Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Dall’Agnol, Fernando F.; Assis, Thiago A. de; Forbes, Richard G.

doi:10.1088/1361-648x/aad84c

Cited by 20 publications

(14 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For the lateral boundary, the origin of the power-law exponent 3 can be understood by considering a small angular element of the circular mirror-dipole. This acts as in the same way as the distant dipole in the two-post-likeemitter situations analysed in Refs [69,70]. The apexfield reduction for the chosen emitter shape is related to the value of the depolarizing field at point "b" due to the mirror-dipole; for sufficiently large values of box-radius A, this depolarising dipole-field falls off as (A −3 ).…”

Section: A Hemisphere-on-plane (Hsp) Emittersmentioning

confidence: 85%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

View full text Add to dashboard Cite

This review of the quantitative electrostatics of field emitters, covering analytical, numerical and "fitted formula" approaches, is thought the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is "polarity independent", so that the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors-which exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant that the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant of this that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many "related considerations" that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

show abstract

Section: A Hemisphere-on-plane (Hsp) Emittersmentioning

confidence: 85%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In such configurations, the protrusions proximity induces electrostatic screening. This simple, well documented phenomenon [Dall'Agnol et al 2018] -also named mutual depolarization [Forbes 2016] -reduces overall the field enhancement capability of the protrusions and consequently the local electric field around the apex. This effect is here quantified by the relative loss of the apex electric field δ a :…”

Section: Phenomenology Of Interactions In 3dmentioning

confidence: 99%

Thermal effects in field electron emission from idealized arrangements of independent and interacting micro-protrusions

Mofakhami¹,

Seznec²,

Minea³

et al. 2021

J. Phys. D: Appl. Phys.

View full text Add to dashboard Cite

Modeling studies of thermo-field electron emission (TFE) from protrusions at a cathode surface usually use simulations in 2D axial symmetry. Indeed, time-dependent simulations in 3D are very demanding in computation time. Often, 3D simulations have been restricted to stationary pure field electron emission to account for the drastic current decrease caused by electric field screening when the emitters are close. Little interest has therefore been granted to the heat exchanges occurring between nearby emitters. Although the temperature is a second order parameter in TFE compared to the electric field, thermal effects become non-negligible in high current density regimes, where self-heating is well established. The present study focuses on the thermal effects occurring during the TFE from micro-protrusions. Our model considers a DC voltage, but solves in time the temperature evolution coupling the heat equation and the current continuity equation. The protrusions are modelled as hemiellipsoids with 2D axial symmetry. Emission enhancement due to the increase of the temperature in the thermo-field regime compared to the pure field regime is detailed as a test case for isolated protrusions. Then, full 3D simulations are used to investigate the thermal coupling between multiple neighbouring protrusions via their outwards heat fluxes inside the cathode. The results show a higher current increase due to thermal coupling for dome-like protrusions with low field enhancement factor. The current increases up to 13% of the total current for aspect ratios of 1 but this value is reached for an extreme applied electric field, hardly reachable in experiments. For sharper protrusions with higher field enhancement, the interaction range through the cathode being shorter, the thermal coupling is suppressed by electrostatic screening. Nevertheless, in arrangements of densely distributed field emitter, when the screening is compensated by a higher voltage, our model predicts the possibility of a moderate but noticeable thermal coupling even for sharp protrusions: a parametric study indicates up to 14.5% of the emitted current being caused by a thermal coupling through the cathode bulk, for protrusions with an aspect ratio of 10 under a fixed applied electric field of 0.4 GV/m in DC mode.

show abstract

“…Это поле в общем случае связано с приложенным напряжением через размерный коэффициент усиления поля α e f f : F = α e f f U. В плоскопараллельной геометрии электродов, когда силовые линии поля параллельны друг другу, а высоты неоднородностей много меньше расстояния между электродами d s e p , используется соотношение γ e f f = α e f f d s e p . В реальности же коэффициент усиления поля определяется формой эмиттера и имеет неравномерное распределение по поверхности [15]. Как было показано в [10], понятие площади эмиссии имеет несколько видов теоретического определения и также зависит от формы эмиттера.…”

unclassified

Тест На Соответствие Режиму Холодной Полевой Эмиссии С Применением Приближений Элинсона-Шредника И Форбса-Дина (Координаты Мерфи-Гуда)

Попов¹,

Колосько²,

Филиппов³

2020

Письма В Журнал Технической Физики

View full text Add to dashboard Cite

A test is described in the paper, which allows one to determine the correspondence of experimental data to the classical field dependence. The test is presented in two versions: using the Elinson-Shrednik approximation to the current-voltage characteristics in the classical Fowler-Nordheim coordinates, as well as the modern Forbes-Deane approximation with modified Murphy-Good plot. The application of the test is shown by the example of a study of a multi-tip emitter based on carbon nanotubes. The technique of online calculation of the effective parameters of the emitter and the test is presented.

show abstract

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Cited by 20 publications

References 13 publications

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Thermal effects in field electron emission from idealized arrangements of independent and interacting micro-protrusions

Тест На Соответствие Режиму Холодной Полевой Эмиссии С Применением Приближений Элинсона-Шредника И Форбса-Дина (Координаты Мерфи-Гуда)

Contact Info

Product

Resources

About