An exact tunneling model and its application to transmission and reflection delay times
Abstract
Electron emission into a nanogap is not instantaneous, which presents a difficulty in simulating ultra-fast behavior using particle models. A method of approximating the transmission and reflection delay (TARD) times of a wave packet interacting with barriers described by a delta function, a metal–insulator–metal (MIM, rectangular) barrier, and a Fowler Nordheim (FN, triangular) barrier is given and has application to simulation. It is based on the superposition of a finite number of exact basis states obtained from Schrödinger’s equation, analogous to how quantum carpets are simulated. As a result, it can exactly and uniquely follow exponentially small tunneling currents. A Bohm-like trajectory is obtained from the time evolution of the density: it shows delay in both the transmitted and reflected packets that can be simply evaluated. The relations to prior studies of the analytic [Formula: see text]-function barrier and the Wigner distribution function (WDF) methods are described. A comparison of the TARD times is contrasted to alternate times in the Büttiker–Landauer (BL) and McColl–Hartman (MH) times; the MH approach is further reformulated explicitly in terms of Gamow factors to consider how the McColl–Hartman effect is to be related, particularly in the case of the FN barrier of field emission.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 28, 2022
- Source ID
- 10.1063/5.0096568
Entities
People
- D. Shiffler
- Jeanne Riga
- Joel Lebowitz
- Kevin L. Jensen
- Rebecca Seviour
Organizations
- Air Force Office of Scientific Research
- Air Force Research Laboratory
- Rutgers University
- United States Naval Research Laboratory
- University of Huddersfield