  In this work we investigate a generalized tunneling barrier for planar
emitters at zero-temperature. We present the evidence of the emergence of a
non-Fowler-Nordheim-type general behavior for the field emission current
density in the case that the Fermi energy ($\mu$) is comparable with or smaller
that the decay width ($d_F$). Therefore, for some non-metals or materials that
have very small Fermi energy the standard Fowler-Nordheim-type theory may
require a correction. In the opposite regime, i.e., for $\mu$ much larger that
$d_F$, we confirm that the conventional theory is suitable for metals.
