Graphene heterostructures for spin and charge transport
Zomer, Paul Joseph
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Chapter 1
Introduction
Abstract
Graphene, a single atom thick layer of graphite, is a material that has always been around us, but only recently became accessible to researchers worldwide. This could happen due to a very simple process dubbed the scotch tape method, where the graphite is pulled apart by tape and deposited on a substrate. The initially produced graphene devices showed good electronic properties, but this significantly improved after the substrate was com-pletely removed or substituted by hexagonal boron nitride. One area where graphene immediately showed its potential is in spintronics, where the electron spin is used to convey information similar to charge in electronics. Micrometer spin transport length scales could be reached at room temperature in graphene and by placing graphene on hexagonal boron nitride, even larger distances can be bridged. This thesis contains two approaches to fabricate high quality heterostructures of graphene and hexagonal boron nitride. These heterostructures are then used for studying the capacitance profile near the graphene edge as well as spin transport in high mobility graphene. Finally the robustness of spin transport in few layer graphene devices is demonstrated using devices that have been intentionally damaged by proton irradiation.
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1.1
Graphene
Carbon atom chicken wire. This would be a very basic description of what graphene looks like; a single atom thick layer of hexagonally arranged carbon atoms as shown in figure 1.1. Only over the past decade this deceivingly simple material has become world famous[1, 2]. Yet interestingly, it has been present around us for a much, much longer time. Graphene is the elemental building block of graphite, which can be seen as a stack of graphene sheets bound together by van der Waals force. To give an indication, 1 mm thick graphite would contain a stack of almost 3 million graphene layers, given that the interlayer spacing in graphite is 3.5 ˚A. The weakly bound layered structure of graphite is in fact at the core of many of its application. Layers can easily slide over each other, which makes a good lubricant, for example. An even more common example are pencils. When writing or drawing with a pencil one is actually, on a microscopic scale, depositing thin layers of graphite and maybe even graphene on paper. Fittingly, the word graphene originates from the Greek word graphein which means to write. And so it seems that we all have been creating graphene since we were making our first pencil drawings, but the story is not that simple.
Figure 1.1: Graphical impression of what graphene looks like, the black carbon atoms are arranged in a hexagonal lattice. The atoms are spaced by ∼0.14 nm.
Until 2004 graphene in fact mostly remained the domain of theoreticians. Mo-tivated by building an understanding of graphite, graphene was described theoret-ically for the first time in 1947 by P.R Wallace[3]. Further efforts where fueled by the interest in carbon nanotubes (CNT)[4, 5], the 1 dimensional allotrope of graphite. Single layers of graphene were however deemed to be too unstable to exist thermo-dynamically by themselves[6]. This belief was proven wrong when a method was developed and demonstrated in 2004 by Andrei Geim and Konstantin Novoselov that is as simple as effective for the mechanical exfoliation of graphene[1]. They demonstrated that by pulling a piece of graphite apart using simply adhesive tape
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1.1. Graphene 3
and pressing the tape on a substrate one could obtain monolayers of graphite, a procedure which has become known as the ”scotch tape method”. The discovery of graphene quickly turned it into the subject of intense study[7], demonstrating graph-ene’s remarkable properties such as its electrical properties[1, 8], strength[9], thermal conductivity[10] or impermeability[11]. Andrei Geim and Konstantin Novoselov have been awarded the Nobel prize in physics of 2010 for their discovery.
However, the scotch tape method also has it’s downside. This method has a relatively low yield of small flakes (typically in the 10 µm order) that are distributed randomly on the substrate. As a consequence the process of producing an actual graphene device requires one to first identify a useable flake. This may work in a laboratory environment, but is unacceptable for larger scale use. Therefore, after graphene was demonstrated to exist in a stable form, more methods for graphene production have been developed. These include chemical vapor deposition[12–17], epitaxial growth on silicon carbide[18–20] and liquid exfoliation[21, 22]. While these are important developments for graphene to find its way into real life applications or to realize large area graphene, none of these methods have exceeded the scotch tape method in terms of quality so far. But that does not mean that there is no room for quality improvement where exfoliated graphene is concerned.
The fact that graphene is merely a single atom thick layer makes it also extremely sensitive to its environment. This can be considered an interesting characteristic to exploit for sensor application[23–25]. However, this additional functionality is un-desired in other applications of graphene. Graphene’s excellent mobility, which can be used as a measure of quality, is for example considerably limited by the typically used silicon dioxide substrate. Furthermore, unwanted adsorbates on the graphene can unintentionally dope the graphene. Therefore, new fabrication methods were required to truly explore the intrinsic properties of graphene.
1.1.1
Quality improvement
The first and most straightforward method to obtain something closer to pristine graphene is to remove the substrate. Several methods were developed to do so by removing the substrate underneath the graphene[26–29]. However, the processing steps required to fabricate a graphene device also introduce a considerable amount of contaminants that need to be removed. For suspended devices this was done by current annealing, meaning that a large current is sent through the graphene in order to heat it up and hence clean it of adsorbates. Current annealing is effective since it can be done in situ, however it is also difficult to control and in most cases the graphene will break[30].
A safer method was developed with the use of hexagonal boron nitride (h-BN)[31– 33], which is also referred to as white graphene as might be understood from fig-ure 1.2. The indicated similarity comes from its crystal structfig-ure, which is hexagonal
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a)
b)
Figure 1.2: a) Graphite flakes (size ∼1 to 2 mm). b) Hexagonal boron nitride flakes (size ∼1 mm). Copyright HQ Graphene.
with layers held together by van der Waals force. The in plane lattice constants of h-BN are actually very similar to graphene with a mismatch of only 1.7%[34]. Be-sides that h-BN makes a good dielectric, with a relative permittivity ≈ 3.9 similar to SiO2and breakdown voltage of ∼0.7 V/nm[31]. By including a sufficiently thick
(∼15 nm) h-BN layer between the SiO2and graphene the influence of the original
substrate can be eliminated and indeed the initial reports showed a considerable in-crease in graphene mobility. While this new substrate yielded promising results, the mobilities were still lagging to what could be achieved for suspended devices.
The next developments focused on reducing the possible contamination of the graphene and h-BN flakes to the absolute minimum during the fabrication of a het-erostructure. Since building stacks of graphene and h-BN is done by using polymers which will always leave some contaminants behind, this required another approach. Instead of building the stack by depositing one layer at a time, the inverse was done by picking up the layers one by one, stacking them in the process[33, 35]. No more polymer is included in the stack this way. The reported devices realized this way have shown the highest possible quality, on par with suspended devices.
1.2
Spin transport
In electronics the charge of an electron is used to convey information. In a transistor for example, a voltage applied to a gate is used to electrostatically deplete a semicon-ducting channel of charge carriers, switching the transistor from an on to an off state
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1.2. Spin transport 5
where no charge current can flow. In spintronics on the other hand, the electron spin is used to carry information. The electron spin is an intrinsic magnetic moment with two eigenstates, spin up and spin down. The imbalance between electrons with spin up or down is the main source for the occurrence of ferromagnetism, which plays an important role in spintronic devices. Graphene made its entry in the field of spin-tronics in 2007 and since then secured its position well, for reasons that will follow. First, we will shortly address the relevance of spintronics.
A key element for spintronics is the spin transistor, the equivalent of a regular transistor for electronics. A simple spin transistor can be created by applying a volt-age between two ferromagnets separated by a non-magnetic material. By individu-ally controlling the magnetization of the ferromagnets with respect to each other one can either align them parallel or anti-parallel. Respectively this results in a low or high resistance, the equivalence of an on and an off state. The significant change in resistance due to a switch from parallel to anti-parallel magnetization of the ferro-magnets in a spin transistor is known as giant magnetoresistance (GMR). This effect was discovered by Albert Fert and Peter Gr ¨unberg in 1988, a discovery that was awarded with the Nobel prize in physics of 2007. GMR mainly finds its application in magnetic field sensors. Well known examples that are of great importance today are the hard disk drive (HDD) and magnetic random access memory (MRAM) or more recently spin transfer torque random access memory (STT-RAM). In a HDD the data is essentially stored by magnetizing a thin ferromagnetic layer on a disk with a write head. The data can be subsequently read with a read head which is sen-sitive to the relative magnetization between the head and the disk due to GMR. In MRAM two perpendicularly aligned grids of wires are separated by memory cells. The memory cells, consisting of a pinned and a free magnetic layer spaced by a tun-nel barrier, can be magnetized by sending simultaneous current pulses through the crossing wires. This allows for creating parallel or anti-parallel aligned cells, which can be seen in terms of computer language as a ”1” and ”0” respectively. What sepa-rates STT-RAM from MRAM is that spin transfer torque is used to assist in switching the free magnetic layer. A spin polarized current injected into the free layer will ap-ply a torque to the layer when their magnetizations are misaligned. With the help of this torque a lower writing current is needed to switch the free layer.
In the devices just described, the separating medium between the (ferro-) mag-nets acts just as a spacer. However, in the charge-based transistor mentioned at the start of this section the medium between the source and drain electrodes is acted upon by an external gate. When something similar could be used for the spin tran-sistor, this would add extra functionality. Spins can then be acted upon while they move between the source and drain electrodes. And indeed, a similar approach can be taken for the spin transistor by using ferromagnetic source and drain electrodes. The medium that connects the two needs to meet certain specific requirements how-ever and that is where graphene comes in.
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1.2.1
Graphene based spin transistors
An important requirement is that spins traversing the medium in between the fer-romagnets do not lose their orientation, i.e. information, on their way. Spins will unavoidably relax to the equilibrium state of the medium, but some factors will influence the rate at which relaxation takes place. One factor is the sporbit in-teraction, the interaction between the magnetic moment and orbital motion of an electron. The magnitude of this effect scales with the atomic weight as Z4.
An-other source for spin relaxation is hyperfine interaction between the electron spin and nuclear spin. Graphene appears as a favorable choice where both mechanisms are concerned[36, 37]. Firstly, carbon is a relatively light atom and secondly, it has no nuclear spin1. A key measure to determine the relaxation rate is the relaxation
time τs, which represents the time it takes to reduce the spin imbalance by a
fac-tor e−1. When the space between the two ferromagnets is concerned, spin diffusion is another important factor. The spin diffusion constant Dsprovides a measure for
the speed at which spin travels through the medium. Combining Ds and τs, the
spin relaxation length can be obtained: λ =√τsDs. Initial experiments on the spin transport in graphene confirmed that it indeed carries great potential[38–40], with spin relaxation lengths of ∼2 µm at room temperature[41]. The improvement of the electronic quality of graphene is also relevant for spintronic devices. By changing from a SiO2 substrate to h-BN, spin signals could be observed after actually being
transported over 20 µm[42]. Further improvements in device fabrication such as encapsulation with h-BN[43, 44] or following a bottom-up procedure with h-BN on top [45] allowed for increasing spin relaxation lengths, up to 30 µm. The improve-ment in spin relaxation length is achieved both through higher diffusion constants and longer relaxation times.
1.3
Outline
• In Chapter 2 the theoretical background of graphene will be discussed. This starts with the crystallographic and electronic properties and concludes with graphene spintronics.
• Chapter 3 mainly discusses the fabrication steps involved when preparing graph-ene h-BN heterostructure devices as well as the basic measurement setup used for device characterization.
• Chapter 4 shows a method for fabricating a h-BN graphene stack by using a sac-rificial polymer layer. Importantly it also demonstrates for the first time that
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1.3. Outline 7
with commercially available h-BN one can achieve high quality heterostruc-tures.
• In Chapter 5, a fabrication method for heterostructures comprised of more than two layers is developed. Individual flakes are picked up from a substrate while creating the stack instead of being deposited one by one. This is an important step in order to achieve clean interfaces.
• Chapter 6 shows how by using a high electronic quality graphene device, one can probe the charge density profiles at graphene’s edges using the quantum Hall effect.
• In Chapter 7 spin transport is measured on graphene h-BN heterostructures, allowing for the detection of non-local spin signals over much longer distances than before.
• Chapter 8 takes another approach to demonstrate the potential of graphene for spintronic applications. Few layer graphene devices are damaged using proton irradiation and nevertheless show remarkably robust spin transport.
• Chapter 9 concludes this thesis and gives a brief outlook of how the techniques developed here are applied in other research.
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