Stacking domains in bilayer Van der Waals materials

(1)

Stacking domains in bilayer Van der

Waals materials

THESIS

submitted in partial fulfillment of the requirements for the degree of

MASTER OFSCIENCE

in PHYSICS

Author : Tobias A. de Jong

Student ID : sxxxxxxx

Supervisor : Johannes Jobst, PhD

Dr.ir. Sense Jan van der Molen

2ndcorrector : Prof.dr. Jan Aarts

(2)

(3)

Stacking domains in bilayer Van

der Waals materials

Tobias A. de Jong

Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands

August 22, 2017 Abstract

Van der Waals materials such as graphene are layered materials that can be created in single atom thickness. In most cases there is more than one way to stack subsequent layers, often leading to domains of different stack-ings. In this work stacking domains in few layer stacks of graphene and MoS2are studied using Low Energy Electron Microscopy. From dark field

LEEM measurements on few layer epitaxial graphene on SiC it is concluded that two different types of domains exists: domains created from nucle-ation during growth and triangular stress domains induced from lattice mismatch with the underlying SiC. A detailed comparison between epitax-ial and quasi-freestanding graphene is made. As part of this comparison deintercalation of the latter to reform the former is performed. The hydro-gen diffusion out of the material occurring here is studied and linked to defects in the material and aforementioned stacking domains. For MoS2no

domains were analysed within the scope of this project, but a comparison of flatness for different substrates is made and using µLEED measurements a method to determine the number of layers is demonstrated and the two different orientations of the 2H polytype are experimentally identified.

(4)

(5)

Chapter

1

Introduction

In 2004 graphene was first isolated to a true monolayer [1], the first truly two-dimensional material of only one atom thick. This was done by exfoli-ation, also known as the ’scotch tape method’: as graphite sticks to scotch tape better than the individual layers of atoms stick together, it is possi-ble to separate down to single layers by repeatedly sticking it between two pieces of scotch tape. Since then it has been recognized a whole zoo of two-dimensional materials exists, such as hexagonal boron nitride (hBN) and several different combinations of transition metals and chalcogenides such as MoS2and TaSe2[2]. These materials have different properties: graphene

is a conductor, MoS2 is a semiconductor, hexagonal boron nitride is an

sulator and even weirder properties such as strange metals, topological in-sulation and superconductivity appear in these so-called Van der Waals materials. As such, exciting possibilities emerge when combining these in stacks of different materials.

When stacking layers of different or even the same material, angular and lateral orientation and lattice mismatch create all kind of different phe-nomena, such as stress, stacking faults and Moir´e patterns. If multiple en-ergetically equivalent possibilities for the precise stacking of layers exist, stacking domains can form: both stackings will coexist in the material, sep-arated by domain walls. In particular the existence of different stacking domains in bilayer graphene due to strain has been shown and character-ized [3–6].

Although exfoliation is a nice prove-of-principle method, it does not scale well. Creating high quality large area graphene through other meth-ods has turned out to be a challenge. A major contender in the pursuit of this goal is the growth on silicon carbide (SiC), where silicon is sublimated out of the SiC substrate, and the remaining carbon forms graphene. This allows for wafer-size graphene samples, although intermixed with bilayer areas. Here, the existence of stacking domains has been connected to mag-netoresistance effects [7]. Of the graphene layers grown in this way the lowest is still connected to the SiC substrate and not a true graphene layer, but a buffer layer. A treatment with hydrogen can lift this lowest layer to create so-called quasi freestanding graphene.

This work aims to characterize domains formed in Van der Waals ma-terials and form a hypothesis about their formation processes. Both forms graphene grown on SiC, as well as stacked exfoliated MoS2are studied

(8)

us-2 Introduction

ing Low Energy Electron Microscopy (LEEM∗_{) techniques.}

In the next chapter the experimental LEEM techniques used in this work are presented. The third chapter is dedicated to an explanation of the dif-ferent lattice structures of graphene and MoS2 and the theoretical

calcula-tions of the expected electron reflectivity, followed by details of the fabri-cation of the samples on page 23. In Chapter 5 the experimental results on graphene samples are presented and discussed, followed by results ob-tained on MoS2in Chapter 6 and finally the conclusion and outlook.

∗_{A glossary is included as an appendix at page 57}

2

(9)

Chapter

2

Experimental techniques

To analyze the samples of multilayer graphene and the MoS2 samples, a

wide variety of experimental techniques based on Low Energy Electron Microscopy (LEEM) was used. In the first part of this chapter those will be explained. The second part is dedicated to the data analysis on the gathered data.

2.1 Low Energy Electron Microscopy

gun (-15 kV) detector prism 1 sample (-15 kV + V_E) objective lens mirror prism 2 contrast aperture illumination aperture DEFL1 DEFL3

Figure 2.1: Schematic of an abber-ation correcting Low Energy Elec-tron Microscope such as the ES-CHER LEEM used in this research. The electron beam path is indi-cated in red.

In traditional microscopy, photons are used to image samples. Photons have the advantage that they are visible to the human eye and sources are abun-dant. Using photons as imaging particles has however one distinct disadvantage: due to the diffraction limit no structures smaller than roughly half of the wave-length of the imaging particles can be dis-tinguished (Rayleigh criterion). For vis-ible photons the wavelength is roughly half a micron, thus imaging structures smaller than 250 nm is in general not pos-sible.

As the wavelength of electrons is or-ders of magnitude smaller, the usage of electrons for imaging purposes en-ables the imaging of much smaller struc-tures, down to individual atoms in (scan-ning) transmission electron microscopy. In LEEM, reflected electrons with landing energies of only a few electron-volt (eV) are used to image samples. This combines the resolution advan-tage with another aspect: as electrons are fundamentally different particles compared to photons, with different spin, charge and mass, other aspects of materials can be imaged. The eV energy scales involved in LEEM are comparable to the energy scale of many atomic and structural aspects and processes in materials, e.g. electronic transitions, band widths and -gaps

(10)

4 Experimental techniques

and interlayer states [8].

The microscope used for the measurements presented in this work is the ESCHER LEEM at the Leiden Center for Ultramicroscopy [9]. The micro-scope is an aberration correcting LEEM built by SPECS GmbH, following the design of Ruud Tromp [10, 11].

As shown in Figure 2.1, electrons get accelerated by an electron gun at VG = −15 kV. After passing the alignment deflectors, the beam goes through a magnetic electron prism towards the sample, which can be pre-cisely positioned in the beam using a fine-mechanical piezo stage.

As the sample is at VS = −15 kV+VE, the electrons get decelerated again to a landing energy E0 corresponding to VE. Reflected and emitted electrons at the sample get accelerated by this same voltage back into the objective lens towards the prism. As the prism works with a magnetic field through the Lorentz force, the electrons are now deflected down, towards the imaging column to form an image.

Creating electron lenses without chromatic and spherical aberration is impossible. Particularly the cathode objective lens of the setup has severe aberrations, limiting the resolution in standard LEEMs. However, electro-static mirrors are much more amenable to tuning chromatic and spherical aberrations. Therefore a second prism is located further down the imaging column, deflecting the electron beam towards a tunable mirror. The aber-rations of this mirror are now tuned to compensate for the aberration of the cathode objective lens. This aberration correction enables a maximum resolution of 1.4 nm [12].

After the second prism the electron beam passes the projector lenses and gets imaged on the imaging system. This is described in more detail in Section 2.2.1.

2.1.1 Spectroscopy

Basic imaging is performed by choosing a landing energy E0at which the

contrast is optimal and capturing an image, where intensity on the CCD corresponds to reflected electron intensity. By controlling and varying the landing energy, spectroscopic measurements can be performed.

The simplest of such measurements is an IV-LEEM curve where the measured reflection intensity (I) of a region of interest (ROI) is plotted ver-sus the landing energy/voltage (V). For such a measurement the same area is imaged at a range of different landing energies, creating a stack of im-ages. One can then select different ROIs within the illuminated part of the sample and average over each area within each image in the stack. Each ROI now yields an intensity as a function of energy: an IV-curve. A typical example can be seen in Figure 5.3 on page 28.

The reflectivity is closely related to the density of states: in order for electrons to be absorbed in or transmitted through the material an electron 4

(11)

2.1 Low Energy Electron Microscopy 5

state with energy and momentum corresponding to the incoming electrons must be available in the material. As such high reflectivity at a particu-lar energy and momentum corresponds to a low density of states and low reflectivity to a high density of states. These IV-curves vary wildly for dif-ferent materials and states of matter, as they are influenced by a wide range of aspects of the material structure. Examples include the layer thickness of graphene and local stoichiometry [13, 14].

2.1.2 LEED

In optics, focal planes and backfocal planes are dual concepts. Rays origi-nating from a single location in a focal plane are all parallel in a backfocal plane, rays leaving a sample in a focal plane all parallel will converge in a single point in a backfocal plane. As photons (or electrons) diffracting from a sample will leave under specified angles according to Bragg’s law, the backfocal plane is often called the diffraction plane. Many of the more ad-vanced (electron-) optical techniques make use of this duality of diffraction and real space imaging. In particular the projector column of LEEM instru-ments can quickly be adjusted such that either a focal plane or a backfocal plane is imaged. The imaging of the backfocal diffraction plane is called Low Energy Electron Diffraction (LEED), or even VLEED for very low en-ergy, as compared to dedicated LEED instruments, which image at slightly higher energies (E0≈50 eV−500 eV)

The LEED data yields structural information: the diffraction criteria stipulate that constructive interference occurs for angles corresponding to multiples of the inverse unit vectors spanning the unit cell of the mate-rial. As such the symmetry of the unit cell is directly observable, but more information can be gained from a LEED pattern, in particular (Moir´e) re-constructions and periodicity shifts can be observed in LEED, a famous example being the 7×7 reconstruction of Si(111) [15–17].

Of particular note is that also while imaging the diffraction plane the landing energy can be varied. The resulting IV-LEED curves, where the re-gions of interest are now the different diffraction spots, can yield additional information about the surface of the material.

2.1.3 Bright Field, Dark Field and µLEED

The art of aperture application would be an adequate subtitle for this section, as all the techniques described here use various apertures. In a certain sense the use of apertures has already been introduced: the selection of a region of interest from an image as introduced for IV-curve, is in fact an aperture, albeit a software implemented one.

To perform measurements probing more specific properties, different hardware apertures are implemented in the LEEM as well:

(12)

Most often used is the Contrast Aperture. This aperture, as indicated in Figure 2.1, lies in a backfocal plane just on top of the projector column. Its name is derived from the fact that it is most commonly used to enhance contrast, in particular for higher landing energies. As the energy of the in-coming electrons increases, a large number of inelastic processes or decay pathways open up. The electrons coming back after such an inelastic event have a broad distribution of random energies and momenta, although their energy will always be lower than the landing energy. These electrons are of-ten referred to as plainly ‘secondary electrons’, although inelastically scat-tered electrons form the bulk contribution here. They are however also imaged, yielding a uniform disc in the diffraction plane, referred to as the Ewald sphere. The radius of the disc is quadratic in the landing energy, as the maximum momentum parallel to the sample k_k (which determines the radial position in diffraction) is capped by the landing energy via the (vacuum) dispersion relation: E= ¯h2k2

2me.

In real space images, the secondary electrons yield a background, de-creasing the dynamic range and resolution of the signal. To retrieve this contrast, the contrast aperture can be inserted around the specular reflec-tion, this way blocking most of the secondary electrons forming the Ewald sphere far around the specular reflection. This imaging mode is referred to as Bright Field imaging or simply BF-LEEM as only the (bright) specular reflected beam is used.

Putting the contrast aperture around a diffracted beam and imaging in real space is called Dark Field (DF-LEEM) imaging and can reveal spatial information about the structure and symmetry of the atomic lattice. The canonical method to perform Dark Field measurements is to tilt the illumi-nating beam using the alignment deflectors (DEFL1 and DEFL3 in Figure 2.1) such, that the reflected beam of interest leaves the sample normal to the surface, along the optical axis. This way the beam traverses the imag-ing column along the optical axis, minimizimag-ing aberrations. DF imagimag-ing and DF-IV spectroscopy, where in DF mode the landing energy is varied, are the primary tools to study the stacking domains as introduced in Section 3.1.

Tilted alignment

For graphene however, the angle of the diffracted beam is very large, as the unit cell is extremely small. Due to this large angle, it is not feasible to do DF measurements with the canonical alignment. Instead, as illustrated in Figure 2.2, an alignment was used where the refracted beam of interest was at equal angle to the normal and optical axis as the specularly reflected beam. Coincidentally, since the angle of incidence equals angle of reflec-6

(13)

2.1 Low Energy Electron Microscopy 7 (a) K′ K (0, 0) (b) (0,0) 2K K (c) (0,0) 2K K K′

Figure 2.2: Illustration of beam paths in (a) Bright Field, (b) canonical dark field and (c) tilted dark field alignment and corresponding LEED images for hexagonal symmetry. Different diffracted and reflected beams are color coded for equiva-lence classes in trigonal symmetry, optical axis is indicated in gray.

tion, this means that the refracted electrons leave along the same trajectory as the illumination beam comes in.

Another notable aspect of this alignment is that also for the specularly reflected beam the rotational symmetry is broken: Although the picture with the incoming and reflected beam seems symmetrical with respect to time inversion, the transmitted and absorbed electrons break the symmetry. A second aperture is the Illumination Aperture. This aperture is lo-cated in a focal plane in the upper prism (See Figure 2.1), in the beam path before the beam reaches the sample. As such it can be used to limit the size of the illuminated spot on the sample to a minimum of about 200 nm in diameter. Obviously, with a resolution of about 1.4 nm real space imaging is not really useful in this mode. However, using this aperture diffraction information of very local areas can be obtained, and the technique is aptly named µLEED.

2.1.4 Angular Resolved Reflective Electron Spectroscopy

In Angular Resolved Reflective Electron Spectroscopy (ARRES) an extra parameter is added to IV-measurements, by varying the angle of incidence upto angles corresponding to the edge of the Brillouin zone, respectively the K- and M-point [18]. Throughout all these angles the primary spot

(14)

is measured. In fact the outermost angle at the M-point corresponds to the tilted bright field alignment. The combination with variation of energy yields an ARRES map of reflection intensity as a function of angle and en-ergy.

Where a IV-curve can be related to the density of states, the addition of angle of incidence means that ARRES maps can be related to the un-occupied band structure of the material, that is everything above the vac-uum energy. In that sense it is complementary to Angular Resolved Photon Emission Spectroscopy (ARPES), which measures on the occupied bands.

These ARRES measurements can be performed either while imaging the image plane or while imaging the diffraction plane, where the loss of spatial information is traded for an increased intensity resolution.

The original stated goal of this project was to apply ARRES to measure on the domain walls appearing in graphene and other Van der Waals ma-terials (See Section 3.2). As such real space ARRES measurements of both types of graphene sample as well as MoS2and MoTe2were performed.

However, the real space image shifts over the CCD due to the changing angles of the electron beam in the optics that come with tilting the electron beam to the edges of the Brillouin zone. Within the scope of this project no drift correction algorithm was found that achieved sufficient accuracy to resolve the domains, see Section 2.2.4.

2.2 Image analysis

A LEEM is a microscope, i.e. it takes images. To convert those images to quantitative data, the images are post-processed in software to relate them to physical quantities and to extract features. In this section the techniques used for this are elaborated on.

2.2.1 Detection system

The detector system of the ESCHER LEEM instrument consists of a stacked pair of microchannel plates to amplify the number of electrons, a phosphor screen to convert the amplified electron signal to photons and finally a CCD camera to convert those photons to a digital signal.∗

2.2.2 High dynamic range measurements

The amplification of the microchannel plates is exponential in the applied high voltage, which can be varied from 0 to approximately 1.8 kV. The am-plification has been characterized and calibrated as a function of applied

∗_{de facto again electrons. If this seems somewhat devious, you are not the first, but} ini-tiatives to develop a direct imaging method for electrons have proven to be not without difficulties and were only fairly recently successful [19, 20].

8

(15)

2.2 Image analysis 9

voltage. High Dynamic Range (HDR) measurements take advantage of this aspect by actively tuning the high voltage on the channelplate to the measured signal and recording the voltage applied to the channelplate in addition to the image itself. By correcting for the channelplate setting after-wards, the measurement of signals over more than 5 orders of magnitude is achieved, while maintaining a similar signal-to-noise ratio.

2.2.3 Detector correction

Both the microchannel plates as well as the CCD introduce systematic er-rors, including dark count, thermal noise and spatially uneven amplifica-tion. In addition to that the current emitted from the gun and reaching the sample is not perfectly constant in time.

We use techniques well-known from astronomy and light imaging in general to compensate for these errors.

Dark frames

Any CCD will have a certain dark count rate: pixels get excited at a certain rate even in the total absence of light. The electronics of the CCD will also contribute a constant to the recorded signal, independent of exposure time. In literature compensation for this effect is referred to as a bias frame.

The CCD camera in the ESCHER setup is actively cooled using a Peltier element to minimize thermal excitation. If thermal noise becomes the limit-ing factor the only further remedy is to increase acquisition time and aver-age over multiple imaver-ages. The random Poisson distribution of the thermal noise means the variance due to thermal noise will decrease by a factor n when averaging per pixel for a set of n images, equivalent to a factor√n in the standard deviation or width of the distribution.

The spatial variance in gain and dark count is statistically independent from the thermal noise. For independent randomly distributed variables, the variances add up, and as such we have:

Var(ICCD) =Var(Itherm+Ispatial) =Var(Itherm) +Var(Ispatial)

To characterize the dark count, dark frames without any exposure, i.e. the channel plate voltage turned down to zero, were taken. The statistics of frames with an exposure of 16×250 ms (mcount=16), both for the total data set of 16 frames as well as for the average per pixel (effectively creating one 16_×16_×250 ms=64 s measurement) are shown in Figure 2.3.

(16)

10 Experimental techniques 740 760 780 800 820 840 860 P ix el v al u e 700 750 800 850 900

Pixel value @mcount16 0 20000 40000 60000 80000 100000 #p ix el s Single frame 16 frame average 800 1100 0 4 8

Figure 2.3: (left)An averaged dark image with a total exposure of 64s and (right) the corresponding histograms of a single image (blue) and for a by-pixel average of 16 images (red). The inset shows the∼ 30 hot pixels with consistently higher

dark count.

Var16 = 1

16Var(Itherm) +Var(Ispatial) =46.231 Var1 =Var(Itherm) +Var(Ispatial) =123.434 ⇒Var(Itherm) = 16 15· (123.434−46.231) =82.35 Var(Ispatial) =41.08 σ(Ispatial) = q Var(Ispatial) =6.4

As we almost exclusively take images with an exposure time of 250 ms, dark count and CCD electronics form on average a constant addition of IDC(x)to the signal IS(x), therefore compensation for it is possible by sub-tracting an averaged set of dark count frames, taken at the same 250 ms exposure.

The spatial standard deviation turns out to be 6.4 on a value of 800, cor-responding to about 1 per cent variation, which is smaller than the actual discretization error for a single 250 ms frame. Therefore we chose to even further simplify this compensation by subtracting a constant dark count value from the entire image, equal to the mean:

IDC(x) = 801

16 images =50.1/image

Special care is taken to prevent negative values: due to the thermal fluctu-ations, the value of a very dark pixel can actually be below the dark count value. These values are rounded up to zero:

IS(x) =max(ICCD(x) −IDC, 0) 10

(17)

Do note however that the rounding does influence the statistics of the pixel values, which can become important when fitting functions with diminish-ing values, e.g. fittdiminish-ing a diffraction peak in LEED!

Flat Fielding

The amplification of microchannel plates is in general spatially not very uniform. As is inherent to the name, they consist of microchannels, for our system about a million. This means our microchannel plates have about as many pixels as our 1MP detector, so Moir´e effects between both microchan-nel plates and the detector are nearly unavoidable. In addition to that, overexposure tends to physically harm the channelplate, locally reducing the gain. Both these effects have in common that they distort the bright-ness of areas of the images, but do so by a factor (approximately) constant in time.

The process of compensating for these effects is known as flat fielding and constitutes the division by a reference picture of constant illumination. Of course we first need to correct this reference picture for dark count. In our system images taken far in mirror mode, where the electrons never reach the sample, form a good source for flat field images IFF.

IS(x) =Amax(ICCD(x) −IDC, 0) max(IFF(x) −IDC, 0)

In principle this procedure could yield a division by zero, however the flat field image is in general optimized for exposure and as such has so much stray light exposure that this never occurs, even in the area outside the channelplate. The normalization factor A is chosen in one of two ways. Most often the mirror mode, where all electrons are reflected, is normal-ized 1. This results in a signal expressed as the reflected part of the electron beam. Another way is to chose A such that the signal corresponds to the actual beam current. The normalization is stored separately for each frame. This way the correction for the set channelplate bias for HDR measure-ments as well as compensations for other fluctuations such as the emission current of the gun can be incorporated, while preserving dynamic range in the images stored in intermediate stages of the data analysis.

2.2.4 Drift correction

In order to select an area and create an IV curve from it, the image of the sample should not shift over the detector as a function of energy. Unfortu-nately, thermal drift and imperfect alignment mean this is almost never the case. In order to create IV-curves the stacks of images are drift corrected. Unfortunately the strong changes and inversions in contrast make many conventional algorithms only partially sufficient. In order to nevertheless

(18)

create driftless stacks, first specific features are chosen in the image. Using this part of the image as a template for template matching, like in conven-tional drift correction, it is attempted to automatically detect the position of this feature for all images in the stack. If the match is better than a cer-tain threshold value, the x-shift and y-shift compared to the template are recorded. A polynomial is then fitted through all detected shifts and these fitted polynomial x and y shifts are applied to the image.

2.2.5 Visualizing spectroscopy

The spectroscopy data sets produced by a IV-LEEM measurements are three-dimensional and as such hard to fully visualize in an intuitive way:

Although IV-curves visualize the full spectral information, spatial in-formation is limited here to comparing different IV-curves. A sequence of images from the IV on the other hand (either as separate images or as a movie) gives full spatial information as well as a relevant subset of the spectral information, but the way to compare an area for different energies is non-intuitive. 0 1 2 3 4 5 6 7 energy (eV) 10−2 10−1 100 in te n si ty (a.u .) TRILAYERPRIME BILAYER TRILAYER

Figure 2.4: IV-curves of some areas and susceptibility curves of red, green and blue used to produce the cover image.

In an attempt to create a more intuitive way, I adapted a method to view spectral data known from nature: colour. The human eye is separately sen-sitive for light from three different energy ranges, canonically known as the colours red, green and blue. The measured intensities are then combined by the brain and interpreted as colour. As this interpretation is at the same time very natural and intuitive to humans as well as quite sophisticated, presenting spectroscopic data using as much of this interpretation pipeline as possible might yield qualitative benefits, although inferior for quantita-tive interpretation.

12

(19)

Using colour is of course well established in electron microscopy: com-posite images using different colour channels for bright field and differ-ent order dark field images are common place, as well as represdiffer-enting ar-eas obtained from IV characterization in different colours. These methods are however no direct representation of the spectroscopic data: abstraction steps are applied and imposed as colour over a single intensity image.

I interpreted electron energies as photon energies and integrated IV data for each colour channel over its susceptibility range. This integration has as additional benefit that more data is used, reducing noise. A pre-requisite is however that the drift of the image across the used integration range is minimal, to prevent chromatic distortion of features. In Figure 2.4 the susceptibility curves used to create the cover image together with some IV-curves of the same datasets are plotted.

It turned out this produced “true color” images that allowed for intu-itive classification of different areas. In some cases an offset in energy was used to select an region of the spectrum with enough contrast differences between areas. This could be extended by selecting energy ranges for the different colours, but this is not done within the scope of this work.

(20)

(21)

Chapter

3

Theory

3.1 Stacking of hexagonal lattices

The two-dimensional unit cell of graphene contains two carbon atoms to create a hexagonal lattice. Thus the lattice of graphene consists of two trig-onal sublattices containing an atom, which we label per convention a and b, as depicted in Figure 3.1 for the gray lattice. The difference between a hexagonal and a trigonal lattice is now that there is no atom at the third trigonal sublattice, which we call c. Although the unit cell contains two atoms, note that for this single layer description perfect six-fold symmetry is conserved for the lattice. Thus for a single layer graphene one would expect a perfectly sixfold symmetric LEED pattern.

3.1.1 Graphene

The perfect symmetry is however destroyed when multiple layers of graphene are stacked on top of each other. The potential landscape, as depicted in Figure 3.3, has been calculated and experimentally confirmed to be such that configurations with an atom of the unit cell in the second layer on top of the empty c sublattice have minimum energy [21]. Whereas the sit-uation of direct vertical stacking of the lattices corresponds to an energy maximum. There are however now two commensurate choices to put the second atom of the unit cell: either on top of the a sublattice or 180 degrees rotated on top of b.

The different stacking geometries are named after the lattice position of the primary atom in the unit cell. If we define the primary atom of the unit cell for a fixed rotation of the unit cell, we note that the second atom we place in the unit cell of the top layer is either the primary or the secondary atom. When looking at the shift of the unit cell, we conclude that these lattices should be called AB and AC, as the primary atom either sits on the empty lattice site c or the secondary atom when comparing the to first layer. Note however that only the relative position of the lattices is relevant and as such the primary layer can always be called A. A stacking where all carbon atoms lay directly on top of each other would therefore be called AA.

When adding a third layer, it can not be in the same position as its neigh-bour, so starting with AB we either get ABC or ABA. Thus for a triple layer

(22)

16 Theory

there are in total 4 possible stackings: ABA, ABC, ACA and ACB. 3.1.2 Molybdenum disulphide

Transition metal dichalcogenides have layered structures somewhat sim-ilar to graphene. For the transition metal dichalcogenides in general dif-ferent polytypes, i.e. how the difdif-ferent layers are oriented with respect to each other, exist. Polytypes are designated by a number reflecting the number of layers in the unit cell, and a letter indicating whether the unit cell is hexagonal (H), rhombohedral (R) or trigonal (face-centered cubic, T). As for different polytypes the bond orientations can be different, material properties can differ widely, especially between different unit cell shapes.

Figure 3.2: Top view and sideview of the atomic structure of the different poly-types of MoS2. In the sideview for each

polytype the full layer count of the unit cell is shown. Adapted from [22].

For molybdenum disulphide three polytypes are known: 1T, 2H and 3R, as shown in Figure 3.2. The unit cell for the natu-rally most abundant, semiconduct-ing, 2H polytype consists of two Van der Waals layers:

In the first layer, one trian-gular sublattice is occupied by the molybdenum atoms, cova-lently bonded to the two vertically stacked sulfur atoms at the other lattice site.

The second layer now contains the same, but the sulfurs go on top of the molybdenum atom of the bottom layer and vice versa. It is worth noting however that the

sin-Figure 3.1:The two possible stackings of a bilayer of hexagonal graphene lattices, where the primary atom of the second stacked layer either goes in the b position (blue) or in the c position (red) on top of a bottom lattice in a and b (grey,solid). (Adapted from Hibino et al. [6])

16

(23)

3.2 Domain formation 17

gle layer already breaks the sixfold symmetry due to the two different occupations of the lattice sites. This symmetry breaking is visible using diffraction techniques such as LEED and Dark Field and will be explored in Section 6.2.

3.2 Domain formation

When there is a mismatch between the stacked lattices, be it due to stress, strain or twist, the stacking costs more energy, due to atoms in the one layer being in all kind of unfavorable places compared to the adjacent layer. In such cases it is sometimes energetically favorable to form domains of well-stacked areas, separated by dislocation lines in which all stress and stacking errors are concentrated.

Figure 3.3: (a)The potential landscape of a bilayer graphene as a function of rel-ative position. The six minima correspond to AB and BA = AC stacking, the maximum to AA stacking. From each minimum three different minimum energy paths to the other stacking exist (Labelled with red, blue and green arrows). (b) The potential energy along such a path. (c) RGB Composed DF-TEM image show-ing the boundary structure with the three types of domain walls. (d) Moir´e pattern of two twisted graphene layers giving a topological equivalent structure as for the strained case. Figure adapted from [3].

This is the case for graphene, as explored before by e.g. Alden et al. [3]: From the potential landscape as shown in Figure 3.3, it can be seen that there exists three least-energy paths from AB stacking to AC, correspond-ing to relative shifts of the lattices in directions 120 degrees from each other.

(24)

18 Theory

As shifts in these direction are energetically favoured compared to other directions, domain walls will form preferentially in these directions. Cross-ings of domain walls can relatively freely move along a domain wall and meet up. A combination of the three types of domain walls costs less en-ergy than two combinations of two, and as such triangular domains with one border of each kind form, as elegantly visualized by Alden et al. using DF-TEM (Figure 3.3c).

In addition, when epitaxially growing a material where multiple ener-getically equivalent stackings are possible, nucleation domains can form as in general the growth will not start in one place and spread uniformly from there. Instead the growth will start at multiple nucleation sites, but as none of the stackings is energetically favoured, growth will start from each site more or less randomly choosing a stacking orientation. As the layer com-pletely fills and the growing domains of different orientation start to touch, nucleation domains form, somewhat reminiscent of magnetic domains in a cooling Ising model. As observed by Alden et al., these domains may also move when heated above 1000◦C.

For twisted MoS2bilayers the domain forming mechanism is somewhat

more complicated [23, 24]. In literature five different stackings are distin-guished, of which two are unstable as these would stack sulfur atoms of neighbouring layers on top of each other.

If the relative orientation of the layers is close to 0◦, two rotated 3R-like stackings are available (AbA−BcB and AbA−CaC in the notation of Fig-ure 3.2). As these are mirror inversions (rotation and mirroring are here the same as the lattice itself is mirrorsymmetric), the stacking energy is equal, but the symmetry is broken as the sulfurs in the top layer lie either on top of a molybdenum atom or on top of the empty trigonal sublattice (In which case the sulfurs of the bottom layer lay beneath the top molybdenum). This means a contrast might exist at some landing energies.

If however the relative orientation is close to 180◦, there is no other stacking equivalent to the ground state 2H stacking available, but a shifted stacking (AbA₋CbC) where the sulfurs go on top of the empty sublattice, yielding a higher energy, exists. This means in this case all domains are the same 2H stacking, but as in the graphene case, three types of boundaries exist, where the relative shifts go through the AbA−CbC stacking, with the sulfur on sulfur stacking occuring where domain boundaries cross.

3.3 Electron diffraction

As mentioned in Section 2.1.2, the diffraction spots in a backfocal plane are related to the crystal structure of a sample. In this section a short in-18

(25)

3.3 Electron diffraction 19

troduction of the formulas involved is given, in order to derive the lattice constant of a material from LEED data. The electrons in vacuum have an energy related to their momentum by the dispersion relation:

Ek = ¯h

2 |k_|2

2me

Where the wave vector k is related to the wavelength: k= 2π_λ .

For electrons with incoming wave vector k0 = k₀k+k⊥0 to

construc-tively interfere from a real space 2D lattice with lattice vectors{a, b}, they must satisfy the Laue condition:

kk₋kk₀ = Glm = la∗+mb∗

Where Glmis the reciprocal lattice spanned by the reciprocal lattice vectors

a∗and b∗, related to their realspace counterparts as follows:

a∗ = 2πb× ˆn

|a_×b_| , b

∗ ₌ 2πa× ˆn

|b_×a_|

Such that they lie perpendicular to the corresponding realspace vector and have a length inversely proportional to the realspace lattice vector.

Diffraction is an elastic process, so momentum and energy are con-served. For landing energies where |k_| is smaller than |a∗_|, the electron would need to gain energy to exit with the momentum specified by Bragg criteria. As such, the diffraction spots appear when the energy of the in-coming electrons corresponds to a momentum equal to the reciprocal lat-tice vector:

√

2meEk

¯h ≥ |Glm|

Where Glmis the reciprocal lattice vector of the appearing diffraction spot. For a hexagonal lattice the first order reciprocal lattice vectors are related to the real space lattice constant a= |a_{| = |}b_|as follows:

|G01| = 2π

a sin π/3 = 2π a1₂√3

The combination we can use to calculate the lattice constant from the en-ergy at which the diffraction spots appear:

a= ₁ 2π¯h 2

√

(26)

20 Theory

3.4 Reflection curves

Using multiple scattering theory [8], the reflection, refraction and trans-mission under tilted illumination were calculated by E. Krasovskii for free-standing bilayer graphene and both ABC- and ABA-like stacked trilayers. Here the optical potential modeling inelastic processes was not taken into account. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R el at iv e in te n si ty AB ABA ABC 10 20 30 40 50 60 energy (eV) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R el at iv e in te n si ty AB ABA ABC AC ACA ACB

Figure 3.4: (top):Tilted bright field reflectivity of multilayers graphene calculated using multiple scattering theory. (bottom): Reflectivity of multilayers graphene in tilted dark field.

It is important to note that even for the different stackings, trigonal sym-metry is always conserved. As such, always two equivalence classes of first order refracted beams exist, labeled K and K′. Furthermore, inversion sym-metry means that the K beam of AB stacking is equivalent to the K′ of AC and vice versa.

This can be seen from Figure 3.1: the AB lattice is a mirrored version of the AC lattice, so a beam coming in tilted from below on an AC lattice is the same as a beam coming in tilted from above on an AB lattice. This holds 20

(27)

3.4 Reflection curves 21

equally for the combination of ABA and BAB stackings and the combina-tion ABC and ACB.

(28)

(29)

Chapter

4

Sample Fabrication

Samples used for this research were fabricated at the University of Erlangen-N ¨urnberg and at Harvard University, as described in this section.

4.1 Graphene on silicon carbide

For the study of stacking domains in few layer graphene, graphene on sil-icon carbide samples were grown by Christian Ott from the Weber group at the University of Erlangen-N ¨urnberg, Germany. The process used to fabricate the samples is atmospheric pressure graphitisation of silicon car-bide [25]. As the vapor pressure of silicon is higher than that of carbon, it sublimates at lower temperatures. Therefore one can create a layer of car-bon on SiC by simply heating the sample to high temperatures. The carcar-bon formed in this process is highly crystalline. Without further treatment, the layer closest to the SiC will still covalently bond to the SiC and form a so-called buffer layer. All higher layers will however form graphene as shown in Figure 4.1. The graphene will form preferentially at the step edges of the SiC surface. As such, step edges are in general surrounded by a higher number of carbon layers. The non-intercalated samples used in this work were grown on 6H-SiC(0001) in a 900 mbar Argon atmosphere at 1800◦C for 30 minutes.

4.1.1 Intercalation

Figure 4.1:Illustration of the atomic structure for both epitaxial graphene (EG, left) and Quasi Freestanding (QFG, right) samples. For the EG samples the lowest layer of carbon forms a buffer layer covalently bonded to the SiC, unakin to graphene. For QFG the bonds with the SiC are substituted by hydrogen, ‘promoting’ the buffer layer to a true graphene layer. Adapted from [26].

(30)

24 Sample Fabrication

When these samples are annealed in a hydrogen atmosphere, hydro-gen will diffuse under the buffer layer and bond to the dangling bonds of the SiC, replacing the bonds between the buffer layer and the SiC [27]. The general process of inserting foreign atoms in a lattice in this way is known as intercalation. As the bonds of the buffer layer are released, the buffer layer now transforms in an additional layer of graphene. Because graphene layers are in this situation only bonded by Van der Waals interac-tion to the hydrogen terminated SiC, these intercalated samples are known as ‘quasi free standing few layer graphene’ (QFG or in the case of bilayer: QF-BLG). Intercalated samples used for this research were grown at 1675◦C for 30 minutes in a 900 mbar Argon atmosphere and after that intercalated at 970◦C for 90 minutes in a hydrogen atmosphere. Before growth these samples were heated to 970◦C in a SiC container to induce step bunching, i.e. to move the step edges of the SiC surface closer together to form larger homogeneous areas.

It has been shown that the hydrogen does not permeate the graphene, but seeps in from the edges and through defects [26]. This process of in-tercalation is reversible: when heated to a high enough temperature, the hydrogen will dissociate from the SiC and the bottommost graphene layer will transform back into a buffer layer covalently bonded to the SiC. This process and the effects of impurities on it are studied using LEEM in Sec-tion 5.3.

4.1.2 Sample characterization by SEM

After fabrication in Erlangen, Scanning Electron Microscopy (SEM) imag-ing was performed to inspect the samples. Images are shown for reference in Figure 4.2.

Samples were not optimized for homogeneous layer count, but to have general coverage and some different layer counts.

24

(31)

4.2 Molybdenum disulphide on silicon nitride membranes 25

Figure 4.2:SEM images of sections of the EG (top) and QFG (bottom) samples. For EG two different magnifications are shown, for QFG both as grown (left) and after intercalation (right) are shown. The lines of lower intensity are higher layer count carbon areas, formed around the step edges of the SiC substrate.

4.2 Molybdenum disulphide on silicon nitride

mem-branes

The goal of this research was to study a synthetic bilayer of MoS2 where

a small twist angle between both layers is created. Due to the twist, like in graphene, stacking domains form due to Moir´e reconstruction, as elabo-rated in Section 3.2.

Hyobin Yoo from the Philip Kim group at Harvard University fabri-cated samples of Molybdenum disulphide (MoS2) on silicon nitride

mem-branes. These membranes consist of a silicon substrate with a silicon nitride layer, where in the center the silicon has been etched away to create a SiN window less than 200 nm thick. By mounting the sample on such a mem-brane, it is possible to study the sample both using transmission electron microscopy (TEM) as well as LEEM.

The MoS2flakes were created by exfoliation and stacked together using

stamping techniques, where a stamp with a sticky polymer is used to pick up flakes and deposit them on the substrate [28].

(32)

26 Sample Fabrication

TEM, exposure to high energy electrons from the TEM beam made further study in LEEM unfeasible, as discussed in Section 6.1.

Subsequently, a sample of native few layer MoS2 on hexagonal Boron

Nitride (hBN) was mounted on a membrane and first sent to Leiden, to study in LEEM before being sent back for TEM studies. The intermedi-ate layer of hBN was introduced to creintermedi-ate an atomically flat substrintermedi-ate for the MoS2in order to reduce corrugations and other irregularities impeding

sharp diffraction peaks needed for dark field imaging.

Results of the LEEM study on this sample are presented in Section 6.2. 4.2.1 Optical images

Figure 4.3:Optical microscope images of the native few layer MoS2flake: before

transfer, after transfer onto the hBN and finally on the TEM window with a lead attached. Images courtesy of Hyobin Yoo.

26

(33)

Chapter

5

Few layer graphene

We studied the domain structures of both Epitaxial Graphene grown on SiC (EG) and Quasi Freestanding Graphene (QFG) samples fabricated as described in Section 4.1. The results are split in three parts: First the bright field measurements reproducing results on layer counts and exploring the difference between EG and QFG, then the tilted alignment measurements exploring the stacking domains and finally the measurements on the dein-tercalation of QFG.

5.1 Bright Field measurements

In bright field LEEM, as shown in Figures 5.1 and 5.2, both samples show similar structure of patches of graphene of different layer count, virtually featureless aside from step edges and screw defects from the underlying SiC substrate.

Figure 5.1:Stitched Bright Field overview of EG taken at E0 =2.3 eV. Here

dark-est areas correspond to monolayer graphene, lightdark-est to bilayer, and intermediate to higher layer count. In color indicated areas are used for IV-curves with corre-sponding color in Figure 5.3 to deduce layer count. Scalebar is 1 µm.

BF-IV curves for both samples and different layer thicknesses are shown in Figure 5.3, taken from areas indicated in Figure 5.1 and 5.5.

(34)

28 Few layer graphene

Figure 5.2: Stitched Bright Field overview of QFG taken at E0 = 4.2 eV. Here

darkest areas correspond to bilayer graphene, lightest to trilayer, and intermediate to four layers. Scalebar is 2 µm.

10−2 10−1 100 in te n si ty (a.u .) 7L + buffer 6L + buffer 5L + buffer 4L + buffer 3L + buffer 2L + buffer 1L + buffer 10−1 100 101 102 0 5 10 15 20 25 30 35 40 energy (eV) 10−2 10−1 100 in te n si ty (a.u .) 4L 3L 2L 0 2 4 6 8 energy (eV) 10−1 100 101 102

Figure 5.3: Bright field IV-curves comparing different graphene layer counts on EG (top) with those on QFG (bottom). Both sets of curves are normalized such that for each curve the mirror mode signal corresponds to 1 and shifted such that the mirror mode transition is at E0=0 eV. On the right the minima of the resonant

states for the different layer counts are shown, vertically offset for clarity.

28

(35)

5.2 Tilted alignment measurements 29

As was first shown by Hibino et al. [13], the resonant states between graphene layers form an easy way to determine layer count on graphene samples using (bright field) LEEM-IV. Upon hydrogen intercalation, an ex-tra band, i.e. minimum in reflectivity as a function of energy, will appear, signaling the conversion of the buffer layer to an extra graphene layer [27]. This extra band has an energy almost identical to a band as would be formed by a pure graphene system, even though it is actually due to an interlayer state between the graphene layers and the hydrogen, as calcu-lated by Feenstra et al. [29].

As expected from the contrast seen in SEM characterization (See page 25) and the contrast in plain bright field, the IV-curves show that the sam-ples contained a varied set of carbon layer counts. From the bright field IV-curves it was determined that the samples contained predominantly 2 to 3 layers of carbon (including the buffer layer for EG), with areas of higher layer count up to at least 6 layers around defects and with no areas with a coverage of less than 2 layers.

When comparing with the non-intercalated EG, the minima for corre-sponding carbon layer counts for QFG are shifted around+0.7 eV with re-spect to the mirror mode (See Appendix A). Ristein et al. report a shift of

−0.75 eV of the Fermi level relative to the Dirac point by effective doping when performing intercalation [30]. As the mirror mode is linked to the Fermi level and the band structure with the Dirac point, this is in reason-able agreement. It is however not clear yet how in the tight binding picture the extra interlayer state in the hydrogen – carbon spacing is coupled to the other states.

Another difference in the curves is that the QFG curves lose intensity faster for higher energies compared to the epitaxial graphene, which would correspond to a larger optical potential. It is however very likely that this difference is purely due to a slight difference in alignment.

The calculations from Feenstra et al. predict that the minima of the in-terlayer states should be repeated in the second order minimum between 15 and 20 eV. Experimentally these higher order minima would be broad-ened due to larger scattering losses. Hibino et al. noted that they do not see this repetition on their EG samples. Our data on EG agrees with that: there is indeed no trace of second order minima. For the QFG however clear signs of a number of dips corresponding to the layer count can be seen in that range.

(36)

Figure 5.4:Stitched Dark Field overview of EG sample taken at E0 =20.7 eV.

In-dicated in blue is the area shown in BF in Figure 5.1. Here dark and light areas correspond to the two different stackings for at least 2 graphene layers, intermedi-ate intensity regions correspond to single layer graphene (+ buffer layer). Scalebar is 2 µm.

5.2 Tilted alignment measurements

When measuring in Dark Field using the tilted alignment, as elucidated on page 6∗_{, the graphene that seems so pristine and homogeneous in Bright}

Field, shows a surprisingly rich structure.

Figure 5.5: Bright Field (E0 = 4.3 eV) and Dark field (E0 = 36 eV) images of the

same area on the EG sample. The two dark field images are taken from diffraction spots of different inversion classes and show an inversion of contrast.

On EG samples, as shown in Figure 5.4, the monolayer graphene ar-eas exhibit no clear domains, but many ridge-like striped structures. These structures show similarty to what Speck et al. noticed on monolayer graphene

∗_{Throughout this work the colour of scalebars in plots corresponds to the used} diffrac-tion spot colour in Figure 2.2.

30

(37)

on buffer layer using Dark Field imaging of the much lower angle Moir´e spots due to a reconstruction with the underlaying SiC lattice [31].

Irregularly shaped domains show up in dark and light for areas with more than one layer of graphene. When comparing to bright field images of the same area it becomes clear that these dark and light domains span across areas of different layer count.

As indicated in Figure 5.5, the dark and light domains invert when imaging using a diffraction spot from the other trigonal equivalence class, but yielded similar contrast for other first order diffraction spots in the same equivalence class. This indicates that the domains correspond to something breaking the hexagonal symmetry to a trigonal symmetry, sup-porting that these domains are in fact stacking domains.

Figure 5.6:Stitched Dark Field overview of QFG taken at E0 =17 eV. Scalebar is

2 µm.

On DF images of QFG such as in Figure 5.6, in addition to the irregu-larly shaped dark & light domains found on EG, triangular domains appear with comparable contrast on the bilayer (corresponding to the monolayer graphene + buffer layer on EG samples, indeed no ridged areas of inter-mediate contrast are found on QFG). This type of triangular domains has been observed in TEM before and linked to strain between the stacked lay-ers [3, 4].

Upon closer inspection at particular energies (e.g. at E0 = 30 eV, as

in Figure 5.7, where two such triangular areas with different contrast are marked with green circles.) even within the irregularly domains on the trilayer, contrast between triangular subdomains is observed.

(38)

Figure 5.7: Bright Field (E0 = 2.2 eV) and Dark field (E0 = 30 eV) images of the

same area on the QFG sample. Circles on Bright Field indicate areas used for IV-curves in Figure 5.3, those in the DF image for IV-IV-curves in Figure 5.8.

A comparison of tilted dark field IV-curves taken from different do-mains on EG and QFG with the theoretical IV-curves for different stackings freestanding bilayer and trilayer graphene as calculated by Krasovskii is made in Figure 5.8 (See Section 3.4 for details on the theoretical curves.).

The experimental data differs from the theoretical curves for a number of reasons as discussed in Section 5.2.2. However, using the information from bright field measurements to assign layer counts, the relative intensi-ties of IV-curves allow identification of each domain type with a different stacking order:

For EG the curves of domains in bilayer graphene areas and domains in trilayer areas correspond reasonably well to respectively both bilayer possibilities and the two possible orientations of the top layers of a trilayer. The matching of nB, i.e. the dark curves, to AC and ACX stacking can be seen for example from the minimum at 17 eV, the relative differences between 2A and 3A yields a well visible correspondence to the theoretical curves for AB and ABA in the 32 to 45 eV range.

For QFG, the triangular domains in the bilayer correspond to AB and AC stacking, as do the irregular domains in the trilayer, also most easily seen in this same 32−45 eV range. Even stronger, when matching a trilayer area similar in brightness to AB bilayer to a theoretical curve it matches corresponding trilayer stackings ABC and ABA here better than the curve for bilayer AB, which has a stronger maximum at 37 eV (and the equivalent statement holds for trilayer areas similar to AC).

The triangular domains within the irregular domains, only showing up if the domain they lie within is bright, correspond with ABA and ABC. As such only the ACA and ACB stacking are not distinguishable in this tilted dark field measurement.

Combining the fact that the triangular domains are only found on QFG 32

(39)

with the matching of the tilted Dark field IV-curves to stackings, we con-clude that the triangular domains only show up in the stacking between the bottom two graphene layers of intercalated samples, where the bottom layer has been ‘upgraded’ from buffer layer to graphene layer during inter-calation. 10 20 30 40 50 10−3 10−2 10−1 100 101 in te n si ty (a.u .) 3B 3A 2B 2A 1L AB AC ABA ACA ABC ACB 10 20 30 40 50 energy (eV) 10−3 10−2 10−1 100 101 in te n si ty (a.u .) 4B 4A 3BB 3AB 3AA 2B 2A AB AC ABA ACA ABC ACB

Figure 5.8: Measured dark field IV-curves on EG (top) and QFG (bottom) com-pared to theoretical curves (dashed, offset for clarity). Experimental curves are labeled for layer count as deduced from bright field, and A and B for similar in-tensities. Measurements were taken in the tilted geometry as described at page 6, curves are normalised at a theoretically equal point E0=26.5 eV.

(40)

Figure 5.9: Tilted Bright Field image at E0= 24 eV of the same

area of the EG sample as in Fig-ures 5.4 and 5.1.

For bright field measurements in the tilted orientation the contrast is a lot less both in theory and practice, making the IV-curves a bit meaningless. But inter-estingly different domains show up on the EG in triple layer areas than for the tilted dark field, as shown in Figure 5.9. Together this signals the four possible stacking orders for a trilayer EG, where the tilted bright field curves would dis-tinguish the lower stacking of the tri-layer, in accordance with the theoretical curves on this. Corresponding tilted bright field IV-Data can be found in Appendix B.

5.2.1 Dislocations in bright field

Upon close inspection of the bright field overview images for the QFG sam-ple, linelike structures were observed in the trilayer areas, as shown in Fig-ure 5.10.

Figure 5.10:Contrast enhanced parts of Figure 5.2, such that structures in the tri-layer are visible.

Although not expected to be visible, the structures are very similar to domain structures observed in some areas using DF imaging. Unfortu-nately there were issues with the sample translation stage. It was non-reproducing, which meant that every now and then it jumped to a random new location on the sample. This was probably due to defective piezo mo-tors, but had a large part in the fact that non of this high resolution bright field data was obtained with overlapping dark field data.

34

(41)

Nevertheless we hypothesize that these lines correspond to the domain walls, where the lattice mismatch creates an intermediary stacking between AB and AC, not symmetrically equivalent to either of those [3], thus yield-ing a different reflectivity. Contrast could even be due to slight bucklyield-ing of the graphene layers, as observed and calculated for truly freestanding graphene by Butz et al.

5.2.2 Deviations from theoretical IV-curves

For both EG and QFG the measured IV-curves show a reasonable agree-ment to the calculated curves for freestanding multilayer graphene. Most sharp features are washed out, but this is attributed to a combination of the energy spread of the incoming electrons and a Heisenberg type un-certainty in the energy: The electron source in the ESCHER LEEM has an energy spread in the order of 200 meV. In addition to this due to the limited time electrons reside in the graphene states, the energy is spread following ∆_E∆t_≥ ¯h

2, corresponding to about 1 eV.

Another aspect affecting the exact curves, especially when comparing curves from different areas is the sometimes uneven illumination, i.e. the electron intensity varying over the gun spot. This results in vertical offsets of the curves, but is normalized away for bright field measurements by shifting the mirror mode to 1. For the tilted dark field curves no mirror mode is available as normalization, but instead the curves are normalized to the value at E0 = 26.5 eV, as according to the theoretical predictions the

contrast should be almost zero here.

Finally for the high energies it becomes clear the optical potential has not been taken into account for the theoretical curves as the experimental curves drop faster in intensity.

(42)

5.3 Heating and deintercalation

After characterization by IV-curves and ARRES, the QFG sample was heated in order to deintercalate it, such that it would revert to an EG state with a buffer layer. While increasing the temperature, a movie was created in Dark field. Once significant changes were noticeable at 830◦C, the sample was cooled down again to 700◦C, at which QFG is stable.

0 25 50 75 100 125 150 Time (minutes) 0 200 400 600 800 1000 T em p er at u re ( ◦C )

Figure 5.11: Temperature during deintercalation measurements as a function of time. After initial cooldown, the temperature was raised and reduced twice, to do measurements on the intermedi-ary state. During red shaded intervals DF images were taken continuously to monitor changes, other measurements were taken during the blue shaded intervals.

Figure 5.12: (top): BF image of an area containing different layer counts before deintercalation, the same area as measured in the intermediate cooldown and a color representation of the IV data showing the different areas (as described in section 2.2.5). (bottom): Corresponding DF images beforeheating, during inter-mediate cooldown and during final deintercalation (left to right). Indicated on the BF are the regions of interest of the IV curves in Figure 5.13.

36

(43)

5.3 Heating and deintercalation 37

At this temperature additional measurements on this semi deinterca-lated state were performed, followed by a second heating cycle to complete the deintercalation process. The temperature during this process of dein-tercalation and measurement, as measured with a pyrometer, is shown in Figure 5.11.

Bright Field and Dark field images before and during heating are shown in Figure 5.12. It shows in Dark Field that the areas with triangular stack-ing domains on the QFG sample deteriorate and finally revert to the fea-tureless/ridged structure of monolayer graphene + buffer layer areas on non-intercalated samples (although the ridges are not visible in the fast-rate image shown here, unfortunately the non-reproducing sample stage again resulted in analyzable data of non-corresponding areas.).

Also within other domains defects appear in Dark Field and seem to correspond to newly appearing areas in the Bright Field image, taken in during the intermediate measurements. The contrast between the different areas in bright field is enhanced by creating an RGB image from an IV taken in the semi-deintercalated state.

Extended measurements, i.e. extra IV’s in BF and DF were performed on the semi-deintercalated state. From these measurements we can distin-guish four different areas, showing up in different colors in the RGBplot in Figure 5.12. 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 energy (eV) 10−1 100 in te n si ty (a.u .) APRIME A BPRIME B

Figure 5.13: Bright field IV-curves for the different area types in the halfway-deintercalated state. A corresponds to the bilayer carbon, B to the triple layer carbon area. Both prime curves correspond to areas formed around defects (areas indicated in Figure 5.12). Curves normalized to mirror mode and mirror mode shifted to 0.

IV-curves of the different domains in this semi-intercalated state are shown in Figure 5.13. When comparing these to the BF IV-curves for the QFG before deintercalation and the IV-curves for the non-intercalated

(44)

sam-38 Few layer graphene

ple, areas around impurities can be matched to the IV-curves of the non-intercalated samples, especially when looking at the energy of the inter-layer state minima: The shift of ∆E ≈ 0.7 eV when comparing QFG to EG is also observed here, as shown in Figure 5.13, confirming that the areas around defects correspond to deintercalation.

The different structures are compared between different imaging modes in more detail in Figure 5.14:

Firstly on the bilayer area carbon, regions exhibiting triangular domains in DF before deintercalation are in the intermediary state only partially deintercalated. As compared in Figure 5.14c, deintercalated lines have formed at the domain boundaries of the stacking domains.

The other areas of bilayer showed thin striped domains before heating as shown in the right panel of Figure 5.14a. These are already fully deinter-calated in the intermediate measurements.

The trilayer areas are nowhere fully deintercalated as can be seen in the overview of Figure 5.14. However, we observe two types of areas, sepa-rated by step edges, which are compared in Figure 5.14b:

On the trilayer areas with little deintercalation, deintercalated spots have formed around pre-existing defects, which were already visible in Bright Field before heating.

But finally there are areas where deintercalation was faster and deinter-calation lines seem to coincide with ridged structures as observed in tilted dark and bright field.

The feature size of all deintercalated areas is similar: the round spots in the trilayer have a diameter close to the linewidth on the bilayer. We hy-pothesize that the hydrogen can only exit through the graphene at defects and once deintercalation has started diffuses towards those defects. The hydrogen diffusion speed then determines the feature size.

In particular for the bilayer either the domain boundaries themselves form defects through which the hydrogen can diffuse, or only the domain boundary crossing where the graphene is locally in AA stacking (See Figure 3.3) forms a defect where the hydrogen can diffuse out, with the domain boundaries forming pathways of increased diffusion rate. However in the continuous DF data obtained during heating the precise formation of the deintercalated areas is invisible, yielding a clear followup experiment.

38

(45)

5.3 Heating and deintercalation 39

(a) (left)RGB bright field overview of the semi deintercalated state. (right) Line-like structures in Dark Field

(b) (left)Pre-deintercalation Dark field and (right) pre-deintercalation bright field compared to (middle) deintercalation patterns on the trilayer in RGB bright field.

(c) (left)Pre-deintercalation Dark Field showing domains compared to (right) the corresponding deintercalation pattern in RGB Bright Field.

Figure 5.14:Detailed comparison structures formed in the deintercalation process with Dark Field and Bright Field images.

(46)

5.3.1 Comparison of completely deintercalated to non-intercalated The shift of the minima of ∆E≈0.7 eV when comparing QFG to EG is also observed for the fully deintercalated sample, as shown in Figure 5.15 and the curves correspond to the IV-curves of the non-intercalated sample in Figure 5.3. 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 energy (eV) 10−1 100 in te n si ty (a.u .) 2L + buffer 1L + buffer 3L + buffer

Figure 5.15: (right)Bright Field IV-curves after deintercalation, normalized to mir-ror mode, which is shifted to zero (compare Figure 5.3. (left) BF image taken at

E0=2.3 eV, with the ROIs used for these IV-curves indicated. Note the similarity

in structure to Figure 5.1.

40

Stacking domains in bilayer Van der Waals materials

Stacking domains in bilayer Van der

Waals materials

Stacking domains in bilayer Van

der Waals materials

Contents

Chapter

1

Introduction

Chapter

2

Experimental techniques

2.1

Low Energy Electron Microscopy

2.2

Image analysis

Chapter

3

Theory

3.1

Stacking of hexagonal lattices

3.2

Domain formation

3.3

Electron diffraction

3.4

Reflection curves

Chapter

4

Sample Fabrication

4.1

Graphene on silicon carbide

4.2

Molybdenum disulphide on silicon nitride

mem-branes

Chapter

5

Few layer graphene

5.1

Bright Field measurements

5.2

Tilted alignment measurements

5.3

Heating and deintercalation