# Non-thermal light-assisted resistance collapse in a V2O3-based Mottronic
device

A. Ronchi<EMAIL_ADDRESS>Department of Physics and Astronomy, KU
Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium  Department of Mathematics
and Physics, Università Cattolica del Sacro Cuore, Brescia I-25121, Italy
ILAMP (Interdisciplinary Laboratories for Advanced Materials Physics),
Università Cattolica del Sacro Cuore, Brescia I-25121, Italy  P. Franceschini
Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001
Leuven, Belgium  Department of Mathematics and Physics, Università Cattolica
del Sacro Cuore, Brescia I-25121, Italy  ILAMP (Interdisciplinary Laboratories
for Advanced Materials Physics), Università Cattolica del Sacro Cuore, Brescia
I-25121, Italy  P. Homm  Department of Physics and Astronomy, KU Leuven,
Celestijnenlaan 200D, 3001 Leuven, Belgium  M. Gandolfi  CNR-INO, Via Branze
45, 25123 Brescia, Italy  Department of Information Engineering, University of
Brescia, Via Branze 38, 25123 Brescia, Italy  G. Ferrini  Department of
Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia
I-25121, Italy  ILAMP (Interdisciplinary Laboratories for Advanced Materials
Physics), Università Cattolica del Sacro Cuore, Brescia I-25121, Italy  S.
Pagliara  Department of Mathematics and Physics, Università Cattolica del
Sacro Cuore, Brescia I-25121, Italy  ILAMP (Interdisciplinary Laboratories for
Advanced Materials Physics), Università Cattolica del Sacro Cuore, Brescia
I-25121, Italy  F. Banfi  Université de Lyon, Institut Lumière Matiére (iLM),
Université Lyon 1 and CNRS, 10 rue Ada Byron, 69622 Villeurbanne Cedex, France
M. Menghini  IMDEA Nanociencia, Cantoblanco, 28049 Madrid, Spain  Department
of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven,
Belgium  J-.P. Locquet  Department of Physics and Astronomy, KU Leuven,
Celestijnenlaan 200D, 3001 Leuven, Belgium  C. Giannetti
<EMAIL_ADDRESS>Department of Mathematics and Physics,
Università Cattolica del Sacro Cuore, Brescia I-25121, Italy  ILAMP
(Interdisciplinary Laboratories for Advanced Materials Physics), Università
Cattolica del Sacro Cuore, Brescia I-25121, Italy

###### Abstract

The insulator-to-metal transition in Mott insulators is the key mechanism for
a novel class of electronic devices, belonging to the Mottronics family.
Intense research efforts are currently devoted to the development of specific
control protocols, usually based on the application of voltage, strain,
pressure and light excitation. The ultimate goal is to achieve the complete
control of the electronic phase transformation, with dramatic impact on the
performance, for example, of resistive switching devices. Here, we investigate
the simultaneous effect of external voltage and excitation by ultrashort light
pulses on a single Mottronic device based on a V2O3 epitaxial thin film. The
experimental results, supported by finite-element simulations of the thermal
problem, demonstrate that the combination of light excitation and external
electrical bias drives a volatile resistivity drop which goes beyond the
combined effect of laser and Joule heating. Our results impact on the
development of protocols for the non-thermal control of the resistive
switching transition in correlated materials.

##  I  Introduction

Mott insulators are a class of quantum materials exhibiting the most promising
properties and functionalities for the next generation of solid-state devices
belonging to the Mottronics familyTokura2017 ; Yang2011 ; Zhang2014 ;
Basov2017 . Correlated vanadium-oxides have been intensively studied due to
the possibility of selectively controlling the resistive switching process at
the core of resitive memories and neuromorphic computingZhou2015 ; Janod2015 ;
delValle2018 ; Salev2019 . The conventional route to control the resistive
switching dynamics is based on the tuning of chemical dopingKuwamoto1980 ;
Homm2015 ; delvalle2017 , temperature Ronchi2019 ; Mcleod2016 ,
pressureMcWhan1969 ; Jayaraman1970 ; Valmianski2017 ; Limelette89 ,
strainDillemans2014 ; Lee2018 ; Kalcheim2019  and on the application of
external electric fieldsStoliar2013 ; Guenon2013 ; Mazza2016 ; DelValle2019 ;
Kalcheim2020 . More recently, the sudden excitation via ultrashort laser
pulsesMansart2010 ; Liu2011 ; Abreu2015 ; Morrison2014 ; Abreu2017 ; Lantz2017
; Ronchi2019 ; Otto2019 ; Giorgianni2019  has been introduced as a novel
control parameter, although the nature of the photoinduced insulator-to-metal
transition is still subject of intense debate. Much effort has been so far
dedicated to the study of the transient optical, electronic and lattice
propertiesMansart2010 ; Liu2011 ; Abreu2015 ; Morrison2014 ; Abreu2017 ;
Lantz2017 ; Ronchi2019 ; Otto2019 ; Giorgianni2019  and on the role of
intrinsic nanoscale inhomogeneitiesLupi2010 ; Mcleod2016 ; Ronchi2019  with
the goal of understanding to what extent the photoinduced transition is
similar to the thermally driven one. In contrast, little is known about the
actual resistive state that is induced by light excitation possibly combined
with external voltage. Recent theoretical works have suggested that, in the
vicinity of the insulator-metal coexisting region, the application of
voltageMazza2016  and the excitation with light pulses capable of manipulating
the band occupationSandri2015 ; Ronchi2019 , can lead to the weakening of the
insulating state and, eventually, to the complete collapse of the Mott
insulating phase and the consequent resistive switching along a non-thermal
pathway.

Here we developed a Mottronic device, based on a micro-bridged V2O3 epitaxial
thin film, in which the resistance state consequent to a controlled excitation
by trains of ultrashort light pulses can be measured. V2O3 is a prototypical
Mott insulator that exhibits a first-order Insulator-to-Metal transition (IMT)
occurring at $T_{IMT}$ $\sim$ 170 $\mathrm{K}$ and characterized by a
resistivity change of several orders of magnitudeMcWhan1969 ; Jayaraman1970 ;
Limelette89 . When a voltage larger than a temperature-dependent threshold
$\Delta V_{th}$ is applied in the insulating state ($T<T_{IMT}$), the device
undergoes a resistive switching process, i.e. the resistance suddenly drops to
the metallic value. However, the switching process in V2O3 devices is
associated to the formation of micrometric conductive filamentsKalcheim2020 ,
which usually makes the evaluation of the local heating and the investigation
of the thermal nature of the dynamics rather difficult. In order to avoid this
additional complexity, we investigate the light induced volatile resistance
drop for different applied voltages, always smaller than $\Delta V_{th}$. This
below-threshold resistance drop thus provides information about the weakening
of the insulating phase, triggered by the combined voltage-light excitation,
while avoiding the formation of the conductive channels associated to the
resistive switching process. Starting from the resistance vs temperature
calibration curve of the device, we are able to compare the photoinduced
resistivity drop to the local heating effect, which is carefully estimated by
finite-element simulations. Our main results can be summarized as follows. The
application of a sufficiently long train of light pulses alone drives a
volatile resistance drop that is compatible with that predicted by finite-
element simulations of the thermal problem. The minimum number of pulses
necessary to observe a significant effect suggests that the light-induced
local heating is mediated by the electronic specific heat, which becomes
extremely large as $T_{IMT}$ is approached. Furthermore, when a significant
below-threshold electrical bias ($\Delta V$=0.5 V) is applied, the light-
induced volatile drop of the resistance is twice than what is expected by
considering both the laser-induced and Joule heating. This result leads to the
conclusion that the combined voltage-light excitation protocol makes the
system more fragile towards the collapse of the insulating electronic phase.

##  II Methods

###  II.1 Mottronic device

An epitaxial V2O3 film with thickness $d$=67 nm is deposited by oxygen-
assisted molecular beam epitaxy (MBE) in a vacuum chamber with a base pressure
of $10^{-9}$ Torr. A 37 $\mathrm{n}\mathrm{m}$ Cr2O3 buffer layer is
interposed between the film and the substrate to minimise lattice mismatch and
optimise strain relaxation in the film. A (0001)-Al2O3 substrate is used
without prior cleaning and is slowly heated to a growth temperature of 700
$\mathrm{\SIUnitSymbolCelsius}$. Vanadium is evaporated from an electron gun
with a deposition rate of 0.1
$\mathrm{\SIUnitSymbolAngstrom}\text{\,}{\mathrm{s}}^{-1}$, and an oxygen
partial pressure of $6.2\cdot 10^{-6}$ Torr is used during the growth
Dillemans2014 . Under these conditions, a single crystalline film with the
$c$-axis oriented perpendicular to the surface is obtained. A micro bridge,
constituted by 40 $\mathrm{n}\mathrm{m}$ Au/5 $\mathrm{n}\mathrm{m}$ Ti thick
electrodes with $w$=50 $\mu\mathrm{m}$ width and $s$=2 $\mu\mathrm{m}$
separation, is nanopatterned on the film surface, as shown in Fig. 1a.
Temperature-dependent resistivity measurements (see Fig. 1b) are performed
using a Keithley Sourcemeter 2634B in the 2-points configuration across the
Au/Ti electrodes. The device temperature is controlled by a closed cycle
cryostat equipped with a heater. The temperature sweep rate is set to 0.5
$\mathrm{K}$ per minute. When cooled down, the device undergoes the metal-to-
insulator transition, characterized by a resistance increase of almost three
order of magnitudes. In our device the resistance ranges from 20 $\Omega$ at
room temperature (metallic state) to 130 $\mathrm{k}\Omega$ at $T$=140 K
(insulating state). The heating and cooling branches evidence the typical
hysteresis cycle of the IMT, which spans the insulator/metal coexistence
region from 155 to 185 K. In the following, we will consider
$T_{IMT}\simeq$170 K as the temperature corresponding to the midpoint of the
heating branch of the hysteresis cycle.

###  II.2 Photo-induced resistance drop measurements

---
Figure 1:  Working principle of the experiment. (a) Left: Cartoon of the
experimental set-up. A finite train of laser pulses ($\hbar\omega=1.55$
$\mathrm{eV}$, $50$ $\mathrm{f}\mathrm{s}$ temporal width, $\nu=25$
$\mathrm{k}\mathrm{H}\mathrm{z}$) is used to photoexcite the device. The
change in the 2-points resistance of the device is simultaneously measured
before, during and after the laser excitation by means of Au/Ti electrodes.
The contact resistance can be neglected since is very small ($\sim$ 5
$\mathrm{\SIUnitSymbolOhm}$) with respect to the V2O3 bridge resistance
($\sim$ 15 $\mathrm{k}\mathrm{\SIUnitSymbolOhm}$). Right: Microscopic image of
the device used during the experiment. (b) Equilibrium 2-points resistance
hysteresis measured as function of the temperature. The red (blue) arrows
indicate the heating (cooling) branch. Inset: 2-points I-V curve showing
volatile resistive switching at $T$=160 K. The measurement has been performed
through the 2 $\mu\mathrm{m}$ gap shown in (a). (c) Relative variation of
resistance measured across the device as a function of the time delay at the
base temperature $T_{0}$=161.6 K. The time zero corresponds to the moment when
the first pulse of the laser train arrives. (d) Result of the conversion of
resistance drop measurements (see panel (c)) into effective local temperature
(yellow solid line). The resistance vs temperature curve shown in Fig.1(b) has
been inverted to obtain, for each value of resistance, the corresponding local
temperature. As explained in the main text, the cooling down process takes
place along a resistance-temperature curve which differs from the equilibrium
one reported in panel (b). The dashed line, corresponding to the cooling down
dynamics of the system, is the hypothetical local temperature obtained from
the heating branch of the equilibrium resistance-temperature curve, but does
not necessarily represents the actual local effective temperature of the
system.

Resistance measurements are combined with light excitation by focusing a train
of infrared pulses (0.4 $\mu\mathrm{J}$, 50 $\mathrm{f}\mathrm{s}$) at 800
$\mathrm{n}\mathrm{m}$ wavelength (1.55 eV photon energy) generated by an
optical parametric amplifier pumped by an Yb-laser system. A pulse picker
allows to control both the repetition rate, set to 25
$\mathrm{k}\mathrm{H}\mathrm{z}$, and the total number of pulses impinging on
the sample. The laser output is focused on the device by a 10
$\mathrm{c}\mathrm{m}$ lens. The Full-Width-Half-Maximum (FWHM) of the spot
size on the device is 50 $\mu\mathrm{m}$, as measured using the knife-edge
technique. The pump incident fluence on the device is of the order of 0.2
mJ/cm2, which is below the threshold necessary to photoinduce the complete
insulator-to-metal transitionRonchi2019 . In Fig. 1c we show the typical
resistance drop measured after excitation with a controlled number of light
pulses (200 kpulses at 25 kHz rep. rate). Prior to the experiment the device
is cooled down to 100 K and then heated up to $T\simeq$160 K, i.e. in the
insulator-metal coexistence region. Before light excitation, the system is
thus in a high resistivity state along the heating branch of the hysteresis
curve shown in Fig. 1b. Laser excitation is then switched on and the time-
dependent resistance is obtained by measuring the current flowing across the
bridge at a fixed applied voltage ($\Delta V$=5 mV) and at the nominal
temperature $T$=160 K. After 8 s, i.e. at the end of the pulse train, the
resistance drops by 8 % with respect to the initial value. Once the light
excitation is removed, the relative resistance variation, i.e. $\Delta R/R$,
starts to decrease, until it reaches a plateau corresponding to a non-volatile
change of about 3%. The explanation of this effect resides in the inherent
hysteresis of the IMT (see Fig.1 b): after the laser-induced warming up, which
is not enough to drive the system out of the hysteresis region, the cooling-
down takes place along a curve located somewhere between the complete warming
up and cooling down curves (red and blue curves in Fig. 1b). The final
resistance value is therefore smaller than the initial value, although the
initial temperature is recovered. In order to restore the initial resistance
value, the device must undergo a complete thermal cycle, corresponding to
heating up to 300 K, followed by cooling down to 100 K and further heating up
to $T\simeq$160 K. The same thermal cycle protocol is applied before any of
the resistance drop measurements reported in the following.

The resistance-temperature curve shown in Fig.1b can be used to retrieve the
precise local effective temperature of the V2O3 device during the light
excitation process, as shown in Fig. 1d. The local effective temperature
during the resistance drop is extracted by interpolating and inverting the
heating branch of the resistance-temperature curve (Fig. 1b). The error
associated to the local effective temperature is obtained by considering the
accuracy of the Keithley Sourcemeter ($\pm$ 0.02 %) in the voltage range used
during the experiments. We stress that the resistance-temperature relation is
single-valued only along the heating branch. Therefore, the resistance value
can be converted in the actual local temperature only during the heating up
process in the 0-8 $\mathrm{s}$ time span. During the cooling down (8-120 ps)
the resistance moves back along a non-equilibrium resistance-temperature
curve, which differs from that used for calibration (Fig. 1b) and cannot
therefore be used to retrieve the actual local temperature.

###  II.3 Finite Elements Method simulation of the thermal problem

---
Figure 2:  Finite elements method simulations. (a) The solid line represents
the temperature increase due to the single pulse excitation (black dashed
area) as function of the time (logarithmic scale). The black arrow indicates
the instant ($t=40$ $\mu\mathrm{s}$) at which the following pulse arrives.
Inset: sketch of the geometry used in the Comsol simulations. The red dot
indicates the point at which the temperature has been evaluated ($r=50$
$\mathrm{n}\mathrm{m}$; $z$=33.5 $\mathrm{n}\mathrm{m}$). (b) The temperature
variation at saturation, induced by $2\cdot 10^{5}$ laser pulses, is shown.
The temperature is evaluated at half of the total thickness, i.e. $r=50$
$\mathrm{n}\mathrm{m}$ and $z$=33.5 $\mathrm{n}\mathrm{m}$. The maximum
temperature reached after the excitation with the pulse train is used as input
to build the curves reported in Fig. 3.

The heating induced by the laser excitation is numerically simulated by
finite-element methods (Comsol Multiphysics). In the simulations we consider
the 67 $\mathrm{n}\mathrm{m}$ thick V2O3 film on top of a 500 $\mu\mathrm{m}$
thick (0001)-Al2O3 substrate. The Cr2O3 buffer-layer is omitted since its
thermal and optical properties are very similar to the sapphire’s ones. The
problem is solved in 2D axial symmetry in a region with 800 $\mu\mathrm{m}$
diameter. A representation of the sample cross section is reported in the
inset of Fig. 2a. Thermal insulating boundary conditions are applied on the
top and lateral boundaries, whereas the sapphire bottom boundary ($z=-500$
$\mu\mathrm{m}$) is kept at the constant temperature $T_{0}=161.6$
$\mathrm{K}$, which corresponds to the actual initial effective temperature of
the device, as extracted from the resistance value.

The thermal problem for single pulse excitation is initially addressed. In
this configuration, a single pulse with temporal and spatial gaussian profiles
matching the experimental ones, excites the sample. We consider an energy
density delivered to the system (0.66
$\mathrm{k}\mathrm{J}\mathrm{/}\mathrm{c}\mathrm{m}^{3}$) such that the time
and spatial integral matches the total energy released by the laser pulse upon
accounting for reflection losses. The estimated energy absorbed within the 67
$\mathrm{n}\mathrm{m}$ V2O3 film is calculated with a multireflection model
(total absorption $A$= 0.22), assuming the optical constants reported in the
literatureQazilbash2008 . Using Fourier’s law, the energy balance within the
volume of the V2O3 film reads:

$-\nabla\cdot\bigl{[}-\kappa(T(r,z,t))\nabla T(r,z,t)\big{]}+\\\
+P(r,z,t)=\rho\ c_{p}((r,z,t))\frac{\partial T(r,z,t)}{\partial t}$ (1)

where $P(r,z,t)$ is the absorbed pulsed power density profile, $\kappa(T)$ is
the temperature dependent thermal conductivityAndreev1978 , $\rho$ the mass
density, and $c_{p}(T)$ the temperature-dependent total specific heat at
constant pressureKeer1976 . For sake of completeness, the parameters used in
the simulation are reported in Table 1.

Table 1: Summary of materials parameters values adopted in the present work for FEM simulations. Parameter | Value | Units | Ref.
---|---|---|---
$c_{p}(T)\big{|}_{V_{2}O_{3}}$ |  $c_{p}$($T$=160 K) =480 | $\mathrm{J}\ \mathrm{k}\mathrm{g}^{-1}\ \mathrm{K}^{-1}$ | Keer1976
|  $c_{p}$($T_{IMT}$)=2400 | $\mathrm{J}\ \mathrm{k}\mathrm{g}^{-1}\ \mathrm{K}^{-1}$ | Keer1976
|  $c_{p}$($T$=190 K)=530 | $\mathrm{J}\ \mathrm{k}\mathrm{g}^{-1}\ \mathrm{K}^{-1}$ | Keer1976
$c_{p}\big{|}_{Al_{2}O_{3}}$ | 776 | $\mathrm{J}\ \mathrm{k}\mathrm{g}^{-1}\ \mathrm{K}^{-1}$ | Weber2001
$\kappa(T)\big{|}_{V_{2}O_{3}}$ |  $\kappa(T)$ ($\sim$3.1 @160 $\mathrm{K}$) | $\mathrm{W}\ \mathrm{m}^{-1}\ \mathrm{K}^{-1}$ | Andreev1978
$\kappa\big{|}_{Al_{2}O_{3}}$ | 35 | $\mathrm{W}\ \mathrm{m}^{-1}\ \mathrm{K}^{-1}$ | Caddeo2017
$\rho_{V_{2}O_{3}}$ | 4870 | $\mathrm{k}\mathrm{g}\ \mathrm{m}^{-3}$ | Weber2001
$\rho_{Al_{2}O_{3}}$ | 3980 | $\mathrm{k}\mathrm{g}\ \mathrm{m}^{-3}$ | Weber2001
Re($\tilde{n}_{V_{2}O_{3}}$) | 1.997 @800 nm | $\mathrm{k}\mathrm{g}\ \mathrm{m}^{-3}$ | Qazilbash2008
Im($\tilde{n}_{V_{2}O_{3}}$) | 0.382 @800 nm | $\mathrm{k}\mathrm{g}\ \mathrm{m}^{-3}$ | Qazilbash2008
Re($\tilde{n}_{Al_{2}O_{3}}$) | 1.76 @800 nm | $\mathrm{k}\mathrm{g}\ \mathrm{m}^{-3}$ | Malitson1962

The following heat flux continuity boundary condition is used at the V2O3/
Al2O3 interface:

$k_{V_{2}O_{3}}\frac{\partial T}{\partial
z}\bigg{|}_{z=0^{+}}=k_{Al_{2}O_{3}}\frac{\partial T}{\partial
z}\bigg{|}_{z=0^{-}}.$ (2)

The initial condition is $T_{0}=161.6$ $\mathrm{K}$ throughout the sample and
the substrate. The equation is solved via the finite element method, covering
a time scale spanning seven orders of magnitude. Since the presence of a
thermal boundary resistance (TBR) at the V2O3/ Al2O3 interface can affect the
temperature of the V2O3 film, simulations with different TBR values were
performed. Assuming a TBR (10-7 m2KW-1) one order of magnitude larger than
typical values reported for similar materialsHamaoui2019 , leads to a
correction of the V2O3 temperature profile smaller than 10%, i.e. within the
experimental uncertainty. The thermal dynamics of the single pulse excitation
is shown in Fig. 2a. We remark that we are interested in thermal dynamics on
timescales longer than the pulse duration and electron-phonon coupling.
Therefore, we assume the complete thermalization between the electron and
lattice subsystems, as implied by the use of the total specific heat and
thermal conductivity values.

After the impulsive energy absorption, the temperature reaches its maximum
value ($\sim$ 250 $\mathrm{K}$) within few picoseconds. Subsequently, the
energy diffusion through the sapphire substrate drives the slower cooling down
process. If we consider the time needed to reduce the initial temperature
variation by a factor 2, we obtain a half-life of about 2 ns. The cooling down
to the initial temperature $T_{0}$=161.6 K is almost completed within $\sim$
40 $\mu\mathrm{s}$, although a small temperature increase $\sim$ 0.04
$\mathrm{K}$ persists. The simulations also demonstrate that, in the device
region, the temperature variation within the V2O3 film is rather homogeneous,
with less than 1% difference between the top and bottom temperatures. For sake
of simplicity, in the following we will refer to the temperature of the point
at 33.5 nm distance from the device surface (see Fig. 2a).

In the multi-pulse experimental configuration, the heating associated to each
pulse accumulates on top of the temperature increase triggered by the previous
ones. Considering a pulse distance of 40 $\mu$s (25 kHz rep. rate), the small
temperature difference accumulated after each pulse leads to a progressive
increase of the local effective temperature, until the external heat flux is
balanced by the dissipation. In this condition, the average effective
temperature does not further increase and it reaches a saturation value, which
ultimately drives the resistance drop across the bridge observed after the
light excitation. For simplicity, the effect of the total thermal heating
induced by the multi-pulse excitation is simulated by considering a laser beam
with step-like temporal profile extending over the same time span of the pulse
train and with the same average power Giannetti2009 ; Banfi2010 ; Caddeo2017 .
An example of the temperature dynamics, for a train of $2\cdot 10^{5}$ pulses,
is shown in Fig. 2b. The heat accumulation leads, at saturation, to a final
temperature of 162.1 $\mathrm{K}$. The discrepancy between this value and the
experimental one (see Fig. 2b) will be clarified in the next section. Once the
input power is removed, the system rapidly cools down to the initial
temperature. For a better comparison with the experimental data, the time-
dependent temperature curves obtained by the simulations and reported in Fig.
2b were subsequently filtered by a low-pass filter with a bandwidth
corresponding to the cut-off frequency (10 Hz) of the electrical circuit used
for the resistance measurements.

##  III Results and discussion

The comparison between the experimental results and the numerical simulations
is shown in Fig. 3a. The applied voltage for the resistance measurements is
$\Delta V$=5 $\mathrm{m}\mathrm{V}$, i.e. much smaller than the threshold
$\Delta V_{th}\simeq$2.5 V necessary to obtain the resistive switching at the
working temperature. The experimental points (green circles) represent the
maximum effective temperature increase, estimated by the volatile resistance
drop described in Sec II.2, as a function of the number of excitation pulses.
We stress that each experimental point is obtained after a complete thermal
cycle, necessary to restore the initial resistance of the device (see Sec.
II.1). The data show that no significant temperature increase is detectable
below $\sim 10^{4}$ pulses. Above this threshold the temperature increases and
saturates after approximately $10^{6}$ pulses. The temperature achieved in the
saturation regime, i.e. when the excitation average power matches the thermal
losses towards the substrate, is $\sim$ 162.06 $\mathrm{K}$.

On general grounds, the dynamics of the V2O3 temperature $T(t)$ can be
described in terms of a simple lumped-element model:

$C_{t}\frac{d(T-T_{0})}{dt}=W-\frac{1}{R_{th}}(T-T_{0})$ (3)

where $T_{0}$=161.6 K is the initial temperature, $C_{t}$ represents the total
heat capacity of the device, $W$ is the total absorbed power, $R_{th}$ is a
constant with the dimensions of a thermal resistance and effectively accounts
for the total heat dissipation. Independently of the specific values of the
effective coefficients entering in the lumped-element model, the general
solution of Eq. 3 is the exponential function $T(t)$=$T_{0}$+$\delta
T_{sat}$(1-$e^{-t/\tau}$), where $\tau$=$R_{th}C_{t}$ is the time constant of
the heating up process and $\delta T_{sat}$=$R_{th}W$ is the temperature
variation at saturation. This exponential function can be used to fit the data
and retrieve the experimental time constant of the system. The red solid line
in Fig. 3a is the exponential fit, which provides $\tau$=18.5$\pm$0.8 s
corresponding to (4.6$\pm$0.2)$\times$105 pulses.

The local effective temperature retrieved by the resistance drop is compared
to the results of calculations of the full thermal problem, as described in
Sec. II.3. The black solid line in Fig. 3a represents the saturation
temperature increase obtained by finite-element calculations, when an average
power corresponding to that of the pulse train exciting the device is
considered. The calculated saturation temperature increase, i.e. $\delta
T_{sat}$=0.5 K perfectly matches the experimental value. Considering that
$\delta T_{sat}$ depends only on the adsorbed power $W$ and on $R_{th}$, we
can conclude that the finite element calculations perfectly account for the
heat dissipation, which is ultimately regulated by the heat diffusion
throughout the V2O3 film and the substrate.

The difference between the calculated and measured time constants of the
exponential heating dynamics can be attributed to an underestimation of the
total heat capacity $C_{t}$. Throughout the calculations of the thermal
problem, we assumed perfect electron-phonon thermalization and we have thus
considered the V2O3 temperature-dependent total specific heat Keer1976 .
Nonetheless, the absorption of each single light pulse is mediated by the
electronic population which undergoes a large temperature increase. The
effective electronic temperature dynamically overcomes the Mott insulator-to-
metal transition temperature $T_{IMT}$, which is accompanied by a divergence
of the electronic effective mass $m^{*}$. Considering that the electronic
specific heat of an electron gas $c_{el}\propto{m^{*}}^{3/2}$, the dynamical
crossing of $T_{IMT}$ is naturally accompanied by a large increase of $c_{el}$
Keer1976 , which is characterized by a narrow cusp centered at $T_{IMT}$ (see
Tab. 1). In the vicinity of the Mott transition, the electron gas thus behaves
like a reservoir capable of absorbing a large quantity of energy but limiting
the impulsive increase of the effective temperature of the electron-phonon
system. Our experimental results are compatible with
$c_{el}$=(30$\pm$6)$\times c_{p}(T_{IMT})\big{|}_{V_{2}O_{3}}$, which suggests
an effective mass increase of 10, perfectly compatible with what recently
observed in VO2 Lee2017  and attributed to the strong electronic correlations.

---
Figure 3:  Comparison between experimental and numerical results. (a) Maximum
variation of the sample’s temperature induced by the laser pulses as function
of the total number of pulses (green circles). The applied voltage is $\Delta
V$=5 mV. The solid black line represents the simulated data where the maximum
temperature has been extracted for each finite number of pulses. The grey area
shows the error interval associated to the model assumptions and numerical
approximations. The red solid line represents the exponential fit to the
experimental data. (b) Maximum laser-induced drop of the device resistance
when a constant voltage bias $\Delta V$=0.5 $\mathrm{V}$ is applied across the
Au/Ti electrodes (green circles). The solid black line represents the outcome
of numerical simulations, from which the expected resistance drop is retrieved
from the local effective heating for each finite number of pulses. The
dissipated power related to the Joule heating has been added to the power
dissipated by the laser excitation. The grey areas show the error interval
associated to the model assumptions and numerical approximations. The solid
red line represents the exponential fit to the experimental data.

Once assessed the validity of the thermal model to evaluate the laser induced
heating in the saturation regime, we can compare the expected thermally
induced resistance drop to what is actually measured when the laser pulses are
combined to a voltage that is no longer negligible with respect to $\Delta
V_{th}$. In Fig. 3b we report the resistance drop, measured following the
procedure previously described, with $\Delta V$=0.5 V applied voltage. In this
case, although the resistance drop is described by an exponential function
(solid red line) with the same time constant ($\tau$=18.7$\pm$1.6 s), the
value achieved in the saturation regime ($\delta$R${}_{sat}\simeq$2.6
k$\Omega$) is twice the value measured ($\delta$R${}_{sat}\simeq$1.3
k$\Omega$) for $\Delta V$=5 mV.

The resistance drop measured under the applied bias $\Delta V$=0.5 V is
compared to the value expected by considering the laser-induced heating (the
parameters of the thermal calculations are the same than the previous low-
voltage case) and also including the effect of Joule heating induced by the
current flowing throughout the V2O3 bridge. We stress that the voltage applied
through the device is smaller than threshold value necessary for the resistive
switching. Therefore, in this regime no metallic filamentsKalcheim2020 ,
possibly responsible for large local Joule heating, are created and the system
can be treated as homogeneous. The additional dissipated power can be thus
written as:

$\Delta P_{J}=\frac{\Delta V\times I}{swd}$ (4)

where $\Delta P_{J}$ is the power density dissipated by the electrical current
$I$ flowing through the electrodes and $swd$ is the device effective volume
(see Fig. 1a). $\Delta P_{J}$ is added to the total power density $P(r,z)$,
provided by the pulse train, in Eq 1. The black solid line in Fig. 3b
represents the result of the numerical simulation converted in the expected
resistance drop by means of the resistance vs temperature calibration curve
(see Fig. 1b). We note that the Joule heating induced by the current is of the
order of 2$\times 10^{-5}$ $\mathrm{W}$ and is negligible as compared to the
laser power, which amounts to $\sim 10^{-2}$ $\mathrm{W}$. As a conclusion,
the additional Joule heating does not account for the measured resistivity
drop in the stationary regime, which is twice than that expected from heating
alone.

The present results can be rationalized on the basis of recent theoretical
workMazza2016 , which showed that in the insulator-metal coexistence region,
the application of a significant electric field is able to induce the non-
thermal weakening of the Mott insulating phase via the formation of new
metallic states at the Fermi level with no counterpart at equilibrium. This
mechanism is in sharp contrast with the conventional Zener tunneling mechanism
that is usually invoked to describe the resistive switching dynamics.
Interestingly, the state variable that characterizes the transition and
controls the free energy of the system is the orbital polarization, defined as
$p$=$n_{e_{g}^{\pi}}$-$n_{a_{1g}}$, where $n_{e_{g}^{\pi}}$ is the occupation
of the lowest energy V-3$d$ $e_{g}^{\pi}$ orbitals and $n_{a_{1g}}$ is the
occupation of the V-3$d$ $a_{1g}$ orbitals. The Mott insulating phase is
characterized by $p$=2, whereas the application of an electric field induces
the formation of a metallic state with $p$=1.2-1.6 Mazza2016 . As recently
shownRonchi2019 , the excitation with infrared light pulses with 1.55 eV
photon energy can induce a further orbital polarization decrease of the order
of $\delta p\simeq$-10${}^{-3}-10^{-2}$, which in turns leads to a change of
1.3-13 meV of the difference between the free energies of the insulating and
metallic phases. The photo-induced change of the free energy difference
largely overcomes the thermal effect, i.e. $k_{B}\delta T\simeq$50 $\mu$eV,
thus inducing the growth of already existing metallic domains in the
insulator-metal coexistence region. The combination of below-threshold voltage
and the excitation with infrared light pulses capable of modifying the
occupation of vanadium orbitals thus weakens the insulating state well beyond
what can be ascribed to thermal effects. The scenario emerging from our
results can be understood also within the resistor network model Stoliar2013 ,
which is commonly adopted to describe the insulator-to-metal switching
dynamics. In this model, the physical system is divided in nanometric cells
representing small regions, which are either in the insulating (high-
resistance) or metallic (low-resistance) states. The combined action of
voltage and laser excitation leads to a non-thermal increase of the number of
the metallic cells, thus triggering the observed volatile resistance drop.
Working with below-threshold voltage and with weak laser excitation avoids the
creation of connected filamentary metallic paths which are responsible for the
resistive switching process observed above $\Delta V_{th}$.

##  IV Conclusions

In conclusion, we investigated the simultaneous action of a train of infrared
light pulses and an external voltage on a Mottronic device based on V2O3,
which undergoes an IMT at $T_{IMT}\simeq$170 K. When the device is in the
insulator-metal coexisting region ($T\simeq$160 K) and a 0.5 V voltage is
applied across the device, the measured resistance drop induced by a pulse
number exceeding 106 is twice than that expected from the simple local heating
of the device. Our results suggest that although the 0.5 V applied voltage is
below the threshold ($\Delta V_{th}$=2.5 V) necessary for inducing the
complete and irreversible resistive switch, it brings the insulating phase
close to the insulator-to-metal instability. The simultaneous weak excitation
with a sufficient number of infrared pulses modifies the occupation of the
vanadium 3$d$ orbitals enough to trigger the non-thermal growth and
proliferation of already existing metallic nodes, well beyond what can be
ascribed to the total local heating induced by the laser/voltage combination.
The present results also call for the development of time-resolved microscopy
techniques to investigate the real time dynamics of the metallicity in
Mottronics and resistive switching devices subject to the simultaneous
application of electric fields and light pulses.

###### Acknowledgements.

C.G., A.R. and P.F. acknowledge Andrea Tognazzi for the support in the
development of the experimental set-up. C.G. and A.R. acknowledge Dr.
Alessandro Bau’ and Prof. Vittorio Ferrari (Information Engeenering Dept.,
Università degli Studi di Brescia) for the support given during the
wirebonding of the device. We thank Frederik Ceyssens for his help with the
fabrication of electrical contacts on the samples. C.G., A.R., P.F.
acknowledge financial support from MIUR through the PRIN 2017 program (Prot.
20172H2SC4_005). G.F., and C.G. acknowledge support from Università Cattolica
del Sacro Cuore through D.1, D.2.2, and D.3.1 grants. F.B. acknowledges
financial support from Université de Lyon in the frame of the IDEXLYON
Project-Programme Investissements d’Avenir (ANR-16-IDEX-0005) and from
Université Claude Bernard Lyon 1 thorugh the BQR Accueil EC 2019 grant. P.H.,
M.M., and J.-P.L. acknowledge support from EU-H2020-ICT-2015 PHRESCO Project,
Grant agreement No. 688579. P.H. acknowledges support from Becas Chile-
CONICYT. M. G. acknowledges financial support from the CNR Joint Laboratories
program 2019-2021.

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