Strong field electron emission and the Fowler-Nordheim-Schottky theory

We found that the well-established Fowler-Nordheim-Schottky field emission theory needs to be revisited for strong electric fields F. The classical derivation of the electron tunneling probability through the triangular potential barrier is re-examined and specified. This probability is studied in the fields of arbitrary strength and found as a function with a maximum at some value of the field and decaying when F goes to zero and to ∞. The location and height of this maximum depend only on the ratio of the electron kinetic energy to the work function, but the maximum cannot be realized for real materials. A simple interpolation formula for all possible electric fields is given. The domain of validity of the standard Fowler-Nordheim approximation is shown to be very wide and evaluated in detail. By solving the Schroedinger equation with the help of a power series expansion of the electron wavefunction, the standard Schottky potential is shown to make the tunneling impossible. This can be fixed tentatively by replacing the image potential with a more realistic modification which eliminates its non-physical singularity. The power series method promises to find a wider application in the field emission theory.