# Purely electronic insulator-metal transition in rutile VO2

Shaobo Cheng, Henry Navarro, Zishen Wang, Xing Li, Jasleen Kaur, Alexandre Pofelski, Qingping Meng, Chenyu Zhou, Chi Chen, Mark Dean, et al.

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Shaobo Cheng, Henry Navarro, Zishen Wang, Xing Li, Jasleen Kaur, et al. Purely electronic insulator-metal transition in rutile VO2. Nature Communications, 2025, 16 (1), pp.5444. 10.1038/s41467-025-60243-0. hal-05344986

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# Purely electronic insulator-metal transition in rutile VO₂

Received: 29 April 2024

Accepted: 19 May 2025

Published online: 01 July 2025

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Shaobo Cheng<fnref n="1" />,²,⁹, Henry Navarrocircled{3,4,9}, Zishen Wang⁵, Xing Licircled{1,2}, Jasleen Kaur⁵,⁶, Alexandre Pofelskicircled{1}, Qingping Meng<fnref n="1" />, Chenyu Zhoucircled{7}, Chi Chen⁵, Mark P. M. Deancircled{1}, Mingzhao Liucircled{7}, Ali C. Basaran³, Marcelo Rozenbergcircled{8}, Shyue Ping Ong⁵, Ivan K. Schullercircled{3} & Yimei Zhucircled{1}✉

Volatile resistive switching in neuromorphic computing can be tuned by external stimuli such as temperature or electric-field. However, this type of switching is generally coupled to structural changes, resulting in slower reaction speed and higher energy consumption when incorporated into an electronic device. The vanadium dioxide (VO₂), which has near room temperature metal-insulator transition (MIT), is an archetypical volatile resistive switching system. Here, we demonstrate an isostructural MIT in an ultrathin VO₂ film capped with a photoconductive cadmium sulfide (CdS) layer. Transmission electron microscopy, resistivity experiments, and first-principles calculations show that the hole carriers induced by CdS photovoltaic effect are driving the MIT in rutile VO₂. The insulating-rutile VO₂ phase has been proved and can remain stable for hours. Our finding provides a new approach to produce purely electronically driven MIT in VO₂, and widens its applications in fast-response, low-energy neuromorphic devices.

In the cognitive era, volatile and nonvolatile resistive switching has been proposed as the building block to engineer the next generation energy efficient neuromorphic computing technologies<fnref n="1" />,². Among the volatile switching, metal-insulator transition (MIT) in Mott systems is particularly promising because of its low energy consumption, fast reaction speed, controllable, and repeatable behavior<fnref n="1" />. Most of the current methods for modulating resistive switching in MIT materials are mainly limited by heating and/or biasing, which largely restricts their applications. Furthermore, the MIT, which manifest itself in the electronic transport, is also intertwined with the structural phase transition, further limiting the switching speed<fnref n="4" />⁻⁷. Since metal-to-insulator and structural transitions on the same material are difficult to separate, additional functionality can be brought to a hybrid system by interfacing the MIT material with another functional material that may

have high sensitivity to different external stimuli⁸⁻¹². Therefore, it is exciting and urgent to understand and manipulate the resistive switching process in hybrid systems.

Vanadium dioxide (VO₂) is a model MIT system, with a near room-temperature transition, making it suitable for electronic device applications¹³,¹⁴. VO₂ changes from insulating monoclinic to conductive rutile phases from low temperature to high temperature. The electronic MIT is accompanied by structural transition, and monoclinic phase has dimerization of V ions along the c-axis. However, ultrafast experiments have shown that the electronic transition could be decoupled from the structural phase transition¹⁵. Moreover, some experiments have shown that the nonequilibrium metallic monoclinic phase can be obtained by photo-excitation, showing that isostructural MIT is possible under nonequilibrium conditions¹⁵,¹⁶. Recently, Lee et

<footnote n="1">¹Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, USA. ²School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, China. ³Department of Physics, Center for Advanced Nanoscience, University of California San Diego, La Jolla, CA, USA.</footnote>

<footnote n="4">⁴Department of Physics, Andrews University, Berrien Springs, MI, USA. ⁵Department of NanoEngineering, University of California San Diego, 9500 Gilman Dr, Mail Code 0448, La Jolla, CA, USA. ⁶Department of Materials Science & Engineering, University of California San Diego, 9500 Gilman Dr, Mail Code 0448, La Jolla, CA, USA. ⁷Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY, USA. ⁸Laboratoire de Physique des Solides, CNRS, Université Paris Saclay, Orsay Cedex, France. ⁹These authors contributed equally: Shaobo Cheng, Henry Navarro. ✉e-mail: zhu@bnl.gov</footnote>
al. successfully realized isostructural MIT in monoclinic VO₂ by elec-
tron doping¹⁷. Moreover, Mondal et al. used modulation doping
(electron doping) to control the electronic structure of VO₂¹⁸. It is
therefore interesting to consider the potential isostructural MIT in
rutile VO₂ system, especially by doping effect.

In this work, we use a photoactive CdS layer to experimentally and theoretically explore hole doping effects on VO₂. Our results surprisingly establish a doping driven transition in VO₂, i.e., creating a (meta) stable insulating rutile VO₂. This finding completes the VO₂ electronic-crystal structure phase diagram (as shown in Supplementary fig. 1). The MIT can occur entirely within the monoclinic phase and now entirely within the rutile phase. The full elucidation of the pure electronic transition would represent a major step forward in the understanding of the MIT in this important material.

Results

Basic structural characterizations and property measurement

An ultrathin 8 nm VO₂ film was epitaxially grown on a TiO₂ substrate to maximize the effect on the interfacial coupling. A CdS layer was subsequently deposited (about 80 nm thick), forming a CdS/VO₂/TiO₂ heterostructure. Illumination of CdS (band gap of 2.4 eV) with visible light creates photoinduced carriers¹⁹⁻²⁴ which can then drift into the VO₂ and modify its electronic properties. It is worthwhile to mention that the 80 nm CdS was chosen because this is the minimum thickness for which we can conveniently measure the electrical transport, as thinner films have too high a resistance (see Supplementary fig. 2). Figure 1A shows the schematic of experimental geometry. The samples and the Au/Pt layers were prepared using a standard focused ion beam (FIB) lift-out process²⁵. The physical and structural properties were measured before and after exposure to a solar light generator. Figure 1B shows the resistance vs. temperature measurement (R-T) obtained from the cooling branch with the light on and off states. The red line is the R-T result measured before shining solar light (off state), and the black line is the result acquired after shining light (on state). The whole R-T loops and time related relaxation study results are shown in the Supplementary figs. 3–6. In the blue region, the VO₂ is insulating, while in the pink region, the VO₂ is conductive, no matter the light is on or off. However, in the yellow region (near room

temperature), the VO₂ changes from insulating to metallic state when the light is turned on. Figure 1C shows a high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image of the cross-section of the FIB sample. The energy dispersive spectrometer mapping results of the sample are shown in Supplementary fig. 7.

Since the system will relax back in 8 h after shining light (Sup-
plementary fig. 3), systematic transmission electron microscopy (TEM)
studies can be carried out to understand the mechanism of this photo-
assisted MIT. For consistency, the TEM experiments (including elec-
tron diffraction and spectroscopy) were conducted within 3 h after the
illumination. Figure 1D shows the selected area electron diffraction
pattern acquired at room temperature at the VO₂/TiO₂ interface in
CdS/VO₂/TiO₂ system before exposing light. Both VO₂ and TiO₂ exhibit
a rutile structure, since the ultrathin VO₂ is under in-plane tensile strain
from TiO₂ substrate, which is consistent with the published results<sup>25,26</sup>.
After light exposure, yellow region in Fig. 1B, the conductivity changes
dramatically (from insulating state to metallic state), while the VO₂
maintains the rutile structure as seen in Fig. 1E. This shows that the
light-driven transition from insulator to metallic state is purely elec-
tronic and not driven by a structural phase transition. During the TEM
observation, less than 1 nA beam current was used, which will cause
less than 1 °C temperature increase<sup>27</sup>.

Numerous studies have examined the metal–insulator transition
in ultrathin VO₂ films<sup>17,18,28–30</sup>. The reported behavior varies significantly
depending on parameters such as film thickness, substrate choice, and
the presence of capping layers. While some investigations observe
behavior consistent with that of bulk VO₂<sup>18,28</sup>, others suggest that
ultrathin films may undergo an isostructural MIT<sup>17,29,30</sup>. In this work, we
investigate VO₂ films capped with CdS—a configuration that has rarely
been studied. To probe possible temperature-induced structural
changes, we performed X-ray diffraction (XRD) measurements above
and below the transition temperature (360 K and 260 K, respectively).
Clear structural changes are observed in our samples consisting of
uncapped VO₂ on TiO₂ substrates (see Fig. 1F), consistent with the well-
known rutile-to-monoclinic transition upon cooling<sup>18</sup>. In contrast, XRD
data for our CdS-capped VO₂ on TiO₂ (Fig. 1G) show no detectable
structural changes across the same temperature range, suggesting the

<figure><img src="image_4.png" /><figcaption>**Fig. 1 |** Effect of light illumination on CdS/VO₂. A Schematic experimental geometry. A cross-sectioned FIB (focused ion beam) sample illuminated by white light. B Change in the resistance across the metal-insulator phase transition measured on the cooling branch with the light ON and OFF. C Low magnification high angle annular dark field (HAADF) image showing the layered configuration of the sample. D, E Selected area electron diffraction patterns for the “ON” and “OFF” light states.</figcaption></figure>

The dashed rectangular areas are enlarged in the upper left corner of the micro-
graph. The TEM experiments (imaging, electron diffraction, and spectroscopy)
were conducted at room temperature. Temperature dependent XRD results of (F)
VO₂/TiO₂ system and (G) CdS/VO₂/TiO₂ system. The thickness of VO₂ film for
measuring the XRD is 8 nm.
<figure><img src="image_5.png" /><figcaption>**Fig. 2** | Extracted valence EELS line scans. A High-resolution HAADF-STEM image of the CdS/VO₂/TiO₂ interface. The white arrow indicates the EELS line scan position. Horizontal dashed lines have marked the interfaces. B Typical experimental EELS spectrum for CdS. Two Lorentzian functions were used to fit the spectrum. C Experimental EELS spectrum for VO₂. Three peaks were fitted. EELS spectra were</figcaption></figure>

measured at different positions from the CdS/VO₂ interface with light OFF (D) and ON (E). (F, G) are the calculated EELS spectra using the experimentally extracted dielectric function from (D, E), respectively. The black arrows show the blue shift of the spectra across the interface from CdS to VO₂.

absence of a structural transition. Given that electron diffraction confirms the rutile structure at room temperature (see Fig. 1D), we attribute the observed MIT in the capped films to a rutile-to-rutile transition, consistent with an isostructural mechanism.

## Electron energy loss spectroscopy results

Electron energy loss spectroscopy (EELS) in TEM has been widely applied to study the electronic structure of materials. The signal of valence EELS (low-loss part of the spectrum) is two orders of magnitude stronger than the core-loss part. The dominant feature of valence EELS is from collective excitations (plasmons). The position of the plasma peak (the highest peak) is related to the density of valence electrons (and their effective mass)³¹⁻³³. Thus, the peak position change reflects the evolution of valence electrons (the details can be found in the Supplementary Information).

Figure 2A is a typical HAADF-STEM image showing the CdS/VO₂/TiO₂ structure. EELS line scan was taken across CdS/VO₂ interface (the white arrow area). Figure 2B, C show the reference valence EELS spectra of CdS and VO₂ acquired from the regions far from the interface, respectively. To retrieve plasma components from these valence EELS, multiple Lorentzian functions have been used to fit every valence EELS spectrum³³⁻³⁵. The position of the plasma peak is determined from the fitting (as shown in Fig. 2A, B). Two peaks were identified for CdS, and three peaks were fitted for VO₂. Figure 2D shows typical extracted valence EELS spectra from different positions before light exposure, i.e., the black line is the valence EELS acquired in CdS (3.24 nm from the CdS/VO₂ interface). The extracted valence EELS spectra after light exposure are shown in Fig. 2E.

The valence EELS in an inhomogeneous medium reflects the electron state at the measured point and the dielectric coupling between the measured point and nearby areas. The dielectric coupling in valence EELS has been considered based on the dielectric function theory³⁶⁻³⁸. Figure 2F, G are calculated valence EELS spectra by using the dielectric functions retrieved from the experiments (see Supplementary Information), which share similarities to the experimental spectra in Fig. 2D, E, respectively³⁶. The current dielectric function theory³⁶⁻³⁸ assumes that the materials at the two sides of the interface

are homogeneous, and their dielectric functions have step changes across the interface. However, this ideal case may not represent experimentally obtained interfaces and the homogeneity near the interface may be destroyed by interfacial strain³⁹⁻⁴², atomic rearrangement, charge transfer, etc.⁴³,⁴⁴. So, the deviation between calculated and experimental EELS mainly comes from aforementioned inhomogeneous structure near the interface.

The plasma peak dominates the valence EELS, and the position of the plasma peak relates to the density of valence electrons (the details can be found in Supplementary Information):

$$E = h\omega_p = h\sqrt{\frac{4\pi e^2 N_v}{m}} \quad (1)$$

where E is the energy loss of plasma peak (i.e. the highest plasma peak position in EELS), $N_v$ is the density of the valence electrons, $\omega_p$ is the plasmon frequency, e and m are electron charge and mass³³. The shift of plasma peak is related to the change of the density of the valence electrons.

Figure 3A, B show the energy of the plasma peak as a function of distance x from the interface. x < 0 and x > 0 are the CdS and VO₂ areas, respectively. The figures show that the plasmon peaks shift to lower energy after the light is turned on (Fig. 3B). Figure 3C, D show the plasmon peak positions (i.e., the highest peak positions illustrated in Fig. 2B, C) at different coordinates and the corresponding calculation results (i.e., the highest peak positions acquired from the calculated EELS) before and after light exposure. A comparison of Fig. 3C, D shows that both CdS and VO₂ lost electrons (gained holes) upon turning the light on, implied by their plasma peaks shifting to lower energy. The shift of plasma peaks caused only by the inhomogeneous electron density near the CdS/VO₂ interface can be obtained by subtracting the shift caused by the dielectric coupling. This is accomplished by subtracting the red data points from the black data points in Fig. 3C, D. Using Eq. 1, the changes in electron density can be estimated, and the results before and after illumination are shown in blue and orange in Fig. 3E. Figure 3E shows that the change in the electron density near the interface is slightly different for the two data sets,
<figure><img src="image_6.png" /><figcaption>**Fig. 3 | The comparison of the valence EELS before and after illumination.**</figcaption></figure>

A, B Contour maps of the EELS line scan intensity across the VO₂/CdS interface before and after illumination. The intensity of EELS in the figures decreases from red to blue. Comparing (A, B), the peak positions shift to lower energy (redshift) in each location after the light exposure. The vertical dashed lines are located at 20 eV and guided to the eyes. C, D The energy of the highest plasmon peak vs. position coordinate before and after light exposure. The calculation corresponds to the

maximum of the peaks computed in Fig. 2E, F. E Uneven electron density distributions caused by interfacial inhomogeneity as a function of position. The blue and orange dots are the electron density changes measured before and after light exposure. F Differences in electron density changes caused by beam shining (the orange dots (after light exposure) subtract the blue dots (before light exposure) in (E), since the interfacial inhomogeneity effects have been removed.

indicating the effect of the illumination on the electron density. This difference obtained by subtracting the blue data points from the orange ones in Fig. 3E is a measure of the changes in electron density caused by illumination as shown in Fig. 3F.

## Theoretical calculations

To develop an understanding of the mechanism behind the experimentally observed phenomena in rutile VO₂, density functional theory (DFT) calculations were carried out. Figure 4A illustrates the original band structures of Au/Pt, CdS, and VO₂. The band gap, valence band (E_v), conduction band (E_c), and work function (W) are listed in the figure⁴⁵⁻⁴⁷. The work function of rutile VO₂ (4.7 eV) is slightly lower than that of CdS (4.8 eV), thereby facilitating hole doping into the VO₂. The

strained rutile VO₂, that results from anchoring to the TiO₂ substrate, is insulator at room temperature, as indicated in Fig. 4A.

We have performed DFT + U calculations to investigate the effect of photodoping on the electronic structure of the strained rutile system by introducing holes in the system. Because the change of electron density is about $-4 \times 10^{27}$ electron/m³ (Fig. 3F) at the interfacial area and changes to 0 away from the interface (within 5 nm), we assume an average doping density of $-2 \times 10^{27}$ electron/m³, i.e., $2 \times 10^{27}$ hole/m³. The unit cell parameters for rutile VO₂ are a = b = 4.6 Å, c = 2.9 Å, which means each VO₂ has $2 \times 2 \times 10^{27}$ hole/m³ × 4.6 × 10⁻¹⁰ × 4.6 × 10⁻¹⁰ × 2.9 × 10⁻¹⁰ m³/cell ≈ 0.25 hole/cell. Thus, we adopted 0.25 hole per cell for an order of magnitude calculation. These calculations show that introducing 0.25 holes per VO₂ unit closes the insulating gap, as shown
A

<figure><img src="image_7.png" /></figure>

B

<figure><img src="image_8.png" /></figure>

C

<figure><img src="image_9.png" /></figure>

**Fig. 4 | Band structures of Au/Pt, CdS, and VO₂.** A Schematic diagrams of the Au/Pt, CdS, and R VO₂ band structures. The Fermi energy in each material is indicated by dashed lines. B Total (green), O (red), and V (blue) DOS for the VO₂ systems, (C)

0.25 holes per formula unit of rutile VO₂. The system with no holes is insulating, whereas the system with 0.25 holes exhibits a metallic behavior.

in Fig. 4B, C. This finding mimics our experiment shown in Fig. 1B, in which illumination of CdS switches the rutile VO₂ from an insulating to a conductive state.

In the unstrained state, rutile VO₂ is a metal, which can be observed from the band structure obtained from the Materials Project (mp-19094). However, when under tensile strain from TiO₂ substrate, our calculations using the same parameters as the Materials Project find that a band gap of 0.6 eV opens up in rutile VO₂. This gap is closed with hole doping. While the DFT + U calculation of hole-doped VO₂ shows metallic behavior, the experimental temperature-resistance curve in Fig. 1B shows semiconducting behavior. The physical scenario that is suggested by our calculations is as follows: At low temperature, no matter the light is on or off, VO₂ is rutile with a relatively big gap and hence holes are uneasy to be injected. The presence of the gap at low temperatures suggests the emergence of an ordered state with our DFT + U calculations, indicating that AFM ordering is the most likely candidate. Moreover, our calculations also suggest that, as the temperature increases reaching the proximity of the ordinary T<sub>MIT</sub>, the gap may weaken facilitating the hole-injection by the CdS. This process, eventually drives down the transition by 15 K.

Discussion

Though CdS could dope carriers inside of VO₂, its thickness matters. We measured the resistance of several films with different CdS thicknesses as a function of temperature with and without applied light (see Figure S2). We see a strong trend towards higher resistivity in thinner films and a strong reduction in resistivity in the light on state with respect to the light off. The resistivity of the 80 nm film was so high that it could not be conveniently measured without illumination.

The insulating rutile VO₂ has a nominal filling of d¹, thus it should be a Mott insulator. Our experiments and calculations suggest that its MIT through photo doping is a filling-controlled Mott transition. It should be mentioned that, in the current device configuration, we couldn't directly measure the electronic structure of the equilibrium for the hole-doped rutile VO₂. A direct angle-resolved photoemission spectroscopy of a related system, V₂O₃, concluded a different mechanism for the MIT⁴⁸. The MIT in V₂O₃ is caused by a progressive decrease in spectral weight of an itinerant, dispersive quasi particle conduction band without noticeable changes in its dispersion and effective mass. This is accompanied by an energy shift and increase in spectral weight, of a quasi-localized state, which goes from an energy close to the Fermi energy in the metallic state to an energy close to the bottom of the vanishing dispersive band in the

insulating state. In our case, the doping is the driving force of the transition.

A more comprehensive measurement of the detailed structure of CdS-capped VO₂ on TiO₂ would be a valuable future study. This would ideally include both electron diffraction, which has excellent sensitivity to small sample volumes, and X-ray diffraction measurements on off-specular Bragg peaks, which has the advantage of macroscopic sampling of the film, along with more straightforward possibilities to model the structure due to the kinematic interaction of X-rays.

In conclusion, a photo-assisted, isostructural doping-driven MIT was found in ultrathin rutile VO₂ film capped with photoactive CdS. The TEM and transport studies together with DFT calculations show that besides the previously reported insulating monoclinic phase, conductive rutile phase, and (meta)stable conductive monoclinic phase, an insulating rutile phase can be stabilized by anchoring between rutile TiO₂ substrate and CdS capping layer. Thus, another missing piece of the puzzle in the VO₂ electronic-crystal structural phase diagram has been found. The tensile strain induced by the substrate puts VO₂ in a new type of stable state, which is the whole idea of hybrid multilayer materials. In contrast, the gradual decay over time of the "on-state" reflects a slow relaxation process rather than a true metastability phenomenon. In addition to the commonly investigated thermal and electric field induced transitions, our results show that heterostructuring a Mott insulator with a photoactive material adds a new degree of freedom. This provides a new way to modulate the MIT, thus widening the applications of VO₂ to photo-active electronic devices. In particular, the isostructural transition reported here shows that VO₂ is a potential material platform for implementing (quasi) nonvolatile, low-energy, fast-response switching devices.

Methods

TEM characterization

A FEI Helios G4 FIB was used for the TEM sample preparation. A JEOL 200CF TEM at Brookhaven National Laboratory was used for the TEM studies. Dual EELS was used, and all EELS spectra were corrected by the zero-loss peaks. For HAADF images, the convergent angle is 21.2 mrad, and the collection angle is between 67 and 275 mrad.

Film growth

An 8 nm thick epitaxial VO₂ film was grown by reactive sputtering on the TiO₂ substrate (oriented along the (001) plane). A 4-mtorr argon/oxygen mixture (8% O₂) was used during deposition, and the substrate was kept at 350 °C during the growth and later cooled down at a rate of 12 °C/min. The CdS, 80 nm thick film was grown on top of the VO₂ using radio frequency magnetron sputtering from a CdS target in a 2
mTorr pure argon atmosphere at 150 °C. Two Au (20 nm) electrodes were patterned on the CdS/VO₂ heterostructure films. Room temperature XRD measurements were done in a Rigaku SmartLab system. Single-phase growth was confirmed by XRD, textured along (002) for VO₂ and H(002) for CdS. Transport measurements were carried out on a Montana C2 S50 Cryocooler and TTPX Lakeshore cryogenic probe station, using a Keithley 6221 current source and a Keithley 2182 A nanovoltmeter.

## Solar light generator

The simulated solar light is provided by a 150 W solar simulator equipped with an air mass 1.5 global (AM 1.5 G) filter (Newport), and the light power was calibrated to 1 Sun (100 mW/cm²) using a quartz-windowed Si solar cell (Newport).

## Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its supplementary information file. Source data are provided with this paper.

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## Acknowledgements

We would like to acknowledge Tianxing D. Wang and Juan A. Hofer from University of California San Diego (UCSD) for the help with XRD measurements. The structural characterization, transport, TEM and collaboration between Brookhaven National Laboratory (BNL), CNRS and the UCSD were supported through an Energy Frontier Research Center program funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Grant DE-SC0019273. Electron microscopy work at BNL and the use of BNL's Center for Functional Nanomaterials were supported by DOE-BES, the Division of Materials Science and Engineering, and the Division of Science User Facility, respectively, under Contract no. DE-SC0012704.

## Author contributions

T.E.M. studies: S.B.C., X.L., A.P.; Thin film growth: H.N.; Theoretical calculations: Z.W., J.K., Q.M., C.C., M.R., S.P.O.; Methodology: S.B.C., H.N., C.Z., M.L., A.C.B., M.P.M.D.; Supervision: I.K.S., Y.Z.; Writing—Original draft: S.B.C., H.N., Z.W.; Writing—review & editing: M.R., I.K.S., Y.Z.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41467-025-60243-0.

**Correspondence** and requests for materials should be addressed to Yimei Zhu.

**Peer review information** *Nature Communications* thanks Teruo Kanki, and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.

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