  In this paper we present a new family of solutions to the singularly
perturbed Allen-Cahn equation $\alpha^2 \Delta u + u(1-u^2)=0, \quad \hbox{in
}\Omega\subset \R^N $ where $N=3$, $\Omega$ is a smooth bounded domain and
$\A>0$ is a small parameter. We provide asymptotic behavior which shows that,
as $\alpha \to 0$, the level sets of the solutions collapse onto a bounded
portion of a complete embedded minimal surface with finite total curvature that
intersects orthogonally $\partial \Omega$ of the domain and that is
non-degenerate respect to $\Omega$. We provide explicit examples of surfaces to
which our result applies.
