# Near-field imaging of domain switching in in-operando VO2 devices

Sergio Salvía Fernández  van der Waals - Zeeman Institute, University of
Amsterdam, Sciencepark 904, 1098 XH Amsterdam, the Netherlands  Xing Gao
Faculty of Science and Technology and MESA+ Institute for Nanotechnology,
University of Twente, Enschede, the Netherlands  Silvia Cassanelli  van der
Waals - Zeeman Institute, University of Amsterdam, Sciencepark 904, 1098 XH
Amsterdam, the Netherlands  Stephan Bron  van der Waals - Zeeman Institute,
University of Amsterdam, Sciencepark 904, 1098 XH Amsterdam, the Netherlands
Hans Hilgenkamp  Faculty of Science and Technology and MESA+ Institute for
Nanotechnology, University of Twente, Enschede, the Netherlands  Erik van
Heumen<EMAIL_ADDRESS>van der Waals - Zeeman Institute, University of
Amsterdam, Sciencepark 904, 1098 XH Amsterdam, the Netherlands  QuSoft,
Science Park 123, 1098 XG Amsterdam, The Netherlands

###### Abstract

Experimental insight in the nanoscale dynamics underlying switching in novel
memristive devices is limited owing to the scarcity of techniques that can
probe the electronic structure of these devices. Scattering scanning near-
field optical microscopy is a relatively novel approach to probe the optical
response of materials with a spatial resolution well below the diffraction
limit. We use this non-invasive tool to demonstrate that it provides detailed
information on the origin and memory behaviour of ultra-thin films of vanadium
dioxide. Simultaneously recorded $I(V)$ characteristics and near-field maps
show that discontinuities in the I(V) characteristics arise from the sudden
switching of insulating domains to metallic domains. At the threshold voltage,
the domains form a continuous current path. The metallic domains persist once
the bias voltage is removed, but narrow monoclinic regions appear around the
domain boundaries. The key advantage of our approach is that it provides
detailed information on the electronic structure at length scales raging from
tens of nanometers up to tens of microns and is easily applied under in
operando conditions.

Scattering scanning near field optical microscopy (sSNOM) is a versatile, non-
invasive probe of the dielectric and plasmonic response of correlated and 2D
materials. Based on tapping-mode atomic force microscopy (AFM), an sSNOM can
map out optical contrast on a scale of a few tens of nanometers at any
wavelength due to the interaction between a polarizable AFM cantilever, an
incoming laser and the sample under study. Some of the more recent
enhancements of the sSNOM implementation include enabling broadband
spectroscopy [1, 2], ultra-fast pump-probe microscopy [3, 4, 5] and THz sSNOM
[6]. An equally important endeavour has been improving the ability to
manipulate material parameters in-situ. Examples include manipulating the
optical response of a material through changing the carrier concentration [7,
8] or exploring phase transitions with variable temperature microscopy [9,
10]. Invariably, adding new capabilities to the sSNOM repertoire have led to
new insights in the electronic properties of materials on nanometer length
scales [11, 12].

In this article we map out the near-field optical response in operando on a
memristive device as it is driven through switching events. The device is
based on a vanadium dioxide thin film, which features a reversible insulator
to metal transition. Vanadium dioxide is a poster child for the application of
complex oxide materials in a variety of room temperature, energy saving
applications [13, 14]. As platform for a memristor device, VO2 has been
investigated in a variety of different forms [15, 16, 17, 18, 19, 20, 21].
Depending on the details, switching can be as fast as a few 100’s of
femtoseconds [22, 5]. Particular interest has gone to fully strained films
[23, 24, 25]. These ultra-thin films are fully in the rutile phase in both the
insulating and metal phases, which is expected to lead to enhanced durability
of devices.

Several studies have investigated whether the current driven transition arises
from electric field effects [26, 27, 16, 25, 28] or from Joule heating [29,
30, 15, 31]. It appears that both effects are present to some degree and that
the balance depends on detailed properties of the structures studied (film
thickness, substrate etcetera). In-operando probing of device switching has
provided insight in the parameters determining the switching speed [19], in
the role played by film thickness and crack formation [25] and in the role
played by nanoscale domains in unstrained films [16].

Scattering near-field optical microscopy has proven to be a valuable tool for
the study of VO2 crystals and films [32, 33, 34, 35, 36, 37], but to the best
of our knowledge has not been applied to the study of in-operando devices or
fully strained thin films. In this article we use it to compare the insulator
to metal transition (IMT) both as function of temperature and applied electric
field with 20 nm spatial resolution. We investigate the heating induced by the
CO2 laser and its effect on the onset of the MIT. We use the sSNOM contrast to
elucidate the mesoscopic changes in the electronic structure as a current is
applied. Combined with simultaneously measured $I(V)$ characteristics, this
enable us to pinpoint the origin of irregular steps in $I(V)$ traces.

In our experiments, we combine scattering scanning near-field optical
microscopy (sSNOM) with transport measurements. Strained VO2 films of 13 nm
thickness are grown on a single crystal TiO2 substrate using pulsed laser
deposition [18]. Subsequently, sets of eight gold contacts are created using
photolithography (Fig. 1a). Each set consists of two rows of four contacts
that are separated by 3 $\mu\text{m}$, while the rows are separated by 12
$\mu\text{m}$. This layout allows us to determine the two-point resistance
from $V_{S}/I_{S}$ by using pairs of contacts or a four-point resistance,
$R\,=\,V_{R}/I_{R}$, by employing the four contacts on a row. The smaller
spacing between contacts on a row is less ideal for the sSNOM experiments, as
only a small region between the contacts can be probed. We therefore use two-
point $I_{S}(V_{S})$ measurements between a contact in the top and bottom row
to simultaneously record the resistance, while scanning the near-field
response over a large 15 $\mu\text{m}$ by 10 $\mu\text{m}$ area. We choose
this area to be in between the contacts (yellow square in Fig. 1a) over which
a voltage $V_{S}$ is applied, so that the current flows approximately
perpendicular to the scanning direction. We use the gold contacts as reference
for the near-field maps, enabling quantitative comparisons between experiments
and eliminating small changes in the CO2 laser intensity. All sSNOM data is
displayed on a color scale labelled as S2/S2,Au. In other words, the value of
the second harmonic of the demodulated near-field signal in every pixel, is
divided by the average value of the corresponding signal measured on a nearby
gold contact. Such gold reference images are recorded frequently, e.g. after
changing temperature or voltage. AFM topographies are collected as well,
showing an atomically smooth surface over the entire field of view with only a
few domain lines across the field of view (white, diagonal lines in Fig. 1a).
The near-field optical response is measured at a wavelength
$\lambda\,=\,10.7\,\mu\text{m}$ (116 meV). At this wavelength large optical
contrast is expected between metallic and insulating regions [32].

Figure 1: (a) Experimental geometry. The yellow square indicates the relation
between AFM topography (on the right) and the contacts. (b): Resistance
($R\,=\,V_{R}/I_{R}$) recorded during heating and cooling cycle. Also
indicated are the two-point resistances $V_{S}/I_{S}$, measured during the
sSNOM experiments (yellow squares). A small shift in temperature is due to
laser-induced heating. Red solid circles indicate temperatures where we
investigated heating due to the CO2 laser, see panel (e). (c): $I_{S}(V_{S})$
characteristic measured at 293.2 K. In the first cycle the resistance is high
until a threshold voltage is reached at 1.7 V. The $I_{S}(V_{S}$)
characteristic then follows a different voltage dependence until the sample is
reset by cooling well below the IMT. (d) sSNOM image recorded at 292 K during
a heating cycle. The arrow indicates the sudden appearance of a metallic
domain induced by laser heating. (d): change in local temperature determined
from the corresponding change in resistance when the CO2 laser is focused on
the sample. See the text for more details.

X-ray diffraction measurements on the as-deposited VO2 film indicate that the
film was principally in rutile phase. The associated strain is accommodated by
monoclinic-phase planar defects representing the domain lines mentioned above.
As observed previously, films with thickness below 35 nm are almost completely
in the rutile phase [24, 25]. The insulator-to-metal transition (IMT) in our
films is therefore purely electronic in nature. Figure 1b shows that the
resistance changes by almost three orders of magnitude with transition
temperatures during $T_{C}$ = 289 K and $T_{H}$ = 295 K, recorded during
cooling (C) and heating (H) respectively. The width of the transition is
approximately 2 K, with a hysteresis of 6 K.

The application of a voltage while in the insulating state can also trigger
the IMT [38, 29, 30, 25, 18], as shown in Fig. 1c. Starting from a temperature
below the IMT (293 K in Fig. 1c), the system is in a high resistance state
until a threshold voltage is reached. Beyond this threshold the current
increases hundredfold, signalling the formation of a metallic state. We will
call this the forming cycle. In subsequent $I(V)$ cycles the metallic state
persists, as evidenced by the distinctly different cycles 2 and 3 in Fig. 1c.
In these subsequent cycles small steps in current at particular voltages are
also present, which are close to reproducible from cycle to cycle. The
insulating state can be restored by cooling below $T_{C}$.

Figure 2: Top row: Gold referenced near-field scattering amplitude
$S_{2}/S_{2,Au}$ maps recorded at selected temperatures while cooling from the
metallic state. Bottom row: $S_{2}/S_{2,Au}$ recorded at various voltages
V${}_{\text{S}}$ during a forming $I(V)$ cycle (at 293.2 K). The threshold
voltage for this measurement occurred at 1.25 V. The panel labelled with 0.0*
V was recorded immediately after turning off the applied voltage. Blue squares
in the two right-most panels indicate the same domain.

One of the interesting aspects of VO2 is that, besides dc electric fields, the
IMT can be induced through other external knobs such as strain [34] and
ultrafast light pulses [39, 28]. This also plays an important role in our
experiments as demonstrated in Fig. 1d. The sSNOM data is taken at T = 292 K
close to $T_{H}$ in the insulating state. Indeed, a large part of the field of
view (FOV) has a low near-field amplitude, indicative of the insulating state
[32]. In the middle of the scan we observe that the CO2 laser used in the
experiment is also capable of inducing the IMT. This can be seen by the sudden
switching of a domain (indicated by a yellow arrow). Our experimental geometry
allows us to determine the laser-induced heating by effectively using the
induced change in resistivity as thermometer.

For this, we start by cooling the sample to 283 K and then slowly heat the
film to a selected temperature. With the AFM engaged, we turn the CO2 laser
‘on’ and ‘off’ with a flip mounted mirror. The effective temperature increase
in the film can now be estimated by monitoring the change in resistivity that
is measured in the dark and illuminated state. To convert resistivity to
temperature readings, we invert the resistivity data of Fig. 1b at the
temperatures shown by dark-red solid circles. Figure 1e shows the resulting
$\Delta T$ traces as function of time. Depending on the starting temperature
the effect of the laser is to increase the temperature of the film by as much
as 0.6 K for the lowest measured temperature. The magnitude of $\Delta T$
decreases with increasing starting temperature. This is likely related to the
changes in absorption coefficient, specific heat and thermal conductivity that
take place near the IMT. We notice that close to $T_{H}$ the resistivity does
not return to the original value, resulting in a finite $\Delta T$ also in the
‘off’ state. This can be related to the switching of a large domain to the
metallic state induced by the laser, similar to what is observed in Fig. 1d.
As we will follow the IMT using sSNOM and would like to exclude sudden
switching resulting from laser heating, we carry out all subsequent
experiments while cooling from the metallic state. For every measurement, we
set the temperature and record the two-point resistance between contacts at
the top and bottom of the image. The $V_{S}/I_{S}$ values obtained in this way
are shown in Fig. 1c as yellow squares. Note that they cannot be directly
compared to the four-point resistance (solid lines) since the two-point
resistance probes a different area of the surface.

Figure 2 shows the main experimental result of this paper: sSNOM images
recorded as function of temperature (top row) and as function of applied
voltage $V_{S}$ (bottom row). We first focus on the evolution of the near-
field signal, recorded while cooling down from 343 K. Initially, the near-
field response is fully metallic, but near the phase transition, some domains
start to become insulating. As has been observed previously [25], thin films
often consist of domains that can have slightly different critical
temperatures. In films with a thickness below 15 nm, the domains can become
very large and even occupy the whole film.

The 294 K panel shows an almost completely metallic film (corresponding to
yellow in our color scale), with thin lines (dark) that follow the white
domain lines observed in the topography of Fig. 1a. We note again that these
lines are thought to be VO2 in a monoclinic phase. At 288.5 K meandering,
insulating filaments emerge that creep in from the domain boundary. These
filaments permeate the domain as temperature is further decreased. One novel
aspect compared to previous experiments [32, 33, 34, 40, 41, 37] is that our
films consist of large single crystalline domains that are fully strained and
thus already in the rutile phase. The transition within each domain is
therefore purely electronic and this reflects itself in only weak pinning of
the nucleation sites of the filaments. As the experiment is repeated, the
formation of filaments starts from different points on the boundary.

In the bottom row panels of Fig. 2 we contrast the temperature dependence of
the near-field signal with the voltage dependence of the signal. As starting
point we first cool the film to 283 K and subsequently heat the film to 293.2
K, two degrees below $T_{H}$. Without applying any voltage, we observe that
some domains are already metallic (panel labelled 0.0 V). Comparing the
$V_{S}$ = 0 V data with the data presented in the top row of Fig. 2, we note
that the formation of the metallic state is reversed as compared to the
formation of the insulating state. One can still see insulating filaments
within the domain that are absorbed in the metallic matrix as the voltage is
increased. As we increase the voltage from $V_{S}$ = 0 V to $V_{S}$ = 0.8 V,
we observe two small steps in the current that flows between the contacts.
This change in current appears to correspond to the switching of two complete
domains: one in the middle of our field of view and one on the far left side
of it. Time domain reflectivity experiments suggest that the formation of
filaments within a domain can take place on microsecond time scales [19],
which is too fast for our scanning method to register and we consequently only
see the end state in which the domain is fully metallic.

While performing the sSNOM measurements, we noticed a large step in current is
observed at $V_{S}$ = 1.15 V, at a lower threshold voltage than the step seen
in Fig. 1c. This offset in threshold voltage is due to the additional heating
induced by the CO2 laser as can be verified by repeating the experiment with
the laser in the ‘off’ state. In the $V_{S}$ = 1.3 V data presented in Fig. 2
we see that all domains in our field of view are fully in the metallic state,
with the exception of a few narrow domains in the top right corner. We also
note that the average intensity of the domains increases and that insulating
filaments within a domain have disappeared.

Unexpectedly, only a small change is observed when the voltage is set to zero,
$V_{S}$ = 0* V. The most notable change is that the lines between domains
become more prominent and increase in width. However, the average sSNOM
intensity within domains hardly decreases. We monitored the persistence of
this state over time using a small probing current (1 $\mu$A). We observed no
significant change in the resistivity over a 17 hour period in this way. We
have therefore clearly identified the source for the forming effect in the
first cycle: starting from a mostly insulating phase ’low’ state (0.0 V),
metallic domains form upon application of a voltage (0.8 V). As the voltage
increases, more domains become conducting and the device changes to a ’high’
state when all domains between the contacts are in the metallic state (1.2 -
1.3 V). As the device is turned off, the interior of the domains remain
metallic while the domains are isolated from each other through narrow
insulating regions. When we go through a second cycle, these insulating
regions will again become metallic giving rise to the small steps seen in
cycle 2 and 3 in Fig. 1c).

Figure 3: (a): histograms corresponding to the sSNOM images recorded during
$I(V)$ cycles. The signal below 0.1 V corresponds to insulating domains. At
1.2 V there is a notable shift in the position of the high signal maximum.
When the voltage is set to zero, a small insulating component reappears,
indicated by the arrow. (b): Comparison of the relative changes
$P(V_{S})/P(V\,=\,0)$ of the resistance and insulating area. (c): topography
measured at 5 V and 292 K partly overlayed with S2/S2,Au. The large height
differences (8 nm) are not observed at lower voltages. Scale bar corresponds
to 1$\mu$m. (d): comparison of monoclinic areas around domain lines observed
in topography at 294 K, at $V_{S}$ = 1.3 V and $V_{S}$ = 0* V. The topography
does not change at $V_{S}$ = 1.3 V, but the surrounding area noticeably
undergoes an IMT. Scale bars correspond to 500 nm.

A more quantitative picture of the changes underlying the $I(V)$
characteristics can be obtained by plotting the intensity variation within a
field of view in a histogram representation. Fig. 3a shows the histograms for
the (extended) series of measurements presented in the bottom row of Fig. 2.
At $V_{S}$ = 0 V, most of the domains are insulating and this is represented
by a large, sharp peak in the histogram with average signal intensity S2/S2,Au
$\approx$ 0.02. A broader peak centred around S2/S2,Au $\approx$ 0.25 can also
be seen and corresponds to the metallic domains. As $V_{S}$ is increased, some
weight shifts from the S2/S2,Au $\approx$ 0.02 peak to S2/S2,Au $\approx$ 0.25
until the threshold voltage $V_{S}$=1.15 is reached. As can be seen from the
histogram, at $V_{S}$ = 1.2 V the maximum around S2/S2,Au $\approx$ 0.25
suddenly shifts to higher signal values (S2/S2,Au = 0.35) and the sharp peak
at S2/S2,Au = 0.02 is strongly reduced. Finally at $V_{S}$ = 1.3 V the
remaining insulating regions around the domain lines turn metallic and the
S2/S2,Au $\approx$ 0.02 peak disappears. When the voltage is set to $V_{S}$ =
0, a small signal at S2/S2,Au $\approx$ 0.02 reappears, signalling a small
contribution from the insulating phase.

The mesoscopic transport behaviour of the film can be largely predicted by the
changes taking place in the histograms. Figure 3b compares relative changes in
the insulating area at a particular voltage to the insulating area at $V_{S}$
= 0 V (e.g. $A_{ins.}(V_{S})/A_{ins.}(V_{S}\,=\,0))$, with the relative change
in resistance ($R(V_{S})/R(V_{S}\,=\,0$). To obtain the relative change in
insulating area, $A_{ins.}(V_{S})$, we integrate the histograms of panel 3a up
to S2/SAu = 0.1. As Fig. 3b shows, the changes in resistance are accompanied
by distinct changes in the total area of insulating domains. Small differences
(for example, the step in resistance around $V_{S}$ = 0.8 V) are due to the
fact that some domains that contribute to the total current path fall outside
our field of view.

Structural effects have little influence on the mesoscopic properties of the
film, as demonstrated in Fig. 3c. Here we show a partial overlay of near-field
(right half) on the topography (left half) under the application of $V_{S}$ =
5 V at 292.5 K. At such large applied voltages, which were applied only as our
final measurements, it is sometimes seen that the film partly detaches from
the underlying substrate. Despite the 8 nm height variations between some
domains, we observed only a weak impact on the resistance or the near-field
signal. The dominant effect underlying the memristive device in our
experiments, is therefore consistent with Joule heating [29, 30, 15, 31]. In
contrast to earlier work [15], we find that the current flow between contacts
selectively heats domains above their transition temperature. This points to
small variations of $T_{H}$ in individual domains as has been observed
previously [25]. Although we cannot completely exclude electric field effects,
we note that reversing the sign of the voltage resulted in the same overall
behaviour of the current and near-field signal.

It has been pointed out previously that strain release in thicker films will
lead to domain formation and that domain boundaries can become monoclinic or
will have lower strain as compared to the larger domain areas [25]. Our direct
measurement of the local optical response shows that these regions are quite
sharp (Fig. 3d). Above the IMT, the data taken at 294 K shows large metallic
domains separated by domain lines from which a narrow insulating region
extends. The spatial resolution in our experiments is approximately 20 nm,
enabling us to determine that the insulating regions along the domain lines
are 100 - 300 nm wide. Interestingly, the physical domain lines observed in
topography are much sharper than this as Fig.’s 1a and 3c demonstrate. As
temperature is increased, these regions eventually turn metallic as well. In
areas of the film with a large domain line density, the intermediate area has
a distinctly higher critical temperature as can be clearly seen in the 294 K
data presented in Fig. 2 (top right corner). Similarly, the small,
reproducible steps in cycle 2 and cycle 3 (Fig. 3d), are a result of the
switching of insulating domain lines separating the large metallic domains. To
conclude, we note that the near-field signal near the insulating strips is a
bit lower, indicating perhaps weak effects of reduced strain within the domain
itself.

To summarise, nanoscale near-field imaging of in operando devices is a
feasible and promising new tool to probe the connection between microscopic
electronic properties and mesoscopic transport. When applied to rutile VO2
devices, it shows that a memory effect is created by persistent switching of
large domains. Our 20 nm spatial resolution allows us to demonstrate that
$I(V)$ characteristic can be accurately explained from the behaviour of 100 -
300 nm wide insulating strips that are connected to domain boundaries in the
film.

## References

  * Huth  _et al._ [2012a] F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, Nano-FTIR Absorption Spectroscopy of Molecular Fingerprints at 20 nm Spatial Resolution, Nano Letters 12, 3973 (2012a).
  * Huth  _et al._ [2012b] F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, Nano-FTIR Absorption Spectroscopy of Molecular Fingerprints at 20 nm Spatial Resolution, Nano Letters 12, 3973 (2012b).
  * Xu and Raschke [2013] X. G. Xu and M. B. Raschke, Near-Field Infrared Vibrational Dynamics and Tip-Enhanced Decoherence, Nano Letters 13, 1588 (2013).
  * Wagner  _et al._ [2014] M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro-Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, Ultrafast and Nanoscale Plasmonic Phenomena in Exfoliated Graphene Revealed by Infrared Pump–Probe Nanoscopy, Nano Letters 14, 894 (2014).
  * Dönges  _et al._ [2016] S. A. Dönges, O. Khatib, B. T. O’Callahan, J. M. Atkin, J. H. Park, D. Cobden, and M. B. Raschke, Ultrafast Nanoimaging of the Photoinduced Phase Transition Dynamics in VO ${}_{\textrm{2}}$, Nano Lett. 16, 3029 (2016).
  * Stinson  _et al._ [2018] H. T. Stinson, A. Sternbach, O. Najera, R. Jing, A. S. Mcleod, T. V. Slusar, A. Mueller, L. Anderegg, H. T. Kim, M. Rozenberg, and D. N. Basov, Imaging the nanoscale phase separation in vanadium dioxide thin films at terahertz frequencies, Nature Communications 9, 3604 (2018).
  * Fei  _et al._ [2012] Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, Gate-tuning of graphene plasmons revealed by infrared nano-imaging, Nature 487, 82 (2012).
  * Chen  _et al._ [2012] J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Optical nano-imaging of gate-tunable graphene plasmons, Nature 487, 77 (2012).
  * Yang  _et al._ [2013] H. U. Yang, E. Hebestreit, E. E. Josberger, and M. B. Raschke, A cryogenic scattering-type scanning near-field optical microscope, Rev. Sci. Inst. 84, 023701 (2013).
  * McLeod  _et al._ [2017] A. S. McLeod, E. van Heumen, J. G. Ramirez, S. Wang, T. Saerbeck, S. Guenon, M. Goldflam, L. Anderegg, P. Kelly, A. Mueller, M. K. Liu, I. K. Schuller, and D. N. Basov, Nanotextured phase coexistence in the correlated insulator V2O3, Nature Physics 13, 80 (2017).
  * Liu  _et al._ [2017] M. Liu, A. J. Sternbach, and D. N. Basov, Nanoscale electrodynamics of strongly correlated quantum materials, Rep. Prog. Phys. 80, 014501 (2017).
  * Chen  _et al._ [2019] X. Chen, D. Hu, R. Mescall, G. You, D. N. Basov, Q. Dai, and M. Liu, Modern Scattering‐Type Scanning Near‐Field Optical Microscopy for Advanced Material Research, Adv. Mater. 31, 1804774 (2019).
  * You Zhou and Ramanathan [2015] You Zhou and S. Ramanathan, Mott Memory and Neuromorphic Devices, Proc. IEEE 103, 1289 (2015).
  * Cui  _et al._ [2018] Y. Cui, Y. Ke, C. Liu, Z. Chen, N. Wang, L. Zhang, Y. Zhou, S. Wang, Y. Gao, and Y. Long, Thermochromic VO2 for Energy-Efficient Smart Windows, Joule 2, 1707 (2018).
  * Kumar  _et al._ [2013] S. Kumar, M. D. Pickett, J. P. Strachan, G. Gibson, Y. Nishi, and R. S. Williams, Local Temperature Redistribution and Structural Transition During Joule‐Heating‐Driven Conductance Switching in VO ${}_{\textrm{2}}$, Adv. Mater. 25, 6128 (2013).
  * Madan  _et al._ [2015] H. Madan, M. Jerry, A. Pogrebnyakov, T. Mayer, and S. Datta, Quantitative Mapping of Phase Coexistence in Mott-Peierls Insulator during Electronic and Thermally Driven Phase Transition, ACS Nano 9, 2009 (2015).
  * del Valle  _et al._ [2019] J. del Valle, P. Salev, F. Tesler, N. M. Vargas, Y. Kalcheim, P. Wang, J. Trastoy, M.-H. Lee, G. Kassabian, J. G. Ramírez, M. J. Rozenberg, and I. K. Schuller, Subthreshold firing in Mott nanodevices, Nature 569, 388 (2019).
  * Rana  _et al._ [2020] A. Rana, C. Li, G. Koster, and H. Hilgenkamp, Resistive switching studies in VO2 thin films, Scientific Rep. 10, 3293 (2020).
  * del Valle  _et al._ [2021] J. del Valle, N. M. Vargas, R. Rocco, P. Salev, Y. Kalcheim, P. N. Lapa, C. Adda, M.-H. Lee, P. Y. Wang, L. Fratino, M. J. Rozenberg, and I. K. Schuller, Spatiotemporal characterization of the field-induced insulator-to-metal transition, Science 373, 907 (2021).
  * Nikoo  _et al._ [2022] M. S. Nikoo, R. Soleimanzadeh, A. Krammer, Y. Park, J. Son, A. Schueler, P. Moll, and E. Matioli, Electrical control of glass-like dynamics in vanadium dioxide for data storage and processing, Nature electronics 5, 596 (2022).
  * Gao  _et al._ [2022] X. Gao, C. M. M. Rosário, and H. Hilgenkamp, Multi-level operation in VO ${}_{\textrm{2}}$ -based resistive switching devices, AIP Advances 12, 015218 (2022).
  * Cavalleri  _et al._ [2001] A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, Femtosecond Structural Dynamics in VO 2 during an Ultrafast Solid-Solid Phase Transition, Phys. Rev. Lett. 87, 237401 (2001).
  * Muraoka and Hiroi [2002] Y. Muraoka and Z. Hiroi, Metal–insulator transition of VO2 thin films grown on TiO2 (001) and (110) substrates, Appl. Phys. Lett. 80, 583 (2002).
  * Kittiwatanakul  _et al._ [2014] S. Kittiwatanakul, S. A. Wolf, and J. Lu, Large epitaxial bi-axial strain induces a Mott-like phase transition in VO ${}_{\textrm{2}}$, Applied Physics Letters 105, 073112 (2014).
  * Rodríguez  _et al._ [2020] L. Rodríguez, E. del Corro, M. Conroy, K. Moore, F. Sandiumenge, N. Domingo, J. Santiso, and G. Catalan, Self-Pixelation Through Fracture in VO ${}_{\textrm{2}}$ Thin Films, ACS Appl. Electron. Mater. 2, 1433 (2020).
  * Gopalakrishnan  _et al._ [2009] G. Gopalakrishnan, D. Ruzmetov, and S. Ramanathan, On the triggering mechanism for the metal–insulator transition in thin film VO2 devices: electric field versus thermal effects, J. Mater. Sci. 44, 5345 (2009).
  * Goldflam  _et al._ [2014] M. D. Goldflam, M. K. Liu, B. C. Chapler, H. T. Stinson, A. J. Sternbach, A. S. McLeod, J. D. Zhang, K. Geng, M. Royal, B.-J. Kim, R. D. Averitt, N. M. Jokerst, D. R. Smith, H.-T. Kim, and D. N. Basov, Voltage switching of a VO ${}_{\textrm{2}}$ memory metasurface using ionic gel, Appl. Phys. Lett. 105, 041117 (2014).
  * Sternbach  _et al._ [2021] A. J. Sternbach, F. L. Ruta, Y. Shi, T. Slusar, J. Schalch, G. Duan, A. S. McLeod, X. Zhang, M. Liu, A. J. Millis, H.-T. Kim, L.-Q. Chen, R. D. Averitt, and D. N. Basov, Nanotextured Dynamics of a Light-Induced Phase Transition in VO ${}_{\textrm{2}}$, Nano Lett. 21, 9052 (2021).
  * Kim  _et al._ [2010] J. Kim, C. Ko, A. Frenzel, S. Ramanathan, and J. E. Hoffman, Nanoscale imaging and control of resistance switching in VO2 at room temperature, Appl. Phys. Lett. 96, 213106 (2010).
  * Zhong  _et al._ [2011] X. Zhong, X. Zhang, A. Gupta, and P. LeClair, Avalanche breakdown in microscale VO ${}_{\textrm{2}}$ structures, J. Appl. Phys. 110, 084516 (2011).
  * Zimmers  _et al._ [2013] A. Zimmers, L. Aigouy, M. Mortier, A. Sharoni, S. Wang, K. G. West, J. G. Ramirez, and I. K. Schuller, Role of Thermal Heating on the Voltage Induced Insulator-Metal Transition in VO 2, Phys. Rev. Lett. 110, 056601 (2013).
  * Qazilbash  _et al._ [2007] M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, Mott Transition in VO ${}_{\textrm{2}}$ Revealed by Infrared Spectroscopy and Nano-Imaging, Science 318, 1750 (2007).
  * Jones  _et al._ [2010] A. C. Jones, S. Berweger, J. Wei, D. Cobden, and M. B. Raschke, Nano-optical investigations of the metal-insulator phase behavior of individual vo2 microcrystals, Nano Lett. 10, 1574 (2010).
  * Atkin  _et al._ [2012] J. M. Atkin, S. Berweger, E. K. Chavez, M. B. Raschke, J. Cao, W. Fan, and J. Wu, Strain and temperature dependence of the insulating phases of VO 2 near the metal-insulator transition, Phys. Rev. B 85, 020101 (2012).
  * Liu  _et al._ [2013a] M. K. Liu, M. Wagner, E. Abreu, S. Kittiwatanakul, A. McLeod, Z. Fei, M. Goldflam, S. Dai, M. M. Fogler, J. Lu, S. A. Wolf, R. D. Averitt, and D. N. Basov, Anisotropic Electronic State via Spontaneous Phase Separation in Strained Vanadium Dioxide Films, Phys. Rev. Lett. 111, 096602 (2013a).
  * Liu  _et al._ [2014] M. Liu, M. Wagner, J. Zhang, A. McLeod, S. Kittiwatanakul, Z. Fei, E. Abreu, M. Goldflam, A. J. Sternbach, S. Dai, K. G. West, J. Lu, S. A. Wolf, R. D. Averitt, and D. N. Basov, Symmetry breaking and geometric confinement in VO ${}_{\textrm{2}}$ : Results from a three-dimensional infrared nano-imaging, Appl. Phys. Lett. 104, 121905 (2014).
  * O’Callahan  _et al._ [2015] B. T. O’Callahan, A. C. Jones, J. Hyung Park, D. H. Cobden, J. M. Atkin, and M. B. Raschke, Inhomogeneity of the ultrafast insulator-to-metal transition dynamics of VO2, Nature Comm. 6, 6849 (2015).
  * Berglund [1969] C. Berglund, Thermal filaments in vanadium dioxide, IEEE Trans. Electron Devices 16, 432 (1969).
  * Lysenko  _et al._ [2006] S. Lysenko, A. Rua, V. Vikhnin, J. Jimenez, F. Fernandez, and H. Liu, Light-induced ultrafast phase transitions in VO2 thin film, App. Surf. Sc. 252, 5512 (2006).
  * Liu  _et al._ [2013b] M. K. Liu, M. Wagner, E. Abreu, S. Kittiwatanakul, A. Mcleod, Z. Fei, M. Goldflam, S. Dai, M. M. Fogler, J. Lu, S. A. Wolf, R. D. Averitt, and D. N. Basov, Anisotropic Electronic State via Spontaneous Phase Separation in Strained Vanadium Dioxide Films, Phys. Rev. Lett. 111, 096602 (2013b).
  * Liu  _et al._ [2015] M. Liu, A. J. Sternbach, M. Wagner, T. V. Slusar, T. Kong, S. L. Bud’ko, S. Kittiwatanakul, M. M. Qazilbash, A. McLeod, Z. Fei, E. Abreu, J. Zhang, M. Goldflam, S. Dai, G.-X. Ni, J. Lu, H. A. Bechtel, M. C. Martin, M. B. Raschke, R. D. Averitt, S. A. Wolf, H.-T. Kim, P. C. Canfield, and D. N. Basov, Phase transition in bulk single crystals and thin films of V O 2 by nanoscale infrared spectroscopy and imaging, Phys. Rev. B 91, 245155 (2015).