Field electron emission and the Fowler-Nordheim equation

Princeton University, New Jersey, USA

November 13, 2018

Consider a metallic field emitter shaped like a thin needle, at the tip of which a large electric field is applied. Electrons spring out of the metal under the influence of the field. The celebrated and widely used Fowler-Nordheim equation predicts a value for the current outside the metal. In this talk, I will show that the Fowler-Nordheim equation emerges as the long-time asymptotic solution of a Schrodinger equation with a realistic initial condition, thereby justifying the use of the Fowler Nordheim equation in real setups. I will also discuss the rate of convergence to the Fowler-Nordheim regime.

Slides

PDF:

• Jauslin_Princeton_2018b.pdf

• tarball: 18princetonB-1.0.tar.gz
• git repository: 18princetonB-git (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).

References

This presentation is based on

• [CCJL18]: Solution of the time dependent Schrodinger equation leading to Fowler-Nordheim field emission
  Ovidiu Costin, Rodica Costin, Ian Jauslin, Joel L. Lebowitz, 2018
  (published in Journal of Applied Physics, volume 124, number 213104, 2018)
  pdf, source