energy scan, $y_{0}$ represents
the attenuation of X-ray intensity due to photoelectric absorption and
$y_{\varphi}(z)$ indicates the shift of diffraction planes due to lattice
deformation. In the latter equations, the geometry factor $\beta$ is defined
as $\beta=\Gamma_{\boldsymbol{0}}/|\Gamma_{\boldsymbol{h}}|$, where
$\Gamma_{\boldsymbol{0}}=k_{\boldsymbol{0}z}/K$ and
$\Gamma_{\boldsymbol{h}}=k_{\boldsymbol{h}z}/K$ are the direction parameters
with $K=2\pi/\lambda_{B}$ and $\lambda_{B}$ is the Bragg wavelength. The
extinction length represents the penetration depth of the XSW field and is
defined as
$L_{ex}=(\lambda_{B}\Gamma_{\boldsymbol{0}})/(\pi\sqrt{\beta}X_{\mathrm{r}})$.

The parameter $C_{1}$ has the form $C_{1}=C(1-\mathrm{i}p)\exp(-W(z))$, where
$p=-X_{\mathrm{i}}/X_{\mathrm{r}}$ and $C$ is the polarization factor which is
equal to 1 for $\sigma$ polarization and $\cos{2\theta_{B}}$ for $\pi$
polarization, with $\theta_{B}$ being the Bragg angle. The parameters
$Y=\sqrt{\chi_{\boldsymbol{h}}/\chi_{\bar{\boldsymbol{h}}}}=|Y|\exp(\mathrm{i}\Phi_{Y})$,
$X_{\mathrm{r}}=Re\Big{[}\sqrt{\chi_{\boldsymbol{h}}\chi_{\bar{\boldsymbol{h}}}}\Big{]}$
and
$X_{\mathrm{i}}=Im\Big{[}\sqrt{\chi_{\boldsymbol{h}}\chi_{\bar{\boldsymbol{h}}}}\Big{]}$
are derived from crystal susceptibilities $\chi_{0}$, $\chi_{\boldsymbol{h}}$,
$\chi_{\bar{\boldsymbol{h}}}$ corresponding to vectors
$\boldsymbol{0}*\boldsymbol{h}$, $\boldsymbol{h}$, and $-\boldsymbol{h}$ with
$\boldsymbol{h}=2\pi\boldsymbol{H}$. The crystal susceptibility
$\chi_{\boldsymbol{h}}$ is generally a complex number
$\chi_{\boldsymbol{h}}=\chi_{\boldsymbol{h}\mathrm{r}}+\mathrm{i}\chi_{\boldsymbol{h}\mathrm{i}}$,
where
$\chi_{\boldsymbol{h}\mathrm{r}}=-\Big{(}\mathrm{e}^{2}\lambda_{B}^{2}/mc^{2}\pi\Omega\Big{)}F_{\boldsymbol{h}\mathrm{r}}$
represents X-ray elastic scattering, while
$\chi_{\boldsymbol{h}\mathrm{i}}=\Big{(}\mathrm{e}^{2}\lambda_{B}^{2}/mc^{2}\pi\Omega\Big{)}F_{\boldsymbol{h}\mathrm{i}}$
stands for X-ray absorption. The structure factor
$F_{\mathrm{h}}=\sum_{j}f_{j}\exp(-W_{j})\exp(-\mathrm{i}\boldsymbol{h}\boldsymbol{\rho}_{j})$
is computed from the atomic scattering factor $f_{j}$ of $j$th atom at
position vector $\boldsymbol{\rho}_{j}$ in the unit cell. The atomic
scattering factor
$f_{j}=f_{0}(\theta_{B},\lambda_{B},Z)-Z+f_{1}(0,\lambda_{B},Z)+\mathrm{i}f_{2}(0,\lambda_{B},Z)$
describes the interaction between X-rays and atoms, where $Z$ is the atomic
number, $f_{0}$, $f_{1}$, and $f_{2}$ are tabulated in Ref. [92, 93].

Finally, besides the reflection amplitude, solving the Takagi-Taupin equations
also provides the transmission amplitude through the sublayer $L_{i}$ [47]:

$T(E_{\nu},z)=\exp[\mathrm{i}\Phi(E_{\nu})\Delta
z_{i}/2]\Bigg{(}\frac{1-x_{3}\exp(-\sigma\Delta z_{i})}{1-x_{3}}\Bigg{)},$ (8)

where
$\Phi(E_{\nu})=(2\pi\chi_{\boldsymbol{0}})/(\lambda_{B}\Gamma_{\boldsymbol{0}})-2C_{1}x_{1}/L_{ex}$.

###  B.10 Deformation phase calculation

The deformation phase $\varphi_{0}$ in Equation 3 in the article, is derived
from the bicrystal model [47] and is defined as
$\varphi_{0}=2\pi(c_{0}-\overline{c})t_{0}/\overline{c}^{2}$. The bicrystal
model assumes: a crystal, in which the XSW is formed, and a deformed overlayer
of thickness $t_{l}$ that induces a shift of the diffraction planes
$\varphi_{0}=2\pi(c_{l}-c_{c})t_{l}/c_{c}^{2}$, where $c_{l}$ and $c_{c}$ are
the out-of-plane lattice parameters of the deformed layer and the crystal,
respectively. In our samples, the XSW forms in the BTO film itself with a
deformation given by an inhomogeneous strain. Therefore the deformation phase
cannot refer to the $c$ parameter of a single crystal underneath. Instead,
$\varphi_{0}$ refers to the average out-of-plane lattice parameter
$\overline{c}$, calculated from the experimental diffraction curves (Section
B.1). This is equivalent to modelling the thin film as a crystal with an
average out-of-plane parameter $\overline{c}$ and an increasing [decreasing]
deformation phase towards the interface with SRO [towards the surface]. The
validity of this choice is confirmed by the coherent position of the Ba atoms
(Table II) being close to $1$, i.e., near the diffraction planes. Conversely,
referring, e.g., the deformation phase to the bottom sublayer $L_{n-1}$ would
lead at the top unit cells to unphysical positions of the Ba atoms
$1\text{\,}\mathrm{\text{Å}}$ away from the diffraction planes.

###  B.11 The uncertainty of Ba and Ti atomic positions

The attainable structural accuracy in the determination of the average atomic
positions depends ultimately on the error bar of the PE yield profiles
according to Poisson statistics. We observe that the error bars of data of the
BTO/SRO/SSO sample ($1\%<\sigma_{\kappa}<7\%$) are generally larger than those
of the other two samples ($\sigma_{\kappa}<2\%$). This is due to the greater
amount of adsorbates on the BTO/SRO/SSO surface, which attenuated the measured
PE intensity (Section B.4). Besides, lower PE intensity is also expected with
a decreasing $\gamma$ or smaller $\lambda_{l,\gamma}$. This explains the trend
of increasing $\sigma_{\kappa}$ with decreasing $\gamma$ and the larger
uncertainty in Ti positions compared to Ba (Table 2). The latter observation
is also due to the smaller photoionization cross-section of Ti 2p as compared
to Ba 4d core levels [90, 91].