### 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 language | English |
---|---|

Article number | 043301 |

Journal | Physics of Plasmas |

Volume | 15 |

Issue number | 4 |

DOIs | |

State | Published - 2008 May 8 |

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*Physics of Plasmas*,

*15*(4), [043301]. https://doi.org/10.1063/1.2907365

}

*Physics of Plasmas*, vol. 15, no. 4, 043301. https://doi.org/10.1063/1.2907365

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solution for space charge limited field emission current densities with injection velocity and geometric effects corrections

AU - Feng, Y.

AU - Verboncoeur, J. P.

AU - Lin, Ming-Chieh

PY - 2008/5/8

Y1 - 2008/5/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=42949095514&partnerID=8YFLogxK

U2 - 10.1063/1.2907365

DO - 10.1063/1.2907365

M3 - Article

AN - SCOPUS:42949095514

VL - 15

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 4

M1 - 043301

ER -