Electrostatics of two suspended spheres

Dall’Agnol, Fernando F.; Mammana, Victor Pellegrini; Engelsen, Daniel den

doi:10.1590/s1806-11172012000300008

Cited by 3 publications

(4 citation statements)

References 4 publications

(3 reference statements)

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“…Assuming a spherical tip, the value of this potential along the cylindrical symmetry axis (coordinate z) can be calculated according to Ref. [16] and will depend on the effective radius R of the tip, the bias voltage and the tip-sample separation z 0 + Z(V).…”

Section: Resultsmentioning

confidence: 99%

Light emission from Ag(111) driven by inelastic tunneling in the field emission regime

Martínez-Blanco¹,

Fölsch²

2015

J. Phys.: Condens. Matter

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Abstract. We study the light emission from a Ag(111) surface when the bias voltage on a scanning tunneling microscope (STM) junction is ramped into the field emission regime. Above the vacuum level, scanning tunneling spectroscopy (STS) shows a series of well defined resonances associated with the image states of the surface, which are Stark shifted due to the electric field provided by the STM tip. We present photonenergy resolved measurements that unambiguously show that the mechanism for light emission is the radiative decay of surface localized plasmons excited by the electrons that tunnel inelastically into the Stark shifted image states. Our work illustrates the effect of the tip radius both in the STS spectrum and the light emission maps by repeating the experiment with different tips.

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Section: Resultsmentioning

confidence: 99%

Light emission from Ag(111) driven by inelastic tunneling in the field emission regime

Martínez-Blanco¹,

Fölsch²

2015

J. Phys.: Condens. Matter

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“…By symmetry, the electric field distribution in this system is the same as for a pair of grounded spheres (figure 2). We employ the method of images to determine the electric field distribution [7][8][9]. Hereafter, variables in bold repre sent a vector, and the corresponding nonbold symbols rep resent the norm of the vector.…”

Section: Sphere-sphere Electrostatic Interactionmentioning

confidence: 99%

“…As two spheres come closer, the dipole of strength p 0 from each sphere induces an image dipole of strength p 1 in the other, which in turn generates a further image dipole of strength p 2 , and so on. The x-coordinate and the magnitude of the i-th dipole are obtained from the following recurrence relations [9]:…”

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confidence: 99%

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Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Dall’Agnol

Assis

Forbes

2018

J. Phys.: Condens. Matter

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Recent analyses of the apex field enhancement factor (FEF) for many forms of field emitter have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest [Formula: see text] (c being the separation and h is the height of the emitters) and large separations ([Formula: see text]) has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this work, we use first principles to derive a simple two-parameter formula for fractional reduction that can be useful for experimentalists for modeling and interpreting the FEFs for small clusters of emitters or arrays at separations of interest. For the structures tested, the agreement between numerical and analytical data is ∼1%.

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Physical electrostatics of small field emitter arrays/clusters

Forbes

2016

Journal of Applied Physics

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This paper aims to improve qualitative understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays/clusters. Using the "floating sphere at emitter-plate potential" (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. An adequate approximation is to consider only the effects of sphere charges and (for significantly separated emitters) image charges. For the 2-emitter system, formulas are found for charge-transfer ("charge-blunting") effects and neighbor-field effects, for widely spaced and for "sufficiently closely spaced" emitters. Mutual charge-blunting is always the dominant effect, with a formulas. This discrepancy needs to be investigated, using systematic Laplace-based simulations and appropriate results analysis. FSEPP models might provide a useful provisional guide to the qualitative behaviour of small field emitter clusters larger than those investigated here.

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Electrostatics of two suspended spheres

Cited by 3 publications

References 4 publications

Light emission from Ag(111) driven by inelastic tunneling in the field emission regime

Light emission from Ag(111) driven by inelastic tunneling in the field emission regime

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Physical electrostatics of small field emitter arrays/clusters

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