Polycrystallinity of Lithographically Fabricated Plasmonic

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Polycrystallinity of Lithographically Fabricated Plasmonic Nanostructures Dominates Their Acoustic Vibrational Damping Chongyue Yi, Man-Nung Su, Pratiksha Dongare, Debadi Chakraborty, Yi-Yu Cai, David M Marolf, Rachael N Kress, Behnaz Ostovar, Lawrence J. Tauzin, Fangfang Wen, WeiShun Chang, Matthew Jones, John Elie Sader, Naomi J. Halas, and Stephan Link Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00559 • Publication Date (Web): 01 May 2018 Downloaded from http://pubs.acs.org on May 1, 2018

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Polycrystallinity of Lithographically Fabricated Plasmonic Nanostructures Dominates Their Acoustic Vibrational Damping Chongyue Yi1, ‡, Man-Nung Su1, ‡, Pratiksha D. Dongare2,3, Debadi Chakraborty4, Yi-Yu Cai1, David M. Marolf1, Rachael N. Kress1, Behnaz Ostovar1, Lawrence J. Tauzin1, Fangfang Wen1, Wei-Shun Chang1, Matthew R. Jones1*, John E. Sader4*, Naomi J. Halas1,3,5,6*, and Stephan Link1,3,6* 1. Department of Chemistry, Rice University, Houston, Texas, 77005, USA. 2. Applied Physics Graduate Program, Rice University, Houston, TX 77005, USA. 3. Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA. 4. ARC Centre of Excellence in Exciton Science, School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia 5. Department of Physics and Astronomy, Rice University, Houston, Texas, 77005, USA. 6. Laboratory for Nanophotonics, Rice University, Houston, Texas, 77005, USA.

Corresponding authors: [email protected], [email protected], [email protected], [email protected]

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ABSTRACT The study of acoustic vibrations in nanoparticles provides unique and unparalleled insight into their mechanical properties. Electron-beam lithography of nanostructures allows precise manipulation of their acoustic vibration frequencies through control of nanoscale morphology. However, the dissipation of acoustic vibrations in this important class of nanostructures has not yet been examined. Here we report using single-particle ultrafast transient extinction spectroscopy the intrinsic damping dynamics in lithographically fabricated plasmonic nanostructures. We find that in stark contrast to chemically synthesized, monocrystalline nanoparticles, acoustic energy dissipation in lithographically fabricated nanostructures is solely dominated by intrinsic damping. A quality factor of 𝑄 = 11.3 ± 2.5 is observed for all 147 nanostructures, regardless of size, geometry, frequency, surface adhesion, and mode. This result indicates that the complex Young’s modulus of this material is independent of frequency with its imaginary component being approximately 11 times smaller than its real part. Substratemediated acoustic vibration damping is strongly suppressed, despite strong binding between the glass substrate and Au nanostructures. We anticipate that these results, characterizing the optomechanical properties of lithographically fabricated metal nanostructures, will help inform their design for applications such as photoacoustic imaging agents, high-frequency resonators, and ultrafast optical switches.

KEYWORDS: surface plasmon, optomechanics, ultrafast spectroscopy, single-particle spectroscopy, gold nanoparticles, electron-beam lithography


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Nano-objects composed of metals, semiconductors, and other materials have recently begun to receive tremendous attention because of their unique shape-, size-, composition-, and surrounding environment-dependent coherent phonon modes, which occur at GHz and even THz frequencies. These nano-objects, behaving as nanomechanical resonators, have been applied in optomechanics1-4, ultrasensitive mass detection5, 6, high-precision sensors7-9, and mechanical computational devices.10,

11

However, as a result of their large surface-to-volume ratio, their

performance in these applications is often limited by short coherent phonon mode lifetimes and strong phonon interactions between the resonators and their local environment.12-15 To sustain high frequency oscillations and prevent mechanical energy dissipation, rigorous efforts have been devoted to extending coherent phonon survival times and vibrational dephasing times through careful insulation, using lithography, suspension over trenches, and solution phase chemistry.16-21 Despite these efforts, a clear picture of vibrational dynamics and mechanical energy dissipation channels in nanomechanical resonators prepared by different methods is not well established. Plasmonic metal nanostructures with large resonant absorption cross-sections provide an ideal platform to investigate vibrational dynamics because their coherent phonon modes are efficiently excited under ultrashort laser pulse irradiation. Strong light-matter interaction upon photon excitation results in a collective electron oscillation in the metal nanostructure that is known as the surface plasmon resonance (SPR).22 After SPR decay and electron-electron scattering, thermalized hot electrons impulsively transfer heat to the metal lattice. Subsequently, this impulsive excitation of the lattice gives rise to coherent phonons because the intrinsic vibrational period of the nanostructure (tens to hundreds of picoseconds) is much slower than the lattice displacement excitation (typically few picoseconds).23-28 As a result, coherent phonon


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oscillations and acoustic normal modes are launched within the nanostructure.29 For small The expansion of volume also leads to a reduction in electron density and, in the simplest model, a modification of the Drude term in the dielectric function, resulting in a shift of the SPR optical response. One of the benefits offered by plasmonic nanostructures is that sensitive detection of their vibrational dynamics can be realized in the time domain by monitoring the SPR frequency shifts using femtosecond time-resolved transient extinction spectroscopy.30-37 However, ultrafast measurements performed in ensemble suffer from inhomogeneous dephasing because of the significant size distribution frequently found in nanoparticle samples. Therefore, transient extinction measurements at the single-particle level have become the preferred experimental diagnostic to precisely determine the frequency, phase, and especially the damping time of acoustic vibrations in metal nanostructures.38-45 Recently, the origins of acoustic damping in plasmonic metal nanostructures prepared through chemical methods have been the subject of numerous experimental and theoretical investigations.21, 34, 46-52 Studies on the vibrational quality factor (𝑄 factor), which is determined by the vibrational frequency and lifetime, revealed the presence of multiple acoustic energy damping mechanisms. A reduction of 𝑄 factor was consistently observed when the nanostructures were immersed in a viscous medium.24, 34, 46, 50 The elastic energy can transfer to the medium at the metal-medium interface. Thus, the acoustic impedance mismatch between metal and environment is one of the most critical factors for determining the 𝑄 factor and hence mechanical energy dissipation. Furthermore, Yu et al. found that passivating ligand-induced hydrodynamical lubrication forces between Au nanorods and a glass substrate can accelerate the damping of acoustic vibrations.46 Also, the intrinsic contribution of vibrational damping was found to be less significant than other damping factors in both Au nanowires and bipyramids


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prepared by chemical synthesis.27, 34 Additional studies comparing polycrystalline nanoparticles to monocrystalline nanoparticles revealed that the latter exhibited a slower damping rate because they possessed fewer internal crystal defects.45,

53-55

Though progress has been made in

understanding the acoustic damping in chemically prepared metal nanostructures, the mechanical properties of nanostructures prepared by top-down lithography are less understood.39-41 Precise manipulation of optomechanical properties has been achieved in a few nanostructures prepared by electron-beam lithography.39, 41 Utilizing this fabrication approach, more complicated structures, such as Swiss-crosses,40, 43 have been designed to realize modeselective

acousto-plasmonic

coupling.

However,

unlike

bottom-up

prepared

metal

nanostructures, the damping of coherent vibrations in lithographically prepared samples can also be attributed to a number of additional factors, including crystal defects and strong binding with the supporting substrate.39-41,

47, 56

Because of these additional inherent complexities,

determination of the contributions to the 𝑄 factor by each possible decay channel in samples prepared by electron-beam lithography remains challenging, although top-down fabrication opens the possibility for designing arbitrarily shaped nanostructures with tailored optomechanical properties. Characterizing the mechanical properties of lithographically fabricated nanostructures is therefore crucial to expanding our fundamental knowledge of photonics and phononics of metal nanomaterials. In this letter, we quantitatively characterize the acoustic vibration damping mechanisms in lithographically prepared Au nanostructures with a variety of sizes and shapes using singleparticle transient extinction spectroscopy. Our measurements reveal that the 𝑄 factor is independent of nanostructure size, geometry, frequency, surface adhesion, and mode when comparing Au nanodisks and nanorods with varying dimensions. We find that mechanical


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contact between the metal and the glass substrate has no effect on the 𝑄 factor regardless of the binding induced vibrational frequency shift, indicating that top-down acoustic energy transfer to the substrate is suppressed in this type of Au nanostructures. Instead, intrinsic crystal defects dominate the acoustic energy dissipation process, giving rise to faster damping than that exhibited by chemically prepared and photothermally annealed nanoparticles.

Figure 1. (a) Schematic illustration of the pump-probe measurement on a single Au nanostructure. Au nanodisks with a thickness of 35 nm and a 2 nm Ti adhesion layer were fabricated using electron-beam lithography on a glass substrate. Both the pump (blue) and probe (red) were collinearly focused on a single nanostructure by passing through the same objective.


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The excitation wavelength was 405 nm and the probe wavelength was 810 nm. (b) Timedependent transient transmission of a single 178 nm diameter Au nanodisk (solid red). The pump and probe powers were 150 and 50 µW, respectively. The data was fitted to a bi-exponential decay which was convolved with a Gaussian instrument response function (solid black). Then a damped sine function was used to fit the oscillation amplitude (dashed black). Lower panel: The bi-exponential fit was subtracted from the collected data and the residuals were plotted in order to isolate the vibrational amplitude. The exponential decay term extracted from the damped sine wave function is also included as solid black lines. Inset: Fourier transform analysis of the timedependent vibrational amplitude.

Femtosecond time-resolved pump-probe measurements were performed at the singleparticle level to determine the acoustic vibration properties of plasmonic Au nanostructures as shown in Figure 1a (see Supporting Information (SI) and Figure S1 for experimental details). To launch acoustic vibrations, a femtosecond 405 nm laser pulse was used, creating a large temperature difference between the electron gas and metal lattice. Following excitation, hot electrons rapidly transfer energy to the nanoparticle lattice within a few picoseconds through electron-phonon coupling. Impulsive excitation of the lattice results in a coherent phonon oscillation inside of the Au nanostructure, producing a periodic change in particle dimension. Eventually, the energy dissipates from the metal into the environment through phonon-phonon coupling.23,

24

All of these energy relaxation processes can be tracked in the transient

transmission of a delayed probe pulse following the excitation pulse. Figure 1b displays a typical time-resolved transient transmission recorded at a probe wavelength of 810 nm measured on a single 178 nm Au nanodisk (red line in Figure 1b). Experimental transient transmissions were


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first fit to a bi-exponential decay (first 2 terms in equation (S1), black solid line in upper panel of Figure 1b). Then, to isolate the acoustic vibrations, the residuals (lower panel of Figure 1b) were obtained by subtracting this fit (the detailed data analysis is provided in the SI). Fourier transform analysis of the transient residuals (inset of Figure 1b) reveals that the coherent phonon oscillation frequency for a 178 nm Au nanodisk is 10.1 ± 0.5 GHz. The damping time can be extracted from the residuals by describing the oscillatory behavior as a damped sine wave (last term in equation (S1)). For 178 nm nanodisks, we determined a damping time of 341 ±63 ps. All the error bars reported for transient extinction data correspond to the standard deviation from several measurements performed on at least 7 different nanostructures with the same size and geometry. To understand the factors contributing to mechanical energy dissipation in lithographically prepared Au nanostructures we varied the nanodisk diameter, changed the environment, studied nanorods as a function of aspect ratio, and finally compared the results to colloidal nanoparticles. Au nanodisks with different diameters were prepared and first characterized using darkfield scattering spectroscopy. The Au nanodisks were fabricated with a 2 nm Ti adhesion layer on top of a glass substrate by electron-beam lithography (see SI). As determined from scanning electron microscopy (SEM), the diameters of the Au nanodisks of interest ranged from 120 nm up to 240 nm (Figure 2a, Table S1). Prior to pump-probe measurements, scattering spectra of these Au nanodisks were obtained using dark-field scattering spectroscopy (Figure 2b) to determine acceptable probe wavelengths for the transient transmission experiments. The Lorentzian-shaped SPR peak shifted to lower energies and broadened as expected with increasing Au nanodisk diameter and hence increasing aspect ratio. This broadening of the SPR peak is further visualized by plotting the scattering spectra against an energy scale (Figure S2).


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When the diameter increased from 120 nm to 240 nm, the dipolar plasmon resonance peak redshifts from 650 nm to 950 nm, and broadens from 0.26 eV to 0.42 eV. Small shoulders on the high-energy side attributed to the quadrupole mode were also observed in the scattering spectra of the 205 nm and 240 nm Au nanodisks. The quadrupole mode was excited in the dark-field spectra due to phase retardation. To compare the transient transmission response from every structure directly, we set the probe laser wavelength to 810 nm, where small changes in transmission can be detected for all Au nanodisk dimensions although absolute amplitudes varied depending on exact spectral overlap with the probe beam. As the fundamental wavelength of the Ti:Sapphire laser, 810 nm is also the most stable probe available to accurately determine the acoustic properties and minimize experimental errors. This probe wavelength overlapped only with the dipolar and not the quadrupolar resonances of the nanodisks. Probing at different sides of the plasmon band also results in a flip of the oscillation phase24 making it difficult to compare all of the oscillation parameters across nanodisk sizes. In ensemble measurements, the vibrational frequency and damping time were found to be dependent on the probe wavelength due to size and shape polydispersity.57, 58 However, single-particle measurements eliminate the probe-wavelength dependence and can be used to quantitatively evaluate the mechanical properties for all nanodisks under the same experimental conditions.24


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Figure 2. Size dependent optical and mechanical properties of Au nanodisks. (a) SEM images of sample nanodisks with different diameters: 120 nm (magenta), 160 nm (blue), 178 nm (green), 205 nm (orange), and 240 nm (red). The thickness of the Au nanodisks was 35 nm with an additional 2 nm Ti adhesion layer. The size of each SEM image is 640 × 550 nm. (b) Experimental single-particle scattering spectra of these Au nanodisks. (c) Acoustic frequencies (red) and damping times (blue) as a function of inverse diameter. Error bars specify one standard deviation from measurements on individual disks of that size. Note that error bars for the damping times are larger than those for the frequencies. The solid green line represents simulation results of vibrational frequencies based on a free surface model. The solid orange line


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represents simulation results of vibrational frequencies based on a fixed surface model. (d) Scatter plot of the size-dependent measured frequencies versus damping times for the Au nanodisk breathing mode. Colors coincide with the sizes specified in (a). (e) 𝑄 factors of Au nanodisks as a function of diameter. The black line represents the average 𝑄 factor calculated from all 65 Au nanodisks with 2 nm Ti adhesion layer measured.

Vibrational frequencies are inversely proportional to the Au nanodisk diameter 𝐷. The vibrational frequencies and damping times extracted from the data using equation (S1) are plotted as a function of inverse diameter (1/ 𝐷) in Figure 2c with typical transient transmissions for Au nanodisks of each size shown in Figure S3. The direct relationship between frequency (red dots, Figure 2c) and the inverse diameter confirms that the two-dimensional, in-plane breathing mode, which is parallel to the substrate, was excited and detected in our measurements. The Finite Element Method (FEM) has been shown to provide a reliable depiction of the vibrational properties. Considering an Au nanodisk as freely oscillating without binding to the glass substrate (green line, Figure 2c) consistently underestimates the vibrational frequencies compared to experimental values. Another extreme case is the fixed surface model (orange line, Figure 2c), where the bottom surface of the nanostructure is rigidly fixed to the Ti layer and glass substrate. This rigidity restraint results in an overestimation of the vibrational frequencies. The offset between experimental data and simulated results for the free surface model is a clear signature of mechanical coupling between the Au and the glass mediated by the Ti adhesion layer.41 The damping time, which represents the lifetime of the coherent phonons in the nanoparticle resonator, is also sensitive to the nanostructure size. The average damping time as a


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function of 1/ 𝐷 is plotted in Figure 2c (blue dots). However, opposite to the oscillation frequency, the damping time is proportional to 𝐷. Damping of the resonator occurs faster when the coherent phonon oscillation operates at a higher frequency. Figure 2d shows a scatter plot of vibrational frequencies versus damping times for all 65 Au nanodisks measured, with each color representing a different Au nanodisk diameter, quantifying the variation in damping times from individual nanodisks. To eliminate the size dependence of the vibrational frequency (𝜈) and damping time (𝜏), the 𝑄 factor, defined by 𝑄 = 𝜋𝜈𝜏, is used to describe the rate of energy loss relative to the stored energy of coherent phonons. We obtain an average 𝑄 factor of 11.0 ± 2.2. for all 65 nanodisks (Figure 2e). Furthermore, by changing the thickness of the 178 nm diameter nanodisks from 15 nm to 35 nm and hence varying the ratio of surface contact area to volume, we still obtained similar 𝑄 factors (Figure S4). Previous reports on phononic materials demonstrate that large mechanical contact areas enable efficient vibrational energy dissipation from coherent phonons to the environment.18,

59, 60

This conclusion is also supported by FEM simulations for glass-

supported metal nanodisks (Figure S5): the 𝑄 factor decreases as the contact area increases due to stronger coupling with the substrate. However, for nanodisks prepared by electron-beam lithography, increasing the contact area does not change the observed energy propagation (Figure 2e). Despite the fact that the Ti adhesion layer facilitates strong binding between the metal and the glass, the lack of a correlation between nanodisk diameter and 𝑄 factor suggests that vibrational energy flow to the substrate through mechanical contact plays a negligible role in the damping of the acoustic vibrations in these particular nanostructures. Furthermore, it should be noted that the simulated 𝑄 factors (Figure S5), solely due to the radiation of acoustic sound waves into the substrate, are much larger than the experimentally measured values.


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We also examined the acoustic properties of 178 nm nanodisks on top of different substrates as well as different adhesion layer thicknesses (Figure S6). Strong mechanical energy propagation into the environment can also be attributed to a large acoustic impendence mismatch. To eliminate this possibility, a thin film (50 nm thickness) of Al2O3 on glass was utilized as an alternative substrate61 because it is an ideal material to receive acoustic energy from gold based on the small acoustic impendence mismatch. Measuring 178 nm Au nanodisks on an Al2O3 layer reveals that the vibrational damping time is not affected and suggests independence of the substrate material. In addition to varying the substrate material, we can also tune the binding strength between the metal and the glass support by changing the thickness of the Ti layer from 0 nm to 4 nm.41 Comparing 0 and 2 nm adhesion layers, the damping time of the nanodisks again does not change (Figure S6a). Indeed, the 𝑄 factor of the nanodisk vibrational mode does not shift as a function of Ti layer thickness when varying over an even larger range (Figure S6c). Damping of acoustic modes in electron-beam lithographically prepared nanostructures is therefore independent of an adhesion layer mediated substrate binding. Because the damping time does not change with either contact area, the substrate, or binding strength, we conclude that the supporting substrate does not provide an efficient energy relaxation channel for the decay of coherent phonons in lithographically prepared nanostructures. We also observed that although energy flow into the substrate is not efficient, the acoustic vibrations can still be strongly damped when the sample is immersed in a liquid environment, such as water (Figure S7, Table S2). In our experiments we determined the total 𝑄 factor, which includes both intrinsic and environmental damping mechanisms. The relationship between the total 𝑄 factor (𝑄total ) and its


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contributing factors including intrinsic (𝑄intrinsic ) and environmental (𝑄environment ) terms can be written as: 1/𝑄total = 1/𝑄intrinsic + 1/𝑄environment

(1)

For a nanodisk on top of a glass substrate, coherent phonons can interact with either air or the glass. Thus, 𝑄environment can be expressed as: 1/𝑄environment = 1/𝑄air + 1/𝑄substrate

(2)

As our experiments showed, energy flow to the substrate does not appear to be significant and the 1/𝑄substrate term can be neglected. Finite element analysis reveals that damping due to the surrounding air is negligible relative to that observed (data not shown). We must therefore conclude that the intrinsic damping channel constitutes the majority of energy loss in these nanostructures. By averaging all of the 𝑄 factors obtained from 104 individual Au nanodisks, of varying size and adhesion layer thickness, 𝑄intrinsic was determined to be 10.9 ±2.4. To further explore the origins of acoustic energy dissipation, we also analyzed the effect of nanostructure geometry on acoustic mode damping in lithographically fabricated samples. A series of Au nanorods with different aspect ratios was prepared and characterized by SEM, darkfield spectroscopy, and transient extinction spectroscopy (Figures S8 and S9, Table S3). Consistent with the observed trends for nanodisks, the vibrational damping time decreases while the oscillation frequency increases as the nanorod length was decreased from 160 nm to 80 nm (Figures S10a and S10b). Converting the damping times and frequencies to average 𝑄 factors (Figure S10c) clearly demonstrates that the 𝑄 factor of the extensional mode exhibits no dependence on the nanorod length. We obtain a mean value for all 43 nanorods studied of 𝑄intrinsic = 12.6 ± 2.2, which is very close to that of the Au nanodisks presented in Figure 2e. This conclusion is also consistent with results obtained on Au nanorods with varying widths


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between 35 nm and 75 nm at a constant length of 100 nm (Figures S11 and S12). Again, we found a size and shape independent 𝑄 factor when analyzing both the extensional and breathing modes. The shape-independence of the 𝑄 factor not only serves as further evidence of the absence of substrate-mediated damping, but also helps us to elucidate the origin of the intrinsic damping mechanism. Internal crystal defects, ubiquitous in polycrystalline materials, appear to dominate elastic energy dissipation. In addition to crystal defects inside the nanostructure, defects on the surface may also play a significant role in intrinsic damping, especially because of the large surface-to-volume ratios of nanostructures. To assess this latter possibility, we note that the relative contribution of surface defects scales with the surface-to-volume ratio of the nanostructure, neglecting here the bottom surface area that makes contact with the substrate. For the 35 nm wide and 80 nm long Au nanorods the surface-to-volume ratio of 0.111 nm-1, while for the largest nanodisks this number drops by two and half times to 0.0452 nm-1. Despite this difference in surface-to-volume ratios, similar 𝑄 factors were measured for the breathing mode of the 240 nm Au nanodisks and the extensional mode of the 35 × 80 nm Au nanorods, suggesting that intrinsic damping arises mostly from internal crystal defects rather than a surface mediated effect. Based on the measurements of all lithographically fabricated Au nanostructures, our pump-probe measurements yield the conclusion that energy dissipation arises mainly from intrinsic damping channels – and given the polycrystalline material structure, internal crystal defects are primarily responsible for this dissipation. To further substantiate this claim and to provide additional insight into intrinsic damping processes, monocrystalline, chemically prepared Au nanostructures were compared to the polycrystalline lithographically generated samples. Monocrystalline Au nanorods with a width of


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18 ± 2 nm and a length of 95 ± 10 nm were synthesized using a seed-mediated growth method as reported previously62 and characterized using transmission electron microscopy (Figure S13). By probing

the

acoustic

vibrations

in

these

Au

nanorods,

with

and

without

the

cetyltrimethylammonium bromide (CTAB) surfactant, we confirm that the organic ligand layer can provide an additional damping channel (Figure S14). This effect was identified as a lubrication effect, which is attributed to the interaction between the capping molecules and the substrate.46 Therefore, to minimize ligand-mediated damping and to focus only on intrinsic damping caused by internal crystal defects, we removed CTAB and residual solvent molecules from the sample through ultraviolet ozone treatment and baking at ~ 260 oC. After removing the ligands from the surface, we extracted a 14.5 ± 1.8 GHz frequency and a damping time of 501 ± 62 ps. The average 𝑄 factor we obtained from the measurement of more than 15 chemically prepared Au nanorods is 22.0 ± 2.4, in agreement with a 𝑄 factor of 24 reported previously for similar conditions.46 Any small differences might be due to discrepancies in residual ligands and water on the metal nanoparticle surface. This 𝑄 factor for chemically prepared Au nanorods is almost twice as large as the length independent 𝑄 factor of lithographically prepared Au nanorods (Figure 3a). Note that the oscillation period did not change after ozone treatment and baking (Figure S14) confirming that the nanorod shape did not change. It is also necessary to distinguish the substrate contact condition between chemically synthesized and lithographically prepared nanostructures. Instead of an organic layer as in chemically synthesized nanorods, a Ti adhesion layer mediates the interaction between the metal and glass substrate in lithographically prepared nanorods. As discussed above, this adhesion layer assisted damping channel has been demonstrated to be to be insignificant (Figure S6).


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Figure 3. Acoustic mode damping in chemically and lithographically prepared Au nanostructures. (a) Length dependent 𝑄 factors of polycrystalline lithographically fabricated Au nanorods (green) and chemically synthesized Au nanorods (blue, average dimensions of 18 × 95 nm). The average 𝑄 factor of all lithographically fabricated nanorods is shown as the black line. Their length varied from 80 nm, 100 nm, 120 nm, 140 nm, to 160 nm with a constant width and thickness of 35 nm. (b) Acoustic vibrations of a single Au nanorod prepared by chemical


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synthesis (blue, 18 × 95 nm) compared to one fabricated by electron-beam lithography (green, 35 × 100 nm). These two particles were chosen because they have similar vibration frequencies. (c) Acoustic vibrations of a single Au nanodisk prepared by a chemical synthesis (blue, 7.5 × 92 nm) compared to one fabricated by electron-beam lithography (green, 35 × 160 nm, 2 nm Ti layer). These two particles were chosen because they have similar damping times. The dashed black line represents the fit based on a damped sine wave. The extracted exponential decay terms are plotted as black solid lines. Data are normalized and offset for better comparison.

Figure 3b shows representative vibrational dynamics of colloidal, monocrystalline versus polycrystalline Au nanorods. For this comparison, lithographically prepared nanorods with a length of 100 nm were chosen to be most similar to the size of the colloidal sample. As a result, visualizing the effect of crystallinity on the intrinsic damping for both samples is straightforward because the vibrational frequencies of the extensional modes are similar. The decay of the oscillation amplitudes in the polycrystalline nanorods is significantly faster than that of the chemically prepared nanorods. This difference is also evident from the resulting 𝑄 factors, 13.2 compared to 22.0. The faster damping in the lithographically prepared polycrystalline nanorods is consistent with the property that propagation of confined coherent phonons inside nanostructures can be significantly affected by lattice defects where mechanical energy is converted to heat.63 It is well known that, compared to single crystal growth driven by the chemical potential in the solution phase, evaporation of metal on top of a substrate in a vacuum results in high lattice disorder and surface roughness. In contrast, most chemically prepared Au nanorods exhibit few crystal impurities and surface defects.54


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We also performed the same comparison between mono- and polycrystalline Au nanodisks (Figure 3c). Circular Au disks with a well-defined shape were chemically synthesized according to a previous report.64 The diameter of the circular disk was 92 nm with a thickness of 7.5 nm (Figure S15). Because we were unable to match exactly the dimensions to the colloidal sample, we selected the 160 nm diameter nanodisks made by electron-beam lithography as in both cases we then observed a similar acoustic damping time of ~ 300 ps. The larger oscillation frequency for the chemically prepared nanodisks therefore results in an improved 𝑄 factor of 18.2 ± 2.0, which is significantly higher than the value for the 160 nm lithographically prepared polycrystalline nanodisks (𝑄 factor of 10.8 ±1.8). Additional experimental evidence that intrinsic damping due to the polycrystalline nature of lithographically prepared nanostructures dominates the mechanical energy dissipation comes from photothermal annealing of polycrystalline nanodisks. Upon continuous wave laser excitation of a single 178 nm diameter Au nanodisk (see SI for details), internal crystal defects and disorder were mitigated, as evident from the SPR linewidth narrowing (Figure S16). The 𝑄 factor for the same nanodisks indeed increased from 11.0 ± 1.8 to 14.8 ± 0.8 after photothermal treatment. It is important to note that for all samples prepared by electron-beam lithography, the 𝑄 factor exhibited a much larger variation (~ 25%) than the size dispersion (~ 2%), primarily caused by the wider distribution of damping times compared to oscillation frequencies. Previously, this larger standard derivation of 𝑄 factors was proposed to arise from particle to particle variations in surface contact area or binding strength.41, 47 However, our results here demonstrate that the supporting substrate has a limited effect on the damping time. Instead, it is more likely that the large distribution of coherent phonon damping times in these


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lithographically prepared nanostructures is primarily caused by variations in the Au polycrystallinity. Thus, the internal crystal defects contribute not only to increased damping but also to fluctuations in damping time, even though precise size and shape control is achieved using lithographic fabrication methods.

Figure 4: (a) 𝑄 factor histograms for 104 Au nanodisks with diameters in the range of 120 nm to 240 nm and a constant thickness of 35 nm. The Ti adhesion layer varied from 0 to 4 nm. < 𝑄 > = 10.9 ± 2.4. (b) 𝑄 factor histograms for 43 Au nanorods with lengths varied from 80 nm to 160 nm with a constant width and thickness of 35 nm and a 2 nm Ti layer. < 𝑄 >= 12.6 ±


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2.2. (c) Results for all 147 nanostructures, resulting in an average value of < 𝑄 >= 11.3 ± 2.5.

Finally, to provide more insight into the damping mechanism of gold nanodisks and nanorods, histograms of the 𝑄 factor for each shape are given in Figure 4a and 4b, respectively, where we have combined data from all sizes. Both histograms are approximately Gaussian and the standard deviations of the nanorod and nanodisk data are nearly identical at ~ 25%. It is striking that (i) the observed standard deviation in 𝑄 is almost identical, and (ii) the 𝑄 factor is independent of nanoparticle size, geometry, frequency, surface adhesion, and vibrational mode. Frequency independent 𝑄 factors for these nanoparticles also discount the possibility of a viscous dissipation mechanism (e.g. Kelvin-Voigt model) in the material. Polycrystalline gold nanoparticles are prone to defects, and it appears that such a defect driven dissipation mechanism is producing a constant 𝑄 factor. All data can be explained if we consider a constant imaginary part of the material Young’s modulus, 𝐸. Using 𝐸 = 𝐸r + 𝑖𝐸𝑖 , where 𝐸r and 𝐸𝑖 are the real and imaginary parts of Young’s modulus, respectively, it follows that 𝐸𝑖 = 𝐸r /𝑄. In the present measurements, we find that the average 𝑄intrinsic is 11.3 ± 2.5 (Figure 4c). Consequently, this analysis produces an average value of 𝐸𝑖 = 𝐸r /11. Our study, for the very first time, thus establishes a predictive model for the intrinsic 𝑄 factor of any nanoparticle made of this polycrystalline gold: the intrinsic quality factor is universally, 𝑄 ≈ 11. This number is also consistent with previous reports for lithographically prepared gold nanostructures,40, 44, 47, 56, 65 as well as our own previous results39, 41 (see SI part 1e for more details). In summary, we investigated the damping mechanism of acoustic vibrations in metal nanostructures fabricated by electron-beam lithography. Femtosecond time-resolved pump-probe


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measurements were carried out on single nanoparticles to eliminate the influence of inhomogeneous broadening and accurately determine the mechanisms of damping. Examining nanostructures of different sizes and shapes demonstrated that elastic energy leakage through the metal-substrate interface is minimal. Instead, we established that intrinsic material damping – most likely caused by crystal defects – governed the mechanical energy relaxation process. This produces a constant intrinsic quality factor of 𝑄 = 11.3 (with ~25% standard deviation) irrespective of size, geometry, frequency, surface adhesion, and mode of the gold nanoparticles. This result motivates research into other polycrystalline (and crystalline) nanomaterials to establish whether they also exhibit such a constant intrinsic quality factor. Finally, it is important to note that the most detailed fundamental understanding of the coherent phonons – especially vibrational period and damping – is only possible through single-particle measurements. However, applications will more likely involve arrays of nanostructures that, with respect to interparticle size and shape control, can be more precisely fabricated by top-down methods and might therefore dominate in applications despite lower 𝑄 factors compared to their colloidal counterparts. We anticipate that these results on the mechanical properties of polycrystalline metal nanostructures will provide a foundation for nanomaterial design in photoacoustic imaging, high-frequency resonators, and ultrafast optical switching applications.


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ASSOCIATED CONTENT Supporting Information. Sample preparation and characterization; dark-field scattering spectroscopy; single-particle transient extinction spectroscopy; fitting procedure; FEM modeling; dependence of acoustic vibrations on nanodisk size, environment including ligands, nanorod length and width, and laser annealing.

AUTHOR INFORMATION Corresponding Authors *Email: mrj@rice,edu, [email protected], [email protected], [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT N.J.H and S.L. thank the Robert A. Welch Foundation (Grants C-1220 to N.J.H., and C-1664 to S.L.) and the Air Force (MURI FA9550-15-1-0022) for financial support. S.L. acknowledges support from the National Science Foundation (ECCS- 1608917). D.C. and J.E.S. acknowledge support from the Australian Research Council grants scheme and the ARC Centre of Excellence


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in Exciton Science (CE170100026). M.R.J. acknowledges the Robert A. Welch Foundation for young investigator support. We thank Dr. Anneli Joplin for help with editing the manuscript.


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TOC figure


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TOC figure 45x34mm (300 x 300 DPI)


Polycrystallinity of Lithographically Fabricated Plasmonic

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