  The Fowler-Nordheim tunneling current formula has been widely used in the
design of devices based on metal/insulator (metal/semiconductor)
heterojunctions with triangle potential barriers, such as the flash memory.
Here we adopt the model that was used to derive the Landauer formula at finite
temperature, the nearly-free electron approximation to describe the electronic
states in semi-infinite metal electrode and the Wentzel-Kramers-Brillouin (WKB)
approximation to describe the transmission coefficient, and derive a tunneling
current formula for metal/insulator heterojunctions under large bias and
electric field. In contrast to the Fowler-Nordheim formula which is the limit
at zero temperature, our formula is generalized to the finite temperature (with
the thermal excitation of electrons in metal electrode considered) and the
potential barriers beyond triangle ones, which may be used for the design of
more complicated heterojunction devices based on the carrier tunneling.
