Solution for space charge limited field emission current densities with injection velocity and geometric effects corrections

Y. Feng, J. P. Verboncoeur, Ming-Chieh Lin

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

When particles are injected according to the Fowler-Nordheim (FN) field emission equation, the transmitted current density will transition to the space charge limited (SCL) current density, with increasing applied diode voltage. The actual transmitted current density is the so-called SCL-FN current density. In this work, Barbour's analytic solution for the SCL-FN current density is modified with consideration of injection velocity and also geometric effects, by solving the advanced FN equation with the effective field enhancement factor, the energy conservation equation with an initial velocity term, and Poisson's equation simultaneously. The solution is also extended to the relativistic regime where similar transition process is found. This solution has been verified using particle-in-cell simulation with varying diode voltage, electron injection velocity, and field enhancement factor.

Original languageEnglish
Article number043301
JournalPhysics of Plasmas
Volume15
Issue number4
DOIs
StatePublished - 2008 May 8

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space charge
field emission
injection
current density
diodes
augmentation
conservation equations
energy conservation
electric potential
Poisson equation
cells
electrons
simulation

Cite this

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Solution for space charge limited field emission current densities with injection velocity and geometric effects corrections. / Feng, Y.; Verboncoeur, J. P.; Lin, Ming-Chieh.

In: Physics of Plasmas, Vol. 15, No. 4, 043301, 08.05.2008.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Lin, Ming-Chieh

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