Electron dynamics in metallic nanoparticles

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<ul><li><p> .Chemical Physics 251 2000 181203www.elsevier.nlrlocaterchemphys</p><p>Electron dynamics in metallic nanoparticlesJ.-Y. Bigot ), V. Halte, J.-C. Merle, A. Daunois</p><p>Institut de Physique et Chimie des Materiaux de Strasbourg, Groupe dOptique Nonlineaire, Unite Mixte a 7504 CNRS-ULP-ECPM, 23 rue du Loess, 67037 Strasbourg Cedex, France</p><p>Received 10 March 1999</p><p>Abstract</p><p>We studied the dynamics of electrons in copper and silver nanoparticles embedded in a transparent matrix, using thetechnique of pumpprobe femtosecond spectroscopy. Comparative measurements are made in thin films of the same metals.In the case of the nanoparticles, the electron dynamics is strongly influenced by the surface at the boundary of the metal andthe surrounding dielectric matrix. A detailed study of the pumpprobe signals near the plasmon resonance of thenanoparticles reveals the importance of electronelectron scattering during several hundreds of femtoseconds. The influenceof these scattering processes on the real and imaginary parts of the metal dielectric function is compared in the nanoparticlesand thin films. In addition, the non-thermal component of the electrons and the heat transfer to the surrounding dielectric aremeasured. The results are analyzed with a model of effective medium, where the metal dielectric function is described in therandom phase approximation, including the surface effects in a phenomenological way. q 2000 Elsevier Science B.V. Allrights reserved.</p><p>1. Introduction</p><p>The behavior of the electron dynamics in metallicnanoparticles is different than the one observed inthe corresponding bulk metal. In order to examinethese differences, let us consider the relaxationmechanisms that take place in a metallic particlewhen it is excited with a short optical pulse. In Fig.1, we have sketched the energy relaxation followingthe excitation of the nanoparticle with a femtosecondpulse. Different time scales are involved. Initially,the energy is transferred to the electrons by absorp-tion of photons via interband and intraband transi-tions. During this quasi-instantaneous process, the</p><p>) Corresponding author.</p><p>phase memory is conserved between the electromag-netic field and the electronic states, and the densityof excited states depends on the spectral shape of thelaser pulse. The corresponding electron distributionis non-thermal as expected in any metallic systemw x1,2 . In this time scale of a few femtoseconds, theelectronic system is strongly correlated and its col-lective character is important.</p><p>The next step of the energy relaxation corre-sponds to a thermalization of the electrons. Theoccupied electronic states tend to a FermiDiracdistribution with a well defined temperature whichdepends on the laser pulse intensity. The increase oftemperature can easily reach several hundreds ofdegrees. The phase coherence is lost and the collec-tive modes have decayed into quasi-particle pairs.Several time resolved photoemission experiments,</p><p>0301-0104r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. .PII: S0301-0104 99 00298-0</p></li><li><p>( )J.-Y. Bigot et al.rChemical Physics 251 2000 181203182</p><p>Fig. 1. Sketch of the relaxation processes in a metallic nanoparti-cle.</p><p>performed in noble metal films, have shown that thetemporal scale of this thermalization process is of a</p><p>w xfew hundreds of femtoseconds 18 . For small par-ticles, with a diameter typically less than a few tensof nanometers, the scattering time of the electrons atthe particle surface is less than one hundred fem-toseconds. It can be deduced simply by assuming aneffective damping V rR where V is the velocityF eff Fof electrons at the Fermi level and R an effectiveeffparticle radius which takes into account the effect ofquantum confinement on the density of states in the</p><p>w xmetal 9 . In this time scale, the electronelectron .ee scattering is also very efficient to redistributethe energy to thermalize the electrons. Therefore thetwo mechanisms of surface and ee scattering are incompetition. As we will see in the next sections ofthe present paper, this difference shows up in a time</p><p>dependent broadening and shift of the surface plas-mon associated to the nanoparticle.</p><p>Another difference between the particles and bulkmetal comes from the surface induced polarization.As it is well known, the dielectric confinement be-comes important when the size of the particles ismuch smaller than the optical wavelength of the</p><p>w xexcitation 1013 . In the nanoparticles, it gives riseto eigenmodes of the electromagnetic field which areanalogous to the cavity modes of a resonator. Forsmall enough particles, the first order mode is pre-dominant and the model of MaxwellGarnett of the</p><p>w xeffective medium applies 14,15 . In a similar man-ner, the Coulomb potential inside the nanoparticle isrenormalized by the surface induced polarization.This results in a modification of the dynamical</p><p>w xscreening of the ee interaction 16 . In the third partof the paper, we will discuss how it influences thedynamics of the electrons in the particle as comparedto the bulk metal.</p><p>Another important mechanism in the electron dy-namics, which is shown in Fig. 1, is the energytransfer to the lattice. This process, which has beenstudied with great detail in thin films made of vari-</p><p>w xous metals 1725 , can be described by two coupled .baths the electrons and the lattice . It also displays</p><p>differences when comparing the dynamics in metal-lic particles and the corresponding bulk. At themicroscopic level, it is the electronphonon interac-tion which couples the two baths. Therefore, due tothe reduced dimensionality of the nanoparticles, thesurface modes of the metallic particle influence theenergy transfer between the electrons and the lattice.In addition, the coherent behavior of the latticevibrations shows up when the electrons are in equi-</p><p>w xlibrium with the lattice temperature 2628 . The laststep in the relaxation is the energy transfer to thedielectric matrix. This transfer corresponds to theheat diffusion from the metal to the environment. Itis therefore sensitive to the thermal conductivity ofthe surrounding medium. We will show how thisenergy transfer is affected by the matrix.</p><p>One should mention that the above considerationsare relevant for metallic particles with small enoughsizes, so that surface effects are important. On theother hand, they do not apply to clusters smaller thana few tens of angstroms. The discrete nature of the electronic states has then to be considered. Here, the</p></li><li><p>( )J.-Y. Bigot et al.rChemical Physics 251 2000 181203 183</p><p>metal is still considered as a three-dimensional sys-tem where the surface affects both the many-bodyinteractions between the electrons and the electronlattice relaxation. It is important to stress that thesurface effects will be added as ad hoc phenomena.A more rigorous way would be to consider theelectron correlation in finite systems. It is an interest-ing and challenging numerical task for the futuresince it requires very large computer capacities whichare not yet available.</p><p>In Section 2, we first present experimental resultsobtained in thin films of copper and silver. Theelectron dynamics is then compared to the corre-sponding nanoparticles made of the same metal. Wethen present a model based on the dielectric functiondescribed in the effective medium approximation.The dynamics is incorporated via the time dependenttemperatures of the electrons and the lattice and theinfluence of the surface is incorporated in a phe-nomenological way in the case of the nanoparticles.</p><p>2. Experimental results</p><p>2.1. Experimental technique</p><p>The electron dynamics has been studied in thinfilms and nanoparticles of copper and silver. Thenanoparticles are obtained by a nucleation-growthtechnique. The metal oxide is first introduced in themelted glass where the germination process takesplace. The glass composition is made of SiO , PbO,2Na O, K O. The lead oxide PbO is added to in-2 2crease the refractive index of the matrix and Na O,2K O allow to lower the viscosity and to enlarge the2temperature range where the glass is processed. Thedoped glass is then annealed in order to increase thesize of the initial germs. It is the Oswald maturation</p><p> .process. By adding a reducing agent Sb, Sn , or bya processing under hydrogen atmosphere, the germi-</p><p>w xnation and growing processes are promoted 29 . Theaverage diameter of the nanoparticles obtained withthis technique is larger than 5 nm with low concen-</p><p> y3 y6.trations in volume typically 10 to 10 . Themicroscopy electronic transmission observationsdemonstrate that the nanoparticles are spherical witha relatively homogeneous size distribution. Let us</p><p>notice that such samples have a high chemical stabil-ity. For instance, they can be washed in a solution ofaceton or ethanol without damage. In addition, theypresent a high optical breakdown threshold to the</p><p> 10 y2 .laser power more than 10 W cm . In contrast,we noticed that samples made by a co-deposition of</p><p>the nanoparticles and the matrix like with the tech-w x.nique of Low Energy Cluster Beam Deposition 30</p><p>have a breakdown threshold about ten times lower.Fig. 2 shows typical absorption spectra of copper . .2a and silver 2b nanoparticles. The optical den-sity is represented as a function of wavelength for</p><p> .particles with an average diameter of 10 nm Cu .and 6.5 nm Ag . Both samples display a plasmon</p><p> .resonance situated respectively at 2.22 eV 558 nm .for Cu and 2.85 eV 434.5 nm for Ag. In the case of</p><p>copper, the resonance is situated near the interband .transitions dp E s2.17 eV or 571 nm fromdp</p><p>the filled d band to the unoccupied states in the pconduction band. This spectral degeneracy is at theorigin of the large absorption on the high energy sideof the plasmon resonance. As discussed in Section2.3, it is an ideal situation to study the effect ofcollision broadening of the plasmon by the quasipar-ticle states excited by the femtosecond pulses. In thecase of silver, the resonance is situated well below</p><p>Fig. 2. Optical density of nanoparticles of copper and silverembedded in a glass matrix near the plasmon resonance.</p></li><li><p>( )J.-Y. Bigot et al.rChemical Physics 251 2000 181203184</p><p>the interband transition thresholds dp E s3.99dp. .eV or 310 nm and ps E s3.85 eV or 322 nmps</p><p>from the occupied p states to the unoccupied s states.The resonance is therefore well defined and, bycontrast to Cu, it allows the observation of thedynamics associated to the heating of the electronpopulations, without probing directly the excitedelectronic population. In the next sections, we willsee that the two types of materials allow to clearlydistinguish the effects of the electron dynamics onthe real and imaginary parts of the dielectric functionof the metal.</p><p>The Cu and Ag polycrystalline thin films havebeen evaporated on a glass substrate under highvacuum. Their thicknesses, of a few hundreds ofAngstroms, is determined by X-ray diffraction atgrazing incidence. The complex linear refractive in-dex NsN y i N , is determined by ellipsometry1 2and by measuring the linear transmission and reflec-tion. In the case of silver, the real and imaginaryparts of N are almost constant since they have aweak dispersion in the spectral range of interest .2.23.5 eV . We obtain the following values: N s10.09 and N s1.6. They are comparable to those2</p><p>w xgenerally reported for silver films 3133 and thelow N value of our samples is an indication of their2good crystalline quality. In the case of copper, thereis an important dispersion of the refractive index dueto the interband transitions in the spectral region of</p><p> .interest 1.72.6 eV . During the experiments thesamples, which are exposed to the ambient air, aresubject to oxidation. However, we have checkedwith ellipsometric measurements that no significantchange of the optical constants occur within a fewdays. The oxidation layer, which rapidly forms whenthe films are taken out of the vacuum chamber,stabilizes after reaching a thickness of a fewAngstroms.</p><p>Time resolved transmission and reflection mea-surements have been performed using different laserapparatus. For the silver thin films and nanoparticles,the femtosecond pulses are produced by a tunabletitanium sapphire laser. The pulses issued from anoscillator operating at 80 MHz are amplified in a</p><p>regenerative amplifier pumped by a Nd:YLF yt-.trium lithium fluoride laser with a repetition rate of</p><p>5 kHz. The maximum energy per pulse is ;200 mJtunable in the range 760860 nm and the pulse</p><p>duration is ;100 fs. One part of the amplified beamis used to generate a broad band continuum 0.351</p><p>.mm in a 3 mm sapphire plate. The group velocitydispersion of this continuum is only partially com-pensated with a sequence of four prisms. A chirp of;1 ps in the spectral region 360560 nm has beendetermined from cross-correlation measurements.The second part of the amplified beam is frequencydoubled in a 1 mm thick BBO crystal. Two pumpand probe configurations are used depending on theinformation that is required. In the first one, thepump and probe are degenerate in frequency andtunable in the spectral range 430380 nm. Thisconfiguration is used either with the amplified laserat 5 kHz repetition rate or with the frequency dou-bled non-amplified beam issued from the oscillatorat 80 MHz. Using the two repetition rates allows theenergy density of the pump beam, absorbed in the</p><p>samples, to be varied in a broad range 0.15002 .mJrcm . Fig. 3 shows the laser set-up and the</p><p>experimental configuration.For the case of copper thin films and particles, the</p><p>femtosecond pulses are produced by a collidingpulsed mode locked cavity operating at 620 nm andamplified at 5 kHz with a copper vapor laser. Theamplified pulses of 80 fs duration are divided intotwo parts. One beam corresponds to the pump andthe other one is used to generate pulses of 10 fsduration in a compression line with a fiber, gratingsand prisms. These pulses are used as a broad spec-trum probe. For both types of material, the differen-</p><p> . .tial transmission DTrT t s T T rT is mea-on off offsured as a function of the temporal delay t between</p><p> .the pump and probe, T T being the normalizedon off .probe transmission with without the pump. In the</p><p>case of the thin films, we also measured the differen- .tial reflection D RrR t . The detection scheme is a</p><p>synchronous detection using a chopper and a lock-inamplifier for the measurements at a fixed wave-</p><p> .length. The spectral measurements DTrT l,t aremade as a function of the probe wavelength l, forvarious pumpprobe delay t, using a monochro-mator and a dual array CCD camera. The experi-ments are performed at room temperature. For theglass embedded Ag nanoparticles, additional mea-surements at liquid helium temperature have beenmade in order to compare the electronlattice relax-ation for different electron and lattice specific heat.</p></li><li><p>( )J.-Y. Bigot et al.rChemical Physics 251 2000 181203 185</p><p>Fig. 3. Laser experimental set-up to study the dynamics of Ag nanoparticles and films.</p><p>The ratio of...</p></li></ul>