  We discuss ultra-cold Fermi gases in two dimensions, which could be realized
in a strongly confining one-dimensional optical lattice. We obtain the
temperature versus effective interaction phase diagram for an s-wave superfluid
and show that, below a certain critical temperature T_c, spontaneous
vortex-antivortex pairs appear for all coupling strengths. In addition, we show
that the evolution from weak to strong coupling is smooth, and that the system
forms a square vortex-antivortex lattice at a lower critical temperature T_M.
