Experimental study of vacuum diodes under partial space-charge regime

Gonçalves, J.A.N.; Barroso, Joaquim J.; Sandonato, G. M.

doi:10.1016/j.diamond.2003.08.021

Cited by 6 publications

(8 citation statements)

References 10 publications

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“…This is the dimensionless equation derived by Gonçales et al 33 Eqs. ͑23͒-͑26͒ are most useful in so-called "partial space-charge conditions."…”

Section: ͑24͒mentioning

confidence: 99%

“…This differs from other reported dimensionless FE-VSC equations. 7,8,15,26,30,33 Equations ͑14a͒ and ͑14b͒ have an exact solution for the field reduction factor in terms of the FEVSC "strength" ͑see definitions below͒. The main empirical parameters involved ͑V , F P , F L , J P , and J L below͒ have definitions that make them positive for both positive and negative particle emissions.…”

Section: Introductionmentioning

confidence: 99%

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Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

Forbes

2008

Journal of Applied Physics

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This paper reports ͑a͒ a simple dimensionless equation relating to field-emitted vacuum space charge ͑FEVSC͒ in parallel-plane geometry, namely 9 2 2 −3 −4 +3=0, where is the FEVSC "strength" and is the reduction in emitter surface field ͑ = field-with/field-without FEVSC͒, and ͑b͒ the formula j =9 2 / 4, where j is the ratio of emitted current density J P to that predicted by Child's law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between J P and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler-Nordheim plots, a "turn-over" effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting on the basis of Monte Carlo calculations might yield formulae adequate for real situations.

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“…This is the dimensionless equation derived by Gonçales et al 33 Eqs. ͑23͒-͑26͒ are most useful in so-called "partial space-charge conditions."…”

Section: ͑24͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

Forbes

2008

Journal of Applied Physics

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“…In many cases the current is source limited rather than space charge limited, e.g., when the thermionic current from a cathode is lower than the CL current. 216 From Sec. V A it is apparent that the electric field at the surface can affect the current source by changing the shape of the surface barrier, particularly in the case of field emission.…”

Section: B Space Charge Limited Emission Below the Child-langmuir Limitmentioning

confidence: 99%

100 years of the physics of diodes

Zhang

Valfells

Ang

et al. 2017

Applied Physics Reviews

190

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The Child-Langmuir Law (CL), discovered a century ago, gives the maximum current that can be transported across a planar diode in the steady state. As a quintessential example of the impact of space charge shielding near a charged surface, it is central to the studies of high current diodes, such as high power microwave sources, vacuum microelectronics, electron and ion sources, and high current drivers used in high energy density physics experiments. CL remains a touchstone of fundamental sheath physics, including contemporary studies of nanoscale quantum diodes and nano gap based plasmonic devices. Its solid state analog is the Mott-Gurney law, governing the maximum charge injection in solids, such as organic materials and other dielectrics, which is important to energy devices, such as solar cells and light emitting diodes. This paper reviews the important advances in the physics of diodes since the discovery of CL, including virtual cathode formation and extension of CL to multiple dimensions, to the quantum regime, and to ultrafast processes. We review the influence of magnetic fields, multiple species in bipolar flow, electromagnetic and time dependent effects in both short pulse and high frequency THz limits, and single electron regimes. Transitions from various emission mechanisms (thermionic-, field-, and photoemission) to the space charge limited state (CL) will be addressed, especially highlighting the important simulation and experimental developments in selected contemporary areas of study. We stress the fundamental physical links between the physics of beams to limiting currents in other areas, such as low temperature plasmas, laser plasmas, and space propulsion.

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“…Barbour et al [8] used approximate methods to achieve this self-consistency, while modern iterative numerical methods allow to find a more accurate solution at relatively low computational costs [12]. Equation ( 2) can be simplified by introducing the reduced dimensionless variables [23][24][25]…”

Section: General Formulationmentioning

confidence: 99%

“…The general SC problem, which is relevant for field electron and ion emission, was solved for the planar case by Stern et al [22]. This solution has been widely used as a reference model to estimate the SC effects on field emission [5,[23][24][25], due to its simplicity and intuitiveness. The connection of the planar diode model to an experimental emitter geometry is typically done via the equivalency introduced by Barbour et al [8], i.e.…”

Section: Introductionmentioning

confidence: 99%