Mechanical Properties of Ag Nanoparticle Thin Films Synthesized by

Article pubs.acs.org/JPCC

Mechanical Properties of Ag Nanoparticle Thin Films Synthesized by Supersonic Cluster Beam Deposition Simone Peli,† Emanuele Cavaliere,† Giulio Benetti,‡,† Marco Gandolfi,¶,† Mirco Chiodi,§ Claudia Cancellieri,§ Claudio Giannetti,† Gabriele Ferrini,† Luca Gavioli,*,† and Francesco Banfi*,† †

Interdisciplinary Laboratories for Advanced Materials Physics (I-LAMP) and Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, 25121 Brescia, Italy ‡ Laboratory of Solid State Physics and Magnetism, KU Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium ¶ Laboratory of Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium § Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Joining and Interface Technology, Ü berlandstrasse 129, 8600 Dübendorf, Switzerland S Supporting Information *

ABSTRACT: The morphological and mechanical properties of nanoparticles-based ultrathin Ag films, synthesized by supersonic cluster beam deposition over a sapphire substrate, are unveiled exploiting ultrafast optoacoustic, atomic force microscopy, Xray photoelectron spectroscopies, and X-ray diffraction techniques. The films, with thicknesses in the 10−50 nm range, have a porous structure composed of metallic Ag nanoparticles with a crystalline structure and average diameter of 6 nm. The films acoustic modes are in the hypersonic frequency range, the thinner films frequencies exceeding 100 GHz. The acoustic spectra are well accounted for modeling the nanoparticles film as an effective continuous medium. The modes quality factors show the existence of acoustically quasi-dark and bright states. The film effective density and effective elastic stiffness constants are respectively 0.8 and 0.5 that of bulk Ag. The present results are relevant in view of applications for optoacoustic transducers in the hypersonic frequency range, for optical coatings technology and for the production of mechanically stable bactericidal coatings.

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INTRODUCTION Nanophase materials present unique physical and chemical properties and are investigated for applications in fields ranging from medicine1 and energy2,3 to microbiology.4,5 As for the mechanical properties, work has been done on single6 and diluted nanoparticles (NPs)7,8 while a lack of informations remains for NPs deposited on a substrate and forming a thin film. Control on the NP composition, NP size, film thickness and uniformity, together with non-destructive probes for mechanical nanometrology, are needed in order to obtain mechanical information on such systems. Supersonic cluster beam deposition (SCBD) is emerging as a high throughput, versatile, cost-effective technique for the synthesis of metallic thin films over a variety of substrate materials.9 This is primarily due to the SCBD working principle and versatility that essentially parallels that of a spray-paint, the deposited film being composed of metallic NPs rather than paint droplets. Recently, SCBD has been exploited to synthesize highly bactericidal Ag nanoparticles films,5 opening the possibility to coat surfaces with Ag NP films with controlled properties for intrahospital use. Moreover metallic thin films are being explored as high frequency opto-acoustic transducers10 in application ranging from mass-sensing to opto-acoustic resonators.11 Within this frame SCBD might represent a viable © XXXX American Chemical Society

option in terms of components unit cost, production throughput and versatility in tuning the NP properties. Whatever the application, the mechanical properties of Ag NP thin films synthetised by SCBD need to be explored in order to determine the film behavior and stability. In this work, the mechanical properties of Ag NP thin films deposited by SCBD on a sapphire substrate are obtained. The film thickness is varied between 15 and 50 nm. The choice of a sapphire substrate is driven by its widespread deployment as supporting material in a variety of fields ranging from optoelectronics to biotechnology. Morphology and composition are obtained by Atomic Force Microscopy (AFM), X-ray Photoemission Spectroscopy (XPS), Auger Spectroscopy, and X-ray Diffraction (XRD), while mechanical properties are measured by ultrafast opto-acoustic techniques. The films mechanical modes, their lifetime, quality factors and acoustic energy reflection coefficient at the interface are retrieved. An effective continuum model allows retrieving the sound velocity and the elastic stiffness constants of the Ag NPs films and provide indications on the film−substrate interface quality. Received: January 6, 2016 Revised: January 29, 2016

A

DOI: 10.1021/acs.jpcc.6b00160 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) High resolution AFM topography of the Ag NP film deposited by means of SCBD on a (0001) Al2O3 substrate. The zero height reference is taken at the Al2O3 substrate. (b) Height distribution histogram of the film surface. The average film thickness is indicated in red. The zero height reference is taken at the Al2O3 substrate surface (bottom axis) and at the minimum film thickness tF,min (top axis). See main text for further details.

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EXPERIMENTAL AND THEORETICAL METHODS NP Film Synthesis and Characterization. Nanostructured Ag films were deposited at room temperature in medium vacuum conditions (base pressure 1 × 10−6 mbar) by supersonic cluster beam deposition (SCBD)5,12,13 directly on the substrate surface. The principle of SCBD relies on the pulsed ablation of a 99.99% purity Ag target rod. The injection of a He carrier gas pulse (50 bar) in the ablation chamber is synchronized with a suitable delayed high voltage and high current (800 V/2000 A) discharge pulse, generating the plasma and sputtering atoms from the target. The carrier gas conveys sputtered atoms to form an NP beam through an aerodynamic lens/nozzles system, up to the vacuum chamber. The pressure gradient from the ablation chamber to the vacuum chamber sustains the supersonic expansion of the NP beam. A skimmer of 2 mm diameter selects the central part of the beam directed on the substrate surface, in this case the (0001) α-Al2O3 single crystal, optically polished surface of a 0.48 mm thick slab (from MaTeck GmbH). The nominal film thickness and deposition rate were measured by a quartz microbalance, while film properties where obtained ex situ by AFM (Solver-pro NTMDT), XPS, Auger Spectroscopy and XRD. The NPs composition was investigated by means of photoelectron spectroscopies. Data were collected in an Omicron MultiScanLAB UHV apparatus (base pressure better than 2 × 10−10 mbar) equipped with a SPECS Phoibos 100 hemispherical electron energy analyzer and a standard X-ray source (Mg−Kα line, 1.25 keV photon energy). The analyzer was operated at normal emission in Medium-Area mode with Fixed Analyzer Transmission and 30 eV pass energy. Singlecrystal Ag(110) was used as reference for metallic Ag. The crystal surface was cleaned by several cycles of sputtering with 1 keV Ar ions and annealing up to 400 °C, until no sign of O or C contamination was detected by XPS. A Shirley-like background was removed from all the XPS and Auger spectra. X-ray Reflection (XRR), Grazing-Incidence X-ray Diffraction (GIXD), and stress measurements were performed using a Bruker D8 Discovery diffractometer equipped with a Cu Kα Xray source (wavelength 1.54 Å). Refer to Supporting Information (SI) for details on the X-ray measurements geometrical configurations and angles definitions. The SCBD deposited Ag film mass density was investigated by means of XRR estimating the critical angle for total reflection, the details of the technique are reported in ref 14.

XRR data were analyzed using Bruker Leptos 7.0 software package for XRR/XRD analysis and modeling. Ex situ X-ray diffraction analysis of the as-deposited SCBD Ag sample was performed in grazing-incidence geometry (GIXD). 2θ scans were collected with a fixed incident angle of 1.2° to enhance the signal contribution from the deposited layer while minimizing the contribution arising from the substrate, these measurements providing an estimate of the average Ag crystallites size D. Residual stress was investigated using the same equipment in a point-focus, Bragg−Brentano configuration. The residual stress analysis is carried out using the so-called “sin2(ψ) method”, ψ being the tilt angle.15 The most intense Ag(111) reflection was chosen for this study. Picosecond Acoustics. The SCBD deposited Ag films mechanical properties were investigated by means of picosecond photoacoustic, a technique that proved very effective in a variety of mechanical nanometrology applications.16−18 The scheme relies on photoacoustic excitation of the Ag film breathing modes and their detection via the acousto-optic effect. In the photoacoustic excitation step, energy is delivered to the film by a laser pump pulse1560 nm central wavelength, 100 fs pulse duration at fwhm, and 30 μm beam diameter at fwhm. The substrate is transparent at this wavelength and hence does not absorb energy from the laser. The film lattice’s heating, occurring on the ps time-scale, triggers an impulsive thermal expansion of the film, ultimately exciting the film’s acoustic breathing modes. The oscillating strain field modulates the Ag film dielectric constant, thus resulting in a time-periodic modulation of the sample’s optical transmission and reflectivity. These modulations are revealed recording the transmitted, ΔTr/Tr0, and reflected, ΔR/R0, relative intensity variation of a time-delayed laser probe pulse 780 nm central wavelength, 100 fs pulse duration at fwhm, and 15 μm beam diameter at fwhm as retrieved from pump and probe measurements. Pump and probe measurements were performed implementing the Asynchronous Optical Sampling (ASOPS) technique exploiting a MENLO C-Fiber 780 High Power ASOPS system. The transmission (reflectivity) intensity variations, ΔTr = Tr(t) − Trref, (ΔR = R(t) − Rref) are acquired taking the difference between the intensity, Tr(t) (R(t)), of the probe beam transmitted through (reflected from) the sample and the intensity of a reference beam, Trref (Rref), identical to the probe beam, that did not interact with the sample. The B


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Figure 2. (a) Core-level Ag 3d XPS spectra; (b) valence-band XPS spectra; and (c) Ag MNN Auger spectra. Blue-dotted curves are relative to the Ag(110) crystal whereas black-dotted curves are relative to the Ag NP film. The black-dotted curves have been displaced vertically for clarity.

reference beam is conditioned so that ΔTr (ΔR) is null when the pump beam is turned off. The difference ΔTr (ΔR) was taken feeding the probe and its reference beam to a THORLABS PDB430A Fixed Gain Balanced Differential Si Photodiode350 MHz bandwidth. The analog signal out of the differential photodiode was then digitized via a SPECTRUM M3i.4841−16 bit, 105 MS/sacquisition board. The transmission (reflectivity) intensity variation ΔTr (ΔR) are then normalized against the transmission (reflectivity) recorded in the absence of the pump beam, Tr0 (R0). From now on ΔTr/Tr0 (ΔR/R0) will be simply addressed as ΔTr/Tr (ΔR/ R) for sake of simplicity. Refer to the SI for further details on experimental aspects. In the ASOPS system, the pump−probe time delay is managed electronically, avoiding any moving mechanical parts.18 This fact, together with a laser repetition rate of 100 MHz, allows detection of relative transmission (reflectivity) changes in the 10−7 range. For these reasons ASOPS is arising as the go-to photoacoustic technique for the investigation of the mechanical properties of nanoscale materials.18−21

Consequently, the estimated NP diameter spans between 5.5 and 6.1 nm. Crystallite Size. The rough extrapolation performed above is consistent with an estimated average grain size D = 6.5 nm ± 0.5 nm as obtained from GIXD measurements using the Sherrer formula, D = (0.94λ)/βcos θ, where λ is the photon wavelength, β is the fwhm (in radians) of the selected diffraction peak, and θ is the corresponding Bragg angle. It should be noted that this value provides an estimate of the average coherency length of the chosen family of planes, rather than a direct measure of the actual grain size of the crystallites.22 Density. The NPs film density, as obtained from XRR measurements, is ρNP = 8400 ± 600 kg/m3. This value is 0.8 times the density value of bulk Ag, ρAg = 10 490 kg/m3.23 This evidence is compatible with scenarios where voids are present among the NPs. Residual Stress. Residual stress analysis indicates a compressive stress σres = 70 ± 20 MPa for the Ag NPs composing the film grown on Al2O3 (0001). However, the same analysis on Ag layers deposited on the same substrate by means of Magnetron Sputtering, with no bias applied in order to minimize the residual stress arising during the film growth, reveals a remarkably higher residual stress amounting to 180 ± 30 MPa. This evidence suggests that the NPs are juxtaposed and that voids are present among the NPs allowing for residual stress relaxation. Refer to SI for details on the X-ray measurements geometrical configurations and X-ray data. NP Composition. Figure 2 shows the XPS data of 3d corelevel (a), valence-band (b), and Auger MNN line (c) obtained for a metallic (i.e., nonoxidized) monocrystal Ag reference (blue dots) and the NPs film grown by SCBD (black dots). For each curve, a Shirley-type background was subtracted and each peak intensity was normalized. The Ag 3d data were fitted with Voigt functions, keeping the spin orbit splitting of 6.00 eV and the spin orbit ratio of 2/3. The resulting binding energy of Ag on the NP film (368.25 eV) is in very good agreement with the measured metallic Ag reference (368.26 eV). The valence-band spectra of the NPs film and of the metallic Ag reference present the typical asymmetric shape with two main features at 6.2 and 4.5 eV, distinctly different from the Ag2O and AgO XPS valence-band shape.24 Moreover, the Auger MNN sharp line shape of the Ag NPs film spectrum is almost identical to the metallic Ag reference spectrum, with main identifiable peaks at 357.8 eV kinetic energy. The Auger Parameter (AP) obtained from these data is 726.10 eV for the NPs film and 726.1 eV for the metallic Ag reference, in very good agreement with the literature’s value for metallic Ag (726.1 eV)25 and distinctly

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RESULTS AND DISCUSSION Morphology and Composition. Film Topography. The as-deposited film topography is investigated by AFM. Four samples were investigated with measured average films thicknesses of h = 15, 20, 35, 50 nm. The films are composed of nanoparticles (NPs), as shown in the high resolution AFM topography image reported in Figure 1 (a) for the case of the 35 nm-thick film. This is a paradigmatic case, the images acquired on films of different thicknesses being similar. From now on the SCBD-grown films will be addressed as NPs films. The lateral dimension of the NPs is not a reliable measure of their size, due to the finite radius of curvature of the AFM tip and the consequent tip−surface convolution effects on the observed NP morphology. The height distribution’s average referenced to tF,min, h − tF,min, is a more reliable index of the actual NP size, see Figure 1(b). In the previous definition tF(x, y) is the coordinate-dependent film thickness referenced to the substrate’s surface, tF,min = 30.4 nm is the minimum film thickness and h = ⟨tF⟩ is the height distribution’s average referenced to the substrate’s surface. A set of hypothesis is needed to correlate the average height h − tF,min = 4.6 nm to the average NP radius R, specifically (a) monodispersed and spherical NPs, (b) an ideal needle-like tip termination of the AFM tip, and (c) a flat substrate around the single NP. Values of h − tF,min span between (5/3)R (single NP) and 5π/(6 3 )R (hexagonal close packed arrangement of neighbor NPs). C


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Figure 3. (a) Relative transmission variation vs delay time acquired on the 35 nm thick NP film. Inset graph: zoom of the relative transmission variation highlighting the oscillating signal in the 100 ps time scale (full black line) and the function fitting the nonoscillating background (dashed blue line). Inset picture: schematics of the sample and the experimental setup. (b) Residue of the two traces addressed in the inset of Figure 1(a) (black line) and its fit based on two damped oscillators (red line).

different from the AP of oxidized silver (from 723.9 to 724.4 eV).26,27 Therefore, the NPs forming the film grown by SCBD are composed of metallic Ag. Within the sensitivity of our XPS measurements, there is no evidence of spectral feature related to Ag oxides. In summary, the body of evidence gathered so far is well rationalized in terms of a thin film composed of Ag NP crystallitesaverage dimensions in the 6−7 nm rangeand inter-NPs voids. Photoacoustic Nanometrology. The trace ΔTr/Tr as a function of the delay time for the 35 nm thick film case is reported in Figure 3(a). The fast negative transient, occurring on a few ps time scale, entails information on the electron− phonon thermalization within the NP film. The longer dynamics, beyond tens of ps, are related to the thermal fluxes taking place both between the film and the substrate and within the substrate itself. However interesting, these dynamics are not within the scope of the present work. Informations on the mechanical behavior are conveyed by the small amplitude oscillations occurring over a time delay window ranging from few ps to 100 ps and superimposed on the signal of thermal origin, see inset Figure 3(a). The inset also reports the fit of the nonoscillating background of thermal origin (dashed blu line). The black line in Figure 3(b) is the residue (difference) between the two curves shown in the inset of Figure 3(a). The residue is taken in order to disentangle the mechanical problem from the thermal one. The ΔTr/Tr oscillation amplitude is in the order of few 10−7, and fades out on the 100 ps time scale, submerged in the background noise. The residue in Figure 3(b) is well fit by the sum of two exponentially damped oscillators of periods T0 and T1 and decay time constants τ0 and τ1 respectively, see red curve in Figure 3(b). The damped oscillator of shorter period, T1, is by far the most important in the reconstruction of the residue. The same applies for the case of other films thicknesses and for measurements in reflection geometry also, with the exception of the reflection measurements on the 50 nm thick film that gave no appreciable oscillating signal, the reason for the latter being yet under investigation. The oscillation periods T0 (gray markers) and T1 (black markers), retrieved from the fits of the residues, are reported as a function of film thickness in Figure 4. For ease of visualization the error bars for T0 are not shown, being of the order of T0 itself. These conspicuous uncertainties are due to the fact that T0 > τ0, resulting in values of the quality factor Q0 < 1, where Qn = π(τn/Tn) and n = {0, 1}. Hence the oscillations last for a

Figure 4. Oscillation period (left axis) and frequency (right axis) vs film thickness. Markers: periods retrieved from the residues as obtained in transmission (circle) and reflection (triangle) geometry. The vertical error bars for the n = 0 cases are not reported for sake of visualization being of the order of the period. The vertical error bars for the n = 1 cases fall within the markers size. Fundamental (n = 0) film’s breathing mode (gray color), and first harmonic (n = 1) (black color). Full lines: linear fit through the origin of the data. Red dashdotted lines delimit the 1σ confidence level boundaries. Dashed lines: fundamental (n = 0) and first harmonic (n = 1) breathing mode period calculated from eq 7 assuming bulk Ag values for the thin film.

period or less and this mode is addressed as a “quasi-dark” state. On the contrary, the error bars for T1 are exiguous, in the order of the ps, and fall within the markers size. This is due to the fact that T1 < τ1 with Q1 ≈ 5, resulting in fully developed underdamped oscillations. Figure 5 reports τ1 (black circles) and Q1

Figure 5. Attenuation time (black, left axis) and Quality factor (red, right axis) for the first harmonic breathing mode (n = 1) vs film thickness. Markers: experimental attenuation time and quality factors. Dashed line: theoretical radiative attenuation time and quality factor calculated adopting the perfect interface model between the sapphire substrate and an homogeneous film with the same density, ρNP, and longitudinal sound velocity, vL,NP, as the ones experimentally obtained for the Ag NP films. D


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The Journal of Physical Chemistry C (red circles) as a function of the film thickness. The damping time τ0 is affected by a large error bar and will not be object of further speculation. The experimental evidence is rationalized mimicking the NP film with an effective homogeneous and isotropic thin film. The NP film morphology is granular rather than homogeneous, nevertheless simulating the actual NP film with an homogeneous one allows defining an effective density ρNP and an effective stiffness tensor CNP that are constants throughout the film. The experimental symmetry allows to excite longitudinal acoustic waves. The mechanical problem may be considered as one-dimensional (1D). Referring to the coordinate system reported in the inset of Figure 3(a), the longitudinal displacement field component uz(z,t) satisfies the wave equation, ∂ 2uz(z , t ) ∂t 2

=

∂ vL,2 i

expected since the regressive propagating wave in the substrate has been forcibly avoided, leaving the elastic wave radiated from the NP film to the substrate as the only possible solution within the substrate. The acoustic problem is thus energetically open, and the solutions are promoted to quasi-stationary states, the film’s breathing modes being exponentially damped harmonic oscillations of time period Tn = 2π/Re{ωn} and radiative lifetime τr,n = 1/|Im{ωn}|: Tn =

τr, n =

uz(z , t ) (1)

where z is the direction perpendicular to the film surface, the subscript i = {NP, s} identifies the NPs film and sapphire substrate, respectively, and vL,i the longitudinal wave velocity in the respective medium. The equation is separable, and the solution may be cast in the form uz(z, t) = U(z)T(t). Solutions of the type U(z) = uki exp(jkiz) + u−ki exp(−jkiz) and T(t) = uω exp(−jωt) are here assumed, resulting in the dispersion relation ω2 = v2L,ik2i with ω and ki the angular frequency and the wave vector in material i, respectively. As for the boundary conditions, the film surface (z = h) is stress free (eq 2), the interface (z = 0) between the Al2O3 (z < 0) and the NP film (z > 0) is assumed as “perfect”. The perfect interface is formally defined requiring continuity of displacement (eq 3) and stress (eq 4) at the junction of the two media: ∂U ∂z

=0 (2)

z=h

U ( z = 0 − ) = U (z = 0 + ) C⊥, s

∂U ∂z

= C⊥,NP z=0−

∂U ∂z

z=0+

(3)

(4)

where C⊥,i is the out-of-plane longitudinal elastic constant of the medium identified by the subscript i, its relation with the longitudinal propagation velocity being vL,i = C⊥, i /ρi . The Al2O3 substrate is taken as semi-infinite. For this reason, the plane wave solution propagating from the substrate toward the interfaceregressive solutionis set to zero, resulting in U(z) = u−ks exp(−jksz) for z < 0. Forcing U(z) to satisfy the abovementioned boundary conditions, and accounting for the fact that ZNP < Zs, results in a dispersion relation allowing for complex solutions ωn = Re{ωn} + jIm{ωn} only: vL,NP Re{ωn} = π (1 + 2n) (5) 2h Im{ωn} =

⎛ Z − Z NP ⎞ ln⎜ s ⎟ 2h ⎝ Zs + Z NP ⎠

2 vL,NP

⎛ Z − Z NP ⎞ ln⎜ s ⎟ ⎝ Zs + Z NP ⎠

(7) −1

h (8)

the subscript r standing for radiative since eq 1 does not account for intrinsic losses. Eq 8 shows that the radiative lifetime τr,n is actually independent of mode index n. The experimental periods T0 and T1 reported in Figure 4 are well fitted by a linear function through the origin, T = anh, an being the fitting parameter with n = {0, 1}. The fits have been performed accounting for error bars on both the oscillation period and the film’s height.28 The best-fit parameters to the data obtained in transmission measurements are a0 = 1.35 ± 0.08 × 10−3 s/m and a1 = 4.63 ± 0.07 × 10−4 s/m. Fitting to both transmission and reflection data gives the same fitting parameters to within the error bar. The confidence level boundaries for the n = 1 case are indeed very good, not so for n = 0. The ratio a0/a1 = 2.9 ± 0.2 is compatible with the theoretical ratio T0/T1 = 3 as obtained from eq 7. The experimental periods are thus attributed to the fundamental (n = 0) and first (n = 1) film breathing mode addressed in eq 7. Should different interface conditions apply, the ratio a0/a1 would be different. For example, if the film adhesion to the substrate were poor, then one could at first instance assume the film as free-standingstress free boundary conditions at z = 0. This would result in a value of 2 for the ratio between the periods of the first two oscillating modes. The present results are at variance with respect to the bulk Ag thin films case. In order to highlight this difference the fundamental (n = 0) and first harmonic (n = 1) breathing mode period calculated from eq 7, assuming bulk Ag values for the thin film, are also reported as gray (n = 0) and black (n = 1) dashed lines in Figure 4. Equating an to the linear coefficient in eq 7 one retrieves vL,NP = 2950 ± 200 m/s and 2880 ± 40 m/s for mode n = 0 and n = 1 respectively. These values coincide within the experimental error. In the following, the value vL,NP = 2880 ± 40 m/s will be assumed, being the most reliable. This value is to be compared against vL,Ag = 3646 m/s for bulk polycrystalline Ag.23 Since the ef fective film is homogeneous and isotropic, the following apply: (a) the two elastic stiffness tensor elements C11,NP and C44,NP suffice to describe the material elastic properties, (b) vL,NP = C11,NP/ρNP and (c) C⊥,NP = C11,NP. Substitution of the measured values of ρNP and vL,NP results in a value C11,NP = 70 ± 5 GPa. This value is half of that reported for bulk polycrystalline Ag, C11,Ag = 140 GPa,23 and is bulk consistent with the trend for Cfilm for various metallic ⊥ /C⊥ 29,30 film films reported in the literature, C⊥ and Cbulk ⊥ being the outof-plane longitudinal elastic stiffnesses for thin films and bulk metals, respectively. A full mechanical characterization would imply measuring C44,NP too. The value C44,NP is linked to the

2

∂z 2

4 h vL,NP(1 + 2n)

vL,NP

(6)

where Zi = ρivL,i is the acoustic impedance of material i and n = {0, 1, ...}. It is worth mentioning that Im{ωn} < 0, and it does not depend on the mode index n. A complex solution is to be E


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Table 1. Summary of the Mechanical Properties Introduceda

transverse acoustic wave velocity of the Ag NP film by vT,NP = C44,NP/ρNP . The experimental symmetry does not allow detecting transverse acoustic waves, thus preventing the measurement of C44,NP. Nevertheless, one may expect C44,NP < C44,Ag = 27 GPa, the latter being the value reported for bulk polycrystalline Ag.23 The morphology of the Ag NP films together with a density ρNP inferior by 20% with respect to polycrystalline bulk Ag both suggest that a certain degree of porosity is present in the Ag NP films. The voids present among the NPs do not sustain shear stresses, hence do not sustain transverse acoustic waves. Within this view only the volume fraction occupied by Ag NPs contributes to C44,NP. The focus is now turned on the breathing mode lifetime for the n = 1 breathing mode. The attenuation time conveys informations on interface quality and adhesion,31,32 two relevant aspects for any technological exploitation of NP thin films. The experimental attenuations τ1 vs film thickness are reported as full black circles in Figure 5. The experimentally observed attenuation time may be interpreted as arising from the contribution of two decay channels in parallel, τ−1 = τ−1 r + , where τ and τ are, respectively, the radiative and intrinsic τ−1 b r b attenuation time, the latter occurring within the film bulk. Disparate sample-dependent physical mechanisms may contribute to τb preventing a comprehensive understanding of the frequency dependence of τb in the hypersonic frequency range. Whatever the mechanism, the contribution of two decay channels in parallel implies τ ≤ {τr, τb}, the measurements hence set an inferior boundary to the radiative and the intrinsic attenuation times in the Ag NP film. Previous works on the adhesion properties of metallic thin films31,32 assumed the radiative channel as the leading mechanism ruling attenuation times. The ansatz was supported by experimental evidence showing the impact of surface preparation on τ. The same line of thought is adopted in the present context. The radiative attenuation time τr,1, calculated from eq 8 upon insertion of the densities, ρNP = 8400 kg/m3 and ρs = 3986 kg/ m3,23 and longitudinal sound velocities, vL,NP = 2880 m/s and vL,s = 11 260 m/s,23 is reported as a dashed black line in Figure 5. The same figure also reports the quality factor Q1 retrieved from the experiments (red full circles) and theory (red dashed lines). The perfect interface model grasps the main experimental features but underestimates both the attenuation times and the quality factors. The presence of a molecular layer between the NP film and the Al2O3 substrate, modifying the interface properties, is the forefront alternative scenario that should be considered.31,32 A water layer is a plausible cause of surface contamination that might be present on the substrate before film’s deposition. A layered interface model is here adopted to account for this scenario. An aqueous monolayer of thickness dw = 0.3 nm, density ρw, and longitudinal sound velocity vw is interposed between the Ag NP film and Al2O3, the matching of the water layer with both the NP film and the substrate interfaces being perfect. The acoustic parameters for the aqueous layer have been taken assuming both bulk water, ρw = 1000 kg/m3 and vw = 1433 m/s,33 and interfacial water34 values, ρw = 3610 kg/m3 and vw = 978 m/s. Mechanical properties of interfacial water have been reported for water layers at the free surface of a supporting Al2O3 substrate (Table 1). In the present case, the water layer is sandwiched between two interfaces. For these reasons, both extreme case scenarios, that of bulk (H2O (I)) and interfacial (H2O (II)) water properties, are here

ρNP ρAg ρs ρw(I) ρw(II) vL,NP vL,Ag vL,s vw(I) vw(II) ZNP ZAg Zs Zw(I) Zw(II) C11,NP C44,NP C11,Ag C44,Ag σres

8400 ± 600 10 490 3986 1000 3610 2880 ± 40 3646 11 260 1433 978 24.2 38.2 44.9 1.4 3.5 70 ± 5 < 27 140 27 70 ± 20

kg m−3 kg m−3 kg m−3 kg m−3 kg m−3 m s−1 m s−1 m s−1 m s−1 m s−1 × 106 kg × 106 kg × 106 kg × 106 kg × 106 kg GPa GPa GPa GPa MPa

s−1 s−1 s−1 s−1 s−1

m−2 m−2 m−2 m−2 m−2

[*] 23 23 33 34 [*] 23 23 33 34 [*] [*] [*] [*] [*] [*] [*] 23 23 [*]

a

[*] values obtained in the present work; (I) and (II) identify bulk and interfacial water properties, respectively.

considered. Extending the formalism previously used for the single interface case to the layered interface model, one finds the following equation for the complex valued ω: ⎛ h ⎞ ⎟⎟ rNP,w exp⎜⎜ −j 2ω vL,NP ⎠ ⎝ ⎡ ⎛ h d ⎞⎤ + rw,s exp⎢ −j 2ω⎜⎜ + w ⎟⎟⎥ ⎢⎣ vw ⎠⎥⎦ ⎝ vL,NP ⎛ d ⎞ − rNP,wrw,s exp⎜ −j 2ω w ⎟ − 1 = 0 vw ⎠ ⎝

(9)

where rNP,w = (ZNP − Zw)/(ZNP + Zw) and rw,s = (Zw − Zs)/(Zw + Zs) are the acoustic reflection amplitudes for the NP/water and water/sapphire interfaces, respectively, Zw = ρwvw being the water acoustic impedance. The spectrum is discrete, ωn = Re{ωn} + jIm{ωn} with n = {0, 1, ...}, and has to be determined numerically. The oscillation period, 2π/Re{ω1}, radiative lifetime, 1/|Im{ω1}|, and quality factors for the n = 1 modes are reported as a function of h in Figures 6, 7(a), and 7(b) respectively. The same quantities for the perfect interface model are repeated, within the same figures, for sake of comparison. In all three graphs, the dashed lines are a guide to the eye except for the perfect interface case where they represent the plot of the functions T1, τ1, and Q1 for the continuum of h values. The layered interface model overestimates the oscillation periods, see Figure 6, whereas predictions based on the absence of an interlayer match the experimental data. The experimental lifetimes fall, within the error bars, between the radiative lifetimes predicted by the perfect interface model (diamonds) and those calculated assuming the presence of a water interlayer with interfacial water acoustic properties (crossed circles), see Figure 7(a). The former model provides the best estimates for small films thickness, the latter for the higher thickness case. Similar considerations apply for the quality factors. In this case, F


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Figure 6. Period for the n = 1 breathing mode vs film thickness. Experimental (full circles) and theoretical data calculated assuming no water interlayer (diamonds), the presence of a water monolayer with bulk (asterisks) and interfacial (crossed circles) water acoustic properties, respectively.

Figure 8. Acoustic energy reflection coefficient for the n = 1 breathing mode vs film thickness. Experimental (full circles) and theoretical data calculated assuming no water interlayer (diamonds), the presence of a water monolayer with bulk (asterisks), and interfacial (crossed circles) water acoustic properties.

the perfect interface model predicts a constant Q1 value, and the performance of the layered interface model seems fortuitous since it predicts values of Q1 monotonically decreasing with h as opposed to the experimental case, see Figure 7(b). The acoustic energy reflection coefficient allows comparing different interface models against the actual interface. The acoustic energy reflection coefficients for the layered interface model reads as follows:35

(Zs − ZNP) 2/(Zs + ZNP)2, are reported as diamonds for the same h values. The reflection coefficients retrieved from the experiment, R = |r|2 = exp[ − 4h/(τ1vNP,L)], are shown as full circles. [A methodological note is here due. The above reported formula for R, linking the reflection coefficient to the experimentally obtained τ1, is obtained from acoustic cavity losses calculations assuming an exponential decay of the displacement field for the film breathing mode and no specific model for the interface (that is solely accounted for by the existence of a generic reflection amplitude r). The assumption of an exponential decay is consistent with the fact that the decay times have been obtained fitting the experimental data with exponentially damped oscillators. In the case of the perfect interface model, the same formula naturally stems from eq 8, a solution that is obtained without any assumption on the functional form for the decaying oscillation.] The dashed lines are a guide to the eye except for the perfect interface case where it represents the plot of Rp for the continuum of h values. Rl is monotonously decreasing vs h, within the h range explored in the experiment, irrespective of the kind of aqueous interlayer considered, let it be H2O (I) or H2O (II). The perfect interface model results in a constant value Rp (diamonds), that, with the exception of the 15 nm thick film, underestimates the experimental values. The Rl values, calculated assuming interfacial water acoustic properties (crossed circles), overestimate the experimental findings except for the 50 nm thick NP film, see Figure 8. The outcome qualitatively parallels that for Q1, the layered interface model predicting Rl monotonically decreasing with h as opposed to the experimental case.

R l= ⎡ ⎛d ⎞ ⎢Zw2(Zs − Z NP)2 cos2⎜ w Re{ω}⎟ ⎢⎣ ⎝ vw ⎠ ⎛d ⎞⎤ + (Zw2 − Z NPZs)2 sin 2⎜ w Re{ω}⎟⎥ ⎝ vw ⎠⎥⎦ ⎡ ⎛d ⎞ × ⎢Zw2(Zs + Z NP)2 cos2⎜ w Re{ω}⎟ ⎢⎣ ⎝ vw ⎠ −1 ⎛d ⎞⎤ + (Zw2 + Z NPZs)2 sin 2⎜ w Re{ω}⎟⎥ ⎝ vw ⎠⎥⎦

(10)

With reference to Figure 8, the asterisks (crossed circles) are the values of Rl vs h for the n = 1 mode calculated inserting Re{ω} = 2π/T1 in eq 10, with T1 evaluated from the layered interface model assuming bulk (interfacial) water acoustic properties as reported in Figure 6. The mode independent reflection coefficients for the perfect interface case, Rp = |rp|2 =

Figure 7. (a) Attenuation time and (b) Quality factor for the n = 1 breathing mode vs film thickness. Experimental (full circles) and theoretical data calculated assuming no water interlayer (diamonds), the presence of a water monolayer with bulk (asterisks) and interfacial (crossed circles) water acoustic properties, respectively. G



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In summary, the predictions of the perfect interface model well match the experimental oscillation periods. As for the mode lifetimes and related quantities the prefect interface model underestimates the experimental values for the higher films thicknesses. The layered interface model provides by far the worse performance failing to predict the NP films oscillation periods and predicting trends for the quality factors and acoustic energy reflection coefficient as a function of films thickness opposite to the experimental ones. The presence of a water monolayer may be ruled out as the cause of an augmented mode lifetime, the perfect interface model providing the best overall-performance. Alternative scenarios have to be considered in order to rationalize the attenuation times and acoustic energy reflection coefficients. A possibility, compatible with the suggested morphology, is that of a “patched” interface made of spots with perfect adhesion and spots where the NP film and the substrate are disconnected. Provided the disconnected patches are less than the connected ones, such a model could possibly account for a change in lifetimes without appreciably affecting the NP film’s resonance frequencies. Calculation of the reflection coefficient or attenuation time for such an interface are hard to conceive in analytical terms calling for Molecular Dynamics simulation and casting the acoustic wave problem at the interface in scattering terms.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b00160. X-ray measurements geometrical configurations, X-ray reflectivity, grazing incidence X-ray diffraction, stress measurements, pump probe principle, pump probe setup (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*Phone: +39 030 2406 709. Fax: +39 030 2406 742. E-mail: [email protected] (L.G.). *Phone: +39 030 2406 709. Fax: +39 030 2406 742. E-mail: francesco.banfi@unicatt.it (F.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.B., S.P., and L.G acknowledge the financial support from the MIUR−Futuro in ricerca 2013 Grant in the frame of the ULTRANANO Project. F.B, C.G, G.F, L.G, and E.C acknowledge the support of Università Cattolica del Sacro Cuore through D.2.2 and D.3.1 grants.

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CONCLUSIONS The present work investigated the morphology, composition, and mechanical properties of Ag NPs thin films, thicknesses in the 15−50 nm range, synthesized on a sapphire substrate by the SCBD technique. The films are composed of juxtaposed Ag NP crystallites, average dimensions in the 6 nm range, and inter-NPs voids. Photoacoustic nanometrology shows that the NP Ag films perform well as hypersonic acoustic cavities operating up to and beyond the 100 GHz range, see Figure 4. The fundamental breathing mode, n = 0, may be considered as a “quasi-dark mode”, its quality factor being less than unity. In view of acoustic cavity engineering, the present work suggests exploiting the n = 1 “bright mode” in situation where the acoustic mismatch between the NP film and the substrate is low. Furthermore, the acoustic spectra are well accounted for in terms of continuum mechanics. These results, quite surprising given the granular nature of the NP film, are particularly striking when one considers that the films are composed of only few layers of Ag NPs. The density, longitudinal sound velocity, and elastic stiffness have been measured for Ag NP films down to 15 nm thicknesses. The first two values are 80% and the latter 50% of the respective values for bulk polycrystalline Ag. The films acoustic radiative time, quality factors and acoustic energy reflection coefficient from the film to the substrate are somewhat higher than predicted by the perfect interface model, nevertheless they are lower than what would be expected should a water interlayer be present. The latter suggests a way to improve the acoustic cavity quality factor by interposing a thin polymeric layer between the film and the substrate,32 this being desirable in opto-acoustic transducers applications. The mechanical parameters here determined are of paramount importance in view of any application involving Ag NP films and prove the effectiveness of the SCBD as a cheap, high throughput perspective production technique for optoacoustic transducers in the hypersonic frequency range.

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Mechanical Properties of Ag Nanoparticle Thin Films Synthesized by

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