Device fabrication from graphene 

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Electrical properties

Before graphene, there have been 2D systems in electronic research. Even though these were not truly 2D materials, two dimensional electron gases provided ways to study 2D systems. A two-dimensional electron gas (2DEG) is a system where electrons can freely move in two dimensions, but are confined in the third. This system is commonly encountered in MOSFETs. The knowledge paved the basis for investigating the electrical properties of graphene.
The electron transport in graphene is directed by the relativistic~ Dirac equation. Charge carriers act as massless relativistic particles with a “speed of light” of 106 m/s. [15] Figure 6 is the plot from one of the first gated devices made of graphene. One characteristic that draws the attention right away of is the ambipolarity of charge carriers. Novoselov et al. showed in 2004 that graphene FET on SiO2 has ambipolar characteristics with electron and hole concentrations of 1013 cm-2 and a mobility of 10 000 cm2/Vs at room temperature. That is to say, it is possible to continuously tune charge carriers from electrons to holes and vice versa. Secondly, as expected from the lack of the band gap, graphene shows little change in resistivity between the on and off stage of the transistor. [8] [15]
Another consequence of charge carriers posing as Dirac fermions is the high carrier mobility. ~Mobility of graphene on SiO2 can reach 15 000 cm2/Vs with a corresponding sheet resistivity of 106 Ω cm. [8] To put in perspective, we should note that this value is lower than the resistivity of silver, the material with lowest resistivity at room temperature. [16] [8] And when there is no substrate to interfere with the transport properties, i.e. for the case of suspended graphene, mobility can reach 40 000 cm2/Vs at room temperature and even 200 000 cm2/Vs at low temperature. [17] [18] Furthermore, the first measurements of graphene on SiO2 devices have presented ballistic transport at submicron distances. Later studies showed that the mean free path of charge carriers can reach up to 0.5 mm. [19]
In addition to the favorably high values for mobility, graphene shows low electronic noise from thermal agitation of charge carriers in an electrical conductor at equilibrium, regardless of the voltage applied. Combined with the high values for mobility, it is interesting for graphene to participate in nanoelectromechanical systems (NEMS).
Graphene FETs are tainted with the low on/off ratio. For graphene to ever participate in logic applications, a band gap is needed. Therefore, there have been various studies on how to open a band gap. Two main methods have been suggested; graphene nanoribbons (GNRs) or bilayer graphene. In contrast to the massless Dirac fermions in monolayer graphene, bilayer graphene has massive Dirac fermions. A gate voltage introduces asymmetry between the layers and forms an energy gap. [20] [21] The second way to create an energy gap is through a lateral quantum confinement; i.e. patterning graphene into very narrow ribbons. Depending on their configuration, GNRs show different electronic properties; zigzag GNRs are, in theory, metallic while the armchair GNRs can be either semiconducting or metallic. The energy gap is inversely proportional to their width. [16] For real applications, however, GNRs need to have smooth edges which has been a great challenge in GNR research so far. Several approaches have been presented which involve top-down etching techniques as well as bottom up CNT opening. [22] [23] Yet edge defects still appear to dominate the experimental results related to the realization of possible GNR FETs. Moreover, it was also shown that it is possible to open a band gap of 0.26 eV in epitaxial graphene grown on SiC. The origin of the band gap is attributed the interaction of graphene with the substrate. [24]
Another way to open up a band gap is strain. Figure 7 , shows how strain modifies the electronic structure of graphene by breaking the sublattice symmetry. The two carbon sublattices are inequivalent under uniaxial strain. When one is tensed, the other contracts. A large uniaxial strain in the armchair direction can open an effective band gap as in Figure 7.
Strain is relevant not only for researchers aiming to open a band gap in graphene, but for electronic applications in general. It clearly modifies the electronic structure of graphene; consequently it will have an effect on electrical properties as well. We discussed externally applied strain, but synthesis and fabrication can lead to a built-in strain in the final graphene device. Therefore, it is important to study the evolution of strain in the graphene device and its consequences. We will investigate this in the next chapters more in detail.

Mechanical properties

The strength of graphene has been modeled by atomistic simulation method and measured by nanoindentation technique. A Young’s modulus of ca. 1.0 TPa, which corresponds to the theoretically calculated value, [25] has been deduced from a measured 2D elastic stiffness of 340 N/m. [26] The interlayer spacing of graphite is customarily taken as the sheet thickness. Moreover, a breaking strength of 42 N/m has been measured which translates into a bulk value of 130 GPa. [26] Graphene owes these remarkable values to the strong C-C covalent bond.

Optical properties

The unique electronic properties of graphene generate an unexpectedly high opacity for one atomic monolayer in spite of a rather low white light absorption of 2.3%. [27] The light adsorption increases linearly with the number of layers. [28] The contrast of graphene on 300 nm SiO 2 increases with the layers as well which was the key in locating single layer graphene during mechanical exfoliation.

Thermal properties

Most materials expand upon heating and contract upon cooling, i.e. they have positive thermal expansion coefficients (TEC). Ultra-thin suspended films, on the other hand, have the opposite situation. Many compounds in the form of a layer have a negative TEC which stems from the fact that the frequency of the out-of-plane acoustic phonons increases when the inter-atomic distance is increased. [29] Already before measurements, graphene was predicted to demonstrate a negative TEC. [30] The TEC determined experimentally exceeded theoretical predictions by 2 – 3 times as ~ 7 x 10-6 K-1 at room temperature. This value is larger than the in-plane TEC of graphite.
Through the strong C-C covalent bond and the high phonon speed ( 2 x 10 4m/s), phonons dominate the thermal conductivity of~graphene at room temperature. The thermal conductivity of suspended graphene is estimated as 2000 – 5000 W/mK around room temperature~. [31] [32] To put these values in perspective, the thermal conductivity of Cu is 400 W/mK and of on a substrate. Phonon~ leakage to the substrate and scattering reduce the thermal conductivity of graphene down to 600 W/mK. [33]

Potential applications

Here, we present an outlook on potential applications of graphene. These are neither exhaustive nor in industrial production. That is to say, we aim to give examples of the incorporation of graphene into different fields. The applications are not yet maturely developed such that graphene is in an industrial product. A vast amount of research is done to uncover its properties and still an extensive research into the understanding and control of these properties is necessary to translate them into real applications.

Logic devices vs RF devices

The very commonly known Moore’s law states that the number of transistors on a chip doubles once every two years driven by the demand for faster and more affordable computers and mobile devices. Now that the Si technology is reaching its limits, two new fields emerged in which the semiconductor industry is investing in heavily: Beyond CMOS and More than Moore. Beyond CMOS covers all the technologies that might replace CMOS in future and More than Moore focuses on incorporating new functionalities into existing device architectures.
Carbon electronics have the advantage of retaining FET architecture but replacing the conductive channel with a carbon nanomaterial. Graphene transistors can be divided into two categories; logic devices and RF devices. They have quite different design demands. Logic applications must have low energy consumption in static state. This translates into that the graphene device must be switched off completely to a non-conducting state, i.e. it needs to have a band gap. Another necessary yet debated phenomenon is the current saturation. It is argued that electron-electron interactions in graphene might make velocity saturation impossible.
As we mentioned, the zero band gap does not permit graphene to be employed in logic applications. In fact, IBM stated that it is unlikely for graphene to replace Si technology in future.
[34] Yet again, studies on graphene primarily focused on graphene FETs. Generally, it is simpler to fabricate the transistor with a back-gate for research purposes by choosing the underneath layer as heavily doped Si. (Figure 8a) In that case, graphene is separated from the gate by the dielectric, (mostly a 300 nm of) SiO2. The large parasitic capacitance of the 300 nm oxide interferes with measurements, thus top-gated devices have been fabricated as in Figure 8b.
For graphene to have a share in logic applications, it needs to beat CMOS in the parameters of room temperature operation, speed, scalability, size, device gain and cost. For RF devices, however, there is less requirement for a complete device switch-off. Instead, high speed and low noise are demanded. RF transistors play a key role in wireless communication by amplifying signals and offer gain at high frequencies. They commonly experience problems from series resistance and short channel effects. These could be overcome by employing graphene since it has intrinsically an atomically thin channel which improves electrostatistics.
Beyond academic research [37] [38], companies such as IBM [23] [39] (Figure 9a) Samsung [40] (Figure 11b) and Intel [11] [41] have been doing research in the field of graphene field effect transistors. IBM presented a 100 GHz graphene transistor on SiC with a higher cut-off than Si MOSFETs of the same length. [36] (Figure 9b)

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NEMS sensors

The field of NEMS looks into shrinking device dimensions since low dimensions improve resonant frequency, sensitivity of force and mass. [42] At the same time, narrowing the dimensions can degrade device characteristics and make transduction difficult. The well-known technologies of Si make it an eligible material to fabricate clamped beams and cantilevers by top-down approach. [43] [44] In recent years, nanowires and nanotubes have caught interest in the field of NEMS as a bottom-up approach. Graphene is intrinsically nanoscale and it can be fabricated over large areas allowing for standard lithographic techniques. Thus, it brings together top-down and bottom-up approaches.
Graphene has a combination of properties that makes it well-suited for NEMS. It is chemically inert which enables atomically thin devices. Its high stiffness and low mass result in high resonant frequencies. Furthermore, its frequency is tunable over a large range due to its extraordinary values of strength. Graphene NEMS which have a small built-in tension can be employed in applications which require frequency tuning and a high force sensitivity. Devices which have a large built-in strain, on the other hand, can serve in mass sensing applications which require a high frequency and high quality factor. [47] [46] [45] Examples of graphene made into NEMS devices are given in Figure 10.
Combining extraordinary electrical properties with low thermal noise makes graphene devices excellent candidates for sensors. Considering that it is entirely made of surface, its 2D nature makes it very efficient in detecting adsorbed molecules. Adsorbed molecules act as donors or acceptors and alter the local carrier concentration which then appears as a change in the resistance. Gases such as CO, H2O, NH3 and NO2 were successfully detected by micro-level gas sensor in the form of the truly 2D NEMS made of graphene. [48] [49] Moreover, another study demonstrated that dinitrotoluene (DNT) can also be detected which is of interest in terms of explosive detecting. [50] Next to chemicals, graphene has potential employment in the detection of biological substances as well. One study showed the possibility of glucose sensing by graphene through an enzyme model of glucose oxidase. [51] Additionally, a study demonstrated graphene as a viable dopamine and serotonine sensor just as its predecessor, the CNT was. [52] Another study focused on Cadmium detection, which is a substance commonly used in several industrial areas while being severely damaging to human body. [53]

Transparent electrodes

Transparent electrodes are in demand for in touchscreens, liquid crystal displays, organic photovoltaic cells and organic light-emitting diodes. The combination of the electrical conductivity with high optical transparency promotes the employment of graphene as transparent conducting electrodes as presented in Figure 11b. [16] [40] At the moment, indium tin oxide (ITO) dominates the industry as a conducting transparent material. However, it is brittle, high- cost and scarce in nature. This has driven the research into finding ITO replacements, preferably of flexible nature. Graphene is a promising candidate for this job considering that it is inert to water and oxygen while having high surface area and mobility. [40] [54] [55] An example was given as a dye-sensitized solar cell made of reduced graphene oxide has already been presented. [55] Transparent films made of graphene have also been used in organic solar cells. (Figure 11a) [56]

Photonics

Optical transitions of graphene can be tuned by gate voltage. This and the electrical injection have the potential towards graphene-based optoelectronic devices such as tunable IR detectors, modulators and emitters. [57] Furthermore, when the zero gap is combined with the large surface area, graphene FETs can be used as ultrafast photodetectors. (Figure 12) [58]

Biotechnology

Graphene is searching for its way in biotechnological applications. The fact that it can be functionalized easily has prompted its use in biotechnology. One research made an effort to understand its interaction with DNA nucleobases and nucleosides. [59]

Electrochemistry

Few-layer graphene has been proposed as a part of composite electrodes in Li-ion batteries. Graphite and activated carbon are already embedded in electrochemical systems since they are reversible materials with reasonable specific capacity. And graphene displayed equal or better kinetics for the same task. It possesses superior in conductivity, surface area and chemical tolerance. Thus, it has the potential to replace such materials in energy storage devices such as batteries and supercapacitors. (Figure 13) [60] [61]

Table of contents :

1 Introduction 
1.1. Carbon allotropes
1.2. Properties of graphene
1.2.1. The band structure of graphene
1.2.2. Electrical properties
1.2.3. Mechanical properties
1.2.4. Optical properties
1.2.5. Thermal properties
1.3. Potential applications
1.3.1. Logic devices vs RF devices
1.3.2. NEMS sensors
1.3.3. Transparent electrodes
1.3.4. Photonics
1.3.5. Biotechnology
1.3.6. Electrochemistry
1.4. Objective of this thesis
2 Device fabrication from graphene 
2.1. Different sources of graphene
2.1.1. Mechanical Exfoliation
2.1.2. Chemical Exfoliation
2.1.3. Graphene synthesis from SiC
2.1.4. Graphene synthesis by chemical vapor deposition
2.2. Graphene transfer & transfer-free processes
2.3. Wrinkle and fold formation in CVD graphene
2.4. Device fabrication: State of art
2.4.1. Transfer over existing trenches
2.4.2. Suspending by substrate etch
2.5. Driving lines for our process
2.6. Proposed synthesis and fabrication techniques
2.6.1. CVD synthesis
2.6.2. Transfer onto SiO2/Si
2.6.3. Device fabrication
2.6.3.1. Issues with the existing fabrication techniques
2.6.3.2. Key process steps developed
2.6.3.3. Mask design
2.6.3.4. Final recipe proposed
2.7. Characterizations
2.7.1. Fabrication yield
2.7.2. Periodic fold formation
2.8. Conclusions
3 Raman characterizations 
3.1. Introduction to Raman spectroscopy
3.2. Raman bands of graphene
3.3. Factors influencing Raman spectrum of graphene
3.3.1. Number of layers
3.3.2. Laser energy
3.3.3. Doping and Kohn anomaly
3.3.3.1. Substrate-induced doping
3.3.3.2. Doping by adsorbates
3.3.3.3. Self-doping
3.3.4. Strain
3.3.5. Temperature
3.3.5.1. Heat treatment changes doping levels
3.3.5.2. Heat treatment changes strain
3.3.5.3. High temperature changes defects
3.4. Results & Discussion
3.4.1. Uniformity of Raman spectra of graphene
3.4.2. Raman signal enhancement
3.4.3. Number of layers
3.4.4. Influence of laser energy
3.4.5. Defects
3.4.6. Influence of doping
3.4.7. Influence of strain
3.4.8. Influence of temperature
3.5. Conclusion
4 Electrical Characterization 
4.1. Contact resistance
4.1.1. Measurement configuration
4.1.2. Contact resistance on graphene
4.1.3. Measurement results
4.2. Hysteresis
4.2.1. Possible origins for hysteresis from literature
4.2.2. Measurement results
4.3. Hall mobility at low temperature
4.3.1. Mobility in graphene
4.3.2. Mobility extraction from Hall measurements
4.3.3. Measurement results
4.4. Observation of quantum effects in magnetoresistance
4.4.1. Weak localization
4.4.1.1. Theory and weak localization graphene
4.4.1.2. Discussion of our results
4.4.2. Quantum Hall effect
4.4.2.1. Theory and quantum Hall effect in graphene
4.4.2.2. Observation of Landau levels in our measurements
4.5. Temperature dependence
4.5.1. Scattering mechanisms in graphene
4.5.2. Measurement results
4.6. Conclusion
5 Conclusions & Prospects 
6 References

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