Research Article On the Problem of Metal-Insulator …oxides. Similar consideration is applicable to other compounds of variablecomposition,suchas,forinstance,high-temperature superconductors

Hindawi Publishing CorporationISRN Condensed Matter PhysicsVolume 2013 Article ID 960627 6 pageshttpdxdoiorg1011552013960627

Research ArticleOn the Problem of Metal-Insulator Transitions inVanadium Oxides

A L Pergament G B Stefanovich N A Kuldin and A A Velichko

Physics and Technology Department Petrozavodsk State University Petrozavodsk 185910 Russia

Correspondence should be addressed to G B Stefanovich gstefyandexru

Received 14 May 2013 Accepted 16 June 2013

Academic Editors A N Kocharian A Krimmel and A Oyamada

Copyright copy 2013 A L Pergament et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The problem of metal-insulator transition is considered It is shown that theMott criterion 119886B(119899c)13asymp 025 is applicable not only to

heavily doped semiconductors but also to many other materials including some transition-metal compounds such as vanadiumoxides (particularly VO

2and V

2O3) The low-temperature transition (ldquoparamagnetic metalmdashantiferromagnetic insulatorrdquo) in

vanadium sesquioxide is described on the basis of this concept in terms of an intervening phase between metal and insulatorstates with divergent dielectric constant and effective charge carrier mass Recent communications concerning a possible ldquometal-insulator transitionrdquo in vanadium pentoxide are also discussed

1 Introduction

Strongly correlated transition metal oxides exhibiting metal-insulator transitions (MIT) are currently considered as basicfunctional materials of oxide electronics [1] That is why thetheoretical models describing MITs are of such importanceVanadium oxide Magneli phases forming the homologousseries V

119899O2119899minus1

(3 le 119899 le 9) may be considered as interme-diate structures between the end members VO

2(119899 rarr

infin) and V2O3(119899 = 2) With one exception (V

7O13) the

vanadium Magneli phases exhibit MITs [2] as functions oftemperaturemdashsee Figure 1 and [1ndash10]

In recent years a number of papers [4ndash6] have appearedconcerning a ldquometal-insulator transitionrdquo in V

2O5[3] Here

we do not intend to dispute scientific aspects of these worksand the object of our discussion will be different The fact isthat the term ldquometal-insulator transitionrdquo particularly withrespect to vanadium oxides (and not only to thesemdashgenerallyto a variety of transition metal oxides and related materials[7]) has long been used in the scientific literature to describequite a certain class of phenomena and experimental factsThus in this paper we will comment on the aforecitedreferences [4ndash6] with a more detailed discussion than thatin our brief note [3] in view of the problem of MITs invanadium oxides Also the MITs in V

2O3are discussed and

an attempt ismade to describe them in terms of amodel based

on the Mott criterion concept developing some ideas of ourprevious work [7] However first in Section 21 we have toacquaint a reader with the main general points of discussionand recall some results obtained earlier for vanadium dioxideand other related materials

2 Mott Metal-Insulator Transitions inVanadium Oxides

21 Strongly Correlated Systems and Mott Transition Atpresent there is no unified approach to interpret the elec-tronic properties of transition metal oxides [8] The bandtheory and the crystal field theory are the two limitingdescriptions of the outer electrons in solids and the essenceof difference between metals and insulators can be under-stood in terms of these two models For example in theelementary band theory when atoms are combined to forma macroscopic bulk sample with 119873 primitive unit cells eachelectron energy level per unit cell gives rise to 119873 electronstates in the energy band of a crystal Whether the materialwill be a metal or an insulator depends on whether the bandis filled partially or completely or whether or not the twobands will intersect In the semiconductor state the numberof charge carriers can be increased by adding an impurity andwhen the dopant concentration exceeds a certain value (119899c) asemiconductor undergoes a Mott MIT [9] into a metal state

2 ISRN Condensed Matter Physics

1 2 3 4 5 6 7 8 9 10 11 12 13 1410

minus4

10minus3

10minus2

10minus1

100

101

102

103

104

105

VO2

V3O5

V2O3

V4O7

V6O11

V5O9

V7O13

V8O15

120588(Ω

middotcm)

103T (Kminus1)

Figure 1 Resistivity versus reciprocal temperature for vanadiumoxides

Similar consideration is applicable to other compounds ofvariable composition such as for instance high-temperaturesuperconductors HTCS [8] The value of 119899c is given by thewell-known relation the Mott criterion [9]

119886B11989913

c asymp 025 (1)

where 119886B is the effective Bohr radius for the charge carrierlocalization on an impurity ion

As was repeatedly noted previously [7 10] theMott crite-rion expressed by (1) proved to be very successful in describ-ing MITs in various ordered systems doped semiconductors[8ndash11] and transition metal compounds [7] included (seeFigure 2 and Table 1) The Hubbard model suggests thatldquointeractions between electrons are accounted for via therepulsive Hubbard 119880 term only when they are on the samesiterdquo [11] Then Anderson has shown that for disordered sys-tems at a certain degree of disorder all the electronswould belocalized which renders the system nonconducting [11 14]In compounds exhibiting a temperature- or pressure-inducedMIT instead of the one caused by doping (substitution) ordisorder the Mott transition theory is rather more sophisti-cated [7ndash11] As compared with the above simple picture fordoped semiconductors some new important phenomena areobserved in compounds of 119889 and 119891 elements For exampletransition metal compounds containing atoms with unfilled119889-shells form complex systems of phases with multipleoxidation states andmixed valenceThese compounds belongto a class of strongly correlated systems and strong electron-electron correlations are associated with a specific behaviorof 119889-electrons Since the 119889-bands are narrow the energy ofelectron-electron Coulomb interactions is of the order of thebandwidth119861 (and hence the electron kinetic energy) that is119880 sim119861 It is commonly accepted by now that strong correlationeffects are responsible for some unique properties of such

Table 1 The effective Bohr radius 119886B = 120576ℏ2119898lowast1198902 and the critical

carrier density for anMIT in some compounds (numbers of rows inthe table correspond to numbers of points in Figure 2)

No Material 119886119861 nm 119899

119888 1017 cmminus3 References

1 Si P 135 30

[7 10]

2 Si B 141 413 Si Bi 088 1404 Ge Sb 474 155 n-GaAs 967 0126 n-InSb 577 00017 CdS In 35 258 CdS Cl 33 999 GaP Zn 11 13010 Cu Ar 009 2 sdot 10

5

11 YBa2Cu3O7 045 180012 NH3 Na 08 34013 VO2 18 28 [7 12]14 V2O3 118 100 [7]15 V2O3 (AFI) sim12 0021 [7]16 SmS 073(lowast) 700 [15 16] [15ndash18]17 Sr

1minus119909La119909TiO3

097 30 [19](lowast)For119898lowast = 13119898119890 [17] and 120576 = 18 [18]

materials as HTCS cuprates materials with metal-insulatortransitions heavy-fermion superconductors ferromagneticperovskites with colossal magnetoresistance and so forth

Another well-known example of the influence of correla-tion effects on the band structure is a ldquocorrelated insulatorrdquo(NiO eg) Insulators of this type are also known as Mottinsulators for it wasMottrsquos suggestion that electron repulsionis responsible for a breakdown of normal band properties forthe 119889-electrons which was later formalized in the Hubbardmodel [9 11] Note that high- and low-temperature phasesof vanadium sesquioxide doped by chromium to ca 1 at(Figure 3) are just the ones representing amongst otherssuch Mott insulator phases [9]

As far as vanadium oxides concerns it has been shown[7] that in the case of vanadium dioxide as well as for ahigh-temperature transition ldquoparamagnetic insulator-para-magnetic metalrdquo in vanadium sesquioxide the relation (1) iscompletely fulfilled

In particular for vanadium dioxide the value of thecritical density 119899c is of the order of 119899

119904mdashthe equilibrium

electron density in the conduction band of VO2in the low-

temperature semiconducting phase at 119879 rarr 119879119905(where 119879

119905is

the transition temperature sim340K for vanadium dioxidemdashsee Figure 1) Next 119886

119861= ℏ21205761198902119898lowast where 120576 and 119898lowast are

the dielectric constant and effective mass respectively For120576 = 100 and 119898lowast = 3119898

119890[7 12] this yields 119886B = 177 nm in

vanadium dioxide and the product of 119886B and (119899c)13 turns

out to be just that as predicted by (1)mdashpoint 13 in Figure 2

22 Vanadium Sesquioxide It is really noteworthy that theMott criterion (1) works in the case of vanadiumdioxide and aPI-PM transition in vanadium sesquioxide (see rows 13 and 14inTable 1 aswell as corresponding points in Figure 2) andnot

ISRN Condensed Matter Physics 3

10minus4

10minus3

10minus2

10minus1

100

101

102

103

104

105

106

001 01 1 10 100Effective Bohr radius (nm)

1

2

10

155

6

74

813

14

17

916

312

11

Criti

cal d

ensit

y (1017

cmminus3)

Figure 2 Correlation between the effective Bohr radius and thecritical densities for different systems (see Table 1) Only somerepresentative materials are included other examples one can findin [7 10] Straight line corresponds to (1)

10minus2

10minus1

100

101

102

103

104

105

106

0 1 2 3 4 5 6 7 8 9 10

V2O3 doped with 1 at of Cr AFI

PI

PM

Resis

tivity

(Ωmiddotcm

)

1000T (Kminus1)

Figure 3 Temperature dependence of resistivity for(V1minus119909

Cr119909)2O3 Cr with 119909 = 0012 [8ndash11] AFI-antiferromagnetic

insulator PM-paramagnetic metal and PI-paramagnetic insulator

only for doped semiconductors or some other well-knownMott insulators like YBa

2Cu3O7minus119909

or Sr1minus119909

La119909TiO3

However in the case of a low-temperature AFI rarr PMtransition in V

2O3 the situation becomes more complicated

For this transition as was shown in [7] the product of 119886Band (119899c)

13 is far less than 025 (Figure 2 point 15) that is theDebye screening length 119871Dquant is far in excess of 119886B whichsuggests that the Mott transition to a metallic state wouldseem hardly probable On the other hand in a classic casethe screening length can be written as

119871Dclass = radic119896B119879120576041205871198902119899

(2)

where 119896B and 1205760 are the Boltzmann and vacuum permittivityconstants and 119899 corresponds to the value of 119899c for thetransition point In this case one still obtains 119871D gt 119886Bbecause for 119879 = 119879

119905= 170K (see Figure 3) (2) yields 119871D =

56 nm while 119886B is equal to only 12 nm (this quantity can beobtained for V

2O3from calculation similar to that carried out

for VO2above but with119898lowast = 9119898

119890and 120576 = 200 [7])

Generally expressions of the type 119871D = 119877 (where 119877 is theelectron localization radius for instance 119886B) or119861 = 119880 (where119861 and119880 are the kinetic and potential electron energies resp)are nearly equivalent to the Mott criterion given by (1) seefor example discussions in the works [12 20] related to thisissue Note that the value of 119886B is determined by the dielectricconstant and effective mass Unfortunately we do not knowthe exact values of 120576 and119898lowast near the phase transition becauseof their divergence (or unrestricted growth) and probablythat very factor is responsible for the fulfillment of theequality119871D = 119877This situation is illustrated in Figure 4whichsuggests that an increase of 119877 = 119886B due to increased 120576 close totheMIT as well as a decrease of 119871D due to increased 119899 wouldresult in the intersection of the two curves at the transitionpoint These speculations show that the low-temperatureAFI rarr PM transition in V

2O3might also be described from

the position of theMottMIT In other words the dependence119886B(119879) in Figure 4 can account for the fulfillment of relation (1)in the case of the transition from AFI to PM in chromium-doped vanadium sesquioxide and solve thereby the problemwith this transition formulated in the work [7]

Thus we come to a conclusion that the MITs in somelower vanadium oxides namely VO

2and V

2O3 might be

fairly satisfactory described in terms of the Mott transitionmodel It is to be noted that the relations between structuraland electronic properties should be taken into account whendescribing an exactMITmechanism both in these oxides andin other vanadium Magneli phases [21] Structural aspectsare of particular importance for instance in VO

2where

the MIT is often described in terms of a ldquoMott-Peierlsrdquo (orcorrelation-assisted Peierls) transition [22 23] as well as inV7O13

where neither of the two mechanisms (ie electroncorrelation effects or Peierls-like structural instabilities) isstrong enough to induce a transition [21]

23 Vanadium Pentoxide Is There a Metal-Insulator Transi-tion in This Highest-Valence Vanadium Oxide Now return-ing to the problem of a possibleMIT in the highest vanadiumoxide V

2O5 we should say that the above-described picture

exploded when we learned [3] about a ldquometal-insulatortransition in vanadium pentoxiderdquo [4ndash6] This oxide is nota member of the Magneli V

119899O2119899minus1

series and it has everbeen known as a semiconductor with the band gap width ofsim22 eV [8] exhibiting no trend to a transition into metallicstate Here the point is that we are dealing with a change inphase composition which is not the same thing We are pre-sented with a phase transition of vanadium pentoxide uponheating up to sim280∘C [5] into some other vanadium oxidephases exhibiting metallic properties at these temperaturesas purportedly anMIT in V

2O5 Actually the transformation

described in the article [5] is neither a temperature-inducedMIT nor is it even a composition-induced MIT as for


Temperature

MetalInsulator

Char

acte

ristic

leng

th

Region of phasecoexistence

LD

aB

a998400

B

Figure 4 Schematic temperature dependences of the Debye screen-ing length and localization radius If account is taken of thedependence of 119886B on 119879 via the divergence of 120576 near the transitionpoint (curve 1198861015840B) the transition does occur (vertical dashed line)For more detailed discussion of the 119871D dependence on 119879 see [7] Aregion of phase coexistence (termed as an ldquointermediate staterdquo [12]or a ldquostrongly correlated metalrdquo [13] in case of VO

2) with a divergent

effective mass is also shown

example a transition ldquoV2O5mdashnonstoichiometric V

2O5minus120575

rdquoThis transformation is associated with a reduction of V

2O5

we repeat once more to lower oxides ldquowhen V2O5is

subjected to high temperature thematerial loses oxygenThisinduces a structural inhomogeneity resulting in a mixing ofphases such as V

2O5 V6O13 V2O3rdquo [5]

Such a misunderstanding seems to originate from thework [24] where experiments on memory switching in thin-filmV

2O5-based structures have been described To interpret

the results of these experiments the authors of [24] putforward a hypothesis of some ldquoglass-to-metalrdquo transition inamorphous vanadium pentoxide Afterwards in the litera-ture this assumption somehow transformed into an idea ofan MIT in V

2O5which was further widely circulated (with

no efforts to delve into the problem) and much referred toThe reference was first made in [25] (just as with an MIT inV2O5at 119879119905= 257

∘C) followed by a few refutations [26 27]The subject could have seemed exhausted Meanwhile inthe papers [28ndash33] we have again encountered the samestatement (and again with references to either [24] or someother old works) and finally it has been reported on an ldquoMITin V2O5rdquo as it is asserted in the titles of the articles [4 5]

One cannot but admit that everything is correct inthose articles (as to the results presented) but entering suchterms in the article titles seems to be not quite appropriateThere is certainly no metal-insulator transition in vanadiumpentoxide in the commonly accepted sense discussed aboveIf one even would try to put a corresponding point inFigure 2 it will just exceed the bounds of the figure wellbelow the abscissa axis solely because of too low carrierdensity in dielectric V

2O5

3 Conclusion

In conclusion it is shown in the present study that the Mottcriterion is applicable not only to heavily doped semicon-ductors but also to many other compounds including such

materials important for the MIT problem on the whole asvanadium oxides particularly VO

2and V

2O3 In order to

verify model approximations introduced in this article addi-tional experimental data are likely to be needed Obviouslyfurther studies seem to be of importance focused on thor-oughmeasurements of the dielectric constant effective massand carrier mobility values of both vanadium oxide Magneliphases [21 34ndash37] and other strongly correlated 119891- and 119889-compounds undergoing Mott metal-insulator transitions

The problem of effective mass is of especial importanceWe recall that the value of 119898lowast is necessary in order tocalculate the effective Bohr radius 119886B in theMott criterion (1)Meanwhile the accurate charge carrier effective mass valuesare not always known in case of strongly correlated transitionmetal compounds Even for the much-studied vanadiumdioxide the experimental values obtained by various authorsdiffer nearly by an order of magnitude [36] The difficultiesand vagueness while determining an effective mass are wellknown these are due to both the quality of a sample and themeasuring technique Optical methods (from measurementsof the plasma frequency) and electrical (transport) measure-ments yield as a rule two different magnitudes which is nowonder since the values of 119898lowast of DOS (density of states)and the band effective mass should not necessarily coincide[13] Furthermore in anisotropic substances this physicalquantity depends on direction An approach to calculate theeffective masses in vanadium oxide Magneli phases has beendeveloped in [36] howevermore efforts both theoretical andexperimental are needed in this direction

As to the MIT in vanadium pentoxide [4ndash6 25 28ndash33]it should be emphasized once again that the scientific impor-tance and correctness of results of the works [4 5] are cer-tainly beyond question just we would suggest do not use theterm ldquometal-insulator transitionrdquo for this is confusing in sucha context as we have tried to show in Section 23 The afore-said however does not abolish a feasibility of a temperature-induced MIT in nonstoichiometric [38] or doped [6] V

2O5

For example in vanadium dioxide doping with tungsten toca 10ndash15 at leads tometallizationwithout thematerial heat-ing up to 119879 = 119879

119905[39] However this situation is not the same

as that described in the work [4] for vanadium pentoxidebecause the material (VO

2) does not transform into another

vanadium oxide Magneli phase under such an alloyingFinally we would like to reiterate the idea that we have

started this paper with that is the problems discussed hereare not of solely abstract scientific interest but they areof importance from the practical viewpoint too since thematerials exhibiting MIT find an application for a lot ofvarious electronic and optical devices It is appropriate hereto quote an excerpt from the review [1] where the authorsldquodiscuss the exploration of correlated oxide phase transitionsin novel electronics photonics and related devices Althoughthis area has intrigued researchers for several decades eversince the original observation of MIT in oxides the twenty-first-century grand challenge of continued innovation ininformation processing sciences beyond CMOS scaling cre-ates an opportunity to seriously consider alternate computingvectors that may offer unique advantagesrdquo Particularly vana-dium dioxide can be used as a material for thermochromic


indicators optical filters and controllers bolometers thin-film transistors and switches and many other optical andelectronic devices

Note that vanadium pentoxide has also drawn consid-erable interest in the past decades due to multiple potentialapplications such as electrochromic devices optical switchingdevices reversible cathode materials for Li batteries and gassensors [32] Also V

2O5exhibits thermochromic properties

likewise VO2 It should be stressed however that the ther-

mochromic and photochromic effects in vanadiumpentoxideare both due to a reversible hydrogen injection-extraction[40] and hence thermochromism in V

2O5is not associated

with an MIT as it is mistakenly stated for example in thework [29] Recently vanadium pentoxide was synthesized inthe form of nanowires nanorods and nanofibers [6 32] Thepotential use of such V

2O5nanoobjects provides excellent

possibilities for designing new electronic and optoelectronicnanodevicesThat is why the question about anMIT in V

2O5

is of especial scientific interest and practical importance

Acknowledgments

This work was supported by the Ministry of Education andScience of Russian Federation ldquoScientific and EducationalCommunity of Innovation Russia (2009ndash2013)rdquo Programthrough Contracts no 14740110895 no 14740110137 andno 16740110562 and ldquoDevelopment of Scientific Potentialof High Schoolrdquo Program Grants no 232822011 and no227742011 as well as the Strategic Development Program ofPetrozavodsk State University (2012ndash2016) The authors alsothankVN Andreev for useful discussions andV P Novikovafor her help with the paper preparation

References

[1] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[2] F J Morin ldquoOxides which show a metal-to-insulator transitionat the neel temperaturerdquo Physical Review Letters vol 3 no 1 pp34ndash36 1959

[3] A Pergament G Stefanovich and V Andreev ldquoComment onldquoMetal-insulator transition without structural phase transitioninV2O5filmrdquo [Appl Phys Lett 98 131907 (2011)]rdquoApplied Phys-

ics Letters vol 102 Article ID 176101 1 page 2013[4] R-P Blum H Niehus C Hucho et al ldquoSurface metal-insulator

transition on a vanadium pentoxide (001) single crystalrdquo Physi-cal Review Letters vol 99 no 22 Article ID 226103 2007

[5] M Kang I Kim S W Kim J-W Ryu and H Y Park ldquoMetal-insulator transition without structural phase transition in V

2O5

filmrdquo Applied Physics Letters vol 98 no 13 Article ID 1319072011

[6] T Wu C J Partridge S Banerjiee and G SambandamurthyldquoMetal-insulator transition in individual nanowires of dopedV2O5rdquo American Physical Society APS March Meeting abstract

no V16007 2010[7] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-

tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[8] P A CoxTransitionMetalOxides An Introduction toTheir Elec-tronic Structure and Properties Clarendon Press Oxford UK1992

[9] N FMottMetal-Insulator Transitions Taylor and Francis Lon-don UK 1990

[10] P P Edwards TV Ramakrishnan andCNR Rao ldquoThemetal-nonmetal transition a global perspectiverdquo Journal of PhysicalChemistry vol 99 no 15 pp 5228ndash5239 1995

[11] R Redmer F Hensel and B Holst Eds Metal-To-NonmetalTransitions vol 132 of Springer Series in Materials ScienceSpringer New York NY USA 2010

[12] A Pergament and A Morak ldquoPhotoinduced metal-insulatortransitions critical concentration and coherence lengthrdquo Jour-nal of Physics A vol 39 no 17 pp 4619ndash4623 2006

[13] M M Qazilbash M Brehm B-G Chae et al ldquoMott transitionin VO

2revealed by infrared spectroscopy and nano-imagingrdquo

Science vol 318 no 5857 pp 1750ndash1753 2007[14] D Belitz andT R Kirkpatrick ldquoTheAnderson-Mott transitionrdquo

Reviews of Modern Physics vol 66 no 2 pp 261ndash380 1994[15] V V Kaminskii A V Golubkov and L N Vasilrsquoev ldquoDefect

samarium ions and electromotive-force generation in SmSrdquoPhysics of the Solid State vol 44 no 8 pp 1574ndash1578 2002

[16] V V Kaminskii L N Vasilrsquoev M V Romanova and S MSolovrsquoev ldquoThemechanismof the appearance of an electromotiveforce on heating of SmS single crystalsrdquoPhysics of the Solid Statevol 43 pp 1030ndash1032 2001

[17] B Batlogg A Schlegel and PWachter ldquoDegree of valence mix-ing in themetallic phase of SmS andTmSerdquo Journal de Physiquevol 37 pp 267ndash270 1976

[18] V Zelezny J Petzelt V V Kaminski M V Romanova and A VGolubkov ldquoFar infrared conductivity and dielectric response ofsemiconducting SmSrdquo Solid State Communications vol 72 no1 pp 43ndash47 1989

[19] S Hui Evaluation of Yttrium-doped SrTiO3as a solid oxide fuel

cell anode [PhD thesis] 2000 httpdigitalcommonsmcmastercaopendissertations1659

[20] J Spałek J Kurzyk R Podsiadły and W Wojcik ldquoExtendedHubbardmodel with the renormalizedWannier wave functionsin the correlated state II quantum critical scaling of the wavefunction near the Mott-Hubbard transitionrdquo European PhysicalJournal B vol 74 no 1 pp 63ndash74 2010

[21] U Schwingenschlogl and V Eyert ldquoThe vanadium Magneliphases VnO2nminus1rdquo Annalen der Physik vol 13 no 9 pp 475ndash5102004

[22] J Laverock A RH PrestonDNewby Jr et al ldquoPhotoemissionevidence for crossover from Peierls-like to Mott-like transitionin highly strainedVO

2rdquoPhysical ReviewB vol 86 no 19 Article

ID 195124 5 pages 2012[23] S Kim K Kim C J Kang and B I Min ldquoCorrelation-assisted

phonon softening and the orbital-selective Peierls transition inVO2rdquo Physical Review B vol 87 Article ID 195106 2013

[24] G S Nadkarni and V S Shirodkar ldquoExperiment and theory forswitching in AlV

2O5Al devicesrdquoThin Solid Films vol 105 no

2 pp 115ndash129 1983[25] E E Chain ldquoOptical properties of vanadium dioxide and vana-

dium pentoxide thin filmsrdquo Applied Optics vol 30 pp 2782ndash2787 1991

[26] H Jerominek F Picard and D Vincent ldquoVanadium oxide filmsfor optical switching and detectionrdquoOptical Engineering vol 32no 9 pp 2092ndash2099 1993


[27] Y Dachuan X Niankan Z Jingyu and Z Xiulin ldquoVanadiumdioxide films with good electrical switching propertyrdquo Journalof Physics D vol 29 no 4 pp 1051ndash1057 1996

[28] J Nag The solid-solid phase transition in vanadium dioxidethin films synthesis physics and application [PhD thesis]2011 httpetdlibraryvanderbilteduavailableetd-04202011-182358

[29] P Kiri G Hyett and R Binions ldquoSolid state thermochromicmaterialsrdquo Advanced Materials Letters vol 1 no 2 pp 86ndash1052010

[30] J Nag andR FHaglund Jr ldquoSynthesis of vanadiumdioxide thinfilms and nanoparticlesrdquo Journal of Physics Condensed Mattervol 20 no 26 Article ID 264016 2008

[31] M I Kang I K Kim E J Oh S W Kim J W Ryu and HY Park ldquoDependence of optical properties of vanadium oxidefilms on crystallization and temperaturerdquoThin Solid Films vol520 no 6 pp 2368ndash2371 2012

[32] S Beke ldquoA review of the growth of V2O5films from 1885 to

2010rdquoThin Solid Films vol 519 no 6 pp 1761ndash1771 2011[33] R M Oksuzoglu P Bilgic M Yildirim and O Deniz ldquoInflu-

ence of post-annealing on electrical structural and opticalproperties of vanadium oxide thin filmsrdquo Optics amp Laser Tech-nology vol 48 pp 102ndash109 2013

[34] T Reeswinkel D Music and J M Schneider ldquoCoulomb-potential-dependent decohesion of Magneli phasesrdquo Journal ofPhysics Condensed Matter vol 22 no 29 Article ID 2922032010

[35] B Stegemann M Klemm S Horn and M Woydt ldquoSwitchingadhesion forces by crossing the metal-insulator transition inMagneli-type vanadium oxide crystalsrdquo Beilstein Journal ofNanotechnology vol 2 no 1 pp 59ndash65 2011

[36] A Pergament ldquoMetal-insulator transition temperatures andexcitonic phases in vanadium oxidesrdquo ISRN Condensed MatterPhysics vol 2011 Article ID 60591 5 pages 2011

[37] B G Idlis and Y V Kopaev ldquoOn the theory of phase transitionsin vanadium oxides VnO2nminus1 (Magneli phases)rdquo Solid StateCommunications vol 45 no 3 pp 301ndash304 1983

[38] A L Pergament G B Stefanovich V N Andreev and P ABoldin ldquoElectronic instabilities in crystals of transition metalcompoundsrdquo in Proceedings of the Petrozavodsk State Universityno 6 (127) pp 87ndash98 2012

[39] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[40] A I Gavrilyuk N M Reinov and F A Chudnovskii ldquoPhoto-chromism and thermochromism in amorphous V

2O5filmsrdquo

Soviet Technical Physics Letters vol 5 pp 514ndash515 1979

Submit your manuscripts athttpwwwhindawicom

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1 2 3 4 5 6 7 8 9 10 11 12 13 1410

minus4

10minus3

10minus2

10minus1

100

101

102

103

104

105

VO2

V3O5

V2O3

V4O7

V6O11

V5O9

V7O13

V8O15

120588(Ω

middotcm)

103T (Kminus1)

Figure 1 Resistivity versus reciprocal temperature for vanadiumoxides

Similar consideration is applicable to other compounds ofvariable composition such as for instance high-temperaturesuperconductors HTCS [8] The value of 119899c is given by thewell-known relation the Mott criterion [9]

119886B11989913

c asymp 025 (1)

where 119886B is the effective Bohr radius for the charge carrierlocalization on an impurity ion

As was repeatedly noted previously [7 10] theMott crite-rion expressed by (1) proved to be very successful in describ-ing MITs in various ordered systems doped semiconductors[8ndash11] and transition metal compounds [7] included (seeFigure 2 and Table 1) The Hubbard model suggests thatldquointeractions between electrons are accounted for via therepulsive Hubbard 119880 term only when they are on the samesiterdquo [11] Then Anderson has shown that for disordered sys-tems at a certain degree of disorder all the electronswould belocalized which renders the system nonconducting [11 14]In compounds exhibiting a temperature- or pressure-inducedMIT instead of the one caused by doping (substitution) ordisorder the Mott transition theory is rather more sophisti-cated [7ndash11] As compared with the above simple picture fordoped semiconductors some new important phenomena areobserved in compounds of 119889 and 119891 elements For exampletransition metal compounds containing atoms with unfilled119889-shells form complex systems of phases with multipleoxidation states andmixed valenceThese compounds belongto a class of strongly correlated systems and strong electron-electron correlations are associated with a specific behaviorof 119889-electrons Since the 119889-bands are narrow the energy ofelectron-electron Coulomb interactions is of the order of thebandwidth119861 (and hence the electron kinetic energy) that is119880 sim119861 It is commonly accepted by now that strong correlationeffects are responsible for some unique properties of such

Table 1 The effective Bohr radius 119886B = 120576ℏ2119898lowast1198902 and the critical

carrier density for anMIT in some compounds (numbers of rows inthe table correspond to numbers of points in Figure 2)

No Material 119886119861 nm 119899

119888 1017 cmminus3 References

1 Si P 135 30

[7 10]

2 Si B 141 413 Si Bi 088 1404 Ge Sb 474 155 n-GaAs 967 0126 n-InSb 577 00017 CdS In 35 258 CdS Cl 33 999 GaP Zn 11 13010 Cu Ar 009 2 sdot 10

5

11 YBa2Cu3O7 045 180012 NH3 Na 08 34013 VO2 18 28 [7 12]14 V2O3 118 100 [7]15 V2O3 (AFI) sim12 0021 [7]16 SmS 073(lowast) 700 [15 16] [15ndash18]17 Sr

1minus119909La119909TiO3

097 30 [19](lowast)For119898lowast = 13119898119890 [17] and 120576 = 18 [18]

materials as HTCS cuprates materials with metal-insulatortransitions heavy-fermion superconductors ferromagneticperovskites with colossal magnetoresistance and so forth

Another well-known example of the influence of correla-tion effects on the band structure is a ldquocorrelated insulatorrdquo(NiO eg) Insulators of this type are also known as Mottinsulators for it wasMottrsquos suggestion that electron repulsionis responsible for a breakdown of normal band properties forthe 119889-electrons which was later formalized in the Hubbardmodel [9 11] Note that high- and low-temperature phasesof vanadium sesquioxide doped by chromium to ca 1 at(Figure 3) are just the ones representing amongst otherssuch Mott insulator phases [9]

As far as vanadium oxides concerns it has been shown[7] that in the case of vanadium dioxide as well as for ahigh-temperature transition ldquoparamagnetic insulator-para-magnetic metalrdquo in vanadium sesquioxide the relation (1) iscompletely fulfilled

In particular for vanadium dioxide the value of thecritical density 119899c is of the order of 119899

119904mdashthe equilibrium

electron density in the conduction band of VO2in the low-

temperature semiconducting phase at 119879 rarr 119879119905(where 119879

119905is

the transition temperature sim340K for vanadium dioxidemdashsee Figure 1) Next 119886

119861= ℏ21205761198902119898lowast where 120576 and 119898lowast are

the dielectric constant and effective mass respectively For120576 = 100 and 119898lowast = 3119898

119890[7 12] this yields 119886B = 177 nm in

vanadium dioxide and the product of 119886B and (119899c)13 turns

out to be just that as predicted by (1)mdashpoint 13 in Figure 2

22 Vanadium Sesquioxide It is really noteworthy that theMott criterion (1) works in the case of vanadiumdioxide and aPI-PM transition in vanadium sesquioxide (see rows 13 and 14inTable 1 aswell as corresponding points in Figure 2) andnot


10minus4

10minus3

10minus2

10minus1

100

101

102

103

104

105

106


1

2

10

155

6

74

813

14

17

916

312

11

Criti

cal d

ensit

y (1017

cmminus3)


10minus2

10minus1

100

101

102

103

104

105

106

0 1 2 3 4 5 6 7 8 9 10


PI

PM

Resis

tivity

(Ωmiddotcm

)

1000T (Kminus1)





2Cu3O7minus119909

or Sr1minus119909

La119909TiO3





119871Dclass = radic119896B119879120576041205871198902119899

(2)






119890and 120576 = 200 [7])





2and V

2O3 might be


2where






119899O2119899minus1





Temperature

MetalInsulator

Char

acte

ristic

leng

th


LD

aB

a998400

B


2) with a divergent



2O5minus120575


2O5











2O5

3 Conclusion



2and V

2O3 In order to




2O5

















2O5


Acknowledgments


References







2O5















































2O5filmsrdquo







FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




10minus4

10minus3

10minus2

10minus1

100

101

102

103

104

105

106


1

2

10

155

6

74

813

14

17

916

312

11

Criti

cal d

ensit

y (1017

cmminus3)


10minus2

10minus1

100

101

102

103

104

105

106

0 1 2 3 4 5 6 7 8 9 10


PI

PM

Resis

tivity

(Ωmiddotcm

)

1000T (Kminus1)





2Cu3O7minus119909

or Sr1minus119909

La119909TiO3





119871Dclass = radic119896B119879120576041205871198902119899

(2)






119890and 120576 = 200 [7])





2and V

2O3 might be


2where






119899O2119899minus1





Temperature

MetalInsulator

Char

acte

ristic

leng

th


LD

aB

a998400

B


2) with a divergent



2O5minus120575


2O5











2O5

3 Conclusion



2and V

2O3 In order to




2O5

















2O5


Acknowledgments


References







2O5















































2O5filmsrdquo







FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Temperature

MetalInsulator

Char

acte

ristic

leng

th


LD

aB

a998400

B


2) with a divergent



2O5minus120575


2O5











2O5

3 Conclusion



2and V

2O3 In order to




2O5

















2O5


Acknowledgments


References







2O5















































2O5filmsrdquo







FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics













2O5


Acknowledgments


References







2O5















































2O5filmsrdquo







FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



















2O5filmsrdquo







FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Documents

Research Article On the Problem of Metal-Insulator …oxides. Similar consideration is applicable to other compounds of variablecomposition,suchas,forinstance,high-temperature superconductors