Method for spatially resolved imaging of energy-dependent photoelectron diffraction

Sy, Tong; Huang, Huan; Wei, C. M.

doi:10.1103/physrevb.46.2452

Cited by 100 publications

(36 citation statements)

References 40 publications

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“…As mentioned previously, in Auger emission applications, the electron source is within atomic distances of the object, while in LEEPS microscopy the electron source is at a large distance from the atomic cluster. It has also been shown that multiple scattering does tend to obscure images in some LEED applications, and that improvements can be made in reconstructing the holograms [21,22]. Images in some LEED applications are also obscured by``twin'' images, which are virtually not present in LEEPS images due to the large distances from source to object.…”

Section: Multiple Scattering In Leed Vs Leepsmentioning

confidence: 99%

“…Images in some LEED applications are also obscured by``twin'' images, which are virtually not present in LEEPS images due to the large distances from source to object. It was shown that by energy averaging [21], and averaging over the angle of collection [22] the e ects of multiple scattering on reconstructed images could be signi®cantly reduced. That is, the quality of the images were improved by averaging holograms of di erent energies and screen positions, respectively.…”

Section: Multiple Scattering In Leed Vs Leepsmentioning

confidence: 99%

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Multiple scattering in low-energy electron holography

2000

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The theory of the low-energy electron point source (LEEPS) microscope is reformulated in matrix form to readily account for multiple scattering. An algorithm is developed for the storage of the structure matrix and an iterative method is used to solve the matrix equation for the structure factor. Examples of small and large clusters of atoms are given to compare single and multiple scattering. A Kirchho 2Helmholtz transform is used for the reconstruction. We ®nd that in some cases the multiple scattering is too strong and reconstruction is not possible. We give examples which show that, even when multiple scattering is important, one can still obtain reconstructions that reveal the atomic structure both along and lateral to the optical axis. We also compare our results with those found in LEED. #

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Section: Multiple Scattering In Leed Vs Leepsmentioning

confidence: 99%

Section: Multiple Scattering In Leed Vs Leepsmentioning

confidence: 99%

Multiple scattering in low-energy electron holography

2000

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“…By applying of multiple-energy reconstruction methods, 6,7 the twin image problems can be overcome. As it was predicted theoretically, [11][12][13] for a certain combination of the atomic distances and the k-vector values the overlapping of the real and twin images may lead to a suppression ͑enhancement͒ of the atomic images in the hologram reconstruction.…”

Section: Introductionmentioning

confidence: 98%

“…A considerable improvement of the real-space reconstruction quality is gained if the holograms are acquired for several different energies and if the multiple-energy reconstruction methods are applied. 6,7 One of the main advantages of multipleenergy measurements is the elimination of the twin images, which can hinder the proper determination of the structure.…”

Section: Introductionmentioning

confidence: 99%

Holography with γ rays: Simulations versus experiment forα−57Fe

Korecki

Karaś

1999

Phys. Rev. B

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The ␥-ray holography was recently applied ͓P. Korecki et al., Phys. Rev. Lett. 79, 3518 ͑1997͔͒ to image the three-dimensional structure of ␣-57 Fe with an atomic resolution. A simple theory of the hologram formation based on single-scattering cluster formalism taking into account the polarization effects in the resonant nuclear scattering and absorption processes is presented. The high quality of the real-space reconstruction is demonstrated, however, problems arising from the cancellation of real twin images are revealed. The realistic simulations are in a good agreement with the experiment. A method for elimination of the real and twin images cancellation taking advantage of the strong dependence of the scattering phase on the detuning from the resonance in the nuclear scattering is proposed. ͓S0163-1829͑99͒03109-4͔

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“…The situation is like using a meter stick to measure the distances of atoms d/, but the origin of the meter stick is at unknown positions dy. The presence of object-wave interference peaks [20] (i.e., artifacts) occurs because the condition that the reference wave is large compared to the object wave is not satisfied for /yv since an adatom's scattering factor is usually smaller than that of the substrate atoms, i.e., l/o"l < \fs~\' In addition, there are artifacts generated by multiple scattering [5][6][7][8]. Therefore, direct inversion of LEED or LEPD integral-order I-V spectra, as proposed in previous studies [11], is not a useful approach.…”

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confidence: 99%

Low-energy electron and low-energy positron holography

1992

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We demonstrate holographic reconstruction using low-energy electron-diffraction (LEED) and lowenergy positron-diffraction (LEPD) intensity spectra. Calculated LEED and LEPD intensity spectra from a multiple-scattering method are inverted to produce high-fidelity images of near-neighbor atoms whose positions are measured from an adatom. We show that low-energy positron diffraction is better suited for holographic reconstruction because positron scattering in solids is weaker than that of electrons. PACS numbers: 68.35.Bs, 61.14.Hg, 61.16.-d, 68.55.-a There is considerable interest in the development of local electron holography in which an adsorbate atom or impurity atom acts as a beam splitter for either emitted electrons [1-3] or scattered electrons [4,5]. Multipleenergy phase-summing methods were introduced to eliminate image artifacts produced by multiple scattering [6-8].While such multiple-energy methods produced essentially artifact-free three-dimensional atom images [5-8], they required a considerable database in (0,^,^) space, thus putting a major burden on data acquisition. In this Letter, we indicate that positron diffraction is better suited than electron diffraction for holographic reconstruction because of the positron's weak scattering and large damping in solids. It is apparent that positrons are close to being the ideal particles for three-dimensional image reconstruction because these particles embody the advantages of both photons (weak elastic scattering) and electrons (high surface sensitivity via a large inelastic damping). We illustrate these observations by inverting low-energy electron-diffraction (LEED) and low-energy positron-diffraction (LEPD) intensity-voltage spectra calculated from identical multiple-scattering methods [9,10], using the respective phase shifts and inelastic dampings for electrons and positrons. We show that for positron holography, multiple-scattering artifacts are rapidly eliminated and high-fidelity atom images emerge after sum-, ming over only a few energies. Inversion of LEED spectra was attempted in the 1970's [11], but the attempt failed because it involved Fourier transforming integralorder /-K spectra. In this paper, we present a data inversion method for fractional-order /-F spectra based on the holographic principle. The first observation of LEPD was made by Rosenberg, Weiss, and Canter in 1980 [12]. This discovery was followed by an experimental advancement in which the concept of "brightness enhancement" was introduced [13]. The theoretical analysis of LEPD spectra was made easy by the ready availability of multiple-scattering methods developed earlier for LEED. The early works of LEPD [14,15] pointed out an important difference between LEPD and LEED: In LEPD, the scattering potential between the positron and the atomic nucleus is repul-sive because they have the same sign. This repulsive interaction has significant consequences [16,17], the most important of which is the considerably weaker positronatom elastic scattering. Classically, a repulsive Coulom...

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Method for spatially resolved imaging of energy-dependent photoelectron diffraction

Cited by 100 publications

References 40 publications

Multiple scattering in low-energy electron holography

Multiple scattering in low-energy electron holography

Holography with γ rays: Simulations versus experiment forα−57Fe

Low-energy electron and low-energy positron holography

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