Field emission tunnelling as a window onto fundamental issues in quantum mechanics

TL;DR

This work uses field electron emission and field ionization as a testing ground for deep foundational questions in quantum mechanics, challenging the conventional point-electron picture and the standard wave-function interpretation. It advocates a matter-distribution viewpoint by introducing an ISQ unit $n_1$ and redefining the wave-function as a concentration of electron matter, while distinguishing matter-distribution and pathway-choice utilisations of quantum mathematics. The analysis highlights the limitations of both tunnelling-integral and overlap-integral transmission theories and discusses implications for field-emission microscopy, quantum imaging, and potential biological relevance, arguing for more accurate theories of quantum transmission and near-surface interactions. The paper also outlines concrete proposals and unresolved issues, prioritizing time-irreversibility, alternative physical principles, and improved atomic-scale ESFI modeling as path to progress.

Abstract

Field electron emission (FE) and electrostatic field ionization (ESFI) are quantum-mechanical tunnelling processes that provide basic theory for important technologies. However, the basic theories of FE and ESF1 are not yet completely understood. This paper attempts to identify related fundamental quantum mechanical issues, problems and relevances. The following topics have been identified as deserving closer investigation or discussion. (a) The implication that if a "real electron" cannot have negative kinetic energy, then this necessarily implies that a "real electron" is a distributed object rather than a point object. (b) The implication that the language we use to discuss quantum mechanics needs to be changed in order to avoid referring to the "position of a (point) electron". (c) The idea that "quantum mathematics" (i.e., the mathematics of quantum mechanics) has different utilisations, namely the "matter distribution" and "pathway choice" utilisations, with "measurement" being observed pathway choice. (d) Difficulties with the present formulations of the uncertainty principle and wave-particle duality. (e) Fundamental difficulties in the exact calculation of exchange-and-correlation effects in both FE and ESFI theory. (f) Conceptual problems associated with "seeing electrons" in the field electron (emission) microscope. (g) Field emission tunnelling and the arrow of time. (h) The choice between tunnelling-integral and overlap-integral formulations of tunnelling theory, and the apparent incompleteness of both types of formulation.

Figures (4)

• Figure 1: (a) Field electron micrograph showing electron bonds associated with a five-membered carbon ring at the apex of a carbon nanotube. (b) Enlarged version of the central ring, with carbon nucleus separation marked. (Adapted from Fig. 2(a) in Ref. C1.) Micrographs were taken at room temperature. Approximate magnification is of order $10^8$. Copyright (2000) The Japan Society of Applied Physics.
• Figure 2: To illustrate schematically that an electron approaching a potential-energy barrier has a choice of two pathways: (1) transmission; or (2) reflection.
• Figure 3: Part of helium-ion image of tungsten emitter, taken near 80 K. A small W(111) crystal facet visible in the figure is circled. In the bottom atom-row, the corner atoms are imaged more brightly than the edge atom or the interior atom. (Adapted from Fig. A:31c in Vol. II of Ref. C33.)
• Figure 4: Schematic diagram illustrating the modelling of electron electrostatic potential energy (EESPE) variations at a charged surface. (a) Fitting of a straight-line equivalent-barrier to the EESPE section through a surface-atom nucleus. (b) Straight-line equivalent barriers for an edge atom (broken line) and for a corner atom (full line). The extra positive charge (actually reduced electron charge) at the corner site means that the ES field is higher there and the critical surface is further out.