Homeland security and military defense technology considerations have stimulated intense interest in mobile, high power sources of millimeter-wave (mmw) to terahertz (THz) regime electromagnetic radiation, from 0.1 to 10THz. While vacuum electronic sources are a natural choice for high power, the challenges have yet to be completely met for applications including noninvasive sensing of concealed weapons and dangerous agents, high-data-rate communications, high resolution radar, next generation acceleration drivers, and analysis of fluids and condensed matter. The compact size requirements for many of these high frequency sources require miniscule, microfabricated slow wave circuits. This necessitates electron beams with tiny transverse dimensions and potentially very high current densities for adequate gain. Thus, an emerging family of microfabricated, vacuum electronic devices share many of the same plasma physics challenges that are currently confronting “classic” high power microwave (HPM) generators including long-life bright electron beam sources, intense beam transport, parasitic mode excitation, energetic electron interaction with surfaces, and rf air breakdown at output windows. The contemporary plasma physics and other related issues of compact, high power mmw-to-THz sources are compared and contrasted to those of HPM generation, and future research challenges and opportunities are discussed.

Plasma physics and related challenges of millimeter-wave-to-terahertz and high power microwave generationa)

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 ...

100 years of the physics of diodes

This paper reviews the recent developments of space-charge-limited (SCL) flow or Child-Langmuir (CL) law in the quantum regime. According to the classical CL law for planar diodes, the current density scales as 3∕2’s power of gap voltage and to the inverse squared power of gap spacing. When the electron de Broglie wavelength is comparable or larger than the gap spacing, the classical SCL current density is enhanced by a large factor due to electron tunneling and exchange-correlation effects, and there is a new quantum scaling for the current density, which is proportional to the 1∕2’s power of gap voltage, and to the inverse fourth-power of gap spacing. It is also found that the classical concepts of the SCL flow such as bipolar flow, transit time, beam-loaded capacitance, emitted charge density, and magnetic insulation are no longer valid in quantum regime. In the quantum regime, there exists a minimum transit time of the SCL flows, in contrast to the classical solution. By including the surface properties of the emitting surface, there is a threshold voltage that is required to obtain the quantum CL law. The implications of the Fowler-Nordheim-like field emission in the presence of intense space charge over the nanometer scale is discussed.

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Space-charge-limited flows in the quantum regime

Triple point, defined as the junction of metal, dielectric, and vacuum, is the location where electron emission is favored in the presence of a sufficiently strong electric field. In addition to being an electron source, the triple point is generally regarded as the location where flashover is initiated in high voltage insulation, and as the vulnerable spot from which rf breakdown is triggered. In this paper, we focus on the electric field distribution at a triple point of a general geometry, as well as the electron orbits in its immediate vicinity. We calculate the orbit of the first generation electrons, the seed electrons. It is found that, despite the mathematically divergent electric field at the triple point, significant electron yield most likely results from secondary electron emission when the seed electrons strike the dielectric. The analysis gives the voltage scale in which this electron multiplication may occur. It also provides an explanation on why certain dielectric angles are more favorabl...

Electric field and electron orbits near a triple point

This Perspective reviews the fundamental physics of space–charge interactions that are important in various media: vacuum gap, air gap, liquids, and solids including quantum materials. It outlines the critical and recent developments since a previous review paper on diode physics [Zhang et al. Appl. Phys. Rev. 4, 011304 (2017)] with particular emphasis on various theoretical aspects of the space–charge limited current (SCLC) model: physics at the nano-scale, time-dependent, and transient behaviors; higher-dimensional models; and transitions between electron emission mechanisms and material properties. While many studies focus on steady-state SCLC, the increasing importance of fast-rise time electric pulses, high frequency microwave and terahertz sources, and ultrafast lasers has motivated theoretical investigations in time-dependent SCLC. We particularly focus on recent studies in discrete particle effects, temporal phenomena, time-dependent photoemission to SCLC, and AC beam loading. Due to the reduction in the physical size and complicated geometries, we report recent studies in multi-dimensional SCLC, including finite particle effects, protrusive SCLC, novel techniques for exotic geometries, and fractional models. Due to the importance of using SCLC models in determining the mobility of organic materials, this paper shows the transition of the SCLC model between classical bulk solids and recent two-dimensional (2D) Dirac materials. Next, we describe some selected applications of SCLC in nanodiodes, including nanoscale vacuum-channel transistors, microplasma transistors, thermionic energy converters, and multipactor. Finally, we conclude by highlighting future directions in theoretical modeling and applications of SCLC.

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Space–charge limited current in nanodiodes: Ballistic, collisional, and dynamical effects

Space-charge-limited (SCL) flows in diodes have been an area of active research since the pioneering work of Child and Langmuir in the early part of the last century. Indeed, the scaling of current density with the voltage to the 3/2’s power is one of the best-known limits in the fields of non-neutral plasma physics, accelerator physics, sheath physics, vacuum electronics, and high power microwaves. In the past five years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries, such as field-emitting arrays. In 1996, computational efforts led to the development of a scaling law that described the increased current drawn due to two-dimensional effects. Recently, this scaling has been analytically derived from first principles. In parallel efforts, computational work has characterized the edge enhancement of the current density, leading to a better understanding of the physics of explosive emission cathodes. In this paper, the analytic and computational extensions to the one-dimensional Child–Langmuir law will be reviewed, the accuracy of SCL emission algorithms will be assessed, and the experimental implications of multidimensional SCL flows will be discussed.

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Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow

Summary form only given. The analytic and computational extensions to the one-dimensional Child-Langmuir law are reviewed, the accuracy of SCL emission algorithms are assessed, and the experimental implications of multi-dimensional SCL flows are discussed.

Beyond the Child-Langmuir law: the physics of multidimensional space-charge-limited emission

The pioneering work of Child and Langmuir in the early part of the last century established the fundamental space charge-limited (SCL) emission current density that can be achieved in a planar vacuum diode of infinite extent. Indeed, the scaling of current density with the voltage to the 3/2's power is one of the best-known limits in the fields of vacuum electronics, non-neutral plasma physics, accelerator physics, sheath physics, and high power microwaves. In recent years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries such as field-emitting arrays, photocathodes, and explosive emission cathodes.

J.J. Watrous

Papers

Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow

Beyond the Child-Langmuir law: the physics of multidimensional space-charge-limited emission

Space charge-limited emission above the 1-D Child-Langmuir limit