Vibrational modes of nanolines**This paper is a contribution of the National Institute of Standards and Technology and isnot subject to copyright in the United States.

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Brillouin-light-scattering spectra previously have been shown to provide information onacoustic modes of polymeric lines fabricated by nanoimprint lithography. Finite-elementmethods for modeling such modes are presented here. These methods provide atheoretical framework for determining elastic constants and dimensions of nanolinesfrom measured spectra in the low gigahertz range. To make the calculationsfeasible for future incorporation in inversion algorithms, two approximations ofthe boundary conditions are employed in the calculations: the rigidity of thenanoline/substrate interface and sinusoidal variation of displacements along thenanoline length. The accuracy of these approximations is evaluated as a functionof wavenumber and frequency. The great advantage of finite-element methodsover other methods previously employed for nanolines is the ability to model anycross-sectional geometry. Dispersion curves and displacement patterns are calculated formodes of polymethyl methacrylate nanolines with cross-sectional dimensions of65 nm × 140 nm and rectangular or semicircular tops. The vibrational displacements and dispersion curvesare qualitatively similar for the two geometries and include a series of flexural,Rayleigh-like, and Sezawa-like modes.