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.
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.
This technical note provides a high-level overview of the present state of basic field electron emission (FE) theory, as suitable for use in the context of technological applications of FE theory. At present there is much theoretical confusion in FE literature, and a partial breakdown of the peer review system. Even in sensitive technological contexts, many papers have stated and used out-of-date theory that makes current-density predictions that are several hundred times less than those of modern FE theory. A primary aim of this note is to help reduce the confusion and error in future published FE literature. It is not intended as a detailed review of FE theory.
The theoretical foundations of quantum mechanics and de Broglie-Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of particles comply with a wave-equation. Including external potentials yields the Schrodinger equation, which, in this context, is arbitrary due to internal energy components. The uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. Aspect's experimental proof of non-locality is rejected, because these measurements imply a violation of the uncertainty relations. The paper finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.
Abstract We have already encountered several aspects of quantum theory: the presence of discrete energy levels in atoms; the exclusion principle which tells us how these levels are occupied; and the formation of energy bands in solids. We did not make a big deal of it at the time since, once we accepted the premise of the band gap in semiconductors, we were able to understand the operation of the transistor without worrying about whether we were using results of quantum theory. However, if we wish to probe further—to understand the devices of the future, those under development, and some which are already commercially available—then there is no escape. We have to confront quantum theory head on. We will not be concerned with any of the deep philosophical questions which arise from quantum theory. These are addressed in many other books, and do not concern us here. Instead, we will concentrate on the practical effects—how quantum theory affects the behaviour of semiconductor devices. From this point of view, there are two principal consequences, and we will devote a chapter to each. This chapter deals with wave-particle duality. If you have not encountered this phrase before, do not worry—all will be revealed in due course. The following chapter describes a phenomenon called tunnelling. It is only after exploring these concepts that it is possible to understand the operation of the quantum transistor, a subject which we turn to in Chapter 9.
A rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron. Since the dispersion in electron momentum is determined by the zero-point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.
With all its remarkable achievements, Quantum Mechanics as established in the fundamental papers written by Heisenberg, de Broglie, Schro¨dinger, Dirac, etc. contains some inconsistencies and internal contradictions. Quantum mechanics deals with quantum processes in which the number and the type of particles do not vary during their interaction, but only their energy and momentum states. The formalism of Quantum Mechanics is not capable of describing neither the variation of the number of particles, nor the transformation of one type of particle into another type. Even if in some cases the number of particles is allowed to change, this is somewhat forced and inconsistent. For example, Quantum Mechanics is not able to give a satisfactory explanation of the spontaneous emission, in which an electron situated on an excited energy level emits a quanta γ and decays to a lower energy level.