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In this work we investigate a generalized tunneling barrier for planaremitters at zero-temperature. We present the evidence of the emergence of anon-Fowler-Nordheim-type general behavior for the field emission currentdensity in the case that the Fermi energy ($\mu$) is comparable with or smallerthat the decay width ($d_F$). Therefore, for some non-metals or materials thathave very small Fermi energy the standard Fowler-Nordheim-type theory mayrequire 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.

Emergence of a non-Fowler-Nordheim-type behavior for a general planar tunneling barrier