100 years of the physics of diodes

Abstract

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.

Generalized High-Energy Thermionic Electron Injection at Graphene Interface

“…We now investigate the current-temperature scaling of the full-band thermionic emission model. For 2D materials, the current-temperature scaling of thermionic emission in the out-of-plane direction follows the universal scaling law, ln (J /T ) ∝ −1/T [25], rather than the classic Richardson-Dushman scaling law of ln J /T 2 ∝ −1/T for 3D materials [48,49]. In Fig.…”

The impact of cathode surface roughness and multiple breakdown events on microscale gas breakdown at atmospheric pressure

“…27 Although mean surface roughness did not impact the breakdown voltage, it did lead to concentration of the discharge at emission sites that impacted subsequent breakdown events; however, this study did not consider the impact of a single, controllable sharptipped emitter on breakdown voltage. Future studies will, thus, further investigate the impact of controllable aspect ratio 17 as a function of gap distance and pressure on gas breakdown and current density to additionally characterize transitions between electron emission mechanisms 10,14 and breakdown phenomena.…”

“…As relevant device sizes transition from microscale to nanoscale, electron emission may shift from field emission to space-charge limited emission, 11,12 motivating additional studies on gas breakdown at a smaller scale. These phenomena also have significant implications in vacuum electronics, where ongoing research in electron sources 13,14 has focused on assessing groups of nanoemitters 15,16 and intentionally modifying device designs to better control field enhancement. 17 Thus, characterizing gas breakdown and electron emission for microscale and smaller devices is important across application and pressure, motivating studies on the responsible physical phenomena.…”

Active control of bright electron beams with RF optics for femtosecond microscopy

“…In the UEM, it is correlated with virtual cathode formation during the electron pulse generation. The virtual cathode limit (VCL) 41,42 sets in due to the attractive image charge field on the photocathode surface left by the emitted electrons, resulting in an increased fraction of recombined electrons and a degradation of beam properties once the critical current is reached 47 . Below the VCL, the high-density electron bunches created at the photocathode also develop unique phase space structures depending on the initial conditions 42,48 .…”