# Sub-millisecond electric field sensing with an individual rare-earth doped
ferroelectric nanocrystal

Athulya K. Muraleedharan  [  Jingye Zou  Maxime Vallet  Abdelali Zaki
Christine Bogicevic  [  Charles Paillard  [  Karen Perronet  François
Treussart  [<EMAIL_ADDRESS>
###### Abstract

Understanding the dynamics of electrical signals within neuronal assemblies is
crucial to unraveling complex brain function. Despite recent advances in
employing optically active nanostructures in transmembrane potential sensing,
there remains room for improvement in terms of response time and sensitivity.
Here, we report the development of such a nanosensor capable of detecting
electric fields with a submillisecond response time at the single particle
level. We achieve this by using ferroelectric nanocrystals doped with rare
earth ions producing upconversion (UC). When such a nanocrystal experiences a
variation of surrounding electric potential, its surface charge density
changes, inducing electric polarization modifications that vary, via converse
piezoelectric effect, the crystal field around the ions. The latter variation
is finally converted into UC spectral changes, enabling optical detection of
electric potential. To develop such a sensor, we synthesized erbium and
ytterbium-doped barium titanate crystals of size $\approx 160$ nm. We observed
distinct changes in the UC spectrum when individual nanocrystals were
subjected to an external field via a conductive AFM tip, with a response time
of 100 $\mu$s. Furthermore, our sensor exhibits a sensitivity to electric
fields of only 4.8 kV/cm/$\sqrt{\rm Hz}$, making possible the time-resolved
detection of a neuron action potential.

###### keywords:

Sensor, Ferroelectrics, Barium titanate, Nanocrystal, Rare-Earth ions, Up-
conversion

LuMIn] Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec,
LuMIn, 91190 Gif-sur-Yvette, France SPMS] Université Paris-Saclay,
CentraleSupélec, CNRS, Laboratoire SPMS, 91190 Gif-sur-Yvette, France SPMS]
Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire SPMS, 91190 Gif-
sur-Yvette, France [UA] Smart Ferroic Materials, Institute for Nanoscience &
Engineering and Department of Physics, University of Arkansas, Fayetteville
72701 Arkansas, USA LuMIn] Université Paris-Saclay, ENS Paris-Saclay, CNRS,
CentraleSupélec, LuMIn, 91190 Gif-sur-Yvette, France

##  1 Introduction

The generation and propagation of electrical signals in neurons and across
neuronal assemblies, which occurs at the nanometer and millisecond scales,
remains poorly understood, despite the development of several theoretical
models. For instance, the theory of core conductor cable and the Goldman-
Hodgkin-Huxley-Katz models of ion motion and voltage propagation have provided
theoretical foundations for neuronal physiology 1, 2. These theories account
for the action potential, the few millisecond lasting voltage variation of 100
mV across the $\approx 5$ nm thick membrane (corresponding to 200 kV/cm peak
voltage), which supports neuron-to-neuron communication. However, these models
neglect electrodiffusion, that is, concentration changes associated with ionic
currents. This assumption is true at millimeter scale like the squid giant
axon but fails to describe accurately the processes taking place at the sub-
micrometer size structure of synapses 3, 4. The Poisson-Nernst-Planck theory
reveals that the geometry of synaptic compartments influences the distribution
of local electric field generated during synaptic transmission, which
subsequently changes the concentration of charged neurotransmitters undergoing
electrodiffusion 5 and therefore has a functional impact. As the shape of the
synapse changes during the execution of cognitive tasks 6, being able to
measure the electric field on this scale would not only be an observable of
such key plasticity but could provide an experimental test of the theory.
There is thus a clear need to develop non-toxic, local methods to sense
electric fields in biological media in order to refine current models of
neuronal activity.

The detection of electric fields at the nanometer scale has initially been
addressed using ultrahigh resolution nanopipette electrophysiology 7. Although
very powerful, this technique can only study a single synapse at a time. On
the contrary, voltage indicators (VI) were designed to stain the entire
neuronal membrane and allow fluorescence recording of transmembrane voltage
dynamics 8 throughout the cell with optical diffraction resolution. Enormous
progress has been made in the development of brighter and faster VI, and in
particular thanks to the development of hybrid chemigenetic systems that
allows to combine optimally chemical compounds with genetically encoded
proteins 9. However, subdiffraction imaging of a large number of synapses at
high temporal resolution has not yet been reported. The development of a
technology offering the necessary high spatiotemporal resolution (typically 1
ms, 200 nm) to reliably interrogate electrophysiological dynamics at multiple
neuronal nanodomains would provide invaluable insights into open questions in
neuronal electrophysiology.

Optically active nanostructures that transduce electric field changes into
optical properties modifications constitute possible candidates, with photon-
shotnoise ultimately limiting the sensitivity. In this domain, quantum dots
(QD) are particularly attractive as their photoluminescence (PL) is redshifted
by the quantum confined Stark effect, and in addition, with a core size of a
few nanometers, they can fit within the neuron membrane lipid double layer
where the field is maximal. Based on a QD-doped polymer layer, Rowland et al.
developed a device that can detect an electric field as small as 10 kV/cm
within 1 ms time scale 10, however obtained by involving about one billion of
QD (estimated from QD concentration, sensing layer thickness and excitation
laser spot size). Another strategy of electric field optical sensing harnessed
the coupling of an electroactive polymer to a metallic nanoantenna that
transduces an external electric field into a detectable change in localized
surface plasmon resonances 11. Compared to sensing based on QD, this approach
benefits from a four orders of magnitude larger interaction cross-section with
the incident light, expected to translate into a higher sensitivity. Indeed
with such a device, Habib et al. were able to sense a stimulated
electroactivity of cultured cardiomyocytes, with submillisecond time
resolution 11 but to achieve such performances, the authors had again to
integrate the light scattered by about a million nanoantenna, hence reducing
the spatial resolution to about 1 mm.

However, to maintain diffraction-limited imaging, an electric field must be
sensed by a single or very few nanoparticles only. There are a few examples of
such systems that are based on electric-field modulation of charge or Förster
resonant energy transfer (FRET) between the nanoparticle and another entity.
For example, Nag et al. used a QD-fullerene (C60) conjugate, with the C60
embedded in the cell membrane 12. At resting membrane potential the
photoexcited QDs relax to the ground state partially by electron transfer to
the C60. This transfer increases upon cell membrane depolarization, leading to
a PL intensity relative quenching $\Delta I/I_{0}$ of a few % that provided a
transmembrane potential variation readout both in cultured cell and in the
cortex of live mouse. While chemical or electrical stimulation leads to QD PL
modulation, the fastest response time was about 100 ms, two order of magnitude
longer than the time response necessary to reproduce an action potential (AP)
with fidelity. Another conjugate introduced by Liu et al. consists of an up-
converting nanoparticle (UCNP) to which voltage sensing dyes were coupled,
that serve on one hand to anchor the UCNP into cell membrane and are also FRET
acceptors 13. The authors of this study report a relative change $\Delta
I/I_{0}$ in UCNP luminescence intensity in the 0.4-6.1% range in cultured
cells, depending on the stimulation conditions, and a time response of about
50 ms, still much longer than the duration of the AP. Hence, the spatial
($\approx 200$ nm) and time (submillisecond) resolution required for membrane
potential sensing remains to be addressed.

Here, we report the development of a $\approx 160$ nm-sized standalone
optically active nanocrystals (NCs) capable of sensing, at the level of a
single particle, a field of $\approx 152$ kV/cm smaller than the peak
amplitude field of an action potential), with a millisecond response time. We
based our sensing principle on a specific UCNP made of a ferroelectric
nanocrystal (NC) host doped with rare earth ions. When the NC is exposed to an
external electric field, its lattice undergoes deformations due to a converse
piezoelectric effect, which leads to spectral changes of the rare-earth ion
up-conversion emission. The effectiveness of this principle was established by
Hao et al. who demonstrated the modulation, by a varying electric field of 125
kV/cm amplitude, of the upconverted (UC) light from an ytterbium (Yb3+) and
erbium (Er3+)-doped epitaxial barium titanate (BTO) thin film 14, at room
temperature (in BTO ferroelectric phase). The authors demonstrated an UC
modulation at a frequency of 0.1 Hz, far below the maximum frequency of
$\approx 10$ kHz limited by the UC process response time of $\approx
100~{}\mu$s in erbium-doped BTO 15. Thus, here we develop BTO:Yb3+,Er3+
individual nanocrystals of size $\approx 160$ nm, which we exposed to a fast
varying electric field with the conductive tip of an atomic force microscope
(AFM), coupled to a fluorescence microscope. We demonstrate that 29% of the
nanocrystals exhibit a variation in UC intensity with a response time of
$\approx 100~{}\mu$s, limited by the duration of the UC optical cycle.
Furthermore, BTO nanocrystals are ideal to develop sensors that could be
rapidly tested in biological contexts due to their pre-existing use in drug
delivery or tissue engineering 16, but also for their intrinsic optical two-
photon excitation response17 (resulting from the crystal second-order
nonlinear response) in cultured cells 18, 19, 20 and larvae of small organisms
21, 22, without or with grafted functional groups 22, 19, 20.

##  2 Results and discussion

###  2.1 Synthesis and characterization of erbium and ytterbium-doped BTO
nanocrystals

Erbium and ytterbium-doped BTO nanocrystals (nanoBTO:Yb,Er) were synthesized
by a combination of coprecipitation and hydrothermal methods. Ytterbium was
used to sensitize erbium up-conversion. By adapting the Ba/Ti stoichiometry,
we aimed at incorporating Er3+ and Yb3+ ions in A and B sites of the ABO3
barium titanate perovskite respectively, because the ytterbium ions have the
closest radius to the one of titanium (B site) in the six coordinated state
23. We targeted the stoichiometry
$\rm{Ba_{0.985}Er_{0.01}Ti_{0.925}Yb_{0.1}O_{3}}$, ensuring charge
compensation, as described in Materials and Methods. The choice of an erbium
concentration of 1% was made based on Zhang et al.24, who showed that higher
concentrations enhance cross-relaxation, leading to lower UC.

The shape of the synthesized particles is mainly cubic with an average size of
158$\pm$27 nm, as deduced from scanning electron microscopy analysis
(Supporting Information Figure S1). Figure 1a displays the powder X-ray
diffractogram (XRD) at the room temperature of 293 K indexed to the
crystallographic planes of the tetragonal phase of BTO according to the
standard International Center for Diffraction Data (ICDD PDF card no. 05-0626)
25. We did not observe any secondary phase structure, indicating the insertion
of the doping ions in substitution of barium or titanium. Rietveld refinement
of this diffractogram (see Figure S2) leads to $a=b=3.9980\pm 0.0001$ Å and
$c=4.0216\pm 0.0002$ Å as the lattice parameters, hence $(c/a)_{\rm
NC}=1.0059$ for the NC, a value lower than for the bulk BTO for which
$(c/a)_{\rm bulk}=1.0101\pm 0.0002$ 26, indicating that NC lattice is slightly
less tetragonal and more cubic than the bulk one, in agreement with other
reports on undoped BTO NCs 27, 25. The lower tetragonality of BTO NCs may
result from a variety of factors, including the presence of lattice defects
which are primarily hydroxide ions (OH-) substituting to oxygen, coming from
hydrothermal synthesis precursor materials, as well as the doped nature of our
BTO NCs, which is known to often result in a smaller $c/a$ ratio 28.

Figure 1: Structural characterisation of erbium and ytterbium-doped barium
titanate nanocrystals. (a) XRD spectrum showing all detectable peaks of
tetragonal BTO lattice. Inset graph: (002) plane peak splitting indicating
tetragonality. (b) Bright-field TEM image of an aggregate of nanocrystals.
Scale bar: 200 nm. (c) SAED pattern corresponding to the particle squared with
a dashed line in (b). The high periodicity of this pattern indicates that the
particle is a single crystal. Scale bar: 2 nm-1

The powder diffraction analysis was confirmed by selected area electron
diffraction (SAED) analysis using transmission electron microscopy (TEM).
Figure 1b displays a bright-field TEM image of a group of BTO nanocrystals,
and Figure 1c shows SAED pattern realized on a single BTO NC after one of its
crystallographic axes has been aligned with the TEM electron beam. The
diffractogram shows a regular pattern of bright spots, which are the result,
in reciprocal space, of constructive interferences caused by electrons
interacting with the periodic atomic structure of the crystal. The presence of
a single rectangular pattern evidences that the particle is made of a single
crystal. Furthermore, the dimensions of the rectangle are $1/a=2.532\pm 0.010$
nm-1 and $1/c=2.516\pm 0.020$ nm-1, leading to $a=0.395\pm 0.002$ nm and
$c=0.397\pm 0.003$ nm, and a tetragonality value $c/a=1.006\pm 0.012$. These
values are in good agreement with the ones derived from the XRD diffractogram
(Fig. 1a).

Figure 2: Evaluation of ytterbium and erbium doping concentration by energy
dispersive X-ray spectroscopy coupled to a scanning transmission electron
microscope. (a) HAADF STEM image of an aggregate of nanocrystals (scale bar:
70 nm) with a zoom, in bright field (BF), on corners of two particles (scale
bar: 9 nm). (b) EDX image of the erbium distribution (scale bar: 70 nm) with a
zoom (on the right, scale bar: 9 nm) on the same particle corners as in (a).
(c) EDX image of the ytterbium distribution (scale bar: 70 nm), with a zoom
(on the right, scale bar: 9 nm) on the same particle corners as in (a) and
(b).

To measure the atomic fraction of erbium and ytterbium incorporated in the BTO
nanocrystals, we conducted an elemental analysis at the individual particle
level, using energy dispersive X-ray spectroscopy (EDX) coupled to the TEM
(Materials and Methods). We aim to observe the characteristic EDX peaks of
erbium at 6.947 keV and ytterbium at 7.414 keV in the particles. Figure 2a
(top) shows the high-angle annular dark-field (HAADF) scanning TEM image of a
group of three nanoBTO:Yb,Er. From the elemental analysis conducted on this
group of NCs, we estimated (Materials and Methods) that erbium (Figure 2b) and
ytterbium (Figure 2c) ions are incorporated at atomic concentrations of 1.7%
and 1.2%, respectively. The erbium concentration is slightly higher than the
targeted 1%, while ytterbium effective concentration is significantly lower
than the target of 10%. In fact, the concentration of ytterbium is almost
equal to that of erbium, likely to maintain charge neutrality by substituting
both Ba2+ and Ti4+ ions equally by RE3+ ions, and thus avoiding the creation
of charged defects such as oxygen vacancies.

One may wonder where Er3+ and Yb3+ ions insert themselves in the BTO
nanocrystal. Previous works 29, 30 indicate that Yb3+ ions predominantly
substitute Ti4+ ions; for charge compensation reasons, it is thus highly
likely that Er3+ substitutes Ba2+. To further investigate effective
substitution sites, other studies, such as UC lifetime measurements 15 would
be necessary but are beyond the scope of this article.

The characterization studies validated that the synthesized BTO nanocrystals
are doped with ytterbium and erbium, and keep a tetragonal structure of
undoped nanocrystals. Hence, nanoBTO:Yb,Er are very likely to maintain the
ferroelectric and piezoelectric properties on which we based the electric
field sensing mechanism. We then investigated the upconversion
photoluminescence (PL) of individual nanoBTO:Yb,Er, and the modulation of its
intensity by an external electric field.

###  2.2 Up-conversion of single nanoBTO:Yb,Er and its modification by an
electric potential

Figure 3: Experimental setup to study single nanoBTO:Yb,Er luminescence
changes under an applied electric field. (a) Conductive AFM-fluorescence
microscope correlated setup. The AFM head along with the AFM piezostage is
positioned above the microscope objective of the fluorescence microscope. (b)
Topography of single nanoBTO (nanoBTO:Yb,Er #1) having a height of 153 nm (its
lateral sizes are 180 nm$\times$180 nm from SEM image, not shown). (c) UC
intensity scan of the same particle as in (b) acquired at 10 mW laser
excitation power. Intensity scale: photocounts in 10 ms bin duration, yielding
9.86 kcounts/s maximum counting rate. Scale bars in (b)-(c): 500 nm. (d)
Energy level diagram of ytterbium-erbium co-doped system showing Er3+
upconversion transitions following direct laser excitation at 977 nm
wavelength via ground state absorption(GSA) and excited state absorption
(ESA), or GSA followed by resonant energy transfer from Yb3+ in its excited
state (dashed curved arrow) and subsequent ESA. The UC spectrum consists of
three series of lines, G1, G2 and R corresponding to
2H${}_{11/2}\rightarrow\,^{4}$I15/2, 4S${}_{3/2}\rightarrow\,^{4}$I15/2 and
4F${}_{9/2}\rightarrow\,^{4}$I15/2 transitions, respectively. Blue dashed
lines represent cross-relaxation (CR). (e) Up-conversion spectrum from the
same single nanocrystal as in (a), under excitation laser power of 10 mW and a
spectrometer Charged-Couple Device (CCD) array sensor integration time of 15
s. In addition to the up-conversion bands G1, G2 and R, we can also observe
the SHG line at 488.5 nm wavelength.

To be able to apply a voltage directly on a single nanocrystal while recording
its up-conversion PL, we used an AFM microscope in an electrical mode, coupled
to a fluorescence microscope and we put the conductive AFM tip in contact with
the top surface of a single nanoBTO:Yb,Er, with its bottom surface lying on a
semi-transparent indium tin oxide (ITO) coated glass coverslip that is
grounded (see Figure 3a, and Materials and Methods). To prevent the particle
from being dragged by the tip while scanning and simultaneously ensure the
electrical contact with ITO, we glued it to this substrate using
poly(3,4-ethylenedioxythiophene) polystyrene sulfonate conductive polymer
(Materials and Methods). Once both microscopes are aligned relative to each
other, topography (Figure 3b) and UC luminescence (Figure 3c) scans can be
acquired simultaneously on the same particle.

The spectral analysis of single nanoBTO:Yb,Er luminescence under near infrared
laser excitation (977 nm wavelength) revealed the three groups of lines in the
visible range resulting from UC by erbium, as displayed in Figure 3d,e. These
lines correspond to the transitions 2H${}_{11/2}\rightarrow\,^{4}$I15/2
(wavelength around 525 nm with multiple peaks due to Stark splitting, labelled
G1), 4S${}_{3/2}\rightarrow\,^{4}$I15/2 (around 550 nm, G2) and
4F${}_{9/2}\rightarrow\,^{4}$I15/2 (around 657 nm, R). The narrow peak in
Figure 3e at 488.5 nm, half the excitation laser wavelength, is due to the
second harmonic generation (SHG) by the NC, confirming the high crystallinity
previously evidenced by XRD and SAED (Figure 1a,c).

Note that 4f-4f electric dipole transitions of lanthanide ions are expected to
be forbidden by quantum mechanics selection rules in a perfectly
centrosymmetric crystalline environment, for which the odd orders of the
crystal field vanish. The mere detection of erbium UC, even in absence of an
external electric field, is the signature of lower local symmetry around
erbium ions. In fact, the splitting of the $(hk\ell)$ Miller indexes (002) and
(200) Bragg peaks near $2\theta~{}45^{\circ}$ in the inset of Fig. 1a already
indicates the presence of the polar (hence non-centrosymmetric) phase of BTO,
enabling the 4f-4f electric dipole transitions of lanthanide ions. Note also
that Zou et al. reported erbium UC even in the high-temperature
centrosymmetric phase of BTO 31, which indicates that the local environment
felt by the RE ions are likely even less symmetric than the symmetry of the
overall matrix, which is consistent with the eight-site model developed in BTO
32 in which local symmetry breakings exist at the unit cell level but vanish
on a macroscopic scale.

Figure 4: Change of up-conversion spectrum of single nanoBTO:Yb,Er exposed to
external electric field. (a) UC spectra of nanoBTO:Yb,Er #1 (same NC as in
Figure 3b-c,e), under an excitation laser power of 10 mW abd spectrometer CCD
integration time of 15 s, at voltage of 0 V (black line), +10 V (red), and
back again at 0 V (blue). (b) UC spectra of another particle, nanoBTO:Yb,Er #2
(excitation laser power: 5 mW, spectrometer CCD integration time: 15 s) at
voltage of 0 V (black line), -10 V (red), and back again at 0 V (blue).
nanoBTO:Yb,Er #2 height as measured by AFM (not shown) was 111 nm. (c) Time
trace of the total UC intensity of nanoBTO:Yb,Er #1 (same as in (a)), while
switching pseudo-periodically the applied voltage between 0 and +10 V. Bin
time: 10 ms. (d) Pie-chart distribution of the different behavior observed for
a total of 28 nanocrystals studied. The number of particles per category is
written in each section. NanoBTO:Yb,Er #1 and #2 are two of the eight
particles displaying a fast change in UC (with constant SHG), which individual
behaviors are summarized in Table S1.

We then investigated the changes of UC spectrum of a single nanoBTO:Yb,Er
(nanoBTO:Yb,Er #1) when we apply a static voltage of $\pm 10$ V across the
particle. For the average particle size of 158 nm, this voltage corresponds to
an electric field of $\approx 630$ kV/cm, more than twice smaller than the
electric field breakdown of 1.5-3 MV/cm reported for thin BaTiO3 in the
literature 33. Figure 4a shows UC spectral changes of nanoBTO:Yb,Er #1 under
static voltage exposure of +10 V, manifested by an overall increase in the
intensity of all peaks. This variation was reversible when the voltage was
returned to 0 V, reverting to its initial value, and no change was detected
with the opposite polarity of -10 V. For another NC (nanoBTO:Yb,Er #2), we
also detected a reversible UC emission increase under an opposite applied
voltage of -10 V (Figure 4b), also with no change for the opposite polarity
(of +10 V). The intensities of the green and red UC emission bands both
increase with the applied voltage, regardless of its polarity. This behavior
differs from the one reported in BTO thin layer by Hao et al.14, where they
observed an increase in the intensity of the green bands but none of the red
one. Hao et al. proposed an interpretation based on the transition probability
predicted by Judd–Ofelt theory, where the dominant contribution for the green
emission transitions involves the intensity parameter $\Omega_{2}$ that
increases when the symmetry of the site occupied by Er3+ is reduced, which is
what happens when the crystal is exposed to the external electric field. In
contrary, the red emission transition does not involve this symmetry sensitive
term and therefore should be almost insensitive to the electric field. Our
observation of a variation of intensity of the red emission transition under
an external electric field indicates that in our sample, there is a more
complex coupling of the red transition to the site symmetry changes. We
hypothesize that the change of intensity of the red line could be due to an
increase of population of the 4F9/2 upper level of the red transition
resulting from a larger cross-relaxation effect. The latter depends on the
distance between ions, which indeed is modulated by the lattice deformation
resulting from the converse piezoelectric effect, under the applied electric
field. Indeed we evidenced that in our nanoBTO:Yb,Er sample the red transition
is governed by the cross-relaxation, because we observed that its intensity
evolves linearly with the excitation laser intensity (see Figure S3),
consistently with two red photons emitted for two infrared excitation photons
absorbed, with one of them experiencing a cross relaxation (see Figure 3d).

As for NC like nanoBTO:Yb,Er #1 and #2 the intensity of both the green and red
bands increases similarly under applied electric field, we considered the
total UC intensity integrated over the whole spectrum. Figure 4c displays this
total UC intensity change under a voltage square modulation for nanoBTO:Yb,Er
#1, if whole the UC light is sent to the single-photon counting module instead
of the spectrometer. UC intensity modulation faithfully follows that of
applied voltage. We observed this overall behavior (fast reversible change of
UC intensity) in 8 of the 28 NCs studied (Figure 4d). As the SHG peak did not
vary at all in these cases during the voltage application and removal process
(see the inset of Fig. 4b), we ruled out a change of focus of the microscope
objective. Furthermore, the SHG peak stability also indicates that the applied
electric field did not degrade the crystal lattice. Among these eight
particles displaying a fast change in UC with constant SHG signal, seven of
them reacted to only one polarity (among which nanoBTO:Yb,Er #1 and #2, Figure
4a,b) and a single one reacted to both polarities in an opposite manner. The
responses of each of the eight nanocrystals to $\pm$10 V are summarized in
Supporting Information Table S1.

To determine whether the change in UC intensity in nanoBTO:Yb,Er is indeed
attributed to the ferroelectric properties of the crystal host as reported for
BTO:Yb,Er thin film 14, we conducted the following control experiments. First,
we checked that the sole mechanical contact of the unbiased tip with the
crystal does not induce a UC spectral change by piezoelectric effect (see
Figure S4). Then, we considered erbium-doped nanocrystals of yttrium oxide
(Y2O3:Er, with 2% doping). Y2O3 has a cubic crystallographic structure and
therefore is devoid of piezoelectric and ferroelectric properties. Supporting
Figure S5 shows that $\pm 10$ V applied to one Y2O3:Er3+ nanocrystal (kind
gift of Diana Serrano, synthesis done by Shuping Liu and detailed in ref.34)
did not induce any change of erbium up-conversion intensity. The absence of UC
change under an applied voltage was confirmed for three other nanocrystals,
evidencing that the ferroelectric BTO matrix is essential for the effect to
happen.

For each of these 8 particles with fast unipolar response, we then
investigated the response time of its UC intensity variation when it was
subjected to a modulated square electric potential (switching duration of only
1 $\mu$s, according to the bandwidth of the AFM electrical mode) with a
frequency of 0.4 Hz and an applied voltage of 10 V. Figure 5 displays, for one
nanocrystal (nanoBTO:Yb,Er #3), the total UC photocount rate time trace at bin
durations of 100 $\mu$s and 10 ms. Based on the 10-ms time base, we observe a
2.7-fold increase of the photocount rate between 0 and 10 V. Moreover, zooming
on the photocount rate trace at the rising and falling edges of voltage
changes, we observe that it changes within a single time step of 100 $\mu s$,
a value matching well the reported nanoBTO:Yb,Er up-conversion time
response15. Furthermore, we estimated the signal-to-noise to be 1.6,
calculated as the ratio of the average amplitude difference (between 0 and 10
V) to the standard deviation of UC intensity when 10 V is applied.

Figure 5: Up-conversion intensity variation response time of a single
nanoBTO:Yb,Er. UC signal variation of a single 130 nm-sized doped-nanocrystal
(nanoBTO:Yb,Er #3) upon applied square voltage (+10 V) modulation (top trace),
with 100 $\mu$s (grey) and 10 ms (red) bin duration (middle traces). Bottom:
zooms on rising (left) and falling (right) edges showing UC intensity changes
within a single time bin of 100 $\mu$s.

The 20 other NCs studied exhibited different behaviors. First, 11 particles
did not show any UC or SHG variation whatever the polarity was (Figure S6a).
Two displayed slow (few seconds) changes in UC with no change in SHG (Figure
S6b); five displayed fast changes in UC and also in SHG (Figure S6c), while
two showed a slow change in UC and SHG (Figure S6d). This diversity of
behaviors is likely to reflect the one of the nanocrystal polarization texture
combined with the one of the orientation of their crystallographic axis $c$
relative to the direction of applied electric field $\boldsymbol{E}$. These
various configurations differ from the well defined one reported in Hao et al.
14, which involved BTO:Yb,Er doped thin film with $c$ oriented faces and
$\boldsymbol{E}$ parallel to $c$. In this later case, $\boldsymbol{E}$ applied
parallel to $c$ (being the direction $z$, indexed by 3) induces, by inverse
piezoelectric effect, a strain $d_{33}E$, where $d_{33}$ is one of the
piezoelectric coefficients of BTO. This strain is accompanied with ions
relative displacement leading to variations of the crystal field around erbium
and ytterbium ions, thereby changing the transition coefficients and
subsequently UC intensity.

The case of BTO NCs is different to the one of BTO thin layer, as we recently
evidenced that NCs do not have out-of-plane polarization in any of their
facets 35. Indeed, we showed by simulations that the polarization along the
polar $c$ axis rotates by 90∘ over about 10 nm, to become in-plane within the
$c$ facets and prevent a strong electrostatic depolarizing field. We confirmed
by piezoresponse force microscopy (PFM) that we detect only in-plane
displacements and not any out-of-plane displacement. An electric field of
amplitude $E$ applied to the $c$ facet by the PFM tip induces a shear strain
displacement of amplitude $d_{15}E$, with $d_{15}=270$ pm/V being even larger
than $d_{33}=191$ pm/V (that gives the strain amplitude in the case of BTO
thin layer) according to Ref.36. This shear strain is also expected to induce
crystal field deformations leading to UC intensity changes. Furthermore, our
simulations showed also that the lateral piezoresponse amplitude is one order
of magnitude larger in $c$ plane than in $a$ and $b$ planes 35. This result
may explain why for a significant fraction of nanoBTO:Yb,Er (39%, “no change”
in Figure 4d) we were not able to detect any PL changes, consistently with the
fact that these particles were oriented with their $c$ axis perpendicular to
$\boldsymbol{E}$. However, this interpretation would require to conduct
correlated UC variation recordings and PFM measurements to be validated. The
four other categories of particles for which PL change was observed (Figure
4d) encompass the case of $\boldsymbol{E}$ aligned with $c$ (likely to be the
situations yielding “large” PL change, as for the 8 particles displaying a
fast change in UC with constant SHG), and $\boldsymbol{E}$ perpendicular to
$c$ but still yielding a detectable PL (case of particles with “large” size or
having a polarization texture more favorable to larger electric field-induced
strain). In a quarter of the cases, we also detected a reversible SHG
intensity increase in the presence of the electric field (Figure S6c,d), which
reflects crystal lattice deformation towards less symmetrical structure.
Finally, we attribute slow UC response (4 particles, 14% of the cases, Figure
S6b,d) to charge accumulation taking place when the conductive polymer glue
does not fully ground the bottom part of the nanocrystal, but further research
would be required to validate these two interpretations.

###  2.3 Sensitivity of the nanoBTO:Yb,Er electric field sensor

With nanoBTO:Yb,Er #3, of size 130 nm, we were able to detect a field
amplitude $E_{\rm min}\equiv 10/(130\times 10^{-7})\approx 770$ kV/cm within
$T=100~{}\mu$s with a signal-to-noise ratio of 1.6. The minimum field
detectable during an optical cycle is then $E_{\rm min}=770/1.6\approx 480$
kV/cm, leading to a sensitivity $S_{\rm 1nanoBTO}\equiv E_{\rm
min}\sqrt{T}=4.8$ kV/cm/$\sqrt{\rm Hz}$. Considering this sensitivity, if we
integrate over 1 ms (a third of the total duration of a neuron action
potential), we should be able to detect a field $E=S_{\rm
1nanoBTO}/\sqrt{10^{-3}}\approx 152$ kV/cm, which is smaller than the peak-to-
peak axonal membrane potential of $\approx 200$ kV/cm. Moreover, the
sensitivity should improve by considering larger particles as the signal
increases with more ions being exposed to the electric field.

We now compare the nanoBTO:Yb,Er sensor sensitivity to that of other single
nanostructures envisioned to sense trans-membrane potential fast changes
mentioned in the introduction. In particular, PL modulation of QDs attributed
to electric field ionization was reported to detect a minimum field of $E_{\rm
min}^{N}\approx 10$ kV/cm with 1 ms time resolution 10, but it involved
$\approx 10^{9}$ QDs. Hence, we extrapolate the single QD sensitivity of this
system to be $S_{\rm 1QD}\approx
10\times\sqrt{10^{9}}\times\sqrt{10^{-3}}=1000$ kV/cm/$\sqrt{\rm Hz}$, which
is 208 times less sensitive than a single nanoBTO:Yb,Er sensor. Similarly, the
FRET couple formed by a voltage detecting dye and an up-conversion
nanoparticle 13 is capable of reporting an electrophysiological signal by
variation in relative intensity, but it also requires a large number of probes
and has a slow response time of 50 ms, which prevents to resolve the temporal
profile of an individual action potential. Finally, the other optical signal-
based neuron activity sensing approach recently reported, harnessing
electroactive polymer coupled to plasmonic nanoantenna 11, yields both a very
low detection threshold of 0.1 kV/cm and a fast (200 $\mu$s) response, but
here also, it requires the accumulation of the signal from a large number (one
million) of antenna reducing the spatial resolution down to 1 mm. Furthermore,
the extrapolated single antenna sensitivity is $S_{\rm
1antenna}=0.1\times\sqrt{10^{6}}\times\sqrt{0.2\times 10^{-3}}\approx
1.4~{}$kV/cm/$\sqrt{\rm Hz}$. Although this extrapolated $S_{\rm 1antenna}$ is
better than $S_{\rm 1nanoBTO}$, its experimental realization has not yet been
demonstrated, contrary to that of a single nanoBTO:Yb,Er.

##  3 Conclusions

Fluorescent voltage indicators, including the advanced genetically encoded
ones (GEVI), have become the gold standard in optical recording of
electrophysiological activity of an assembly of neurons, as they provide the
millisecond time scale resolution required for a faithful rendering of
electrical potential variations 9. However, to yield a sufficiently strong
fluorescence, GEVI need to be over-expressed, which may impact neuron
physiology. Moreover, like all dyes, the fluorescent protein(s) in the GEVI
photobleach(es) over time. Finally, interrogating electrical response with VI
or GEVI at synaptic nanodomains remains challenging. For these reasons,
alternative nanosensors are still worth developing, as the rare earth ions-
doped ferro/piezo-electric nanocrystals we introduced in this article, that
are capable of transducing an applied electric field in changes in the up-
conversion emission intensity.

We synthesized, by hydrothermal method, erbium and ytterbium-doped barium
titanate NCs of average size 158 nm, with effective doping estimated to be
1.7% and 1.2% for Er3+ and Yb3+ respectively. Despite the doping, the nanoBTO
retained its tetragonal structure to which ferro- and piezo-electric
properties are associated at room temperature of 293 K. We observed that 61%
of the nanocrystals displayed a variation of up-conversion intensity upon
application of +10 V, -10 V or rarely for both polarities. Moreover, about
half (47%) of the nanocrystals had a fast response (characteristic duration
<100 $\mu$s), compatible with a faithful sampling of action potential temporal
profile. UC intensity changes are attributed to fast modifications of the
crystal field around erbium ions, that lower the symmetry inducing larger
intra-4f transitions probabilities. We suggested that the NCs which do not
yield a detectable UC change, have their crystallographic axis perpendicular
to the applied electric field (i.e. this axis lies in the substrate plane).
Indeed, we established in a recent piezoresponse force microscopy study 35,
that the PFM displacement amplitude is one order of magnitude smaller for such
nanoBTO crystal axis orientation than for NCs with $c$ axis parallel to the
applied electric field (i.e., perpendicular to the substrate). It is desirable
to make the nanosensor more isotropic and less sensitive to the electric field
orientation. As the largest crystal deformations induced by the electric field
take place at the NC surface, we envision that core-shell perovskite
structures (like the one reported in Ref. 37) may be grown by epitaxy in such
a way that shell $c$ axis orientation is orthogonal to all facets. In such
composite, the in-plane crystal deformation should be large and independent of
the external field direction.

With the nanoBTO:Yb,Er sensor we developed, we demonstrated a single particle
sensitivity to electric field sensing of 4.8 kV/cm/$\sqrt{\rm Hz}$. There are
still some margin for improvement by enhancing erbium emission. In particular,
we could incorporate lithium ions in addition to erbium and ytterbium, as it
has been shown that lithium (by either A site substitution or by interstitial
insertion) can increase the UC intensity by further lowering crystal symmetry
around Er3+ ions 38. Furthermore, a very thin shell (thickness<5 nm) of
silanized ytterbium complex could be used to enhance the absorption cross-
section of the near-infrared excitation light by the nanocrystal.

The application of the nanoBTO:Yb,Er to neuron cell membrane potential
variation sensing will require the sensor to be brought into contact with the
membrane as the Debye layer electric field shielding takes place within a few
nanometers. Grafting of bioconjugates to BTO has been reported by several
groups 19, 20, 21 and could be leveraged to attach molecules that are able to
anchor the sensor in the cell membrane. The nanoBTO:Yb,Er electric field
sensor may also find applications in other scientific areas where electric
field needs to be probed with nanometer and sub-millisecond resolutions at
room temperature. In these domains, the nitrogen-vacancy center in a diamond
nanopillar offers a record sensitivity of only 0.24 kV/cm/$\sqrt{\rm Hz}$, but
its implementation is still complex 39.

##  4 Materials and Methods

###  4.1 Synthesis of erbium and ytterbium-doped BTO nanocrystals

The Yb/Er-doped $\rm{BaTiO_{3}}$ nanocrystals were prepared via the
hydrothermal method in a designed stoichiometric ratio of
$\rm{Ba_{0.985}Er_{0.01}Ti_{0.925}Yb_{0.1}O_{3}}$. Note that the chosen
composition allows charge compensation as the total positive charge is equal
to $0.985\times(+2)+0.01\times(+3)+0.925\times(+4)+0.1\times(+3)=+6$, opposite
to the total negative charges of $3\times(-2)=-6$. We used barium carbonate
(BaCO3) and titanium isopropoxide (Ti(OiPr)4) as the starting materials. BaCO3
was dissolved in diluted acetic acid and warmed on a hot plate of a magnetic
stirrer for complete dissolution. Er(CH3COO)3 and Yb(NO3)3 were added
subsequently. The solution was then cooled down to room temperature, Ti(OiPr)4
was slowly added, and the mixture was agitated during 2 h. Subsequently, the
solution was dried in the oven at 100∘C for 6 h and transferred to a Teflon-
lined autoclave, accompanied by the NaOH. The autoclave was kept in an oven
for hydrothermal reaction at 220∘C for 24 h and naturally cooled down to room
temperature in air. The collected product was washed several times with
distilled water and dried at 100∘C for 12 h.

###  4.2 Characterization instruments and methods

X-Ray diffraction spectrum was acquired using a Bruker D2 diffractometer using
Cu K$\alpha$1 radiation (wavelength: 1.5418 Å) and Cu K$\alpha$2 radiation
(wavelength: 1.5444 Å). XRD data were collected at room temperature between
angles 20∘ and 60∘ by steps of 0.02∘. The EVA software was then used to
determine the phase composition of the material. Transmission electron
microscopy (TEM) analyses in parallel and in scanning mode (TEM - STEM) were
conducted utilising a FEI Thermofisher Titan3 G2 80-300 microscope, operated
at 300 kV and equipped with a Cs probe corrector, STEM detectors, an Ultrascan
1000 XP TEM camera and a SuperX detector for energy-dispersive X-ray (EDX)
analyses. EDX quantifications have been performed by using the Cliff-Lorimer
method 40. As Ti-Kα (4.510 keV) and Ba-Lα (4.465 keV) rays have very close
energies, an optimisation of $k$-factors has been performed using pure BTO.

###  4.3 Electrical mode AFM coupled to a fluorescence microscope

The AFM (Asylum MFP-3D, Oxford Instruments) was coupled to a homemade
fluorescence microscope based on a commercial microscope stand (Eclipse TE300,
Nikon). A conductive ASYELEC-01-R2 tip with titanium/iridium coating (spring
constant: 2.8 N/m) was used to apply a voltage on the nanocrystal. In this AFM
model, the tip is static and the sample is scanned laterally using a
piezostage, whose position can be finely adjusted relative to the microscope
stand so that the AFM tip coincides with the luminescence detection volume.
The upconversion from nanoBTO:Yb,Er was excited using a continuous-wave
fibered Bragg grating laser diode operating at 977 nm wavelength
(BL976-SAG300, Thorlabs). The laser beam is sent through an apochromatic
$\times$100 magnification and 1.49 numerical aperture oil immersion microscope
objective (MRD01991, Nikon) by a short-pass dichroic mirror (700dcsx, Chroma
Technology) which reflects it, and transmits the UC signal. The latter is then
sent to a single photon counting module detector (SPCM AQR-14, PerkinElmer)
through a band-pass filter of transmission range 450-700 nm (FF01-715/SP,
Semrock) to filter out residual excitation laser light, thanks to an optical
density larger than 6 at 977 nm. The UC spectrum is acquired using a 140 mm
focal length imaging spectrometer (MicroHR, Jobin-Yvon/Horiba) using a 600
lines/mm grating blazed at 500 nm. The detector attached to this spectrograph
is a cooled (sensor temperature of -70∘C) front-illuminated open electrode CCD
array (Symphony, Jobin-Yvon/Horiba). All the measurements were performed on
samples maintained at room temperature.

###  4.4 Immobilization of nanoBTO

A 1% weight poly (3,4-ethylenedioxythiophene) polystyrene sulfonate
(PEDOT:PSS) in water suspension was spin coated on a 170 $\mu$m thick cover
glass covered with a semitransparent layer of ITO (80 nm ITO layer thickness),
forming a $\approx 50$ nm thick layer, on top of which the nanoBTO:Yb,Er
aqueous suspension is deposited. Due to the good wettability of BTO by water
41, the concave meniscus on the edges of the NCs drags them down by surface
tension, leading to a final position of the particle emerging from the polymer
layer as we showed in another work 35.

## Author contributions

Conceptualization: CP, CB, KP and FT; Methodology: AKM, JZ, CB, MV, AZ, KP,
and FT; Validation: AKM, KP and FT; Investigation: AKM, JZ, MV, KP and FT;
Resources: CB and JZ; Data curation: AKM, MV, AZ, and FT; Writing – Original
draft: AKM and FT; Writing – Review and Editing: CP, AKM, KP, and FT;
Visualization: AKM, MV, AZ, KP, and FT; Supervision: FT; Project
administration: FT; Funding acquisition: CP and FT. All authors have read and
agreed to the published version of the manuscript.

The authors thank Shuping Liu for the synthesis of non ferroelectric Y2O3:Er3+
nanocrystals used for the control experiment, and Céline Fiorini-Debuisschert
for her help in finding a solution to firmly attach the nanocrystals to the
conductive coverglass substrate. We also thank Brahim Dkhil, Aleix G. Güell,
Julien Boudon, Lionel Maurizi and Nadine Millot for fruitful discussions. The
AFM used in this work was purchased thanks to the FOSTER program of ENS Paris-
Saclay. This work has received financial support to B.D. and F.T. from the
CNRS through the MITI interdisciplinary program and from the French National
Research Agency (ANR, grant numbers ANR-21-CE09-0028 and ANR-21-CE09-0033).

Supporting information file contains Supporting Data Figures: Size and shape
distributions of nanoBTO:Yb,Er; Rietvelt refinement analysis on nanoBTO:Yb,Er;
Variation of intensity of the green and red up-conversion bands with the laser
excitation power; Absence of UC spectrum modification on nanoBTO:Yb,Er due to
the AFM tip mechanical force applied at the contact; Absence of UC spectrum
modification under applied voltage in non-ferroelectric Y2O3:Er nanocrystals;
Examples of other up-conversion signal variation behaviors with applied
electric field, differing from the fast variation with constant SHG.

Supporting information

Sub-millisecond electric field sensing with an individual rare-earth doped
ferroelectric nanocrystal

A. K. Muraleedharan, J. Zou, M. Vallet, A. Zaki, C. Bogicevic, C. Paillard, K.
Perronet and F. Treussart

Figure S1: Size and shape distributions of nanoBTO:Yb,Er. (a) Particle size
distribution as inferred from SEM images (size defined as the arithmetic mean
of the side lengths of the rectangular shaped nanocrystals) with an average
value of $158\pm 27$ nm. (b) Aspect ratio, revealing a majority of particles
with a ratio of 1 (cubic shape). Inset: SEM images (30 kV acceleration voltage
and 100000$\times$ magnification) of single NCs with aspect ratio 1 and 0.75;
scale bars: 100 nm.

Figure S2: Rietvelt refinement analysis on nanoBTO:Yb,Er. Experimental diffractogram data (red open circles), modeled diffractogram (black line), small green vertical bars below the diffractogram indicate $hk\ell$ positions and the blue curve beneath represents the difference between the data and the model. The refinement was carried out using the WinPlotr/FullProf package 42. The peak shape was described by a pseudo-Voigt function, and the background level was modeled using a polynomial function. Figure S3: Variation of intensity of the green and red up-conversion bands with the laser excitation power. Total area of all the green transition bands (green squares, $(I_{\rm UC})^{\rm Green}$) and the red transition band (red circles, $(I_{\rm UC})^{\rm Red}$) as a function of the infrared laser (977 nm wavelength) excitation laser $P$. Lines are fits to a power law. $(I_{\rm UC})_{\rm red}$ has a linear dependence with $P$. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
---|---|---|---|---|---|---|---|---
UC$\nearrow$ with +10 V |  |  |  |  |  |  |  |
UC$\searrow$ with +10 V |  |  |  | slow |  | slow |  |
UC$\nearrow$ with -10 V |  |  |  |  | slow |  |  |
UC$\searrow$ with -10 V |  |  |  |  |  |  |  |
Table S1: Different responses to positive or negative applied voltage for the
eight nanoBTO:Yb,Er (same numbering as in the main text) displaying fast up-
conversion intensity variation. The checkmark indicates observed fast
variation (within one time bin duration of 100 $\mu$s), while “slow” means a
response lasting up to a few seconds. Figure S4: Absence of UC spectrum
modification on nanoBTO:Yb,Er due to the AFM tip mechanical force applied at
the contact. Spectra recorded at 10 mW excitation laser power and 10 s
exposure duration. We do not see any difference between the NC spectrum
acquired with the tip not in contact (dark grey) and with the tip in contact
with no applied voltage (red). Figure S5: Absence of UC spectrum modification
under applied voltage in non-ferroelectric Y2O3:Er nanocrystals. (a) AFM
topography image of a small aggregate. The particle surrounded by the dashed
circle is the one on top of which the conductive tip is placed to apply
voltage. (b) Up-conversion spectra of aggregate shown in (a), at 400 $\mu$W
excitation laser (977 nm wavelength) power and with 1 s exposure duration, in
various conditions: no applied voltage (black), +10 V applied (red) and -10 V
(blue). (c) Total UC intensity time trace during the square variation of
applied voltage between 0 and 10 V displayed on top. Figure S6: Examples of
other up-conversion signal variation behaviors with applied electric field,
differing from the fast variation with constant SHG. (a) Example of a
nanocrystal with no variation of UC or SHG (inset) intensities whatever the
polarity of applied voltage is. (b) Example of a nanocrystal for which the UC
intensity varies (decreases) with a slow response time when -10 V is applied,
and without any change in SHG signal. (b1): UC and SHG peak (inset) spectra.
(b2): total UC intensity time trace function of applied voltage. (c) Example
of a nanocrystal with fast variation of UC intensity and SHG signal. (c1): UC
and SHG peak (inset) spectra. (c2): total UC intensity time trace function of
applied voltage. (d) Example of a nanocrystal with slow variation of UC
intensity and SHG signal. Left (d1): UC and SHG peak (inset) spectra. Right
(d2): total UC intensity time trace function of applied voltage.

## References

  * Goldman 1943 Goldman, D. E. Potential, Impedance, and Rectification in Membranes. _The Journal of General Physiology_ 1943, _27_ , 37–60
  * Hodgkin and Huxley 1952 Hodgkin, A. L.; Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. _The Journal of Physiology_ 1952, _117_ , 500–544
  * Savtchenko et al. 2017 Savtchenko, L. P.; Poo, M. M.; Rusakov, D. A. Electrodiffusion phenomena in neuroscience: a neglected companion. _Nature Reviews Neuroscience_ 2017, _18_ , 598–612
  * Lagache et al. 2019 Lagache, T.; Jayant, K.; Yuste, R. Electrodiffusion models of synaptic potentials in dendritic spines. _Journal of Computational Neuroscience_ 2019, _47_ , 77–89
  * Sylantyev et al. 2008 Sylantyev, S.; Savtchenko, L. P.; Niu, Y.-P.; Ivanov, A. I.; Jensen, T. P.; Kullmann, D. M.; Xiao, M.-Y.; Rusakov, D. A. Electric Fields Due to Synaptic Currents Sharpen Excitatory Transmission. _Science_ 2008, _319_ , 1845–1849
  * Magee and Grienberger 2020 Magee, J. C.; Grienberger, C. Synaptic Plasticity Forms and Functions. _Annual Review of Neuroscience_ 2020, _43_ , 1–23
  * Jayant et al. 2017 Jayant, K.; Hirtz, J. J.; Plante, I. J.-L.; Tsai, D. M.; Boer, W. D. A. M. D.; Semonche, A.; Peterka, D. S.; Owen, J. S.; Sahin, O.; Shepard, K. L.; Yuste, R. Targeted intracellular voltage recordings from dendritic spines using quantum-dot-coated nanopipettes. _Nature Nanotechnology_ 2017, _12_ , 335–342
  * Peterka et al. 2011 Peterka, D. S.; Takahashi, H.; Yuste, R. Imaging Voltage in Neurons. _Neuron_ 2011, _69_ , 9–21
  * Knöpfel and Song 2019 Knöpfel, T.; Song, C. Optical voltage imaging in neurons: moving from technology development to practical tool. _Nature Reviews Neuroscience_ 2019, _20_ , 719–727
  * Rowland et al. 2015 Rowland, C. E.; Susumu, K.; Stewart, M. H.; Oh, E.; Mäkinen, A. J.; O’Shaughnessy, T. J.; Kushto, G.; Wolak, M. A.; Erickson, J. S.; Efros, A. L.; Huston, A. L.; Delehanty, J. B. Electric Field Modulation of Semiconductor Quantum Dot Photoluminescence: Insights Into the Design of Robust Voltage-Sensitive Cellular Imaging Probes. _Nano Letters_ 2015, _15_ , 6848–6854
  * Habib et al. 2019 Habib, A.; Zhu, X.; Can, U. I.; McLanahan, M. L.; Zorlutuna, P.; Yanik, A. A. Electro-plasmonic nanoantenna: A nonfluorescent optical probe for ultrasensitive label-free detection of electrophysiological signals. _Science Advances_ 2019, _5_ , 9786
  * Nag et al. 2017 Nag, O. K.; Stewart, M. H.; Deschamps, J. R.; Susumu, K.; Oh, E.; Tsytsarev, V.; Tang, Q.; Efros, A. L.; Vaxenburg, R.; Black, B. J.; Chen, Y.; O’Shaughnessy, T. J.; North, S. H.; Field, L. D.; Dawson, P. E.; Pancrazio, J. J.; Medintz, I. L.; Chen, Y.; Erzurumlu, R. S.; Huston, A. L. et al. Quantum Dot–Peptide–Fullerene Bioconjugates for Visualization of in Vitro and in Vivo Cellular Membrane Potential. _ACS Nano_ 2017, _11_ , 5598–5613
  * Liu et al. 2020 Liu, J.; Zhang, R.; Shang, C.; Zhang, Y.; Feng, Y.; Pan, L.; Xu, B.; Hyeon, T.; Bu, W.; Shi, J.; Du, J. Near-Infrared Voltage Nanosensors Enable Real-Time Imaging of Neuronal Activities in Mice and Zebrafish. _Journal of the American Chemical Society_ 2020, _142_ , 7858–7867
  * Hao et al. 2011 Hao, J.; Zhang, Y.; Wei, X. Electric-induced enhancement and modulation of upconversion photoluminescence in epitaxial BaTiO3:Yb/Er thin films. _Angewandte Chemie - International Edition_ 2011, _50_ , 6876–6880
  * Mahata et al. 2015 Mahata, M. K.; Koppe, T.; Mondal, T.; Brüsewitz, C.; Kumar, K.; Rai, V. K.; Hofsäss, H.; Vetter, U. Incorporation of Zn2+ ions into BaTiO3 :Er3+ /Yb3+ nanophosphor: an effective way to enhance upconversion, defect luminescence and temperature sensing. _Physical Chemistry Chemical Physics_ 2015, _17_ , 20741–20753
  * Sood et al. 2023 Sood, A.; Desseigne, M.; Dev, A.; Maurizi, L.; Kumar, A.; Millot, N.; Han, S. S. A Comprehensive Review on Barium Titanate Nanoparticles as a Persuasive Piezoelectric Material for Biomedical Applications: Prospects and Challenges. _Small_ 2023, _19_ , e2206401
  * Genchi et al. 2016 Genchi, G. G.; Marino, A.; Rocca, A.; Mattoli, V.; Ciofani, G. Barium titanate nanoparticles: promising multitasking vectors in nanomedicine. _Nanotechnology_ 2016, _27_ , 232001
  * Hsieh et al. 2009 Hsieh, C.-L.; Grange, R.; Pu, Y.; Psaltis, D. Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging. _Optics Express_ 2009, _17_ , 2880
  * Sugiyama et al. 2018 Sugiyama, N.; Sonay, A. Y.; Tussiwand, R.; Cohen, B. E.; Pantazis, P. Effective Labeling of Primary Somatic Stem Cells with BaTiO3 Nanocrystals for Second Harmonic Generation Imaging. _Small_ 2018, _14_ , 1703386
  * Jordan et al. 2020 Jordan, T.; O’Brien, M. A.; Spatarelu, C.-P.; Luke, G. P. Antibody-Conjugated Barium Titanate Nanoparticles for Cell-Specific Targeting. _ACS Applied Nano Materials_ 2020, _3_ , 2636–2646
  * Pantazis et al. 2010 Pantazis, P.; Maloney, J.; Wu, D.; Fraser, S. E. Second harmonic generating (SHG) nanoprobes for in vivo imaging. _Proceedings of the National Academy of Sciences_ 2010, _107_ , 14535–14540
  * Čulić Viskota et al. 2012 Čulić Viskota, J.; Dempsey, W. P.; Fraser, S. E.; Pantazis, P. Surface functionalization of barium titanate SHG nanoprobes for in vivo imaging in zebrafish. _Nature Protocols_ 2012, _7_ , 1618–1633
  * Xue et al. 1988 Xue, L.; Chen, Y.; Brook, R. The influence of ionic radii on the incorporation of trivalent dopants into BaTiO3. _Materials Science and Engineering: B_ 1988, _1_ , 193–201
  * Zhang et al. 2011 Zhang, Y.; Hao, J.; Mak, C. L.; Wei, X. Effects of site substitutions and concentration on upconversion luminescence of Er3+-doped perovskite titanate. _Optics Express_ 2011, _19_ , 1824
  * Lee et al. 2012 Lee, H. W.; Moon, S.; Choi, C. H.; Kim, D. K. Synthesis and size control of tetragonal barium titanate nanopowders by facile solvothermal method. _Journal of the American Ceramic Society_ 2012, _95_ , 2429–2434
  * Megaw 1945 Megaw, H. Crystal Structure of Barium Titanate. _Nature_ 1945, _155_ , 484–485
  * Huang et al. 2017 Huang, Y.; Lu, B.; Li, D.; Tang, Z.; Yao, Y.; Tao, T.; Liang, B.; Lu, S. Control of tetragonality via dehydroxylation of BaTiO3 ultrafine powders. _Ceramics International_ 2017, _43_ , 16462–16466
  * Hao et al. 2022 Hao, S.; Yao, M.; Vitali-Derrien, G.; Gemeiner, P.; Otoničar, M.; Ruello, P.; Bouyanfif, H.; Janolin, P.-E.; Dkhil, B.; Paillard, C. Optical absorption by design in a ferroelectric: co-doping in BaTiO3. _Journal of Materials Chemistry C_ 2022, _10_
  * Tsur et al. 2001 Tsur, Y.; Dunbar, T. D.; Randall, C. A. Crystal and Defect Chemistry of Rare Earth Cations in BaTiO3. _Journal of Electroceramics_ 2001, _7_ , 25–34
  * Vega et al. 2017 Vega, M.; Alemany, P.; Martin, I. R.; Llanos, J. Structural properties, Judd–Ofelt calculations, and near infrared to visible photon up-conversion in Er 3+ /Yb 3+ doped BaTiO 3 phosphors under excitation at 1500 nm. _RSC Advances_ 2017, _7_ , 10529–10538
  * Zou et al. 2023 Zou, J.; Hao, S.; Gemeiner, P.; Guiblin, N.; Ibder, O.; Dkhil, B.; Paillard, C. Photoluminescence and structural phase transition relationship in Er-doped BaTiO3 model ferroelectric system. _Journal of Materials Chemistry C_ 2023, _12_ , 600–606
  * Pirc and Blinc 2004 Pirc, R.; Blinc, R. Off-center Ti model of barium titanate. _Physical Review B_ 2004, _70_ , 134107
  * Wu et al. 2020 Wu, H.; Ponath, P.; Lin, E. L.; Wallace, R. M.; Young, C.; Ekerdt, J. G.; Demkov, A. A.; McCartney, M. R.; Smith, D. J. Dielectric breakdown in epitaxial BaTiO3 thin films. _Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena_ 2020, _38_ , 044007
  * Alqedra et al. 2023 Alqedra, M. K.; Deshmukh, C.; Liu, S.; Serrano, D.; Horvath, S. P.; Rafie-Zinedine, S.; Abdelatief, A.; Rippe, L.; Kröll, S.; Casabone, B.; Ferrier, A.; Tallaire, A.; Goldner, P.; de Riedmatten, H.; Walther, A. Optical coherence properties of Kramers’ rare-earth ions at the nanoscale for quantum applications. _Physical Review B_ 2023, _108_ , 075107
  * Muraleedharan et al. 2024 Muraleedharan, A.; Co, K.; Vallet, M.; Zaki, A.; Karolak, F.; Bogicevic, C.; Perronet, K.; Dkhil, B.; Paillard, C.; Fiorini-Debuisschert, C.; Treussart, F. Ferroelectric texture of individual barium titanate nanocrystals. _ACS Nano_ 2024, doi: 10.1021/acsnano.4c02291
  * Berlincourt and Jaffe 1958 Berlincourt, D.; Jaffe, H. Elastic and Piezoelectric Coefficients of Single-Crystal Barium Titanate. _Physical Review_ 1958, _111_ , 143–148
  * Fujii et al. 2013 Fujii, I.; Yamashita, K.; Nakashima, K.; Kumada, N.; Magome, E.; Moriyoshi, C.; Kuroiwa, Y.; Wada, S. The Dielectric and Piezoelectric Properties of KNbO3 / BaTiO3 Composites With A Wide BaTiO3 Size Distribution. _Transactions of the Materials Research Society of Japan_ 2013, _38_ , 57
  * Chen et al. 2011 Chen, X.; Liu, Z.; Sun, Q.; Ye, M.; Wang, F. Upconversion emission enhancement in Er3+/Yb3+-codoped BaTiO3 nanocrystals by tridoping with Li+ ions. _Optics Communications_ 2011, _284_ , 2046–2049
  * Huxter et al. 2023 Huxter, W. S.; Sarott, M. F.; Trassin, M.; Degen, C. L. Imaging ferroelectric domains with a single-spin scanning quantum sensor. _Nature Physics_ 2023, _19_ , 644–648
  * Cliff and Lorimer 1975 Cliff, G.; Lorimer, G. W. The quantitative analysis of thin specimens. _Journal of Microscopy_ 1975, _103_ , 203–207
  * Li et al. 2014 Li, X.; Wang, B.; Zhang, T. Y.; Su, Y. Water adsorption and dissociation on BaTiO3 single-crystal surfaces. _Journal of Physical Chemistry C_ 2014, _118_ , 15910–15918
  * Rodríguez-Carvajal 1993 Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. _Physica B: Physics of Condensed Matter_ 1993, _192_ , 55–69