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.

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.

Since the invention of chirped pulse amplification, which was recognized by a Nobel Prize in physics in 2018, there has been a continuing increase in available laser intensity. Combined with advances in our understanding of the kinetics of relativistic plasma, studies of laser–plasma interactions are entering a new regime where the physics of relativistic plasmas is strongly affected by strong-field quantum electrodynamics (QED) processes, including hard photon emission and electron–positron (e⁻–e⁺) pair production. This coupling of quantum emission processes and relativistic collective particle dynamics can result in dramatically new plasma physics phenomena, such as the generation of dense e⁻–e⁺ pair plasma from near vacuum, complete laser energy absorption by QED processes, or the stopping of an ultra-relativistic electron beam, which could penetrate a cm of lead, by a hair's breadth of laser light. In addition to being of fundamental interest, it is crucial to study this new regime to understand the next generation of ultra-high intensity laser-matter experiments and their resulting applications, such as high energy ion, electron, positron, and photon sources for fundamental physics studies, medical radiotherapy, and next generation radiography for homeland security and industry.

This Letter presents a consistent quantum and relativistic model of short-pulse Child-Langmuir (CL) law, of which the pulse length $\tau$ is less than the electron transit time in a gap of spacing $D$ and voltage $V$. The classical value of the short-pulse CL law is enhanced by a large factor due to quantum effects when the pulse length and the size of the beam are, respectively, in femtosecond duration and nanometer scale. At high voltage larger than the electron rest mass, relativistic effects will suppress the enhancement of short-pulse CL law, which is confirmed by particle-in-cell simulation. When the pulse length is much shorter than the gap transit time, the current density is proportional to $V$, and to the inverse power of $D$ and $\tau$.

Fundamental processes for electric breakdown, i.e., electrode emission and bulk ionization, as well as the resultant Paschen’s law, are reviewed under various conditions. The effect of the ramping rate of applied voltage on breakdown is first introduced for macroscopic gaps, followed by showing the significant impact of the electric field nonuniformity due to gap geometry. The classical Paschen’s law assumes uniform electric field; a more general breakdown scaling law is illustrated for both DC and RF fields in geometrically similar gaps, based on the Townsend similarity theory. For a submillimeter gap, effects of electrode surface morphology with local field enhancement and electric shielding on the breakdown curve are discussed, including the most recent efforts. Breakdown characteristics and scaling laws in microgaps with both metallic and non-metallic (e.g., semiconductor) materials are detailed. For gap distance down to micro/nano scales, the breakdown characteristics and the breakdown mode transition from the secondary electron emission to the electric field emission or thermionic emission dominant regime. Additionally, the combined thermo-field emission regime is also reviewed. Previous efforts, including key simulations and experiments, have been devoted to diagnosing breakdown path evolution, measuring breakdown fields, and quantifying breakdown dependence on frequencies for gaps down to micro/nano scales. By summarizing and analyzing fundamental theories, recent progress, and on-going challenges, this tutorial review seeks to provide basic understanding and the state of the art of electric breakdown, which aids in advancing discoveries and promoting application prospects for discharge devices engineered in a wide range of regimes.

When two conductors are separated by a sufficiently thin insulator, electrical current can flow between them by quantum tunneling. This paper presents a self-consistent model of tunneling current in a nano- and subnano-meter metal-insulator-metal plasmonic junction, by including the effects of space charge and exchange correlation potential. It is found that the J-V curve of the junction may be divided into three regimes: direct tunneling, field emission and space-charge-limited regime. In general, the space charge inside the insulator reduces current transfer across the junction, whereas the exchange-correlation potential promotes current transfer. It is shown that these effects may modify the current density by orders of magnitude from the widely used Simmons’ formula, which is only accurate for a limited parameter space (insulator thickness > 1 nm and barrier height > 3 eV) in the direct tunneling regime. The proposed self-consistent model may provide a more accurate evaluation of the tunneling current in the other regimes. The effects of anode emission and material properties (i.e. work function of the electrodes, electron affinity and permittivity of the insulator) are examined in detail in various regimes. Our simple model and the general scaling for tunneling current may provide insights to new regimes of quantum plasmonics.