Previous measurements of the superfluid density ρs and specific heat for 4 He have identified effects that are manifest at distances much larger than the correlation length ξ3D [1-3]. We report here new measurements of the superfluid density which are designed to explore this phenomenon further. We determine the superfluid fraction ρs/ρ from the resonance of 34 nm films of varying widths 4 ≤ W ≤ 100 µm. The films are formed across a Corbino ring separating two chambers where a thicker 268 nm film is formed. This arrangement is realized using lithography and direct Si-wafer bonding. We identify two effects in the behavior of ρs/ρ : one is hydrodynamic, for which we present an analysis; and the other, a correlation-length effect which manifests as a shift in the transition temperature Tc relative to that of a uniform 34 nm film uninfluenced by proximity effects. We find that one can collapse both ρs/ρ and the quality factor of the resonance onto universal curves by shifting Tc as ∆Tc ∼ W −ν. This new scaling is a surprising result on two counts: it involves a very large length scale W relative to the magnitude of ξ3D; and, the dependence on W is not what is expected from correlation-length finite-size scaling which would predict ∆Tc ∼ W −1/ν .

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Measurements of the heat capacity and superfluid fraction of confined (4)He have been performed near the lambda transition using lithographically patterned and bonded silicon wafers. Unlike confinements in porous materials often used for these types of experiments(3), bonded wafers provide predesigned uniform spaces for confinement. The geometry of each cell is well known, which removes a large source of ambiguity in the interpretation of data. Exceptionally flat, 5 cm diameter, 375 µm thick Si wafers with about 1 µm variation over the entire wafer can be obtained commercially (from Semiconductor Processing Company, for example). Thermal oxide is grown on the wafers to define the confinement dimension in the z-direction. A pattern is then etched in the oxide using lithographic techniques so as to create a desired enclosure upon bonding. A hole is drilled in one of the wafers (the top) to allow for the introduction of the liquid to be measured. The wafers are cleaned(2) in RCA solutions and then put in a microclean chamber where they are rinsed with deionized water(4). The wafers are bonded at RT and then annealed at ~1,100 °C. This forms a strong and permanent bond. This process can be used to make uniform enclosures for measuring thermal and hydrodynamic properties of confined liquids from the nanometer to the micrometer scale.