Photogeneration of hot plasmonic electrons with metal nanocrystals: quantum description and potential applications

Availableonlineatwww.sciencedirect.com

ScienceDirect

jo u rn al h om ep a ge : w w w . e l s e v i e r . c o m / l o c a t e / n a n o t o d a y

REVIEW

Photogeneration

of

hot

plasmonic

electrons

with

metal

nanocrystals:

Quantum

description

and

potential

applications

Alexander

O.

Govorov

,

Hui

Zhang

,

Hilmi

Volkan

Demir

,

Yurii

K.

Gun’ko

a_{DepartmentofPhysicsandAstronomy,OhioUniversity,Athens,OH45701,USA}

b_{DepartmentofElectricalandElectronicsEngineering,DepartmentofPhysics,UNAM—Instituteof}

MaterialsScienceandNanotechnology,BilkentUniversity,Ankara06800,Turkey

c_{SchoolofElectricalandElectronicEngineering,SchoolofPhysicalandMathematicalSciences,Nanyang}

TechnologicalUniversity,NanyangAvenue,Singapore639798,Singapore

d_{SchoolofChemistryandCRANN,UniversityofDublin,TrinityCollege,Dublin2,Ireland}

e_{SaintPetersburgNationalResearchUniversityofInformationTechnologies,MechanicsandOptics,197101}

SaintPetersburg,Russia

Received5November2013;receivedinrevisedform20January2014;accepted4February2014

KEYWORDS Plasmon; Plasmonicelectrons; Injectionof electrons; Nanostructures; Photoelectriceffect; Photodetectors; Photocatalysis

Summary Thepaperreviewsphysicalconceptsrelatedtothecollectivedynamicsof plas-monexcitationsinmetalnanocrystalswithafocusonthephotogenerationofenergeticcarriers. Usingquantumlinearresponsetheory,weanalyzethewavefunctionofaplasmonin nanostruc-turesofdifferentsizes.Energeticcarriersareefficientlygeneratedinsmallnanocrystalsdueto thenon-conservationofmomentumofelectronsinaconfinednanoscalesystem.Ontheother hand,largenanocrystalsandnanostructures,whendrivenbylight,producearelativelysmall numberofcarrierswithlargeexcitationenergies.Anotherimportantfactoristhepolarization ofthe excitinglight. Mostefficientgeneration andinjectionofhigh-energycarriers canbe realizedwhentheopticallyinducedelectriccurrentisalongthesmallestdimensionofa nano-structureandalsonormaltoitswallsand,forefficientinjection,thecurrentshouldbenormalto thecollectingbarrier.Otherimportantpropertiesandlimitations:(1)intra-bandtransitionsare preferableforgenerationofenergeticelectronsanddominatetheabsorptionforrelativelylong wavelengths(approximately>600nm),(2)inter-bandtransitionsefficientlygenerateenergetic holes and (3) the carrier-generation and absorption spectra can be significantly different.

∗_{Correspondingauthor.Tel.:+17405939430.} E-mailaddress:govorov@ohiou.edu(A.O.Govorov). http://dx.doi.org/10.1016/j.nantod.2014.02.006 1748-0132/©2014ElsevierLtd.Allrightsreserved.

The describedphysicalproperties ofmetal nanocrystalsareessentialfor avarietyof poten-tial applications utilizinghot plasmonic electrons includingoptoelectronic signal processing, photodetection,photocatalysisandsolar-energyharvesting.

©2014ElsevierLtd.Allrightsreserved.

Introduction

Whereas plasmonic properties of metal nanocrystals in termsofopticalresponsehavebeen sointensively investi-gated[1,2],the internal quantumstatesof photo-excited

electrons inside plasmonic systems are much less known

becauseelectrons in nanocrystals oscillatein a nontrivial

way, creating a collective excitation, a plasmon. Under

optical illumination, the electrons simultaneously form a

plasmonexcitationandscatterbyeachotherandfromthe

wallsandphonons. Experimentally,opticallyexcited

elec-tronsin a metal can be registered via a photocurrent in

asemiconductor—metalSchottky-barrierphotodetector[3]

(Fig.1a)orusingsurfacephotochemistry[4,5](Fig.1b).It

hasbeenrecognizedrecentlythatplasmonicnanostructures

and nano-antennas can be used for hot carrier

genera-tion,photocatalysis,andinjection.Metalnanocrystalshave

largeabsorptioncrosssectionsandcanefficientlyenhance

andtraplight[6—8].Plasmonicenhancementof

photocur-rents and chemical processes can be induced via direct

electron transfer from a metal or indirectly via a local

amplification of electromagnetic field at functional

ele-ments of a device [9]. Several recent papers reported

plasmon-enhancedphotochemistry[9—22](whenplasmonic

nanocrystalsareincontactwithaliquid)andplasmon-driven

photocurrentresponsesinoptoelectronicdevicesand

nano-structures[23—33].

Thephoto-excitedplasmonicelectronslookvery

attrac-tive for applications in photochemistry, solar cells, and

photodetectors because metal nanocrystals can absorb

light much more efficiently compared to inorganic

semi-conductors and organic dye molecules. Here are some

advantagesofmetalnanocrystals:

• Largeabsorptioncrosssections.

• Alargenumberofelectronswithappropriateenergy

lev-elsforelectrontransfer.

• Efficienttuningoftheplasmonicresonances,absorption

spectraandlocalenhancementusingthesize,shape,

ori-entationandarrangementofnanocrystals[1,2,34—36].

Fig. 2 illustrates gold nanocrystals of various shapes

and shows their absorption spectra. We can see that the

position of plasmon resonance in absorption can be

con-venientlytunedwiththeshapeofananocrystal.However,

therearesignificantfundamentallimitationsfortheuseand

extractionofplasmonicelectronsinphotocatalyticandsolar

conversionapplications.Theselimitationsinclude:

• Fast relaxation and relatively short mean free path of

electronsinmetals.

• Limitedmomentumtransferandoftenalargenumberof

excitedelectronswithlowenergies.

• Reflection of electrons from the metal—semiconductor

interface.

Inthisperspectivearticle,wewilladdressphysical

prop-erties of plasmons in metalnanocrystals, focusingon the

microscopicquantumstructureofplasmonicoscillationsand

thenon-equilibriumelectrondistributionsinopticallydriven

confinedsystems.Thefirstsectionswilldescribeenergy

dis-tributionsanddynamicsofexcitedelectronsintheplasmon

wavesinthebulkandinconfinednanocrystals.The

follow-ingsectionswilladdressmodelphysicalsystemsanddevices

aswellasprovideabriefreviewofexperimentalworkinthe

field.

Wave

functions

of

plasmons

in

the

bulk

and

in

nanostructures

3Dmetal

Electronsin metals forma Fermigas,which is

character-izedbytheFermivelocity(vF),Fermienergy(EF),andbulk

plasmonfrequency,(ωp,bulk).Thenon-interactingFermi-gas

modelgivesthefollowingequationsfortheabove

parame-ters[38,39] EF= m0vF2 2 = 2_(32_n 0) 2/3 2m0 ,ωp,bulk=  4e2_n 0 ε0m0 ,

wheren0isthe3Delectrondensity,m0istheelectronmass

and ε0 is the background dielectricconstant comingfrom

the atomic core electrons. For gold, these numbers are

EF=5.5eV,vF=1.39×108cm/s,andωp,bulk=3.96 eV[40].

Thequantumdescriptionofelectrongasisbasedonthe

den-sity matrix, mn [38]. The elements of thedensity matrix

giveuspopulationsofquantumsingle-particlestatesinan

electrongasdrivenbyopticalexcitation.Thepopulationof

asingle-particlequantumstateinaFermigasissimplythe

correspondingmatrixelement

nn(t)=



 (t)ˆc+nˆcn (t) 

,

where (t)isanon-equilibriumwavefunction,which

may be quite complicated in its exact form, and the

operators ˆc+n and ˆcn are the creation and annihilation

operators,respectively.Then,theoperator ˆc+nˆcn‘‘probes’’

the many-bodywavefunction (t)and revealsthe

pres-ence of equilibrium or non-equilibrium electrons in the

Fermisea.Intheabsenceofillumination, thesystem isin

equilibriumandthe populationis, ofcourse,givenby the

Fermidistributionfunctionnn=fF(E),whereEisthe

elec-tronenergy.When theelectronplasma isilluminated,the

non-diagonal elements, like nn(t)=



 (t)ˆcn+ˆcn (t) 

,

revealthepresenceofanexcitation,anelectron—holepair,

in the Fermi gas (Figs. 3b and 4a). In the election—hole

Figure1 (a)Schematicsetupforphotoelectricexperimentwithametal-semiconductorSchottkycontactandtherelated energy-banddiagramforthephotoexcitationprocesses.ReprintedwithpermissionfromRef.[3].Copyright©2007byJohnWiley&Sons, Inc.(b)Schematicillustrationofhot-electrontransferfromametaltoanunoccupiedmolecularorbitalatthesurface.Thelaser lightgenerateshotelectronsinthebulkandtheseelectronshaveafiniteprobabilitytotunneltotheadsorbate.Reprintedwith permissionfromRef.[4].Copyright(2013)AmericanChemicalSociety.

below the Fermi level to the non-equilibrium state |n

above the Fermi-sea level (Figs. 3band 4a). The density

matrix describes the quantum state of electron gas and

shouldbefoundfromthesolutionoftheequationofmotion

[38,41]

∂ˆ

∂t =i[ˆ, ˆH(t)]− ˆrelˆ, (1)

Figure2 (a)Schematic illustration ofgold nanocrystalsandtheir absorptionspectra inwater. The absorptionspectra were calculatednumericallyusingthelocaldielectricconstantofgold.[37](b)Physicalprocessesinaphoto-excitedelectrongasthat isincontactwithasemiconductor.(c)Optoelectronicprocesses inaconfinednanocrystal incontactwithmolecularadsorbate. Photogeneratedplasmoniccarriershavechancetobetransferredtothemoleculesadsorbedonthesurface.

Figure3 (a)and(b)SchematicillustrationsforapropagatingplasmonwaveinabulkcrystalandtheFermiseaofelectronsinthe bulkwithaplasmonexcitation.(c)SurfaceplasmonpolaritoninanAuwaveguide.(d)Plasmonicelectrondistributioninthebulk plasmon.Thepositive(blue)partrepresentsthepopulationofelectronsabovetheFermienergywhilethenegative(red)partis theholepopulationbelowtheFermienergy.TheFermienergyEF=5.5eV,whichcorrespondstothecaseofbulkgold.Thedashed curveshowstheequilibriumFermidistributionofelectronsatroomtemperature.

Figure4 (a)Schematicsofelectrontransitionsinametalnanocrystal.AFermi-seaelectronbecomesfirstopticallyexcitedand thenundergoesenergy relaxation.Inthisway, asteady-statedistributionofhigh-energyelectronsinalocalizedplasmonwave becomesformed;qL=/LNCisthecharacteristicchangeofthemomentumoftheelectronandqLvF istheelementaryexcitation energy ofanelectron atthe Fermi levelina nanocrystal due tothe non-conservation oflinear momentum.(b) Modelofan Aunanocubewithelectronsbouncingoffthewalls.(c)Plasmonicelectrondistributioninthelocalizedplasmonina10nmgold nanocube.The dashedcurve shows theequilibrium Fermidistributionofelectrons. The data for thenanocubewere obtained numericallyfromEq.(3).Forthemoderatelightintensitiestypicallyusedintheexperiments,thenon-equilibriumpopulationof energeticcarriersismuchsmallerthattheequilibriumFermidistribution.

where ˆH istheHamiltonianincludingtheopticalexcitation

and ˆrel is an operator describing energy relaxation. The

equationofmotionintheform(1)providesuswithavery

convenient approach for treating many quantum systems

[38,39,41].

Westartwithaplasmonwaveinthebulkandinthe

sys-tems with large dimensions (Fig. 3a and c).The dynamic

responseofthe Fermigas inthepresence oftheexternal

fieldisdescribedbythebulkdielectricfunction[38]:

ε3D(ω,q)=1− 4e2 q2_V  k fF(k)−fF(k+q) ω−Ek+q+Ek+i rel (2)

where q is wave vector of excitationin the gas and V

isthecrystalvolume.Thezerosofthisfunctionshouldgive

self-oscillationsofthesystem.Indeedonecanshowthatthe

equation ε3D(ω)=0 produces the plasmon frequency ω=

±ωp,bulk.

Now we look at the structure of a plasmon wave, i.e.

the electron distribution.The steady-state distributionof

hotplasmonicelectronscanbeobtaineddirectlyfromthe

diagonalelements

ın(E)=2·

n

ınn·ı(E−En),

whereı(E−En)isanumericalı-function,Enistheenergy

of the singe-particle state |n, and the factor 2 accounts

forspins.Theequationforthetime-averagedfunctionınn,

derivedfromthelinearresponsetheoryinRef.[42],reads:

ınn= 2 rel  n (f0 n−f 0 n)|eϕnn|2  rel (ω−En+En) 2 + rel2 + rel (ω+En−En) 2₊ rel2  . (3) where ϕnn = n| ϕω(r)n 

is the matrix elements of optical excitations, ϕω(r) is a

complexamplitudeofthetime-oscillatingelectricpotential

induced by the illumination and rel is the energy

relax-ation rate of electrons. These matrix elements produce

quantumamplitudesofopticaltransitionsbetweenthe

elec-tron states. Fig. 3d shows the calculated hot plasmonic

distributions in a bulk plasmon taken from Ref.[42]. We

assumethattheplasmonwaveexcitedinanelectrongashas

the wavelength =760nm. The excited-electron

distribu-tionın(E)=n(E)−fF·D(E)ispositiveforE>EFandnegative

forE<EF;hereD(E)istheelectrondensity ofstatesofthe

bulk system. The function ın(E) reveals the presence of

electron—holepairexcitationsintheopticallydriven

elec-tronFermisea.Becauseoftheconservationofmomentum

inthe bulk,the transitionsoccur onlybetweenthe states

|n =k and|n =k+q,whereqis thewavevectorof

thebulkplasmon.Consequently,thesum(3)includesonly

the transitions between states k and k+q that have

smallexcitationenergiesE=Ek+q+Ek∼qvF.The energy

qvF issmallandtypicallyless thantheplasmonand

ther-malenergies,qvF <kBTωp,bulk.Foramodelsystemwith

theFermienergyof goldat roomtemperature,whichhas

ωp,bulk=3.96eV and kBT=0.026eV , theexcitation energy

qvF=0.007eVassumingaplasmonwavewithawavelength

of760nm.Therefore,thetypicalenergyofanexcited

car-riercountedwithrespecttotheFermienergyintheplasmon

wave

Eexcited electrons∼3kBT+qvF =0.08eV (4)

undertheusualconditionqkF.Weseeaninteresting

prop-ertyofthebulkplasmonwave:Electronsintheplasmonwith

alargeenergyquantum(ωp,bulk∼3eV)haveverysmall

exci-tationenergiesofsingleelectrons.Inmanycases,itismore

convenienttoperformplasmonicexperimentsusinga

pla-narwaveguide(Fig.3c)[1,2]whereplasmonswithoptical

energies(ω∼1−2eV )canbelaunchedandthendetectedat

differentlateralpositions.

Plasmonsinawaveguide

Coupled plasmon-electromagnetic waves in a waveguide

are called Surface Plasmon Polaritons (SPPs). For

exam-ple, a SPP in a Au waveguide with a wavelength 760nm

hasthe energyquantumωSPP∼1.5eV [43].To launchaSPP

wave, one can use a grating (Fig. 3c) [1,43]. The width

ofthemetalwaveguideistypicallylarge(∼150nminRef.

[43]),muchlongerthanthemean-free-pathofanelectron.

Therefore,we can usethe bulktheory tounderstand the

electronicstructureofaSPPwave.Estimatingtheexcitation

energywithEq.(4),weseeagainthatSPPswitharealistic

wavelength create mostly very low-energy electron

exci-tations, Eexcited electrons∼3kBT∼0.08eV«ωSPP=1.5eV . We,

therefore, conclude that plasmonic systems with large

dimensions have the serious limitation for efficient

elec-tronphoto-injectionintoasemiconductorsincetheexcited

plasmonicelectrons need high enough energy topass the

Schottkybarrier.In other words, it is expectedthat SPPs

launchedina waveguidecannot create manyhigh-energy

electrons, which can be detected by a Schottky barrier

withatypicalheightof0.5—1eV.Nevertheless,the

exper-iment with an Au—Si photo-detector has shown injected

currents.[24]Thephysical explanationforthisobservation

canbe in breakdown of momentum conservationof

elec-tronsduetodefects, phonons,andinterfaces. Thissimple

argumentsuggeststhat the size of metalnanocrystal can

beveryimportantfortheplasmonicgenerationofelectrons

withlargeexcitationenergies.Wewilldescribethisphysical

behaviorinthenextsection.

Plasmonicnanocrystals(NCs)

Generalremarks

The pictureof electron excitations ina confined electron

gasisdramaticallydifferent[42].Thephysicalreasonisthe

non-conservation of electron momentum due topotential

walls of the nanocrystal. Fig. 4 illustrates this case. The

energy of electrons is quantized and optical transitions

occurbetweenthediscretestates(Fig.4a).Thedistribution

ofexcitedelectronsinalocalizedplasmonisverydifferent

Figure5 (a)SchematicillustrationofaplasmonicAuslabinwaterdrivenbytheelectricfieldofincidentlight.(b)Distributions ofplasmoniccarriersintheslabswithavariablewidth.Theexcitingelectricfieldofincident illuminationisnormaltotheslab walls.Thepositiveregionofın(E)describesexcitedelectronsintheFermisea,whereasthenegativepartindicatesthepresence ofexcitedholes.Forconvenience,weshowbothnon-normalizedandnormalizeddistributions.Theuppergraphshowsthattheflat partsofthedistributionfunctiondonotdependontheslabwidth.Thisindicatesthatthephotogenerationinthesepartsisdueto thesurfacescatteringofcarriers.

electronsinaconfinednanocrystaloccupythewholeregion

oftheallowedenergies[42]

EF<Eexcited electrons<EF+ω.

This canbe understood usingthe followingarguments.

Because of the conservation of energy, an excited

elec-troncanacquiretheenergyEexcited=E+ω.Therefore,the

maximum allowed energy of the electron in the system

isEmax=EF+ω and,aswe see,the excited-electron

dis-tributionextends fromtheFermienergytothe maximum

value(the bluepart of thecurve inFig.4c).

Correspond-ingly,theenergyintervalforphoto-excitedholesisEF−ω<

Eexcited holes<EF(theredpartonthecurveinFig.4c). Plasmonicslab

As the simplest example, we consider now a plasmonic

platelet(slab) with the smallest dimension LNC along the

z-axis(Fig.5a).Theincidentelectromagneticwaveis polar-izedinthez-direction.This dynamicelectricfieldcreates

oscillatingelectric currentsthat hitthe walls oftheslab.

Therefore,theFermigas becomesstronglyperturbedand

wecanexpectasignificantnumberofelectronswithlarge

energies.Theelectrondistributioncalculatedbyusingthe

theory developed in Ref. [42] confirms our expectation

(Fig.5b).Moreover,thenumberofhighlyexcitedelectrons

islarge onlyfor relativelysmallsizes LNC.Withincreasing

LNC,thenumberofelectronswithlargeexcitationenergies

decreasesrapidly andalreadyfor LNC=40nmthe electron

distributionresemblesthebulkplasmon(Fig.5b).To

quali-tativelyexplainthisbehavior,welooknowattheelectron

excitation of aquantized system. In ananocrystal with a

quantizedmotionalongthez-direction,theelectrons

spec-trumtakestheformof

En,k_||= 2_2_n2 2m0L2NC + 2_k2 || 2m0 ,

where n is the quantum number for the z-motion and k_||

is the electron momentum in the plane of aslab. A

pho-tonexcitesan electronfromthestate |n tothestate |n

and the change in the electron number can only be odd,

n=1,3,5,...,due to the parity.Then, the characteristic

energyofelectronexcitationsinaconfinedsystemisgiven

bytheequation E=En+n+En≈ 2_2_n·n m0L2NC ∼vF n LNC , n=1,3,5,..., (4)

assuming n/LNC<kF and that all optical transitions

occur in the vicinity of the Fermi sea: En,k_|| ≈EF or 0<

(n)/(LNCm0)≤vF. Importantly, the effective momentum

transfer,whichcomesfromtheelectronconfinement,can

besignificantandisgivenby

k= n LNC =n·kL

where n can bea large numberand kL=␲/LNC is the

characteristic change of electron momentum due to the

NC confinement. Since n can be large, this momentum

transfer from the nanocrystal to single electrons permits

efficientexcitationofelectronswithenergiesinthewhole

intervalEF<Eexcited electrons<EF+ω(Fig.4cand5b).The

excitationenergiesofsingleelectronsarenowintheoptical

range,1—3eV, andsuchelectrons canbeusedfor

chemi-calreactions at the surface or for efficientinjection into

asemiconductor. Inthenexttwosections,wewilldiscuss

suchapplications. Due tothe conservationof energy, the

mostimportantmomentumtransfernumbersnshouldbe

in theintervaln>ncritical,where thecriticalnumberis

givenbythecondition[42]

vF ncritical LNC =ω.

The effect of generation of high-energy electrons is

strong if the above number (i.e. ncritical) is not too

large [42]. The above consideration is also applied to

the hotplasmon holes generated inthe interval EF−ω<

Eexcited holes<EF. Some other properties of the function

␦n(E)canbeseenfromthisequationfortheplasmonicslab

takenfromRef.[42]:

ın(E)∼ A rel Ez,inside 2 for EF+3kBT+qvF<E<EF+ω (5)

where relistheenergyrelaxationrateintheelectrongas

andA=LxLyisthecross-sectionalareaoftheslabandEz,inside

istheinternalfieldnormaltotheslabwalls(Fig.5a).Note

thatthenumberofhigh-energyelectronsdoesnotdepend

on the slab width, LNC. From Eq. (5), we see now three

importantproperties:(1)theeffectofphotogenerationof

high-energycarriers(electronsandholes)isasurfaceeffect

sinceitdoesnotdependonthesizeoftheslab,ın(E)∼L0

NC.

(2) This effect weakens withincreasing energy-relaxation

rate,ın∼1/ rel.(3)Theeffectisverysensitivetothe

direc-tionoftheexcitingelectricfield,ın(E)∼Ez,inside

2

.Electrons

withhighexcitationenergiesbecomegeneratedonlybythe

electricfieldnormaltothewall.

To estimate the energy-relaxation rate, we adopted

the experimental results from the time-resolved studies

of gold nanocrystals [44] that give the energyrelaxation

time =0.5ps (also see Fig. 12 below). Therefore, for

the relaxation rate we obtain rel=/=1.3meV. This

relaxation rate describes the energyrelaxation and

ther-malization of the Fermi gas and involves both phonons

andelectron—electronscattering.Forsimplicity,wedonot

involve here theradiative channelof relaxation assuming

NCsofsmallsizes.

Sinceaconfined systemhasa quantizedspectrum, the

calculated electron distribution exhibits steps due to the

2Delectronicsub-bandsintheslab(Fig.5).Inaddition,we

haveperformed an averagingoftheelectron spectraover

thewidthoftheslabintheinterval|L−LNC|<ıL=1nm,

assuming the presence of variations of the slab thickness

[45].

Figure 6 Illustrations of plasmonic processes within the linear-responseandphenomenologicalmodels.Thetheoretical treatmentofplasmonicdynamicsinthispaperisbasedonthe linear-responsemany-bodytheory.

Phenomenologicalpictureofplasmondynamics

Itisinterestingtolookattheplasmonkineticsusinga

phen-omenological picture (Fig. 6). Within the linear-response

many-bodyapproach, theFermigasdrivenbytheac

exci-tation field resides in a dynamic steady state (Fig. 6a).

Electronsandholesareconstantlybeingcreatedand

relax-ing.Inthequantumplasmonicpicture,weshouldconsider

a plasmon as an excited quantum state of the electron

system (Fig. 6, lower panel). Then, the plasmon

under-goesfastde-phasingwithcreationofelectron—holepairs.

Plasmon de-phasing comes from collisions with phonons

and defects and also from electron—electron scattering

[46]. The related plasmon coherence time is very fast,

plasmon∼9fs(seeSection‘‘RelaxationMechanisms’’).

Qual-itatively this coherence time of electron oscillations can

be regarded as a plasmon lifetime. Consequently, the

electron—holepairsrelaxandthermalizefurtherwithinthe

relaxation time rel. A balance equation for the plasmon

populationinaNCcanbewrittenas

dnplasmon dt = absI0 ωp − npl plasmon ,

wherenplasmonisthenumberofplasmonscreatedintheNC,

andabsandI0aretheabsorptioncrosssectionandlightflux,

respectively. In thesteady state, dnplasmon/dt=0 andthe

plasmon number nplasmon=plasmon(absI0/ωp). In relatively

smallNCswithin thelinear regime,the plasmonnumbers

aresmall,asexpected.Forexample,npl∼0.02fora60nm

Aunanosphereinwater,illuminatedwithI0=104 W/cm2

Nanocrystalsofvariousshapes

Nowwebrieflyconsidernanocrystalsofvariousshapes.So

far,afull theoryof photogenerationof plasmoniccarriers

hasbeendevelopedonlyforthesimplestgeometryofaslab

(oraplatelet).However,thistheorycanbeapplied

qualita-tivelytoothershapes(nanospheres,nanocubes,nanorods,

nanowires, etc.). In all these nanocrystals, an external

electricfieldefficientlyexciteslocalizedsurfaceplasmons

resonancesandgenerates surfacecharges.Therefore,the

electroncurrentsin thesegeometriesshouldhitthewalls

of these nanostructures and enablethe creation of

high-energyelectrons.Thekeyfunctionfortheplasmonic-carrier

generationisthemagnitudeoftheelectricfieldinsidethe

nanocrystal.Theeffectofgenerationof excitedelectrons

comesfromthe plasmon-enhancedelectric fieldsinside a

NC.

Theoverallenhancementofthefieldinsideaplasmonic

NCcanbeconvenientlyquantifiedwiththefollowing

func-tion: FENC=  V_NC EωEω∗ E2 0 dV 1/2

where E0and Eωarethedrivingandinternalelectricfields,

respectively.Fortheslab,sphereandellipsoidgeometries,

thisfield-enhancementfunctioncanbecalculated

analyti-cally.Inparticular,thefunctionFENCforaslabandasphere

isgivenby[47] Pslab(ω)=  ε0 εAu  , Psphere(ω)=   3ε0 2ε0+εAu  ,

whereεAu andε0arethedielectricconstantsofthemetal

andthematrix.InFig.7,we nowplotthecalculatedfield

enhancementsforthefourtypesofNC.Nano-ellipsoidsare

obviouslyadvantageous,duetoastrongamplificationofthe

fieldinthelongitudinalplasmonicresonance.

Applicationtophotochemistry

Plasmonic elections are being actively studied in

experi-mentsonphotocatalysis[10—20].Fig.8showsasimplified

energydiagramforthetransferofplasmoniccarrierstothe

externalelectronstates.Suchexternalelectronstatescan

be:(1)Moleculesadsorbedonthemetalsurface,(2)alayer

ofmaterialdeposited onthesurface,or (3) anelectronic

contact. This scheme is similar to that used for water

splittinginthecurrentexperiments[9](seefurtherFig.14a

inthesection onexperimental work).In thisscheme,the

energyofexcitedplasmonicelectronsistransferredtothe

externalstates,creatingreducedmoleculesorhigh-energy

carriers in the external electrodes. Consequently, such

energeticcarriersormoleculescanbeusedfor

photochem-istry.Thisschemehastwoenergyparametersimportantfor

theextractionofelectronsandholesfromNCs:Thebarrier

energiesεe andεh.Theseenergiesarecalculatedfrom

the Fermisurface. Apparently, for efficientinjection, we

need to have sufficiently large numbers of electrons and

holesattheenergiesεeandεh.Suchbarrierenergiesare

Figure7 (a)Modelsofnanocrystals.(b)Calculated enhance-ment factorsfor theelectricfield ofincident lightinsideAu nanocrystalsofvariousshapes.Nanocrystalsareassumedtobe inadielectricmatrix(water).

typically ∼eV. Therefore,the photons of visible light are

abletogeneratecarriersforinjection,butthenanocrystal

should beof a sufficientlysmallsize. As we have seen in

the previous section,only smallNCs havea large number

of highlyexcited carriers.The efficiencyof generation of

electrons(holes)withenergyεe(h) canbedefinedas

Effe(h)(ω,LNC)= Ratee(h)(ω) Rateabsorption ∝ ın(EF± εe(h),ω,LNC) VNC ,

where Rateabsorption is the rate of absorption of incident

photons by a NC and Ratee(h)(ω) is a rate of injection of

electrons(holes)intothesurfacestates.Heretheelectron

injection rate is proportional to the population at the

energy EF+ εe: Ratee(ω)∝ıne(EF+εe). Similarly, for

the holes, we have Rateh(ω)∝−ın(EF− εe).

Simultane-ously,theabsorptionrate Rateabsorption∝VNC,where VNC is

theNCvolume.Fig.8showsthecalculatedefficiencytaken

fromRef.[42].Thecarriergenerationefficiencydecreases

with increasing NC size since the energies required for

injectionaretypicallylarge,about eV,andonly relatively

smallNCs cangenerate efficientlysuch high-energy

carri-ers. The number of energetic electrons (with E∼eV) is

proportional to the surface area of the nanocrystal and,

therefore,forasphericalorcubicnanoparticle

Effe(h)∝

ANC

VNC

∼ 1

Figure8 (a)Energydiagramfor thetransferprocesses.(b) Calculatedefficienciesofgenerationofplasmonicelectronswith thebarrier energiesE=EF+εe.Insert:ModelofacubicAu NC. Reprintedwith permissionfromRef. [42].Copyright(2013) AmericanChemicalSociety.(c)Calculatednumberofhigh-energyelectrons(E−EF=εe=1eV)andtheabsorptioncrosssection, bothnormalized.

Injectionofplasmoniccarriersintoa

semiconductor

Anotherstreamofresearchconcernsinjectionofplasmonic

carriersintosemiconductorsandorganicmaterials[24—31].

Oneexampleisthesemiconductor—metalSchottkycontact

withabarrierheightEB(Fig.9a).Ingeneral,theinjection

processdependsontheboundaryconditionsattheinterface

betweenthemetalandthesemiconductor.Foranidealflat

interface,an electron crossingthe interfaceconservesits

parallelmomentum.Therefore,theconditionsforinjection

ofsuchelectronshouldbewrittenas

EF+ω≥E≥EF+EB and

p2

z

2m >EB+EF. (6)

The first conditionis thesimple energyargument: The

photoexcited electron should have energy abovethe

bar-rier (Fig.9a) while the energies of excited electrons are

limitedbyEF+ω.Thesecondonegivesanotherrestriction;

thistellsthatthez-component ofenergyshouldbelarger

thanthebarrier height[49] (Fig.9b). Physically,itmeans

that,foragivenenergy,anelectroncanenterthecontact

onlyifitsmomentumiswithintheinjectioncone(Fig.9b).

Bothconditionscreaterestrictionsforthenumbersof

elec-tronsthatcanbeinjectedintoacontact.However,ifthe

metal—semiconductorboundaryisrough,thesecond

condi-tioncanberemoved andmoreelectronscanbeinjected.

In Fig.9cand d, we show calculatedrates of generation

foracontactwithabarrier EB=1eV .Weseethe

limita-tioncomingfromtheconditions(6).First,thetotalrateof

generationof plasmoniccarriers exceeds therate of

gen-eration of carriersabovethe barrier EF+ω≥E≥EF+EB.

However,thenumberofelectronsthatcanenterthecontact

is even smaller because of the second restrictive

condi-tion,p2

z/2m>EB+EF.Asexpected,thecalculatedcurves

inFig.9exhibitoscillationsowingtothesize-quantization

ofelectronsin a 20nm-thick metalslab.Fig.9 illustrates

theproperties of a 1eV injection barrier, asan example.

In real junctions, the barrier height varies in the range

0.5—1.5eV[3].Theexperimentalnumbersforafew

exam-plesofSchottkybarriersaregiveninTable1.Moredataon

theSchottkybarrierscanbefoundelsewhere[3].

Therateofinjectionatthethresholdcanbewell

approx-imatedbytheresultfromtheFowlertheory[49]:

Iphoto−current=I0·(ω−EB)2

The quadratic Fowler law is based on the conditions

(6). A full quantum mechanical solution to the problem

of the photo-electric effectwas given by Tamm[50] and

further developed in Refs. [51,52]. The rate of injection

fromthefull quantum treatment includes also the effect

Table1 DatatakenfromRefs.[3,48].

Contact Barrierheight,EB=eB(eV)

n-Si—Au 0.83

p-Si—Au 0.34

TiO2—Au 0.87—0.94

ZnO—Au 0.65

Figure9 (a)and(b)EnergydiagramandschematicoftheSchottkybarrieremployedforinjectionofplasmonicelectrons.(c) CalculatedgenerationandinjectionratesforaplasmonicAuslab.(d)Thisgraphshowscloselytheinjectionrateanditscomparison withtheFowlerlaw.The graphs(c)and(d) arereprinted withpermissionfromRef.[42].Copyright(2013)American Chemical Society.

of over-barrier reflection of electrons and under certain

conditionsbecomes:

Iphoto−current=I1·(ω− EB) 5/2

Recentlyatheoryofinternalphoto-effecthasbeen

fur-therdevelopedincludingseveraleffects characteristicfor

theplasmonicsystems.Inparticular,therecentstudies

con-cerneda reflectionof electronwaves inslabs [53,54]and

plasmoniceffectsinsolarcellsandphotodetectors[55—57].

Thequantum theoryfor surface photo-electriceffectwas

usedto calculate the photo-injection efficienciesin

plas-monicnanostructuresinRefs.[58,59].Arecentpaper[60]

describedthenon-equilibriumsteadystateofelectronsinan

opticallydrivenmetalnanoparticleusingtheenergybalance

equations.

Band

structure

effects:

inter-band

and

intra-band

transitions

Thebanddiagramofarealmetalismorecomplexthanthe

spectrumofafreeelectron (Fig.10a).Forthecase ofAu

andAg,the bandstructurecan beunderstoodinterms of

sp-andd-bands.The sp-bandresemblesthefree-electron

dispersionand crosses the Fermi level. Transitions within

thesp-band are intra-band excitations formingthe Drude

partofthedielectricconstant.Opticaltransitionsbetween

thefilledd-bandandthe emptystatesofthesp-band are

inter-band excitations. We can see contributions of both

types of transitions in the empirical dielectric function

takenfromRef.[37] (Fig.10b).A dielectricfunctionof a

bulkmaterialcanbewrittenasasumoftwocontributions,

εmetal=εDrude+εinter-band[2].TheDrudecontributioncoming

fromtheintra-bandtransitionshastheform

εDrude(ω)=ε0−

ω2

p

ω(ω+ibulk)

(7)

wherethe coefficientsshouldbefound fromfittingtothe

empiricaldielectricconstantatlongwavelengths(Fig.10b).

Indeed,weseethattheDrudeformula(7)givesan

excel-lentfittotheexperimentaldata,usingbulk=0.076eVand

ωp=8.9eV[62].Thisindicatesthatgoldbehaveslikeagood

metal.Then,wecanseethecontributionoftheinter-band

transitions bysubtractingtheDrudecontributionfromthe

empirical dielectric constant εinter-band(ω)=εempirical(ω)−

εDrude(ω).Sincewenowknowtheinter-bandandintra-band

contributionstothedielectricconstant(Fig.10b),we can

calculatethecorrespondingcomponentsofabsorption.The

absorptioninaNCcanbewrittenasasumoftwoterms

Qtotal=Qintra_−band+Qinter_−band=2·Re  dV (j·E∗) = ω 2Im[εempirical(ω)]·  dV (E·E∗) = ω

2Im[εDrude(ω)+εinter−band(ω)]·

Figure10 (a)Banddiagramofgold,reproducedfromRef.[61].Wealsoshowtheintra-bandandinter-bandtransitions(redand bluearrows).Copyright1971byTheAmericanPhysicalSociety.Insert:Schematicofthedensityofstatesinthesp-andd-bands.(b) Imaginarypartofthedielectricfunctionofgold[37]andtheDrudefitforthelongwavelengthlimit.Thedifferencebetweenthese twocurvesshowsthepresenceofintensiveinter-bandtransitions.Theverticallineshowsthetransitionbetweentworegimesin theabsorption;<600nm(ω>2.07 eV)theimaginarypartofthedielectricconstantandtheabsorptionaredominatedbythe inter-bandtransitions,whileinthisinterval>600nmtheintra-bandDrude-liketransitionsgovernthepicture.(c)Distributionof hotplasmonicelectronsandholesgeneratedthroughtheinter-bandtransitionsinbulkgold.ThecalculationisdoneusingtheDFT theory.

where j and E are the complex amplitudes of electric

currentandelectricfieldinsideaNC,respectively.Fig.11c

shows the calculated contributions to the absorption for

three different shapes. We see that the most common

spherical NChasa smallnumber ofphotogenerated

intra-band carriersandthe majorityof absorptioninthese NCs

comes from the inter-band transitions. When we shift

the plasmon resonance to the red, the contribution of

intra-band transitions grows strongly. For structures with

plasmon resonances longer than 600nm, the intra-band

Drude-likeabsorptiondominates.IntheinsetinFig.11c,we

showtheparameterAforAuellipsoid,whichisdefinedas

A=

3eV

1.5eVQintrabanddω 3eV

1.5eVQtotaldω

Weseeastrongincreaseofthecontributionfrom

intra-bandtransitionswithincreasingtheaspectratioa/b.Thisis

becausetheplasmonresonanceofanellipsoidshiftstothe

redwhentheaspectratioincreases.

To summarize this section, we show qualitatively the

spectrumofplasmonicelectronsandholesinaNCexcited

with the photon energy 2.3eV (Fig. 11b). While the

intra-band transitions produce energetic electrons and

holes inthe whole intervalEF−ω<Eexcited electrons<EF+

ω,theinter-bandtransitions(atthethresholdphoton

ener-gies ω∼2.1−2.4eV ) create mostly energetic holes with

Eexcited holes∼EF−2.3eV (Fig. 10c).Simultaneously,

photo-generated electrons for such inter-band transitions are

not energetic and have energies near the Fermi level,

Eexcited electrons∼EF.

Relaxation

mechanisms

Relaxation mechanisms of electrons and plasmons are

summarized in Fig. 12. The data on the mean-free

path of excited electrons in gold can be found in

Refs. [63,64]. The relaxation mechanisms of hot

elec-tronsinvolveelectron—electronscatteringandemissionof

phonons and photons (rel=0.5—1ps) [44,46]. These

pro-cessesinvolve both intra-band and inter-band relaxations

assistedbyphonons, photons,andelectron—electron

scat-tering(Fig.12a)[65].Ingold,opticallygeneratedelectrons

with excitation energies 1—2eV have mean-free path in

theinterval17nm<1mfp<50nm.Thislengthdeterminesthe

Figure11 (a)Simplifieddiagramshowingtheinter-bandandintra-bandtransitionsingold.(b)Distributionsofplasmoniccarriers createdviatheintra-bandtransitions(blueandredbands)andthedistributionsofcarriersexcitedthroughtheinter-bandtransitions (solidlines).Asanexample,theenergyofexcitingphotonsistakenas2.2eV.(c)Totalabsorptionsandthecontributionsfromthe inter-andintra-bandtransitions.Thecalculationswerecarriedoutusingthelocaldielectricfunction.Insets:Dielectricmodelsof nanocrystals.Insetinthemiddlegraphshowstheratioofintra-bandandtotalabsorptionsforanAuellipsoidasafunctionofthe parametera/b,whereaandbarethesizesofellipsoid.

dimension of 50nm are the most advantageous since an

energeticcarrierinsuchadevicecanpropagatetothe

sur-facewithout essentialrelaxation.Anotherpossibilityis to

usehigh-quality metals witha long mean-free path,such

as very high quality silver films fabricated in Ref. [66].

As we can see the mean free path of electron in gold is

relatively short and the related lifetimeis shortas well,

lmfp/vF∼20fs. This can be understood involving collisions

withdefectsandphononsandalsoduetoelectron—electron

scattering[67].Thefastestprocessinthecollective

dynam-icsis the de-phasing (coherentlifetime) ofplasmon. This

plasmoncoherence time plasmon∼5—10fs and can be

esti-mateddirectlyfromtheempiricaldielectricfunctionofgold

asplasmon∼/bulk∼9fs.Theplasmoncoherencelifeshownin

Fig.12d is shorter due to the inter-band transitions that

createanadditionalde-phasingmechanismforplasmons.

Current

experimental

work

and

potential

applications

Herewe briefly review some of the experimental reports

in the field. The mechanisms responsible for

plasmon-enhancedphotocurrentsandphotocatalysiscanbedivided

intothreegroups:Thermallyactivatedprocesses,processes

amplified by the plasmon electromagnetic enhancement

effect,anddirectelectrontransfer/injection.

Thermaleffectsandcharacteristictemperaturesin

thephoto-excitedmetalnanocrystals

One essential aspect of the problem is the photothermal

effectintheplasmonicNCs[68,70—73].PlasmonicNCs

effi-cientlydissipatelightenergy,whichmayleadtoanincrease

in local temperature of the system. This temperature

increase can bea reasonfor thephotocurrent generation

[69],increasedratesofchemicalreactions[74,75],and

pho-tomeltingofpolymersandDNAs[76—78],plasmonicwelding

[79],etc.The increaseintemperatureat thesurfaceofa

singlesphericalnanoparticlederivedfromthethermalheat

equationis TsingleNC= Qtotal 4k0 1 RNC

where k0 is an averaged thermal conductivity of the

sur-rounding matrix and RNC is a radius of heated NC. This

temperatureincreaseistypicallysmall(∼1—10K)for

plas-monicNCsinsolutionilluminatedwithmoderatelightfluxes

Figure12 Reviewofrelaxationmechanismsinplasmonicnanocrystals.(a)Inter-bandrelaxationofphotogeneratedcarriersin gold.TakenfromRef.[65].Copyright2004byTheAmericanPhysicalSociety.(b)DynamicsofphotobleachingofAunanoparticles revealingthetypicaltimesofrelaxationduetoelectron—electronandelectron—phononcollisions.Reprintedwithpermissionfrom Ref.[44].Copyright(1999)AmericanChemicalSociety.(c)Illustrationfortherelaxationmechanismsandtheparametersrelated todynamicsofphoto-excitedelectrongasinametal.(d)Calculateddynamicsofrelaxationofplasmonicelectricfieldinside a plasmonicnanoparticleexcitedbyafs-pulse.Thisdynamicsexhibitsashortcoherentlifetimeofplasmon.Thecalculationwasdone usingthelocaldielectricfunctionofgold[37].

generatehigh temperaturesdue tothe collective heating

effect [71,72,80].In thiscase, the resultingtemperature

increasecanbelarge[68,71],

Ttotal=f(NC,RNC)·TsingleNC·NNC2/3

where NNC is the number of NCs inside the volume of

lightbeamandNC istheNCdensityinsolution.Since

typ-ically NNC1, it is easy torealize the collective heating

and boiling regimes when TtotalTsin gleNC and Ttotal

canbeabovetheboilingpoint.Thiseffectcanbeused,for

Figure13 (a)CalculatedtemperatureatthesurfaceofasingleAunanoparticleinwater.ReprintedfromRef.[68],Copyright (2006),withpermissionfromElsevier.(b)and(c)Monolayerofgoldnanoparticlesonasubstrateandmeasuredphotocurrentinthis systemasafunctionoftime.Theoriginofthephotocurrentwasidentifiedasbolometric.ReprintedwithpermissionfromRef.[69]. Copyright2009,AIPPublishingLLC.

Figure14 (a)Schematicsofthewatersplittingreactionutilizingplasmoniccarriers. ReproducedfromRef. [9].Reprintedby permissionfromMacmillan PublishersLtd: NatureMaterials, copyright2011.(b) Thebanddiagramofasolarcellbasedonthe optically-activeadsorbedmoleculesandametalfilmtransmittingelectrons.TakenfromRef.[82].Reprintedbypermissionfrom MacmillanPublishersLtd:Nature,copyright2003.(c)Photo-triggeredreleaseofDNAsfromplasmonicnanorods.Reprintedwith permissionfromRef.[14].Copyright(2011)AmericanChemicalSociety.(d)InjectionofplasmoniccarriersfromtheAunanoparticle tothe semiconductor nanorod ina hybrid architecture. Reprinted with permissionfrom Ref. [32].Copyright (2013)American ChemicalSociety.

example,forboilingandthermaldestructionofthematrix

material[76,81].

Oneofthefirstexperimentsonthephotocurrentsin

plas-monicNCarraysisshowninFig.13b.Astrongphotocurrent

response in this study wasattributed and explainedas a

bolometriceffect;thepresenceofhotelectronsinsidethe

NCsresultedinamplifiedelectriccurrentsthroughthe

junc-tionsintheNCarray.

Elecromagneticenhancementeffects

Plasmonicnanostructuresareabletostronglyenhanceand

trapelectromagneticfieldsandthiseffectoffersinteresting

possibilities for designing more efficient light-harvesting

system and solar cells [6,7]. Using plasmonic NCs and

lithographically fabricated nanostructures, the

electro-magnetic field can be focused on the key regions of the

system where photochemical transformations take place

[9,15,19,13].Inparticular,thestudy[19]presentedhybrid

nanocrystals in which the spatial area of photocatalytic

activity (semiconductor nanoparticle) is separated from

the plasmonic particle by a barrier; in this way it was

demonstrated that the enhancement of chemical activity

in this system comesfrom the plasmonicenergy transfer,

withoutdirecttransferofcarriers.

Electrontransferandinjection

This direction is strongly motivated by the reports on

photo-injectioninpurelysolid-statesdevicesincorporating

aSchottkybarrierandplasmonicwaveguidesandresonators

[24,25]. Potential applications of such structures are in

photo-detectors. Regarding solid-state and dye-sensitized

solarcells,themetalcomponentcanbeusedasthemain

absorbing element [22] or as a mediator participating in

electronandholetransfers[82].Thelattercaseisillustrated

inFig.14b.Inthissystem,themetalgatesupplieselectrons

to theabsorbing molecules andalso transmits

photoelec-tronstothesemiconductor.Theotherschemeisillustrated

Figure15 (a)Modelsofnanocrystalandmolecularabsorbers.(b)AbsorptionscalculatedusingMietheoryandlocaldielectric functionsoftherelatedmaterials;forthedyemolecule,wetookatypicalextinction105_(Mcm)−1_{.(c)Principleofoperationand} energylevelschemeofthedye-sensitizednanocrystallinesolarcell.ReprintedfromRef.[88],Copyright(2003),withpermission fromElsevier.

is simultaneously an absorber of optical energy and a

transmitter of carriers to a semiconductor and adsorbed

molecules. At this moment, plasmonic photocatalysis has

beenusedtodriveseveralchemicalreactions.Recent

exam-plesincludedissociationofO2[75,83]andH2[21],splitting

of water [9,18,20,22,84], ethyleneepoxidation [83], etc.

Searchfornanomaterialswithahighefficiencyofconversion

ofsolarenergyintochemicalfuelsisveryactive.Plasmonic

electrons may also play an active role in bio-conjugated

nanocrystals.Forexample,excitedelectronsofanoptically

drivenNCandheatingcantriggerreleaseofDNAmolecules

[14](Fig.14c).Themechanismsofgenerationandinjection

ofplasmoniccarriersarepresentlyunderactive

investiga-tionusingvariousspectroscopictechniques.Inparticular,a

recentpaper[32]hasreportedatime-resolvedtransmission

studyofelectronsinjectedfromanAuNCtoa

semiconduc-tornanorod.Anothervery recentpaper[85] reportedthe

experiment onfocusing of surface plasmonpolaritions on

the metal—semiconductor junction using a tapered metal

tip.Inthissystem,theelectroninjectionwasenhancedby

compressingtheplasmonwaveintoarelativelysmallvolume

[86].Interestingpossibilitiesforhotelectroninjectionand

generationappearalsointhephoto-excitedmetaljunctions

underastrongelectricbiaswhenasymmetryofajunction

isvoltage-controlled[87].

Conclusions

This review article is mainly focused on the

understand-ing of behaviors of excited electrons in optically driven

metalnanocrystals.IntheconcludingFig.15,weshowthe

absorptioncrosssectionsofvarioustypesofnanomaterials.

Theobviousadvantageofplasmonicnanocrystalsisintheir

strongabsorption.OpticalabsorptionsofmetalNCs

signif-icantlyexceed ones of semiconductor quantum dots, dye

molecules and carbon nanotubes, which are used in

dye-sensitizedsolarcells[88]andotherhybridsystems[89,90]

(Fig. 15b). However, the challenge in the use of metal

nanocrystalsisinefficientextractionoftheenergetic

elec-tronsandholes.Thelifetimeofexcitedcarriersinametalis

short,whereasexcitonsindyemoleculesand

semiconduc-torquantum dots are relatively long-lived. Other limiting

factors for the use of plasmonic electrons are the

trans-ferof momentum from a NC to plasmonic electrons and

thereflectionof carriersatinterfaces. However,weshow

thattheefficiencyofgenerationandinjectionofplasmonic

carriers can be increased by choosing appropriate sizes,

geometriesandexcitationfrequencies.Webelievethatthis

papershouldbeusefulforunderstandingofgenerationand

transport of hot plasmonic electrons in optically excited

canbeusedin arange ofpotential applicationsincluding

optoelectronics,sensing, photochemistry and energy

har-vesting.

Acknowledgments

WethankZ.FanfortheDFTcalculationsofbulkgold.This

workwassupportedbytheScienceFoundationIreland(SFI

11/W.1/12065andSFI07/IN.1/I1862projects),theMinistry

ofEducationandScienceoftheRussianFederation(Grant

No. 14.В25.31.0002), the NSF (project: CBET-0933782),

andVolkswagenFoundation.H.V.D.gratefullyacknowledges

supportfromNRF-RF-2009-09andNRF-CRP-6-2010-2aswell

asTUBAandESFEURYI.

References

[1]S.A. Maier, Plasmonics: Fundamentals and applications, Springer,NewYork,2007.

[2]L. Novotny, B.Hecht, Principlesof Nano-Optics, Cambridge Univ.Press,Cambridge,UK,2006.

[3]S.M.Sze,K.K.Ng,PhysicsofSemiconductorDevices,3rded., Wiley,Hoboken,NJ,2007.

[4]C.D.Lindstrom,X.-Y.Zhu,Chem.Rev.106(2006)4281. [5]C.Frischkorn,M.Wolf,Chem.Rev.106(2006)4207. [6]H.A.Atwater,A.Polman,Nat.Mater.9(2010)205.

[7]J.A.Schuller,E.S.Barnard,W.Cai,Y.C.Jun,J.S.White,M.L. Brongersma,Nat.Mater.9(2010)193.

[8]S.V.Boriskina,H.Ghasemi,G.Chen,Mater.Today16(2013) 375—386.

[9]S.Linic,P.Christopher,D.B.Ingram,Nat.Mater.10(2011)911. [10]C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S.

Kostcheev,L.Billot,etal.,NanoLett.5(2005)615. [11]L.Brus,Acc.Chem.Res.41(2008)1742.

[12]X.Wu,E.S.Thrall,H.Liu, M.Steigerwald,L. Brus,J.Phys. Chem.C114(2010)12896.

[13]Z.Liu,W.Hou,P.Pavaskar,M.Aykol,S.B.Cronin,NanoLett. 11(2011)1111.

[14]R.Huschka,J.Zuloaga,M.W.Knight,L.V.Brown,P.Nordlander, N.J.Halas,J.Am.Chem.Soc.133(2011)12247.

[15]I.Thomann,B.A.Pinaud,Z.Chen,B.M.Clemens,T.F.Jaramillo, M.L.Brongersma,NanoLett.11(2011)3440.

[16]M.Xiao,R.Jiang,F.Wang,C.Fang,J.Wang,J.C.Yu,J.Mater. Chem.1(2013)5790.

[17]H.Tong,S.Ouyang,Y.Bi,N.Umezawa,M.Oshikiri,J.Ye,Adv. Mater.24(2012)229.

[18]S.C.Warren,E.Thimsen,EnergyEnviron.Sci.5(2012)5133. [19]S.K.Cushing,J.Li,F.Meng,T.R.Senty,S.Suri,M.Zhi,etal.,

J.Am.Chem.Soc.134(2012)15033.

[20]D.B.Ingram,S.Linic,J.Am.Chem.Soc.133(2011)5202. [21]S.Mukherjee,F.Libisch,N.Large,O.Neuman,L.V.Brown,J.

Cheng,etal.,NanoLett.13(2013)240.

[22]S. Mubeen, J. Lee, N. Singh, S. Krämer, G.D. Stucky, M. Moskovits,Nat.Nanotechnol.8(2013)247.

[23]H.R.Stuart,D.G.Hall,Appl.Phys.Lett.73(1998)3815. [24]A.Akbari,R.N.Tait,P.Berini,Opt.Exp.18(2010)8505. [25]M.W.Knight,H.Sobhani,P.Nordlander,N.J.Halas,Science332

(2011)702.

[26]Y.K.Lee,C.H.Jung,J.Park,H.Seo,G.A.Somorjai,J.Y.Park, NanoLett.11(2011)4251.

[27]I.Goykhman,B.Desiatov,J.Khurgin,J.Shappir,U.Levy,Nano Lett.11(2011)2219.

[28]M.Casalino,Int.J.Opt.Appl.2(2012)1.

[29]D. Conklin, S. Nanayakkara, T.-H. Park, M.F. Lagadec, J.T. Stecher,X.Chen,etal.,ACSNano7(2013)4479.

[30]F.Yan,X.W.Sun,Appl.Phys.Lett.102(2013)043303. [31]P. Berini, Laser Photon. Rev. (2013), http://dx.doi.org/

10.1002/lpor.201300019.

[32]K.Wu,W.E.Rodríguez-Córdoba,Y.Yang,T.Lian,NanoLett.13 (2013)5255.

[33]Y.He,P.Basnet,S.Murph,Y.Zhao,ACSAppl.Mater.Interfaces 5(2013)11818.

[34]E.Hao,G.C.Schatz,J.Chem.Phys.120(2004)357. [35]F.J.G.deAbajo,J.Phys.Chem.C112(2008)17983.

[36]M.Liu,P.Guyot-Sionnest,T.W.Lee,S.K.Gray,Phys.Rev.B76 (2007)235428.

[37]P.B.Johnson,R.W.Christy,Phys.Rev.B6(1972)4370. [38]P.M.Platzman,P.A.Wolff,WavesandInteractionsinSolidState

Plasma,AcademicPress,NewYork,1973.

[39]G.D. Mahan, Many-particle Physics, 3rd ed., Kluwer Aca-demic/PlenumPublishers,NewYork,2000.

[40]Forgold,wecanuseε0=9.01asthebackgrounddielectric con-stant,whichdescribesthescreeningeffectcomingfromthe reactionofthecoreelectronsofAuions.Inthereality,thisis stillasimplisticapproximationforgoldbecauseofthepresence ofintensiveinter-bandtransitions.

[41]A.Yariv,QuantumElectronics,3rded.,JohnWiley&Sons,New York,1989.

[42]A.O.Govorov, H.Zhang, Y.K.Gun’ko,J. Phys.Chem.C117 (2013)16616.

[43]E.Devaux,T.W.Ebbesen,J.-C.Weeber,A.Dereux,Appl.Phys. Lett.83(2003)4936.

[44]S.Link,M.A.El-Sayed,J.Phys.Chem.B103(1999)8410. [45]A.O.Govorov,H.Zhang,J.Phys.Chem.C(2014),http://dx.

doi.org/10.1021/jp500009k.

[46]G.V.Hartland,Chem.Rev.111(2011)3858.

[47]J.D.Jackson,ClassicalElectrodynamics,3rded.,JohnWiley& Sons,NewYork,1998.

[48]N.Szydlo,R.Poirier,J.Appl.Phys.51(1980)3310. [49]R.H.Fowler,Phys.Rev.38(1931)45.

[50]I.Tamm,S.Schubin,Z.Phys.68(1931)97. [51]K.Mitchel,Proc.R.Soc.Lond.146(1934)442—464.

[52]A.M.Brodsky,YuYa.Gurevich,Sov.Phys.JETP27(1968)114. [53]C.Scales,P.Berini,IEEEJ.Quant.Elect.46(2010)633. [54]Q.Y.Chen,C.W.BatesJr.,Phys.Rev.Lett.57(1986)2737. [55]T.P.White,K.R.Catchpole,Appl.Phys.Lett.101(2012)073905. [56]S.Zhu,G.Q.Lo,D.L.Kwong,Opt.Exp.19(2011)15843. [57]F.B.Atar, E.Battal,L.E.Aygun, B.Daglar,M.Bayindir, A.K.

Okyay,Opt.Exp.21(2013)7196.

[58]I.E.Protsenko,A.V.Uskov,Physics-Uspekhi55(2012)508. [59]A. Novitsky, A.V. Uskov, C. Gritti, I.E. Protsenko, B.E.

Kar-dynał, A.V. Lavrinenko, Prog. Photovolt Res. Appl. (2012), http://dx.doi.org/10.1002/pip.2278.

[60]M.Kornbluth,A.Nitzan,T.Seideman,J.Chem.Phys.138(2013) 174707.

[61]N.E. Christensen, B.O. Seraphin, Phys. Rev. B 4 (1971) 3321.

[62]A. Vial, A.-S.Grimault,D.Macías,D. Barchiesi,M.L. deLa Chapelle,Phys.Rev.B71(2005)085416.

[63]C.R.Crowell,S.M.Sze,in:G.Hass,R.E.Thun(Eds.),Physics ofThinFilms,AcademicPress,1967.

[64]C.R.Crowell,S.M.Sze,Phys.Rev.Lett.15(1965)659. [65]E.Dulkeith,T.Niedereichholz,T.A.Klar,J.Feldmann,G.von

Plessen,D.I.Gittins,etal.,Phys.Rev.B70(2004)205424. [66]Y.-J.Lu,J.Kim,H.-Y.Chen,C.Wu,N.Dabidian,C.E.Sanders,

etal.,Science337(2012)450.

[67]K.W.FreseJr.,C.Chen,J.Electrochem.Soc.139(1992)3234. [68]A.O.Govorov,H.H.Richardson,NanoToday2(2007)30. [69]M.A.Mangold,C.Weiss,M.Calame,A.W.Holleitner,Appl.Phys.

Lett.94(2009)161104.

[70]G.V.Hartland,Phys.Chem.Chem.Phys.6(2004)5263. [71]A.O.Govorov, W.Zhang,T.Skeini,H.Richardson,J.Lee,N.

[72] P.Keblinski,D.G.Cahill,A.Bodapati,C.R.Sullivan,T.A.Taton, J.Appl.Phys.100(2006)054305.

[73] G.Baffou,C.Girard,R.Quidant,Phys.Rev.Lett.104(2010) 136805.

[74] J.R.Adleman,D.A.Boyd,D.G.Goodwin,D.Psaltis,NanoLett. 9(2009)4417.

[75] P.Christopher,H.Xin,S.Linic,Nat.Chem.3(2011)467. [76] A.G.Skirtach,C.Dejugnat,D.Braun,A.S.Susha,A.L.Rogach,

W.J.Parak,etal.,NanoLett.5(2005)1371.

[77] J.Stehr,C.Hrelescu,R.A.Sperling,G.Raschke,M.Wunderlich, A.Nichtl,etal.,NanoLett.8(2008)619.

[78] A.S.Urban,M.Fedoruk,M.R.Horton,J.O.Rädler,F.D.Stefani, J.Feldmann,NanoLett.9(2009)2903.

[79] E.C.Garnett,W.Cai,J.J.Cha,F.Mahmood,S.T.Connor,M.G. Christoforo,etal.,Nat.Mater.11(2012)241.

[80] H.H.Richardson, Z.Hickman, A.O.Govorov, A. Thomas, W. Zhang,M.E.Kordesch,NanoLett.6(2006)783.

[81] D.Hühn,A.O.Govorov,P.R.Gil,W.J.Parak,Adv.Funct.Mater. 22(2012)294.

[82] E.W.McFarland,J.Tang,Nature421(2003)616.

[83] P.Christopher,H.Xin,A.Marimuthu,S.Linic,Nat.Mater.11 (2012)1044.

[84] G.Wang,Y.Ling,H.Wang,X.Lu,Y.Li,J.Photochem.Photobiol. CPhotochem.Rev.19(2014)35.

[85] A. Giugni, B. Torre,A. Toma, M.Francardi, M. Malerba,A. Alabastri,etal.,Nat.Nanotechnol.8(2013)845.

[86] P.J.Schuck,Nat.Nanotechnol.8(2013)799.

[87] A.Stolz,J.Berthelot,L.Markey,G.ColasdesFrancs,A. Bouhe-lier,(2013)arXiv:1308.4508.

[88] M.Grätzel, J.Photochem. Photobiol. C:Photochem. Rev.4 (2003)145.

[89] M.J.Berr,P.Wagner,S.Fischbach,A.Vaneski,J.Scheider,A.S. Susha,etal.,Appl.Phys.Lett.100(2012)223903.

[90] K.T.Dembele, G.S.Selopal, C.Soldano, R. Nechache, J.C. Rimada, I. Concina, et al., J. Phys. Chem. C 117 (2013) 14510—14517.

AlexanderO. Govorovis Professorof Theo-reticalPhysicsatOhioUniversityinAthens, USA. PhD: 1991, Institute of Semiconduc-tor Physics, Novosibirsk, Russia. Research positionin theaboveInstitute:1987—2001. In2001,he movedto theU.S.and became Professor at Ohio University. His research is focused on the theory of optical and electronic properties of nanostructures whichincorporatesemiconductor,metal,and molecularcomponents. His theoretical pre-dictionsmotivatedexperimentsinmanyresearchlabsworldwide. He isanauthor ofmorethan170papers.He is aFellow ofthe AmericanPhysicalSocietyandarecipient oftheBesselResearch Award(HumboldtFoundation,Germany),theIkerbasqueResearch Fellowship (Spain), the E. T. S. Walton Visitor Award (Ireland), ChangJiangChairProfessorshipoftheScholarProgramofMOEof Chinaand2014Jacques-BeaulieuExcellenceResearchChairAward (INRS,Montreal,Canada).

HuiZhangreceivedhisB.Sc.degreeinApplied Physics from the University of Science and TechnologyofChinain2006,andPh.D.in The-oreticalPhysicsfromtheInstituteofPhysics, Chinese Academy of Sciences in2011. Cur-rently,heisapostdoctoralresearcheratthe groupofProf.A.O.GovorovatOhio Univer-sity,U.S.Hiscurrentresearchisonplasmonics andexcitonicsofhybridnanostructureswitha focusonquantumphenomena.Heisanauthor of several recentpapers published inNano Letters,ACSNanoandotherjournals.

HilmiVolkanDemirisaprofessorof electri-calengineeringandphysics.Hereceivedhis M.S. and Ph.D.degreesat Stanford Univer-sity.HewasnamedaFellowbytheSingapore National ResearchFoundation and was also appointedtoaNanyangAssociate Professor-shipatNTUSingapore.Concurrently,heisthe EURYI AssociateProfessorat Bilkent Univer-sity,Turkey.HeservesastheDirectorofthe Luminous!Center ofExcellence. Amonghis research interests are light-matter interac-tionsatthenanoscaleandsemiconductordevicephysics.Dr.Demir hascontributedtocommercializationandlicensingofseveralnew enablingtechnologiesaswellasestablishingasuccessfulcompany and led to >20 patent applications, several of which have cur-rentlybeenused,ownedorlicensedbytheindustry.Thesescientific andentrepreneurshipactivitiesresultedinseveralimportant inter-nationalawardsincludingEuropeanScienceFoundationEuropean YoungInvestigatorAwardandTheOutstandingYoungPersoninthe WorldAwardbyJCIFederationofYoungLeadersandEntrepreneurs. Yurii Gun’ko graduated from the Chemistry Department of Moscow State University in 1987. He hasalsoreceivedhis Ph.Ddegree in Inorganic Chemistry from Moscow State Universityin1990.Thenheworkedasa lec-turerinChemistryinBelorussianInstituteof Technology(Belarus). In1994hereceiveda postdoctoralpositioninthegroupof profes-sorM.F.LappertintheUniversitySussex(UK). Thenin1995hewasawardedAlexandervon Humboldtfellowshipandworkedinthe Uni-versityofMagdeburg(Germany)withprofessorF.T.Edelmann.After thathereturnedbacktotheUniversitySussexandworkedwhere as a postdoctoral researcher. In 1999 Dr. Gun’ko moved to the ChemistryDepartmentofTrinity CollegeDublin(Ireland)to take uptheposition ofthelecturerin InorganicChemistry.Currently YuriiGun’koworksasaProfessorintheSchoolofChemistryanda PrincipalInvestigatorinCRANNInstituteinTrinityCollege.Hismain researchinterestandactivitiesare:carbonnanomaterials, photo-voltaiccells,magneticnanostructures,plasmonicandquantumdot basedmaterials.