Graphene an Introduction to the Material, Its Application As a Photodetector and Possible Future Uses

Graphene An Introduction to the Material, its Application as a Photodetector and possible future Uses

Daniel Schmid, W14b Kantonsschule Enge, Zürich 18.12.2017 Supervised by Erich Schurtenberger

Abstract In this paper, the two-dimensional material graphene is investigated. The characteristics of graphene are stated and how this material can lead to technological progress. Its structure and fundamental properties are exhibited and with the basic functioning principles of photodetectors, the practical use of graphene is shown by means of a specific application. The last chapter provides an outlook on the variety of other possible future applications.

3 Abstract

Table of Contents Abstract ...... 3 Table of Contents ...... 5 Preamble ...... 7 Introduction ...... 8 History of Graphene ...... 9 What is Graphene ...... 11 Structure ...... 11 Properties ...... 12 Electrical Properties ...... 12 Optical Properties ...... 16 Mechanical Properties ...... 16 Fabrication ...... 17 Mechanical Exfoliation ...... 17 Chemical Vapour Deposition (CVD) ...... 17 Experiment ...... 18 Method ...... 18 Results ...... 21 Discussion ...... 22 What is a Photodetector ...... 23 Graphene Photodetector ...... 28 Conclusion and Outlook ...... 30 Declaration of Authenticity ...... 32 Appendix ...... 33 Calculation of Photon Energy ...... 33 Resistivity of the Graphene Flake ...... 33 Indices ...... 34 List of Figures ...... 34 List of Literature ...... 36

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Preamble Carbon is one of the most important elements in the world concerning living beings, as every organic molecule contains carbon and hydrogen atoms. This incredible element can, in its pure form, exist in a variety of different states. The best known are probably graphite and diamond. At first, I wanted to write my matura paper about diamonds and how their optical properties change with different impurities in the carbon lattice, hence with different colours, but it turned out to be really difficult to get hold of diamonds in various colours. About the same time, I read an article in the news about a new nanomaterial that could revolutionise the way we’re living. This new material was supposed to be the first truly two-dimensional material ever isolated, only one layer of atoms thick, yet stronger than steel, flexible and the best electrical conductor known to mankind. This material is graphene, another compound made up solely of carbon atoms. As the Royal Swedish Academy of Science put it when announcing the winners of the 2010 Nobel Prize in physics: “Carbon, the basis of all life on earth, has surprised us once again.” I was fascinated by the prospect of the new technologies which could be made true because of graphene straight away. Some media even said the 21th century would be the century of graphene. I wanted to spread the news about graphene and show its amazing properties and possible future applications. To make sure that this paper wouldn’t just be fantasies about future technologies, I decided to show the potential of graphene on one specific application. As I didn’t want to ditch my original idea completely, I looked into the application of graphene as a photodetector.

I owe great thanks to my former physics teacher and mentor Erich Schurtenberger, who was really supportive from the beginning and helped me throughout the process of researching and writing by answering my questions, supplying me with additional literature and by organising a meeting with Dr. Ivan Sholubalko at EMPA in Dübendorf, who has already conducted research on graphene and graphene based photodetectors for years. Dr. Shorubalko dedicated a whole day to show me around the institute, share his knowledge and conduct simple experiments with me and supply me with lots and lots of literature concerning the subject. Wherefore, I’m deeply grateful.

I also have to thank my parents and my brother who pushed me when I was lacking drive to carry on and were there to discuss the matter and help me find solutions. Special thanks also to my girlfriend, who was always supporting me and giving me motivation when I didn’t have any.

7 Preamble Introduction The main goal in this paper is to introduce the material graphene, describe its physical and chemical properties and demonstrate the potential of graphene on the basis of a specific application on level of difficulty which is understandable for a grammar school student. Graphene can only be manufactured since roughly fifteen years, but in today’s nanotechnology research it has become rather important and the European Union has been funding graphene research with a budget of one billion euros. Especially in the electronics industry, graphene can lead to new breakthroughs due to its extraordinary electrical properties, stability and flexible structure. Graphene also exhibits remarkable optical properties which enables it to be used in optoelectronic devices, such as photodetectors. To demonstrate the practicability of graphene, the possible application as a photodetector is described.

This paper can be divided into two parts. The first one is dedicated to graphene itself. The history and discovery of graphene, its properties and how graphene can be fabricated. The focus lies on the properties which come to play in the application as a photodetector described in the second part of this work. The theoretical part about graphene is concluded with a simple experiment I was able to conduct at EMPA with Dr. Ivan Shorubalko, who is an expert on graphene. This experiment primarily served the purpose of verifying some of the properties described in the theory section and to lay hands on real graphene.

To understand the future use of graphene as a photodetector, the theory and fundamental physical processes of photodetection and the basic setup of a photodiode are explained in the second main part of this paper. The theory about graphene and about photodetectors are combined to illustrate the metal-graphene-metal photodetector as a practical application of graphene. In the last chapter, the discussed aspects will be concluded, an outlook on other applications of graphene will be provided and what the future could look like.

8 Introduction History of Graphene In the late 1850‘s Benjamin Collins Brodie Jr. specified the structure of thermally reduced graphite oxide and was therefore the first scientist to experiment on a two-dimensional graphite compound (Brodie, 1859). His research was pursued in the early 20th century. The first electron microscopic pictures of few layer graphene were published in 1948 by G. Ruess and F. Vogt (Ruess & Vogt, 1948). However, scientists claimed that strictly two-dimensional crystals were thermodynamically instable and couldn’t exist (Geim & Novoselov, 2007, S. 1). Hanns-Peter Boehm was considered a pioneer on graphene research, coined the name “graphene” and already in 1962, he reported of monolayered sheets of carbon (Boehm, Setton, & Stumpp, 1994). In the late 20th century, graphene was used as a theoretical model for describing quantum electrodynamics on a two- and one-dimensional scale, because the charge carriers of graphene mimic relativistic particles as predicted by the Dirac equation for two- and one-dimensional quantum systems (Geim & Novoselov, 2007, S. 1). The Dirac equation describes, like the Schrödinger equation, the wave function for quantum systems of atomic or subatomic scale where Newton’s laws no longer apply (Wikipedia, 2017). Even though it was known that graphene was the substantial part of graphite, it was assumed not to be stable in a free state and described as a purely “academic” material. The belief that two-dimensional materials couldn’t exist without a three-dimensional base was refuted when free-standing graphene was isolated by the two scientists Andre Geim and Konstantin Novoselov in 2004 at the University of Manchester. In a simple procedure, the first flakes of graphene were exfoliated off a piece of graphite using ordinary scotch tape. During this process, the sticky side of the tape with the graphite on it is folded and pulled apart again so that the graphite flakes get torn apart. After several repetitions, some of the flakes will be just one layer thick [Figure 1]. Under an optical microscope, the potential graphene flakes can be seen if placed on top of a silicon wafer with a carefully chosen thickness of silicon oxide (SiO2).

a b

Figure 1: a) Exfoliation of graphene from graphite of a pencil with the scotch tape method. b) Result of the exfoliation, monolayer graphene flakes cannot be seen by the naked eye.

The veritable proof that the chosen samples are indeed monolayers of graphene, is delivered by Raman spectroscopy. (Geim & Novoselov, 2007, S. 3). This spectroscopy technique is named after C. V. Raman, an Indian physicist who carried out ground-breaking work in the field of light scattering in the early 20th century, and uses a monochromatic laser to illuminate the sample. Most of the light scatters with the same energy, which defines its wavelength and therefore also its colour, when it hits the surface of a material. Nevertheless, a tiny fraction of about 1 in 107 photons lose or gain energy during the impact with the sample due to the molecular vibrations in the material. These “Raman scattered” photons can be analysed by a sensitive spectrometer and used to conclude on the material of the sample and its uniformity (Renishaw, 2017).

9 History of Graphene In 2010, Geim and Novoselov received the Nobel Prize in physics “for groundbreaking experiments regarding the two-dimensional material graphene”. With the discovery of graphene, scientists can now study a whole new class of two-dimensional materials with unique properties (Huss, 2010). A wide range of practical applications appear possible. Scientists all around the world are working to make these applications come true. The European Union even launched a project called “Graphene Flagship” to fund, support and join institutions in their work on graphene. With the budget of one billion Euros over ten years and more than 150 academic and industrial research groups in 23 countries, it is Europe’s biggest ever research initiative (Graphene Flagship, 2016).

10 History of Graphene What is Graphene Graphene is an amazing material with unique structure and remarkable properties. The composition of graphene and its properties will be explained in this section. The focus lies on the properties which are used in the practical application as a photodetector. Besides that, different methods of fabrication are depicted. Structure Graphene is a monolayer of carbon atoms arranged in a honeycomb lattice in which every atom is surrounded by three other atoms [Figure 2 top]. Since the electrons can only move between the atoms on the two-dimensional lattice, graphene is quasi-two-dimensional. The lattice is held together by sp2- bonds, which separate the carbon atoms by about 0.14 nm, making the sheet strong enough to withstand thermal fluctuations from destabilising it (de La Fuente, 2017). Given that carbon forms four bonds, there is one electron of each atom which isn’t locally fixated in a covalent bond. – If every carbon atom was surrounded by four others instead of three, a three-dimensional lattice would be created. This structure is called diamond. – This delocalised electron can float freely within the boundaries of the particular hexagonal comb. These free-floating electrons create a fermi gas or electron gas, which is also found in the structure of metals. The bonding situation in graphene is called a system of conjugated double bonds, which consist of double bonds which alternate with single bonds (Clerc, 2014).

Up to a stack of about ten sheets, it is still considered graphene. Graphene is the building block of other modifications of carbon. It can be wrapped up into zero-dimensional spheres called fullerenes or buckyballs, rolled up into one-dimensional nanotubes and graphite is nothing else than a three- dimensional stack of graphene. Each modification shows different properties and can accordingly be used in different manners (Geim & Novoselov, 2007, S. 2).

Figure 2: Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite (Geim & Novoselov, 2007, S. 2).

11 What is Graphene Properties The lack of a third dimension for the electrons to go to, gives graphene various novel properties, and together with the great strength of the carbon-carbon bonds, these properties are what enable graphene to break many records in terms of strength, electricity and heat conduction. The electrons, for example, interact with the carbon atoms in the lattice in such a way that practically no electrical resistivity is created. This allows charge carriers to move ballistically over the graphene surface, i.e. the carriers experience only negligible resistance caused by scattering, enabling graphene sheets to conduct electricity very well. Other complex interactions between electrons and the hexagonal lattice make graphene transparent, flexible and strong (Pollard, 2011, S. 8-9).

Monolayer graphene is the purest form known and is useful for high-frequency electronics. Bi-layer and tri-layer Graphene exhibit different properties with the increase in the number of layers (Bharech & Kumar, 2015). Here, mainly monolayer graphene is analysed. Electrical Properties One of graphene’s most useful properties is its very high electrical conductivity. It provides both electrons and holes as charge carriers. Holes are positive charge carriers and the counterpart of the negative charged electrons. They describe the lack of electrons at a certain place. Even though, holes are therefore not particles themselves, they are treated as charge carriers, because they can move around as electrons “fill” the holes and create other ones where they left from. Carbon atoms have four electrons in the valence shell available for chemical bonding. In the structure of graphene however, only three of them are used, leaving one electron freely available for electrical conduction. These highly-mobile electrons are called pi (π) electrons and are located either above or below the graphene sheet. The π-orbitals overlap and enhance the carbon-carbon bonds (de La Fuente, 2017).

For characterising a material’s electrical properties, the electron mobility is an important factor. It characterises how quickly an electron can move through the material and is calculating by measuring its average velocity due to an applied electric field. In semiconductors, there is an analogue quantity for holes, called hole mobility. The term carrier mobility refers to both electron and hole mobility (Wikipedia, 2017). The mobility of carriers (μ) in graphene are amazingly high and can exceed 15’000 cm2/Vs even under ambient conditions. Moreover, the mobilities hardly depend on the temperature (Geim & Novoselov, 2007, S. 4), which means that if the impurities of the material can be eliminated, the carrier mobility of graphene reach up to 200’000 cm2/Vs, where its intrinsic mobility limit lies. This would exceed the values of InSb, the inorganic semiconductors with the highest known mobility, by more than the factor 2 (Chen, Jang, Xiao, Ishigami, & Fuhrer, 2017). As a comparison, silicon (Si) has a maximal electron mobility of 14’000 cm2/Vs and a hole mobility of 450 cm2/Vs (Ioffe, 2017). Graphene also exhibits a high charge carrier density (n) of 1012 per cm2 (Chen, Jang, Xiao, Ishigami, & Fuhrer, 2017). Furthermore, it has a very high current carrying capacity, up to 109 A/cm2 (Avouris & Dimitrakopoulos, 2012, S. 91).

12 What is Graphene Most of these record properties refer to pristine graphene under perfect conditions. In reality, it is a bit more complex. For example, electrical transport is subject to a variety of scattering interactions, which means that charge carriers get deflected from their original course. These include scattering through long-range interactions with charged impurities on the graphene layer itself or more likely at the supporting insulator substrate, short-range interactions with neutral defects or adsorbates and by roughness and lattice vibrations. Another problem poses the metal contacts, which are needed to apply a voltage to the graphene channel. Metal and graphene have different work functions, which causes a charge transfer between them (Avouris & Dimitrakopoulos, 2012, S. 91). In solid-state physics, the work function describes the minimal energy required to remove an electron from solid into a vacuum right outside of the body’s surface. Two conductors can have a potential difference due to work function differences (Wikipedia, 2017). A local resistivity from a couple hundred Ω∙μm to several kΩ∙μm occurs (Avouris & Dimitrakopoulos, 2012, S. 91).

An important model to understand a material’s electronic properties is the band structure. The band structure shows the different excitation levels which electrons can occupy in a specific material. To determine if one is dealing with a conductor, a semiconductor or an insulator, the band diagram of the object can be checked for overlaps or bandgaps between the conduction and the valence band. Graphene exhibits a unique band structure. It is a zero-bandgap and zero-overlap semimetal, because the conduction and valence band meet at the so-called Dirac point (Bharech & Kumar, 2015). This point is named after Paul Dirac, a British physicist, who derived a relativistic wave function for quantum mechanics taking the theory of special relativity in account (Wikipedia, 2017). It accurately describes the interaction of electrons with the honeycomb structure of graphene (Geim & Novoselov, 2007, S. 4).

Explanation Band Structure The energy levels of electrons can vary. Because of the interaction of the electrons with each other, no single energy levels occur like in atoms, but vast regions which are called energy bands. Electrons can only linger in these bands, hence only possess the energies of those bands. The valence band is the band of the outmost electron orbitals of an atom. If an electron gets excited, it can jump into the conduction band. Electrons in the conduction band have enough energy to move freely in the material, creating a current. The bandgap is the distance between the valence and the conduction band. As electrons cannot have energies which lie between those bands, a bandgap is basically a forbidden band. The size and existence of a bandgap gives materials some of their distinct properties and discriminates between conductors, semiconductors and insulators [Figure 3] (Hanania, Stenhouse, & Donev, 2017).

Figure 3: A band diagram showing the different sizes of band gaps for conductors, semiconductors, and insulators (Wikimedia Commons, 2017).

13 What is Graphene If there is an overlap of the valence and the conduction band, hence no bandgap, no additional energy is needed for the electrons to jump into the conduction band. Therefore, the material is a conductor. Since it is not a total overlap, only a part of the electrons can move freely and contribute to the conductivity. A semiconductor has a nearly filled valence band and a nearly empty conduction band separated by a bandgap of generally less than 2 eV (1 eV = 1.602 ·10-19 J) (Shackleford, 2016). By applying an external voltage, electrons can overcome the bandgap, hop into the conduction band and contribute to an electrical current. This can happen really fast as the applied voltage can be turned on an off at incredible rates and act as electrical switches without any moving parts, called transistors. Transistors are the base of any modern-day computer and provide the computation power. Transistors are a further development of diodes, which are explained in chapter “What is a Photodetector” section “Diode”, have the same basic principles but aren’t explained in more detail in this paper. The band diagram of an insulator is similar to that of a semiconductor except for the larger bandgap, which separates a completely filled valence band and a completely empty conduction band. Totally filled bands and totally empty bands do not contribute to current conduction, just as there can be no motion of water in a completely filled bottle (Hu, 2009, S. 8). A semiconductor is somewhere between a conductor and an insulator and only a finite number of electrons can reach the conduction band and participate in conduction (Hanania, Stenhouse, & Donev, 2017).

The Fermi energy (EF) describes the highest occupied energy level at absolute zero (푇 = 0 K) in a system of fermions. A fermion is a particle with half-integral spin, such as electrons, protons or neutrons. A particle with spin behaves as though it has some sort of intrinsic angular momentum. This causes electrons to have a small magnetic dipole (Cambridge, 2017).

The process of doping can increase the conductivity of a semiconductor, or create one in the first place. There are different types of doping. Chemical doping is a practise where a small amount of foreign atoms is introduced to the crystalline structure of a semiconductor. The different numbers of electrons and holes of the foreign atoms, compared to the central atoms of the semiconductor, change the overall number of electrons and holes in the crystal, making the charge carriers either more positive (p) or more negative (n). For this reason, this type of doping is called p-n doping. Other doping methods are geometrical restrictive doping, where the crystal is cracked periodically to create impurities, or electrostatic doping, which uses the effect an external applied electric field can have on the electrical properties (Sood, et al., 2015, S. 69-72).

14 What is Graphene Band Structure of Graphene In the case of graphene, the valence and the conduction band have neither overlap nor bandgap. The valence and conduction bands meet the so-called Dirac point. Energies below 1 eV, which corresponds to a photon from the infrared spectrum of the wavelength of at least 1.24 μm, are most relevant for electrical purposes. The detailed calculations are given in the appendix in section “Calculation of Photon Energy”. The band structure of graphene for these energies can be resembled by two symmetrical cones representing the valence and the conduction band touching at the Dirac point (Avouris & Dimitrakopoulos, 2012, S. 68).

conduction Dirac point band E valence band

Figure 4: (i) Diagram showing the Dirac Fermi cone; (ii) the modification of the band structure by chemical or geometry restrictive doping; (iii) the modification of the k states by bilayer graphene; (iv) and finally, the modification of the band structure in doped bilayer graphene (Sood, et al., 2015, S. 61). In Figure 4 (i), the band structure of pristine graphene can be seen. The valence and the conduction band touch at the Dirac point. This allows ballistic transport of charge carriers even at room temperature. For graphene to be used in electronics as a substitute for silicon (Si), a bandgap needs to be introduced, which makes it less attractive for pure conductive applications. This can be achieved by either chemical or geometrical restrictive doping [Figure 4 (ii)]. The added impurities cause imperfections in the carrier transport, which need to be overcome before a current can flow, therefore a bandgap has been created. Depending on the type of doping (p or n), the Fermi level (EF) either gets moved up- or downwards. Figure 4 (iii) shows the band structure of bilayer graphene, which also exhibits the Dirac point, and modifications of it [Figure 4 (iv)] (Sood, et al., 2015, S. 61). This creation of a bandgap enables graphene to be used as a transistor as well.

15 What is Graphene Optical Properties Light or electromagnetic radiation behaves like sinusoidal waves but at the same time also like little massless particles, called photons. The frequency of the wave determines the colour of the light, which corresponds to the energy of the photons [Figure 5]. Besides the outstanding electrical properties, graphene also has unique optical properties over a wide range of wavelengths (Avouris & Dimitrakopoulos, 2012, S. 94). Due to its gaplessness, graphene can absorb light over a very wide energy spectrum, unmatched by any other material. Because there is not gap in the structure of graphene, photons with lots of different energy levels can excite electrons, without increasing their energies to a level within a forbidden band. This includes light from ultraviolet over visible and infrared up to the terahertz range (1012 Hz). The range of wavelengths which can be absorbed are tuneable via electrostatic doping by changing the size of the bandgap, as different wavelengths correspond to differently energetic photons, as pointed out in Figure 5 at the top (Sood, et al., 2015). Overall, a single layer of graphene absorbs 2.3% of the incident light. This is a remarkable value for a material only one atom in diameter, but quite small in absolute terms. By adding another layer, the electromagnetic absorption is increased by approximately the same value of 2.3% (Bharech & Kumar, 2015).

Approximate absorption range of graphene

Figure 5: Electromagnetic spectrum showing wavelength, photon energy in eV and frequency (Lumenlearning, 2017) and approximate absorption range of graphene. Mechanical Properties The amazing electrical and optical properties of graphene are complemented by mentionable mechanical properties. Due to the 2D nature of a graphene crystal with the strong carbon-carbon bonds in a hexagonal ring, the ultimate tensile strength of graphene lies at 130 GPa, whereas A36 structural steel, used for building skyscrapers, bridges or other buildings, only holds an ultimate tensile strength of 0.4-0.55 GPa (MatWeb, 2017). Therefore, graphene is the strongest material ever discovered, while only weighing 0.77 mg/m2 (de La Fuente, 2017). Normal printing paper, for example, weighs about 100’000 times more. Furthermore, graphene is very pliable and can be stretched up to 20%. The one-atom-thick layer is also impermeable to gasses, including helium. The thermal conductivity of graphene at room temperature of 5’000 W/(m∙K) is another intriguing property (Sood, et al., 2015, S. 60). Copper, for instance, conducts heat at room temperature only with a constant of 390 W/(m∙K) (Frei, et al., 2001).

16 What is Graphene Fabrication To use all the amazing properties of graphene, it first must be fabricated. Graphene can be manufactured in several different ways. The most important being the easy mechanical exfoliation and the mostly industrially used chemical vapour deposition (CVD). Both production methods have pros and cons and different uses in application. Mechanical Exfoliation This method is also known as “Scotch tape” or “drawing” method and was used by Geim and Novoselov in their experiments, which lead to the Nobel Prize. An adhesive tape is used to split graphene layers from graphite flakes in multiple steps, as explained in the chapter History of Graphene. This process produces graphene with the lowest number of defects and highest electron mobility (Bharech & Kumar, 2015). The biggest benefits of the mechanical exfoliation are the simplicity, the low costs and the availability of the required materials. This method of production was key to investigate the properties of graphene. The sizes of the exfoliated flakes, however, are often minuscule and cannot be controlled. Furthermore, every flake needs to be searched and identified as a monolayer individually. Mechanically exfoliated flakes are also prone to get damaged due to stress, as they need to be replaced onto the wanted substrate. The scotch tape method was refined to address these problems by using highly ordered graphite. Another mechanical method uses ultrasonic waves to disperse the layers of graphite when mixed with two substrate immiscible liquids. When the liquids are evaporated, the graphene flakes get isolated (Sood, et al., 2015, S. 63-64). Chemical Vapour Deposition (CVD) The CVD-method is a substrate based technique of producing graphene. Under high temperature, a gaseous carbon compound will react with a metal substrate and stick to it. Typically, copper is used, as it functions as a catalyst in this reaction, can relatively easily be removed from the graphene and be reused (de La Fuente, Figure 6: Diagram of a typical CVD reactor (AZOnano, 2017). 2017). In Figure 6, the CVD process is illustrated. Once a carbon atom occupies a spot on the surface of the substrate, no other carbon atom will be able to adhere to the same position, as no direct contact to the metal is possible anymore. As the temperature is lowered, the carbon crystallises into a layer of graphene. This process will start at several places on the surface. As the crystal regions grow bigger, their border will meet and some discrepancies will probably occur between the lattice orientations of the different sheets. These boundaries act as weak barriers for charge transport. Therefore, it is desirable to maximise the size of the domains and therefore minimise the number of boundaries (Pollard, 2011, S. 23-25).

This method is quite costly, specialised equipment and lots of energy is needed, but it can produce fairly high-quality graphene in variable sized sheets. It is a common solution for the deposit of films in the semiconductor industry, as well as in optoelectronics, due to the low costs involved compared to the high purity of films created (Graphenea, 2017). The flake’s sizes can be determined precisely by the shape of the substrate.

17 What is Graphene Experiment My goal for this experiment was, on one hand, to actually get in contact with graphene and, on the other hand, to conduct simple experiments on its electrical properties as graphene exhibits extraordinary and characteristic electrical properties which enable most of its possible future uses. I wanted to get a reference to the theoretical values I researched and got fascinated about. My mentor Erich Schurtenberger organised a meeting with Dr. Ivan Shorubalko at the EMPA, who is an expert in graphene research and its application in photodetectors. With his generous help and time, I could exfoliate graphene, look at the flakes under an optical microscope and conduct a simple electric experiment. Method Like K. Novoselov and A. Geim in their first isolation of graphene, ordinary scotch tape was used to exfoliate single layers of graphene from graphite powder. Samples of the created graphene flakes were applied to a silicon oxide (SiO2) wafer of one square centimetre and the thickness of 285 nm. The SiO2 provides optimal optical characteristics so even a monolayer graphene flake can be observed with an optical microscope. The graphene flakes need to have a minimal size of a couple of micrometres to be used in electrical experiments as gold (Au) electrodes need to be added for a voltage to be applied. The flake used in this experiment measured about 5.5 to 3.5 μm. The method used to fabricate these electrodes is a special type of lift-off technique, called electron-beam lithography. As electron-beam lithography is a lengthy and costly process, a pre-fabricated wafer with already established contacts was used for the experiment.

Electron-beam Lithography Like other lift-off processes, electron- beam lithography is used to create sacrificial material (photoresist) substrate structures of a target material, here gold, etching of the sacrificial on a substrate, here the SiO2 wafer with material the graphene flake. In a first step, a deposition of target material sacrificial material is applied to the (Au) substrate. Photoresist is typically used as dissolution of the sacrificial material with the unwanted a sacrificial material. After the appli- target material cation, the wanted pattern is etched into structured target material on the material. This is done by illuminating the substrate the resist, thus altering it on a molecular Figure 7: Schematic diagram of the lift-off process (Wikipedia, 2017). level so it becomes locally soluble (similar to the process of developing photographs). To create patterns on nanometre scale, electron-beams are used instead of electromagnetic waves, as the wavelengths of light can cause inaccuracies when used for such delicate scales. The target material (Au) is then deposited over the whole area of the wafer by thermal evaporation. Thereafter, it covers the substrate in the etched regions and the top of the sacrificial material. In a last step, the sacrificial material is washed away with a solvent, leaving only the desired pattern of the target material on the surface of the substrate behind (Wikipedia, 2017). The whole process is schematically shown in Figure 7 and the resulting gold structures in Figure 8a & b.

18 Experiment The wafer with the established electrodes was placed under an optical microscope, that stood on a shock- and vibration-eliminating table [Figure 8c]. In order to minimise noise from incoming radiation, the apparatus was additionally protected by a metal hood. To construct an electric circuit, the tungsten needles were connected to the gold contacts as illustrated in Figure 8a by the black triangles. Different voltages could then be applied and the generated currents measured. The drain bias is the applied bias between the drain and the source of the current, hence the two needles. A back- gate bias (Vg) could also be applied on the wafer (green and white cable in Figure 8c). For the main measurement, the drain bias was held constant at 100 mV and the gate bias was gradually increased from 0 to 100 V in 1 V steps and then back to 0 V again. The resulting drain current is plotted in Figure 9. By altering the back-gate bias, the Fermi level is moved upwards or downwards. When the Fermi level no longer lies on the Dirac point, there isn’t one completely full and one completely empty band in the band structure anymore, but either a completely full valence band and a partially filled conduction band (Fermi level is moved upwards) or a partially full valence band and an empty conduction band (Fermi level is moved downwards). As a current can only flow when the bands are not completely full, the charge carrier density (n) is modified when changing the gate bias. At the Dirac point, the carrier concentration vanishes theoretically: 푛=0. In reality, the carrier concentration will not reach 0 (no conductivity) as there are other mechanisms that create charge carriers. Accordingly, the resistivity (ρ) gets greater the closer to the Dirac point (Wojtaszek, 2009, S. 3). Figure 8d shows the shift of the Fermi level according to the gate bias. S

a) b)

20 μm

Figure 8: a) Graphene sample used in the experiment on SiO2 wafer with established Au-electrodes under an optical microscope. The black triangles symbolise the tungsten needles. S, source. D, drain. b) Magnification of the black square in a). c) SiO2 wafer with graphene sample hooked up in an electric circuit with tungsten needles. d) Shift of the Fermi level as Vg gets altered. Here, the Dirac point is at Vg=0, where the resistivity is greatest (Geim & Novoselov, 2007, S. 5).

19 Experiment The graphene flake and the SiO2 behave like a capacitor. The carrier density (n) is calculated as follows (Wojtaszek, 2009, S. 3),

휀표 ∙ 휀푟 푛 = 푉푔 − 푉퐷푖푟푎푐 (1) 푑푟 ∙ 푒

where 휀 = 8.854∙ 10 (permittivity of vacuum), 휀 = 3.9 (relative permittivity of SiO2), 푒 = 1.602 ∙ 10 C (charge of an electron) and 푑 = 285 nm (the thickness of the SiO2 wafer). VDirac is the bias where the Dirac point is and Vg the gate bias. The carrier mobility (μ) is calculated as follows (Wojtaszek, 2009, S. 5),

1 휇 = 휌푛푒 (2) where the resistivity can be calculated, using equation 3.

1 푈 휌 = = (3) 휎 퐼

To calculate ρ, a second measurement was conducted plotting the resulting drain current to an altering drain bias at 푉 = 0 V. As this series of data is only complementary to the first one, the plot of the data can be found in the appendix under title Resistivity of the Graphene Flake.

20 Experiment Results

5 A] μ 4

Drain Current [ Current Drain 2

0 0 10 20 30 40 50 60 70 80 90 100 Gate Bias [V]

Drain Current, 0-100 V V(g)Vg Drain Current, 100-0 V V(g)Vg

Figure 9: Resulting drain current at a constant drain bias of 100 V plotted against the change in gate bias (Vg). The two measurements were taken right after each other, the first one from 0-100 V gate bias and the second one the other way around from 100-0 V gate bias.

In Figure 9, the Dirac point is visible for the first measurement at 40 V gate bias. The second measurement, done immediately after, exhibits its Dirac point at about 65 V gate bias. There is a hysteresis of roughly 25 V to the right. At 푉 = 0 V for example, the carrier density can be calculated using equation 1:

As As 8.854 ∙ 10−12 ∙ 3.9 푛 = Vm Vm |0 V − 40 V| = 3.0∙1016 m−2 (4) 285 ∙ 10−9 m∙ 1.602 ∙10−19 C

According to the additional measurement in the appendix and equation 3, the resistivity (ρ) of the used graphene flake is:

푈 100 mV 휌= = = 20000 Ω (5) 퐼 5 µA

By combining equation 2,4 and 5, the carrier mobility (μ) at 푉 = 0 V can be calculated:

1 m cm 휇= =1∙10 = 100 (6) 20000 Ω ∙ 3.0∙ 1016 m−2 ∙ 1.602 ∙ 10−19 C Vs Vs

21 Experiment Discussion The graphene sample used in the experiment was a CVD flake. Therefore, there are lots of boundaries between the domains, where the individual graphene crystals grew together, which hinder the electron flow within the material and lead to a lower carrier mobility. There wasn’t a new sample prepared for the experiment and the used one was already stored in an ordinary office drawer for a couple of months. The experiment was conducted in a room full of air under normal pressure. All these circumstances are responsible for the Dirac point not being at 푉 = 0 V and the low charge carrier mobility. Even though the calculated charge carrier mobility doesn’t reach the literature values, one can observe that the change in gate bias leads to a change in carrier mobility. The carrier density, however, matches the literature values of 푛 ≥10 cm. For high-end measurements, a freshly prepared freestanding sample and an ultrahigh vacuum in a cleanroom are required. As a monolayer of graphene is so thin and has a very big surface area. Therefore, it is vulnerable to encounters with air and water molecules. The interaction between the graphene and water from the air is responsible for the hysteresis of Figure 9, according to Dr. Shorubalko. It is notable how easily the electrical properties of graphene can be changed when the conditions around it change.

22 Experiment What is a Photodetector After becoming familiar with graphene, I want to show a genuine application where some of its properties can be used to enhance today’s technology. Graphene can act as a photodetector due to its optical and electronical properties. A photodetector is an electronic device that absorbs light and turns it into electrical energy. The resulting current is called photocurrent. Photodetectors are widely used in energy generation (solar cells) or optical communication systems. In these applications, detectors receive optical signals, convert them with as little loss as possible into electronic signals which can be interpreted by a computer, telephone or any other capable device. Most devices make use of the photovoltaic effect to achieve this. The graphene-metal-graphene photodetector also makes use of the photo-thermoelectric effect to create a photocurrent (Koppens, et al., 2014, S. 783).

Photovoltaic Effect The photovoltaic effect is related to the photoelectric effect. The photoelectric effect is based on the idea that electromagnetic radiation (light) is made of little charged particles, called photons. When light gets absorbed by atoms, electrons can be emitted and ejected from the material, due to their excitation caused by the impact of the photons [Figure 10]. This causes the generation of electron-hole pairs, which result in a photocurrent. The same thing happens in the photovoltaic effect, the only difference being that the excited electrons stay within the material (Wikipedia, 2017). They only move from the valence into the conduction band [Figure 11]. In either case, an electric potential is produced, if the light has enough energy to overcome the bandgap of the material, hence the energy of the photon needs to be greater than the bandgap energy. Every photon carries an amount of energy inversely proportional to its wavelength. Therefore, light of shorter wavelength has more energetic photons than light of longer wavelength, as Figure 5 illustrates (Wayback Machine, 2017).

Figure 10: Diagram of the photoelectric effect (Zimmernan Figure 11: Diagram of the photovoltaic effect (Green Rhino Energy, Jones, 2017). 2017).

23 What is a Photodetector Photo-Thermoelectric Effect The photo-thermoelectric effect is based on the thermoelectric effect, which is the result of a temperature gradient within a conducting or semiconducting material. A temperature gradient causes electrons to diffuse within a solid-state body. There are three types of thermoelectric effects, that are all connected: The Seebeck effect, the Peltier effect and the Thomson effect, which are named after their discoverers. The Seebeck effect describes the existence of an electrical potential in a circuit of two conductors when the junctions are held at different temperatures. This effect can be turned around to achieve cooling or heating with an electrical current that runs through the same kind of circuit (Peltier effect). W. Thomson (Lord Kelvin) described the connection of the previous two effects and predicted a third thermoelectric effect. Absorbed heat causes a current to flow in a material with a temperature gradient (California Institute of Technology, 2017). The photo-thermoelectric effect uses the principles of the thermoelectric effect but the heating is achieved by the absorption of light. The photo-generated hot electrons can induce a photovoltage by the photo-thermoelectric effect, which is illustrated in Figure 12. The Seebeck coefficient describes how much voltage is induced with increased temperature in a specific material. It is measured in V/K (Koppens, et al., 2014, S. 781).

Figure 12: Red shaded area indicates elevated electron temperature with ΔT the temperature gradient; S1 and S2, Seebeck coefficient in graphene areas with different doping (Koppens, et al., 2014, S. 782).

There are basically two types of photodetectors: the photodiode and the phototransistor. A photodiode creates a low output current and is mainly used for quick response. A phototransistor works with the same mechanisms to create a first photocurrent but then amplifies the output current. Its responses are slower than the ones of a photodiode (Stanley Electric CO., Ltd., 2017).

24 What is a Photodetector Diode A diode is basically a one-way street for electricity. It allows a current flow in one direction, but not in the other. A diode is made up of a semiconductor, such as silicon (Si). The silicon (Si) PN diode is explained here as it is the most basic and most common. Other diodes work with the same principles. Pure Si has no free electrons, all four valence electrons are bonded within its tetrahedral crystalline structure. But the Si used in diodes is not pure. One half is doped with n-type impurities, the other half with p-type impurities. For the n-type doping, a small number of atoms with five electrons in their valence shell, like Phosphorus (P), is injected. As it brings an extra electron, the semiconductor has more negative mobile charge carriers (n-type) making it more conductive. In p-type doping, an element with only three valence electrons, like Boron (B), is introduced. This creates a lack of electrons in the lattice which also increases the conductivity, as the electrons can move into the vacant spots. One can also say that these holes can move around, giving the p-type doped part more positive charge carriers [Figure 13a]. The n and p only stand for the sign of charge that can move within the doped material and not for the charge of the semiconductor itself. The semiconductor is still neutral as the number of electrons always match the number of protons, even if it is doped (Veritasium, 2017).

a) b)

Figure 13: a) Principle of a p-n doped semiconductor before interaction. b) p-n junction with depletion region and barrier potential (electrical4u, 2017). Even though after the doping process the n-doped region mostly holds negative and the p-doped mostly positive charge carriers, a minority of the other charge is always left, due to thermal activity. If the two regions are put together, the electrons and holes are getting attracted by the opposite charge, which causes electrons to migrate from the n- to the p-type doped side, where the holes are. Because the whole lattice was neutrally charged before, the movement of the electrons create a slight negative charge on the p-type doped side of the p-n junction, leaving a slightly positive charge on the n-type doped side [Figure 13b)]. This charged band is called depletion region as there are no charge carriers left anymore. The depletion region also prevents further migration of electrons to the other side; hence it builds up a barrier potential opposing electron flow (electrical4u, 2017).

As mentioned before, a diode can act either as closed or open switch, depending on the direction of the applied current. If the negative anode is connected to the n-type doped side and the positive cathode to the p-type doped side, the diode is under forward biased condition and acts like a closed switch [Figure 14a)]. The barrier potential across the junction acts in the opposite direction of the forward applied voltage. Therefore, there is no electrical current before the applied voltage isn’t bigger than the barrier voltage. This voltage is called forward biased voltage (about 0.7 V for Si). Beyond that point, the current can only be limited by connecting an external resistance in series with the diode (electrical4u, 2017).

25 What is a Photodetector a) b)

Figure 14: a) p-n diode under forward biased condition. b) p-n diode under reversed biased condition. Blue arrows show the direction of movement of the majority charge carriers, red arrows show the direction of movement of the minority charge carriers result in in the reverse saturation current (electrical4u, 2017).

If the negative terminal of the voltage source is connected to the p-type doped side and the positive terminal to the n-type doped side, the diode acts like an open switch and is under reversed biased condition [Figure 14b]. Due to the attraction of the positive potential, the electrons in the n-type region go away from the junction. In the p-type region, the same happens with the holes, due to the negative potential. This makes the depletion region wider with increasing reverse applied voltage. In this situation, the current does not flow through the diode, because the majority carriers cannot cross this wide barrier due to the electrostatic forces of the applied voltage. Only the minority charge carriers can flow through the depletion region, as they do not oppose the polarity of the reverse applied voltage and create a small current from the n- to the p-type region, called reverse saturation current or dark current. As the amount of minority charge carriers is really small, under normal circumstances, the reverse saturation current can practically be ignored, hence no current flows through a diode under reversed biased condition (Engineering, 2017). If the reverse biased voltage reaches a certain magnitude, called avalanche breakdown voltage, the kinetic energy of the minority charge carriers gets big enough to destroy the covalent bonds in the depletion layer, leading to carrier multiplication and eventually to an avalanche-like breakdown of the depletion region. This results in a huge reverse current running through the diode, which can damage the diode permanently (electrical4u, 2017).

26 What is a Photodetector Photodiode There are several different types of diodes and photodiodes. The most basic photodiode is the PN photodiode. The other ones are basically refined versions of the PN photodiode and work with the same principles. Figure 15 shows an ordinary silicon based photodiode.

The PN photodiode is basically a PN diode in reversed biased condition with a screen or lens that allows light to fall on the device (Braley, 2017). Because of the photovoltaic effect, every absorbed photon causes the generation of an additional electron- hole pair. This may or may not lead to the generation of a photocurrent. It depends where the photons hit the diode. If the Figure 15: General purpose silicon photodiode generation occurs in the depletion region, the electrons and holes (Centronic, 2017). are separated by the barrier potential, leading to a reverse current flow. The Internal quantum efficiency (IQE), which is the ratio of the number of collected electron-hole pairs and the absorbed photons, was 100%, if all of the absorbed photons create an electron-hole pair. If the generation occurs in one of the neutral regions (p or n) the electric field in most places is too weak to pull apart the electron from the hole. Therefore, it is desirable to design a photodiode in such a way that all the light is absorbed in the depletion region (Decoster & Harrari, 2009, S. 28). The current varies almost linearly with the flux of the light, which can be seen in Figure 16. Therefore, a higher photocurrent can be detected when the optical power is stronger. Accordingly, the luminance of a light source can be determined by the magnitude of photocurrent it causes the photodiode to produce. Because of the reverse biased condition, the current through the junction is (nearly) zero when no light is present. This allows the diode to be used as a switch when light is present (Braley, 2017).

To improve the absorption rate, an intrinsic (undoped) layer can be added between the p- and n-doped regions. Devices with an intrinsic layer are called PIN photodiodes. Due to the larger depletion region, PIN photodiodes can create more electron-hole pairs at a lower capacitance (Braley, 2017).

Figure 16: Photodiode characteristics plotted as a graph of the reverse current in μA to different levels of luminance in lux (ECE Tutorials, 2017).

27 What is a Photodetector Graphene Photodetector Applications like video imaging, optical communication, motion detection, night vision or gas sensing are based on the conversion of light into an electrical signal and have gained a high level of maturity due to the development of high-performance materials and large-scale production. As these applications gain in importance in our day-to-day lives, the need for photodetection units with higher performance in terms of speed, efficiency or wavelength range, as well as flexibility and transparency is becoming more eminent (Koppens, et al., 2014, S. 780).

The key principle of photodetection, which is the conversion of absorbed photons into an electrical signal, can be achieved with graphene through several different mechanisms. These include the photovoltaic effect, the photo-thermoelectric effect and three others, which are not discussed in this paper as they are not of importance to the metal-graphene-metal photodetector discussed in this paper (Koppens, et al., 2014, S. 783). The graphene based photodetectors work with the principles of ordinary photodiodes. In the vicinity of metal, graphene gets p-type doped and the middle of the graphene channel turns n-type, because of the electrostatic doping due to an applied gate bias (Xia, Mueller, Lin, Valdes-Garcia, & Avouris, 2009, S. 840).

The metal-graphene-metal photodetector was one of the first graphene based photodetectors ever researched. In addition to the photovoltaic effect, the photo-thermoelectric effect can also contribute to the photocurrent generated by the absorption of light (Koppens, et al., 2014, S. 783). The sepa- ration of the photo-generated carriers only occurs in a narrow region of about 0.2 μm around the metal-graphene interfaces. That’s why an interdigitated comb-like structure is introduced to increase the effective photodetection area [Figure 17], which leads to a higher electric field. If both electrodes consist Figure 17: Metal–graphene–metal (MGM) photodetectors with of the same metal however, no resulting asymmetric metal contacts. Main panel: three-dimensional schematic of the MGM photodetector. Bottom right: scanning electron micrograph of current will flow as the electric field profiles the MGM photodetector. Scale bar, 5 mm. The spacing between the metal between neighbouring metal fingers would be fingers is 1 mm and the finger width is 250 nm (Mueller, Xia, & Avouris, 2010, S. 297). symmetric, and henceforth also the attraction of the carriers. An asymmetrical metallisation must therefore be used to create an overall photocurrent. In this particular photodetector, one electrode is made of palladium/gold and the other of titanium/gold (Mueller, Xia, & Avouris, 2010, S. 297). The electrical field, and thus the resulting photocurrent, can be adjusted by the right choice of metal. Metal-graphene-metal photodetectors on

Si/SiO2 substrates reach IQEs between 6-16%. There is still room for improvement, as the values of suspended graphene go up to 35% (Koppens, et al., 2014, S. 784).

28 Graphene Photodetector The high carrier mobility and their short lifetime in graphene allow metal-graphene-metal photodetectors to operate at high data rates. This makes graphene desirable for high-speed applications, like optical switches, where a quick annihilation of the carriers is essential (Xia, Mueller, Lin, Valdes- Garcia, & Avouris, 2009). An error-free data stream of 10 Gbit/s was achieved with a titanium- graphene-palladium photodetector, as seen in Figure 17 (Koppens, et al., 2014, S. 785).

The low light absorption of 2.3% can be appealing for flexible and transparent applications based on optoelectronics. For other uses however, it is desirable to enhance the absorption of graphene. By mirroring the incident light, with a so-called distributed Bragg mirror (DBR), more than 60% light absorption and a responsivity of 21 mA/W can be achieved [Figure 18]. A DBR consists of alternating materials of about quarter-wavelength-thick layers which reflect the incident light and trap it inside. The responsivity, in the case of photodetectors, describes how much electrical current is generated be the power of the incident light. Without this technique, the responsivity would only reach 6.5 mA/W. Although, the improved responsivity comes at the expanse of the bandwidth of the absorbable spectrum, the device can be tuned to a specific wavelength range to reach these improved values on the desired wavelengths (Koppens, et al., 2014, S. 785).

To get an enhanced photo-response across the whole bandwidth of optical telecommunications, an optical waveguide can be integrated of the graphene sheet [Figure 19]. The waveguide channels the incident light and guides it over the graphene sample. Bandwidths of over 20 GHz, which exceed all conventional germanium (Ge) detectors, were obtained and the measured responsivities of 50-130 mA/W are as good as the best photodetectors made from GeSn (Koppens, et al., 2014, S. 785).

Figure 18: Schematic layout of a microcavity-integrated Figure 19: Scanning electron microscope image of a waveguide- photodetector. DBR, distributed Bragg mirror (Koppens, integrated device. GND, ground (Koppens, et al., 2014, S. 783). et al., 2014, S. 783).

One must note that metal-graphene-metal photodetectors were the first graphene based photodetectors to be investigated (Koppens, et al., 2014, S. 783). It was the first try to see if photodetection was even possible at viable rates. This means that ordinary thoroughly refined photodetectors based on other semiconductors, such as silicon or germanium, may exhibit better values. By now, there might be other graphene based photodetectors which exceed this particular one by far.

29 Graphene Photodetector Conclusion and Outlook The use of graphene in photodetectors does not reinvent the technology. It doesn’t turn the world upside down and lead to a new way of living. It simply is the enhancement of an already existing technology and one of the first ways to make use of a new and rising material. This example is here to show that graphene can already be used today and isn’t just a novel material, talked about in laboratories of universities with no use for ordinary people. It also points out that the applications today haven’t reached the limit of graphene’s capability yet, and that a lot more can be expected in the future. Graphene has only been studied intensively for a bit over a decade, yet there has already been immense progress in understanding its properties, developing new means of manufacturing and applying it in several fields of applications. Time and more research will provide a deeper and more complete view of graphene and will enable us to use it more specifically and more efficiently. With the general and basic knowledge about graphene gathered in this paper, one can easily imagine lots of other possible applications of graphene besides photodetection.

Its toughness, lightness and flexibility could be used to create super strong, thin, flexible and lightweight materials for manufacturing cars, airplanes or satellites. Due to the dense web of the structure and the mechanical resilience, graphene membranes don’t allow any other substance to pass through, not even hydrogen gas, if the membrane is perfect and doesn’t feature any faults. Therefore, it would be possible to create fireproof coatings for furniture or even whole houses because the oxygen needed for the combustion process wouldn’t be able to reach the surface. Rain protection on jackets or boots could also be improved by using graphene coatings. Another application which makes use of the dense structure of graphene is the creation of filters. Tiny holes in the desired diameter can be created in the graphene lattice by chemical reactions. As the filter only consists of one layer of atoms, the molecules which can pass through it experience hardly any drag. This leads to a fast filtering process. Salt water could be filtrated in an easy and cheap manner to create drinking water.

Especially the electric and optical properties of graphene combined with its flexibility and transparency can lead to breakthroughs in the electronics industry. As graphene can act as a semiconductor, is could substitute lots of the current semiconductors used in today’s electronics. Carbon is cheap and available in abundance on our planet. The production of electronical devices wouldn’t rely on availability of rare metals so much anymore, which would eventually even lower the price and the environmental impact as less rare metals need to be mined and refined. The thinness of graphene would also decrease the space needed for transistors (electrical switches) and would therefore enable more computing power in smaller processors. Besides the enhancement of already existing technologies, new ones could also be created. Bendable phones, tablets or laptops could be created with graphene based technology. Integrated electronics in clothing to monitor heartrate and body temperature are no longer out of reach and transparent solar cells could be integrated in every window to generate electricity. Longer lasting and faster charging batteries are also possible by using graphene. In biomedicine, another field of application can be seen. Graphene can work as sensitive electromechanical sensors or stimulate nerves and therefore be used as brain implants. Due to its large surface area graphene could also make a more effective drug delivery platform.

30 Conclusion and Outlook This list merely is a compilation of some of the most apparent or most desirable possible applications of graphene in my opinion and not terminal at all. There are lots of other potential uses of graphene. On the webpage of the Graphene-Flagship (graphene-flagship.eu), there is a wide range of graphene application areas for further research under the heading Material > Graphene Application Areas. Graphenea (www.graphenea.com) also provides a listing of graphene applications and uses under the column Let’s learn > Learn about Graphene. Scientific magazines like Nature Nanotechnology, IEEE Spectrum or Cosmos published copies about applications of graphene as well. These, however, might not be available for free.

Graphene truly is a material of the superlatives. Even though it has lost some of its originally assigned titles like best heat conductor or only two-dimensional material, its outstanding properties cannot be denied. Besides having nearly unlimited future application possibilities, graphene also played another important role. Its first isolation in 2004 by A. Geim and K. Novoselov showed the world that two- dimensional materials are more than an academic material and stable even in ambient conditions. This lead to a boom in the research of graphene related materials (GRMs) such as silicene (2D-silicon) or germanene (2D-germanium). The GRMs have many similar properties to graphene and may even exceed graphene in some of them, making the range of future applications of two-dimensional materials and their perfection even wider.

According to Dr. Shorubalko, the science behind a lot of these future applications has been done. It is technically possible to create these new technologies. The only thing that’s missing is sufficient funding and the collaboration between universities and companies to convert the possibilities and concepts into competitive and saleable products. I’m confident that graphene based technology will make its way into our houses and everyday life already very soon.

31 Conclusion and Outlook Declaration of Authenticity I declare hereby, that this paper has been composed solely by myself without the use of any sources other than the ones provided.

Au ZH, 18.12.2018 Signature: Daniel Schmid

32 Declaration of Authenticity Appendix Calculation of Photon Energy The energy of a photon can be described by the following equation.

ℎ∙푐 퐸 = (i) 휆

Where 퐸 = 푝ℎ표푡표푛 푒푛푒푟푔푦, 휆 = 푤푎푣푒푙푒푛푔푡ℎ, 푐 = 2.998∙10 ms (speed of light in a vacuum) and ℎ = 6.626∙10 Js (Planck constant). The constants ℎ and 푐 can be combined to form one constant.

ℎ∙푐 = 2.998∙10 ms ∙ 6.626∙ 10 Js = 1.986∙10 Jm (ii)

When speaking of photons, the electronvolt (1 eV = 1.602∙ 10 J) is more commonly used than the Joule (J) and the wavelength is given in micro meters (μm). Equation ii can be written as,

1 eV 10 µm ℎ∙푐 = 1.986∙10 Jm ∙ ∙ = 1.240 eV ∙ µm 1.602 ∙ 10 J m (iii)

Equation iii is integrated into equation i.

1.240 eV ∙ µm 퐸[eV] = (iv) 휆[µm]

The wavelength of a photon with the energy of one electronvolt is therefore,

1.240 eV ∙ µm 휆= = 1.240 µm (v) 1 eV Resistivity of the Graphene Flake

4 A]

μ 2

0 Drain Current [μA] 1 -2 Drain Current [μA] 2 Drain Current [ Current Drain

-4

-6 0 10 20 30 40 50 60 70 80 90 -90 -80 -70 -60 -50 -40 -30 -20 -10 100 -100 Drain Bias [mV]

Figure 20: Resulting drain current plotted against an altering drain bias from -100 mV to 100 mV in steps of 1 mV at Vg=0 V. Figure 20 shows the graph of the additional measurement to calculate the resistivity of the graphene flake used in the experiment. The resulting drain current is plotted against the induced drain bias from -100 to 100 mV altering in steps of 1 mV at a gate bias of 0 V. The measurement was conducted two times and the results nearly fully correlate. The resistivity is the inverse gradient on the graph and calculated according to equation 3. 33 Appendix Indices List of Figures Cover: https://www.newyorker.com/wp-content/uploads/2014/12/141222_r25925- 878.jpg, accessed 5.12.2017

Figure 1: a) Exfoliation of graphene from graphite of a pencil with the scotch tape method. b) Result of the exfoliation, monolayer graphene flakes cannot be seen by the naked eye. (p.9)

Figure 3: A band diagram showing the different sizes of band gaps for conductors, semiconductors, and insulators (Wikimedia Commons, 2017). (p.13)

Figure 5: Electromagnetic spectrum showing wavelength, photon energy in eV and frequency (Lumenlearning, 2017) and approximate absorption range of graphene. (p.16)

Figure 6: Diagram of a typical CVD reactor (AZOnano, 2017). (p.17)

Figure 7: Schematic diagram of the lift-off process (Wikipedia, 2017). (p.18)

Figure 8: a) Graphene sample used in the experiment on SiO2 wafer with established Au- electrodes under an optical microscope. The black triangles symbolise the tungsten needles. S, source. D, drain. b) Magnification of the black square in a). c) SiO2 wafer with graphene sample hooked up in an electric circuit with tungsten needles. d) Shift of the Fermi level as Vg gets altered. Here, the Dirac point is at Vg=0, where the resistivity is greatest (Geim & Novoselov, 2007, S. 5). (p.19)

Figure 10: Diagram of the photoelectric effect (Zimmernan Jones, 2017). (p.23)

Figure 11: Diagram of the photovoltaic effect (Green Rhino Energy, 2017). (p.23)

Figure 13: a) Principle of a p-n doped semiconductor before interaction. b) p-n junction with depletion region and barrier potential (electrical4u, 2017). (p.25)

34 Indices Figure 14: a) p-n diode under forward biased condition. b) p-n diode under reversed biased condition. Blue arrows show the direction of movement of the majority charge carriers, red arrows show the direction of movement of the minority charge carriers result in in the reverse saturation current (electrical4u, 2017). (p.26)

Figure 15: General purpose silicon photodiode (Centronic, 2017). (p.27)

Figure 16: Photodiode characteristics plotted as a graph of the reverse current in μA to different levels of luminance in lux (ECE Tutorials, 2017). (p.27)

Figure 17: Metal–graphene–metal (MGM) photodetectors with asymmetric metal contacts. Main panel: three-dimensional schematic of the MGM photodetector. Bottom right: scanning electron micrograph of the MGM photodetector. Scale bar, 5 mm. The spacing between the metal fingers is 1 mm and the finger width is 250 nm (Mueller, Xia, & Avouris, 2010, S. 297). (p.28)

Figure 18: Schematic layout of a microcavity-integrated photodetector. DBR, distributed Bragg mirror (Koppens, et al., 2014, S. 783). (p.29)

Figure 19: Scanning electron microscope image of a waveguide-integrated device. GND, ground (Koppens, et al., 2014, S. 783). (p.29)

Figure 20: Resulting drain current plotted against an altering drain bias from -100 mV to 100

mV in steps of 1 mV at Vg=0 V. (p.33)

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38 Indices