Interferometric methods for mapping static electric and magnetic fields

Pozzi, Giulio; Beleggia, Marco; Kasama, Takeshi; Dunin-Borkowski, Rafal E.

doi:10.1016/j.crhy.2014.01.005

Cited by 34 publications

(15 citation statements)

References 162 publications

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“…Accurate, sensitive imaging of the electron phase signal has important applications in the study of the magnetic properties of materials 38 and in semiconductor characterisation 39 40 . Our Future work aims to optimise our experiments, to critically compare performance to that of the two principle kinds of holography, and to apply SAP to the measurement of variations in potential across doped semiconductor junctions.…”

Section: Discussionmentioning

confidence: 99%

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

Maiden

Sarahan

Stagg

et al. 2015

Sci Rep

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As it passes through a sample, an electron beam scatters, producing an exit wavefront rich in information. A range of material properties, from electric and magnetic field strengths to specimen thickness, strain maps and mean inner potentials, can be extrapolated from its phase and mapped at the nanoscale. Unfortunately, the phase signal is not straightforward to obtain. It is most commonly measured using off-axis electron holography, but this is experimentally challenging, places constraints on the sample and has a limited field of view. Here we report an alternative method that avoids these limitations and is easily implemented on an unmodified transmission electron microscope (TEM) operating in the familiar selected area diffraction mode. We use ptychography, an imaging technique popular amongst the X-ray microscopy community; recent advances in reconstruction algorithms now reveal its potential as a tool for highly sensitive, quantitative electron phase imaging.

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Section: Discussionmentioning

confidence: 99%

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

Maiden

Sarahan

Stagg

et al. 2015

Sci Rep

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“…Model-based measurement of the charge density in the APT needle was performed by fitting the part of the recorded phase image that lies outside the boundary of the needle to a simulated phase image, which was generated by approximating the needle by a line of constant charge density, 18 for which an analytical solution for the phase shift takes the form where 2c is the length of the line charge, r is the charge density, x and y are in-plane coordinates, and 2 h is the distance between the electrodes, 22,25 as shown schematically in Fig. 3.…”

Section: B Model-based Approachmentioning

confidence: 99%

“…A key advantage of the present approach, which is based on integration of the Laplacian of the phase or, equivalently, contour integration of the gradient of the phase, is that it is insensitive to perturbation of the vacuum reference wave used to generate the hologram by the electromagnetic field of the specimen itself, 19 so long as the region from which the reference wave is obtained is itself charge-free. [20][21][22] However, in the past, it has suffered from an important limitation resulting from the effect of the mean inner potential contribution to the phase shift on the measured charge density distribution. 23 We show that this limitation can be overcome by analysing the difference between electron holographic phase images acquired with different voltages applied to the specimen.…”

Section: Introductionmentioning

confidence: 99%

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

Migunov

London

Farle

et al. 2015

Journal of Applied Physics

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Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle J. Appl. Phys. 116, 024305 (2014) Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects The one-dimensional charge density distribution along an electrically biased Fe atom probe needle is measured using a model-independent approach based on off-axis electron holography in the transmission electron microscope. Both the mean inner potential and the magnetic contribution to the phase shift are subtracted by taking differences between electron-optical phase images recorded with different voltages applied to the needle. The measured one-dimensional charge density distribution along the needle is compared with a similar result obtained using model-based fitting of the phase shift surrounding the needle. On the assumption of cylindrical symmetry, it is then used to infer the three-dimensional electric field and electrostatic potential around the needle with $10 nm spatial resolution, without needing to consider either the influence of the perturbed reference wave or the extension of the projected potential outside the field of view of the electron hologram. The present study illustrates how a model-independent approach can be used to measure local variations in charge density in a material using electron holography in the presence of additional contributions to the phase, such as those arising from changes in mean inner potential and specimen thickness.

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“…It is well established that a thin, biased conducting needle does not maintain a constant line charge density [29,30]. Experiments have shown that a thin, insulating needle aquires a negative charge under the incident electron beam [31], and it is possible that the charge density on such an insulating needle is nearly constant.…”

Section: Resultsmentioning

confidence: 99%

“…However, it seems that the value of the charge density, and therefore the parameters of the sorter, might depend more strongly on the incident beam current than is desirable for a robust, tunable device. A more controllable approach involves the use of a biased conductor with a physical surface fabricated to match the equipotential surfaces of a constant line charge density [29]. In particular, to produce a potential that corresponds to a line charge density Q/L and a length of the line charge L, the needle should be held at a voltage V U with a surface defined by the equipotential which corresponds to equation (A.1) in the limit that  ¥ h .…”

Section: Resultsmentioning

confidence: 99%

Efficient sorting of free electron orbital angular momentum

2017

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We propose a method for sorting electrons by orbital angular momentum (OAM). Several methods now exist to prepare electron wavefunctions in OAM states, but no technique has been developed for efficient, parallel measurement of pure and mixed electron OAM states. The proposed technique draws inspiration from the recent demonstration of the sorting of OAM through modal transformation. We show that the same transformation can be performed on electrons with electrostatic optical elements. Specifically, we show that a charged needle and an array of electrodes perform the transformation and phase correction necessary to sort OAM states. This device may enable the analysis of the spatial mode distribution of inelastically scattered electrons. U 2 2

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Interferometric methods for mapping static electric and magnetic fields

Cited by 34 publications

References 162 publications

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

Efficient sorting of free electron orbital angular momentum

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