Since the first isolation of graphene in 2004 interest in superconductivity and the superconducting proximity effect in monolayer or few-layer crystals has grown rapidly. This thesis describes studies of both the proximity effect in single and fewlayer graphene flakes, as well as the superconducting transition in few unit cell chalcogenide flakes. Optical and atomic force microscopy and Raman spectroscopy have been used to characterise the quality and number of molecular layers present in these flakes. Graphene structures with superconducting Al electrodes have been realised by micromechanical cleavage techniques on Si/SiO2 substrates. Devices show good normal state transport characteristics, efficient back-gating of the longitudinal resistivity, and low contact resistances. Several trials have been made to investigate proximity-induced critical currents in devices with junction lengths in the range 250-750 nm. Unfortunately, no sign of proximity supercurrents was observed in any of these devices. Nevertheless the same devices have been used to carefully characterise proximity doping, (due to the deposited electrode), and weak localisation/anti-localisation contributions to the conductivity in them. In addition this work has been extended to investigations of the superconducting transition in few unit-cell dichalcogenide flakes. Four-terminal devices have been realised by micromechanical cleavage from a 2H-NbSe2 single crystal onto Si/SiO2 substrates followed by the deposition of Cr/Au contacts. While very thin NbSe2 flakes do not appear to conduct, slightly thicker flakes are superconducting with an onset ܶ௖ that is only slightly depressed from the bulk value (7.2K). The resistance typically shows a small, sharp, high temperature transition followed by one or more broader transitions, which end in a wide tail to zero resistance at low temperatures. These multiple transitions appear to be related to disorder in the layer stacking rather than lateral inhomogeneity. The behaviour of several flakes has been characterised as a function of temperature, applied field and back-gate voltage. The resistance and transition temperatures are found to depend weakly on the gate voltage. Results have been analysed in terms of available theories for these phenomena.

Two-dimensional materials with atomic thickness have attracted a lot of attention from researchers worldwide due to their excellent electronic and optical properties. As the silicon technology is approaching its limit, graphene with ultrahigh carrier mobility and ultralow resistivity shows the potential as channel material for novel high speed transistor beyond silicon. This thesis summarises my Ph.D. work including the theory and modelling of graphene field-effect transistors (GFETs) as well as their potential RF applications. The introduction and review of existing graphene transistors are presented. Multiscale modelling approaches for graphene devices are also introduced. A novel analytical GFET model based on the drift-diffusion transport theory is then developed for RF/microwave circuit analysis. Since the electrons and holes have different mobility variations against the channel potential in graphene, the ambipolar GFET cannot be modelled with constant carrier mobility. A new carrier mobility function, which enables the accurate modelling of the ambipolar property of GFET, is hence developed for this purpose. The new model takes into account the carrier mobility variation against the bias voltage as well as the mobility difference between electrons and holes. It is proved to be more accurate for the DC current calculation. The model has been written in Verilog-A language and can be import into commercial software such as Keysight ADS for circuit simulation. In addition, based on the proposed model two GFET non-Foster circuits (NFCs) are conducted. As a negative impedance element, NFCs find their applications in impedance matching of electrically small antennas and bandwidth improvement of metasurfaces. One of the NFCs studied in this thesis is based on the Linvill's technique in which a pair of identical GFETs is used while the other circuit utilises the negative resistance of a single GFET. The stability analysis of NFCs is also presented. Finally, a high impedance surface loaded with proposed NFCs is also studied, demonstrating significant bandwidth enhancement.

The thesis presents experimental studies of device characteristics and vibrational properties of atomic layer thin graphene and molybdenum disulphide (MoS2). We carried out Raman spectroscopic studies on field effect transistors (FET) fabricated from these materials to investigate the phonons renormalized by carrier doping thus giving quantitative information on electron-phonon coupling. Below, we furnish a synoptic presentation of our work on these systems. Chapter1: Introduction Chapter1, presents a detailed introduction of the systems studied in this the¬sis, namely single layer graphene (SLG), bilayer graphene (BLG) and single layer molybdenum disulphide (MoS2). We have mainly discussed their electronic and vibrational properties in the light of Raman spectroscopy. A review of the Raman studies on graphene layers is presented. Chapter2: Methodology and Experimental Techniques Chapter 2 starts with a description of Raman instrumentation. The steps for isolating graphene and MoS 2 flakes and the subsequent device fabrication procedures involving lithography are discussed in detail. A brief account of the top gated field effect transistor (FET) using solid polymer electrolyte is presented. Chapter3: Band gap opening in bilayer graphene and formation of p-n junction in top gated graphene transistors: Transport and Raman studies In Chapter3 the bilayer graphene (BLG) field effect transistor is fabricated in a dual gate configuration which enables us to control the energy band gap and the Fermi level independently. The gap in bilayer energy spectrum is observed through different values of the resistance maximum in the back gate sweep curves, each taken at a fixed top gate voltage. The gate capacitance of the polymer electrolyte is estimated from the experimental data to be 1.5μF/cm2 . The energy gap opened between the valence and conduction bands using this dual-gated geometry is es¬timated invoking a simple model which takes into account the screening of gate induced charges between the two layers. The presence of the controlled gap in the energy band structure along with the p-n junction creates a new possibility for the bilayer to be used as possible source of terahertz source. The formation of p-n junction along a bilayer graphene (BLG) channel is achieved in a electrolytically top gated BLG FET, where the drain-source voltage VDS across the channel is continuously varied at a fixed top gate voltage VT(VT>0). Three cases may arise as VDS is varied keeping VT fixed: (i) for VT-VDS0, the entire channel is doped with electron, (ii) for VT-VDS= 0, the drain end becomes depleted of carriers and kink in the IDS vs VDS curve appears, (iii) for VT-VDS « 0, carrier reversal takes place at the drain end, accumulation of holes starts taking place at the drain end while the source side is still doped with electrton. The verification of the spatial variation of carrier concentration in a similar top gated single layer graphene (SLG) FET device is done using spatially resolved Ra¬man spectroscopy. The signature 2D Raman band in a single layer graphene shows opposite trend when doped: 2D peak position decreases for electron doping while it increases for hole doping. On the other hand, the G mode response being symmetric in doping can act as a read-out for the carrier concentration. We monitor the peak position of the G and the 2D bands at different locations along the SLG FET channel. For a fixed top gate voltage V T , both G and the 2D band frequencies vary along the channel. For a positive VTsuch that VT-VDS= 0, the peak frequencies ωGand ω2DωG/2D occur at the undoped frequency (ωG/2D)n=0 near the drain end while the source end corresponds to non-zero concentration. When VT-VDS<0, Raman spectra from hole doped regions (drain end) in the channels show an blue-shift in ω2Dwhile from the electron doped regions (near source) ω2Dis softened. Chapter4: Mixing Of Mode Symmetries In Top Gated Bilayer And Multilayer Graphene Field Effect Devices In Chapter4, the effect of gating on a bilayer graphene is captured by using Raman spectroscopy which shows a mixing of different optical modes belonging to differ¬ent symmetries. The zone-center G phonon mode splits into a low frequency (Glow) and a high frequency (Ghigh) mode and the two modes show different dependence on doping. The two G bands show different trends with doping, implying different electron-phonon coupling. The frequency separation between the two sub-bands in¬creases with increased doping. The mode with higher frequency, termed as Ghigh, shows stiffening as we increase the doping whereas the other mode, Glow, shows softening for low electron doping and then hardening at higher doping. The mode splitting is explained in terms of mixing of zone-center in-plane optical phonons rep¬resenting in-phase and out-of-phase inter-layer atomic motions. The experimental results are combined with the theoretical predictions made using density functional theory by Gava et al.[PRB 80, 155422 (2009)]. Similar G band splitting is observed in the Raman spectra from multilayer graphene showing influence of stacking on the symmetry properties. Chapter5: Anomalous dispersion of D and 2D modes in graphene and doping dependence of 2D ′and 2D+G bands Chapter 5 consists of two parts: Part A titled “Doping dependent anomalous dispersion of D and 2D modes in graphene” describes the tunability of electron-phonon coupling (EPC) associated with the highest optical phonon branch (K-A) around the zone corner K using a top gated single layer graphene field effect transistor. Raman D and 2D modes originate from this branch and are dispersive with laser excitation energy. Since the EPC is proportional to the slope of the phonon branch, doping dependence of the D and 2D modes is carried out for different laser energies. The dispersion of the D mode decreases for both the electron and the hole doping, in agreement with the recent theory of Attaccalite et. al [Nano Letters, 10, 1172 (2010)]. In order to observe D-band in the SLG samples, low energy argon ion bombardment was carried out. The D peak positions for variable carrier concentration using top-gated FET geometry are determined for three laser energies, 1.96 eV, 2.41 eV and 2.54 eV. However, the dispersion of the 2D band as a function of doping shows an opposite trend. This most curious result is quantitatively explained us¬ing a fifth order process rather than the usual fourth order double resonant process usually considered for both the D and 2D modes. Part B titled “Raman spectral features of second order 2D’ and 2D+G modes in doped graphene transistor” deals with doping dependence of 2D’ and 2D+G bands in single layer graphene transistor. The phonon frequency blue shifts for the hole doping and whereas it red shifts for electron doping, similar to the behaviour of the 2D band. The linewidth of the 2D+G combination mode too follows the 2D trend increasing with doping while that of 2D’ mode remains invariant. Chapter6: New Raman modes in graphene layers using 2eV light Unique resonant Raman modes are identified at 1530 cm−1 and 1445 cm−1 in single, bi, tri and few layers graphene samples using 1.96 eV (633 nm) laser excitation energy (EL). These modes are absent in Raman spectra using 2.41 eV excitation energy. In addition, the defect-induced D band which is observed only from the edges of a pristine graphene sample, is observed from the entire sample region using E L = 1.96 eV. Raman images with peak frequencies centered at 1530 cm−1, 1445 cm−1 and D band are recorded to show their correlations. With 1.96 eV, we also observe a very clear splitting of the D mode with a separation of ∼32 cm−1, recently predicted in the context of armchair graphene nanoribbons due to trigonal warping effect for phonon dispersion. All these findings suggest a resonance condition at ∼2eVdue to homo-lumo gap of a defect in graphene energy band structure. Chapter7: Single and few layer MoS2: Resonant Raman and Phonon Renormalization Chapter 7 is divided into two parts. In Part A “Layer dependent Resonant Raman scattering of a few layer MoS2”, we discuss resonant Raman scattering from single, bi, four and seven layers MoS2. As bulk crystal of MoS2is thinned down to a few atomic layers, the indirect gap widens turning into a direct gap semiconductor with a band gap of 1.96 eV in its monolayer form. We perform Raman study from MoS 2 layers employing 1.96 eV laser excitation in order to achieve resonance condition. The prominent Raman modes for MoS 2 include first order E12g mode at ∼383 cm−1 and the A1gmode at ∼408 cm−1 which are observed under both non resonant and resonant conditions. A1gphonon involves the sulphur atomic vibration in opposite direction along the c axis (perpendicular to the basal plane) whereas for E12g mode, displacement of Mo and sulphur atoms are in the basal plane. With decreasing layer thickness, these two modes shifts in opposite direction, the E12g mode shows a blue shift of ∼2cm−1 while the A1gis red shifted by ∼4cm−1 . Under resonant condi¬tion, apart from E12g and A1gmodes, several new Raman spectral features, which are completely absent in bulk, are observed in single, bi and few layer spectra pointing out the importance of Raman characterization. New Raman mode attributed to the longitudinal acoustic mode belonging to the phonon branch at M along the Γ-M direction of the Brillouin zone is seen at ∼230 cm−1 for bi, four and seven layers. The most intense region of the spectrum around 460 cm−1 is characterized by layer dependent frequencies and spectral intensities with the band near 460 cm−1 becoming asymmetric as the sample thickness is increased. In the high frequency region between 510-630 cm−1, new bands are seen for bi, four and seven layers. In Part B titled “Symmetry-dependent phonon renormalization in monolayer MoS2transistor”, we show that in monolayer MoS2the two Raman-active phonons, A1g and E21 g, behave very differently as a function of doping induced by the top gate voltage in FET geometry. The FET achieves an on-off ratio of ∼ 105 for electron doping. We show that while E12g phonon is essentially unaffected, the A1gphonon is strongly influenced by the level of doping. We quantitatively understand our experimental results through the use of first-principles calculations to determine frequencies and electron-phonon coupling for both the phonons as a function of carrier concentration. We present symmetry arguments to explain why only A1g mode is renormalized significantly by doping. Our results bring out a quantitative under¬standing of electron-phonon interaction in single layer MoS2.

This thesis describes the conductivity fluctuations or noise measurements in graphenebased field effect transistors. The main motivation was to study the effect of disorder on the electronic transport in graphene. In chapter 4, we report the noise measurements in graphene field effect (GraFET) transistors with varying layer numbers. We found that the density dependence of noise behaves oppositely for single and multilayer graphene. An analytical model has been proposed to understand the microscopic mechanism of noise in GraFETs, which reveals that noise is intimately connected to the band structure of graphene. Our results outline a simple portable method to separate the single layer devices from multi layered ones. Chapter 5 discusses the noise measurements in two systems with a bandgap: biased bilayer graphene and graphene nanoribbon. We show that noise is sensitive to the presence of a bandgap and becomes minimum when the bandgap is zero. At low temperature, mesoscopic graphene devices exhibit universal conductance fluctuations (UCF) arising due to quantum interference effect. In chapter 6, we have studied UCF in single layer graphene and show that it can be sensitive to the presence of various physical symmetries. We report that time reversal symmetry exists in graphene at low temperature and, for the first time, we observed enhanced UCF at lower carrier density where the scattering is dominated by the long-range Coulomb scattering. Chapter 7 presents the transport and noise measurements in single layer graphene in the quantum Hall regime. At ultra-low temperature several broken symmetry states appear in the lowest Landau level, which originate possibly due to strong electron-electron interactions. Our preliminary noise measurements in the quantum Hall regime reveal that the noise is sensitive to the bulk to edge transport and can be a powerful tool to investigate these new quantum states.

This thesis work contains electrical transport and low frequency (1/f) noise measurements in ultrathin graphene and Molybdenum disulphide (MoS2) field effect transistors (FET). From the measurements, We mainly focus on the origin of disorder in both the materials. To address the orgin of disorder in graphene, we study single and bilayer graphene-FET devices on SiO2 substrate. We observe that both conductivity and mobility are mainly determined by substrate induced long range, short range, and polar phonon scattering. For further confirmation, we fabricate suspended graphene devices which show extremely high mobility. We find that, in contrast to substrate-supported graphene, conductivity and mobility in suspended graphene are governed by the longitudinal acoustic phonon scattering at high temperature and the devices reach a ballistic limit at low temperature. We also conduct low frequency 1/f noise measurements, known to be sensitive to disorder dynamics, to extract more information on the nature of disorder. The measurements are carried out both in substrate-supported and suspended graphene devices. We find that 1/f noise in substarted graphene is mainly determined by the trap charges in the SiO2 substrate. On the other hand, noise behaviour in suspended graphene devices can not be explained with trap charge dominated noise model. More-over, suspended devices exhibit one order of magnitude less noise compared to graphene on SiO2 substrate. We believe noise in suspended graphene devices probably originate from metal-graphene contact regions. In the second part of our work, We present low temperature electrical transport in ultrathin MoS2 fields effect devices, mechanically exfoliated onto Si/SiO2 substrate. Our experiments reveal that the electronic states in MoS2 are localized well up to the room temperature over the experimentally accessible range of gate voltage. This manifests in two dimensional (2D) variable range hopping (VRH) at high temperatures, while below ~ 30 K the conductivity displays oscillatory structures in gate voltage arising from resonant tunneling at the localized sites. From the correlation energy (T0) of VRH and gate voltage dependence of conductivity, we suggest that the charged impurities are the dominant source of disorder in MoS2. To explore the origin of the disorder, we perform temperature dependent I - V measurements at high source-drain bias. These measurements indicate presence of an exponentially distributed trap states in MoS2 which originate from the structural inhomogeneity. For more detailed investigation, we employ 1/f noise which further confirms possible presence of structural disorder in the system. The origin of the localized states is also investigated by spectroscopic studies, which indicate a possible presence of metallic 1T-patches inside semiconducting 2H phase. From all these evidences, we suggest that the disorder is internal, and achieving high mobility in MoS2 FET requires a greater level of crystalline homogeneity.