Space-charge-limited bipolar flow in a nano-gap

Koh, W. S.; Ang, L. K.; Lau, Shu Ping; Kwan, Thomas J. T.

doi:10.1063/1.2130526

Cited by 14 publications

(7 citation statements)

References 17 publications

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“…The classical value of the SCL bipolar electron flow is also greatly enhanced due to the electron tunneling through the space charge field created by both the electrons and ions, and it is no longer equal to the classical limit which is 1.86 times that of the classical CL law. 158 To realize the quantum SCL current in a nano gap, there were also studies to model the transition from field emission to SCL current in a nano gap at different conditions. 159 By assuming the field emission to be governed by the Fowler-Nordheim (FN) law, 160 it was found that the emission current can go beyond the classical CL law to reach the quantum CL law for a nanometer gap in the high current regime.…”

Section: B Quantum Scl Scalingmentioning

confidence: 99%

100 years of the physics of diodes

Zhang

Valfells

Ang

et al. 2017

Applied Physics Reviews

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186

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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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Section: B Quantum Scl Scalingmentioning

confidence: 99%

100 years of the physics of diodes

Zhang

Valfells

Ang

et al. 2017

Applied Physics Reviews

Self Cite

186

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“…20 The classical CL law has also been extended to quantum regime to include the quantum effects on the dynamic of SCL electron flows in a nanogap. [21][22][23][24][25] The shortpulse CL law has been also studied in classical, 26,27 quantum, and weakly relativistic 28 regimes. Recent developments of the CL law in multidimensional models and quantum models can be found in two review papers, respectively.…”

Section: Introductionmentioning

confidence: 99%

Short-pulse space-charge-limited electron flows in a drift space

et al. 2008

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In this paper, the space-charge-limited (SCL) electron flows in a drift space is studied by including the effect of finite electron pulse length, which is smaller than the gap transit time. Analytical formulas are derived to calculate the maximum SCL current density that can be transported across a drift space under the short-pulse injection condition. For a given voltage or injection energy, the maximum current density that can be transported is enhanced by a large factor (as compared to the long-pulse or steady-state case), and the enhancement is inversely proportional to the electron pulse length. In drift space, the effect of pulse expansion is important at very short-pulse length, and the short-pulse enhancement factor is smaller as compared to a diode. The enhancement factor will be suppressed when the injection energy is larger than the electron rest mass, and effect of pulse expansion is less critical at relativistic energy. The analytical formulas have been verified by performing a particle-in-cell simulation in the electrostatic mode.

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“…This maximum value arises because the space charge in the diode presents a potential barrier to the incident electrons. In the research of vacuum electronics on a scale down to a few or tens of nanometers, the quantum effects should be considered and cannot be neglected [1][2][3][4][5]. In a previous work of Lau et al…”

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confidence: 99%

Space charge limited current in quantum regime by solving the Schröodinger-Poisson equation based on finite element method

Chang

Lin

2007

2007 IEEE 20th International Vacuum Nanoelectronics Conference

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The Child-Langmuir law gives the maximum electron current, known as the space-charge-limited current. This maximum value arises because the space charge in the diode presents a potential barrier to the incident electrons. In the research of vacuum electronics on a scale down to a few or tens of nanometers, the quantum effects should be considered and cannot be neglected [1][2][3][4][5]. In a previous work of Lau et al.[1], they extended the classical work of Child and Langmuir to the quantum regime by considering a parallel, planar gap. On such a microscopic scale, they used the familiar mean-field theory expressed by the self-consistent, coupled Schrödinger and Poisson's equation in the Hartree approximation. Thus, they solved the one-dimensional Schrödinger equation 2 2 2 , (1) 2 d eV E m dx ψ ψ ψ − − = h and the Poisson's equation 2 * 2 0 .(2) d V e dx ψψ ε = in the gap region, by using the Wentzel-Kramers-Brillouin-Jefferys (WKBJ) method, they found that the classical value for the space-charge-limited current in such a diode can be exceeded by a large factor due to the effect of tunnelling.In this work, we quantitatively investigate the space-charge-limited current in quantum regime by solving the Schrödinger-Poisson equation based on the finite element method (FEM). Figure 1 shows the schematic of the self-consistent model of coupled Schrödinger and Poisson's equation for a nano-diode gap, where Ψ i (x)=A exp(ik 1 x) is an incident plane wave, and Ψ r (x)=B exp(-ik 1 x) and Ψ t (x)= C exp(ik 2 x) are a reflected plane wave and a transmitted plane wave, respectively. The boundary conditions to Eqs. (1) and (2) are formulated as follows. Let V g be the gap bias voltage, which may be zero, positive, or negative. In the nano-diode, the gap region is defined to be 0

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Space-charge-limited bipolar flow in a nano-gap

Cited by 14 publications

References 17 publications

100 years of the physics of diodes

100 years of the physics of diodes

Short-pulse space-charge-limited electron flows in a drift space

Space charge limited current in quantum regime by solving the Schröodinger-Poisson equation based on finite element method

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Space-charge-limited bipolar flow in a nano-gap

Cited by 14 publications

References 17 publications

100 years of the physics of diodes

100 years of the physics of diodes

Short-pulse space-charge-limited electron flows in a drift space

Space charge limited current in quantum regime by solving the Schr&#x00F6;odinger-Poisson equation based on finite element method

Contact Info

Product

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Space charge limited current in quantum regime by solving the Schröodinger-Poisson equation based on finite element method