LETTER pubs.acs.org/NanoLett
Damping of the Acoustic Vibrations of Individual Gold Nanoparticles Renaud Marty,† Arnaud Arbouet,*,† Christian Girard,† Adnen Mlayah,† Vincent Paillard,† Vivian Kaixin Lin,‡ Siew Lang Teo,‡ and Sudhiranjan Tripathy‡ † ‡
CEMES, UPR 8011, CNRS-Universite de Toulouse, 29, rue Jeanne Marvig, BP 94347, F-31055 Toulouse, France Institute for Materials Research and Engineering, A*STAR, 3 Research Link, 117602 Singapore ABSTRACT: In this letter, the ultrafast vibrational dynamics of individual gold nanorings has been investigated by femtosecond transient absorption spectroscopy. Two acoustic vibration modes have been detected and identified. The influence of the mechanical coupling at the nanoparticle/substrate interface on the acoustic vibrations of the nano-objects is discussed. Moreover, by changing the environment of the nanoring, we provide a clear evidence of the impact of the surrounding medium on the damping of the acoustic vibrations. Such results are reported here for the first time on individual nanoparticles. This work points out a new sensing method based on the sensitivity of the acoustic vibration damping to the surrounding medium. KEYWORDS: individual nano-object, acoustic vibration modes, time-resolved spectroscopy, vibration damping, gold nanorings
G
old nanoparticles sustain collective electronic excitations named surface plasmons that efficiently absorb light.1,2 Their ability to mediate a fast conversion of optical to thermal energy on a picosecond time scale makes them ideal heat nanosources for many applications at the crossroads of physics, chemistry, and biology, for example, laser nanowriting, nanoablation, or hyperthermia. Energy transfer from an optically excited metal nanoparticle to its environment involves several steps starting from electronic thermalization to heat dissipation away from the metallic nano-object.3 The impact of size reduction on these fundamental processes has been addressed in many time-resolved optical spectroscopy experiments on large collections of nano-objects and a clear picture of the ultrafast electronic and vibrational dynamics inside metal nanoparticles is now established.37 For instance, it has been shown that the lowfrequency acoustic vibration modes display a discrete sizedependent frequency spectrum.8,9 Complementary to frequency-resolved optical techniques such as Raman scattering, transient absorption spectroscopy provides access to both acoustic periods and damping times.1012 However, experiments performed on large ensembles suffer from averaging on the size and shape distributions. Indeed, information on the coupling of a nano-object to its surrounding medium can be extracted from the vibration damping time but the latter is only accessible with highly monodisperse samples and modeling10,12 or experiments addressing individual nano-objects.1317 A deep understanding of the optical, vibrational, and thermal properties of metal nanoobjects therefore demands investigation of the ultrafast dynamics of individual nano-objects in order to get rid of inhomogeneous broadening due to size and shape fluctuations in nano-object ensembles. Recently, ultrasensitive optical techniques have been developed to overcome this challenge and important results have been obtained.13,16,18,19 For example, it has been shown that the continuous elastic model and bulk values of the elastic constants r 2011 American Chemical Society
can describe the vibrational dynamics of metal nanoparticles down to the nanometer size range9,15,20 These breakthroughs open up exciting perpectives including the use of metal nanoparticles as mass sensors or nanosized probes of the elastic properties of the local environment. In the present letter, we investigate the acoustic vibrations of individual gold nanorings by femtosecond transient absorption spectroscopy. Two different vibration modes are detected and identified. The impact of the particle/susbtrate interface on both the period and damping times is evidenced. Local environment variations are shown to induce large fluctuations of the measured damping times. Furthermore, the investigation of identical nanostructures in two different environments enables us to examine the strong impact of the surrounding medium on the damping of the acoustic vibrations and paves the way to quantitative determination of the effective elastic coupling between the metal nanoparticles and the substrate. Materials and Method. In the following, we investigate gold nanorings fabricated by electron beam lithography (EBL) and thermal evaporation of gold on quartz substrates. A square lattice array of 100 μm 100 μm has been processed. In order to achieve the optical addressing of individual nano-objects, the separation between nano-objects is fixed at 2 μm. To prepare samples with appropriate geometries, we have first designed the pattern masks using e-beam resist. The patterned templates are then loaded into the evaporation chamber for deposition of a 3 nm chromium adhesion layer followed by a 22 nm thick gold layer. The purity of the metal targets used is Cr (99.99%) and Au (99.99%). The lift-off process is performed using dimethyl Received: May 17, 2011 Revised: June 17, 2011 Published: June 21, 2011 3301
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Figure 1. Dimensions (a) and AFM image (b) of an individual gold nanoring. (c) Red solid line: Microtransmission spectrum acquired from around 60 nanorings. Blue dashed line: Extinction spectrum of a single gold nanoring computed with parameters shown in (a). The experimental spectrum has been shifted for clarity.
sulfoxide. Figure 1b shows a typical atomic force microscopy (AFM) image of an individual nanoring. The optical properties of nanoring ensembles have been first studied by microtransmission measurements. The spectra were collected using a CRAIC microspectrophotometer in which the transmitted light was sent to a spectrometer through a 32 microscope objective. The incident spot size was about 250 μm2 and the number of probed nanorings was around 63. As shown in Figure 1c, the extinction spectrum displays a large optical resonance around 980 nm. This feature is known to originate from the coupling of dipolar surface plasmon modes at the inner and outer surfaces of the nanorings.21 In addition, numerical simulations performed in the framework of the Green dyadic method are in very good agreement with the experimental data.22 These calculations have taken into account both the ring morphology extracted from AFM data and the optical coupling with the substrate. The width of the experimental spectrum is slightly broader than the calculated one confirming the weak size and shape dispersion of our samples. Femtosecond Transient Absorption Spectroscopy. We performed time-resolved pumpprobe spectroscopy to address the low-frequency acoustic vibrations of individual nanorings. Our high-sensitivity femtosecond pumpprobe setup is based on a commercial high repetition rate Ti:Sapphire femtosecond laser source (150 fs, 6801080 nm, 80 MHz). The probe beam has been tuned to the blue wing of the surface plasmon resonance of the nano-objects at 875 nm to maximize the sensitivity to the spectral shifts of the SPR induced by the coherently excited acoustic vibrations.15 To excite the metal nanorings by interband absorption, pump pulses at 437 nm with crossed polarization were generated by frequency doubling the infrared pulse train in a BBO crystal. Pump and probe were made colinear and tightly focused by a NA = 0.8 air objective in a homemade microscope. The probe pulses being nearly resonant, care has been taken to keep their intensity at a low level to prevent any laser induced damage of the nanorings. The pump power at the back port of the
Figure 2. (a) Transient absorption map at zero pumpprobe delay. (b) Relative transmission change ΔT/T from an individual gold nanoring. Inset: enlarged short time scale signal showing oscillations with two different periods.
microscope objective was 300 μW. The pump pulse train was modulated at 100 kHz using an acousto-optic modulator and the probe pulses were detected by an avalanche silicon photodiode. This detection scheme with sensitivity levels in the 107 range allows monitoring the acoustic vibrations of individual nanoobjects. Transient absorption maps were obtained by scanning the sample mounted on a XY piezostage. Figure 2a shows a color-coded map of the relative transmission change obtained at zero pumpprobe delay to maximize the signal.23 The periodicity and amplitude of the detected signals show unambiguously that individual nanorings are detected. The dispersion of the transmission change detected on different nanorings reflects the size and shape distribution of our sample.16 After carefully positioning a selected individual nano-object under the laser focal spot, we perform femtosecond pump probe spectroscopy. Data were acquired from 20 different individual gold nanorings. Figure 2b shows the typical time evolution of the relative transmission change measured on one of the individual gold nanorings. The large transient signal apparent on a short time scale is due to the ultrafast heating of the electron gas followed by rapid (few ps) thermalization with the lattice vibrations of the gold nanorings.37 On a longer time scale, clear periodic oscillations are visible together with a slowly varying background that can be ascribed to the thermalisation of the nano-object with its environment.24 It is well-known from ensemble measurements that in timeresolved experiments, the ultrafast heating of both the electron gas and the atomic lattice of a metal nanoparticle can trigger acoustic vibrations that modulate the electronic properties of the nano-objects.7 The acoustic vibrations induce periodic shifts of 3302
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lattice-mediated displacive mechanism due to ultrafast lattice heating.7 Ensemble measurements have shown that in time-resolved experiments, the vibrational response of a metal nanoparticle is dominated by low-frequency, highly symmetric vibrations, the so-called breathing mode.7 To identify the observed low-frequency vibrations (100 ps period), we assumed that our nanoring is homogeneous and isotropic. As a first approximation, we neglect the influence of the substrate and consider the vibration eigenmodes of a free-standing ring of diameter D. From NavierStokes equation,26,27 the period of the lowest order axisymmetric vibration mode is given by rffiffiffi F T ¼ πD ð1Þ E
Figure 3. (a) Displacement of the lowest order axisymmetric vibration mode for a rectangular shaped ring with free bottom surface. (b) Same but for a nanoring with half-elliptical cross section and fixed bottom surface. (c) Investigation of shape effects: H = 22 nm is the total height of the ring as measured by AFM and h/H varies from h = 0 for a halfelliptical cross section to h = 1 for a rectangular cross section. (d) Distribution of the measured periods of the low-frequency mode of individual nanorings. Computed period of the lowest order axisymmetric acoustic vibration mode for different ring cross sections characterized by the shape parameter h/H and either free (black solid line) or fixed (red dashed line) bottom surface.
the surface plasmon resonance that ultimately show off as a relative transmission change (Figure 2b). Two different acoustic vibration modes are detected. As shown in the inset of Figure 2b, oscillations with a period close to 13 ps are visible on a short time scale. These fast oscillations, not clearly visible for all investigated nanorings, are consistent with nanoring thickness oscillations and have already been observed on gold nanoprisms.14,25 In the following, we will focus on the long time scale vibrational response. On this time scale, oscillations with a period of the order of 100 ps are observed (Figure 2b). Their period have been systematically extracted by Fourier analysis and timedomain fitting of the data, both procedure yielding very similar results. As shown in Figure 3d, the periods measured on different individual gold nanorings have a mean value of 99.8 ps with a relative standard deviation of 8.6%. Given the proportionality of the periods and size of the nanoparticles, this relatively small deviation is consistent with the narrow size dispersion of the nanorings previously determined by AFM and scanning electron microscopy (SEM). In every investigated nano-object, the detected oscillations show a cosine-like behavior. This is consistent with the phase measured in similar conditions in large nanoparticles and suggests that the dominant excitation mechanism is the
in which E and F are Young’s modulus and metal density, respectively. Using the bulk values of gold elastic constants and the mean ring diameter determined by AFM, eq 1 predicts T = 140 ps which is larger than the measured period (around 100 ps) (Figure 2). To go further and address the origin of this discrepancy, we performed finite element simulations and considered possible shape deviations from the ideal nanoring as well as the role of the underlying chromium adhesion layer. As shown in Figure 3, rings with different geometries have been considered. The ring maximal height H and wall thickness have been kept constant and equal to the values extracted from AFM measurements. Different shapes, characterized by the height h of the straight portion of the ring wall have been considered. The extreme cases of a perfectly rectangular or a half-elliptical cross section correspond respectively to h/H = 1 and h/H = 0 (Figure 3c). To address the influence of the underlying chromium adhesion layer, two different boundary conditions have been used: the bottom surface of the nanoring is either free or fixed (Figure 3a,b). We assume that the mechanical properties of the nanorings fabricated by EBL are well described by the elastic constants of polycrystalline gold. Figure 3d shows the periods calculated for the lowest order axisymmetric vibration mode for different geometries and boundary conditions. The influence of the ring cross section on the period of the breathing mode is minor for a free bottom surface as the mean diameter is nearly unchanged. As can be seen in Figure 3d, free boundary conditions overestimate the periods as already observed in previous studies.14 On the contrary, with a fixed bottom surface, the calculated periods are significantly shorter due to the reaction of the substrate and vary on a broader range in comparison with free boundary conditions. Additional calculations addressing the possible influence of the ring height or variations of the elastic constants confirm these conclusions. As a consequence, we can conclude that the chromium adhesion layer underneath the gold nanostructures yields intermediate elastic boundary conditions that strongly impacts the acoustic vibrations of the nanorings. Damping of the Acoustic Vibrations: Influence of the Environment. Time-resolved experiments provide unique insight into the energy relaxation processes and associated rates. In particular, fitting of the data in the time-domain allows to extract the characteristic damping time of the acoustic vibrations thus yielding valuable information on the coupling of the nano-object with its environment. Previous ensemble investigations have addressed the influence of the environment on the damping of 3303
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Table 1. Longitudinal Sound Velocity, Density, Acoustic Impedance Z = Fνl and Normalized Eigenfrequency Im(x0) of Chromium, Quartz, Air, and Glycerol at 300 K
Figure 4. (a) Damping time distribution measured in two different media: air and glycerol. (b) Extracted oscillating contribution to the relative transmission change of gold nanorings in air (solid line) or glycerol (dashed line).
the acoustic vibrations but quantitative analysis of the experimental data requires either extremely monodisperse samples and/ or sophisticated modeling.10,12 The possibility to probe individual nano-objects allows to get rid of ensemble averaging and inhomogeneous broadening: the measured damping time directly reflects energy dissipation from the nano-object to the environment. Figure 4a displays the measured damping times of air exposed gold nanorings. The average value is 311 ps and the relative standard deviation is 27%. This value is more than three times larger than the size dispersion of the nanorings. As will be detailed below in the case of a nanosphere, a simple continuous elastic model predicts that both the period and damping time of the breathing mode are proportional to the size of the nanoobject. In our case however, the dispersion of the measured damping times is three times higher than the dispersion of the periods and no correlations exists between the two data sets. As already pointed out, these strong fluctuations are probably due to variations of the mechanical interaction between the metallic nanoparticles and the susbtrate.10,1217 Our results obtained on individual nanoparticles are consistent with the results of experiments performed on glass-embedded nanoparticle ensembles. By increasing the environment pressure, these experiments showed that the modification of the interface quality has a much stronger impact on the damping times than on the periods.10 In the following, we identify and investigate the different contributions to the damping and the impact of the environment. The acoustic mode that dominates the vibrational response of our gold nanorings is the fundamental axisymmetric vibration mode and is associated to a periodic expansion-contraction
material
νl m 3 s1
F kg 3 m3
Z ( 106 N 3 s 3 m3)
chromium
6630
7150
47.4
0.58
quartz
5500
2200
12.1
0.12
glycerol
1904
1261
2.4
0.04
air
346
1.18
408 106
∼0
gold
3240
19300
62.5
Im (ξ0)
movement in the radial direction very similar to the fundamental radial mode of a spherical nanoparticle. Therefore, a simple analogy with the so-called breathing mode of nanospheres can be reasonably invoked to interpret our experiments. The radial acoustic vibrations of a homogeneous elastic nanosphere embedded in an infinite homogeneous elastic environment have been studied extensively.28,29 The period and damping time of the breathing mode are respectively related to the real and imaginary part of the complex eigenfrequency ω0 = ξ0vsl /R in which vsl is the longitudinal sound velocity of gold and R the radius of the spherical NP. Following ref 29, the normalized eigenfrequency ξ0 is calculated using the acoustic properties of the metal nanoparticle and of the environment. The elastic properties of chromium, quartz, air, and glycerol as well as the corresponding normalized eigenfrequency Im(χ0) are given in Table 1. The period of the radial vibration mode is weakly influenced by the environment. In contrast, Im(χ0) and thus the damping rate γ0 = 1/τ0 are strongly affected by the mechanical properties of the surrounding medium. Indeed, the ability of the elastic waves to escape from the metal nanoparticle to the matrix is directly related to the acoustic impedance mismatch at the nanoparticle/matrix interface.10 It is important to note that for liquid environments, this model is questionable as viscosity is not taken into account.12 However, the influence of viscosity on damping is expected to be stronger for vibration modes involving transverse surface displacement at the metal/liquid interface and for small (sub-10 nm) nanoparticles.12,30 Because of the large acoustic impedance mismatch at a gold/ air interface, acoustic vibrations in the 10 GHz (T = 100 ps) frequency range do not propagate in air. Therefore, for an air exposed nanoring, the main dissipation channel for elastic energy involves the chromium adhesion layer and quartz substrate. The large dispersion of the measured damping rates (Figure 4a) can therefore be ascribed to fluctuations of the interface quality between either the gold nanoring and the adhesion layer or the adhesion layer and the substrate. In order to investigate further the damping of the acoustic vibrations, we have changed the mechanical properties of the surrounding medium. By opening additional relaxation channels, we demonstrate on a single gold nano-object the possibility of controlling the energy dissipation from a metal nano-object to its environment. To do so, the gold nanorings have been immersed in glycerol. The latter was chosen because of its high viscosity. The probe wavelength has been tuned to 975 nm to anticipate the redshift of the surface plasmon resonance due to the new refractive index of the environment. Figure 4b shows the transmission modulations measured with and without glycerol. A clear increase of the damping of the acoustic vibrations is observed with glycerol. This is confirmed by systematic measurements shown in Figure 4a. A decrease of the average damping 3304
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time from 311 to 128 ps together with a drop of the relative standard deviation from 27 to 13% are observed (Figure 4a). To interpret these observations, a simple argument can be used. The total damping rate γt of acoustic vibrations can be written as the weighted sum of the contributions related to the energy dissipation through the bottom surface and the remaining interface (lateral and top surface) in contact with air or glycerol γt ¼ γAu=subs
Sb Senv + γAu=env Sb + Senv Sb + Senv
ð2Þ
in which γAu/subs and γAu/env are effective damping rates per unit area associated with elastic energy flow through respectively the bottom surface Sb and the remaining surface Senv in contact with air or glycerol. From our nanoring geometry, we have Sb ≈ St/3 where St = Sb + Senv is the total surface of the nano-object. When the gold nanorings are exposed to air, the large acoustic impedance mismatch at the gold/air interface yields γAu/air ≈ 0 and therefore the measured damping rate γair t is directly connected to the characteristic damping rate of the metal/substrate surface: γAu/subs ≈ 3 γair t . When the gold nanorings are immersed in glycerol, both contributions must be taken into account glycerol
γt
1 2 ¼ γAu=subs + γAu=glycerol 3 3
ð3Þ
This allows to compare damping rates through the Au/ substrate and Au/glycerol interface from the measured γair t and γglycerol t γAu=subs 2γair ¼ glycerol t 1:4 γAu=glycerol γt γair t
ð4Þ
On the other hand, according to Table 1, the model described above predicts γAu/quartz/γAu/glycerol = 3 and even γAu/Cr/γAu/glycerol = 14.5. These values are much larger than our experimental value. This indicates that the mechanical coupling between the nanorings and the substrate is significantly weaker with respect to a gold/ glycerol interface in our case. Moreover, the significant decrease of the relative standard deviation (Figure 4a) when the gold nanorings are immersed into glycerol can be explained by the lower impact of the interface quality due to the opening of additional relaxation channels characterized by comparable dissipation rates. In other words, since the coupling of the elastic vibrations through the bottom surface of the gold nanorings is no more the dominant relaxation channel, the impact of the fluctuations of the quality of the interface is smaller. It is important to notice that the previous model involves compression waves with displacement perpendicular to the interface between the gold nanosphere and its environment. The picture is more complex in our supported nanorings; the vibrations induce a displacement parallel to the nanoring/substrate (Figure 3a, b). Further interpretation of the damping of the acoustic vibrations of these nano-objects must therefore take into account the detailed displacement profile of the involved acoustic vibration modes. Conclusion. In this letter, the acoustic vibrations of individual gold nanorings have been investigated using time-resolved optical spectroscopy. The role of the particle/substrate interface on both the period and the damping of the acoustic vibrations has been addressed. By embedding the metallic nanoparticles into an environment with different elastic properties, a drastic change of the damping of the acoustic vibrations has been evidenced. This allows a comparison of the strength of the mechanical coupling between the metal nanoparticle and the substrate to a reference
elastic medium. Our results show that elastic energy dissipation to the substrate is less efficient than predicted by an elastic model involving compression waves perpendicular to the interface. In the near future, investigations of the influence of the nano-object material, size, and shape as well as the impact of the solvent elastic properties will further refine our understanding of elastic energy dissipation in nanostructures. These experiments pave the way toward passive control of energy dissipation from metallic nanoparticles. Promising applications in all-optical mass-sensing and local investigations of the elastic properties at the nanoscale are expected to surge from similar experiments on individual nano-objects.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors thank funding support from CPER “Gaston Dupouy” 2007-2013. The authors are grateful for funding support from the Agency for Science, Technology, and Research (A*STAR) Singapore and the French Embassy Merlion Project Program. This work was also supported by the computing facility center CALMIP of Paul Sabatier University. ’ REFERENCES (1) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: New York, 1995. (2) Maier, S. Plasmonics: Fundamentals and Applications; Springer: New York, 2007. (3) Link, S.; El-Sayed, M. A. J. Phys. Chem. B 1999, 103, 8410–8426. (4) Hodak, J.; Martini, I.; Hartland, G. J. Phys. Chem. B 1998, 102, 6958–6967. (5) Voisin, C.; Christofilos, D.; Del Fatti, N.; Vallee, F.; Prevel, B.; Cottancin, E.; Lerme, J.; Pellarin, M.; Broyer, M. Phys. Rev. Lett. 2000, 85, 2200–2203. (6) Arbouet, A.; Voisin, C.; Christofilos, D.; Langot, P.; Fatti, N. D.; Vallee, F.; Lerme, J.; Celep, G.; Cottancin, E.; Gaudry, M.; Pellarin, M.; Broyer, M.; Maillard, M.; Pileni, M. P.; Treguer, M. Phys. Rev. Lett. 2003, 90, 177401. (7) Hartland, G. V. Annu. Rev. Phys. Chem. 2006, 57, 403–430. (8) Hodak, J.; Martini, I.; Hartland, G. J. Chem. Phys. 1998, 108, 9210–9213. (9) Juve, V.; Crut, A.; Maioli, P.; Pellarin, M.; Broyer, M.; Del Fatti, N.; Vallee, F. Nano Lett. 2010, 10, 1853–1858. (10) Voisin, C.; Christofilos, D.; Del Fatti, N.; Vallee, F. Phys. B: Condens. Matter 2002, 316-317, 89–94. (11) Burgin, J.; Langot, P.; Arbouet, A.; Margueritat, J.; Gonzalo, J.; Afonso, C. N.; Vallee, F.; Mlayah, A.; Rossell, M. D.; Van Tendeloo, G. Nano Lett. 2008, 8, 1296–1302. (12) Pelton, M.; Sader, J. E.; Burgin, J.; Liu, M.; Guyot-Sionnest, P.; Gosztola, D. Nat. Nanotechnol. 2009, 4, 492–495. (13) Van Dijk, M. A.; Lippitz, M.; Orrit, M. Phys. Rev. Lett. 2005, 95, 267406. (14) Burgin, J.; Langot, P.; Del Fatti, N.; Vallee, F.; Huang, W.; El-Sayed, M. A. J. Phys. Chem. C 2008, 112, 11231–11235. (15) Zijlstra, P.; Tchebotareva, A. L.; Chon, J. W. M.; Gu, M.; Orrit, M. Nano Lett. 2008, 8, 3493–3497. (16) Staleva, H.; Hartland, G. V. J. Phys. Chem. C 2008, 112, 7535–7539. (17) Tchebotareva, A.; Ruijgrok, P.; Zijlstra, P.; Orrit, M. Laser Photon. Rev 2010, 4, 581–597. 3305
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