Tunneling happens. You want to look at the applied voltage
and the "oxide" quality & composition, to decide on a Tox.
You also may elect to tolerate some tunneling, based on
whether or not you see damage or intolerable gate current;
maybe some other reliability effect is more important in the
end.
Especially in high-K dielectrics, which are thinner and of
poorer quality, I see thing like a nitride final layer to get
the insulation. Then you're into heterogenous strangeness
as far as the physics.