Vibrational density of states and thermodynamics at the nanoscale: the 3D-2D transition in gold nanostructures

Abstract

Surface enhanced Raman scattering (SERS) is generally and widely used to enhance the vibrational fingerprint of molecules located at the vicinity of noble metal nanoparticles. In this work, SERS is originally used to enhance the own vibrational density of states (VDOS) of nude and isolated gold nanoparticles. This offers the opportunity of analyzing finite size effects on the lattice dynamics which remains unattainable with conventional techniques based on neutron or x-ray inelastic scattering. By reducing the size down to few nanometers, the role of surface atoms versus volume atoms become dominant, and the “text-book” 3D-2D transition on the dynamical behavior is experimentally emphasized. “Anomalies” that have been predicted by a large panel of simulations at the atomic scale, are really observed, like the enhancement of the VDOS at low frequencies or the occurrence of localized modes at frequencies beyond the cut-off in bulk. Consequences on the thermodynamic properties at the nanoscale, like the reduction of the Debye temperature or the excess of the specific heat, have been evaluated. Finally the high sensitivity of reminiscent bulk-like phonons on the arrangements at the atomic scale is used to access the morphology and internal disorder of the nanoparticles.

On the extraction of resistivity and area of nanoscale interconnect lines by temperature-dependent resistance measurements

“…Indeed, surface-sensitive phonon spectroscopy has demonstrated a reduction of the Debye temperature due to the presence of the surface and the resulting change in bonding geometry [30][31][32]. In nanowires, the surface-to-volume ratio is large and therefore, the reduction of the surface Debye temperature may affect the Bloch-Grüneisen resistivity.…”

Plasmon‐enhanced inelastic scattering by 2D and 3D superlattices made of silver nanocrystals

“…At first, some well‐defined lines at low wavenumber are ascribed to Lamb modes of the AgNCs. They are superimposed to a rather continuous signal in which we extract the second and third contributions: a poorly structured contribution below 170 cm −1 that we will assign to Ag bulk phonons and a background (gray area in Figure ), which intensity decreases monotonously with wavenumber. This last contribution is certainly due to fluctuations among the smooth assembly of ligands as its unstructured shape is characteristic of a viscous medium: It will be not discussed in this work and indeed simply treated as a background.…”

“…It has been recently shown that the VDOS gives a signature of the atomic arrangements, and the best agreement between the calculated and the measured VDOS is obtained for the ICO morphology for small AgNCs embedded in SiO 2 . To access information about the VDOS of the present samples, we have used the experimental procedure based on plasmon‐enhanced Raman scattering for small metallic nanostructures . The only exploitable data were obtained with supercrystals of Type A (〈 D 〉 = 4.3 nm).…”

“…Comparison of the VDOS for a silver nanocrystal extracted from the Raman spectrum (black circles and continuous black line) of a supercrystal of Type A (〈 D 〉 = 4.3 nm) and calculated ones using atomic scale simulations: The continuous blue (or red) line corresponds to an icosahedral (or decahedral) structure of 2,057 (or 1,926) silver atoms . The dotted blue line delineating the color area corresponds to the simulated VDOS for the ICO morphology with a reduced wavenumber scale by 10%.…”

“…For an exhaustive description of all the vibrational modes of a NC, the atomic motions have to be considered: Most of them correspond to short wavelength modes in the bulk material and they give the largest contribution to the vibrational density of states (VDOS). Accessing experimentally to the VDOS has been shown to give accurate information on atomic arrangements, force constants, and surface versus volume effects …”