Experimental investigation of transition from Fowler–Nordheim field emission to space-charge-limited flows in a nanogap

Bhattacharjee, Sudeep; Chowdhury, Tathagata

doi:10.1063/1.3194297

Cited by 38 publications

(15 citation statements)

References 20 publications

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“…4 of Ref. 15), the current appears to be space charge limited with the exponent α ≃ 1.5 which is consistent with the first order WKB results presented here.…”

Section: Fig 2 (Color Online) a Comparison Of The Amplitude R(x)supporting

confidence: 91%

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Transport across nanogaps using self-consistent boundary conditions

Biswas

Kumar

2012

Eur. Phys. J. B

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Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density (J c ) is found to obey the local scaling law J c ∼ V α g /D 5−2α with the gap separation D and voltage V g . The exponent α > 1.1 with α → 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.

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“…4 of Ref. 15), the current appears to be space charge limited with the exponent α ≃ 1.5 which is consistent with the first order WKB results presented here.…”

Section: Fig 2 (Color Online) a Comparison Of The Amplitude R(x)supporting

confidence: 91%

“…3 of Ref. 15), the 70nm gap shows good agreement with the Fowler-Nordheim emission law for V g 6V. Above this (see Fig.…”

Section: Fig 2 (Color Online) a Comparison Of The Amplitude R(x)supporting

confidence: 68%

Transport across nanogaps using self-consistent boundary conditions

Biswas

Kumar

2012

Eur. Phys. J. B

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“…Further assessing the sensitivity of the electron mechanism to external perturbations, such as resistance 46 or nonuniform electrodes, 48,49 will illuminate likely triple point ranges in future experiments. Future experimental measurements of current as a function of applied voltage for various gap distances and gases, extending previous experiments assessing the transition from FN to CL for nanogaps 50 may further refine the theory.…”

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confidence: 60%

Unification of field emission and space charge limited emission with collisions

Darr

Loveless

Garner

2019

Applied Physics Letters

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Electron emission plays a vital role in device design for systems with pressures ranging from vacuum to atmospheric pressure. Nonuniform pressure in vacuum devices and gap sizes below microscale for electronics near atmospheric pressure necessitate further theoretical characterization of the transition between electron emission phenomena. This letter incorporates collisions into analytical equations describing the transition from the Fowler-Nordheim (FN) equation for field emission to space-charge limited emission (SCLE). We recover the Child-Langmuir (CL) law for vacuum, SCLE at high mobility l, and the Mott-Gurney (MG) law for collisional SCLE at low l. The exact solutions follow asymptotic solutions for FN at low voltage V, before transitioning to MG at higher V, and, ultimately, to CL independent of l. We also define a never before seen "triple-point," where the asymptotic solutions of all three electron emission regimes converge. Fixing V, l, or gap distance D uniquely specifies the other two parameters to achieve this triple point, which defines a regime where the electron emission mechanism is very sensitive to experimental conditions. The implications on device design are discussed.

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“…In the two experiments conducted by others [7,8], the voltage V 1=2 g scaling has been confirmed in nanogaps of 50 and 70 nm, which is sensitive to the cathode conditions. Thus, the dependence of the quantum CL law is more related to the physical boundary conditions related to the emission process, which will be explained below.…”

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confidence: 69%

Ang Replies:

Ang

2012

Phys. Rev. Lett.

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Experimental investigation of transition from Fowler–Nordheim field emission to space-charge-limited flows in a nanogap

Cited by 38 publications

References 20 publications

Transport across nanogaps using self-consistent boundary conditions

Transport across nanogaps using self-consistent boundary conditions

Unification of field emission and space charge limited emission with collisions

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