Behavior of 4He near Tλ in films of infinite and finite lateral extent

We report studies of a He-4 film confined between two silicon wafers separated by 3189 A. The film is connected to a bulk helium reservoir via small channels 100 Angstrom high, 8 mum wide by 2000 mum long. This cell design has allowed us to study the heat capacity in a planar confinement (a film of infinity lateral size), and the superfluid density in the connecting channels (a film of finite lateral size). This work is relevant to finite-size scaling of the specific heat for 2D confinement and it is compared with earlier data. It is also relevant to finite-size 2D behavior for the superfluid density which is related to the recent theory of Sobnack and Kusmartsev. Analysis of the data is presented as well as a discussion of future cell designs to address, in particular, the behavior of laterally confined films.