The size effects on the optical properties of vanadium dioxide nanoparticles in ordered arrays were investigated. It was observed that the optical contrast between the semiconducting and metallic phases is enhanced in the visible region, presenting size-dependent optical resonances and size-dependent transition temperatures. The collective optical response as a function of temperature was found to present an enhanced scattering state during the evolving phase transition. These observations were suggested to provide critical insights into statistical processes occurring in materials at the nanoscale

Feldman, L.C.

Haglund Jr., R.F.

Lopez, R.

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VOLUME 93, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R Sweek ending22 OCTOBER 2004Size-Dependent Optical Properties of VO2 Nanoparticle ArraysR. Lopez,* L. C. Feldman,† and R. F. Haglund, Jr.Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA(Received 9 June 2004; published 20 October 2004)177403-1The size effects on the optical properties of vanadium dioxide nanoparticles in ordered arrays havebeen studied. Contrary to previous VO2 studies, we observe that the optical contrast between thesemiconducting and metallic phases is dramatically enhanced in the visible region, presenting size-dependent optical resonances and size-dependent transition temperatures. The collective opticalresponse as a function of temperature presents an enhanced scattering state during the evolving phasetransition. The effects appear to arise because of the underlying VO2 mesoscale optical properties, theheterogeneous nucleation behind the phase transition, and the incoherent coupling between the nano-particles undergoing an order-disorder-order transition. Calculations that support these interpretationsare presented.DOI: 10.1103/PhysRevLett.93.177403 PACS numbers: 78.67.Bf, 36.40.Ei, 64.70.NdThe study of photon-matter interactions at nanometerlength scales has as its ultimate goal the optimization ofthe coupling between selected radiation modes and spe-cific material excitations. Among the most exciting pros-pects are those that incorporate metal or semiconductornanostructures into periodic arrays, with potential appli-cations as photonic crystals [1], biochemical sensors [2],and near-field electromagnetic waveguides [3]. In peri-odic arrays of nanostructures, new properties arisefrom the combination of nanoscale material featuresand the periodicity of the arrays. These include thesize-dependent and shape-dependent shift of opticalresonances, and near-field or far-field coupling alreadyobserved in two-dimensional metal nanoparticle arrays[4–7].In this Letter, we describe first observations of thecollective optical response of vanadium dioxide nano-particle (NP) arrays during a reversible semiconductor-to-metal phase transition (SMT). A previously unre-ported resonance in the visible region is found in thespectral signature of the SMT, and the resonance peak,apparently due to multipole effects, is blueshifted withdecreasing NP size. Unlike the hysteretic response of VO2NPs with inhomogeneous size and spatial distributions,the hysteresis associated with the NP arrays shows adistinctive three-state behavior resulting from the differ-ential scattering efficiency between the metal and semi-conducting phases of VO2. This unique optical responsemay be viewed as an order-disorder transition in thespectral response of the array, superimposed on the hys-teretic response of individual NPs, and contains signifi-cant new insights about the stochastic nature of themechanism that triggers the metal-insulator transition.VO2 exhibits a SMT at a critical temperature Tc 67 C that is a result of an atomic rearrangement.Above Tc, VO2 has a tetragonal rutile structure and ex-hibits metallic properties. Below Tc, VO2 is a narrow-gapsemiconductor with a monoclinic unit cell [8]. The re-versible VO2 SMT displays a 104 jump in conductivity and0031-9007=04=93(17)=177403(4)$22.50 large changes in the optical properties, especially in theinfrared (IR) where VO2 tends to some degree of trans-parency when a semiconductor and great opacity when ametal. Apart from the long and controversial history ofmechanistic questions about this phase transition [9,10],VO2 is a candidate material for a variety of technologicalapplications that encompass, among others, ultrafast op-tical limiting since the SMT (both lattice and electronicstructures) occurs in less than 500 fs [11].VO2 NP arrays were fabricated by a combination of ionbeam lithography, pulsed laser deposition, and thermaloxidation. A solution of poly(methyl-methacrylate)(PMMA) (standard molecular weight of 950 kDa) inanisole (1.7% by weight) was spun onto a Si substrateand baked on a hot plate at 180  C for 3 min to obtain auniform 50 nm layer. The arrays were patterned on thePMMA layer with a FEI/Philips FIB200 focused ionbeam writer, having a liquid Ga ion source operatingat 30 kV. The Ga beam is then focused to a 30 nm spot tocreate the pattern of single-pixel dot arrays on thePMMA; typical beam current is 1 pA and dwell times(  100 s) are varied to change the dot size. The ex-posed PMMA was then developed in a 1:3 mixture ofmethyl isobutyl ketone and isopropyl alcohol. The devel-oped samples were coated by a VO1:7 layer of 50 nm bypulsed laser ablation (KrF excimer laser at 4 mJ=cm2,  248 nm, and 25 Hz) of a vanadium metal target in a5 mTorr background O2 pressure at room temperature. Inthe lift-off step, the remaining PMMA layer togetherwith its overlayered VO1:7 film were removed by a com-mercial resist remover (Microposit 1165), leaving theVO1:7 nanoclusters resting on the Si surface. Finally,oxidation of the NPs was needed to complete their con-version to stoichiometric VO2. Since vanadium oxidecan exist in wide range of stoichiometries, careful controlof the oxidation conditions (450  C for 20 min in250 mTorr O2) is necessary to secure the correct 2:1oxygen/vanadium ratio in the NPs. The stoichiometry ofthe pulsed laser deposition grown particles before and2004 The American Physical Society 177403-1FIG. 1. (a) The dark-field confocal setup used to study thesamples. o  60. (b) and (c) Scanning electron micrographsof VO2 arrays with the particle radii r  26, 35, 44, 49 nm andcorresponding lattice constant L  166, 222, 278, 310 nm.Scale bar is 200 nm.FIG. 2. (a) Scattering spectrum from a VO2 array (r 44 nm) at 23 C and 90 C normalized to the lamp intensity.(b) Peak position and (c) relative scattered intensity vs particlesize in the metallic and semiconducting states (filled and opencircles, respectively).VOLUME 93, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R Sweek ending22 OCTOBER 2004after annealing was confirmed by Rutherford backscat-tering and x-ray diffraction in a separate experiment [12].Figure 1(b)–1(e) presents micrographs of four of thefive used in this experiment. VO2 does not wet Si and theresulting particles are mostly hemispherical [12]. Theparticles were arranged in square matrices (60 m 60 m) with varying periodicities (L) and particle sizes(r), but keeping the ratio L=r constant 6:3. Keeping L=rconstant automatically normalizes the scattering crosssection, which is proportional to r=L2. More impor-tantly, choosing L=r > 5 minimizes near-field particle-particle interactions. It has been shown [5] that for L=r <5, near-field coupling is strong enough to induce shifts inthe optical resonances and therefore could potentiallyobscure our study of the optical size dependence. ThusL=r ratio >5 is a safe regime for our lithography con-ditions, whereas L=r  5 would make the array parame-ters uncomfortably close to the wavelength of visiblelight. In that case unwanted ordinary diffractive effectswould predominate over the scattering.We performed dark-field spectroscopy of the NP arrayswith a focused nonpolarized white light source as illus-trated in Fig. 1(a). The sample is mounted on a Peltierheater and a precision thermocouple is placed near thearrays. The collection objective used to gather the scat-tered light had a 0.25 numerical aperture (NA) and wasoperated in confocal mode with a 100 m multimodeoptical fiber that delivers the light to an spectrometerwith a cooled charge coupled device detector. Thisdark-field confocal microscopy makes it possible to re-cord spectra from the heart of the NP array with negli-gible background light. The grating constants of thearrays were kept under 360 nm to avoid diffractive orderscollected by the system thus allowing only incoherentscattering [see Eq. (1)].Figure 2(a) shows the typical spectrum observed of thescattered light from the VO2 NPs. The blue-green widepeak falls in intensity (  35%) and blueshifts slightlywhen the particles switch to the metallic state. This is aunique feature that has not been observed previously in177403-2VO2 bulk samples or thin films, where the largest opticaldifference between the phases is in the IR. However, wecan see that for these NPs, the optical scattering in the IRis quite small. This is because the scattering from smallparticles presents unique resonances due to the electronicconfinement that can be explained in the framework ofMie theory as we show later. Figure 2(b) shows theevolution of this resonance as function of the particlesize. There is a pronounced blueshift with smaller sizes,while the shift between the two phases tends to be re-duced. The use of these designer arrays allows us tocontrol the intensity of the scattering. With r=L2 con-stant, the scattering intensity is found to be proportionalto r as shown in Fig. 2(c).Another extraordinary behavior is the temperature evo-lution of the scattered signal at all wavelengths. In VO2thin films, one observes narrow, monotonically increas-ing or decreasing hysteresis curves connecting the twostates of the film. In sharp contrast to this behavior,Fig. 3(a) shows that the NP arrays exhibit a broad hys-teresis loop with a three-state behavior, the two expectedphases plus an additional enhanced intensity state be-tween them. The size effects are not only present in theoptical properties but also in the features of the phasetransition itself. Figure 3(b) and 3(c) show a correlationbetween size and phase transition temperatures withhigher Tc’s for the smaller NPs as well as larger under-coolings and wider hysteresis loops.177403-2FIG. 4. Calculated optical properties of VO2 nanoparticles.(a) Mie extinction and scattering effective cross sections fora r  80 nm nanoparticle. (b) Wavelength of resonance vsparticle radius. (c) Scattering efficiency vs particle radius.(d) Collective scattered intensity (solid line) for a given proba-bility function (dashed line) of the nanoparticles undergoingphase transition in the array. Notice the less steep cooling sidein agreement with observations on Ref. [20].FIG. 3. (a) Temperature evolution of the scattered signal at  600 nm. (b) Typical hysteresis loop of the scattered lightwith indicator points along the phase transition from the VO2nanoparticles in array. (c) Temperatures of indicator pointsduring a cycle of the VO2 semiconductor-to-metal phase tran-sition as a function of size. Solid lines are only a guide for theeye.VOLUME 93, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R Sweek ending22 OCTOBER 2004The extraordinary switching in the visible region isparticularly interesting because a resonant response inVO2 was previously observed only in the infrared due tothe surface plasmon of the metallic phase.We can accountfor the strong size dependence and the visible resonancein the following way. The spatially organized ensemble ofVO2 hemispheres on Si is complicated to model opticallyfrom first principles. However, the hemispherical shapeand the presence of the Si-air interface has been treated indetail in previous analyses of other NPs, in particularregarding plasmon resonances of metals [13–15]. It hasbeen found that the shape and substrate factors contributeprimarily to small redshifts of the spectral features, butdo not alter the qualitative features that can easily bemodeled using conventional Mie theory. We have per-formed full Mie calculations [16] using the opticalconstants [17] of both VO2 phases. The results shownin Fig. 4(a) present the scattering and total effectiveextinction cross sections for r  80 nm VO2 spheres inair. The qualitative agreement with our observation isclear since the scattering cross section presents a peakin the visible region. The contrast between the two phasesis evident in the vicinity of that peak but very small in theIR region consistent with our observation. It is importantto note that our experiment is mostly blind to absorptioneffects and the onset of a plasmon resonance at   1 mwould be only observed in a complete extinctionmeasurement.177403-3Our calculation also predicts the observed blueshift ofthe resonance with smaller particle size and the lowerscattering efficiency for the metallic phase [Fig. 4(b) and4(c)]. In terms of size comparisons, we observe that theexperimental data are redshifted by the presence of thesubstrate. However, smaller particles will probablyquench the effect since the scattering effects are domi-nant in large particles (r 	 50 nm) whereas absorptiondominates for small ones (r < 10 nm) [18]. The naturalconclusion is that in contrast to the plasmon resonance at  1 m that persists in small NPs and is known tohave a dipolar source [19], the observed scattering reso-nance that we have found in the visible is definitely ofhigher multipolar origin.Regarding the size dependence of the observed tem-peratures of the phase transition [Fig. 3(c)], we first pointto agreement with previous work [20,21] showing that Tcand the width of the hysteresis loop decreases with in-creasing particle size. This phenomenon has been ex-plained by the hypothesis that the SMT in VO2 can bedescribed on the model of a martensitic transformation,in which a density of heterogeneous nucleation centersplays the essential role in triggering the phase transfor-mation [20,22]. For isolated NPs with the same crystal-linity, the probability to trigger the structural phasetransition at a certain temperature decreases with de-creasing NP size as the number of defects within therelevant volume is reduced. Our samples confirm those177403-3VOLUME 93, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R Sweek ending22 OCTOBER 2004previous observations but with the tremendous advantageof controlled average size and narrow size distribution,allowing new insights into the size dependence of thephase transition. We can show that a defined size does nothave a unique Tc, but a probability of switching centeredat that temperature.The strict periodicity of the array works as the idealtool to prove this hypothesis that in earlier studies wasclouded by the broad size distribution of particles.Recalling Fig. 3(b), we observe an intermediate intensescattering in the transit region between the two phases.This result arises from the underlying stochastic nature ofthe phase transition. The VO2 NPs are arranged in peri-ods L on top of the substrate. When irradiated with lightof wavelength , the coherent scattered field in the direc-tion  from each row of NPs will be proportional to:XNn1PneinL; with  2sin0  sin: (1)Pn is the scattering efficiency of the nanoparticle n.Clearly when  is a multiple of 2=L, the scatteringwould be coherent. For L<  and large N the sum tendsto cancel by destructive interference at the collectionangle sin  NA, resulting in a low intensity, character-istic of the Pn scattering efficiency of the nanoparticles.This efficiency was shown above to be greater for parti-cles in the semiconducting state than in the metallic one,Psemiconductorn > Pmetaln . However, when the particles start totransform, the incoherent scattering fails to minimize thesum in Eq. (1) since the lowest Fourier frequency neededto describe the array becomes smaller than 2=L. Thisexplanation is modeled in Fig. 4(d) for a linear chain of100 particles switching with a probability function thattransforms particles of the chain with a random numbergenerator. At the point of maximum disorder of the chain,the scattering peaks, in a clear order-disorder-order trans-formation that the array follows in transforming into theother phase. For all samples, the onset of the phase risingis at bulk Tc [point B in Fig. 3(b)], but the peak shifts[point C in Fig. 3(b)] with particle size in evidence of thestochastic nature governing the actual size dependence.In summary, the optical contrast between the semi-conducting and metallic phases of VO2 NPs in orderedarrays is dramatically enhanced in the visible region,exhibiting size-dependent multipole optical resonanceand transition temperatures. The collective optical re-sponse shows an enhanced scattering state as the phasetransition progresses, due to the intrinsic variability inthe transition temperature of the individual elements ofthe optical array. These new observations provide criticalinsights into statistical processes occurring in materialsat the nanoscale. These properties also constitute animportant set of size-dependent features that becomemore and more relevant as VO2 approaches nanotechnol-ogy applications [23,24].177403-4This material is based upon work supported by theNational Science Foundation under Grant No. DMR-0210785. The authors acknowledge useful technical dis-cussions with A. B. Hmelo.*Electronic address: rene.lopez@vanderbilt.edu†Also at The Condensed Matter Division, Oak RidgeNational Laboratory, Oak Ridge, TN 37831, USA.[1] J. D. Joannopoulos, P. R. Villenueve, and S. Fan, Nature(London) 386, 143 (1997).[2] A. J. Haes and R. P.V. Duyne, J. Am. Chem. Soc. 124,10 596 (2002).[3] S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E.Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2,229 (2003).[4] N. Félidj, G. L. J. Aubard, J. R. Krenn, G. Shider, A.Leitner, and F. R. Aussenegg, Phys. Rev. B 65, 075419(2002).[5] L. Zhao, K. L. Kelly, and G. C. Schatz, J. Phys. Chem. B107, 7343 (2003).[6] H. R. Stuart and D. G. Hall, Phys. Rev. Lett. 80, 5663(1998).[7] S. Linden, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 86,4688 (2001).[8] J. B. Goodenough, J. Solid State Chem. 3, 490 (1971).[9] R. M. Wentzcovitch, W.W. Schulz, and P. B. Allen, Phys.Rev. Lett. 72, 3389 (1994).[10] A. Zylbersztejn and N. F. Mott, Phys. Rev. B 11, 4383(1975).[11] A. Cavalleri, C. Tóth, C.W. Siders, J. A. Squier, F. Raksi,P. Forget, and J. C. Kieffer, Phys. Rev. Lett. 87, 237401(2001).[12] J.Y. Suh, R. Lopez, L. C. Feldman, and R. F. Haglund Jr.,J. Appl. Phys. 96, 1209 (2004).[13] R. Chauvaux and A. Meessen, Thin Solid Films 62, 125(1979).[14] J. L. Bijeon, P. Royer, J. P. Goudonnet, R. J. Warmack, andK. L. Ferrett, Thin Solid Films 155, L1 (1987).[15] G. Videen, J. Opt. Soc. Am. A 8, 483 (1991).[16] H. C. van de Hulst, Light Scattering by Small Particles(Dover, NY, 1981).[17] H.W. Verleur, A. S. Baker, and C. N. Berglund, Phys. Rev.172, 788 (1968).[18] I. O. Sosa, C. Noguez, and R. G. Barrera, J. Phys. Chem. B107, 6269 (2003).[19] R. Lopez, T. E. Haynes, L. A. Boatner, L. C. Feldman, andR F. Haglund Jr., Opt. Lett. 27, 1327 (2002).[20] R. Lopez, T. E. Haynes, L. A. Boatner, L. C. Feldman, andR. F. Haglund Jr., Phys. Rev. B 65, 224113 (2002).[21] V. A. Klimov, I. O. Timofeeva, S. D. Khanin, E. B.Shadrin, A.V. Ilinskii, and F. Silva-Andrade, TechnicalPhysics 47, 1134 (2002).[22] I. A. Kharhaev, F. A. Chudnovskii, and E. B. Shadrin,Phys. Solid State 36, 898 (1994).[23] A. A. Bugayev and M. C. Gupta, Opt. Lett. 28, 1463(2003).[24] S. Chen, H. Ma, X. Yi, H. Wang, X. Tao, M. Chen, X. Li,and C. Ke, Infrared Phys. 45, 239 (2004).177403-4

Size-dependent optical properties of VO2 nanoparticle arrays

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Size-dependent optical properties of VO2 nanoparticle arrays

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