Time-evolution of electron emission from a metal surface

Mathematical Physics at the Crossings, VirginiaTech, Virginia, USA

May 24, 2019

The electrons in a metal can be extracted from the metal by a variety of processes: for instance by applying a strong electric field (field emission), or shining an intense laser pulse (photoemission). In the case of field emission, the celebrated and widely used Fowler-Nordheim equation predicts a value for the current of electrons 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. As for photoemission, the expression for the current has been predicted by Faisal et al, and I will discuss ongoing work to show that this prediction emerges as the long-time asymptotic solution of a Schrodinger equation. In both cases, I will discuss the time scale of the convergence.

Slides

PDF:

• Jauslin_Hagedornfest_2019.pdf

• tarball: 19hf-1.0.tar.gz
• git repository: 19hf-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