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That would want some more details on just how far below
VTH. In weak inversion, it's still inversion and channel
carriers will be source species. In depletion you may still
see some state- or trap-hopping / tunneling transport.
But I question altogether the validity of saying a FET
will be biased by an arbitrary current and an unknown
(other than very crudely) Vgs.
Now if Vgs "<<" VTH, I'd say the channel is gone and
surface will be near body doping (or even accumulated)
and carriers would then be holes, but there's a continuuum
there. Holes, to nothing but traps, to electrons as the
Vgs goes from below to above.
BJTs' operation involves both electrons and holes, s. here.
... most of the BJT collector current is due to the flow of charges injected from a high-concentration emitter into the base where they are minority carriers that diffuse toward the collector, and so BJTs are classified as minority-carrier devices.