The handle http://hdl.handle.net/1887/32852 holds various files of this Leiden University dissertation
Author: Kautz, Jaap
Title: Low-energy electron microscopy on two-dimensional systems : growth, potentiometry and band structure mapping
Issue Date: 2015-04-30
Introduction to 1
Low-Energy Electron Microscopy
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S.M. Schramm, J. Kautz, A. Berghaus, O. Schaff, R.M. Tromp, S.J. van der Molen, Low-energy electron microscopy and spectroscopy with ESCHER: Status and prospects, IBM Journal of
Research and Development 4, 1:1 (2011)
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1.1 Introduction
Low-Energy Electron Microscopy (LEEM) and Photo Emission Electron Mi- croscopy (PEEM) are powerful surface science techniques. They enable real- time, in-situ imaging of surfaces and interfaces, at elevated temperatures and with nanometer resolution[1–5]. In the following, we give a comprehensive de- scription of the various imaging modes available. We then describe how our specific LEEM/PEEM setup, ESCHER, can achieve a 1.4 nm resolution by employing an aberration correcting electrostatic mirror.
1.2 Imaging Modes
A LEEM/PEEM instrument provides a wide range of imaging modes. In this section we will discuss all the available techniques and explain their usage.
We will start by discussing how we can create both real-space and reciprocal- space images and then continue to techniques which combine real-space and reciprocal-space information like bright-field and dark-field imaging.
1.2.1 Low-Energy Electron Microscopy
LEEM is a microscopy technique where the sample is illuminated by a beam of electrons and an image is formed using the reflected electrons. The basic principle behind LEEM is identical to that of an optical microscope: we use lenses to project an image of an illuminated sample onto a pixelated detector.
However, instead of light, we use electrons and instead of glass lenses, electro- magnetic lenses are used to focus the beam. Just like in an optical microscope, the whole field of view is illuminated simultaneously so no scanning is required.
These same principles also hold for Transmission Electron Microscopy (TEM) and in fact, most LEEM image-formation techniques are very similar to those used in TEM. One big difference with TEM however, is that in LEEM the image is formed with the reflected instead of with the transmitted electrons.
Therefore, the electron source and detector are on the same side of the sample.
This causes the need for a beam splitter, which separates the incoming from the outgoing electrons.
A simplified schematic of our LEEM setup is given in Fig. 1.1. The electrons follow the optical axis indicated in red. The cold field emission gun generates an electron beam with an energy of 15 keV. A combination of a gun lens and a condenser lens serves to focus the electron beam. Next, a so-called magnetic prism array[6], deflects the electrons by 90 degrees towards the objective lens and the sample. The sample itself is held at a tunable negative potential close to that of the field emitter in the electron gun. In this so called cathode objective lens configuration, the electric field between the sample and the
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e-Gun
Sample
Detector Prism
Fig. 1.1: Simplified LEEM setup. The electrons travel from the electron gun to the sample along the optical axis indicated in red. After interaction with the sample the electrons travel towards the detector, where an image is formed. A magnetic prism array separates the incoming and outgoing electron beams.
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objective lens decelerates the electrons to a selected energy in the range of 0-100 eV. This energy is low compared to the energies used in other electron microscopy techniques like Scanning Electron Microscopy (SEM) (0.1 - 40 keV) or TEM (30 - 2000 keV). This makes LEEM highly surface sensitive and, as discussed in the preface, ideally suited for surface science. After interaction with the sample, the same electric field which slowed down the electrons now accelerates them again to 15 keV in the direction of the magnetic prism array.
This electric field also functions as a lens, creating a virtual image of the sample in a plane behind the sample[6]. The prism array subsequently deflects the electrons by 90 degrees, towards the projector system, which projects an image on the detector.
The LEEM/PEEM setup offers a great variety of imaging methods. The most straightforward method is the direct imaging of spatial variations of the reflection intensity (c.f. Fig. 1.2a). An example of this is shown in Fig. 1.2b, which depicts the anisotropic growth of Au on Si(001). Before discussing the more advanced real-space imaging techniques, we will first explain how diffraction images are created.
1.2.2 Low-Energy Electron Diffraction
In addition to real-space images, we can also make reciprocal-space images and thereby analyze the crystal structure of the material. Crystalline mate- rials diffract the electron beam, leading to constructive interference in those directions obeying the Laue conditions[7]. Figure 1.3a shows how electrons leaving the sample in a certain direction are focused into a point in the back focal plane of the objective lens. By adjusting the settings of the projector column we can image this diffraction pattern onto the detector. An example of such a low-energy electron diffraction (LEED) image is shown in Fig. 1.3b.
From the shape of the LEED pattern, the symmetries of the surface crystal structure can be derived. For instance, this 7x7 LEED pattern of a Si(111) surface indicates that the reconstructed surface has the same sixfold symmetry as the unreconstructed surface and has a unit cell which is seven times larger than the unreconstructed unit cell. By analyzing spot shapes and the energy dependence of the LEED pattern, one can completely determine the sample’s crystal structure. However, multiple scattering and inelastic scattering effects complicate this procedure. Even without performing a complete structural determination, the energy dependence of the intensity of the LEED spots, the so called IV-curves, can be used as a fingerprint for a certain surface structure.
In chapter 2, we will demonstrate this use of IV curves as a fingerprint, while in chapters 4 and 5 we will show how IV curves can be used for potentiometry experiments.
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Fig. 1.2: a) Simplified ray diagram for real-space imaging in LEEM. An image of the sample (depicted by an arrow) is projected onto the detector (green). b) LEEM image of the anisotropic growth of Au on Si(001) without using a contrast aperture. At the chosen electron energy of 5eV, the reflectivity of the Au stripes is higher than that of the Si substrate.
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a) b)
Fig. 1.3: a) Ray diagram for LEED imaging. Electrons diffracted under a certain angle are focussed onto a point in the backfocal plane of the objective lens. By projecting this plane onto the detector, a LEED pattern is obtained. b) 7x7 LEED pattern of the reconstructed Si(111) surface. The sixfold symmetry of the bulk crystal is retained, but the size of the unit cell is seven times that of the original unit cell. The contrast in the LEED images in this thesis has been inverted for clarity. Thus, the dark spots correspond to high intensities.
1.2.3 Combining Real-Space and Reciprocal-Space Infor- mation
The real strength of LEEM is that the information from the reciprocal-space and real-space images can be combined. In microspot LEED or microdiffrac- tion, a small part of the real-space image is selected to form a LEED pattern.
In a polycrystalline sample this makes it possible to locally analyze the crystal structure. This will be extensively used in chapter 2.
Instead of selecting a part from real space and forming a reciprocal-space image, we can also select a part from reciprocal space and form a real-space image. By inserting a contrast aperture in the backfocal plane of the objective lens or an equivalent plane, electrons from one diffraction spot can be selected.
This allows us to do bright-field and dark-field imaging.
In bright-field imaging, only the central LEED spot is selected as shown in 1.4a. This way, we create an image using only the specularly reflected electrons. Two types of contrast can be distinguished. Amplitude contrast, i.e. variation in the reflectivity amplitude, is caused by variations in crystal structure which lead to differences in structure factor. Phase contrast on the other hand is caused by interference between electrons reflected from adjacent areas of the sample and is therefore only present under slightly defocused conditions. Figures 1.4b,c show examples of both these types of contrast on a Silicon Carbide sample with epitaxially grown graphene. In Fig. 1.4b phase contrast is created at the step edges due to interference between reflection from the top and bottom step. In Fig. 1.4c, an image of the same area is
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shown, taken with a different landing energy of the electrons. Now interference between electrons reflecting from different layers of graphene interfere to create amplitude contrast between monolayer and double layer graphene, which were indiscernible in Fig. 1.4b. Thus by selecting the proper focus conditions and adjusting the electron energy and thereby altering the electron wavelength, we can select the desired contrast.
Fig. 1.4: Bright-field imaging a) By placing a contrast aperture over the central LEED spot, an image is formed with the specularly reflected electrons. b) SiC sample with epitaxially grown graphene. The electron landing energy (2.5 eV) and defocus is chosen such that phase contrast makes the atomic steps show up dark. c) Same area as in b). At an electron energy of 4.5 eV interference between the reflection from different graphene layers creates amplitude contrast between single and double layer graphene.
In dark-field imaging the electrons from an off-center diffraction spot are used to form a real-space image (c.f. Fig. 1.5a). Contrast is then created between materials with different crystal structure or crystal orientation, which otherwise would have been indistinguishable. Figure 1.5 shows an example of dark-field imaging on Si(001). The terraces of this surface alternatingly have
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Fig. 1.5: a) By placing a contrast aperture over an off-center LEED spot a dark-field image is created. b) LEED pattern of the reconstructed Si(001) surface. LEED spots corresponding to the (2x1) and (1x2) reconstruction are indicated in green and red respectively c) Dark- field image created by selecting one of the spots of the (2x1) reconstruction. Only the (2x1) reconstructed areas are bright. d) Dark-filled image created by selecting one of the spots of the (1x2) reconstruction. Compared to c) the contrast is inverted.
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a (2x1) and (1x2) reconstruction. The LEED pattern of the reconstructed Si(001) surface is shown in Fig. 1.5b. The spots marked in red and green correspond to the (2x1) and (1x2) reconstruction respectively. Figure 1.5c and d show two dark-field images creating by selecting the spots indicated in Fig. 1.5b. Only those areas which contribute to the selected LEED spot become bright in the resulting image. By selecting a spot unique for either of these reconstructions, we create contrast between these two structures.
In an actual dark-field experiment, we do not place the contrast aperture in an off-center position. Instead, we tilt the illuminating beam such, that the desired LEED spot lies on the optical axis and place the aperture there. The main advantage is that the image-forming electrons travel close to the optical axis and therefore suffer less from spherical aberrations. A second advantage is that we can quickly shift between different dark-field configurations by tilting the incident beam. This allows for real-time monitoring of different domains simultaneously. As an example, Fig. 1.6 shows frame shots from a movie of the growth of Au on Si(111). Au grown on Si(111) forms a (5x2) structure for low Au coverages. This (5x2) structure can have three different orientations. By switching between the dark-field conditions for the different (5x2) orientations and assigning each orientation a different color, we can monitor the evolution of the different domains in real time. The growth of Au on Si(111) is extensively investigated in chapter 2
time 1 μm
Fig. 1.6: Frame shots of the growth of Au on Si(111). For low Au coverages the system forms a (5x2) structure, which exists in three orientations. By rapidly switching between the dark-field imaging conditions for these orientations and assigning the results for each orientation a different color, the growth can be followed in real time. The orientation of the step edges with respect to the crystal causes a strong preference for one orientation, but differently oriented domains can be observed as well.
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1.2.4 PEEM
In PEEM experiments, the image-forming electrons do not come from the gun, but are emitted from the sample itself due to the photoelectric effect, induced by irradiating the sample with UV-light. We can illuminate the sample us- ing either a Hg-discharge lamp, or a focused HeI/HeII-discharge source. The emitted electrons are accelerated away from the sample and follow the same path as in a LEEM experiment. In real space this gives an image of the vari- ation in photoelectric effect over the sample. To extend the possibilities even further, the ESCHER set-up also has been equipped with an in-line energy filter[8]. This filter is based on the fact that the deflection angle of a magnetic prism is highly sensitive to the precise energy of the electrons. The current design provides an energy resolution of 150-200 meV at 15 keV electron energy (∆E/E≈ 1.10−5), without the need for deceleration optics. In this configura- tion the microscope can be used as a SPace- and Angle-Resolved Ultraviolet Photoemission Spectroscopy (SPARUPS) facility for surface electronic struc- ture studies. By combining information from real space and reciprocal space, spectroscopy can be carried out locally (microspectroscopy), or the spectro- scopic information can be used to create contrast in real-space images (spectro- microscopy). Alternatively, when the sample is illuminated with the electron beam, the energy filter can be used to perform spatially resolved Electron Energy Loss Spectroscopy (EELS) experiments.
1.3 The ESCHER setup
In this section, we describe our advanced aberration-corrected LEEM/PEEM facility, ESCHER (Electronic, Structural and CHEmical nanoimaging in Real time), located at the Leiden Center for Ultramicroscopy (LCU) at Leiden Uni- versity. The instrumental goals of this Dutch national facility are three-fold:
(i) to reach the ultimate spatial resolution promised by electron mirror-based aberration correction; (ii) to develop, optimize, and exploit the spectroscopic possibilities afforded by in-line, real- and reciprocal-space resolved electron en- ergy spectroscopy; (iii) to extend the sample temperature range to cryogenic temperatures in the 10 K range or lower. In combination, these three goals will facilitate novel interdisciplinary experiments in scientific areas like nano- electronics, condensed matter physics, and biophysics. This will significantly broaden the scientific impact of LEEM/PEEM beyond the traditional areas of surface and materials science. The ESCHER set-up is based on the commer- cially available FE-LEEM P90 instrument (SPECS GmbH, Berlin) designed by Tromp at IBM[6,9]. Figure 1.7 shows a schematic image of the ESCHER set-up.
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e-Gun
Mirror Mirror
Prism 2 Sample
10-300K Sample
300-1800K
Detector Prism 1
Fig. 1.7: LEEM setup, In the center we see the vertical electron column that extends from the gun (top) to the image screen (bottom). Extending to the sides are the high- temperature imaging chamber (right) and the low-temperature imaging chamber (left), plus their respective sample loadlock systems.
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Compared to the simplified image shown in Fig. 1.1, two differences are immediately clear. Instead of only one beam splitter, the ESCHER setup is equipped with two magnetic prism arrays. The extra prism is used to guide the electrons towards an aberration correcting electrostatic mirror, which will be discussed later in this section. The second difference is the implementa- tion of two sample chambers positioned around a single vertical gun/projector column. This unique feature of ESCHER provides two experimental locations using only one set of central column components. In the right chamber the sample temperature can be varied between 300 K and 1800 K. The left chamber will be equipped with a cryogenic stage and objective lens to cool the sample to around 10 K. By changing the polarity of the magnetic field in the prisms, we are able to switch between the high and low temperature imaging systems (see Fig. 1.7).
The base pressure in the ESCHER set-up is ≈ 10−10mbar. Experiments can be performed at pressures up to ≈ 10−5mbar. Samples are annealed in- situ by heating via electron bombardment. As images are obtained in real time, processes such as growth, interface formation, phase transitions and phase transformations can be followed at high resolution, and at video rate.
The high-temperature imaging chamber is equipped with evaporator sources, as well as with Chemical Vapor Deposition (CVD) facilities with a direct line of sight to the sample. A Hiden Hal 7 quadrupole mass spectrometer with a mass range of 500 amu gives a tight control over these processes.
For distinguishing nanostructures the highest possible spatial resolution as well as the highest possible electron transmission is desired. Clearly, elec- tronic and mechanical stability are a first requirement for this. We minimize the effects of chromatic aberrations by using a cold field emitter with a small energy spread (0.25 eV). Even with correction of the chromatic aberration co- efficient, Cc, higher rank aberrations make the choice of the electron source relevant. This is particularly important for experiments at electron energies at the sample below 5 eV, as preferred for imaging organic systems. Passive elec- tromagnetic shielding of the entire electron path and active vibration isolation reduce external influences to a minimum.
1.3.1 Aberration Correction
LEEM is an example of a cathode objective lens microscopy technique. The resolution for an uncorrected LEEM instrument is limited by the chromatic and spherical aberrations of this cathode objective lens[10]. To correct for these aberrations the ESCHER setup has been equipped with an electrostatic aberration correcting mirror as shown in Fig. 1.7. This mirror improves the image resolution from 5 nm to < 2 nm. On the path towards the mirror, an
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uncorrected image is placed in the mirror object plane. The mirror reflects the image into that same plane, with a magnification of 1, removing chromatic and spherical aberration in the reflection process. The corrected image is then projected onto the detector. Note that ESCHER is equipped with two aberration correcting mirrors, one for the left and one for the right sample chamber. For the aberration correction to work, the 90 degree deflection angles provided by the magnetic prism arrays must always be of the same sense (either clockwise or counterclockwise) so that the dispersion of one prism is canceled by the other.
1.3.2 Resolution
In this section we discuss the ultimate resolution for aberration-corrected LEEM in theory and in a real experiment. Recently, a wave-optical approach for image calculations in aberration-corrected electron microscopes has been introduced[10]. This approach is based on the so-called contrast transfer func- tion (CTF) formalism which has been in use in the transmission electron mi- croscopy (TEM) community already for over 30 years, for the case of so-called weak-phase objects. Here, the image modifications introduced by the system are considered by the CTF in an analytical form. The two main causes for these modifications are on the one hand geometric and chromatic aberrations of the objective lens and on the other hand the cutoff of high spatial frequency components by the contrast aperture in the diffraction plane. The image in- tensity, I(r), of a given object, f (r), is given by I(r) = |f (r) ⊗ h(r)| , where ⊗ indicates the convolution between f (r) and h(r), where the latter represents the inverse Fourier Transform of the CTF of our microscope[10].
Figure 1.8a shows the calculation of the image intensity as a function of x for a 1 : √1
3 amplitude object[11]. A 1 : √1
3 amplitude object is an object where the image amplitude is 1 for x <0 and √1
3 for x ≥ 0 , leading to an image intensity ratio (amplitude squared) of 3. Furthermore, the phase of the electrons leaving the sample is taken to be invariant with x. All calcu- lations presented here are performed for an electron energy at the sample of eVE=10 eV and an energy spread of the electron source of ∆E=0.25 eV - a typical value for cold-field emitters. The geometric and chromatic aberrations of objective lens and electron mirror up to 5th order are incorporated in the calculation. The defocus of the objective lens is set to zero. Using these pa- rameters we obtain the plots in Fig. 1.8a for non-aberration-corrected (black line) and aberration-corrected (red line) LEEM.
We define the resolution of an amplitude object as the lateral separation between 84% and 16% of the step size. This calculation was performed for
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a) b)
Fig. 1.8: a) Image intensity profiles with aperture angles of 2.34 mrad and 7.37 mrad for non-aberration-corrected (nac, black line) and aberration-corrected (ac, red line) LEEM, respectively. The horizontal dashed lines indicate intensity values corresponding to 84% and 16% of , as used to obtain the spatial resolution plotted in b). Aberration correction gives rise to improved spatial resolution, and a much finer fringe spacing in the intensity profile.
b) LEEM resolution as a function of aperture angle for non-aberration-corrected (nac, black line) and aberration-corrected (ac, red line) optics.
a series of different aperture angles α and for each angle the resolution was extracted. Figure 1.8b shows the resolution as a function of aperture angle α.
The resolution closely follows a 0.61λ/α behavior for small aperture angles due to k-space cutoff by the contrast aperture (often called the diffraction limit).
Note that the wavelength λ here represents the wavelength of the electrons at 15 keV (≈ 10 pm) For larger aperture angles the resolution starts to oscillate until it remains constant. This is caused by the damped oscillations of the CTF at larger k values as explained in reference[10]. We find that the ultimate resolution, i.e. the global minima in Fig. 1.8b, is 3nm and 0.9nm for non- aberration-corrected and aberration-corrected LEEM, respectively. The image profiles depicted in Fig. 1.8a are calculated at the corresponding optimum aperture sizes of 2.34 mrad and 7.37 mrad for non-aberration-corrected and aberration-corrected LEEM, respectively, at magnification M = 1. In these images one can observe intensity fringes around the amplitude step at x = 0.
The amplitude of the intensity fringes decays with increasing distance from the step position. More intensity fringes with higher oscillation frequencies are observed for the aberration-corrected case compared to non-aberration- corrected LEEM, as the larger contrast aperture transmits larger k-values, i.e.
higher spatial frequencies.
So far, the best resolution obtained in an aberration-corrected LEEM ex- periment is about 2 nm[6]. Our goal was to improve this resolution to ≈ 1 nm - close to the theoretical limit. In order to reach this performance, several
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measures have been taken to reduce the level of vibrations introduced into the system and to increase mechanical stability. First, a new sample stage was installed[12]. This stage is directly attached to the objective lens, elimi- nating any direct mechanical coupling to other parts of the vacuum system.
Additionally, we have incorporated a mu-metal shield around the sample to suppress electromagnetic disturbances. Shielding is most important in the vicinity of the sample, since the electron energy is at its lowest value. Fur- thermore, the vibration and acoustic isolation of the microscope have been optimized. The system is installed on its own vibration-isolated building foun- dation and is equipped with an active vibration isolation system (AVI-400/LP and AVI-350/LP from TABLE STABLE, Switzerland). Vibrations transmit- ted through incoming wires, tubes and vacuum pumps are decoupled where possible. Other sources of interference include AC magnetic fields that are present in the vicinity of the microscope. Even small fields can cause oscilla- tory displacements of the image and therefore degrade the resolution. This is minimized by passive magnetic shielding, especially of the sensitive magnetic prism arrays.
All these measures have significantly improved the resolution of our mi- croscope. Figure 1.9a shows an image of graphene grown on a silicon carbide substrate. In this image we see both contrast at the step edges and between areas with a different number of graphene layers. A line scan along the line indicated in Figure 1.9a is given in Figure 1.9b. By measuring the lateral separation between 20% and 80% of the step size, the resolution is determined to be 1.4 nm(1). With this enormous improvement from ≈ 5 nm for an un- corrected LEEM instrument to 1.4 nm one of the main goals of the ESCHER project is fulfilled. Recently it was shown that increasing the resolution even further will be challenging due to the stringent requirement this would put on the stability of the entire system[13].
1.3.3 Cryogenic LEEM
LEEM has proven to be a very powerful technique to study dynamic processes at surfaces, such as phase transitions and growth phenomena in-situ at elevated temperatures[2–5]. There are, however, also numerous interesting phenomena that take place at temperatures below room temperature. For example, com- plex oxides with their rich phase diagrams show magnetic and electronic phase transitions at low temperatures[14]. Nucleation and growth phenomena at low
(1)Note that this result is not directly comparable to the theoretical calculations of the resolution, for which the separation between 84% and 16% was used. In the rest of this work we will use the 20%-80% definition
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a) b)
100 nm 600 10 20 30 40 50 60 70 80
80 100 120 140 160 180
Intensity(A.U.)
Posi t i on(nm) 20%
80%
Fig. 1.9: a) Graphene grown on Silicon Carbide. At the chosen energy both the step edges and the local variations in number of graphene layers, create contrast. b) Line scan across the line indicated in a). From the distance over which the intensity rises from 20% to 80%
of the step height, a resolution of 1.4 nm is determined.
temperatures are also interesting topics due to strongly decreasing diffusion coefficients with decreasing thermal energy.
Present day LEEM systems generally have a limited temperature range of the sample extending from 300 K up to about 1800 K. Only a few LEEM/PEEM systems exist with the capability of cooling the sample below room tempera- ture, but typically not lower than 100 K. The lowest temperature achieved in a LEEM experiment, which was obtained with a liquid Helium cooled sample stage, is around 50 K[15]. One goal of the ESCHER project is to build a LEEM sample stage with the capability of maintaining the sample at a temperature in the entire range between 10 K and 300 K. This low temperature stage is located in the sample chamber on the left-hand side of the first prism array (see Fig. 1.7).
Upon successful completion of the cryogenic sample stage, the ESCHER set-up will give access to physical phenomena at a very broad temperature range from 10 K up to 1800 K. This allows one to perform a vast number of novel and interesting experiments. We expect the low temperature set-up to be operational by year-end 2015.
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References
[1] W. Telieps and E. Bauer, An analytical reflection and emission UHV surface electron microscope, Ultramicroscopy 17, 57 (1985).
[2] E. Bauer, Low energy electron microscopy, Reports on Progress in Physics 57, 895 (1994).
[3] R. M. Tromp, Low-energy electron microscopy , IBM Journal of Research and Development 44, 503 (2000).
[4] R. J. Phaneuf and A. K. Schmid, Low-energy electron microscopy: Imag- ing surface dynamics, Physics Today 56, 50 (2003).
[5] J. B. Hannon and R. M. Tromp, Low -Energy Electron Microscopy of Surface Phase Transitions, Annual Review of Materials Research 33, 263 (2003).
[6] R. M. Tromp, J. B. Hannon, A. W. Ellis, W. Wan, A. Berghaus, and O. Schaff, A new aberration-corrected, energy-filtered LEEM/PEEM in- strument. I. Principles and design., Ultramicroscopy 110, 852 (2010).
[7] A. Zangwill, Physics at Surfaces (Cambridge University Press, 1988), ISBN 978-0521347525.
[8] R. M. Tromp, Y. Fujikawa, J. B. Hannon, A. W. Ellis, A. Berghaus, and O. Schaff, A simple energy filter for low energy electron mi- croscopy/photoelectron emission microscopy instruments., Journal of physics. Condensed matter : an Institute of Physics journal 21, 314007 (2009).
[9] R. M. Tromp, J. B. Hannon, W. Wan, A. Berghaus, and O. Schaff, A new aberration-corrected, energy-filtered LEEM/PEEM instrument II. Opera- tion and results., Ultramicroscopy 127, 25 (2013).
[10] S. M. Schramm, A. B. Pang, M. S. Altman, and R. M. Tromp, A Con- trast Transfer Function approach for image calculations in standard and aberration-corrected LEEM and PEEM., Ultramicroscopy 115, 88 (2012).
[11] S. M. Schramm, Phd thesis, Leiden University (2013).
[12] A. W. Ellis and R. M. Tromp, A versatile ultra high vacuum sample stage with six degrees of freedom., The Review of scientific instruments 84, 075112 (2013).
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[13] S. M. Schramm, S. J. van der Molen, and R. M. Tromp, Intrinsic In- stability of Aberration-Corrected Electron Microscopes, Physical Review Letters 109, 163901 (2012).
[14] B. G. Levi, Interface between nonmagnetic insulators may be ferromag- netic and conducting , Physics Today 60, 23 (2007).
[15] M. S. Altman, Electron Microscopy, URL http://physics.ust.hk/
department/phaltman/leem/.
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