  The electrical resistivity of a pure sample of a thin metallic film is found
to depend on the boundary conditions. This conclusion is supported by a
free-electron model calculation and confirmed by an ab initio relativistic
Korringa-Kohn-Rostoker computation. The low-temperature resistivity is found to
be zero for a free-standing film (reflecting boundary conditions) but nonzero
when the film is sandwiched between two semi-infinite samples of the same
material (outgoing boundary conditions). In the latter case, this resistivity
scales inversely with the number of monolayers and is due to the background
diffusive scattering by a finite lattice.
