Quantitative measurement of charge accumulation along a quasi-one-dimensional W<sub>5</sub>O<sub>14</sub> nanowire during electron field emission

Zheng, Fengshan; Pozzi, Giulio; Migunov, Vadim; Pirker, Luka; Remškar, Maja; Beleggia, Marco; Dunin‐Borkowski, Rafal E.

doi:10.1039/d0nr00739k

Cited by 8 publications

(6 citation statements)

References 34 publications

(39 reference statements)

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“…Holographic-type electron microscopy experiments have been carried out in order to verify the form of line charges, and find [116] that an extra charge near a rod/needle apex is required: this finding is consistent with the basic version of the FSEPP model, where only a single point charge is used to model the emitter.…”

Section: E Line-charge Modelssupporting

confidence: 60%

See 1 more Smart Citation

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

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This review of the quantitative electrostatics of field emitters, covering analytical, numerical and "fitted formula" approaches, is thought the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is "polarity independent", so that the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors-which exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant that the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant of this that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many "related considerations" that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

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Section: E Line-charge Modelssupporting

confidence: 60%

“…Line-charge arguments can be applied in both field electron and field ion emission, but have found more use in FE. The theory of applying line-charge distributions to needle-shaped emitters and to field emission has been discussed, for example, by Harris et al [115] and Zheng et al [116].…”

Section: E Line-charge Modelsmentioning

confidence: 99%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis¹,

Dall’Agnol²,

Forbes³

2022

Preprint

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“…The cumulative charge integrated along the length of the needle, which is shown in Figure d, follows an almost linear trend, suggesting that the line charge density along the needle is almost constant, as expected from analytical solutions. , The slope of the cumulative charge profile is slightly greater close to the apex of the needle than in the shank, indicating a greater line charge density in this region, perhaps because of its more insulating character or because of a local deviation from an ellipsoidal geometry …”

supporting

confidence: 58%

“…21,35 The slope of the cumulative charge profile is slightly greater close to the apex of the needle than in the shank, indicating a greater line charge density in this region, perhaps because of its more insulating character or because of a local deviation from an ellipsoidal geometry. 44 The 3D electrostatic potential and electric field can be calculated from the 3D reconstructed charge density by removing the artificial charges in the buffer voxel region and assuming that image charges in the counter electrode can be defined to have a norm vector with respect to the apex of the needle of (0,−4.5, 0) μm, as determined from the experimental setup (Figure 1b). It should be noted that charges outside the FOV also contribute to the electrostatic potential and electric field inside the FOV.…”

mentioning

confidence: 99%

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

et al. 2023

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The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

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Section: Line-charge Modelsmentioning

confidence: 99%

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Assis

Dall’Agnol

Forbes

2022

J. Phys.: Condens. Matter

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This review of the quantitative electrostatics of ﬁeld emitters, covering analytical, numerical and “ﬁtted formula” approaches, is thought to be the ﬁrst of its kind in the 100 years of the subject. The review relates chieﬂy to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is “polarity independent”, so the review applies to both ﬁeld electron and ﬁeld ion emitters. It also applies more generally to charged, pointed electron-conductors—which exhibit the “electrostatic lightning-rod eﬀect”, but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than ﬁelds) becomes apparent. Space and time limitations have meant the review cannot be comprehensive in both detail and scope. Rather, it focuses chieﬂy on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called “screening” or “shielding”). Core to the review are discussions of the “minimum domain dimensions” method for implementing eﬀective ﬁnite-element-method electrostatic simulations, and of the variant that leads to very precise estimates of dimensionless ﬁeld enhancement factors (error typically less than 0.001 % in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many “related considerations” relevant to the electrostatic situations, methods and results described. Many areas of ﬁeld emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

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Quantitative measurement of charge accumulation along a quasi-one-dimensional W₅O₁₄ nanowire during electron field emission

Abstract: Electric field map and equipotential contour lines of a quasi-one-dimensional W5O14 nanowire under an electrical bias of 150 V. Experimental cumulative charge profiles along the length of the nanowire are consistent with theoretical simulations.

Cited by 8 publications

References 34 publications

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

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Quantitative measurement of charge accumulation along a quasi-one-dimensional W5O14 nanowire during electron field emission

Abstract: Electric field map and equipotential contour lines of a quasi-one-dimensional W5O14 nanowire under an electrical bias of 150 V. Experimental cumulative charge profiles along the length of the nanowire are consistent with theoretical simulations.

Cited by 8 publications

References 34 publications

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

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Product

Resources

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Quantitative measurement of charge accumulation along a quasi-one-dimensional W₅O₁₄ nanowire during electron field emission