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

Abstract

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 Schrödinger 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.