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Structural kinetics of laser-excited metal nanoparticles supported on a surface
Chemical Physics 299 (2004) 183–191 www.elsevier.com/locate/chemphys
Structural kinetics of laser-excited metal nanoparticles supported on a surface A. Plech a
a,*
, S. Gresillon b, G. von Plessen c, K. Scheidt d, G. Naylor
d
Fachbereich Physik der Universit€at Konstanz, Universit€atsstr. 10, D-78464 Konstanz, Germany b ESPCI, 10, rue Vauquelin, F-75005 Paris, France c I. Physikalisches Institut, RWTH Aachen, D-52056 Aachen, Germany d ESRF, BP 220, F-38043 Grenoble, France Received 29 July 2003; accepted 28 October 2003
Abstract Gold nanoparticles have been adsorbed as monolayers on silicon and glass substrates and the structure evolution following femtosecond laser excitation has been analyzed by means of time resolved X-ray scattering. The synchronization of the laser to the X-ray pulse structure emitted from a third generation synchrotron source allows to obtain a natural time resolution of 100 ps for the lattice kinetics. The prospects of using a picosecond X-ray streak camera are explored. The lattice kinetics are dominated by the fast heating of the particle lattice and nanosecond cooling times. However, the analysis of peak shapes reveals the presence of nonthermal motion within the lattice. Unexpectedly large relaxation times for the thermalization of vibrational modes are found and are attributed to the weak mechanical coupling to the substrate. Strong nonuniform strain develops within the domain of electron– phonon interaction time regime after the laser excitation as seen with the X-ray streak camera. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Nanoparticles; Picosecond time resolution; Structure; Femtosecond laser excitation; Thermal kinetics
1. Introduction Metal and semiconductor nanoparticle systems attract presently a strong attention due to their interesting optical properties [1–4]. In particular the ultrafast relaxations observable in femtosecond pump–probe experiments have been the subject of a large number of studies in the past decade. Elementary interactions such as electron–electron and electron–phonon coupling have been explored in detail [2,5–9]. The effort goes into understanding nonlinear and ultrafast optical response by size and shape modifications. Such approaches can comprise synthesis issues as well as laser induced shaping [3,10–12]. While the main focus has been on understanding and controlling the electronic response, increasing efforts are made to understand the structural reactions and control the phononics of the nanostruc-
*
Corresponding author. Tel.: +497531884682; fax: +497531883127. E-mail address: [email protected] (A. Plech).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.10.041
tures, which is of importance for the understanding of, e.g., structural phase transitions or applications as laser cleaning. Those structural transitions are of special interest, which could be used for permanent or transient nanostructuring for e.g. device applications. Particle cleaning from surfaces can probably be enhanced by exciting vibrational resonances of the particles; this could help to overcome damage thresholds [13]. For the investigation of such issues, it is unfortunate that the optical response from lattice and other structural reactions occurs only via the coupling to the electron system and thus only gives indirect information on structural processes. Therefore X-ray scattering in conjunction with ultrafast laser excitation is explored as a new tool to investigate structural dynamics. This paper deals with the structural kinetics of laserexcited, supported, metal nanoparticles. Experiments with nanoparticles (mostly of gold and silver, but also semiconductor quantum dots [14,15]) have established a detailed picture of the cascade of relaxations observable after femtosecond laser excitation [2,4,9,16–19]. The
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electron gas can gain energy via excitation of the plasmon band resonance or interband transitions and forms an nonequilibrium electron distribution. This decays into a thermalized Fermi distribution within /1 ps and couples to the lattice. The energy transfer to the lattice can not only raise the lattice temperature, but can impulsively induce coherent lattice vibrations. For these vibrations, in general a good agreement with the description of vibrational eigenmodes of a continuous medium is found. Coherent vibrations have been observed as oscillations of time-resolved optical pump–probe signals. Damping of oscillations stem from different mechanisms as internal damping within a particle or inhomogeneous broadening effects in a polydisperse ensemble. So far it is clear that the surrounding of the particles plays an important role in the structure relaxations. Glass embedded silver particles have displayed very fast damping times due to the strong mechanical contact to the environment, whereas gold solutions or nanoparticles on a surface have longer lifetimes either for vibrational damping or for lattice cooling. Studies of the vibrational and lattice cooling lifetimes are difficult, due to the selective nature of the spectroscopical response from the particles, which is mainly connected to volume changes. Raman scattering [20,21] as well as Brillouin scattering [22] in comparison are sensitive to thermally activated modes of radial motion within the particle as well as spheroidal modes involving radial motions of the atoms together with torsional displacements. Time resolution however is not routinely available with the latter techniques. X-ray scattering is a promising tool to resolve the atomic displacement in space as well as in time [23,24]. This field is still in its beginning, considering the development in ultrashort X-ray pulsed sources. In this paper we present the results of time-resolved optical pump X-ray probe experiments in which the structural dynamics of optically excited metal nanoparticles are investigated. Two different time-resolved experiments are presented. Using a conventional area detector, we follow the lattice kinetics of nanoparticles with the 100 ps time resolution. The lattice response to femtosecond laser pulses is explained by means of lattice heating and shape vibrations. In a second experiment the ultrafast response is resolved by an X-ray streak camera synchronized to the laser excitation source with low jitter. The picosecond resolution allows to explore the early steps of lattice reaction.
2. Materials and techniques Thin film self-assembly from solution has become a versatile tool to produce molecularly ordered soft matter and composite films. We employ a method for sample preparation first described by Decher and coworkers
[25], which uses charged dissolved polymers to adsorb on surfaces. As gold nanoparticles tend to be negatively charged in aqueous solution, glass (Marienfeld, Germany) and silicon wafers were coated by polyetylene-imine (Fluka) after hydrophilic etching in a concentrated KOH solution (water–isopropanol mixture in the case of silicon). The polymer coated wafers are then immersed in solutions containing a low concentration of gold nanoparticles (details found in [26]). The particles were purchased from BBInternational (GB) and displayed very narrow size distributions of about 10%. The wafers are washed and dried in a nitrogen stream after the adsorption step. It is known that the adsorption process on the charged surface is diffusion controlled, with diffusional times in the range of hours. This allows to control the coverage in a rather straightforward manner [27] by variation of the immersion time. Time resolution for the nanoparticle structure changes was achieved at the beamline ID09B at ESRF using a setup of a femtosecond laser synchronized to the X-ray pulse structure emitted by the synchrotron [28,29]. Briefly, the radio frequency signal from the electron storage ring at 88.05 MHz is used to phase lock a Ti:Sa femtosecond oscillator (diode pumped, Coherent) at the same repetition rate. The weak 800 nm pulses emitted by the oscillator are amplified in a regenerative Ti:Sa amplifier (Spectra physics) to achieve intense pulses of 1 mJ at a repetition rate of 896.6 Hz. This frequency is chosen such, that a vacuum mounted ultrasonic chopper wheel can run at this subharmonic frequency of the storage ring to isolate single X-ray pulses of 100 ps length. The laser light is frequency doubled in a BBO crystal and focussed on the surface of the wafer to give a focal spot of 0.25 0.8 mm. The incidence angle of the laser was about 18° with respect to the surface, whereas the X-rays hit the surface at the Bragg angle of 10.15°. The momentum transfer in the plane of reflection is therefore purely vertical, while for vectors out of the plane of reflection a component parallel to the surface is present. The corresponding scattering geometry is displayed in Fig. 1. The scattering from the particle lattice was recorded on a fiber optics coupled CCD camera (Mar research) with a spatial resolution of 65 lm. The resulting resolution of the setup was determined to be about 0.055° in angle. One main difficulty in the observation of the nanoparticles by X-ray techniques is the low scattering cross section for hard X-rays. Firstly the amount of particles whose absorption cross section matches the laser absorption is very low and secondly although single particles are of good crystallinity (grain size of the order of 30–50 nm at the present particle sizes of 60–150 nm) the ensemble itself is disordered, giving rise to Debye Scherrer rings. It is thus advantageous to use a moderate resolution CCD camera, which in turn collects X-ray
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3. Results and discussions 3.1. Spectroscopy and X-ray scattering
Fig. 1. Scattering geometry for the X-ray diffraction from the nanoparticles on the sample surface. The X-ray intensity on the CCD screen forms a Debye Scherrer ring, whose nonshadowed part is recorded. The laser beam strikes the surface at a higher angle, so that the footprints of the narrow X-ray beam and the wider laser beam on the surface are similar.
photons in a large solid angle region. The flux of the beamline was optimized by introducing an in-vacuum undulator having the first harmonics at 15 keV, which is a good balance of flux and heat load. The narrow shaped emission spectrum can even be used for highest flux applications at moderate resolution [30]. In the combination with the CCD camera a silicon (1 1 1) monochromator was used to define the X-ray wavelength. A toroidal mirror focuses the X-rays to 70 70 lm2 on the sample at a flux level of 105 photons per pulse and mA beam current. Still about 2000 X-ray pulses have to be accumulated on the detector for sufficient signal to noise ratio to record relative lattice parameter changes (at each pump–probe delay step) below 103 . The time resolution is achieved by electronically delaying the excitation laser pulse with respect to the X-ray pulse. The accuracy due to jitter and beam drifts is much better than the X-ray pulse length (10 versus 100 ps). In an exploratory experiment we used an X-ray streak camera, which can resolve X-ray photons in time within the pulse length. The X-ray generated photo-electrons in the cathode are accelerated and deflected by a fast switching electric field converting time information into spatial information. The projected time pattern is imaged onto a microchannel-plate enhanced CCD chip. The technique of jitter-free recording is described in detail elsewhere [31]. As the efficiency of the photocathode and aperture further reduce the detected scattering intensity dramatically, the only way to observe a signal from the photo-excited nanoparticles was to use the full emission of single line undulator with 2.5% bandwidth and compromise with the resolution. The results are discussed in Section 3.3.
The adsorption process of particles onto the surface during sample preparation is checked by ex situ extinction measurements and surface sensitive X-ray scattering methods. Varying the adsorption time in the gold solution from a few minutes to 10 h changed the coverage from 1% to 10% mass fraction within the film. The absorbance spectra for different coverage where measured with a fiber optics spectrometer with a diode array (Ocean Optics). Fig. 2 displays a set of spectra for particles of 60 nm in diameter in the visible range. The prominent plasmon resonance maximum is found at 530 nm and the absorbance increases steadily with immersion time, indicating a larger amount of adsorbed gold colloids. We find a second red shifted maximum evolving with coverage, which is explained by a delocalized plasmon resonance extending over several adjacent particles. With increasing coverage the average distance in between proximate particles decreases, which in turn enhances the near field coupling of the particles. The coupling produces a new resonance at lower energy [1]. It should be noted that if the particles tended to aggregate on the surface even at low coverages one would expect the second maximum to be present from the beginning of adsorption. The red-shifted maximum becomes important only for large coverage fractions, where the nearest neighbor distances decrease and the probability for finding close packed particles increases. The particle distribution can also be revealed by surface sensitive small angle scattering (not shown here), from where the particle–particle pair correlation function can be derived [32]. The coverage with the particles is derived from X-ray reflectivity [26]. For the following pump–probe experiments samples of intermediate coverage below 5% were used, where the clustering is negligible.
Fig. 2. Absorbance of the monolayered gold particles with 60 nm diameter on a float glass surface as measured in 90° transmission. The different curves with increasing absorbance represent increased adsorption times and consequently a higher coverage with particles.
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We concentrate mainly on the evaluation of the (1 1 1) Debye Scherrer ring of the gold fcc lattice. For best angular resolution only the (1 1 1) and (2 0 0) reflections were collected on the CCD screen. The (2 0 0) reflection can be analyzed as well, but the noise is higher due to the smaller structure factor. So far no differences with respect to the discussion of the (1 1 1) reflections were observed. The rings were usually integrated azimutally [33] and the resulting radial profile was normalized by using the glass and diffuse scattering background. Fig. 3 is a visualization of the change of the Debye Scherrer ring due to the interaction of the sample with the laser pulse. The ring pattern is transformed into rectangular coordinates with azimutal and radial angles as x and y axes. In both cases the scattering peaks shift to lower angles and immediately after the laser excitation the ring is considerably broadened (in this case at time delays of 100 ps). There is one distinct difference in between the scattering from particles supported on silicon and on glass. In the case of silicon the intensity is strongly increased in the specular direction (scattering vector perpendicular to the surface plane). We conclude that particles adsorbed on silicon tend to orient the crystallographic facets such, that the (1 1 1) scattering peaks perpendicular to the surface. We exclude a direct interaction of substrate lattice and particle lattice because of the intermediate polymer buffer layer. Instead the gold particles are probably less strongly bound to the silicon (oxide) surface and are allowed to rotate so that (1 1 1) facets orient parallel to the surface. This is in agreement with the observed lower laser power necessary for inducing laser cleaning of the surface. The details of this effect will be described elsewhere. We have analyzed different scattering vectors with respect to the surface and found the same behaviour of lattice expansion irrespective of the orientation of the lattice planes to the substrate surface.
As reported previously, the laser pulses cause a rapid expansion of the nanoparticle lattice mediated by electron excitation and subsequent electron–phonon scattering. The expansion can in first place be regarded to be of thermal origin. A calculation of the absorbed energy of particles embedded in a glass matrix versus the amplitude of expansion gives the approximate coefficient of expansion as known from bulk material. The estimation of absorbed energy for the supported particles is less precise due to the more complicated electric field distribution close to the geometrical interface, but a rough estimate is still in agreement with the assumption that the largest fraction of absorbed energy is transferred into lattice excitation. The maximum lattice temperature that is reached within the first 100 ps can be calculated to be 710 K, if the bulk coefficient of expansion is assumed. 3.2. Thermal kinetics A characteristic decay of the lattice expansion is observed for increasing delay s between laser and X-ray pulse. The energy stored in the particle lattice is transferred within several nanoseconds to the environment. The decay of expansion (see Fig. 4) can be fitted quite well by an exponential decay, implying that the temperature of the particle is reduced accordingly h s i aðsÞ t ¼ DTmax a exp þ1 2 ð1Þ erf a0 t0 ds with the lattice parameter a as function of delay time s and maximum heating of the nanoparticle DTmax . The thermal expansion coefficient is denoted by a, and the time resolution of the experiment by ds, which is taken to be 35 ps (HWHM). In Fig. 4 the relative lattice expansion is depicted as function of s for particles of 100 nm diameter deposited on glass substrate. The solid line represents a fit according to Eq. (1).
Fig. 3. CCD false colour image of the (1 1 1) ring scattered from the nanoparticle layer for gold particles on silicon (top) as well as on glass (bottom). The rings are converted into a rectangular representation of radial (vertical) and azimutal (horizontal) angles. A comparison is made between nonexcited state ()80 ps) and immediately after laser excitation (120 and 100 ps, respectively), where the Bragg angle has shifted.
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Fig. 4. Relative increase of the lattice parameter derived from the (1 1 1) reflection of 100 nm gold particles on a glass surface. A laser fluence of 38 mJ/cm2 was applied to the surface. The time axis represents the delay time with respect to the exciting laser pulse. The solid line represents a fit to the data with an exponential decay function convoluted with a resolution limited error function for the initial signal rise.
For embedded particles (silver particles in glass matrix) the relaxation times are found to be in the range of hundreds of picoseconds. They depend linearly on the particle size, which is explained by interface limited heat transport to the matrix [24]. Hu and Hartland [34] observe somewhat different cooling rates in gold nanoparticles in water. They use stretched exponentials for the fits and interpret their data with a domination of bulk heat transfer in the medium as limiting step [35]. Clearly the boundary between the particles and the matrix is completely different in our study, where particles supported on a surface are investigated. Here the cooling rates are decreased by almost one order of magnitude due to the reduced contact area. There is considerable spread for repeated experiments in the dependence of relaxation time on the particle size due to the presence of several control parameters such as the influence of facetting, coverage or the polymer cushion. Additionally a water meniscus may form on the hydrophilic polyethylene-imine covered surface, depending on the humidity, which was not controlled. A closer analysis of the decay of expansion reveals a slight deviation from the exponential law within the first nanosecond after excitation as can be seen in the fit residue in Fig. 5. Initially the observed expansion is less than would be expected from the single exponential decay, and gradually reaches the fit function. At the same time a strong increase of the radial width of the reflection is observed which decays on the same time scale. In the case of an infinite lattice the Scherrer width is fixed by the resolution function and crystallite size. Purely thermal effects do not result in any broadening but only a reduction in scattering intensity, quantified by the so called Debye–Waller factor (DWF). In contrast to the Scherrer width however, the DWF does not display any anomaly in time as seen in Fig. 5 [36]. The
Fig. 5. (a) Residue of the fit in Fig. 4 together with a simulation of the contribution due to decaying vibrational excitations (see text). (b) Plot of the Scherrer width (crosses, left hand sided scale) and integrated intensity (dots, right-hand sided scale) of the (1 1 1) reflection. The solid lines mark the decay of the width change and the computed thermal Debye–Waller factor, respectively.
peak intensity is shown together with a DWF calculation assuming bulk thermodynamic values [37]. In the case of very small nanoparticles one can consider a relaxation of the outermost lattice layers to modify the peak shape and the intensity. In the present case the particles consist of 250 units cell of the fcc lattice in diameter, so that this effect should be negligible. On the other hand lattice distortions within the particle can cause broadening, which is transient in nature in this case. This leads us to conclude that a part of the absorbed energy is not transformed into thermal motion immediately after the laser impact, but is present in nonthermal excitations. Ultrafast laser absorption studies as well as Raman or Brillouin light scattering studies have given evidence for particle vibrations in various classes of nanosystems. In spherical metal particles (mostly of silver or gold) oscillations of the transient signal are observed that are consistent with the excitation of the lowest vibrational modes in elastic bodies. Voisin et al. [16] have pointed out that the laser signal from the plasmon band is most sensitive to the lowest spheroidal vibration mode without torsional movements, which can be regarded as homogeneous volume increase of the sphere. Indeed most investigations in transient absorption spectroscopy on excited nanoparticles do not observe higher order modes, with exception of a few experiments [38].
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The spheroidal modes for a free particle can be calculated with the formula [39] xn;l ¼ Sn;l
cl ; R
ð2Þ
with the longitudinal sound velocity cl and the eigenvalue Sn;l with radial and angular quantum numbers n and l. For l ¼ 0 the eigenvalue is calculated by solving 2 the equation S1;0 cot S1;0 ¼ 1 S1;0 =ð4 ðct =cl ÞÞ for the material dependent ratio of cl and the transverse sound velocity ct . Inserting the values for gold results in an oscillation period of 33 ps for 100 nm particles or 50 ps for 150 nm particles. In contrast, Raman scattering is mostly sensitive to spheroidal modes with l ¼ 2, which have been observed in silver nanoparticles. It is therefore probable that a range of vibrational modes are excited with femtosecond laser pulses, of which those of higher order are not resolved in optical pump–probe experiments. The relationship between the mechanism of phonon excitation and the phonon population in metal nanoparticles is still not clarified [18,38]. For example one can imagine that the stability of different modes (and therefore their lifetimes) critically depends on geometrical properties, such as particles shape and local environment. In particular the surface could act as a source of symmetry breaking for the supported particles, giving rise to a splitting of degenerate vibration modes. The (1,2) mode can become more stable than the (1,0) mode due to the smaller translational motion of the center of mass of the particle. The period of this mode is typically longer by a factor of 2 than the purely spherical (1,0) mode [20]. These considerations have a strong influence on the observability and lifetimes of modes. The experimental data as represented by the lattice parameter change in Fig. 4, however indicates peak position changes for adjacent time points, but no clear harmonic oscillation is found. X-ray scattering is, in contrast to spectroscopical methods, sensitive to strain in the particle lattice, regardless whether volume changes are present or not. Higher order modes manifest themselves in a change of the scattering profile rather than a shift of the peak position. The effect of active particle vibrations on the scattering profiles is then less straightforward. We have simulated the scattering from a two dimensional cubic centered crystal with the atoms occupying the coordinates at (0; 0) and (0.5; 0.5) within the unit cell along the ðffÞ direction by simply adding up the phases from all scattering centers within a 145 unit cells circle. The resulting scattering profiles are displayed in Fig. 6. This procedure is supposed to give a realistic impression of the scattering from a particle of 60 nm in diameter. The lattice strain ~ uðx; yÞ has been added upon the individual positions of the atoms by adding the following, simplified model of displacements:
Fig. 6. Simulated X-ray scattering profiles along the ðffÞ direction of a two dimensional cubic centered lattice of 145 units cells for different lattice distortions. From top to bottom: symmetrical breathing mode with free boundary condition, third order spherically symmetric vibration and first dipolar spheroidal mode, see text for details.
~ uðx; yÞ ¼
sin
px py n ; sin n 2R 2R
for the spherically symmetric modes; px py ~ uðx; yÞ ¼ sin n ; sin n 2R 2R
ð3Þ
for the ð1; 2Þ spheroidal mode; where n marks the radial quantum number (n ¼ 1 for the ground order ‘‘breathing’’ mode of the spherical vibration and n ¼ 2 for the first order mode) and R the radius of the particle in unit cells. The second formula describes a quadrupolar vibration with nonvanishing angular momentum of the radial motion [40] (often nicknamed as ‘‘football’’ mode) as observed in Raman scattering. Note that the curves in Fig. 6 do not display time averages, but instead a snapshot at the point of maximum strain. This strain is uniformly expansive for the breathing mode, which therefore shifts the scattering peak to smaller q vectors. For the next order spherical mode volumes of expansion and compression coexist within the particle, while the net volume effect is expansive. Therefore a slight shift of the peak can be observed which is overruled by the large distribution of lattice parameters present at the same instant. A similar effect appears for the spheroidal mode, where the change in volume and thus the mean change in atomic distance
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is negligible against the spread in interatomic distances. A strong broadening is the consequence. It is clear that only the breathing mode gives rise to a clear shift of the Bragg positions. The strongest effect in the higher mode (center panel of Fig. 6) consists in a decrease of intensity at the center of the Bragg position and at the same time excess scattering as sidebands of the peak, which can be regarded as ‘‘superlattice’’ peaks due to the new spatial frequency in the lattice spacing. For a size dispersive ensemble of particles this effect is certainly smeared out to a certain extent. Along with the intensity decrease a broadening of the peak width will be observed. For the time average of the curves, imposed by the limited time resolution of our experiment, the broadening will be the strongest effect. The overall signal will thus be a sum of the shift of the Bragg peak to lower angles due to thermal expansion and a nearly symmetric peak broadening due to the presence of particle vibrations. X-ray scattering is expected to be sensitive to all modes of vibrations in the nanoparticles, but the different modes apart from the breathing mode manifest themselves as specific changes in the scattering profile rather then a simple peak shift. Even when the oscillations can not be resolved in time the broadening of the peak is the next to leading effect and is still observable. For further investigation of the vibrational mode population in laser-excited particles the peak shape has to be analyzed with great precision. The superlattice peaks from samples with narrow size distribution can in principle resolve the order of vibrations in more details. We find in the present setup a considerable increase in the peak width, which even doubles in the first 100 ps after the laser excitation (see Fig. 5(b)). This broadening decays on the sub-nanosecond time scale. In transient absorption measurements usually much shorter damping times of vibrations are observed. The measured lifetimes (mainly of the (1,0) mode) are influenced not only by the energy dissipation within one particle but also by the cumulative effect of signal decrease due to a distribution of oscillation frequencies in a sample with a finite particle size dispersion [4,16,38,41,42] (inhomogeneous damping). In that sense the decay of peak broadening in X-ray scattering is a better measure for vibrational damping, as it does not depend on size effects. The cumulative effect of all modes is observed here and is not affected by the size dispersion of the particle ensemble. We conclude that the particles are not fully thermalized as long as peak broadening in the X-ray scattering is observed. The broadening is the signature of particle vibrations, which decay on the nanosecond time scale, resulting in uniformly heated particles. Such behaviour is in agreement with the observed deviation of heat transfer from the exponential decay on the same time scale (as plotted in Fig. 5).
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3.3. Picosecond dynamics The conventional scattering setup with a 2D X-ray detector is limited in time resolution to the 100 ps pulse length available from the electron storage ring. In order to overcome this limit we attempted to use an X-ray streak camera which can give picosecond time resolution [31]. The gain in time resolution is however compromised by the strong reduction in quantum efficiency for X-ray detection. The input aperture of the streak camera accepts less than 1% of the full Debye Scherrer ring from the particles and the photocathode has a quantum efficiency below 5%. In order to compensate for this penalty we used the full spectrum of the undulator with 500 eV bandwidth instead of 2.2 eV when using a silicon crystal monochromator. The reduction in angular resolution then only allows the detection of strong modulations of the Bragg intensity as the aperture was set to accept the ring maximum in specular reflection geometry. Fig. 7 depicts the change in Bragg intensity from 60 nm particles on silicon due to the laser impact at s ¼ 0 relative to the streak intensity without laser illumination. The accumulated exposure time was about 6 h at 900 Hz repetition rate. The time resolution due to the long accumulation time was determined to better than 4 ps. An initial decrease of intensity is observed, whose time scale of 5 ps is essentially determined by the time resolution. This time scale is in reasonable agreement with the electron–phonon coupling time observed in optical experiments [6,7,43]. Strain develops as soon as electrons scatter with the lattice phonons, irrespective of the amplitude of atomic movement. The occurrence of strain and the observed drop in scattering intensity can therefore closely follow the electron–phonon coupling time. After this intensity drop a slower recovery takes place which can not sufficiently modeled by a single exponential function. The recovery lifetime in the range
Fig. 7. Streak camera signal from laser-excited gold nanoparticles of 60 nm diameter. The plot shows the ratio between the time streak recorded with laser excitation and the reference streak without laser. The recovery from the ultrafast drop in intensity consists of decays on different time scales as indicated by the two exponentials that serve as guides to the eye.
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of 50 ps is clearly shorter than the larger kinetic lifetimes observed in our system, which we assign to vibrational damping and cooling lifetimes. The CCD data shows a similar effect of intensity drop and recovery within the 100 ps pulse length as can be seen in Fig. 5(b). This implies the occurrence of strong strain in the particle lattice. The fact that the signal recovers considerable from the initial drop within the first 30 ps suggests that the strain is not only explained by the onset of the known low order vibrations in addition to the thermal expansion. Instead a multitude of modes are excited, which decay into the most stable vibrations in tens of picoseconds. Yet we do not observe clear indications of periodic intensity changes due to the breathing mode vibration for longer times. This is partly due to the reduced sensitivity resulting from the large X-ray bandwidth, but is as well consistent with the assumption, that a multitude of modes is populated in this interval. These contribute with differently spaced oscillations, reducing the possible magnitude of intensity variation. The streak camera experiment demonstrates that the electron– phonon coupling and strong strain in the particles can be detected. Detailed studies of the vibrational properties meanwhile seem to be restricted to future experiments, that employ the projected picosecond pulse sources (energy recovery linacÕs or free electron lasers), as the X-ray peak brilliance severely determines the detail of information.
4. Conclusion and outlook We have investigated the ultrafast lattice kinetics and dynamics of gold nanoparticles supported on a solid substrate. Following the peak shape and position of the Debye Scherrer scattering in time allows to determine the thermal kinetics of laser-excited nanoparticles and several lifetimes can be observed. The slowest lifetime of the lattice relaxation is connected to the cooling of the heated particles via contact to the substrate. A dynamic broadening of the (1 1 1) reflection is observed, which is assigned to nonthermal motion present in the lattice. This broadening decays within hundreds of picosecond, at much longer lifetimes than observed so far. The reasons for these long lifetimes are the sensitivity of X-ray scattering to all modes of strain, the insensitivity to inhomogeneous signal damping and the weak vibrational coupling of the particles to the substrate. Indeed the supported particle can be regarded as almost free from external forces. The influence of the symmetry breaking due to the substrate still remains to be explored. X-ray scattering experiments seem to be indispensable for clarifying the questions connected to the nonthermal lattice oscillations in nanoscale material. There are no selection rules that apply for the detection of coherent vibrational modes in the X-ray regime (as compared to
plasmon laser spectroscopy or Raman scattering). As the modal effects are of subtle nature, a high spatial and time resolution is required in order to decompose the transient signals into all contributing modes. The availability of intense sub-picosecond X-ray pulses could allow for instance to resolve the vibrational modes as periodic changes in the Bragg peak profile. In the case of radial symmetric modes the identification is simple. The peaks will display side band intensity, whose connection to the order of the vibration is straightforward by the linear relation to the momentum transfer relative to the main peak. This concept is equivalent to the Raman principle only that X-ray scattering is based on atomic resolution. Symmetry breaking effects can be studied by carefully taking into account the transient signal changes resolved in spatial orientation relative to the surface. Picosecond dynamics have been addressed by an Xray streak camera experiment, which shows the occurrence of strong strain due to the coupling of the hot electron gas to the lattice.
Acknowledgements We wish to thank Michael Wulff and Lorenc Maciej for the help with the beamline and the ESRF for support. This project is funded by the Deutsche Forschungsgemeinschaft and Zentrum f€ ur den wissenschaftlichen Nachwuchs Konstanz.
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[26] A. Plech, T. Salditt, in: H.S. Nalwa, S. Tripathy (Eds.), Handbook of Polyelectrolytes and their Applications, vol. 1, American Scientific Publishers, 2002. [27] J. Schmitt, P. M€achtle, D. Eck, H. M€ ohwald, C.A. Helm, Langmuir 15 (1999) 3256, and supporting information. [28] F. Schotte, S. Techert, P.A. Anfinrud, V. Srajer, K. Moffat, M. Wulff, in: D. Mills (Ed.), Third-Generation Hard X-ray Synchrotron Radiation Sources, Wiley, New York, 2002. [29] M. Wulff, A. Plech, L. Eybert, R. Randler, F. Schotte, P. Anfinrud, Faraday Discuss. 122 (2003) 13. [30] A. Plech, R. Randler, A. Geis, M. Wulff, J. Synchrotron Radiat. 9 (2002) 287. [31] G.A. Naylor, K. Scheidt, J. Larsson, M. Wulff,, J.M. Filhol, Meas. Sci. Technol. 12 (2001) 1858. [32] A. Plech, unpublished. [33] A.P. Hammersley, S.O. Svensson, M. Hanfland, A. Fitch, D. H€ausermann, High Pressure Res. 14 (1996) 235. [34] M. Hu, G.V. Hartland, J. Phys. Chem. B 106 (2002) 7029. [35] A. Harata, J. Taura,, T. Ogawa, Jpn. J. Appl. Phys. 39 (2000) 2909. [36] A. Tamura, K. Higeta, T. Ichinokawa, J. Phys. C 16 (1983) 1585. [37] J.M. Ziman, Principles of the Theory of Solids, second ed., Cambridge University Press, London, 1972. [38] W. Qian, H. Yan, J.J. Wang,, Y.H. Zoua, L. Lin, J.L. Wu, Appl. Phys. Lett. 74 (1999) 29. [39] A. Tamura, K. Higeta, T. Ichinokawa, J. Phys. C 15 (1982) 4975. [40] For the dipolar mode special care has to be taken to average over all orientations of polar axis against the lattice direction. This has been done by summing curves from several orientations from 0 to 180 degrees. For the sake of simplicity we did not calculate torsional modes.. [41] G.V. Hartland, J. Chem. Phys. 116 (2002) 8048. [42] N. del Fatti, C. Voisin, F. Chevy, F. Vallee, C. Flytzanis, J. Chem. Phys. 110 (1999) 11484. [43] J.H. Hodak, A. Henglein, G.V. Hartland, J. Chem. Phys. 112 (2000) 5942.
Structural kinetics of laser-excited metal nanoparticles supported on a surface A. Plech a
a,*
, S. Gresillon b, G. von Plessen c, K. Scheidt d, G. Naylor
d
Fachbereich Physik der Universit€at Konstanz, Universit€atsstr. 10, D-78464 Konstanz, Germany b ESPCI, 10, rue Vauquelin, F-75005 Paris, France c I. Physikalisches Institut, RWTH Aachen, D-52056 Aachen, Germany d ESRF, BP 220, F-38043 Grenoble, France Received 29 July 2003; accepted 28 October 2003
Abstract Gold nanoparticles have been adsorbed as monolayers on silicon and glass substrates and the structure evolution following femtosecond laser excitation has been analyzed by means of time resolved X-ray scattering. The synchronization of the laser to the X-ray pulse structure emitted from a third generation synchrotron source allows to obtain a natural time resolution of 100 ps for the lattice kinetics. The prospects of using a picosecond X-ray streak camera are explored. The lattice kinetics are dominated by the fast heating of the particle lattice and nanosecond cooling times. However, the analysis of peak shapes reveals the presence of nonthermal motion within the lattice. Unexpectedly large relaxation times for the thermalization of vibrational modes are found and are attributed to the weak mechanical coupling to the substrate. Strong nonuniform strain develops within the domain of electron– phonon interaction time regime after the laser excitation as seen with the X-ray streak camera. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Nanoparticles; Picosecond time resolution; Structure; Femtosecond laser excitation; Thermal kinetics
1. Introduction Metal and semiconductor nanoparticle systems attract presently a strong attention due to their interesting optical properties [1–4]. In particular the ultrafast relaxations observable in femtosecond pump–probe experiments have been the subject of a large number of studies in the past decade. Elementary interactions such as electron–electron and electron–phonon coupling have been explored in detail [2,5–9]. The effort goes into understanding nonlinear and ultrafast optical response by size and shape modifications. Such approaches can comprise synthesis issues as well as laser induced shaping [3,10–12]. While the main focus has been on understanding and controlling the electronic response, increasing efforts are made to understand the structural reactions and control the phononics of the nanostruc-
*
Corresponding author. Tel.: +497531884682; fax: +497531883127. E-mail address: [email protected] (A. Plech).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.10.041
tures, which is of importance for the understanding of, e.g., structural phase transitions or applications as laser cleaning. Those structural transitions are of special interest, which could be used for permanent or transient nanostructuring for e.g. device applications. Particle cleaning from surfaces can probably be enhanced by exciting vibrational resonances of the particles; this could help to overcome damage thresholds [13]. For the investigation of such issues, it is unfortunate that the optical response from lattice and other structural reactions occurs only via the coupling to the electron system and thus only gives indirect information on structural processes. Therefore X-ray scattering in conjunction with ultrafast laser excitation is explored as a new tool to investigate structural dynamics. This paper deals with the structural kinetics of laserexcited, supported, metal nanoparticles. Experiments with nanoparticles (mostly of gold and silver, but also semiconductor quantum dots [14,15]) have established a detailed picture of the cascade of relaxations observable after femtosecond laser excitation [2,4,9,16–19]. The
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electron gas can gain energy via excitation of the plasmon band resonance or interband transitions and forms an nonequilibrium electron distribution. This decays into a thermalized Fermi distribution within /1 ps and couples to the lattice. The energy transfer to the lattice can not only raise the lattice temperature, but can impulsively induce coherent lattice vibrations. For these vibrations, in general a good agreement with the description of vibrational eigenmodes of a continuous medium is found. Coherent vibrations have been observed as oscillations of time-resolved optical pump–probe signals. Damping of oscillations stem from different mechanisms as internal damping within a particle or inhomogeneous broadening effects in a polydisperse ensemble. So far it is clear that the surrounding of the particles plays an important role in the structure relaxations. Glass embedded silver particles have displayed very fast damping times due to the strong mechanical contact to the environment, whereas gold solutions or nanoparticles on a surface have longer lifetimes either for vibrational damping or for lattice cooling. Studies of the vibrational and lattice cooling lifetimes are difficult, due to the selective nature of the spectroscopical response from the particles, which is mainly connected to volume changes. Raman scattering [20,21] as well as Brillouin scattering [22] in comparison are sensitive to thermally activated modes of radial motion within the particle as well as spheroidal modes involving radial motions of the atoms together with torsional displacements. Time resolution however is not routinely available with the latter techniques. X-ray scattering is a promising tool to resolve the atomic displacement in space as well as in time [23,24]. This field is still in its beginning, considering the development in ultrashort X-ray pulsed sources. In this paper we present the results of time-resolved optical pump X-ray probe experiments in which the structural dynamics of optically excited metal nanoparticles are investigated. Two different time-resolved experiments are presented. Using a conventional area detector, we follow the lattice kinetics of nanoparticles with the 100 ps time resolution. The lattice response to femtosecond laser pulses is explained by means of lattice heating and shape vibrations. In a second experiment the ultrafast response is resolved by an X-ray streak camera synchronized to the laser excitation source with low jitter. The picosecond resolution allows to explore the early steps of lattice reaction.
2. Materials and techniques Thin film self-assembly from solution has become a versatile tool to produce molecularly ordered soft matter and composite films. We employ a method for sample preparation first described by Decher and coworkers
[25], which uses charged dissolved polymers to adsorb on surfaces. As gold nanoparticles tend to be negatively charged in aqueous solution, glass (Marienfeld, Germany) and silicon wafers were coated by polyetylene-imine (Fluka) after hydrophilic etching in a concentrated KOH solution (water–isopropanol mixture in the case of silicon). The polymer coated wafers are then immersed in solutions containing a low concentration of gold nanoparticles (details found in [26]). The particles were purchased from BBInternational (GB) and displayed very narrow size distributions of about 10%. The wafers are washed and dried in a nitrogen stream after the adsorption step. It is known that the adsorption process on the charged surface is diffusion controlled, with diffusional times in the range of hours. This allows to control the coverage in a rather straightforward manner [27] by variation of the immersion time. Time resolution for the nanoparticle structure changes was achieved at the beamline ID09B at ESRF using a setup of a femtosecond laser synchronized to the X-ray pulse structure emitted by the synchrotron [28,29]. Briefly, the radio frequency signal from the electron storage ring at 88.05 MHz is used to phase lock a Ti:Sa femtosecond oscillator (diode pumped, Coherent) at the same repetition rate. The weak 800 nm pulses emitted by the oscillator are amplified in a regenerative Ti:Sa amplifier (Spectra physics) to achieve intense pulses of 1 mJ at a repetition rate of 896.6 Hz. This frequency is chosen such, that a vacuum mounted ultrasonic chopper wheel can run at this subharmonic frequency of the storage ring to isolate single X-ray pulses of 100 ps length. The laser light is frequency doubled in a BBO crystal and focussed on the surface of the wafer to give a focal spot of 0.25 0.8 mm. The incidence angle of the laser was about 18° with respect to the surface, whereas the X-rays hit the surface at the Bragg angle of 10.15°. The momentum transfer in the plane of reflection is therefore purely vertical, while for vectors out of the plane of reflection a component parallel to the surface is present. The corresponding scattering geometry is displayed in Fig. 1. The scattering from the particle lattice was recorded on a fiber optics coupled CCD camera (Mar research) with a spatial resolution of 65 lm. The resulting resolution of the setup was determined to be about 0.055° in angle. One main difficulty in the observation of the nanoparticles by X-ray techniques is the low scattering cross section for hard X-rays. Firstly the amount of particles whose absorption cross section matches the laser absorption is very low and secondly although single particles are of good crystallinity (grain size of the order of 30–50 nm at the present particle sizes of 60–150 nm) the ensemble itself is disordered, giving rise to Debye Scherrer rings. It is thus advantageous to use a moderate resolution CCD camera, which in turn collects X-ray
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3. Results and discussions 3.1. Spectroscopy and X-ray scattering
Fig. 1. Scattering geometry for the X-ray diffraction from the nanoparticles on the sample surface. The X-ray intensity on the CCD screen forms a Debye Scherrer ring, whose nonshadowed part is recorded. The laser beam strikes the surface at a higher angle, so that the footprints of the narrow X-ray beam and the wider laser beam on the surface are similar.
photons in a large solid angle region. The flux of the beamline was optimized by introducing an in-vacuum undulator having the first harmonics at 15 keV, which is a good balance of flux and heat load. The narrow shaped emission spectrum can even be used for highest flux applications at moderate resolution [30]. In the combination with the CCD camera a silicon (1 1 1) monochromator was used to define the X-ray wavelength. A toroidal mirror focuses the X-rays to 70 70 lm2 on the sample at a flux level of 105 photons per pulse and mA beam current. Still about 2000 X-ray pulses have to be accumulated on the detector for sufficient signal to noise ratio to record relative lattice parameter changes (at each pump–probe delay step) below 103 . The time resolution is achieved by electronically delaying the excitation laser pulse with respect to the X-ray pulse. The accuracy due to jitter and beam drifts is much better than the X-ray pulse length (10 versus 100 ps). In an exploratory experiment we used an X-ray streak camera, which can resolve X-ray photons in time within the pulse length. The X-ray generated photo-electrons in the cathode are accelerated and deflected by a fast switching electric field converting time information into spatial information. The projected time pattern is imaged onto a microchannel-plate enhanced CCD chip. The technique of jitter-free recording is described in detail elsewhere [31]. As the efficiency of the photocathode and aperture further reduce the detected scattering intensity dramatically, the only way to observe a signal from the photo-excited nanoparticles was to use the full emission of single line undulator with 2.5% bandwidth and compromise with the resolution. The results are discussed in Section 3.3.
The adsorption process of particles onto the surface during sample preparation is checked by ex situ extinction measurements and surface sensitive X-ray scattering methods. Varying the adsorption time in the gold solution from a few minutes to 10 h changed the coverage from 1% to 10% mass fraction within the film. The absorbance spectra for different coverage where measured with a fiber optics spectrometer with a diode array (Ocean Optics). Fig. 2 displays a set of spectra for particles of 60 nm in diameter in the visible range. The prominent plasmon resonance maximum is found at 530 nm and the absorbance increases steadily with immersion time, indicating a larger amount of adsorbed gold colloids. We find a second red shifted maximum evolving with coverage, which is explained by a delocalized plasmon resonance extending over several adjacent particles. With increasing coverage the average distance in between proximate particles decreases, which in turn enhances the near field coupling of the particles. The coupling produces a new resonance at lower energy [1]. It should be noted that if the particles tended to aggregate on the surface even at low coverages one would expect the second maximum to be present from the beginning of adsorption. The red-shifted maximum becomes important only for large coverage fractions, where the nearest neighbor distances decrease and the probability for finding close packed particles increases. The particle distribution can also be revealed by surface sensitive small angle scattering (not shown here), from where the particle–particle pair correlation function can be derived [32]. The coverage with the particles is derived from X-ray reflectivity [26]. For the following pump–probe experiments samples of intermediate coverage below 5% were used, where the clustering is negligible.
Fig. 2. Absorbance of the monolayered gold particles with 60 nm diameter on a float glass surface as measured in 90° transmission. The different curves with increasing absorbance represent increased adsorption times and consequently a higher coverage with particles.
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We concentrate mainly on the evaluation of the (1 1 1) Debye Scherrer ring of the gold fcc lattice. For best angular resolution only the (1 1 1) and (2 0 0) reflections were collected on the CCD screen. The (2 0 0) reflection can be analyzed as well, but the noise is higher due to the smaller structure factor. So far no differences with respect to the discussion of the (1 1 1) reflections were observed. The rings were usually integrated azimutally [33] and the resulting radial profile was normalized by using the glass and diffuse scattering background. Fig. 3 is a visualization of the change of the Debye Scherrer ring due to the interaction of the sample with the laser pulse. The ring pattern is transformed into rectangular coordinates with azimutal and radial angles as x and y axes. In both cases the scattering peaks shift to lower angles and immediately after the laser excitation the ring is considerably broadened (in this case at time delays of 100 ps). There is one distinct difference in between the scattering from particles supported on silicon and on glass. In the case of silicon the intensity is strongly increased in the specular direction (scattering vector perpendicular to the surface plane). We conclude that particles adsorbed on silicon tend to orient the crystallographic facets such, that the (1 1 1) scattering peaks perpendicular to the surface. We exclude a direct interaction of substrate lattice and particle lattice because of the intermediate polymer buffer layer. Instead the gold particles are probably less strongly bound to the silicon (oxide) surface and are allowed to rotate so that (1 1 1) facets orient parallel to the surface. This is in agreement with the observed lower laser power necessary for inducing laser cleaning of the surface. The details of this effect will be described elsewhere. We have analyzed different scattering vectors with respect to the surface and found the same behaviour of lattice expansion irrespective of the orientation of the lattice planes to the substrate surface.
As reported previously, the laser pulses cause a rapid expansion of the nanoparticle lattice mediated by electron excitation and subsequent electron–phonon scattering. The expansion can in first place be regarded to be of thermal origin. A calculation of the absorbed energy of particles embedded in a glass matrix versus the amplitude of expansion gives the approximate coefficient of expansion as known from bulk material. The estimation of absorbed energy for the supported particles is less precise due to the more complicated electric field distribution close to the geometrical interface, but a rough estimate is still in agreement with the assumption that the largest fraction of absorbed energy is transferred into lattice excitation. The maximum lattice temperature that is reached within the first 100 ps can be calculated to be 710 K, if the bulk coefficient of expansion is assumed. 3.2. Thermal kinetics A characteristic decay of the lattice expansion is observed for increasing delay s between laser and X-ray pulse. The energy stored in the particle lattice is transferred within several nanoseconds to the environment. The decay of expansion (see Fig. 4) can be fitted quite well by an exponential decay, implying that the temperature of the particle is reduced accordingly h s i aðsÞ t ¼ DTmax a exp þ1 2 ð1Þ erf a0 t0 ds with the lattice parameter a as function of delay time s and maximum heating of the nanoparticle DTmax . The thermal expansion coefficient is denoted by a, and the time resolution of the experiment by ds, which is taken to be 35 ps (HWHM). In Fig. 4 the relative lattice expansion is depicted as function of s for particles of 100 nm diameter deposited on glass substrate. The solid line represents a fit according to Eq. (1).
Fig. 3. CCD false colour image of the (1 1 1) ring scattered from the nanoparticle layer for gold particles on silicon (top) as well as on glass (bottom). The rings are converted into a rectangular representation of radial (vertical) and azimutal (horizontal) angles. A comparison is made between nonexcited state ()80 ps) and immediately after laser excitation (120 and 100 ps, respectively), where the Bragg angle has shifted.
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187
Fig. 4. Relative increase of the lattice parameter derived from the (1 1 1) reflection of 100 nm gold particles on a glass surface. A laser fluence of 38 mJ/cm2 was applied to the surface. The time axis represents the delay time with respect to the exciting laser pulse. The solid line represents a fit to the data with an exponential decay function convoluted with a resolution limited error function for the initial signal rise.
For embedded particles (silver particles in glass matrix) the relaxation times are found to be in the range of hundreds of picoseconds. They depend linearly on the particle size, which is explained by interface limited heat transport to the matrix [24]. Hu and Hartland [34] observe somewhat different cooling rates in gold nanoparticles in water. They use stretched exponentials for the fits and interpret their data with a domination of bulk heat transfer in the medium as limiting step [35]. Clearly the boundary between the particles and the matrix is completely different in our study, where particles supported on a surface are investigated. Here the cooling rates are decreased by almost one order of magnitude due to the reduced contact area. There is considerable spread for repeated experiments in the dependence of relaxation time on the particle size due to the presence of several control parameters such as the influence of facetting, coverage or the polymer cushion. Additionally a water meniscus may form on the hydrophilic polyethylene-imine covered surface, depending on the humidity, which was not controlled. A closer analysis of the decay of expansion reveals a slight deviation from the exponential law within the first nanosecond after excitation as can be seen in the fit residue in Fig. 5. Initially the observed expansion is less than would be expected from the single exponential decay, and gradually reaches the fit function. At the same time a strong increase of the radial width of the reflection is observed which decays on the same time scale. In the case of an infinite lattice the Scherrer width is fixed by the resolution function and crystallite size. Purely thermal effects do not result in any broadening but only a reduction in scattering intensity, quantified by the so called Debye–Waller factor (DWF). In contrast to the Scherrer width however, the DWF does not display any anomaly in time as seen in Fig. 5 [36]. The
Fig. 5. (a) Residue of the fit in Fig. 4 together with a simulation of the contribution due to decaying vibrational excitations (see text). (b) Plot of the Scherrer width (crosses, left hand sided scale) and integrated intensity (dots, right-hand sided scale) of the (1 1 1) reflection. The solid lines mark the decay of the width change and the computed thermal Debye–Waller factor, respectively.
peak intensity is shown together with a DWF calculation assuming bulk thermodynamic values [37]. In the case of very small nanoparticles one can consider a relaxation of the outermost lattice layers to modify the peak shape and the intensity. In the present case the particles consist of 250 units cell of the fcc lattice in diameter, so that this effect should be negligible. On the other hand lattice distortions within the particle can cause broadening, which is transient in nature in this case. This leads us to conclude that a part of the absorbed energy is not transformed into thermal motion immediately after the laser impact, but is present in nonthermal excitations. Ultrafast laser absorption studies as well as Raman or Brillouin light scattering studies have given evidence for particle vibrations in various classes of nanosystems. In spherical metal particles (mostly of silver or gold) oscillations of the transient signal are observed that are consistent with the excitation of the lowest vibrational modes in elastic bodies. Voisin et al. [16] have pointed out that the laser signal from the plasmon band is most sensitive to the lowest spheroidal vibration mode without torsional movements, which can be regarded as homogeneous volume increase of the sphere. Indeed most investigations in transient absorption spectroscopy on excited nanoparticles do not observe higher order modes, with exception of a few experiments [38].
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The spheroidal modes for a free particle can be calculated with the formula [39] xn;l ¼ Sn;l
cl ; R
ð2Þ
with the longitudinal sound velocity cl and the eigenvalue Sn;l with radial and angular quantum numbers n and l. For l ¼ 0 the eigenvalue is calculated by solving 2 the equation S1;0 cot S1;0 ¼ 1 S1;0 =ð4 ðct =cl ÞÞ for the material dependent ratio of cl and the transverse sound velocity ct . Inserting the values for gold results in an oscillation period of 33 ps for 100 nm particles or 50 ps for 150 nm particles. In contrast, Raman scattering is mostly sensitive to spheroidal modes with l ¼ 2, which have been observed in silver nanoparticles. It is therefore probable that a range of vibrational modes are excited with femtosecond laser pulses, of which those of higher order are not resolved in optical pump–probe experiments. The relationship between the mechanism of phonon excitation and the phonon population in metal nanoparticles is still not clarified [18,38]. For example one can imagine that the stability of different modes (and therefore their lifetimes) critically depends on geometrical properties, such as particles shape and local environment. In particular the surface could act as a source of symmetry breaking for the supported particles, giving rise to a splitting of degenerate vibration modes. The (1,2) mode can become more stable than the (1,0) mode due to the smaller translational motion of the center of mass of the particle. The period of this mode is typically longer by a factor of 2 than the purely spherical (1,0) mode [20]. These considerations have a strong influence on the observability and lifetimes of modes. The experimental data as represented by the lattice parameter change in Fig. 4, however indicates peak position changes for adjacent time points, but no clear harmonic oscillation is found. X-ray scattering is, in contrast to spectroscopical methods, sensitive to strain in the particle lattice, regardless whether volume changes are present or not. Higher order modes manifest themselves in a change of the scattering profile rather than a shift of the peak position. The effect of active particle vibrations on the scattering profiles is then less straightforward. We have simulated the scattering from a two dimensional cubic centered crystal with the atoms occupying the coordinates at (0; 0) and (0.5; 0.5) within the unit cell along the ðffÞ direction by simply adding up the phases from all scattering centers within a 145 unit cells circle. The resulting scattering profiles are displayed in Fig. 6. This procedure is supposed to give a realistic impression of the scattering from a particle of 60 nm in diameter. The lattice strain ~ uðx; yÞ has been added upon the individual positions of the atoms by adding the following, simplified model of displacements:
Fig. 6. Simulated X-ray scattering profiles along the ðffÞ direction of a two dimensional cubic centered lattice of 145 units cells for different lattice distortions. From top to bottom: symmetrical breathing mode with free boundary condition, third order spherically symmetric vibration and first dipolar spheroidal mode, see text for details.
~ uðx; yÞ ¼
sin
px py n ; sin n 2R 2R
for the spherically symmetric modes; px py ~ uðx; yÞ ¼ sin n ; sin n 2R 2R
ð3Þ
for the ð1; 2Þ spheroidal mode; where n marks the radial quantum number (n ¼ 1 for the ground order ‘‘breathing’’ mode of the spherical vibration and n ¼ 2 for the first order mode) and R the radius of the particle in unit cells. The second formula describes a quadrupolar vibration with nonvanishing angular momentum of the radial motion [40] (often nicknamed as ‘‘football’’ mode) as observed in Raman scattering. Note that the curves in Fig. 6 do not display time averages, but instead a snapshot at the point of maximum strain. This strain is uniformly expansive for the breathing mode, which therefore shifts the scattering peak to smaller q vectors. For the next order spherical mode volumes of expansion and compression coexist within the particle, while the net volume effect is expansive. Therefore a slight shift of the peak can be observed which is overruled by the large distribution of lattice parameters present at the same instant. A similar effect appears for the spheroidal mode, where the change in volume and thus the mean change in atomic distance
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is negligible against the spread in interatomic distances. A strong broadening is the consequence. It is clear that only the breathing mode gives rise to a clear shift of the Bragg positions. The strongest effect in the higher mode (center panel of Fig. 6) consists in a decrease of intensity at the center of the Bragg position and at the same time excess scattering as sidebands of the peak, which can be regarded as ‘‘superlattice’’ peaks due to the new spatial frequency in the lattice spacing. For a size dispersive ensemble of particles this effect is certainly smeared out to a certain extent. Along with the intensity decrease a broadening of the peak width will be observed. For the time average of the curves, imposed by the limited time resolution of our experiment, the broadening will be the strongest effect. The overall signal will thus be a sum of the shift of the Bragg peak to lower angles due to thermal expansion and a nearly symmetric peak broadening due to the presence of particle vibrations. X-ray scattering is expected to be sensitive to all modes of vibrations in the nanoparticles, but the different modes apart from the breathing mode manifest themselves as specific changes in the scattering profile rather then a simple peak shift. Even when the oscillations can not be resolved in time the broadening of the peak is the next to leading effect and is still observable. For further investigation of the vibrational mode population in laser-excited particles the peak shape has to be analyzed with great precision. The superlattice peaks from samples with narrow size distribution can in principle resolve the order of vibrations in more details. We find in the present setup a considerable increase in the peak width, which even doubles in the first 100 ps after the laser excitation (see Fig. 5(b)). This broadening decays on the sub-nanosecond time scale. In transient absorption measurements usually much shorter damping times of vibrations are observed. The measured lifetimes (mainly of the (1,0) mode) are influenced not only by the energy dissipation within one particle but also by the cumulative effect of signal decrease due to a distribution of oscillation frequencies in a sample with a finite particle size dispersion [4,16,38,41,42] (inhomogeneous damping). In that sense the decay of peak broadening in X-ray scattering is a better measure for vibrational damping, as it does not depend on size effects. The cumulative effect of all modes is observed here and is not affected by the size dispersion of the particle ensemble. We conclude that the particles are not fully thermalized as long as peak broadening in the X-ray scattering is observed. The broadening is the signature of particle vibrations, which decay on the nanosecond time scale, resulting in uniformly heated particles. Such behaviour is in agreement with the observed deviation of heat transfer from the exponential decay on the same time scale (as plotted in Fig. 5).
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3.3. Picosecond dynamics The conventional scattering setup with a 2D X-ray detector is limited in time resolution to the 100 ps pulse length available from the electron storage ring. In order to overcome this limit we attempted to use an X-ray streak camera which can give picosecond time resolution [31]. The gain in time resolution is however compromised by the strong reduction in quantum efficiency for X-ray detection. The input aperture of the streak camera accepts less than 1% of the full Debye Scherrer ring from the particles and the photocathode has a quantum efficiency below 5%. In order to compensate for this penalty we used the full spectrum of the undulator with 500 eV bandwidth instead of 2.2 eV when using a silicon crystal monochromator. The reduction in angular resolution then only allows the detection of strong modulations of the Bragg intensity as the aperture was set to accept the ring maximum in specular reflection geometry. Fig. 7 depicts the change in Bragg intensity from 60 nm particles on silicon due to the laser impact at s ¼ 0 relative to the streak intensity without laser illumination. The accumulated exposure time was about 6 h at 900 Hz repetition rate. The time resolution due to the long accumulation time was determined to better than 4 ps. An initial decrease of intensity is observed, whose time scale of 5 ps is essentially determined by the time resolution. This time scale is in reasonable agreement with the electron–phonon coupling time observed in optical experiments [6,7,43]. Strain develops as soon as electrons scatter with the lattice phonons, irrespective of the amplitude of atomic movement. The occurrence of strain and the observed drop in scattering intensity can therefore closely follow the electron–phonon coupling time. After this intensity drop a slower recovery takes place which can not sufficiently modeled by a single exponential function. The recovery lifetime in the range
Fig. 7. Streak camera signal from laser-excited gold nanoparticles of 60 nm diameter. The plot shows the ratio between the time streak recorded with laser excitation and the reference streak without laser. The recovery from the ultrafast drop in intensity consists of decays on different time scales as indicated by the two exponentials that serve as guides to the eye.
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of 50 ps is clearly shorter than the larger kinetic lifetimes observed in our system, which we assign to vibrational damping and cooling lifetimes. The CCD data shows a similar effect of intensity drop and recovery within the 100 ps pulse length as can be seen in Fig. 5(b). This implies the occurrence of strong strain in the particle lattice. The fact that the signal recovers considerable from the initial drop within the first 30 ps suggests that the strain is not only explained by the onset of the known low order vibrations in addition to the thermal expansion. Instead a multitude of modes are excited, which decay into the most stable vibrations in tens of picoseconds. Yet we do not observe clear indications of periodic intensity changes due to the breathing mode vibration for longer times. This is partly due to the reduced sensitivity resulting from the large X-ray bandwidth, but is as well consistent with the assumption, that a multitude of modes is populated in this interval. These contribute with differently spaced oscillations, reducing the possible magnitude of intensity variation. The streak camera experiment demonstrates that the electron– phonon coupling and strong strain in the particles can be detected. Detailed studies of the vibrational properties meanwhile seem to be restricted to future experiments, that employ the projected picosecond pulse sources (energy recovery linacÕs or free electron lasers), as the X-ray peak brilliance severely determines the detail of information.
4. Conclusion and outlook We have investigated the ultrafast lattice kinetics and dynamics of gold nanoparticles supported on a solid substrate. Following the peak shape and position of the Debye Scherrer scattering in time allows to determine the thermal kinetics of laser-excited nanoparticles and several lifetimes can be observed. The slowest lifetime of the lattice relaxation is connected to the cooling of the heated particles via contact to the substrate. A dynamic broadening of the (1 1 1) reflection is observed, which is assigned to nonthermal motion present in the lattice. This broadening decays within hundreds of picosecond, at much longer lifetimes than observed so far. The reasons for these long lifetimes are the sensitivity of X-ray scattering to all modes of strain, the insensitivity to inhomogeneous signal damping and the weak vibrational coupling of the particles to the substrate. Indeed the supported particle can be regarded as almost free from external forces. The influence of the symmetry breaking due to the substrate still remains to be explored. X-ray scattering experiments seem to be indispensable for clarifying the questions connected to the nonthermal lattice oscillations in nanoscale material. There are no selection rules that apply for the detection of coherent vibrational modes in the X-ray regime (as compared to
plasmon laser spectroscopy or Raman scattering). As the modal effects are of subtle nature, a high spatial and time resolution is required in order to decompose the transient signals into all contributing modes. The availability of intense sub-picosecond X-ray pulses could allow for instance to resolve the vibrational modes as periodic changes in the Bragg peak profile. In the case of radial symmetric modes the identification is simple. The peaks will display side band intensity, whose connection to the order of the vibration is straightforward by the linear relation to the momentum transfer relative to the main peak. This concept is equivalent to the Raman principle only that X-ray scattering is based on atomic resolution. Symmetry breaking effects can be studied by carefully taking into account the transient signal changes resolved in spatial orientation relative to the surface. Picosecond dynamics have been addressed by an Xray streak camera experiment, which shows the occurrence of strong strain due to the coupling of the hot electron gas to the lattice.
Acknowledgements We wish to thank Michael Wulff and Lorenc Maciej for the help with the beamline and the ESRF for support. This project is funded by the Deutsche Forschungsgemeinschaft and Zentrum f€ ur den wissenschaftlichen Nachwuchs Konstanz.
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