Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Vibrational modes of nanolines

Published

Author(s)

Paul R. Heyliger, Colm Flannery, Ward L. Johnson

Abstract

Brillouin-light-scattering spectra previously have been shown to provide information on acoustic modes of polymeric lines fabricated by nanoimprint lithography. Finite-element methods for modeling such modes are presented here. These methods provide a theoretical framework for determining elastic constants and dimensions of nanolines from measured spectra in the low gigahertz range. To make the calculations feasible for future incorporation in inversion algorithms, two approximations of the boundary conditions are employed in the calculations, including rigidity of the nanoline/substrate interface and sinusoidal variation of displacements along the nanoline length. The accuracy of these approximations is evaluated as a function of wave number and frequency. The great advantage of finite-element methods over other methods previously employed for nanolines is the ability to model any cross-sectional geometry. Dispersion curves and displacement patterns are calculated for modes of polymethyl methacrylate nanolines with cross-sectional dimensions of 65 nm x 140 nm and rectangular or circular tops. The vibrational displacements and dispersion curves are qualitatively similar for the two geometries and include a series of flexural, Rayleigh-like, and Sezawa-like modes
Citation
Nanotechnology
Volume
19

Keywords

acoustics, Brillouin light scattering, finite-element models, nanoimprint lithography, nanolines, polymers, surface waves, vibrational modes, wave guides

Citation

Heyliger, P. , Flannery, C. and Johnson, W. (2008), Vibrational modes of nanolines, Nanotechnology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50582 (Accessed May 30, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created March 4, 2008, Updated October 12, 2021