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Direct atom imaging by chemical-sensitive holography Tobias Lühr, Aimo Winkelmann, Gert Nolze, Dominique Krull, and Carsten Westphal Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00524 • Publication Date (Web): 12 Apr 2016 Downloaded from http://pubs.acs.org on April 13, 2016

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Direct atom imaging by chemical-sensitive holography Tobias Lühr,

∗, †

Aimo Winkelmann,

‡

Gert Nolze,

Westphal

¶

Dominique Krull,

†

and Carsten

†

†Experimental Physics I, TU Dortmund, Dortmund, Germany ‡Experimental Department I, Max Planck Institute of Microstructure Physics, Halle, Germany

¶Department 5 - Materials Engineering, BAM - Federal Institute for Materials Research and Testing, Berlin, Germany E-mail: [email protected]

Phone: +49 (0)231 755 3511

Abstract In order to understand the physical and chemical properties of advanced materials, functional molecular adsorbates, and protein structures, a detailed knowledge of the atomic arrangement is essential. Up to now, if sub-surface structures are under investigation, only indirect methods revealed reliable results of the atoms' spatial arrangement. An alternative and direct method is three-dimensional imaging by means of holography. Holography was in fact proposed for electron waves, because of the electrons' short wave length at easily accessible energies. Further, electron waves are ideal structure probes on an atomic length scale, because electrons have a high scattering probability even for light elements. However, holographic reconstructions of electron diraction patterns have in the past contained severe image artifacts, and were limited 1

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to at most a few tens of atoms. Here, we present a general reconstruction algorithm that leads to high-quality atomic images showing thousands of atoms. Additionally, we show that dierent elements can be identied by electron holography for the example of FeS2 .

Keywords keywords: holography, electron diraction, atomic imaging, photoemission, electron backscattering

Introduction For many systems and applications the determination of atomic locations is one of the most important aspects. The detailed knowledge about the structure is a prerequisite for calculations on electronic properties. By now, synthetic methods permit preparing systems with well dened properties. Again, knowledge about the structure is of central importance. For structures very near the surface, scanning probe techniques have become very successful during the past decades. However, in the sub-surface region and at internal interfaces, no direct three-dimensional structure probes are available. This long-standing problem has not been solved up to now. One idea of imaging objects in the size of an atom is the holographic approach suggested by D. Gabor in 1948. 1 In order to obtain the hologram from an object, Gabor suggested to interfere the emitted object wave with a reference wave. The hologramm itself is just a coherent interference pattern written into a photographic record. If the record is illuminated with the reference wave again then a part of the emitted wave imitates the object wave both in phases and amplitudes. This idea was proposed for electron waves since electron waves have a sucient small wave-length suitable for atom imaging. In the following years the holographic imaging was shown for photons in the visible regime rst 2,3 and later with

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x-rays. 46 Scientically, it remained an open question why the experimental realisation of the original idea, which is a spatial image of an atom structure obtained from an electron hologram was never as successful as holography with photons. 7 Despite great eort and various attempts, images of 10 atoms or less were found for a few special cases only. 817 In general, the reconstructions of electron diraction patterns were plagued by severe image artifacts preventing an accurate image interpretation. However, electron waves have a much higher inelastic scattering probability compared to photons. Therefore, electron waves are much more surface sensitive. 18,19 Also, electron waves have a much higher dierential crosssection for elastic scattering at light elements of the periodic table. Hence, electrons are well-suited for imaging even the light elements within surface structures. However, the scattered electron waves are not as isotropic as in the case of photons. The electron scatter characteristics depends on the scatter-angle and the scatter-energy 20,21 and therefore a reconstruction becomes much more dicult compared to the case of isotropic photon emission. Thus, electron diraction patterns were compared to ab initio simulations or analysed with iterative-scaling algorithms 2224 in order to determine the corresponding atomic structure. Nevertheless, electron holography at energies of a few keV allows direct and unique imaging of both the spatial and chemical structure in a range of around 2 nm beneath the surface, which is not possible by any other technique presently. In the following, we present a solution to circumvent the problems occurring during a holographic reconstruction of electron diraction patterns.

Hologram generation and reconstruction Usually, holographic techniques apply external reference waves. Here, we use electron emission as an internal wave source, as schematically pictured in gure 1a and 1b. The emitted electron waves generate diraction patterns which allow a structure reconstruction in all three

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dimensions, because the scatter atoms are located in the near-eld of the emitted wave. 25 The emitted electrons can either be generated by the photoelectric eect with subsequent scattering leading to a technique called X-ray Photoelectron Diraction (XPD) 2628 or by inelasticaly backscattered electrons by a technique termed Electron Backscatter Diraction (EBSD). 29,30 Diraction patterns result from interferences of emitted and scattered electron waves. In principle, electron diraction patterns contain all the structure information around the emitter atom, because the recorded electron wave was modulated by the local structure around the emitter. Since all scattered waves contributing to the pattern are coherent to the emitter wave, the structure in the emitter environment should be reconstructable within a holographic approach. For this purpose an image function Γk was dened, which transforms the pattern intensity into a real space image. 8,9,12,14,15,31 Since the intensity modulations only depend on the observation direction, coordinates in electron diraction patterns are usually parametrized by the polar angle Θ and the azimuth angle Φ, as shown in gure 1a. With polar coordinates the image function Γk at the spatial position r = (x, y, z)T can be written as

 2π  Z sin(Θ)  χk (Θ, Φ) eik[x sin(Θ) cos(Φ)+y sin(Θ) sin(Φ)+z cos(Θ)] dΦ dΘ.

Θ Zmax

Γk (r) = 0

(1)

0

In this equation χ(Θ, Φ) = (I(Θ, Φ)−I0 )/I0 corresponds to the modulated part of the pattern √ intensity I with the average pattern intensity I0 . The quantity k ∝ Ekin corresponds to the wavenumber. Typically, electron diraction patterns are recorded with kinetic electron energies of several hundred eV. At these energies strong artifacts arise in the reconstruction, 32 due to the strong anisotropy in electron scattering, as displayed in gure 1c. Therefore, we focussed our investigestion on diraction patterns obtained at higher electron energies. At several keV the electron waves are nearly constrained within a cone, 33,34 as visualised in gure 1c. Within the scatter cone the electron wavefront provides no phase shift. Thus, the scattered 4


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wave is equivalent to an isotropic wave that is observed in a small solid angle, which leads to reconstructable features in the diraction pattern.

Reconstruction of experimental diraction patterns In order to illustrate the imaging properties of electron waves, we discuss the reconstruction of experimental EBSD-patterns of tungsten. Backscattered electrons can be assumed as being emitted from the backscattering atom, since they lose their coherence to the incident beam. 35 Hence, an EBSD-pattern may be treated as if being generated by an internal electron source like the photoelectron waves within an XPD-pattern. As compared in gure 2a, the experimental EBSD-pattern of tungsten provides identical features as the XPD-pattern simulated by Bloch-wave simulations. 36 Due to its well-known structure, tungsten is an ideal rst test system for comparing the reconstructed images with true atom locations. Inserting the W-pattern of gure 2a into the reconstruction integral of equation (1) will lead to poor results instead of the true atoms' locations. This long-standing problem can be circumvented by a simple procedure. Taking multiple scattering eects into account, scattered waves may provide a dierent phase in forward direction compared to all other directions. Therefore, the zeroth-order diraction features must be removed from the diraction pattern in order to avoid artifacts in the reconstruction. They can be removed by taking the dierence of two patterns measured at dierent kinetic energies, 37 as shown in gure 2b. In contrast to higher-order diraction features, zeroth-order modulations are not depending on the electron energy. Hence, the dierence of two dierent diraction patterns contains no zeroth-order modulations, while the higher-order diraction features remain in the dierence pattern. The reconstruction of a dierence pattern is possible by inserting the average wavenumber

k = 12 (k1 + k2 ) in equation (1). 37 Here k1 and k2 are the wavenumbers to the diraction patterns used for calculating the dierence pattern. With an increasing distance to the emitter

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atom, the image peaks corresponding to atom locations may split-up into two individual peaks. In order to avoid peak splitting, the energy dierence ∆E should be as small as possible. With absolute energies between E = 10 keV and E = 20 keV the fraction should be ∆E/E ≤ 10% to obtain single atom peaks up to a distance of at least 2.0 nm to emitter. The reconstruction of a single dierence pattern already provides a reliable image of the crystal structure. Nevertheless, we discuss the results obtained from averaging 20 reconstructed images in order to eciently suppress background noise. The cooresponding diraction patterns were obtained between 10 keV and 20 keV, with an energy dierence of ∆E = 0.5 keV. Since the image functions Γk are complex quantities, we calculated the sum of absolute squares for the visualization. Hence, the image intensity Iimg of tungsten was calculated by 38

2 X ikr e · Γk (r) . Iimg (r) =

(2)

k

At true atom locations the factor eikr avoids destructive interferences between the individual complex image functions Γk from equation (1). Figure 2c shows several reconstructed layers that cut through atom layers, either parallel or perpendicular to the crystal surface. In every layer strong intensity peaks coincide with true atom locations as indicated by the red circles. All atom locations within a range up to 16 Å around the emitter are indicated by intensity peaks. In the environment above the emitter, approximately 1000 peaks have been reconstructed at true atom locations. Figure 2d shows the spatial image intensity within the yellow box of gure 2c. The blue wireframe spheres mark the expected atom locations. In the reconstruction all intensity peaks occur within the spheres, nicely demonstrating that three-dimensional atom imaging from experimental data yields reliable results for the true atoms arrangements of the tungsten crystal.

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Reconstruction of samples with several chemical elements In order to demonstrate that our method even works for more complex systems, e.g. for systems with dierent elements and with lower symmetry, we reconstructed atom images from diraction patterns of pyrite, having a more complex structure. Pyrite contains sulfur and iron atoms that are arranged in dierent sublattices, as displayed in gure 3a. Due to energy-ltered electron detection in XPD-measurements, the diraction patterns of the individual elements can be recorded separately, 26,39,40 since the photoelectrons are emitted at element-specic kinetic energies. For pyrite, the iron pattern diers from the sulfur pattern, already indicating the dierent local environments, as displayed in gures 3b and 3c. In the following, reconstructions of the iron patterns are termed as iron images, while sulfur images refer to reconstructed sulfur patterns. Here, we discuss the reconstruction results obtained by 11 diraction patterns between 10 keV and 20 keV, with an energy dierence of ∆E = 1.0 keV. Figure 3d shows an iron layer in the iron image, which is aligned parallel to the sample surface with z = 5.44 Å above the emitter. All reconstructed peaks match perfectly with the expected peak locations indicated by circles. Red circles mark the Bravais lattice points, whereas the yellow circles indicate all remaining atom locations. As shown in gure 3e, the reconstruction to the sulfur image yields a dierent result than the reconstruction to the iron image. The dierence between iron and sulfur image demonstrates that individual local environments within the same sample can be distinguished within the reconstruction. However, the images contain more intensity peaks than expected for the true pyrite structure. These additional peaks are marked by asterisks in the sulfur image in gure 3e. Also, the peaks should have similar intensities at least roughly, since all atoms are sulfur atoms with the same scatter amplitude in this layer. Pyrite consists of eight sulfur atoms per unit cell, each located within a dierent environment. Therefore, a measured pattern corresponds to a superposition of eight dierent patterns. Since scatter sites appear at locations relative to the emitter location, the reconstructed image corresponds to a superposed image of all 7


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individual emitter environments. Strong intensities can be found at locations for emitters having neighbor atoms at identical sites. Weak intensities reect atom locations in the environment of one or a few emitters. Unfortunatly, some of these weak intensity peaks to true atom locations may disappear in the background noise, as displayed in gure 3f. In order to improve the intensity of the weak peaks in the reconstruction, we superposed the reconstructed complex image function Γk with Γk -functions being shifted by lattice vectors Guvw .

2 X X −ik|r+Guvw | e · Γk (r + Guvw ) . Iclean (r) = k

(3)

uvw

The factor e−ik|r+Guvw | in equation (2) simply changes the phase of the image function. Since the absolute value of this factor is always 1, the amlitude of the image function Γk is not altered. However, after applying the exponential factor to the image function its phase becomes independent from location and energy at all atom locations. All other locations in the image function still depend on position and energy. Therefore, noise and artifacts diers in amplitude and phase from unit cell to unit cell. Summing the image over the lattice vectors will average out these features. In contrast, the atomic peaks sum up, since they all provide the same constant phase. Thus, summing images with a lattice vector translation improves all atomic peaks that are already in the image. In order to apply equation (3), lattice vectors Guvw must be determined. These vectors can easily be found in the reconstruction resulting from equation (1) without including additional information. Regardless of how complicated the investigated structure is, every emitting atom provides images of neighboring atoms with vectors corresponding to lattice vectors. Therefore, the lattice points can easily be identied in the image function from equation (1) by searching for the locations of the strongest intensity peaks. This procedure does not require any a-priori information of the structure. After applying equation (3) even very weak intensities become visible, as shown in gure

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3g, which shows the atom layer of gure 3f. Each reconstructed peak reects the relative location of a scatter atom to at least one emitter atom.

Chemical resolved structure determination The original structure of pyrite as well as the chemical structure can directly be found by comparing the reconstruction results of the iron and sulfur patterns. Figure 4 illustrates the pyrite unit cell obtained from the iron and sulfur images of gure 3b and 3c, respectively. As can be seen in gure 4a, in the iron image the pyrite unit cell reveals 36 intensity peaks per cell. In contrast, in the sulfur image the unit cell contains 59 peaks, as shown in gure 4b. Since the reconstructions provide the atom distances relative to the selected element, a comparison of the two individual images, as iron and sulfur, allows a direct identication of the chemical elements. If an image peak in the sulfur image indicates an iron atom at the location Guvw + rµ , a corresponding peak must be found in the iron image at the location

Guvw − rµ . Therefore, all peaks in the sulfur image without a corresponding peak in the iron image can directly be assigned to sulfur atoms and vice versa, as marked by the colored spheres in gures 4a and 4b. The remaining peaks indicate possible iron and possible sulfur locations in the sulfur and the iron image, respectively. Iron and sulfur images show the pyrite structure from dierent points of view. Thus, we shifted the sulfur image to a possible sulfur location from the iron image, in order to nd the original pyrite structure. The superposition of both images leads to the peak distribution in gure 4c. All peaks appearing in only one of the two reconstructions can be eliminated, since the intensity peaks of the original structure must appear in both images. The remaining peaks shown in gure 4d reect the original pyrite unit cell, as schematically shown in gure 3a. If the sulfur image is shifted to any other possible sulfur location in the iron image, the result will always be the pyrite unit cell. Furthermore, all remaining peaks are assigned

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to the respective element. Therefore, the complete structure information was successfully extracted from the diraction patterns leading to a chemical-resolved spatial image of pyrite.

Conclusion In summary, we demonstrated a direct method to extract the three-dimensional structure from an electron diraction pattern, either as an electron backscattering pattern, or an x-ray photoelectron diraction pattern. For the rst time, strong artifacts in the reconstruction resulting from the electrons' anisotropic nature were eciently removed. For this task, it is neccessary to take the dierence of two electron diraction patterns obtained at high kinetic electron energies. The reconstruction shows a reliable and complete image within 2 nm around the emitting atom. This was demonstrated without any additional structure information. The reconstructions contain ∼ 1000 intensity peaks, which indicate the atom locations in the local emitter environment. Due to the chemical-sensitive electron detection, the method oers a direct element-specic peak assignment as demonstrated in the case of pyrite. A successful demonstration of a chemical-sensitive straight-forward structure reconstruction that always leads to unique results was never reported before. Since the intensity peaks perfectly match to true atom locations in the reconstructions, we found a reliable direct way of spatial and chemical resolved structure imaging. Due to the surface sensitivity of the electron waves, our method grants access to the buried atom layers beneath the surface, complementing established scanning probe techniques by the third dimension.

Contributions T.L. and C.W. developed the reconstruction method. A.W. calculated the diraction patterns by Bloch-wave simulations. G.N. measured the experimental diraction patterns. T.L. wrote this article with contributions of A.W., D.K., and C.W. 10


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.png

Electron diraction with sample-internal electron sources. a, Propagation and scattering of an electron wave starting from an emitter within the sample. b, Formation of a hemispherical electron diraction pattern in the fareld of the emitter wave. c, Comparison of scattered electron waves at low and high kinetic energies. At low energies the electron provides an anisotropic wave front (red line) 41 leading to artifacts in a holographic reconstruction. At high kinetic energies the electron waves are constrained within a cone in forward direction. Within the cone no phase shifts can be obtained. Thus, the scattered wave corresponds to an isotropic wavefront observed within a small solid angle.

Figure 1:

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.png

Figure 2: Experimental EBSD-pattern of a tungsten crystal and its reconstruction. a, Comparison of an experimental EBSD-pattern with a Bloch-wave simulation. b, Dierence pattern of two experimental diraction patterns of tungsten. c, 2-dimensional slices of the reconstructed spatial image obtained by averaging

the reconstruction results of 20 dierence EBSD-pattern measured at kinetic energies between 10 keV and 20 keV. The layers in the top row are aligned perpendicular to the sample surface, while the layers in the bottom row are oriented parallel to the surface. The intersection lines between the individual layers are indicated in red. Bulk atom locations are emphasized by red circles. All intensity maxima are located within these circles, demonstrating the accuracy of the reconstruction scheme. d, Volume rendering (red) of the yellow box in (b). The volume opacity is proportional to the reconstructed intensity. The wireframe spheres are centered at the regular atom locations, while the tungsten unit cell is displayed by a blue cube. 12


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.png Figure 3: Reconstruction of a pyrite crystal (FeS 2 ). a, Pyrite unit cell. b, Close-up view of a simulated iron diraction pattern at 15 keV. c, Same pattern detail as shown in (b) for the sulfur emitters. d, Reconstructed iron layer obtained by applying 10 dierence patterns from simulated iron patterns in the reconstruction scheme. The red circles mark the Bravais lattice points, while the yellow circles refer to the remaining iron atoms expected in this layer. e, Reconstruction of a sulfur layer by including 10 dierence patterns of sulfur in the reconstruction scheme. f, Iron layer in the sulfur image. The blue spheres indicate expected iron peaks, but noise is obtained only. g, The same iron layer as displayed in (f). This time the image was calculated by equation (3) in order to remove the noise. The red crosses mark the x-y-locations of the Bravais lattice points that were used in the calculation.

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.png

Determination of the original pyrite structure by means of peak comparison and elimination. a, Reconstructed pyrite unit cell in the iron image by applying equation (3). b, Reconstructed pyrite unit cell in the sulfur image. c, Comparison of the peak locations in the iron image with the peaks in the shifted sulfur image. The sulfur image was shifted by a vector of a possible iron-sulfur distance (white spheres in (a)). All peaks that appear in only one image (indicated by striped patterns) can be eliminated, since true atom locations must provide matching peaks for both images (marked by checkerboard patterns). d, Remaining peaks after the peak elimination. As a result, the structure of the pyrite unit cell including the corresponding elements to each peak is obtained (compare gure 3a). Figure 4:

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Supporting Information Available • Supplementary information: In a mathematical examination the imaging characteristics of an individual scatter atom are derived from a diraction pattern. The results are used for analysing imaging eects, which occur from applying dierence patterns in the reconstruction scheme. Furthermore, it is demonstrated how past problems of electron holography like twin image formation and distortions from multiple scattering can be circumvented by using electrons with kinetic energies at 10 keV and above. This material is available free of charge via the Internet at http://pubs.acs.org/ .

Note Note: The authors declare no competing nancial interest.

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