Simultaneous measurements of the transmittance and the resistance were carried out on 20-nm-thick VO2 wires during the semiconductor-to-metal transition (SMT). They reveal an offset between the effective electrical and optical switching temperatures. This shift is due to current percolation through a network of nanometer-scale grains of different sizes undergoing a SMT at distinct temperatures. An effective-medium approximation can model this behavior and proves to be an indirect method to calculate the surface coverage of the films

Feldman, L.C.

Haglund, R.F.

Lopez, R.

Rozen, J.

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APPLIED PHYSICS LETTERS 88, 081902 2006Two-dimensional current percolation in nanocrystalline vanadiumdioxide filmsJohn Rozen,a René Lopez, Richard F. Haglund, Jr., and Leonard C. FeldmanDepartment of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 andInstitute of Nanoscale Science and Engineering, Vanderbilt University, Nashville, Tennessee 37235Received 28 July 2005; accepted 5 January 2006; published online 21 February 2006Simultaneous measurements of the transmittance and the resistance were carried out on 20-nm-thickVO2 wires during the semiconductor-to-metal transition SMT. They reveal an offset between theeffective electrical and optical switching temperatures. This shift is due to current percolationthrough a network of nanometer-scale grains of different sizes undergoing a SMT at distincttemperatures. An effective-medium approximation can model this behavior and proves to be anindirect method to calculate the surface coverage of the films. © 2006 American Institute of Physics.DOI: 10.1063/1.2175490Bulk vanadium dioxide undergoes a structural phasetransition from a monoclinic semiconductor to a tetragonalmetal near 68 °C.1,2 This structural transition is accompaniedby abrupt changes in the optical and electrical properties ofthe oxide. VO2 has been the object of widespread interest asa component of electronic and photonic devices because thecritical temperature Tc of this semiconductor-to-metal transi-tion SMT can be adjusted from 20 to 70 °C by doping orstress.3,4 Many of these potentially useful features are pre-served in nanocrystalline VO2. However, a unique aspect ofthe nanocrystals is that the width of the hysteresis looptraced out by the SMT increases as grain size is reduced.5,6Indeed, optical hysteresis loops with widths as large as50 °C have been observed for isolated VO2 nanoparticles.7,8For nanoparticles in electrical contact with one another,the hysteresis loop in conductivity also widens with reduc-tion in the size of the crystalline domains. In particular, itleads to a temperature window within which a nanostruc-tured film is partially semiconducting and partially metallicbecause contiguous VO2 nanoparticles undergo the phasetransition independently.9 Indeed, for the transition to be ef-fective electrically, a continuous path through grains in thesame state needs to exist. In a nanostructured thin film, theelectrical switching behavior is therefore determined by apercolation process.This letter presents simultaneous optical and electricalmeasurements of the SMT in a two-dimensional 2D nano-structured VO2 film and shows that there is an offset betweenthe effective optical and electrical switching temperatures.This shift arises because the hysteresis in optical transmis-sivity is determined by the relative fraction of nanoparticlesin the semiconducting state, while the hysteresis in electricalresistivity is governed by the evolution of a continuous per-colation path. The behavior of the resistance is modeled wellby a 2D effective medium calculation, which also yields anestimate of the spatial coverage of the films.The VO2 wires for the experiment were fabricated bydepositing a layer of vanadium oxide with an equivalentthickness of 20 nm through a 1.00.1 cm mask onto anamorphous alumina substrate optically polished, rms rough-aAuthor to whom correspondence should be addressed; electronic mail:john.rozen@vanderbilt.edu0003-6951/2006/888/081902/3/$23.00 88, 08190ness less than 5 nm using pulsed laser ablation. A vanadiumtarget was sputtered in a 10 mTorr O2 atmosphere by a KrFexcimer laser 248 nm, 25 Hz at a fluence of 4 J /cm2. Asubsequent annealing step at 450 °C in oxygen 250 mTorrfor 45 min produced the correct stoichiometry, as determinedby Rutherford backscattering to an accuracy of 2%.10 Theamount of material deposited was optimized to achieve smallgrain size and sufficient continuity along the film to obtain awide electrical hysteresis loop. The resulting film comprisesa 2D random network of contiguous VO2 nanoparticleshaving a mean diameter of approximately 50 nm Fig. 1.After aluminum contacts were deposited at the ends of awire by thermal evaporation, the sample was fixed on aPeltier thermoelectric heater/cooler stage with a 3-mm-diamhole in its center to facilitate simultaneous electrical and op-tical measurements. An infrared detector located opposite thefilm monitored the transmission of a 1.3 m laser throughthe wire while the resistance along the wire was measuredbetween the aluminum contacts Fig. 2.Figures 3a and 3b show the transmittance and resis-tance hysteresis loops measured for this sample. They are20 °C wide and the asymmetry between the heating andcooling branches is due to the relatively broad sizedistribution.5 The reduction of the grain size has also dimin-ished the resistance jump from the five orders of magnitudeobserved in the highest-quality bulk VO2. Indeed, the prop-erties of nanocrystalline vanadium dioxide can deviate fromthose of bulk material because of the reduced amount ofFIG. 1. Scanning electron micrograph of the sample; the amount of depos-ited material was adjusted to obtain both small grain size and contiguity.© 2006 American Institute of Physics2-1081902-2 Rozen et al. Appl. Phys. Lett. 88, 081902 2006nucleating centers,7 the large number of grain boundaries andthe presence of oxygen vacancies most likely at thesurface.11 The activation energy deduced from the exponen-tial behavior of the resistance in the semiconducting phase isapproximately 0.36 eV, in good agreement with previousreports.12,13To first approximation, the optical transmittance dependslinearly on the volume fraction of the metallic phase and thedrop on the heating branch indicates that the nanocrystalsstart to switch at 54 °C. The measured resistance also be-gins to deviate from semiconducting behavior around 54 °C.However, between 54 and 60 °C, this deviation is smallcompared to the total jump. Significant change in resistancebegins only at approximately 60 °C. This offset constitutesthe difference between the electrical and optical signatures ofthe SMT.FIG. 2. Color online Schematic of the structure allowing simultaneousoptical and electrical characterization. The VO2 wire is deposited on amor-phous Al2O3 and is terminated by Al contacts.FIG. 3. Color online Transmittance a and resistance b curves measuredsimultaneously as a function of temperature. The dashed lines show theextrapolation of the film properties in the semiconducting phase. The dottedlines mark the beginning of the transition for the heating branch and the endof the transition for the cooling branch these temperatures correspond to a5% deviation from the transmittance at room temperature. Crosses indicatethe percolation thresholds 90% of the VO2 is metallic. The full line in bis the reconstructed hysteresis deduced from Eq. 3 using =0.52, m wasextracted from the transmittance.These two regimes of strong and weak dependence ofresistance on temperature occur during both the heating andthe cooling processes; this behavior is emphasized in Fig. 4where the conductance is plotted as a function of the metallicfraction of VO2. Electric current is sensitive to the specificlocation of the metallic grains along the path between elec-trodes. If only a small fraction of particles has turned metal-lic, a continuous low-resistance path does not exist and thetotal resistance is not greatly affected. This explains thenearly constant regime in Fig. 4. As the temperature in-creases, conducting paths form and the resistance change isgreater. The formation of the first metallic path correspondsto a threshold temperature. Current percolation is thus theorigin of the behavior of the resistance in the sample. Aneffective medium approximation EMA can be used tomodel this nonlinear evolution.Bruggeman’s symmetrical effective medium theory hasbeen used to describe the dependence of the dielectricconstant of VO2 films on temperature14,15 and to model theelectrical hysteresis16 when the metallic phase and the semi-conducting phase coexist. This theory treats a particle in aninhomogeneous material as a domain embedded in a mediumwith an effective conductivity e. For inclusions in atwo-dimensional system, the volume fraction i and theconductivity i of each component satisfy17 ii − ei + e= 0. 1In the present case, vanadium dioxide has segregated onthe surface of the substrate and voids of zero conductivitymust be included to model the film as a 2D medium. Thisleads to− a + mm − em + e+ ss − es + e= 0, 2where a is noted for air, m for VO2 in the metallic phase ands for VO2 in the semiconducting phase. Equation 2 can bedivided by the coverage of the film =1−a=m+s, whichsimplifies to − 1+ mm − em + e+ 1 − ms − es + e= 0. 3In this representation, the effective conductivity can be writ-ten as a function of m, the fraction of VO2 that is metallic.The value of e in the high temperature phase m=1 and inFIG. 4. Color online Dependence of the conductance on the fraction ofVO2 that is metallic; this fraction is calculated from the transmittance curveFig. 3a and is then substituted for temperature in the resistance data Fig.3b. The continuous curves are obtained using the effective mediumapproximation.the low temperature phase m=0 can be extracted from081902-3 Rozen et al. Appl. Phys. Lett. 88, 081902 2006Velectrical measurements. This leads to m and s sincem =em = 12 − 1s =em = 02 − 1. 4The expression deduced from Eq. 3 for the effectiveconductance is used to fit the experimental data, defining mand s as constant parameters. The resulting curves success-fully model the behavior of the measured conductance Fig.4. The total vanadium dioxide coverage deduced from thecalculations is found to be 52% on the heating branch and55% on the cooling branch, in good agreement with thevalues extracted from the scanning electron micrographs50% 60% . Similarly, Eq. 3 can be used toreconstruct the electrical hysteresis Fig. 3b.The value for the coverage deduced from the data doesnot depend on the relative change in conductivity, but isinstead related to the minimum fraction of material requiredto form a single metallic path between the electrodes. In theEMA, this threshold c is 50% of the surface. From themeasurements in Fig. 4, this implies that nearly 90% of theVO2 has to be in a metallic state to create a continuousconducting path; the corresponding threshold temperaturesfor the heating and the cooling branch are indicated in Fig. 3.The 2D EMA is in good agreement with percolationtheory18,19 in which c is approximately 45%. In three di-mensions, the value of c has been measured at 16%.18Therefore, for films comprising more than one layer ofgrains, the fraction of metallic material required to reach thethreshold is smaller, so that the apparent shift between theoptical and electrical branches of the hysteresis should begreatly reduced.The percolation effects reported here should be expectedin any nanocrystalline VO2 film in which the grains switchindependently and will affect the electrical as well as thethermal transport properties. However, as the grain size in-creases and the film becomes more uniform and more threedimensional, the transition will occur within a smaller tem-perature range. There is thus a trade-off between the ampli-tude of the changes in the properties of the material and thewidth of the temperature window in which the film is in anintermediate state. Also, the value of c is not universal if thedistance between the electrodes is reduced to a length scaleat which the distributions of the nanocrystals are not statis-tically equivalent. Therefore, the dimensions of reproducibledevices are strongly constrained, unless the size and arrange-iew publication statsments of the nanoparticles are controlled lithographically tomake the percolation threshold deterministic.In summary, this work has shown that current percola-tion leads to an intermediate state in which the film is par-tially opaque but still semiconducting. An effective mediummodel successfully reproduces this behavior and can be usedto extract the spatial coverage of the films. Percolationshould be taken into account in the design of any vanadiumdioxide based electronic element in order to reach the desiredcharacteristics. The offset between the effective electricaland optical switching temperatures opens the possibility ofdesigning tristate optoelectronic devices.A. Tackett and G. Walker are acknowledged for sugges-tions on percolation modeling and S. Dhar is thanked formany fruitful discussions. This work was supported by theNational Science Foundation under the Nanoscience Inter-disciplinary Research Team program DMR-0210785 andby a Major Research Instrumentation grant DMR-9871234.1N. F. Mott, in Metal-Insulator Transitions Taylor and Francis, London,1997.2J. B. Goodenough, J. Solid State Chem. 3, 490 1971.3T. D. Manning, I. P. Parkin, M. E. Pemble, D. Sheel, and D. Vernardou,Chem. Mater. 16, 744 2004.4Y. Muraoka, Y. Ueda, and Z. Hiroi, J. Phys. Chem. Solids 63, 965 2002.5V. A. Klimov, I. O. Timofeeva, S. D. Khanin, E. B. Shadrin, A. V. Ilinskii,and F. Silva-Andrade, Tech. Phys. 47, 1134 2002.6I. A. Khakhaev, F. A. Chudnovskii, and E. B. Shadrin, Phys. Solid State36, 898 1994.7R. Lopez, T. E. Haynes, L. A. Boatner, L. C. Feldman, and R. F. Haglund,Jr., Phys. Rev. B 65, 224113 2002.8R. Lopez, L. A. Boatner, T. E. Haynes, R. F. Haglund, Jr., and L. C.Feldman, Appl. Phys. Lett. 79, 3161 2001.9F. Béteille, L. Mazerolles, and J. Livage, Mater. Res. Bull. 34, 21771999.10J. Y. Suh, R. Lopez, L. C. Feldman, and R. F. Haglund, Jr., J. Appl. Phys.96, 1209 2004.11E. Kusano and J. A. Theil, J. Vac. Sci. Technol. A 7, 1314 1989.12C. N. Berglund and H. J. Guggenheim, Phys. Rev. 185, 1022 1969.13H. Jerominek, F. Picard, and D. Vincent, Opt. Eng. Bellingham 32, 20921993.14P. J. Hood and J. F. DeNatale, J. Appl. Phys. 70, 376 1991.15H. S. Choi, J. S. Ahn, J. H. Jung, and T. W. Noh, Phys. Rev. B 54, 46211996.16L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, Opt. Eng.Bellingham 41, 2582 2002.17R. Landauer, in AIP Proc. 40, Electrical Transport and Optical Propertiesof Inhomogeneous Media, edited by J. C. Garland and D. B. Tanner AIP,New York, 1978, p. 2.18R. Zallen, in The Physics of Amorphous Solids Wiley, New York, 1983.19S. Kirkpatrick, Rev. Mod. Phys. 45, 574 1973.

Two-dimensional current percolation in nanocrystalline vanadiumdioxide films

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Two-dimensional current percolation in nanocrystalline vanadiumdioxide films

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