  The SIS structure---a thin superconducting film on a bulk superconductor
separated by a thin insulating film---was propsed as a method to protect
alternative SRF materials from flux penetration by enhancing the first critical
field $B_{c1}$. In this work, we show that in fact $B_{c1}$ = 0 for a SIS
structure. We calculate the superheating field $B_{sh}$, and we show that it
can be enhanced slightly using the SIS structure, but only for a small range of
film thicknesses and only if the film and the bulk are different materials. We
also show that using a multilayer instead of a single thick layer is
detrimental, as this decreases $B_{sh}$ of the film. We calculate the
dissipation due to vortex penetration above the $B_{sh}$ of the film, and find
that it is unmanageable for SRF applications. However, we find that if a
gradient in the phase of the order parameter is introduced, SIS structures may
be able to shield large DC and low frequency fields. We argue that the SIS
structure is not beneficial for SRF cavities, but due to recent experiments
showing low-surface-resistance performance above $B_{c1}$ in cavities made of
superconductors with small coherence lengths, we argue that enhancement of
$B_{c1}$ is not necessary, and that bulk films of alternative materials show
great promise.
