Molten polymer nanofilms subject to a large transverse thermal gradient can undergo a thermocapillary instability leading to the growth of nanopillar arrays on the cooler side. The array pitch can be estimated from the fastest growing wavelength from linear stability analysis. Here we quantify the influence of gas rarefaction on thermal conduction for cases in which the gas layer thickness above the film approaches dimensions of the molecular mean free path. For experimentally relevant parameters, rarefaction increases the pitch by as much as 65%, an important consideration for noncontact three-dimensional structure formation by thermocapillary lithography. © 2011 American Institute of Physics. ͓doi:10.1063/1.3551535͔Optical lithography has served as the backbone of the semiconductor industry for decades. Reduction in the source radiation wavelength, increase in lens numerical aperture, enhanced proximity correction algorithms, and improved phase shifting masks have led to the fabrication of structures as small as tens of nanometers. While a few methods can compete with this technological achievement, there is nonetheless emerging interest in developing alternative lithographic techniques compatible not only with silicon or other semiconducting materials but also polymers, colloids, and microstructured materials.1 This pursuit is being driven by lower estimates of manufacturing costs from a fewer processing steps as well as the possibility of noncontact patterning methods based on fluid instabilities for producing threedimensional ͑3D͒ structures in a single step. It is well known that interfacial instabilities in thin films can generate periodic deformations whose amplitude and growth are typically suppressed by gravitational leveling.2 At nanoscale dimensions, however, gravitational forces are negligible in comparison to driving forces for shaping liquid structures by modulation of interfacial stresses.3 In this limit, elongated structures become possible, paving the way for fabrication techniques based on interface sculpting. As an added bonus, fluid based techniques tend to produce ultrasmooth surfaces ideally suited to photonic applications since the final structures are obtained directly from in situ solidification of molten shapes.During the past several years, 3D structure formation in nanoscale polymer melts subject to a large thermal gradient has been reported by several groups. Three growth mechanisms have been proposed including radiation pressure from interface reflection of low frequency acoustic phonons, 4,5 image charge induced electrostatic attraction between the film and target substrate, 6 and thermocapillary flow directed toward the cooler target.7 Recent hydrodynamic studies 7,8 suggest that a thermocapillary instability is the predominant driving force and that the phenomenon is basic to any viscous nanofilm not just polymer based films. 7,8 Fluid elongations are caused by a long wavelength Bénard-Marangoni instability in the limit of zero gravity. The wavelength of the fastest growing mode...