Theory of electron emission in high fields from atomically sharp emitters: Validity of the Fowler-Nordheim equation

Field emission from metallic emitters is generally described by the Fowler-Nordheim [F-N] theory, which is based on a planar model of the tip with a classical image correction. Within the free electron model and the WKB approximation, the planar tip model leads to the well-known Fowler-Nordheim equation, which predicts that a plot of log J/F² versus 1/F, where J is the current density and F, the field, should be a straight line within the narrow range of field strengths of typical field emission experiments, 3 - 5V/nm. This has been experimentally confirmed for conventional emitters, (i.e., electrolytically etched tips with radii 50 nm). Field emitters fabricated with today's new techniques are much sharper with radii of curvature of the order of nm's or even the size of a single atom. Hence, the local geometry of the tip may become an important factor in the electron emission process. To investigate the effects of the shape and/or size on emission, the authors, in a recent series of papers, studied the dependence of the current-voltage characteristics on the local geometry of pointed emitters. It was found that the calculated results, plotted as log J/V² vs. 1/V, do not exhibit the straight line behavior predicted by the Fowler-Nordheim theory. In addition, there is a dramatic increase in the tunneling current for a fixed external bias, V, relative to the Fowler-Nordheim result for a planar model of the tip with the same bias voltage. Using the exact current integral additional results have been obtained exhibiting the effects of emitter curvature on field electron energy distributions and on electron emission in high fields and temperatures. These results continue to differ with the predictions of the Fowler-Nordheim equation for the same emitter models. Therefore, the adequacy of a β-factor in the conventional planar model Fowler-Nordheim equation to account for emitter curvature is examined. It is demonstrated that even a β-modified Fowler-Nordheim equation is not valid when applied to sharp emitters (r_t 10nm) and will lead to spurious results when extracting information such as work function, field values or emitting area from experimental F-N curves. The explanation for this is discussed, and an approximate analytic expression for the J(V) characteristics of a prototype sharp emitter is derived which exhibits explicitly the dependence of the current density on field, tip geometry andmaterial parameters.     

Repeat sampling of extreme observations: regression to the mean revisited

The phenomenon of classical regression to the mean was described by Sir Francis Galton in a series of prestigious works in the 19th century. This phenomenon refers to the fact that, in the presence of measurement error, experimental units which give rise to extreme values upon first sampling typically produce less extreme values upon a second independent (or repeat) sampling. This shift from the tails toward the population mean occurs even though there has been no intervention or change in the underlying population or error distributions. The mathematical ideas used to explain this shift typically appeal to correlation arguments and the classical Gaussian model. In this paper we study repeat sampling effects in the tails of arbitrary distributions. Perhaps surprisingly, we are able to show that there are actually three distinct asymptotic repeat sampling effects, of which only one corresponds to Galton’s classical result. These three effects depend on the heaviness of the population tails. In particular, for population distributions with relatively heavy tails the maximum shift occurs in the interior of the distribution. In this case the classical regression effect of Galton actually disappears out in the tails.     

The structure of chaetoglobosin K.

The structure of chaetoglobosin K, a toxic metabolite from Diplodia macrospora, has been determined by single crystal X-ray analysis.     

A review of the theoretical and experimental analyses of electron spin polarization in ferromagnetic transition metals: I. Field emission,photoemission, magneto-optic Kerr effect and tunneling

Until recently studies of solid surfaces have used exclusively photons, atoms, ions, and unpolarized electrons as experimental probes. However, in the last few years polarized electron beams have been used to investigate the electronic and atomic properties of the bulk and surfaces of solids. This has resulted in the development and application of a number of different experimental techniques sensitive to the electron spin polarization (ESP). The experimental results have often been less than definitive and frequently conflicting. For example, the observation of ESP from the ferromagnetic metals by photoemission, field emission, and tunneling experiments lead to contradictory conclusions concerning the validity of the Stoner-Wohl-farth-Slater (SWS) band theory of ferromagnetism. Additional complication of this problem has been introduced by recent magneto-optical Kerr-effect measurements which tend to support the ESP predicted by SWS theory.In this review we present a critical analysis of these experiments and their theoretical interpretation. It is shown that the results of these experiments do not necessarily contradict each other nor any of the current one-electron theories of itinerant ferromagnetism. It is further shown how, based on the use of over-simplified models to describe the physical processes involved in the experiments, the opposite conclusion can be reached. Based on the analyses in this paper, improvements in the theoretical models are suggested. We also discuss, from a theoretical point of view, the relative advantages and the limitations of the different experimental techniques using ESP to probe the electronic and magnetic structures of solids and surfaces.A fundamental objective of this and the following paper is to help develop a theory of spinpolarized electron emission and tunneling phenomena which will provide the basis for a systematic ESP spectroscopy of surfaces, interfaces, and thin films. This has prompted a reexamination of the ferromagnetism of 3d-transition metals and of their surfaces. The present work leads to some observations concerning the current interpretation of itinerant ferromagnetism and possible refinements of the SWS theory to produce better agreement with the ESP sensitive experiments.     

The valence of thallium ions in liquid Tl2Te and Tl2Se

The valence of thallium ions in excess of the stoichiometric compositions of the liquid alloys Tl₂Te and Tl₂Se has been determined in past work by comparing the electrical properties with the results of doping with various third metals. We examine the pertinent equations and show that errors have occured in the original work on both of these systems. The thallium ions have a valence of one rather than three.     

The multiple-image interactions and the mean-barrier approximation in MOM and MVM tunneling junctions

The effect of the multiple image interactions on theI–V characteristics and the reliability of the mean barrier approximation in calculating the current in MOM and MVM tunneling junctions are critically examined. It is demonstrated that the continued use of the uncorrected form of Simmons' original multiple-image force interaction in the analysis of tunneling junctions can lead to serious errors in both the current and the dynamic resistance. An extensive numerical analysis of planar junctions including the image potential suggests that the basic mean barrier approximation formulated by Simmons is essentially a thick barrier approximation. It also is shown that the conventional mean barrier approximation is a relatively poor approximation for the tunneling barriers of interest, and that it is not possible to establish a reliable a priori estimate of its range of validity.This research was supported in part by the NATO Research Grants Program, Grant No. 1902, Scientific Affairs Division, Brussels, Belgium