  Motivated from the experimental observation of metal induced gap states
(MIGS) at insulator/metal interfaces by Kiguchi {\it et al.} [Phys. Rev. Lett.
{\bf 90}, 196803 (2003)], we have theoretically investigated the electronic
properties of MIGS at interfaces between various alkali halides and a metal
represented by a jellium with the first-principles density functional method.
We have found that, on top of the usual evanescent state, MIGS generally have a
long tail on halogen sites with a $p_z$-like character, whose penetration depth
($\lambda$) is as large as half the lattice constant of bulk alkali halides.
This implies that $\lambda$, while little dependent on the carrier density in
the jellium, is dominated by the lattice constant (hence by energy gap) of the
alkali halide, where $\lambda_{\rm LiF} < \lambda_{\rm LiCl} < \lambda_{\rm
LiI}$. We also propose a possibility of the MIGS working favorably for the
exciton-mediated superconductivity.
