crease with respect to the bulk value, depending on the substrate. Recently, we have shown that the interfacial energy, γ_sl, between the substrate and the polymer is a significant parameter that governs the T_g of supported, ultrathin films (Fryer et al., 2001). The T_g of the films was characterized using local thermal analysis (a technique we developed at the University of Wisconsin [Fryer et al., 2000 ]), ellipsometry, and x-ray reflectivity. We have also demonstrated that the T_g of a 100-nm film of a model-resist resin, poly(4-hydroxystyrene) (PHS), is elevated above the bulk T_g by as much as 55°C by grafting the polymer to the substrate (Tate et al., 2001).

In the bulk, transport properties such as diffusion coefficients increase by several orders of magnitude in the narrow range of temperature over which the material undergoes a transition from a glass to a rubber (Nealey et al., 1993, 1994). Similarly, mechanical properties such as the Young’s modulus decrease by 2 to 4 orders of magnitude over this same temperature range. Although the dimension dependence of T_g is now fairly well documented, less is known about mass transport and mechanical properties of polymers that are also likely to be dimension dependent. It is difficult to interpret consistently the current literature on diffusion in supported, thin films. Several studies report that chain diffusion slows in thin films (Frank et al., 1996) while dye diffusion has been reported to increase significantly (Tseng et al., 2000). We are not aware of any published reports on dimension-dependent mechanical properties of amorphous polymers.

In most commercial applications of films and coatings, the thickness of the polymer does not approach the sub-100 nm scale, and the dimension-dependent phenomena referred to above do not affect the properties, processing, or usefulness of the materials. However, in the microelectronics industry, the largest section of the U.S. economy, dimension-dependent properties of polymer nanostructures are anticipated to pose significant challenges, particularly with sub-100 nm patterning of photoresist materials (consisting of a polymer and photo-sensitive additives) by advanced lithography. To reach critical patterning dimensions of less than 100 nm, for example, the industry may be forced to use ultrathin films of polymer photoresist in conjunction with 157 nm and extreme ultraviolet (13.4 nm) lithography, due to the opacity of organic materials at these wavelengths (Brodsky et al., 2000; Stewart et al., 2000). In these systems, resist formulations and processing conditions may have to be optimized as a function of thickness for control over the transport of small molecules (e.g., photo-generated acids in films of chemically amplified photoresists), particularly during postexposure annealing (or “bake”) (Fryer et al., 1999; Postnikov et al., 1999). The thermophysical and mass-transport properties of the films affect the sensitivity, resolution, contrast, and line-edge roughness of the photoresist. Optimization may be difficult because diffusion coefficients of probe molecules change by orders of magnitude as the temperature is varied within 15^oC of T_g.

Dimension-dependent mechanical properties may pose the greatest challenges to the lithographic process and to nanofabrication techniques in general.