Improved approach to Fowler-Nordheim plot analysis

This article introduces an improved approach to Fowler-Nordheim (FN) plot analysis, based on a new type of intercept correction factor. This factor is more cleanly defined than the factor previously used. General enabling theory is given that applies to any type of FN plot of data that can be fitted using a FN-type equation. Practical use is limited to emission situations where slope correction factors can be reliably predicted. By making a series of well-defined assumptions and approximations, it is shown how the general formulas reduce to provide an improved theory of orthodox FN-plot data analysis. This applies to situations where the circuit current is fully controlled by the emitter characteristics, and tunneling can be treated as taking place through a Schottky-Nordheim (SN) barrier. For orthodox emission, good working formulas make numerical evaluation of the slope correction factor and the new intercept correction factor quick and straightforward. A numerical illustration, using simulated emission data, shows how to use this improved approach to derive values for parameters in the full FN-type equation for the SN barrier. Good self-consistency is demonstrated. The general enabling formulas also pave the way for research aimed at developing analogous data-analysis procedures for non-orthodox emission situations.Comment: Paper is extended version of poster presented at the 25th International Vacuum Nanoelectronics Conference, Jeju island, South Korea, July 2012. Third version includes small changes made at proof correction stag

Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength

This technical note relates to the theory of cold field electron emission (CFE). It starts by suggesting that, to emphasize common properties in relation to CFE theory, the term 'Lauritsen plot' could be used to describe all graphical plots made with the reciprocal of barrier field (or the reciprocal of a quantity proportional to barrier field) on the horizontal axis. It then argues that Lauritsen plots related to barrier strength (G) and transmission probability (D) could play a useful role in discussion of CFE theory. Such plots would supplement conventional Fowler-Nordheim (FN) plots. All these plots would be regarded as particular types of Lauritsen plot. The Lauritsen plots of -G and lnD can be used to illustrate how basic aspects of FN tunnelling theory are influenced by the mathematical form of the tunnelling barrier. These, in turn, influence local emission current density and emission current. Illustrative applications used in this note relate to the well-known exact triangular and Schottky-Nordheim barriers, and to the Coulomb barrier (i.e., the electrostatic component of the electron potential energy barrier outside a model spherical emitter). For the Coulomb barrier, a good analytical series approximation has been found for the barrier-form correction factor; this can be used to predict the existence (and to some extent the properties) of related curvature in FN plots.Comment: Based on a poster presented at the 25th International Vacuum Nanoelectronics Conference, Jeju, S. Korea, July 2012. Version 3 incorporates small changes made at proof stag

Implementation of the orthodoxy test as a validity check on experimental field emission data

In field electron emission (FE) studies, it is important to check and analyse the quality and validity of experimental current-voltage data, which is usually plotted in one of a small number of standard forms. These include the so-called Fowler-Nordheim (FN), Millikan-Lauritsen (ML) and Murphy-Good (MG) plots. The Field Emission Orthodoxy Test is a simple quantitative test that aims to check for the reasonableness of the values of the parameter "scaled field" that can be extracted from these plots. This is done in order to establish whether characterization parameters extracted from the plot will be reliable or, alternative, likely to be spurious. This paper summarises the theory behind the orthodoxy test, for each of the plot forms, and confirms that it is easy to apply it to the newly developed MG plot. A simple web tool has been developed that extracts scaled-field values from any of these three plot forms, and tests for lack of field emission orthodoxy.Comment: 14 typescript pages, 2 figure

Numerical testing by a transfer-matrix technique of Simmons' equation for the local current density in metal-vacuum-metal junctions

We test the consistency with which Simmons' model can predict the local current density obtained for flat metal-vacuum-metal junctions. The image potential energy used in Simmons' original papers had a missing factor of 1/2. Besides this technical issue, Simmons' model relies on a mean-barrier approximation for electron transmission through the potential-energy barrier between the metals. In order to test Simmons' expression for the local current density when the correct image potential energy is included, we compare the results of this expression with those provided by a transfer-matrix technique. This technique is known to provide numerically exact solutions of Schrodinger's equation for this barrier model. We also consider the current densities provided by a numerical integration of the transmission probability obtained with the WKB approximation and Simmons' mean-barrier approximation. The comparison between these different models shows that Simmons' expression for the local current density actually provides results that are in good agreement with those provided by the transfer-matrix technique, for a range of conditions of practical interest. We show that Simmons' model provides good results in the linear and field-emission regimes of current density versus voltage plots. It loses its applicability when the top of the potential-energy barrier drops below the Fermi level of the emitting metal.Comment: Paper accepted for publication in Jordan Journal of Physic

Refusal strategies used by Jordanians and Syrian refugees in Jordan

This study investigates the use and linguistic properties of refusal strategies by Jordanians and Syrian refugees in Jordan. To achieve this objective, a Discourse Completion Test (DCT), consisting of 10 situations: three requests, three offers, two invitations, and two suggestions was used. The participants were 40 (20 male and 20 female) Jordanians and 40 (20 male and 20 female) Syrian refugees in Jordan. The mixed-method data analysis resulted in a total of 1351 refusals: 719 Jordanian refusals and 632 Syrian refugees’ refusals. The refusals were classified by semantic formulas, directness (a dimension of communication style), and frequency of semantic formulas. The results show that the two groups utilize different semantic formulas with different frequencies when making their refusals. The two groups used a different number of direct and indirect formulas. Although the two groups belong to the Arabic culture, the differences were significant. One main difference is that Jordanians’ refusals were more direct and were often expressed as negative willingness, while the Syrian refugees’ refusals were less direct, providing an explanation of their refusals. The results also indicate that gender is a significant variable where females in the two samples tended to respond with lengthy responses when making their refusals, employing at least three refusal strategies