Elastic Moduli of Ultrathin Amorphous Polymer Films

The elastic moduli of ultrathin poly(styrene) (PS) and poly(methylmethacrylate) (PMMA) films of thickness ranging from 200 nm to 5 nm were investigated using a buckling-based metrology. Below 40 nm, the apparent modulus of the PS and PMMA films decreases dramatically, with an order of magnitude decrease compared to bulk values for the thinnest films measured. We can account for the observed decrease in apparent modulus by applying a composite model based on the film having a surface layer with a reduced modulus and of finite thickness. The observed decrease in the apparent modulus highlights issues in mechanical stability and robustness of sub-40 nm polymer films and features. Introduction. There are numerous technological drivers for the use of thin (sub-1 μm) and ultrathin (sub-100 nm) polymer films and features. The stability and reliability of these confined polymer systems are critical to numerous existing and emerging technologies such as next-generation lithography, lubricating coatings, sensors, and organic electronics. It is widely accepted that the physical properties of thin polymer films can deviate substantially from their bulk counterparts.1,2 However, most experimental studies have focused on elucidating the thickness dependence of the thermal properties in thin polymer films, specifically the glass transition temperature (Tg), as a function of interfacial interactions and molecular entanglements, often with conflicting results.1 From a nanomanufacturing perspective, a direct measure of the mechanical robustness (e.g., response to deformation) of confined polymers films would be extremely helpful to determine whether the mechanical properties display similar deviations from bulk response. For example, it has been shown that the lack of mechanical strength in polymer nanostructures leads to deformation and subsequent collapse of the structures when subjected to capillary forces induced during solvent evaporation.3 While a number of experimental methods are available for measuring the mechanical properties of thin polymer films, including methods based on indentation,4,5 surface acoustic waves,6 and beam curvature,7 adapting these measurement techniques to ultrathin polymer films remains challenging. To completely understand how confinement affects the mechanical properties and response of polymeric materials, it is critical that a range of experimental and theoretical methods for measuring the mechanical properties of ultrathin films as a function of film thickness be made available. Recent molecular dynamics simulations of deformation in polymer nanostructures suggest that the elastic modulus of these structures remains bulklike for thicknesses down to ≈40 nm.8 Below this critical threshold, the simulations predict that the apparent elastic modulus decays dramatically from bulk value as the thickness is decreased further, reaching 10% of the bulk value for a thickness of ≈7.5 nm. Similar results were obtained using strain-fluctuation simulations,9 which circumvent the necessity that continuum mechanics still be valid at such small length scales. It was also concluded that the elastic constants become anisotropic in polymer nanostructures. Furthermore, recent nonequilibrium simulations10 demonstrate that local dynamic mechanical properties of polymer thin films decrease due to the presence of mechanically soft layers near the free surface of the film. These results are consistent with previous molecular dynamics simulations of the free surface in glassy polymer films, where a 1.5 nm thick region of enhanced mobility was observed.11 There are also recent examples in the literature of experimental methods for measuring the mechanical properties of thin and ultrathin polymer films,5,12,13 the most prevalent being Brillouin light scattering (BLS). BLS has been used to measure the elastic constants of both supported14,15 and free-standing16 polymer films and features with thicknesses from 375 nm down to 29 nm, and it was observed that the high-frequency mechanical properties did not significantly change at these dimensions. Probing thinner free-standing films with BLS becomes difficult due to sample preparation and handing issues, while BLS measurements on thinner supported films are complicated by the presence of the substrate interface. To overcome this issue, a multilayer geometry was employed to generate alternating interfaces between mechanically dissimilar materials, poly(styrene) and poly(isoprene).17 BLS results from this geometry indicate no deviation in the mechanical properties of either material down to layer thicknesses of at least 16 nm. However, there are no free interfaces in such a multilayer geometry; thus, any enhanced mobility at the air interface is negated. In contrast, wafer curvature experiments have been used to measure the low-frequency mechanical properties of supported ultrathin polymer films.7 From these experiments, it was suggested that the biaxial modulus of a 10 nm poly(styrene) film decreases by an order of magnitude from the bulk value. Direct measurements of the mechanical properties of supported thin polymer films using contact techniques such as indentation and atomic force microscopy are convoluted by the presence of the stiff substrate and thus are prohibitively difficult to perform at this time. * Corresponding author: Fax +1 (301) 975-4924; e-mail chris.stafford@ nist.gov. † National Institute of Standards and Technology. ‡ University of Texas. § Present address: Sensor Physics Department, Schlumberger-Doll Research, Ridgefield, CT 06877. ⊥ Present address: Assembly Technology Development, Intel Corporation, Chandler, AZ 85226. 5095 Macromolecules 2006, 39, 5095-5099 10.1021/ma060790i CCC: $33.50 © 2006 American Chemical Society Published on Web 06/28/2006 In this Article, we illustrate a distinctive approach for measuring the mechanical properties of thin and ultrathin polymer films. We apply our recently reported buckling-based metrology18 to measure the elastic properties of polymer films with thicknesses ranging from 200 to 5 nm. Here, a polymer film is adhered to a relatively soft elastic substrate and subjected to a small uniaxial compressive strain. From an energetic point of view, there are three competing terms associated with this geometry: membrane strain energy in the film, bending energy of the film, and near-surface strain energy in the substrate. Long wavelengths are suppressed due to the large strain energy associated with deformation of the soft substrate; short wavelengths are suppressed due to the sizable bending energy associated with the stiff film. Thus, the system undergoes periodic buckling with an intermediate wavelength to minimize the total strain energy. For an elastic film on an elastic substrate, the equilibrium wavelength, λe, of buckling is given by19-21 where hf is the film thickness, Eh ) E/(1 ν2) is the planestrain modulus, E is Young’s modulus, and ν is Poisson’s ratio. The subscripts f and s denote film and substrate, respectively. Equation 1 can be rearranged to solve for the modulus of the