Numerical simulation of field emission and tunneling: A comparison of the Wigner function and transmission coefficient approaches

• DOI: 10.1063/1.352779
• Publication Date: 2002-07-26T12:43:06Z
• Authors: K. L. Jensen; A. K. Ganguly
• Keywords: Transmission coefficient; Wigner distribution function; Airy function

Quantum transport through one-dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or Wigner distribution function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each compared (a) calculating current-field relationships field-emission potentials with silicon parameters (and current-voltage resonant tunneling diodes), (b) their ability to accommodate scattering, self-consistency, time dependence, (c) behavior of ‘‘particle trajectory’’ interpretations. In making comparisons, concern will be on method incorporated into a larger ensemble-particle Monte Carlo simulation; it argued that, in this regard, WDF approach has significant advantages. Since TC calculations rely Airy approach, detailed comparison made widely used Wentzel–Kramers–Brillouin Fowler–Nordheim approaches general problem field emission from material vacuum.