Resolving power of lens‐less low energy electron point source microscopy

Stevens, Gregory B.

doi:10.1111/j.1365-2818.2009.03177.x

Cited by 6 publications

(6 citation statements)

References 45 publications

(66 reference statements)

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“…Consequently, the resulting spatial coherence of such sources has been limited by low beam divergence angles. Here we show that our single-atom tip not only has the property of being completely coherent, but also exhibits a coherence angle much larger than measured previously, and indeed than previously thought feasible [12]. This implies, among other things, a much greater resolution in the point-source holographic imaging with such a tip.…”

supporting

confidence: 60%

“…Whereas no previously studied point source has displayed greater than 5.5 degrees coherent opening angle [25], corresponding to approximately 1 nm [12] resolution for a LEEPS microscope, the tip described here exhibits greater than 14 degrees opening angle, indicating the potential for ∼1.7 Å resolution and a transformative result for electron holography by the LEEPS method. Such measurements are presently underway.…”

mentioning

confidence: 55%

“…Arguably, with the availability of a highly coherent source, the most immediate application would be holographic imaging with electrons, as first recognized by Gabor [10]. Specifically, the degree of spatial coherence can be shown to be the critical limiting factor in the resolution of point-source electron holography [11,12]. 4 As it is difficult, if not impossible, to envision an electron source with a greater spatial coherence than that generated by field emission from a single atom, such emitters are now being explored extensively.…”

mentioning

confidence: 99%

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Nanoscale structuring of tungsten tip yields most coherent electron point-source

Mutus¹,

Livadaru²,

Urban³

et al. 2013

New J. Phys.

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This report demonstrates the most spatially-coherent electron source ever reported. A coherence angle of 14.3 ± 0.5 • was measured, indicating a virtual source size of 1.7 ± 0.6 Å using an extraction voltage of 89.5 V. The nanotips under study were crafted using a spatially-confined, field-assisted nitrogen etch which removes material from the periphery of the tip apex resulting in a sharp, tungsten-nitride stabilized, high-aspect ratio source. The coherence properties are deduced from holographic measurements in a low-energy electron point source microscope with a carbon nanotube bundle as sample. Using the virtual source size and emission current the brightness normalized to 100 kV is found to be 7.9 × 10 8 A sr −1 cm 2 .

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supporting

confidence: 60%

mentioning

confidence: 55%

mentioning

confidence: 99%

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Nanoscale structuring of tungsten tip yields most coherent electron point-source

Mutus¹,

Livadaru²,

Urban³

et al. 2013

New J. Phys.

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“…Here, estimation of the effective source size is mainly essential for the evaluation of the resolution of the imaged objects. The divergence angle of the emitted electron beam as a factor limiting the extent of the hologram was mentioned by Stevens [41]. We now investigate the resolution of objects reconstructed from holograms simulated at different source sizes.…”

Section: Effect Of Source Size On Resolutionmentioning

confidence: 92%

Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects

Latychevskaia

2017

Ultramicroscopy

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Sub-nanometer and nanometer-sized tips provide high coherence electron sources.Conventionally, the effective source size is estimated from the extent of the experimental biprism interference pattern created on the detector by applying the van Cittert Zernike theorem. Previously reported experimental intensity distributions on the detector exhibit Gaussian distribution and our simulations show that this is an indication that such electron sources must be at least partially coherent. This, in turn means that strictly speaking the Van Cittert Zernike theorem cannot be applied, since it assumes an incoherent source. The approach of applying the van Cittert Zernike theorem is examined in more detail by performing simulations of interference patterns for the electron sources of different size and different coherence length, evaluating the effective source size from the extent of the simulated interference pattern and comparing the obtained result with the pre-defined value.The intensity distribution of the source is assumed to be Gaussian distributed, as it is observed in experiments. The visibility or the contrast in the simulated holograms is found to be always less than 1 which agrees well with previously reported experimental results and thus can be explained solely by the Gaussian intensity distribution of the source. The effective source size estimated from the extent of the interference pattern turns out to be of about 2-3 times larger than the pre-defined size, but it is approximately equal to the intrinsic resolution of the imaging system. A simple formula for estimating the intrinsic resolution, which could be useful when employing nano-tips in in-line Gabor holography or point-projection microscopy, is provided.

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“…Since then, all experimentally observed features in LEEPS images have had their smallest feature in the range of ∼2 nm [35,19,1,36]. Recently the resolution gap between these experimental results and theoretical predictions [4,40] was examined by Stevens [41]. In this theoretical work the effect of the limited divergence angle of the electron beam was included in the calculation of the theoretical resolution limit in LEEPS microscopy.…”

Section: Resolutionmentioning

confidence: 99%

Low energy electron point source microscopy: beyond imaging

Beyer

Gölzhäuser²

2010

J. Phys.: Condens. Matter

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Low energy electron point source (LEEPS) microscopy has the capability to record in-line holograms at very high magnifications with a fairly simple set-up. After the holograms are numerically reconstructed, structural features with the size of about 2 nm can be resolved. The achievement of an even higher resolution has been predicted. However, a number of obstacles are known to impede the realization of this goal, for example the presence of electric fields around the imaged object, electrostatic charging or radiation induced processes. This topical review gives an overview of the achievements as well as the difficulties in the efforts to shift the resolution limit of LEEPS microscopy towards the atomic level. A special emphasis is laid on the high sensitivity of low energy electrons to electrical fields, which limits the structural determination of the imaged objects. On the other hand, the investigation of the electrical field around objects of known structure is very useful for other tasks and LEEPS microscopy can be extended beyond the task of imaging. The determination of the electrical resistance of individual nanowires can be achieved by a proper analysis of the corresponding LEEPS micrographs. This conductivity imaging may be a very useful application for LEEPS microscopes.

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Resolving power of lens‐less low energy electron point source microscopy

Cited by 6 publications

References 45 publications

Nanoscale structuring of tungsten tip yields most coherent electron point-source

Nanoscale structuring of tungsten tip yields most coherent electron point-source

Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects

Low energy electron point source microscopy: beyond imaging

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