  Conductivity of quantized multilayer metal films is analyzed with an emphasis
on scattering by rough interlayer interfaces. Three different types of quantum
size effect (QSE) in conductivity are predicted. Two of these QSE are similar
to those in films with scattering by rough walls. The third type of QSE is
unique and is observed only for certain positions of the interface. The
corresponding peaks in conductivity are very narrow and high with a finite
cutoff which is due only to some other scattering mechanism or the smearing of
the interface. There are two classes of these geometric resonances. Some of the
resonance positions of the interface are universal and do not depend on the
strength of the interface potential while the others are sensitive to this
potential. This geometric QSE gradually disappears with an increase in the
width of the interlayer potential barrier.
