The transition from field emission to collisional space-charge limited current with nonzero initial velocity

Breen, Lorin I.; Loveless, Amanda M.; Darr, Adam M.; Cartwright, Keith L.; Garner, Allen L.

doi:10.1038/s41598-023-41615-2

Cited by 5 publications

(1 citation statement)

References 69 publications

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“…This equation can be derived by substituting J(t) = en e v e , eΦ = m e v 2 e /2, and v e = dx/dt into Possion's equation [76], where Φ is the electrostatic potential, v e are the electron velocity, and J(t) is the emission current density. Note that x p ≪ λ ≈ 434 nm (λ is the electron mean free path) indicates that the contributions of collisions might not be significant in the space charge layer, and thus equation ( 4) can be utilized for analyzing the electron transport in the cathode sheath with neutral gases [77][78][79]. Here to simplify the estimation, J(t) can be treated as constant at t = t a , i.e.…”

Section: Resultsmentioning

confidence: 99%

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

Chen,

Lin,

Wang

et al. 2024

Plasma Sources Sci. Technol.

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We report an ultrafast oscillation (up to ∼ 10 4 GHz) in the early stage of field emission-driven microdischarges. Spatiotemporal behaviors of electron density, space charge density, and electric field, exhibiting high-frequency oscillations, are demonstrated based on first-principle particle-in-cell/Monte Carlo collision simulations. Intermittent electron emission fluxes are identified from the electron phase space distributions whereas the ions are rather non-oscillatory in the transient timescale. The mechanisms of oscillation with growing amplitude are found to be related to the rapid modification of the field emission current affected by the space charge electric field, which is also accompanied by the fast response of the electron transport and ionization in a dynamic double-layer sheath. Further, a transport equation for emission current is solved to estimate the oscillation frequency, which agrees well with the simulation results. This study provides a more precise understanding of the formation of the field emission-driven microdischarge, which informs the design and optimization of miniaturized gaseous electronic devices.

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Section: Resultsmentioning

confidence: 99%

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

Chen,

Lin,

Wang

et al. 2024

Plasma Sources Sci. Technol.

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Uniform space-charge-limited current for a two-dimensional planar emitter with nonzero monoenergetic initial velocity

Zhu,

Sree Harsha,

Garner

2023

Journal of Applied Physics

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While characterizing space-charge-limited current (SCLC) is important for numerous applications, no analytical solutions for SCLC with monoenergetic initial velocity exist for two-dimensional (2D) geometries. Here, we derive approximate closed-form solutions for uniform SCLC with monoenergetic emission of electrons in a 2D planar diode, where emission is restricted to a long patch of width W for electrodes separated by a distance D. We also derive a semiempirical approach for estimating the SCLC for these cases by treating the geometric and velocity correction factors as multiplicative corrections to the SCLC for a one-dimensional vacuum diode given by the Child–Langmuir (CL) law. We show that the SCLC for a finite patch with nonzero velocity can exceed the CL law by three orders of magnitude. The theoretically calculated SCLCs for various emission widths and initial velocities in the 2D diode agree well with particle-in-cell simulations using the over-injection method in XOOPIC; they agree with the semiempirical relationship for lower initial velocities. In the limit of high initial velocity, the geometry and velocity corrections to the CL law cannot be decoupled, invalidating the assumption of the semiempirical approach and causing it to diverge from the theoretical solution and XOOPIC simulations. These results provide valuable estimates for determining the onset of virtual cathode formation for photocathodes and thermionic cathodes, which operate in the over-injection regime to avoid beam quality degradation.

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Collisional space-charge-limited current with monoenergetic velocity: From Child–Langmuir to Mott–Gurney

Breen,

Garner

2024

Physics of Plasmas

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All theories coupling electron emission theories ultimately approach the space-charge-limited current (SCLC) in vacuum, given by the Child–Langmuir (CL) law, for sufficiently high voltage, or the Mott–Gurney (MG) law for finite electron mobility and high (but not infinite) voltage. These analyses demonstrate the presence of an SCLC regime that cannot be described by either CL or MG. Here, we derive an exact solution for SCLC for general electron mobility and nonzero velocity. We recover the traditional CL with nonzero initial velocity at high voltage. For low mobility (or infinite collision frequency), we derive corrections to the MG law that depend on the ratio of initial velocity to the product of collision frequency and gap distance or initial velocity to drift velocity for low and high voltage, respectively. Increasing collisionality decreases the correction to SCLC for nonzero velocity, indicating that these corrections are less important for low-mobility materials (e.g., solids) than high-mobility materials (e.g., air or vacuum). For a given gap distance (collision frequency), increasing the collision frequency (gap distance) increases the voltage necessary to make the gap appear more like vacuum. These results provide a generalized SCLC for both collisionality and initial velocity when assessing the transitions between electron emission mechanisms.

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The transition from field emission to collisional space-charge limited current with nonzero initial velocity

Cited by 5 publications

References 69 publications

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

Uniform space-charge-limited current for a two-dimensional planar emitter with nonzero monoenergetic initial velocity

Collisional space-charge-limited current with monoenergetic velocity: From Child–Langmuir to Mott–Gurney

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