• No results found

Title: Low-energy electron microscopy on two-dimensional systems : growth, potentiometry and band structure mapping

N/A
N/A
Protected

Academic year: 2022

Share "Title: Low-energy electron microscopy on two-dimensional systems : growth, potentiometry and band structure mapping "

Copied!
15
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

Cover Page

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

(2)

Resonant Low-Energy 5

Electron Potentiometry:

Contactless Imaging of Charge Transport on the Nanoscale

83

(3)

The results presented in this chapter have been submitted as:

J. Kautz, J. Jobst, C. Sorger, R. M. Tromp, H. B. Weber, S. J.

van der Molen, Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

and have been published as:

J. Kautz, J. Jobst, S.J. van der Molen, Quantum LEEP (Lage-energie-elektronenpotentiometrie): Spanning op de

Nanoschaal!, NEVAC Blad 2015-2 (2015).

(4)

5.1. Introduction

5

5.1 Introduction

Charge transport measurements form an essential tool in condensed matter physics. The usual approach is to contact a sample by two or four probes, mea- sure the resistance and derive the resistivity, assuming homogeneity within the sample. A more thorough understanding, however, requires knowledge of local resistivity variations. In chapter 4, we demonstrated how Low-Energy Elec- tron Potentiometry (LEEP) can be used to determine spatial potential maps of a current-carrying sample. In this chapter, we will show that for layered quasi-two-dimensional (2D) materials, we can improve the the resolution of our potentiometry measurements. We introduce a novel method, coined Res- onant Low-Energy Electron Potentiometry (R-LEEP), which allows for rapid imaging of the potential landscape, with both high resolution and a field of view which can be as large as 10µm. We make use of the property that incom- ing electrons are resonant with interlayer states for well-defined (local) landing energies. We demonstrate our technique by probing the in-plane potential dis- tribution between laterally spaced electrical contacts on a layered quasi-2D sample (single to triple layer graphene). Our method is straightforwardly ex- tendable to other quasi-2D systems, most prominently to the upcoming class of layered van der Waals materials. R-LEEP experiments can be performed on the same sample, and in the same microscope as LEEM and PEEM (Photo Electron Emission Microscopy and Spectroscopy). Whereas LEEM allows us to determine the structure and morphology of 2D materials, and PEEM gives access to electronic band structure, R-LEEP now additionally provides insight into charge transport on the nanoscale. This combination forms an extremely powerful set of complementary tools that has not been available before.

5.2 Experimental Methods and Results

The basic idea behind LEEP, is to determine the local potential at each posi- tion on a sample from the intensity of a reflected electron beam. The landing energy of the electrons at the surface can be tuned by varying the overall sam- ple potential VE(see Fig. 5.1a,b). Importantly, for each material the reflection probability of the electrons depends strongly on the electron landing energy or, equivalently, on the electron wavelength λ as given by the de Broglie re- lation. In fact, a measurement of the signal intensity I versus VE, yielding a so-called IV-curve I(VE), can be considered a fingerprint of a specific surface structure[1]. Such curves form the foundation for our potentiometry method.

In a conductance experiment, an in-plane bias voltage Vbias is applied over a sample. This causes the local electron landing energy (wavelength) to become position-dependent, as depicted in Fig. 5.1c. The result is that for each point

85

(5)

5

5. Resonant Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

on the sample, the local IV-curve is shifted in energy[2]. By quantifying this shift, one can determine a full surface potential map. This is the essence of the potentiometry method introduced here.

c) b)

a)

VE≈0 VE>0 VE Vbias

e- e- e-

Fig. 5.1: The local landing energy of incident electron waves (indicated by red lines) depends on the local electric potential of the graphene (gray) on the silicon carbide substrate (blue). a) For an overall sample potential VE ≈ 0, the electrons barely reach the sample, i.e., their landing energy is almost zero and their wavelength is long. b) By applying a voltage VE to the whole sample the landing energy can be increased, thereby decreasing the electron wavelength. c) An in-plane bias voltage Vbiasapplied over the sample changes the local sample potential. Hence, the landing energy and the electron wavelength become position-dependent. Here, the situation for Vbias< 0 is shown, i.e., the right electrode is at a more negative potential, which resembles the presented experimental situation.

5.2.1 Resonant Coupling

In principle, any clean material has its characteristic IV-curve and can thus be studied by potentiometry. Still, LEEP is expected to work best if the intensity exhibits a strong and well-defined energy dependence. In this sense, van der Waals heterostructures form particularly interesting systems. These consist of a stack of 2D systems like hexagonal boron nitride, graphene or transition metal dichalcogenides, held together by van der Waals forces. The properties of such quasi-2D materials are in principle tunable by choosing a specific stacking[3]. The layered structure also has an interesting consequence for LEEM IV-curves. Typically, a set of unoccupied states will exist, localized between adjacent layers[4]. If more than two layers are stacked, the coupling between the interlayer states causes a splitting of their energy levels. As a result, there are n non-degenerate states for materials with n + 1 layers.

Let us now consider a LEEM experiment, in which a sample is illuminated with electrons. If an incoming electron wave couples resonantly to one of the

86

(6)

5.2. Experimental Methods and Results

5

interlayer states, it will have a high probability to be absorbed. In other words, the reflection probability is low when the electron landing energy is equal to the energy of this particular state. This will yield a minimum in the IV-curve.

Moreover, the number of such minima in an IV-curve will correspond to the number of interlayer states n. Thus, LEEM IV-curves form a powerful tool to characterize novel van der Waals systems, whereas they can also be used as a basis for potentiometry.

5.2.2 Counting Layers

To explore such resonant IV-curves, we use multilayer graphene as a model system for van der Waals materials. Particularly, we choose graphene grown on silicon carbide (SiC), because it is clean and homogeneous over large areas and has a well-defined step direction[5]. Electrical contact to structured graphene on SiC is made via lithographically defined gold electrodes. Subsequently, a thorough cleaning procedure is used to remove remaining resist. In Fig. 5.2a,b we show LEEM images of the area indicated in the inset of Fig. 5.2c, of a graphene device structured perpendicular to the step direction. The images are acquired at two different electron landing energies (VE= 2.7 V and VE= 3.5 V, respectively) with no in-plane bias applied. While the same features can be distinguished in both images, they differ considerably in their contrast. This can be understood by looking at the IV-curves presented in Fig. 5.2c, which are taken on three different spots of the sample (marked by blue, green and red dots in Fig. 5.2a,b). For these areas, we find 1, 2 and 3 minima, respectively. As discussed above, the number of minima corresponds to the number of interlayer states[4]. Note that for graphene on SiC the bottommost carbon layer is a buffer layer that is insulating, but does contribute to the formation of interlayer states. Hence, the number of minima in Fig. 5.2c corresponds to the number of conducting graphene layers. At the blue, green and red spots, we therefore have a monolayer, bilayer and triple layer of electronically well-defined graphene.

Figure 5.2c also shows the energies at which Fig. 5.2a,b have been taken. This allows us to understand the contrast difference between Fig. 5.2a and b. At the energy used for Fig. 5.2a, the bilayer IV-curve exhibits a maximum (appears bright), while the triple layer curve shows a minimum (dark). Figure 5.2b was taken at a different energy, leading to a contrast inversion. We have taken IV-curves at every point of the field of view shown in Fig. 5.2a,b) by recording LEEM images while sweeping VE. From the number of minima in these IV- curves, we deduced the local graphene thickness experimentally, resulting in the spatial map in Fig. 5.2d. It shows enhanced graphene growth around the SiC step edges visible in Fig. 5.2a,b (indicated by black lines in d). The ability to accurately distinguish step edges as well as local thickness variations of

87

(7)

5

5. Resonant Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

layered materials is one of the exciting features of LEEM.

5.2.3 Potentiometry

We next use the rich structure of the graphene IV-curves to precisely measure local potential values. To perform such a R-LEEP experiment, we apply an in- plane bias voltage Vbias= −3 V over the sample as sketched in Fig. 5.1c. Next, we acquire LEEM images while sweeping VE. Figure 5.3a shows a snapshot taken at VE = 5.4 V. The differences between the unbiased case (Fig. 5.2a,b) and the biased case (Fig. 5.3a) are immediately visible. While, for example, bilayer areas show the same intensity for the entire field of view in the unbiased situation, they appear darker on the left than on the right in the biased case.

The latter is a direct result of the landing energy being larger at the left side than at the right side of the image. This leads to a shift ∆V in energy of the local IV-curves and thus to a difference in the local image intensity. To quantify this effect, we have measured local IV-curves for the full field of view, i.e., one IV-curve for every pixel at position (x,y) in the image. Figure 5.3b shows three IV-curves, taken at single pixels within bilayer areas indicated by squares in Fig. 5.3b. They all have a similar shape, featuring two minima, but are shifted in energy with respect to each other as well as to a reference IV-curve taken for the unbiased case. This shift ∆V is a direct measure for the local potential V(x,y). Note that the distinct shape of the IV-curves due to the resonant coupling to interlayer graphene states allows us to deduce this shift particularly precisely and thus enhances the resolution of the R-LEEP technique.

A complete potential map of the sample can now be produced by comparing the IV-curve at every pixel with a reference IV-curve taken at zero bias. This is done in a two-step process. First, we determine the shift of the local IV- curves with respect to a reference curve obtained at the biased sample. We do this by shifting the two curves with respect to each other and minimizing the sum of the squared difference between the two. Second, the shift of this biased reference curve to a reference curve acquired at unbiased conditions is quantified by determining the positions of the minima in both curves. The local potential V(x,y) is then calculated as the sum of these two shifts. By using this two-step process, we overcome a difficulty introduced by the applied bias. The bias voltage gives rise to a lateral electric field which the low-energy electrons have to cross on their way to the sample. Hence, their angle of incidence on the sample surface is changed, which slightly alters the shape of the IV-curve. This effect is discussed in depth in chapter 6. We perform the two-step routine pixelwise, separately for monolayer, bilayer and triple layer areas, e.g., we compare monolayer pixels to a monolayer reference curve, etc.

88

(8)

5.2. Experimental Methods and Results

5

a) b)

c) d)

bilayer triple layer

monolayer

intensity I (arb. units)

0 2

VE (V)

4 6 8 10

0.0 0.5 1.0 1.5

a b 5µm Cr/Au

SiC

1

3 2

500nm 500nm 500nm

Fig. 5.2: Resonant interaction of electron waves with graphene results in a strongly energy- dependent LEEM contrast. a) Bilayer areas appear bright, while monolayer and triple layer regions appear dark in LEEM images (bright-field) taken at an electron energy of VE= 2.7 V.

b) For LEEM images taken at VE = 3.5 V the same features as in (a) are visible but the contrast is inverted. c) The IV-curves taken at positions indicated in (a) and (b) exhibit minima due to resonant absorption of electrons by unoccupied states between graphene layers. For graphene on SiC, the number of minima corresponds to the number of conducting graphene layers. The curves are offset in intensity for clarity. The dotted lines indicate the electron energy in (a) and (b). The inset shows a photoemission electron microscopy image of the device presented. SiC step edges are clearly visible as dark lines. The red circle indicates the field of view for the presented LEEM images. d) A map of graphene thickness can be obtained by studying IV-curves pixel by pixel. Enhanced graphene growth is observed near SiC step edges (black lines), which are also visible in (a) and (b).

(9)

5

5. Resonant Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

500nm

a) b)

0 2

VE (V)

4 6 8 10

intensity (arb. units)

0 1 2 3

∆V1

∆V2

∆V3

reference

Fig. 5.3: Fig. 3. The local IV-curves are shifted in energy due to local potential differences.

a) LEEM image taken at VE= 5.4 V with a sample bias of Vbias= −3 V. Due to the bias the landing energy becomes position dependent (see Fig. 5.1c). Hence, bilayer areas on the left (ground side) appear dark, while they are bright at the right (bias side). b) IV-curves taken at bilayer areas from single pixels in the areas indicated by squares in (a). They show the two characteristic minima but are shifted with respect to the reference curve obtained from the unbiased case in Fig. 5.2c. The shifts ∆V are a direct measure for the local potential.

The curves are offset in intensity for clarity. The dotted line indicates the electron energy in (a).

(10)

5.3. Discussion

5

5.3 Discussion

Figure 5.4a presents a map of the local potential V(x,y), derived using the R-LEEP technique. The grainy structure of the image is mainly caused by residues of the resist used and is considered noise in the following. As ex- pected for an Ohmic material like graphene, a voltage drop from left to right is apparent. However, the different layers identified in Fig. 5.2a are also visible in the potential map. To visualize these features more clearly, Fig. 5.4b shows the potential profile along the line indicated in Fig. 5.4a. The first observa- tion that can be made is that the potential gradient and hence the resistivity within the triple layer is considerably lower than within the single layer. This is consistent with previous experimental reports and can be related to both the increased thickness and the protection of the bottom layers from doping from the ambient[6]. Second, we find no additional voltage drop at the macro- scopic (5-10 nm high[5]) step edges of the SiC substrate below the triple layer graphene. Whereas these step edges are clearly resolved in LEEM images (cf.

Fig. 5.3a) as thin dark lines within the triple layer area, they are barely visible in the potential map and the potential gradient in Fig. 5.4a,b. This indicates that no significant scattering occurs at these substrate steps that are covered with graphene in a carpet-like manner[7]. Remarkably, we do find a voltage drop of ≈ 0.1 V at points where the graphene layer thickness changes. This counter-intuitive behavior has been observed in scanning probe experiments and has been related to wave function mismatch between graphene of different layer number[8].

LEEM, and therefore also LEEP, are ideally suited to discriminate steps in the SiC substrate from a change in graphene layer number. This unambiguous distinction is particularly difficult with many other techniques as graphene layer changes can coincide with SiC steps and are mainly found in the vicinity of macroscopic SiC step edges, where graphene growth is faster[5]. Conse- quently, standard conductivity experiments on devices oriented parallel and perpendicular to SiC step edges attributed the additional resistivity found to these macroscopic steps rather than to the graphene-induced steps[9,10]. The lower resistivity of thicker layers appears to compensate for a fraction of this step resistance, which would thus be underestimated by conventional conduc- tivity experiments[11].

To quantify the energy resolution of the technique, and as a consistency check, we acquired potential maps for different external bias voltages Vbias. A linear relation between bias voltage and local potential is expected according to Ohms law. Figure 5.4c shows the measured local potential for the spot indicated by a cross in Fig. 5.4a as a function of Vbias. Deviations from the

91

(11)

5

5. Resonant Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

a)

500nm

local potential (V)

position (nm)

0 500 1000 1500 2000

ML BL TL ML

-1.8

-2.2 -2.4 -2.0 -1.9 -1.8

-2.1

-2.3 -2.4 -2.5 -2.2 -2.0

local potential (V)

b)

c)

local potential (V)

bias voltage Vb (V) -3

-4

-5 -2 -1 0 1 2 3 4 5

2 0 -2 -4 4

Fig. 5.4: The local electric potential of a biased graphene sample can be mapped out using R-LEEP. a) A potential map of the sample at Vbias= −3 V is obtained by pixelwise calculating the shift ∆V of IV-curves with respect to a zero bias reference. b) A linescan over the potential map in (a) shows the voltage drop over the sample. The linear gradient in the monolayer area is smaller than that in the triple layer area, indicating a lower resistivity for the latter. At the interface between single and triple layer graphene, a sharp drop in the local potential is observed, while the macroscopic SiC step edges remain barely visible in the potential image. The spikes at the interface between areas with different thicknesses are artifacts, caused by image drift during image acquisition. c) Potential at the position indicated in (a) as function of applied bias voltage Vbias. The linear relation confirms the metallic properties expected for graphene and shows that we probe the bias dependent, electric potential only. The deviations from this linear trend (≈ 50 mV) form an upper limit for our absolute potential resolution.

(12)

5.4. Conclusions

5

apparent linear trend yield an estimate for the uncertainty in the absolute value of the local potential of ≈ 50 mV. Here, the main source of error is the bias induced tilt of the electron beam (see discussion above). Interestingly, for a single bias voltage, a higher resolution can be obtained. By using a two-step process to determine the IV-curve shift ∆V , we have separated the measurement of relative potential differences within one image from that of the absolute potential. Thus if one is only interested in relative potential differences between different areas for a given applied bias, one is not limited by beam tilt induced errors. To estimate the error in the relative potential, we quantify the noise in the linescan in Fig. 5.4b. Deviations from linearity give an estimate for the error in relative potential of 25 mV or 7 mV for monolayer or triple layer areas, respectively. This error is mainly caused by residues of the organic resist used during sample fabrication. These residues also limit the lateral resolution of our technique. If this issue could be overcome, we expect a resolution of R-LEEP of < 5 nm given the resolution limit of the microscope of 1.4 nm[12].

5.4 Conclusions

We have presented a new method to analyze the laterally resolved conductivity of 2D systems. The R-LEEP technique introduced is based on the absorption of low-energy electrons resonant with unoccupied states in layered materials.

As it does not rely on an invasive, local probe, it is fast and does not disturb the system studied. This is particularly important in the vicinity of small fea- tures like step edges that contribute to the local resistivity as scatterers. We demonstrate our technique by analyzing the conductance properties of few- layer graphene. We find an additional resistance contribution at points where the graphene layer thickness changes, while macroscopic steps in the SiC sub- strate do not seem to perturb the current flow. We anticipate that R-LEEP is easily extended to other quasi-2D systems like van der Waals heterostructures and topological insulators. Moreover, given the recent developments in LEEM acquisition speed[13], potentiometry of dynamic process comes within range.

93

(13)

5

5. Resonant Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

References

[1] J. I. Flege and E. E. Krasovskii, Intensity-voltage low-energy electron mi- croscopy for functional materials characterization, Physica Status Solidi (RRL) - Rapid Research Letters 8, 463 (2014).

[2] M. Anderson, C. Nakakura, K. Saiz, and G. Kellogg, Imaging Oxide- Covered Doped Silicon Structures Using Low-Energy Electron Microscopy, MRS Proceedings 1026, 1026 (2007).

[3] A. K. Geim and I. V. Grigorieva, Van der Waals heterostructures., Nature 499, 419 (2013).

[4] N. Srivastava, Q. Gao, M. Widom, R. M. Feenstra, S. Nie, K. F. McCarty, and I. V. Vlassiouk, Low-energy electron reflectivity of graphene on copper and other substrates, Physical Review B 87, 245414 (2013).

[5] K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L.

McChesney, T. Ohta, S. A. Reshanov, J. R¨ohrl, et al., Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide., Nature materials 8, 203 (2009).

[6] F. G¨une, H.-j. Shin, C. Biswas, G. H. Han, E. S. Kim, S. J. Chae, J.-Y.

Choi, and Y. H. Lee, Layer-by-layer doping of few-layer graphene film., ACS nano 4, 4595 (2010).

[7] P. Lauffer, K. V. Emtsev, R. Graupner, T. Seyller, and L. Ley, Atomic and electronic structure of few-layer graphene on SiC(0001) studied with scanning tunneling microscopy and spectroscopy, Physical Review B 77, 155426 (2008).

[8] S.-H. Ji, J. B. Hannon, R. M. Tromp, V. Perebeinos, J. Tersoff, and F. M.

Ross, Atomic-scale transport in epitaxial graphene., Nature materials 11, 114 (2012).

[9] B. Jouault, B. Jabakhanji, N. Camara, W. Desrat, A. Tiberj, J.-R.

Huntzinger, C. Consejo, A. Caboni, P. Godignon, Y. Kopelevich, et al., Probing the electrical anisotropy of multilayer graphene on the Si face of 6H-SiC , Physical Review B 82, 085438 (2010).

[10] S. Weingart, C. Bock, U. Kunze, F. Speck, T. Seyller, and L. Ley, Low- temperature ballistic transport in nanoscale epitaxial graphene cross junc- tions, Applied Physics Letters 95, 262101 (2009).

94

(14)

References

5

[11] J. Jobst, D. Waldmann, F. Speck, R. Hirner, D. K. Maude, T. Seyller, and H. B. Weber, Quantum oscillations and quantum Hall effect in epitaxial graphene, Physical Review B 81, 195434 (2010).

[12] S. M. Schramm, Phd thesis, Leiden University (2013).

[13] R. van Gastel, I. Sikharulidze, S. Schramm, J. P. Abrahams, B. Poelsema, R. M. Tromp, and S. J. van der Molen, Medipix 2 detector applied to low energy electron microscopy., Ultramicroscopy 110, 33 (2009).

95

(15)

Referenties

GERELATEERDE DOCUMENTEN

there are exactly n simple C[C n ]-modules up to isomorphism, and that these are all one-dimensional as C-vector

(b) Show (without using Frobenius’s theorem) that the elements of G having no fixed points in X, together with the identity element, form a normal subgroup of

With M- LEEP, however, this optimal microscopy res- olution cannot be reached since the M-LEEP resolution will always be limited by the pres- ence of a lateral electric field above

The notation hx, yi denotes the subspace spanned by x and y, and of course has nothing to do with an inner

Let V be the 3-dimensional vector space of polynomials of degree at most 2 with coefficients in R.. Give the signature of φ and a diagonalizing basis

The flowfram package is designed to enable you to create frames in a document such that the contents of the document environment flow from one frame to the next in the order that

The glossary is a list of special functions, so the equation number has been used rather than the page number. This can be done using the counter=equation

Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus.. Proin