If the gap becomes about 1 eV, we have an insulator at zero Kelvin,
which, however, can collect some thermal energy at normal ambient
temperatures and hop across the gap into the conduction band. This creates
and electron-hole pair, both of which can conduct current. This is a
semi-conductor. When electrons in the valence band hop from atom to atom,
the collective process, where a neighbouring atom gives up an electron
which falls into the void left by the promoted electron and this
continues like a chain, is called hole conduction. These are the
intrinsic semiconductors and the electron and hole concentrations
are the same.
In Ge, Eg ~ 0.785 eV and in Si,
it is ~ 1.21 eV.
If the configuration is such that there is no gap between the valence and conduction bands, or an overlap, the electrons have plenty of near-lying available empty states at slightly higher energies and can conduct current. This is a conductor.
The band gap Eg has some temperature dependence because the inter-atomic spacing is a function of temperature due to the assymmetry of the pseudo-potential (where we try to mimic the effect of the Pauli exclusion principle by introducing artificial forces which try to prevent electrons from occupying the same state) in the crystal.