# Analytical electron microscopy analysis of insulating and metallic phases in
nanostructured vanadium dioxide

Jan Krpenský  [  Michal Horák  [  Jiří Kabát  [  Jakub Planer  [  Peter Kepič
[  Vlastimil Křápek  [  Andrea Konečná  [<EMAIL_ADDRESS>
###### Abstract

Vanadium dioxide (VO2) is a strongly-correlated material that exhibits
insulator-to-metal transition (IMT) near room temperature, which makes it a
promising candidate for applications in nanophotonics or optoelectronics.
However, creating VO2 nanostructures with the desired functionality can be
challenging due to microscopic inhomogeneities that can significantly impact
the local optical and electronic properties. Thin lamellas, produced by
focused ion beam milling from a homogeneous layer, provide a useful prototype
for studying VO2 at the truly microscopic level using a scanning transmission
electron microscope (STEM). High-resolution imaging is used to identify
structural inhomogeneities while electron energy-loss spectroscopy (EELS)
supported by statistical analysis helps to detect VxOy stoichiometries with a
reduced oxidation number of vanadium at the areas of thickness below 70 nm. On
the other hand, the thicker areas are dominated by vanadium dioxide, where the
signatures of IMT are detected in both core-loss and low-loss EELS experiments
with in-situ heating. The experimental results are interpreted with ab-initio
and semi-classical calculations. This work shows that structural
inhomogeneities such as pores and cracks present no harm to the desired
optical properties of VO2 samples.

###### keywords:

vanadium dioxide, vanadium oxides, transmission electron microscopy, electron
energy-loss spectroscopy, microfabrication

IPE]Institute of Physical Engineering, Brno University of Technology,
Technická 2896/2, 616 69 Brno, Czech Republic CEITEC]Central European
Institute of Technology, Brno University of Technology, Purkyňova 123, 612 00
Brno, Czech Republic IPE]Institute of Physical Engineering, Brno University of
Technology, Technická 2896/2, 616 69 Brno, Czech Republic CEITEC]Central
European Institute of Technology, Brno University of Technology, Purkyňova
123, 612 00 Brno, Czech Republic CEITEC]Central European Institute of
Technology, Brno University of Technology, Purkyňova 123, 612 00 Brno, Czech
Republic IPE]Institute of Physical Engineering, Brno University of Technology,
Technická 2896/2, 616 69 Brno, Czech Republic [CEITEC]Central European
Institute of Technology, Brno University of Technology, Purkyňova 123, 612 00
Brno, Czech Republic IPE]Institute of Physical Engineering, Brno University of
Technology, Technická 2896/2, 616 69 Brno, Czech Republic Central European
Institute of Technology, Brno University of Technology, Purkyňova 123, 612 00
Brno, Czech Republic

##  1 Introduction

Vanadium dioxide is a strongly-correlated material that can undergo a volatile
phase transition between the low-temperature monoclinic insulating phase and
the high-temperature rutile metallic phase 1, 2 by an applied thermal 3,
electrical 4, mechanical 5, or optical 6 biasing. In comparison to other
phase-changing materials, VO2 stands out for its ultrafast ($\approx 200$ fs)
IMT with a convenient transition temperature ($\approx 67\,\degree$C) close to
the room temperature 7, which can withstand millions of switching cycles
without degradation 8. All these properties suggest exciting applications of
VO2 in sensing 9, energy storage 10, switching 8, 11, 12, data storage 13, 14,
or active optical metamaterials 15, 16, 17.

The properties of IMT in VO2 can be strongly influenced by crystallographic
defects resulting from a substrate lattice mismatch and specific fabrication
conditions 5. IMT is also often dependent on VO2’s grain size, strain, and
film thickness 18, 19, 20, 21, 22. Further complexity stems from the existence
of multiple stable stoichiometries of vanadium oxide which can coexist within
one sample or functional structure23, 24, 25. Many of the applications of VO2
rely on nanostructuring, for which it is possible to use either top-down or
bottom-up approaches 26, 27, 28, 29. It is thus desirable to analyze IMT and
stoichiometry of vanadium oxide locally.

The IMT is tightly connected with an abrupt change in electronic structure,
which determines electric and optical properties. Conventional ways to
characterize the IMT thus involve measurements of the electric conductivity 30
or optical response 19, 31 as functions of applied temperature. However, these
methods have limited spatial resolution and do not allow the analysis of the
IMT at the level of single nanostructures or even grains. One possible
solution is represented by scanning near-field optical microscopy (SNOM),
which helped to identify local inhomogeneities in the IMT with a spatial
resolution of $\sim 10^{1}$ nm 32, 20, 21, 33, 34. Electron energy-loss
spectroscopy (EELS) in a scanning transmission electron microscope (STEM) 35
is another suitable technique allowing for spatial resolution down to single
atoms, which can also be used to correlate the spectroscopic information with
high-resolution imaging 36, 37. Furthermore, EELS is particularly broadband
and offers information on core-electron excitations with energies $\sim
10^{2}$ eV, optical excitations around $\sim 10^{0}$ eV and recently also
vibrational excitations in $\sim 10^{-2}$ eV range 38.

EEL spectra in the core-loss region are dominated by excitations of electrons
from core shells to unoccupied valence states. The spectral signatures are
thus not only element-specific, but they also provide insights into local
bonding, oxidation states of atoms 39, and geometrical confinement 40. Several
studies have already exploited EELS near-edge fine structure to identify
different stoichiometries of VxOy samples 41, 42, 43, 44, 45, 46, 47, 48.
However, to the best of our knowledge, the studies using (S)TEM in combination
with EELS were up to one exception 31 restricted to room temperature without
the possibility of observing the changes when the material is switched to the
high-temperature phase. Similarly, temperature-dependent low-loss STEM-EELS
data that can be directly linked to optical properties are missing. In
conducting materials, low-loss EELS is contributed by the excitation of
plasmon resonances. This allows for a reliable distinguishing of conducting
and insulating phases.

To gain insights into temperature-dependent properties of VO2 at the
microscopic level, we study a lamella with gradually decreasing thickness
fabricated from a thick evaporated layer of presumably VO2 by focused ion beam
(FIB) lithography. The lamella is attached to a commercial heating chip, which
allows for external control of the lamella temperature. The lamella is then
thoroughly studied by analytical methods available in TEM. We use high-
resolution imaging and STEM with energy-dispersive X-ray spectroscopy (EDX) to
analyze the lamella structure and elemental composition. The optical and
electronic properties of the lamella are characterized by temperature-
dependent STEM-EELS. We complement our experimental observations with ab-
initio calculations of the core-loss probability. Low-loss probability is
retrieved from the experimental dielectric function using a semi-classical
formalism 49.

##  2 Results and Discussion

###  2.1 Sample Fabrication and Pre-Characterization

Figure 1: Pre-characterization of the VO2 thin film. (a) Optical properties
below (blue) and above (red) IMT temperature ($\approx$ 67 $\degree$C). (b)
Illustrative SEM image of the surface of the sample. (c) AFM image of the
surface from a different place than (b). (d) STEM-HAADF image of a thin
lamella “S” displaying a porous character of VO2 layer. (e) STEM-HAADF image
with overlayed EDX maps from the same place as (d) visualizing the presence of
individual elements detected in the sample: Si substrate at the bottom (pink);
V (yellow) and O (red) in the middle; a mixture of C (green), Pt (light blue),
and Ga (dark blue) as components of the Pt protective coating at the top.

A layer of presumably vanadium dioxide (VO2) with a thickness of 550 nm was
prepared by electron beam evaporation and subsequent ex-situ annealing (see
Experimental Section). We first performed macroscopic characterization of the
sample by spectroscopic ellipsometry to verify that it indeed corresponds to
VO2 and that it exhibits the desired optical properties and their switching
across the IMT temperature as reported in literature 19, 50. Figure 1(a) shows
real (solid lines; $\varepsilon_{1}$) and imaginary (dashed lines;
$\varepsilon_{2}$) parts of dielectric function at temperatures below (30 °C,
blue) and above (90 °C, red) the IMT temperature. The high-temperature phase
is metallic, with a negative $\varepsilon_{1}$ function above the wavelength
of 1100 nm, while the low-temperature phase is insulating, with positive
$\varepsilon_{1}$ in the whole inspected spectral region. The onset of
interband electronic absorption is observed below about 500 nm, manifested by
a peak in $\varepsilon_{2}$. Above 500 nm, $\varepsilon_{2}$ increases as
$\sim\lambda$ in the metallic phase as a consequence of the Drude-like
response and remains low in the insulating phase. The IMT in VO2 associated
with the observed qualitative change in its optical properties gives rise to a
possible application of VO2 structures in active photonics 17.

We further characterized the homogeneity of the layer surface by a scanning
electron microscope (SEM) and an atomic force microscope (AFM) as shown in
Figure 1(b,c), respectively. The SEM image shows small cracks throughout the
whole surface of the layer. The AFM image obtained at a different place on the
surface also shows roughness and apparent pores. The presence of
inhomogeneities observable already at the surface triggered the need for a
cross-sectional structural and chemical analysis using TEM.

We prepared a standard TEM lamella (further labelled as “S” which stays for
standard) by FIB. A high-angle annular dark-field (HAADF) image of the $\sim
120$ nm thick lamella (representing a cross-section of the original VO2 layer)
is shown in Figure 1(d). The transverse profile of the layer exhibits pores
and cracks noticeable also in the SEM and AFM images. The TEM image overlayed
by a map of the elemental composition obtained by EDX is shown in Figure 1(e).
From the bottom up we identify the silicon (pink) substrate, vanadium (yellow)
and oxygen (red) forming the layer itself and a protective layer – a mixture
of Pt (cyan), C (green), and minor contribution of implanted Ga (dark blue)
prepared by focused ion beam induced deposition (FIBID). The EDX analysis of
the VO2 layer reveals the elemental composition reading $32\pm 6$ atomic
percent of vanadium, $68\pm 8$ atomic percent of oxygen, and $0.3\pm 0.1$
atomic percent of gallium (only negligible contamination). The mean
stoichiometry VO2.1±0.4 determined by EDX is consistent with the expected VO2
composition of the layer.

To perform in-situ analysis of IMT in the TEM, another lamella (further
labeled as lamella “IS” standing for in-situ) was prepared and attached to a
TEM heating chip (Protochips 51; see Figure S1 of the Supporting Information).
It consisted of a thick support and a thinned layer with gradually decreasing
thickness dedicated for EELS measurements. Figure 2(a) shows a STEM annular
dark-field (ADF) image with an overview of the lamella “IS”. We further
performed high-resolution imaging of the lamella and confirmed its
polycrystallinity with random orientation of grains as shown in Figure S2 of
the Supporting Information. The yellow frame in Figure 2(a) indicates the
thinnest region of the lamella selected for further analysis.

###  2.2 Core-Loss EELS

Figure 2: EELS spectrum line scans at nominal temperatures 25$\,\degree$C and
150$\,\degree$C. (a) STEM-ADF image of the lamella “IS”. Yellow-framed square
marks the region of interest for the spectrum line scans, whereas the small
green square, also denoted by the green arrow, will be used later for the low-
loss EELS experiment. (b) Detail of the yellow-marked area. The blue line
corresponds to a desired spectrum line scan at 25$\,\degree$C, and the red
line corresponds to a line spectrum image at 150$\,\degree$C. Both spectrum
line scans comprise 100 individual EELS measurements. Yellow arrows mark the
crack (C) and pore (P). (c) Relative thickness in the units of IMFP, which
varies around 130 nm for different VxOy stoichiometries extracted from EELS.
Note that the line scan at 25$\,\degree$C slightly drifted from the desired
position displayed in (b). (d) 2D waterfall graph with measured core-loss EEL
spectra at both temperatures. Each spectrum averages ten subsequent EEL
spectra as marked next to them. Vertical gray lines are to guide the eyes.

Our VO2 layer exhibits structural inhomogeneities, which might be associated
with chemical inhomogeneities and irregularities in the switching from the
insulating to the metallic phase. To explore this possible correlation, we
analyze EELS of the lamella ”IS” in the core-loss region. In Figure 2(b), we
show the target line scans along which we acquire $2\times 100$ spectra with
regular spacing. We perform the spectrum line scan close to room temperature
(blue line) and above IMT temperature (red line). The accuracy of the nominal
temperature at the chip is reported to be $5\,\%$ 52, but as contacts between
the lamella and the heating chip might not be perfect and cause losses, we
heated the chip to 150$\,\degree$C to ensure we were certainly above the IMT
temperature. We also note that the designated line scan positions, especially
the one for the measurement at 25$\,\degree$C, slightly differ from the actual
measurements due to sample drift. The thickness profiles extracted from EELS
measurements in the units of the electron inelastic mean free path (IMFP) are
shown in Figure 2(c). The IMFP for our experimental parameters and possibly
occurring different VxOy stoichiometries varies around 130 nm (134 nm for VO2,
131 nm for V2O3 and 127 nm for VO based on the Mean free path estimator 53
with model from Ref. 54). Both line scans correspond to gradually increasing
thickness with several valleys associated with the presence of the pores.

To facilitate visualization of the spectra and preliminary analysis, we binned
the spectra into twenty groups by ten, and represented each bin by the average
spectrum, which was further normalized by its maximum. The spectra shown in
the waterfall plot in Figure 2(d) globally exhibit up to five prominent
distinct peaks. Notably, we can observe energy shifts and intensity changes in
the peaks appearing in the spectra averaged over different beam positions. An
additional feature, a pre-peak (a “shoulder”) of the first peak, is emerging
in the spectra recorded in thicker areas. However, the changes in subsequent
averaged spectra are rather abrupt, suggesting that a finer analysis is
desirable.

Figure 3: Clustering analysis of the spectrum line scans from Figure 2. 200
spectra recorded within the spectrum line scans are sorted into four groups
(clusters) according to similarities. Averaged normalized spectra falling into
the individual clusters are shown in (a). Fitting of the spectra in (a) by a
sum of Gaussians yields peak energies plotted in (b), where the sizes of the
dots are proportional to the spectral areas of the peaks. Line profiles in
(c,d) in the units of mean free path are overlaid by color-coded dots denoting
affiliation of the spectrum recorded at the corresponding position to one of
the clusters. The dots’ size and opacity denote closeness to each cluster’s
averaged spectrum. The color-coding corresponds to (a). (c) is obtained for
the measurement at 150$\,\degree$C and (d) for 25$\,\degree$C. Arrows mark the
position of the crack (C) and the pore (P).

We utilize cluster analysis for a refined sorting of the acquired spectrum
line scans. We first group the spectra acquired at both temperatures (200
spectra in total) and then sort them into clusters using the “k-means”
clustering approach as implemented in Mathematica 12 55. Inspecting the
results of several clustering procedures (with the number of clusters varied
between 3 and 5; and with low-temperature and high-temperature spectra
processed separately or jointly), we identified four clusters as optimum – all
clusters were sufficiently populated and represented physically distinct
spectra. We further notice that one of the clusters can be sorted into two
sub-clusters based on spectral behavior at energies above 535 eV. Averaged
spectra corresponding to the five acquired clusters, referred to as cluster
representants, are plotted in Figure 3(a). The two green spectra emerge from
the sub-clustering.

The cluster representants exhibit multiple peaks, which can be assigned to
transitions from core to unoccupied valence states of vanadium 56 and oxygen
41: i) V L3 peak (518–519 eV; transitions from 2p3/2 to unoccupied 3d states
of V), ii) V L2 peak (521–522 eV; transitions from 2p1/2 to unoccupied 3d
states of V), and iii) up to two O K peaks (529–532 eV; transitions of O
electrons from 1s to hybridized O 2p – V 3d states, which are of $t_{2g}$ and
$e_{g}$ symmetry). Spectral features observable above $\sim 535$ eV arise due
to transitions to O 2p and V 4s mixed states 41, but can be influenced by the
presence of unbound oxygen, or other oxygen compounds (e.g., due to
contamination).

We further fit the cluster representants by a sum of eight Gaussian peaks (for
details on fitting, see Figure S3 of the Supporting Information), whose
energies are plotted in Figure 3(b). Notably, energies and relative strengths
of V and O peaks strongly depend on the local oxidation state. The energies of
V L3 and L2 peaks increase with a higher oxidation state of V, and
importantly, we observe the emergence of a pre-peak, which has been attributed
as a clear signature of crystalline VO2. 56, 43 Another clear signature is the
increasing intensity of the first O K peak at $\sim 529$ eV (V 3d $t_{2g}$
bands) 41. Such analysis allows for the precise assignment of our clusters
with different VxOy stoichiometries. We find that the first cluster can be
attributed to VO. The sub-clustering then results in distinguishing VO and
VO$+$O, where the latter corresponds to areas with the O in other compounds or
free O, yielding an increase of a broad peak centred around 539 eV [green
spectra in Figure 3(a)]. We then identify V2O3 (orange spectrum) with nearly
equal intensities of O K peaks. The last two clusters (blue and red spectra)
exhibit a clear pre-peak around 515 eV and an intense first O K peak, which
for both yields the VO2 assignment. However, a closer inspection reveals a
slight energy shift between the V peaks and a different intensity ratio of O
peaks between these two clusters.

It is interesting to correlate the cluster index of each spectrum (i.e., to
what cluster an individual spectrum belongs) with the parameters at which the
spectrum was taken: the position at the sample, the local thickness of the
sample, and the temperature. We visualize this in Figure 3(c,d). We represent
each spectrum as a point in the sample-position–local-thickness coordinates,
the color of the point represents the cluster index, and each panel
corresponds to one of the two temperatures. For clusters 1a/b and 2
corresponding to VO/VO$+$O and V2O3, respectively, the only discriminating
parameter is the sample thickness, and the spectra taken at both temperatures
at a specific thickness range are assigned to the same cluster. Notably, for
clusters 3 and 4 containing spectra from thicker parts of the sample, the
temperature becomes a discriminating parameter – cluster 3 contains only low-
temperature spectra (77 in total), and cluster 4 contains only high-
temperature spectra (36 in total), with only two exceptions. This allows us to
state already at the phenomenological level that the thicker part of the
sample assigned to clusters 3 and 4 exhibits a pronounced thermal dependence
of its properties (possibly IMT) while the thinner parts assigned to clusters
1 and 2 show no thermal dependence making the occurrence of IMT improbable.

The cluster analysis yields two conclusions: i) With decreasing lamella
thickness, we observe a gradual reduction of vanadium from VO2 to V2O3, and
VO/VO+O. The part of the lamella with the reduced oxides is rather large, with
a thickness up to 0.6 – 0.7 IMFP or 80 – 90 nm and a width (measured from the
lamella edge) up to 60 nm [cmp. Figure 3(c,d)]. This suggests difficulties in
preparing ultrathin VO2 nanostructures, as the reduced oxides do not exhibit
the desired switching of optical properties. On the other hand, a previous
study reported considerably thinner (about 2 nm) diffuse layers of reduced
vanadium oxides at the boundaries of individual VO2 grains 43, suggesting that
with optimized fabrication protocols the detrimental impact of the reduced
oxides can be relieved. ii) The spectra from the thickest areas acquired at
25$\,\degree$C and 150$\,\degree$C are unambiguously sorted into the two
substantially different VO2 clusters [blue vs. red spectrum in Figure 3(a)],
which suggests that the observed spectral and intensity shifts between the two
VO2 clusters could be attributed to the phase change. This assignment is
further corroborated by the ab-initio calculations discussed below.

Finally, we discuss the role of the structural inhomogeneity in the local
properties of the lamella. The line scans shown in Figure 2(b) cross two
pronounced inhomogeneities: a narrow crack at the targeted spectrum indices of
35 (low temperature, blue line) and 40 (high temperature, red line) and a
broad deep pore at the targeted spectrum index range of 60 to 70 for both
temperatures. Both the crack and the pore are visible as depressions in the
thickness profiles shown in Figure 2(c). Here, the real spectrum indices
slightly differ from the targeted ones due to sample drift, which resulted in
an offset of 10 between the targeted and real spectrum indices for the low
temperature. The crack is found at the spectrum index of 22 (low temperature)
and 43 (high temperature), and the pore is located in the spectrum index
ranges of 46 to 64 (low temperature) and 58 to 75 (high temperature).

For the crack at both temperatures and for the pore at the low temperature we
observe no modification of the core-loss EEL spectrum in comparison to the
areas of the lamella adjacent to the inhomogeneity, neither by visual
inspection [Figure 2(d)] nor by cluster analysis represented by the spectrum
cluster index [Figure 3(d)]. On the other hand, the core-loss EEL spectrum is
modified for the deepest part of the pore at the high temperature, where the
stoichiometry changes from VO2 to V2O3 [see Figure 3(c)]. A closer inspection
suggests that this modification is related to a reduced thickness of the
lamella within the pore. In other words, the singular parameter determining
the local electronic and optical properties of the lamella manifested in core-
loss EELS is its thickness. The structural inhomogeneities (cracks and pores)
themselves do not impose any observable modifications (e.g. due to their
elastic or plastic field or local charge) unless they are accompanied by a
modified thickness.

We note that the area of the lamella identified as the crack is present in the
region of V2O3 at the interface with VO2. Further investigation is required to
determine whether this correlation is causal or coincidental, and possibly
determine its mechanism.

###  2.3 Variation of Core-Loss and Low-Loss EELS with Temperature

Figure 4: (a) Comparison of the averaged clustered spectra (cluster
representants) assigned as VO2 obtained at 25$\,\degree$C (solid blue line),
and 150$\,\degree$C (solid red line) with ab-initio-calculated O K peaks
corresponding to the monoclinic phase (dashed blue line) and rutile phase
(dashed red line). The calculated spectra are both offset by 527.8 eV to get
an approximate alignment with the experimental peak positions. (b) Comparison
of the experimentally acquired low-loss EELS at 25$\,\degree$C (solid blue
line), and 150$\,\degree$C (solid red line) from the area marked by the green
square in Figure 2(a) compared with calculations using a classical dielectric
formalism (dashed blue and red lines).

For further verification that the temperature-dependent changes in our core-
loss EELS measurements are due to the IMT of VO2, we perform ab-initio
calculations. We use the TELNES3 package, the extension of the Wien2k all-
electron DFT code 57, to simulate electron loss near-edge structure (ELNES) of
the O K-edge. More details about the calculation setup are given in the
Supporting Information.

In Figure 4(a), we present a comparison between the cluster representants of
core loss EELS obtained in the thick areas of the sample at 25$\,\degree$C and
150$\,\degree$C (solid lines) together with the calculated spectra (dashed
lines; after convolution with 1-eV Gaussian) concerning the O K excitations.
The ab-initio theory predicts changes in the positions and relative strengths
of the convolved O K peaks, in perfect agreement with our experimental
observation. The relative shift of $\sim 0.2$ eV between the high-temperature
and low-temperature experimental spectra on the energy axis is caused by the
band gap opening in the monoclinic phase. Our calculations show 0.1 eV gap. In
line with the previous work of Hebert et al.41, the relative intensity of the
O K peaks is proportional to the number of O(p) states in the t2g band
($\pi$-bonds) and in the $e_{g}$ band ($\sigma$-bonds). Indeed, the ratio of
O(p) states in respective bands changes from 77.4% to 80.7% after IMT, which
explains a relative increase of the first O K peak.

Modifications in the band structure across the IMT are also tightly connected
with changes in valence-electron excitations, which can be probed by EELS in
the low-loss region. In the case of VO2, the IMT could be clearly identified
based on the emergence of plasmons in the rutile (metallic) phase. Plasmons in
VO2 nanostructures were previously detected only with high-resolution EELS 58,
where slow electrons in a broad beam were used to probe sample’s surface.
However, to the best of our knowledge, low-loss STEM-EELS of nanostructured
VO2 samples probed across the IMT have been missing.

Unfortunately, the long time necessary to acquire the core-loss EELS prevented
us from performing the low-loss EELS experiment in the previously analysed
area due to accumulated contamination and beam-induced damage. We therefore
collected the low-loss EEL spectra in the region close by, denoted by the
green square in Figure 2(a). This region is sufficiently thick ($\sim 300$ nm
based on STEM-HAADF images of the lamella and a comparison of intensities with
areas of known thickness) without too many pores, so it contains dominantly
VO2. To avoid beam-induced damage, we collected a spectral image with
$10\times 10$ pixels with regular steps of $\sim 1$ nm and averaged them. We
further fitted and subtracted the zero-loss peak to obtain the results in
Figure 4(b) (solid lines; see raw spectra in Figure S4 of the Supporting
Information). The experiment was again performed below and above the IMT
temperature, at 25$\,\degree$C (blue) and 150$\,\degree$C (red), respectively.

The experimental low-loss EEL spectra in Figure 4(b) exhibit a broad peak
between $1.0-1.5$ eV, which grows in intensity when the sample is heated up.
To interpret this behavior, we perform semi-analytical calculations within the
framework of classical electrodynamics. To that end, we consider the problem
of a line current (representing a focused electron beam) traversing a thin
film characterized by a dielectric function from Figure 1(a) and solve for the
induced electric field entering the formula for electron energy-loss
probability 49. The spectrum calculated for VO2 in the monoclinic (insulating)
phase (dashed blue line) shows only a faint broad peak centered at $\sim 1.25$
eV corresponding to weak absorption contribution, a small portion of radiative
losses and an increasing background above $2.5$ eV due to higher-energy
interband transitions. On the other hand, the intense peak around $1.3$ eV
appears in the calculation for the rutile (metallic) phase (dashed red line),
which can be assigned to bulk plasmon and surface plasmon polariton
excitations. These theoretical results qualitatively support the experimental
observation and confirm that the spectral change could be interpreted as IMT-
induced. However, the experimentally measured loss probability is less
intense, which is particularly apparent in the plasmonic peak in the spectrum
recorded at 150$\,\degree$C. Such quantitative discrepancy can happen due to
differences in the actual and model dielectric responses of the sampled area,
or partially because of the background subtraction procedure, where zero
signal is assumed below 0.5 eV. Multiple scattering, which is not included in
the theory, could also play some role.

##  3 Conclusion

We have studied the insulating and metallic phases of nanostructured vanadium
dioxide (VO2) using analytical electron microscopy. We have focused on
ultrathin lamellas fabricated from a 550 nm thick VO2 film. With the help of
STEM-EELS, we have revealed that the lamellas show both structural and
stoichiometric inhomogeneities at the microscopic level. Results from the
core-loss EELS enhanced by statistical analysis helped to correlate the
stoichiometry with the thickness of the lamella, finding vanadium oxides with
a reduced oxidation number (V2O3 and VO) at thinner parts of the lamella (with
the thickness of 60 nm or less). This represents a challenge for preparing
ultrathin VO2 nanostructures.

The principal contribution of our study is the observation of temperature-
induced changes in both core-loss and low-loss EELS in thicker regions of the
lamella, which were identified to contain dominantly VO2. Changes in the core-
loss spectra were analyzed with the help of ab-initio calculations that were
used to relate the fine structure of the oxygen K peaks with the modifications
in the band structure during the IMT. In the low-loss spectra, the most
significant evidence of IMT is the emergence of a strong plasmonic peak in the
metallic phase.

This work establishes the STEM-EELS with in-situ heating as a suitable
technique to probe the IMT in VO2, and potentially in other materials. We
foresee that STEM-EELS could also be combined with in-situ diffraction studies
to correlate the spectroscopic results with crystal structure and orientation
to further enhance the analysis of the IMT.

##  4 Experimental Section

###  4.1 Preparation of thick VO2 layer

550-nm-thick VO2 layer was fabricated on a silicon substrate by evaporating
VO2 powder (Mateck) in an electron beam evaporator (Bestec, 8 kV, 32 mA, 1
Å/s) at room temperature and subsequent ex-situ annealing for 20 min at
$550\,\degree$C in a vacuum furnace under 10 sccm of O2 flow.

###  4.2 Preparation of the lamella

Lamellas for TEM were fabricated using a gallium FIB Tescan LYRA3. The final
polishing was performed with imaging at low voltage (5 kV) and low current (40
pA) of Ga+ ions for approximately 25 seconds at a glancing angle to reduce the
beam-damaged surface area 59. The positioning of the lamella on the heating
chip is shown in detail in Figure S1 of the Supplementary Information.

###  4.3 Transmission electron microscopy

TEM analysis was performed on TEM FEI Titan equipped with a Super-X
spectrometer for EDX, a monochromator, and a GIF-Quantum spectrometer for
EELS. The heating experiment was performed using in-situ holder Fusion Select
and the corresponding thermal chip by Protochips 51.

####  4.3.1 STEM-EDX

EDX measurement was performed in the scanning regime with the energy of
primary electrons set to 300 keV. The probe current was set to approximately
$600$ pA. We acquired and integrated 100 spectrum images with a pixel size of
0.34 nm and a dwell time of 2 $\upmu$s. The spectrometer dispersion range was
set to 20 keV. Chemical composition was evaluated in Velox software using the
parabolic background model, absorption correction, and Schreiber-Wims
ionization cross-section model (a semi-empirical model recommended for metal
oxides). For the quantification of the vanadium dioxide layer stoichiometry,
we used V K, O K, and Ga K edges.

####  4.3.2 STEM-EELS core-loss

Core-loss EELS was performed in the monochromated scanning regime with the
energy of primary electrons set to 300 keV. We used the following parameter
settings: The probe current of around $200$ pA, the convergence semi-angle of
10 mrad, the collection semi-angle of 18.4 mrad, and the spectrometer
dispersion of 0.25 eV/px. The full-width at half-maximum of the zero-loss peak
(determining the energy resolution) read 0.2 eV. We used the dualEELS option,
which allows us to record both the low-loss and core-loss EELS spectra
simultaneously, resulting in the correct calibration of the energy loss axis
to absolute values 60. The spectrum line scans were acquired with a length of
100 pixels, a pixel size of 1.44 nm, and an exposure time of 0.1 ms for the
low-loss part and 1 s for the core-loss part, respectively. The low-loss part
of the spectrum was further used to determine the thickness profiles in Figure
2(c) in the units of IMFP.

####  4.3.3 STEM-EELS low-loss

Low-loss EELS was performed in the monochromated scanning regime with the
primary electron energy of 120 kV. The reduced value of the primary electron
energy was used to achieve a better signal-to-background ratio 61 and to
suppress relativistic losses like the Čerenkov radiation 62. We used the
following parameter settings: the probe current of approximately $100$ pA, the
convergence semi-angle of 10 mrad, and the collection semi-angle of 11.4 mrad,
the spectrometer dispersion of 0.1 eV/pixel. The full-width at half-maximum of
the zero-loss peak (determining the energy resolution) read 0.14 eV. We summed
100 spectra recorded over a $10\times 10$ pixel spectrum image with a pixel
size of 1 nm and an exposure time of 0.8 ms. The zero-loss peak subtraction
was performed by a background power-law fitting respecting the shape of the
pre-recorded zero-loss peak at vacuum.

Supporting information contains details on the preparation of the lamella on
the heating chip, high-resolution imaging of the lamella, fitting of core-loss
EELS, raw low-loss EEL data, and computational details of ELNES calculations.

This research was supported by the Czech Science Foundation (project No.
22-04859S) and MEYS CR under the project CzechNanoLab (LM2023051, 2023–2026).
JP acknowledges the funding from IMPROVE V, CZ.02.01.01/00/22_010/0002552.

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