Elastodynamic Characterization of Imprinted Nanolines

Abstract

The advancement of imprint lithography as a method for fabricating nanostructures is impeded by a lack of effective tools for characterizing mechanical properties and geometry at the nanoscale. This paper describes progress in establishing methods for determining elastic moduli and cross sectional dimensions of imprinted nanolines from Brillouin light scattering (BLS) measurements using finite-element (FE) and Farnell-Adler models for the vibrational modes. An array of parallel nanoimprinted lines of polymethyl methacrylate (PMMA) with widths of ~65 nm and heights of ~140 nm served as a model specimen. Several acoustic modes were observed with BLS in the low-gigahertz frequency range, and the forms of the vibrational displacements were identified through correlation with calculations using measured bulk-PMMA moduli and density as input. The acoustic modes include several flexural, Rayleigh-like, and Sezawa-like modes. Fitting of Farnell-Adler calculations to the measured dispersion curves was explored as a means of extracting elastic moduli and nanoline dimensions from the data. Some of the values obtained from this inversion analysis were unrealistic, which suggests that geometric approximations in the model introduce significant systematic errors. In forward calculations, the frequencies determined with the FE method were found to more closely match experimental values, which suggests that this method may be more accurate for inversion analysis. Initial estimates of uncertainties in the FE calculations support this conclusion.

Vibrational modes of nanolines

“…Hartschuh et al [5] and Johnson et al [8] presented Farnell-Adler calculations for Rayleigh-like and Sezawa-like modes that neglect the finite widths of nanolines, approximating them as blanket films with a thickness equal to the height of the nanolines. Despite the crudeness of this approximation, the frequencies from such calculations were found by these authors to be fairly close to frequencies measured with BLS, at least for the geometries considered, and the correspondence with measurements provided insight into the general form of the strain fields of the modes.…”

“…Inversion analysis of BLS spectra from imprinted polymethyl methacrylate (PMMA) nanolines was pursued by Johnson et al [8] using Farnell-Adler models, including an approximate correction for the effect of finite nanoline height on the flexural frequencies. The elastic constants and nanoline dimensions determined from this analysis were found to be physically unrealistic, presumably because of inaccuracies arising from the approximation of a blanket film in the models for the Rayleigh-like and Sezawa-like modes.…”

“…In neither the work of Hartschuh et al [5] nor that of Johnson et al [8] were the employed FE or Farnell-Adler methods described in any detail. The nonrectangular geometry of the actual nanolines and the domain of validity of approximations incorporated in the calculations were not considered.…”

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

“…Inversion analysis of BLS spectra from imprinted poly(methyl methacrylate) (PMMA) nanolines was pursued by Johnson et al [8] using Farnell-Adler models. One conclusion of that work was that relatively poor fitting of the calculations to the BLS data can be attributed to inaccuracy of the gross approximation of a blanket film in the Farnell-Adler models for the Rayleigh-like and Sezawa-like modes of the nanolines.…”

“…For example, very different dimensional and stiffness parameters were extracted from fits with and without the Sezawa-like mode included. Johnson et al [8] suggested that FE methods could overcome this problem to provide more accurate nanoline parameters.…”