arXiv subjects

Richard G. Forbes

Publications and source records attributed to Richard G. Forbes.

41 records · Page 3Linked to original sources

arXiv2012

Development of simple quantitative test for lack of field emission orthodoxy

This paper describes a simple quantitative test applicable to current-voltage data for cold field electron emission (CFE). It can decide whether individual reported field-enhancement-factor (FEF) values are spuriously large. The paper defines an "orthodox emission situation" by a set of ideal experimental, physical and mathematical conditions, and shows how (in these conditions) operating values of scaled barrier field (f) can be extracted from Fowler-Nordheim (FN) and Millikan-Lauritsen (ML) plots. By analyzing historical CFE experiments, which are expected to nearly satisfy the orthodoxy conditions, "apparently reasonable" and "clearly unreasonable" experimental ranges for f are found. These provide a test for lack of orthodoxy. For illustration, this test is applied to 17 post-1975 CFE data sets, mainly for carbon and semiconductor nanostructures. Some extracted f-value ranges are apparently reasonable (including many carbon results), some are clearly unreasonable. It is shown that this test applies to any field-emission diode geometry and any form of FN or ML plot. It is proved mathematically that, if the extracted f-value range is "unreasonably high", then FEF-values extracted by the usual literature method are spuriously large. Probably, all new field-emitter materials should be tested in this way. Appropriate data-analysis theory needs developing for non-orthodox emitters.

cond-mat.mes-hall↗

arXiv2012

Extraction of emission parameters for large-area field emitters, using a technically complete Fowler-Nordheim-type equation

In papers on cold field electron emission from large area field emitters (LAFEs), it has become widespread practice to publish a misleading Fowler-Nordheim-type (FN-type) equation. This equation over-predicts the LAFE-average current density by a large highly-variable factor thought to usually lie between 1000 and 1000 000 000. This equation, although often referenced to FN's 1928 paper, is a simplified equation used in undergraduate teaching, does not apply unmodified to LAFEs, and does not appear in the 1928 paper. Technological LAFE papers often do not cite any theoretical work more recent than 1928, and often do not comment on the discrepancy between theory and experiment. This usage has occurred widely, in several high-profile American and UK applied-science journals, and in various other places. It does not inhibit practical LAFE development, but can give a misleading impression of potential LAFE performance to non-experts. This paper shows how the misleading equation can be replaced by a conceptually complete FN-type equation that uses three high-level correction factors. One of these, or a combination of two of them, may be useful as an additional measure of LAFE quality; this paper describes how to estimate factor values using experimental data. Suggestions are made for improved engineering practice in reporting LAFE results. Some of these should help to prevent situations arising whereby an equation appearing in high-profile applied-science journals is used to support statements that an engineering regulatory body might deem to involve professional negligence.

cond-mat.mes-hall↗

arXiv2010

Analytical treatment of cold field electron emission from a nanowall emitter

This paper presents an elementary, approximate analytical treatment of cold field electron emission (CFE) from a classical nanowall. A simple model is used to bring out some of the basic physics of a class of field emitter where quantum confinement effects exist transverse to the emitting direction. A high-level methodology is presented for developing CFE equations more general than the usual Fowler-Nordheim-type (FN-type) equations, and is applied to the classical nanowall. If the nanowall is sufficiently thin, then significant transverse-energy quantization effects occur, and affect the overall form of theoretical CFE equations; also, the tunnelling barrier shape exhibits "fall-off" in the local field value with distance from the surface. A conformal transformation technique is used to derive an analytical expression for the on-axis tunnelling probability.

cond-mat.mes-hall↗

arXiv2007

Formal derivation of an exact series expansion for the Principal Field Emission Elliptic Function v

An exact series expansion is now known for the Principal Field Emission Elliptic Function v, in terms of a complementary elliptic variable l' equal to y*y, where y is the Nordheim parameter. This expansion was originally found by using the algebraic manipulation package MAPLE. This paper presents a formal mathematical derivation. It has been discovered that v(l') is a particular solution of the ordinary differential equation (ODE) l'(1-l')d^2v/dl'^2=nv, when the index n = 3/16. This ODE appears to be new in mathematical physics and elliptic-function theory. The paper first uses an 1876 result from Cayley to establish the boundary condition that dv/dl' satisfies as l' tends to zero. It then uses the method of Frobenius to obtain two linearly independent series solutions for the ODE, and hence derives the series expansion for v(l'). It is shown that terms in ln{l'} are required in a mathematically correct solution, but fractional powers of l' are not. The form of the ODE also implies that it is mathematically impossible for simple Taylor expansion methods to generate good approximation formulae valid over the whole range 0 =< l' =< 1; this conclusion may also apply to barriers of other shapes. It is hoped that this derivation might serve as a paradigm for the treatment of other tunnelling barrier models for cold field electron emission, if in any particular case an ODE can be found for which the tunnelling-exponent correction function is a particular solution.

math-ph↗

arXiv2006

The roles of apex dipoles and field penetration in the physics of charged, field emitting, single-walled carbon nanotubes

A 1 $μ$m long, field emitting, (5,5) single-walled, carbon nanotube (SWCNT) closed with a fullerene cap, and a similar open nanotube with hydrogen-atom termination, have been simulated using the MNDO (Modified Neglect of Diatomic Overlap) quantum-mechanical method. Both contain about 80 000 atoms. It is found that field penetration and band-bending, and various forms of chemically and electrically induced apex dipole, play roles. Field penetration may help to explain electroluminescence associated with field emitting carbon nanotubes. Charge-density oscillations, induced by the hydrogen adsorption, are also found. Many of the effects can be related to known effects that occur with metallic or semiconductor field emitters; this helps both to explain the effects and to unify our knowledge about field electron emitters. However, it is currently unclear how best to treat correlation-and-exchange effects when defining the CNT emission barrier. A new form of definition for the field enhancement factor (FEF) is used. Predicted FEF values for these SWCNTs are significantly less than values predicted by simple classical formulae. The FEF for the closed SWCNT decreases with applied field; the FEF for the H-terminated open SWCNT is less than the FEF for the closed SWCNT, but increases with applied field. Physical explanations for this behavior are proposed. Curved Fowler-Nordheim plots are predicted. Overall, the predicted field emission performance of the H-terminated open SWCNT is slightly better than that of the closed SWCNT, essentially because a C-H dipole is formed that reduces the height of the tunnelling barrier. In general, the physics of a charged SWCNT seems more complex than hitherto realised.

cond-mat.mtrl-sci↗