Elastic constants and dimensions of imprinted polymeric nanolines determined from Brillouin light scattering

Abstract

Elastic constants and cross-sectional dimensions of imprinted nanolines of poly(methyl methacrylate) (PMMA) on silicon substrates are determined nondestructively from finite-element inversion analysis of dispersion curves of hypersonic acoustic modes of these nanolines measured with Brillouin light scattering. The results for the cross-sectional dimensions, under the simplifying assumption of vertical sides and a semicircular top, are found to be consistent with dimensions determined from critical-dimension small-angle x-ray scattering measurements. The elastic constants C(11) and C(44) are found to be, respectively, 11.6% and 3.1% lower than their corresponding values for bulk PMMA. This result is consistent with the dimensional dependence of the quasi-static Young's modulus determined from buckling measurements on PMMA films with lower molecular weights. This study provides the first evidence of size-dependent effects on hypersonic elastic properties of polymers.

Mechanical properties of selected nanostructured materials and complex bio-nano, hybrid and hierarchical systems

“…A more novel technique to ascertain Young's modulus uses FE analysis of Brillouin light-scattering spectra taken from poly(methyl methacrylate) nanolines fabricated by lithography and plasma etching. 99 Results indicated a decrease in elastic modulus of about 10% relative to bulk for nanolines with a height of about 125 nm and a width of 53 nm, which was consistent with previous measurements made on thin films. One advantage that this method has over static buckling measurements is the freedom from interference of plastic and viscoelastic processes.…”

Vibrational modes of GaN nanowires in the gigahertz range

“…No measurements of the vibrational modes of freestanding nanowires have been previously reported. However, several studies involving Brillouin-light-scattering (BLS) measurements have focused on the closely related subject of vibrational modes of polymeric nanolines on substrates or nanoscale membranes [30][31][32][33]. In this report, we present measurements and numerical modeling of the vibrational modes of monocrystalline hexagonal GaN nanowires at frequencies up to 40 GHz.…”

Acoustic vibrations in free‐standing single‐, bi‐layer nanomembranes and patterned wires

“…We also neglect the unlikely interaction between the low frequency acoustic modes in different soft PMMA wires, which may exist by coupling through the hard Si 3 N 4 layer. Analysis of the phonon spectra from polymeric nanolines supported on bulk silicon oxide and silicon substrates showed no significant deviations of the polymer elastic constants from its bulk values [33,34]. We hence utilized the C 11 and C 44 elastic constants of bulk PMMA in our analysis of the vibrational modes in the patterned wires.…”

“…To date there are limited BLS experiments [33,34] that can validate or test theoretical advances on the mechanics of nano-scale structures such as nano-lines and wires. Reasons for a lack of many prior experiments probing the acoustics in confined geometries can be traced to the problem of: (a) phonon isolation in mesoscopic structures, (b) requirement of a non-invasive detection method that does not perturb the dynamics of the sensors integrated within structure and (c) poor signal to noise (S/N) ratio in such miniature systems.…”