Inuence of spin-orbit coupling on the magneto-conductivity

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Electronic transport properties

The motion of charge carriers in graphene has some unique properties as a consequence of its electronics band structure, such as the ambipolar eld eect and minimum conductivity. This phenomenon can be seen if graphene is put in a eld eect transistor conguration. What is usually done is to deposit a monolayer graphene sample on an oxidized Si substrate (which serves also as gate electrode) and it is then contacted for electrical measurements, usually with gold electrodes. The variation of the gate voltage induces a change in the carrier concentration in graphene (exactly like in a MOSFET) by moving the Fermi level from the equilibrium condition in the conduction or the valence band. Thus the gate voltage performs an electron (n) or hole (p) doping, depending on its polarity [2]. Figure 1.7 shows the ambipolar eld eect of graphene deposited on SiO2.

Graphene as transparent conducting electrode

Most of the techniques described above have been used to try to transform the graphene sheet in a transparent conducting electrode (TCE). Graphene is very promising for this kind of application because of its transparency and its impressive transport properties. However, undoped (or slightly doped) graphene has a sheet resistance too high for TCE applications and doping is thus necessary to increase its carrier density and lower RS. Electrostatic doping performed with conventional techniques, like shown in References [37, 38, 39, 40, 41, 42], is not suitable for TCE applications because it involves the use of other materials deposited on the graphene sheet which lower its transparency and may not reach very high doping. Moreover, the depositing materials on graphene signicantly alter its electronic transport properties.
Chemical doping has been successfully used to dope graphene for TCE applications. For example, in Reference [14] CVD graphene doped with nitric acid is used as TCE for display and touchscreen applications, while in References [43, 44] graphene doped with AuCl3 is used for the fabrication of solar cells. As mentioned before, chemical doping has some important and not negligible issues in terms of time stability of the carrier concentration. Another attempt to produce TCE with graphene is by using multi-layer graphene. If more layers of graphene are stuck together the resulting conductivity can be signicantly enhanced with respect to the monolayer, still maintaining the transmittance above to 90% in the visible range [43]. In Reference [50] multi-layer graphene for the fabrication of LEDs has been demonstrated. However, this technique very is inconvenient to use because it involves many transfer processes in order to obtain the desired multi-layer graphene structure with the risk of damaging the whole device at every transfer step.
As we will show later in this thesis, space charge doping can overcome many of these problems and can have thus potential applications in the eld of TCEs.

Characterization methods

Several techniques have been used to characterize the samples fabricated during this thesis. They are: optical characterization with an optical microscope, atomic force microscopy (AFM), Raman spectroscopy and X-ray diraction (XRD).

Optical microscope

The optical microscope is a useful tool for a rst characterization of the graphene and ZnO samples. The images of the samples are recorded with a Leica DM2500 and a CCD camera with 5X, 10X, 50X and 100X objectives in the bright eld imaging mode. For the case of anodic bonded graphene, the optical microscope characterization is useful to determine the number of layers of the sample through the optical contrast while for CVD graphene and zinc oxide it is useful to determine the quality of the surface of the sample.

Atomic Force Microscopy

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Atomic force microscopy (AFM) was invented in 1986 [84] as an evolution of the Scanning Tunneling Microscope (STM). It is a tool which is able to scan the surface of a sample to obtain a topography at extremely high resolution. Contrary to STM which measures the tunneling current between the sample and the scanning tip, AFM measures the forces at the atomic scale and thus it makes possible to scan conductive and insulating samples [85]. The basic principles is described in the following.

Electronic transport measurements setup

Space charge doping, electronic transport and Hall measurements are all carried out under high vacuum (< 10􀀀6 mbar) in a custom made continuous He ow cryostat. It allows to control the temperature of the sample in the range 3 􀀀 420 K, thus allowing to perform the doping of the samples and the low temperature transport measurements in situ. The cryostat is held inside an electromagnet capable of reaching a magnetic eld of 2 T. The doping and resistivity measurements are controlled by a LabVIEW program which coordinates the measurement instruments and saves the data into a le.

Table of contents :

Acknowledgments
Abstract
1 2D materials and doping 
1.1 Introduction
1.2 Electrostatic doping
1.3 Graphene
1.3.1 Electronic structure
1.3.2 Synthesis
1.3.3 Graphene characterization
1.3.4 Electronic transport properties
Scattering mechanisms and mobility
Mobility
Magnetotransport
1.3.5 Doping of graphene
Electrostatic doping
Chemical and substitutional doping
1.3.6 Graphene as transparent conducting electrode
1.4 Zinc oxide
1.4.1 Crystal and electronic structure
1.4.2 Crystal growth
RF magnetron sputtering
Other deposition techniques
1.4.3 Characterization of ZnO
X-ray diraction spectrum of ZnO AFM
1.4.4 Doping of ZnO n-doping ip-doping
1.4.5 Magneto-transport properties
1.4.6 ZnO as TCE
2 Experimental 
2.1 Samples fabrication
2.1.1 Glass substrates involved
2.1.2 Graphene
2.1.3 Zinc oxide
2.2 Characterization methods
2.2.1 Optical microscope
2.2.2 Atomic Force Microscopy
2.2.3 Raman Spectroscopy
The principles of Raman scattering
Raman microscopy in 2D materials
2.2.4 X-ray diraction
2.3 Device fabrication
2.3.1 Van der Pauw method
2.3.2 Contact deposition
2.3.3 Sample shaping
2.4 Electronic transport measurements setup
3 Space Charge Doping 
3.1 The principles of space charge doping
3.1.1 Glass atomic structure
3.1.2 Ionic drift
3.2 Space charge doping applied to graphene
3.2.1 Fabrication of the graphene samples
CVD graphene
Anodic Bonded graphene
Contact deposition and shaping
3.2.2 Results
Ambipolar doping
Fine doping and doping limit
Reversibility
Substrate surface quality
Transmittance
Quality of the doped samples
3.3 Comparison with other doping methods
3.4 Control measurement on quartz
3.5 Conclusions on space charge doping
4 Ultra-high doping of ZnO1􀀀x thin lms 
4.1 ZnO1􀀀x device fabrication
4.1.1 Zinc oxide deposition on glass
4.1.2 X-ray diraction, AFM and transmittance
4.1.3 Sample shaping and contact deposition
4.2 Space Charge Doping applied to the ZnO thin lm
4.2.1 Fine control of doping in the thin lm
4.2.2 Carrier scattering mechanism
Lattice phonon scatterimg
Grain boundary scattering
Ionized impurity scattering
4.3 Variable Range Hopping and mobility edge
4.3.1 Variable range hopping in ZnO thin lms
4.3.2 Mobility edge
4.3.3 2D nature of the doped lm
4.4 Conclusions on space charge doping of ZnO
5 Magneto-transport and spin orbit coupling 
5.1 Weak localization
5.1.1 Backscattering
5.1.2 Temperature dependence of the conductivity
5.2 Magneto-conductivity
5.2.1 Theoretical considerations
Eect of the weak localization
Inuence of spin-orbit coupling on the magneto-conductivity
5.2.2 Magneto-conductivity of ZnO
WL to WAL transition as a function of temperature .
WL to WAL transition as a function of carrier concentration
Considerations on the characteristic transport lengths
5.3 Origin of the spin-orbit coupling
5.3.1 D’Yakonov-Perel’ mechanism
5.3.2 Rashba eect
5.3.3 Elliott-Yafet mechanism
5.4 Considerations on the metal-insulator transition
5.5 Conclusions of the magneto-transport in ZnO
6 Conclusions and perspectives 
List of abbreviations and symbols

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