We report calculations of the electronic structure of silicene and the
stability of its weakly buckled honeycomb lattice in an external electric field
oriented perpendicular to the monolayer of Si atoms. We find that the electric
field produces a tunable band gap in the Dirac-type electronic spectrum, the
gap being suppressed by a factor of about eight by the high polarizability of
the system. At low electric fields, the interplay between this tunable band
gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele
spin-orbit coupling induces a transition from a topological to a band
insulator, whereas at much higher electric fields silicene becomes a semimetal