This document is Matthew Conrad's thesis proposal for a PhD in physics at the Georgia Institute of Technology. The proposal focuses on studying the buffer layer, the first graphene layer that forms on silicon carbide (SiC) substrates. Conrad provides background on graphene and how it forms semiconducting layers on SiC. He summarizes preliminary results characterizing the atomic and electronic structure of the buffer layer using surface x-ray diffraction and angle-resolved photoemission spectroscopy. The future work section outlines plans for detailed experimental and theoretical studies to better understand how the buffer layer can be tailored into a viable form of semiconducting graphene.
This document summarizes a study of two-dimensional materials with a honeycomb geometry. It begins with an artist's impression of an atomic force microscopy (AFM) measurement of the edge of a graphene flake, showing the measured data. The document then provides details of the printed thesis, including the title, author name, university, and date. The main contents include an introduction and chapters discussing graphene on iridium, the moiré structure of graphene on iridium, using AFM to measure atomic positions, the electronic structure of graphene on iridium, electron tomography of quantum dot superlattices, and oriented attachment of quantum dots to form superlattices.
This document describes the tight-binding method for calculating the energy diagram of nanoelectronic systems. It introduces the tight-binding method and its application to calculating the energy diagrams of polyacetylene, single-layer graphene, bilayer graphene, and multi-layer graphene. It also discusses using the tight-binding method to calculate the energy diagrams of two and four layer graphene in a constant electric field and single-layer graphene in a modulated electric field. The document provides the theoretical framework and mathematical equations for applying the tight-binding method to these different nanoscale systems.
Spin Polarisation in Co2CrAl/GaAs 2D Slabs: A computational studyDr. Vishal Jain
This document summarizes a computational study of spin polarization in Co2CrAl/GaAs 2D slabs. Key findings include:
1) Co2CrAl/GaAs (1 1 1) surface shows 80% spin polarization within LDA parameterizations. Spin polarization varies with surface termination and bond length.
2) Introduction of Au and Cu capping layers enhances spin polarization for all surface projections within GGA approximation.
3) Magnetic moment varies from bulk value of 3μB in Co2CrAl/GaAs surfaces due to differences in bond lengths causing strain effects.
Study Electronic And Mechanical Properties Of Carbon, Silicon, And Hypothetic...IOSR Journals
This document discusses a study that uses density functional theory (DFT) with the generalized gradient approximation (GGA) to calculate the electronic and mechanical properties of carbon, silicon, and hypothetical silicon-carbon (SiC) in the diamond crystal structure. The results show that GGA calculations of properties like lattice constant, cohesive energy, density of states, bulk modulus, and band structures correspond well with experimental values. For carbon in diamond structure, GGA predicts a lattice constant, bulk modulus, and indirect bandgap that are close to experimental measurements. For silicon, the results show it has a larger lattice constant than carbon due to its larger atomic radius, and it is calculated to be a semiconductor. Hypothetical SiC is
A facile route for nitrogen doped hollow graphitic carbonumarkhalid532
1) A facile route is presented for synthesizing nitrogen-doped hollow graphitic carbon spheres (NHGCSs) through the direct pyrolysis of solid melamine–formaldehyde (MF) resin spheres.
2) The MF resin spheres are prepared via a hydrothermal method without templates or catalysts, and pyrolyzed at temperatures above 400°C to form hollow carbon spheres with graphitic carbon shells.
3) The NHGCSs exhibit excellent capacitive performance as electrode materials for supercapacitors, achieving a high specific capacitance of 306 Fg-1 at 0.1 A g-1.
The document summarizes research on cobalt-carbon nanocomposites prepared by RF sputtering and RF plasma-enhanced chemical vapor deposition. Three cobalt-carbon nanocomposite films were prepared under different deposition pressures. Atomic force microscopy showed the average particle size and surface roughness decreased with increasing pressure. X-ray diffraction identified cobalt nanoparticles in the FCC phase and cobalt oxide. Optical absorbance measurements showed the surface plasmon resonance band shifted to higher wavelengths with decreasing pressure, indicating larger particle sizes. The composition of the films was confirmed with EDX to contain cobalt, oxygen, and carbon from the matrix. In conclusion, lower deposition pressures favored the formation of larger cobalt nanoparticles while higher pressures increased cobalt oxide formation.
This document describes research on producing multilayer graphene oxide membranes using different oxidation methods of vein graphite. The objectives were to compare the sp2/sp3 carbon ratios in the resulting graphite oxides. Two methods were used: Hummers' method and an improved Hummers' method. Analysis using SEM, XPS, and carbon/oxygen ratios showed the improved method produced a higher fraction of oxidized carbon with a sp3/sp2 ratio of 3.62:1, compared to 1.04:1 for the standard Hummers' method. This indicates the improved method yields better oxidation of the graphite starting material.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document summarizes a study of two-dimensional materials with a honeycomb geometry. It begins with an artist's impression of an atomic force microscopy (AFM) measurement of the edge of a graphene flake, showing the measured data. The document then provides details of the printed thesis, including the title, author name, university, and date. The main contents include an introduction and chapters discussing graphene on iridium, the moiré structure of graphene on iridium, using AFM to measure atomic positions, the electronic structure of graphene on iridium, electron tomography of quantum dot superlattices, and oriented attachment of quantum dots to form superlattices.
This document describes the tight-binding method for calculating the energy diagram of nanoelectronic systems. It introduces the tight-binding method and its application to calculating the energy diagrams of polyacetylene, single-layer graphene, bilayer graphene, and multi-layer graphene. It also discusses using the tight-binding method to calculate the energy diagrams of two and four layer graphene in a constant electric field and single-layer graphene in a modulated electric field. The document provides the theoretical framework and mathematical equations for applying the tight-binding method to these different nanoscale systems.
Spin Polarisation in Co2CrAl/GaAs 2D Slabs: A computational studyDr. Vishal Jain
This document summarizes a computational study of spin polarization in Co2CrAl/GaAs 2D slabs. Key findings include:
1) Co2CrAl/GaAs (1 1 1) surface shows 80% spin polarization within LDA parameterizations. Spin polarization varies with surface termination and bond length.
2) Introduction of Au and Cu capping layers enhances spin polarization for all surface projections within GGA approximation.
3) Magnetic moment varies from bulk value of 3μB in Co2CrAl/GaAs surfaces due to differences in bond lengths causing strain effects.
Study Electronic And Mechanical Properties Of Carbon, Silicon, And Hypothetic...IOSR Journals
This document discusses a study that uses density functional theory (DFT) with the generalized gradient approximation (GGA) to calculate the electronic and mechanical properties of carbon, silicon, and hypothetical silicon-carbon (SiC) in the diamond crystal structure. The results show that GGA calculations of properties like lattice constant, cohesive energy, density of states, bulk modulus, and band structures correspond well with experimental values. For carbon in diamond structure, GGA predicts a lattice constant, bulk modulus, and indirect bandgap that are close to experimental measurements. For silicon, the results show it has a larger lattice constant than carbon due to its larger atomic radius, and it is calculated to be a semiconductor. Hypothetical SiC is
A facile route for nitrogen doped hollow graphitic carbonumarkhalid532
1) A facile route is presented for synthesizing nitrogen-doped hollow graphitic carbon spheres (NHGCSs) through the direct pyrolysis of solid melamine–formaldehyde (MF) resin spheres.
2) The MF resin spheres are prepared via a hydrothermal method without templates or catalysts, and pyrolyzed at temperatures above 400°C to form hollow carbon spheres with graphitic carbon shells.
3) The NHGCSs exhibit excellent capacitive performance as electrode materials for supercapacitors, achieving a high specific capacitance of 306 Fg-1 at 0.1 A g-1.
The document summarizes research on cobalt-carbon nanocomposites prepared by RF sputtering and RF plasma-enhanced chemical vapor deposition. Three cobalt-carbon nanocomposite films were prepared under different deposition pressures. Atomic force microscopy showed the average particle size and surface roughness decreased with increasing pressure. X-ray diffraction identified cobalt nanoparticles in the FCC phase and cobalt oxide. Optical absorbance measurements showed the surface plasmon resonance band shifted to higher wavelengths with decreasing pressure, indicating larger particle sizes. The composition of the films was confirmed with EDX to contain cobalt, oxygen, and carbon from the matrix. In conclusion, lower deposition pressures favored the formation of larger cobalt nanoparticles while higher pressures increased cobalt oxide formation.
This document describes research on producing multilayer graphene oxide membranes using different oxidation methods of vein graphite. The objectives were to compare the sp2/sp3 carbon ratios in the resulting graphite oxides. Two methods were used: Hummers' method and an improved Hummers' method. Analysis using SEM, XPS, and carbon/oxygen ratios showed the improved method produced a higher fraction of oxidized carbon with a sp3/sp2 ratio of 3.62:1, compared to 1.04:1 for the standard Hummers' method. This indicates the improved method yields better oxidation of the graphite starting material.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Nano Capacitor Including Graphene Layers Composed with Doped Boron and Nitr...CrimsonPublishersRDMS
A Nano Capacitor Including Graphene Layers Composed with Doped Boron and Nitrogen by Majid Monajjemi* in Crimson Publishers: Peer Reviewed Material Science Journals
IRJET- The Ab Initio Study of Electronic and Optical Properties of CH3NH3ZnI3...IRJET Journal
This document summarizes an ab initio study of the electronic and optical properties of the perovskite solar cell material CH3NH3ZnI3. Key findings include:
1) CH3NH3ZnI3 has a direct bandgap of 0.34 eV, which is significantly smaller than the 1.53 eV bandgap of the commonly used CH3NH3PbI3 material.
2) X-ray diffraction data analysis showed that CH3NH3ZnI3 retains the original cuboctahedral crystal structure of CH3NH3PbI3.
3) Optical property calculations predicted CH3NH3ZnI3 would absorb electromagnetic radiation in the far UV region and
This document presents an analysis of the B0s → D−s π+ decay mode using LHCb data. The analysis models peaking background contributions and performs mass fits over the range (4800 − 5850)MeV, obtaining Bs mass measurements consistent with previous results. Fits for the Bs lifetime were also performed, giving a lifetime of (1.484 ± 0.096)ps. This was then used to calculate the distance between the primary and secondary vertex of the Bs to be (1.06±0.07)cm. All distributions were modelled well, and values were found to be consistent with the PDG values. The analysis aims to further probe CP violation and search for
This document describes a new nanocomposite material called SuCoLEx that combines high thermal conductivity and very low thermal expansion. The composite is made of copper with highly aligned graphite platelets added. Spark plasma sintering is used to create an excellent interface between the copper and graphite. Testing found the composite has a thermal conductivity of 500 W/m-K, which is 140% of copper's conductivity. Remarkably, its thermal expansion was found to be just 2 ppm/K, much lower than graphite or copper on their own. This combination of properties makes SuCoLEx promising for applications requiring heat sinks and thermal management.
Electronic bands structure and gap in mid-infrared detector InAs/GaSb type II...IJERA Editor
We present here theoretical study of the electronic bands structure E (d1) of InAs (d1=25 Å)/GaSb (d2=25 Å) type
II superlattice at 4.2 K performed in the envelope function formalism. We study the effect of d1 and the offset ,
between heavy holes bands edges of InAs and GaSb, on the band gap Eg (), at the center of the first Brillouin
zone, and the semiconductor-to-semimetal transition. Eg (, T) decreases from 288.7 meV at 4.2 K to 230 meV
at 300K. In the investigated temperature range, the cut-off wavelength 4.3 m ≤ c ≤ 5.4 m situates this sample
as mid-wavelength infrared detector (MWIR). Our results are in good agreement with the experimental data
realized by C. Cervera et al.
Iron, cobalt and Nickel -ligand bonding in metallocene: Differentiation betwe...AI Publications
The electronic structure and geometry optimization of ferrocene, cobaltocene and nickelocene molecules using DFT/B3LYP with the basis set of 6-31G (d) calculations. The Eigen values, Eigen vector and population analysis of the molecules show that the first 13 molecular orbitals in ferrocene, 12 in cobaltocene and 14 in nickelocene have contribution from 2pzorbitals of carbon of (C5H5)− and4s,4pand 3dorbitals of iron, cobalt or nickel, respectively. We found that the extents of involvement of metal orbitals in the three cases are different. In ferrocene the maximum involvement out of 4s and 4porbitals in the order 4pz >4py >4s > 4pxand out of 3d orbitals the order of involvement is 3dyz >3dxz >3d2z>3dx2−y2>3dxy. The involvement of corresponding orbital in cobaltocene with respect to the 4sand 4porbitals is in the order of 4s >4pz >4py >4pxand in 3d orbitals the order is 3dx2−y2>3dxz >3d2z>3dx2−y2 and in the nickelocene molecule it is 4py >4p>4s >4pz and in 3d orbitals the order is 3dyz >3dx2−y2>3dxy >3dxz >3d2z. The total involvement of 3d, 4s and 4porbitals of metal and 2pz orbitals of the ten carbon atoms of both ligands of (C5H5) −in ferrocene, cobaltocene and nickelocene respectively are 42.2528, 40.2388 and 38.3776
10.1016-j.mssp.2015.01.037-Electrochemical investigation of graphene_nanoporo...Mahdi Robat Sarpoushi
This study investigated the effect of mixing graphene nanosheets and nanoporous carbon black on the surface morphology and electrochemical performance of electrodes prepared for supercapacitors. Electrodes containing 80% nanoporous carbon black, 10% graphene nanosheets, and 10% PTFE binder showed the highest specific capacitance of 10.22 F/g. The addition of nanoporous carbon black increased the proportion of outer charge stored on the electrode relative to the total charge stored, indicating higher current response and voltage reversal at the end potentials. Scanning electron microscopy images showed that adding nanoporous carbon black particles arranged the graphene nanosheets in different directions, increasing the specific surface area and changing diffusion characteristics to improve capacitance and reversibility
Structural, Electronic and Gamma Shielding Properties of BxAl1-xAsIJMERJOURNAL
ABSTRACT: The structural and electronic properties of BxAl1-xAs ternary alloys in the zincblende structure were systematically investigated by using the first principles calculations. The local density approximation was used for exchanged and correlation interaction. The calculated band gap bowing parameter was discovered to be mightily composition dependent of the Boron concentration. Additionally, we have calculated some gamma shielding parameters of BxAl1-xAs ternary alloys. Primarily, the values of mass attenuation coefficients (μρ) were calculated using WinXCom computer program and then these parameters were utilized to calculate the values of electron density (Nel) and effective atomic number (Zeff) in the wide energy range (1 keV - 100 GeV).
This document discusses the mechanism of graphene oxide (GO) formation from graphite. The key points are:
1. GO formation involves three distinct steps - first, graphite is converted to a stage-1 graphite intercalation compound (GIC); second, the GIC is converted to "pristine graphite oxide" (PGO); third, PGO is converted to conventional GO upon exposure to water.
2. The first step of GIC formation occurs rapidly. The second step of converting the GIC to PGO is much slower and is the rate-determining step.
3. Partial oxidation experiments show the reaction proceeds from the flake edges inward, with different spectroscopic signatures
A Front Surface Optimization Study for Photovoltaic ApplicationTELKOMNIKA JOURNAL
This document summarizes a study on optimizing the front surface of silicon solar cells to reduce reflectance through antireflection coatings and surface texturing. Silicon nitride films were deposited using plasma-enhanced chemical vapor deposition and hot-wire chemical vapor deposition on silicon substrates, and showed weighted average reflectances of 1.5% and 1.8% respectively. Random pyramid surface textures were formed on silicon using potassium hydroxide etching for 30 minutes, achieving low reflectance. Combining the optimized silicon nitride coatings with the textured surfaces further reduced weighted average reflectances to 1.5% for PECVD and 1.8% for HWCVD coatings.
Analysis of Highly Birefringent Photonic Crystal Fiber Employing Different Ge...ijsrd.com
In this paper we are proposed three different types of photonic crystal fibers and compared them for higher birefringence by using finite element method. Using elliptical holes instead of circular air holes we are getting high birefringence. We also obtained low dispersion for the same structure consist of a defect in the center design flexibility and high index contrast give a better birefringence in the range of 10-3 to 10-2.Also the characteristics of PCF are plotted for a range of wavelength
EVALUATING STRUCTURAL, OPTICAL & ELECTRICAL CHARACTERIZATION OF ZINC CHALCOGE...Editor IJCATR
To evaluate the structural, optical & electrical properties of the zinc chalcogenides (ZnO, ZnS, ZnSe & ZnTe), the Full
Potential Linearized – Augumented Plane Wave plus Local Orbits (FP – LAPW+lo) method. For the purpose of exchange-correlation
energy (Exc) determination in Kohn–Sham calculation, the standard local density approximation (LDA) formalism has been utilized.
Murnaghan’s equation of state (EOS) has been used for volume optimization by minimizing the total energy with respect to the unit
cell volume. With the result of electronic density of states (DOS), the structural, optical and electrical properties of Zinc chalcogenides
have been calculated. The second derivative of energy, as a function of lattice strain has been successfully used to estimate the elastic
constants of these binary compounds. The results are in good agreement with other theoretical calculations as well as available
experimental data.
Effect of al atom doping on band gap of rectangular cross section si nanowireAlexander Decker
This document discusses the effect of aluminum atom doping on the band gap of rectangular cross-section silicon nanowires oriented along the [111] direction. Density functional theory calculations using the generalized gradient approximation were performed on hydrogen-passivated silicon nanowires with and without aluminum atom doping. The results showed that doping reduced the band gap of the nanowire dramatically and caused the nanowire to behave more like bulk silicon.
1) The document investigates the effect of cation and anion sizes on the charge storage capabilities of graphite nanosheets as electrode materials for electrochemical double layer capacitors.
2) Scanning electron microscope images confirm the layered structure of the graphite nanosheets used, which are 12nm thick with 3.36 Angstrom spacing between layers.
3) Electrochemical measurements using cyclic voltammetry and impedance spectroscopy indicate that the graphite electrodes exhibited better charge storage and delivery in 3M NaCl electrolyte compared to NaOH and KOH electrolytes, due to the smaller ion sizes matching better with the graphite structure.
NOVEL BAND-REJECT FILTER DESIGN USING MULTILAYER BRAGG MIRROR AT 1550 NMcscpconf
Novel band-reject filter is proposed using multilayer Bragg mirror structure by computing reflection coefficient at 1550 nm wavelength for optical communication. Dimension of different
layers and material composition are modified to study the effect on rejection bandwidth, and no of layers is also varied for analyzing passband characteristics. GaN/AlxGa1-xN composiiton is taken as the choice for simulation purpose, carried out using propagation matrix method. Refractive indices of the materials are considered as function of bandgap, perating wavelength and material composition following Adachi’s model. One interesting result arises from the computation that band-reject filter may be converted into band-pass one by suitably varying ratio of thicknesses of unit cell, or by varying Al mole fraction. Simulated results can be utilised to design VCSEL mirror as optical transmitter.
Surface and volume energy loss , optical conductivity of rhodamine 6 g dye (...Alexander Decker
Rhodamine 6G dye thin films were prepared and their optical properties were investigated using transmittance spectra from 200-900nm. The dye's optical energy gap was determined to be 2.2eV from direct allowed transitions and 1.3eV from indirect transitions. Dispersion parameters like the oscillation energy Eo, dispersion energy Ed, and refractive index no were calculated using Wemple-DiDomenico and single oscillator models. The optical conductivity and dielectric constant were also determined from the dispersion parameters and transmittance data.
Electrical characterization of semiconductor-insulator interfaces in VLSI:ULS...Dang Trang
The document summarizes an electrical engineering student's research project characterizing semiconductor-insulator interfaces in VLSI/ULSI technology. The student fabricated metal-oxide-silicon capacitors using hafnium oxide and silicon dioxide gate dielectrics. Through capacitance-voltage measurements, the student extracted the dielectric constants of the materials and found the hafnium oxide k-value matched reported values between 18-25. Interface charges in the hafnium oxide caused shifts in the flat-band voltage. Overall, using high-k hafnium oxide allowed thicker dielectric layers while maintaining capacitance, reducing leakage currents.
Recent progress on reduced graphene oxide....suresh kannan
The document summarizes recent progress on using reduced graphene oxide (rGO)-based materials as counter electrodes for dye-sensitized solar cells (DSSCs) as a cost-effective alternative to platinum. It discusses how rGO on its own is not effective as a counter electrode but that adding metal nanoparticles to rGO composites improves their catalytic activity and performance in DSSCs. The document reviews various rGO composites that have been studied, including those with silver, nickel, tungsten and platinum nanoparticles, as well as metal oxides and dichalcogenides. It compares the photovoltaic parameters of DSSCs using these rGO composite counter electrodes to those using conventional platinum counter electrodes
Graphene, the amazing two-dimensional carbon nanomaterial, has attracted extensive interest in recent years and emerged as the most intensively studied material [1]. In 2004, Geim and Nosovelov at Manchester University successfully isolated single layer graphene by the mechanical cleavage of graphite crystal [2]. This ‘‘thinnest’’ known material exhibits extraordinary electronic, chemical, mechanical, thermal and optical properties which bestowed graphene as a miracle material of the 21st Century. From applicative perspectives, graphene holds a great promise with the potential to be used as energy-storage materials, in nanoelectronics, in catalysis, biomedical, in polymer composites and many more.
The electronic band parameters calculated by the Triangular potential model f...IOSR Journals
This work reports on theoretical investigation of superlattices based on Cd1-xZnxS quantum dots
embedded in an insulating material. This system, assumed to a series of flattened cylindrical quantum dots with
a finite barrier at the boundary, is studied using the triangular potential. The electronic states and the effective
mass of 1 Γ miniband have been computed as a function of inter-quantum dot separation for different zinc
compositions. Calculations have been made for electrons, heavy holes and light holes. Results are discussed and
compared with those of the Kronig-Penney and sinusoidal potentials
This study uses density functional theory calculations to examine the interaction between titanium oxide nanostructures and graphene or functionalized graphene nanoribbons (GNRs). The key findings are:
1) Rutile titanium dioxide favors physisorption on pure graphene, while rutile and anatase titanium dioxide show similar chemisorption on functionalized GNRs.
2) Charge density maps show the importance of electron distribution in the chemical interaction between titanium dioxide and graphene.
3) Analysis of partial density of states reveals the strength of binding energies at specific adsorption sites on the titanium dioxide/graphene systems.
4) The results provide insight into controlled growth mechanisms that could have applications in photovolta
The document provides an introduction to the physical properties of graphene, specifically:
- It discusses the carbon atom and its ability to form sp2 hybridized bonds that give rise to graphene's honeycomb lattice structure.
- It describes the different methods used to fabricate graphene, including exfoliation of graphene from graphite and epitaxial growth on metal substrates.
- It previews the tight-binding model that will be used to describe graphene's electronic band structure, noting that this reveals relativistic behavior of electrons in graphene.
A Nano Capacitor Including Graphene Layers Composed with Doped Boron and Nitr...CrimsonPublishersRDMS
A Nano Capacitor Including Graphene Layers Composed with Doped Boron and Nitrogen by Majid Monajjemi* in Crimson Publishers: Peer Reviewed Material Science Journals
IRJET- The Ab Initio Study of Electronic and Optical Properties of CH3NH3ZnI3...IRJET Journal
This document summarizes an ab initio study of the electronic and optical properties of the perovskite solar cell material CH3NH3ZnI3. Key findings include:
1) CH3NH3ZnI3 has a direct bandgap of 0.34 eV, which is significantly smaller than the 1.53 eV bandgap of the commonly used CH3NH3PbI3 material.
2) X-ray diffraction data analysis showed that CH3NH3ZnI3 retains the original cuboctahedral crystal structure of CH3NH3PbI3.
3) Optical property calculations predicted CH3NH3ZnI3 would absorb electromagnetic radiation in the far UV region and
This document presents an analysis of the B0s → D−s π+ decay mode using LHCb data. The analysis models peaking background contributions and performs mass fits over the range (4800 − 5850)MeV, obtaining Bs mass measurements consistent with previous results. Fits for the Bs lifetime were also performed, giving a lifetime of (1.484 ± 0.096)ps. This was then used to calculate the distance between the primary and secondary vertex of the Bs to be (1.06±0.07)cm. All distributions were modelled well, and values were found to be consistent with the PDG values. The analysis aims to further probe CP violation and search for
This document describes a new nanocomposite material called SuCoLEx that combines high thermal conductivity and very low thermal expansion. The composite is made of copper with highly aligned graphite platelets added. Spark plasma sintering is used to create an excellent interface between the copper and graphite. Testing found the composite has a thermal conductivity of 500 W/m-K, which is 140% of copper's conductivity. Remarkably, its thermal expansion was found to be just 2 ppm/K, much lower than graphite or copper on their own. This combination of properties makes SuCoLEx promising for applications requiring heat sinks and thermal management.
Electronic bands structure and gap in mid-infrared detector InAs/GaSb type II...IJERA Editor
We present here theoretical study of the electronic bands structure E (d1) of InAs (d1=25 Å)/GaSb (d2=25 Å) type
II superlattice at 4.2 K performed in the envelope function formalism. We study the effect of d1 and the offset ,
between heavy holes bands edges of InAs and GaSb, on the band gap Eg (), at the center of the first Brillouin
zone, and the semiconductor-to-semimetal transition. Eg (, T) decreases from 288.7 meV at 4.2 K to 230 meV
at 300K. In the investigated temperature range, the cut-off wavelength 4.3 m ≤ c ≤ 5.4 m situates this sample
as mid-wavelength infrared detector (MWIR). Our results are in good agreement with the experimental data
realized by C. Cervera et al.
Iron, cobalt and Nickel -ligand bonding in metallocene: Differentiation betwe...AI Publications
The electronic structure and geometry optimization of ferrocene, cobaltocene and nickelocene molecules using DFT/B3LYP with the basis set of 6-31G (d) calculations. The Eigen values, Eigen vector and population analysis of the molecules show that the first 13 molecular orbitals in ferrocene, 12 in cobaltocene and 14 in nickelocene have contribution from 2pzorbitals of carbon of (C5H5)− and4s,4pand 3dorbitals of iron, cobalt or nickel, respectively. We found that the extents of involvement of metal orbitals in the three cases are different. In ferrocene the maximum involvement out of 4s and 4porbitals in the order 4pz >4py >4s > 4pxand out of 3d orbitals the order of involvement is 3dyz >3dxz >3d2z>3dx2−y2>3dxy. The involvement of corresponding orbital in cobaltocene with respect to the 4sand 4porbitals is in the order of 4s >4pz >4py >4pxand in 3d orbitals the order is 3dx2−y2>3dxz >3d2z>3dx2−y2 and in the nickelocene molecule it is 4py >4p>4s >4pz and in 3d orbitals the order is 3dyz >3dx2−y2>3dxy >3dxz >3d2z. The total involvement of 3d, 4s and 4porbitals of metal and 2pz orbitals of the ten carbon atoms of both ligands of (C5H5) −in ferrocene, cobaltocene and nickelocene respectively are 42.2528, 40.2388 and 38.3776
10.1016-j.mssp.2015.01.037-Electrochemical investigation of graphene_nanoporo...Mahdi Robat Sarpoushi
This study investigated the effect of mixing graphene nanosheets and nanoporous carbon black on the surface morphology and electrochemical performance of electrodes prepared for supercapacitors. Electrodes containing 80% nanoporous carbon black, 10% graphene nanosheets, and 10% PTFE binder showed the highest specific capacitance of 10.22 F/g. The addition of nanoporous carbon black increased the proportion of outer charge stored on the electrode relative to the total charge stored, indicating higher current response and voltage reversal at the end potentials. Scanning electron microscopy images showed that adding nanoporous carbon black particles arranged the graphene nanosheets in different directions, increasing the specific surface area and changing diffusion characteristics to improve capacitance and reversibility
Structural, Electronic and Gamma Shielding Properties of BxAl1-xAsIJMERJOURNAL
ABSTRACT: The structural and electronic properties of BxAl1-xAs ternary alloys in the zincblende structure were systematically investigated by using the first principles calculations. The local density approximation was used for exchanged and correlation interaction. The calculated band gap bowing parameter was discovered to be mightily composition dependent of the Boron concentration. Additionally, we have calculated some gamma shielding parameters of BxAl1-xAs ternary alloys. Primarily, the values of mass attenuation coefficients (μρ) were calculated using WinXCom computer program and then these parameters were utilized to calculate the values of electron density (Nel) and effective atomic number (Zeff) in the wide energy range (1 keV - 100 GeV).
This document discusses the mechanism of graphene oxide (GO) formation from graphite. The key points are:
1. GO formation involves three distinct steps - first, graphite is converted to a stage-1 graphite intercalation compound (GIC); second, the GIC is converted to "pristine graphite oxide" (PGO); third, PGO is converted to conventional GO upon exposure to water.
2. The first step of GIC formation occurs rapidly. The second step of converting the GIC to PGO is much slower and is the rate-determining step.
3. Partial oxidation experiments show the reaction proceeds from the flake edges inward, with different spectroscopic signatures
A Front Surface Optimization Study for Photovoltaic ApplicationTELKOMNIKA JOURNAL
This document summarizes a study on optimizing the front surface of silicon solar cells to reduce reflectance through antireflection coatings and surface texturing. Silicon nitride films were deposited using plasma-enhanced chemical vapor deposition and hot-wire chemical vapor deposition on silicon substrates, and showed weighted average reflectances of 1.5% and 1.8% respectively. Random pyramid surface textures were formed on silicon using potassium hydroxide etching for 30 minutes, achieving low reflectance. Combining the optimized silicon nitride coatings with the textured surfaces further reduced weighted average reflectances to 1.5% for PECVD and 1.8% for HWCVD coatings.
Analysis of Highly Birefringent Photonic Crystal Fiber Employing Different Ge...ijsrd.com
In this paper we are proposed three different types of photonic crystal fibers and compared them for higher birefringence by using finite element method. Using elliptical holes instead of circular air holes we are getting high birefringence. We also obtained low dispersion for the same structure consist of a defect in the center design flexibility and high index contrast give a better birefringence in the range of 10-3 to 10-2.Also the characteristics of PCF are plotted for a range of wavelength
EVALUATING STRUCTURAL, OPTICAL & ELECTRICAL CHARACTERIZATION OF ZINC CHALCOGE...Editor IJCATR
To evaluate the structural, optical & electrical properties of the zinc chalcogenides (ZnO, ZnS, ZnSe & ZnTe), the Full
Potential Linearized – Augumented Plane Wave plus Local Orbits (FP – LAPW+lo) method. For the purpose of exchange-correlation
energy (Exc) determination in Kohn–Sham calculation, the standard local density approximation (LDA) formalism has been utilized.
Murnaghan’s equation of state (EOS) has been used for volume optimization by minimizing the total energy with respect to the unit
cell volume. With the result of electronic density of states (DOS), the structural, optical and electrical properties of Zinc chalcogenides
have been calculated. The second derivative of energy, as a function of lattice strain has been successfully used to estimate the elastic
constants of these binary compounds. The results are in good agreement with other theoretical calculations as well as available
experimental data.
Effect of al atom doping on band gap of rectangular cross section si nanowireAlexander Decker
This document discusses the effect of aluminum atom doping on the band gap of rectangular cross-section silicon nanowires oriented along the [111] direction. Density functional theory calculations using the generalized gradient approximation were performed on hydrogen-passivated silicon nanowires with and without aluminum atom doping. The results showed that doping reduced the band gap of the nanowire dramatically and caused the nanowire to behave more like bulk silicon.
1) The document investigates the effect of cation and anion sizes on the charge storage capabilities of graphite nanosheets as electrode materials for electrochemical double layer capacitors.
2) Scanning electron microscope images confirm the layered structure of the graphite nanosheets used, which are 12nm thick with 3.36 Angstrom spacing between layers.
3) Electrochemical measurements using cyclic voltammetry and impedance spectroscopy indicate that the graphite electrodes exhibited better charge storage and delivery in 3M NaCl electrolyte compared to NaOH and KOH electrolytes, due to the smaller ion sizes matching better with the graphite structure.
NOVEL BAND-REJECT FILTER DESIGN USING MULTILAYER BRAGG MIRROR AT 1550 NMcscpconf
Novel band-reject filter is proposed using multilayer Bragg mirror structure by computing reflection coefficient at 1550 nm wavelength for optical communication. Dimension of different
layers and material composition are modified to study the effect on rejection bandwidth, and no of layers is also varied for analyzing passband characteristics. GaN/AlxGa1-xN composiiton is taken as the choice for simulation purpose, carried out using propagation matrix method. Refractive indices of the materials are considered as function of bandgap, perating wavelength and material composition following Adachi’s model. One interesting result arises from the computation that band-reject filter may be converted into band-pass one by suitably varying ratio of thicknesses of unit cell, or by varying Al mole fraction. Simulated results can be utilised to design VCSEL mirror as optical transmitter.
Surface and volume energy loss , optical conductivity of rhodamine 6 g dye (...Alexander Decker
Rhodamine 6G dye thin films were prepared and their optical properties were investigated using transmittance spectra from 200-900nm. The dye's optical energy gap was determined to be 2.2eV from direct allowed transitions and 1.3eV from indirect transitions. Dispersion parameters like the oscillation energy Eo, dispersion energy Ed, and refractive index no were calculated using Wemple-DiDomenico and single oscillator models. The optical conductivity and dielectric constant were also determined from the dispersion parameters and transmittance data.
Electrical characterization of semiconductor-insulator interfaces in VLSI:ULS...Dang Trang
The document summarizes an electrical engineering student's research project characterizing semiconductor-insulator interfaces in VLSI/ULSI technology. The student fabricated metal-oxide-silicon capacitors using hafnium oxide and silicon dioxide gate dielectrics. Through capacitance-voltage measurements, the student extracted the dielectric constants of the materials and found the hafnium oxide k-value matched reported values between 18-25. Interface charges in the hafnium oxide caused shifts in the flat-band voltage. Overall, using high-k hafnium oxide allowed thicker dielectric layers while maintaining capacitance, reducing leakage currents.
Recent progress on reduced graphene oxide....suresh kannan
The document summarizes recent progress on using reduced graphene oxide (rGO)-based materials as counter electrodes for dye-sensitized solar cells (DSSCs) as a cost-effective alternative to platinum. It discusses how rGO on its own is not effective as a counter electrode but that adding metal nanoparticles to rGO composites improves their catalytic activity and performance in DSSCs. The document reviews various rGO composites that have been studied, including those with silver, nickel, tungsten and platinum nanoparticles, as well as metal oxides and dichalcogenides. It compares the photovoltaic parameters of DSSCs using these rGO composite counter electrodes to those using conventional platinum counter electrodes
Graphene, the amazing two-dimensional carbon nanomaterial, has attracted extensive interest in recent years and emerged as the most intensively studied material [1]. In 2004, Geim and Nosovelov at Manchester University successfully isolated single layer graphene by the mechanical cleavage of graphite crystal [2]. This ‘‘thinnest’’ known material exhibits extraordinary electronic, chemical, mechanical, thermal and optical properties which bestowed graphene as a miracle material of the 21st Century. From applicative perspectives, graphene holds a great promise with the potential to be used as energy-storage materials, in nanoelectronics, in catalysis, biomedical, in polymer composites and many more.
The electronic band parameters calculated by the Triangular potential model f...IOSR Journals
This work reports on theoretical investigation of superlattices based on Cd1-xZnxS quantum dots
embedded in an insulating material. This system, assumed to a series of flattened cylindrical quantum dots with
a finite barrier at the boundary, is studied using the triangular potential. The electronic states and the effective
mass of 1 Γ miniband have been computed as a function of inter-quantum dot separation for different zinc
compositions. Calculations have been made for electrons, heavy holes and light holes. Results are discussed and
compared with those of the Kronig-Penney and sinusoidal potentials
This study uses density functional theory calculations to examine the interaction between titanium oxide nanostructures and graphene or functionalized graphene nanoribbons (GNRs). The key findings are:
1) Rutile titanium dioxide favors physisorption on pure graphene, while rutile and anatase titanium dioxide show similar chemisorption on functionalized GNRs.
2) Charge density maps show the importance of electron distribution in the chemical interaction between titanium dioxide and graphene.
3) Analysis of partial density of states reveals the strength of binding energies at specific adsorption sites on the titanium dioxide/graphene systems.
4) The results provide insight into controlled growth mechanisms that could have applications in photovolta
The document provides an introduction to the physical properties of graphene, specifically:
- It discusses the carbon atom and its ability to form sp2 hybridized bonds that give rise to graphene's honeycomb lattice structure.
- It describes the different methods used to fabricate graphene, including exfoliation of graphene from graphite and epitaxial growth on metal substrates.
- It previews the tight-binding model that will be used to describe graphene's electronic band structure, noting that this reveals relativistic behavior of electrons in graphene.
Graphene is a one-atom thick planar sheet of carbon atoms densely packed in a honeycomb crystal lattice. It is the strongest material ever measured and an excellent conductor of electricity and heat. The document provides an overview of graphene, including its structure, methods of synthesis such as drawing, thermal decomposition of silicon carbide and graphite oxide reduction. It also discusses graphene's extraordinary electrical, optical, thermal and mechanical properties and potential applications in fields such as transistors, solar cells and biosensors. The limitations of current knowledge and future research directions on graphene are highlighted.
This document summarizes the properties and electronic structure of graphene and graphene nanoribbons. It describes how graphene was first theorized in the 1950s but not isolated until 2004. Graphene has exceptional properties such as strength, flexibility, and electron mobility. Confining graphene into nanoribbons can open a bandgap, making it suitable for field effect transistors. The bandgap increases as the nanoribbon width decreases. Graphene nanoribbon field effect transistors could have applications in logic devices and memory due to tunable bandgaps and higher performance compared to devices using only graphene.
This review article summarizes methods for synthesizing graphene through indirect and direct deposition processes. Indirect methods involve first depositing an amorphous carbon layer onto a substrate and then converting it to graphene through a post-treatment process using heat or other energy. Direct methods grow graphene directly on a substrate surface using a solid carbon source. The article groups and assesses these methods and discusses the underlying growth mechanisms and challenges to further advancing graphene synthesis.
Amorphous-nano-crystalline silicon composite thin films (a-nc-Si:H) samples were synthesized by
Plasma Enhanced Chemical Vapor Deposition technique. The measurement of DC conductivities was
accomplished using Dielectric spectroscopy (Impedance Spectroscopy) in wide frequency and temperature range.
In analysis of impedance data, two approaches were tested: the Debye type equivalent circuit with two parallel R
and CPEs (constant phase elements) and modified one, with tree parallel R and CPEs including crystal grain
boundary effects. It was found that the later better fits to experimental results properly describes crystal grains
dielectric effect and hydrogen concentration indicating presence of strain. The amorphous matrix showed larger
resistance and lower capacity than nano-crystal phase. Also it was found that composite silicon thin film cannot
be properly described by equivalent circuit only with resistors and constant phase elements in serial relation
Progress in Synthesis of Graphene using CVD, Its Characterization and Challen...paperpublications3
Abstract: Diamond and Graphite both are natural allotropes of carbon. Graphene is a substance composed of sp2 hybridized carbon atoms that are similar to graphite and arranged in a regular hexagonal pattern. Graphene has astounding physical properties such as high electronic conductivity, excellent mechanical strength and thermal stability. It is capable to maintain its strength up to 3,600°C. It is transparent, high super hydrophobicity at nanometer scale , 100 times stronger than steel with high current density. These unique properties make graphene an interesting candidate for a number of applications currently under development, as for instance Li-ion batteries, transparent touch screens, light weight aircrafts or transistors.
Amongst the synthesis techniques, chemical vapor deposition has proved promising result for advance devices and for numerous applications where high-quality graphene films, High purity, fined grained and low structural defects film is required. CVD process is normally conducted below the atmospheric pressure and relatively lower temperatures , less than 1000°C. Pressure of LPCVD is 10-1000 Pascals.
Keywords: CVD, Graphene, Graphite, Graphene sheets..
Title: Progress in Synthesis of Graphene using CVD, Its Characterization and Challenges: A Review
Author: Sakshi Rana, Harminder Singh
International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
ISSN 2349-7815
Paper Publications
This thesis examines weak localization effects in disordered graphene. The document outlines the fabrication process and experimental setup used. Chapter 1 provides background on graphene's band structure, transport properties, and weak localization effects. Chapter 2 describes the device fabrication process, including cleaning the silicon substrate, exfoliating graphene, identifying samples with Raman spectroscopy, electron beam lithography, metal deposition, and lift-off. Electrical characterization of the fabricated devices is discussed in Chapter 4, focusing on measurements of conductivity, mobility, temperature dependence, and magnetic field effects. The goal is to use weak localization to characterize charge density fluctuations in graphene resulting from defects and trapped charges.
Study of Microstructural, Electrical and Dielectric Properties of La0.9Pb0.1M...Scientific Review SR
The present work studies the microstructural and electrical properties of La0.9Pb0.1MnO3 and La0.8Y0.1Pb0.1MnO3 ceramics synthesized by solid-state route method. Microstructure and elemental analysis of both samples were carried out by field emission scanning electron microscope (FESEM) and energy dispersive spectroscopy (EDS) method, respectively. Phase analysis by X-ray diffraction (XRD) indicated formation of single phase distorted structure. The XRD data were further analyzed by Rietveld refinement technique. Raman analysis reveals that Y atom substitutes La site into the LPMO with shifting of phonon modes. The temperature variation of resistivity of undoped and Y-doped La0.9Pb0.1MnO3 samples have been investigated. The electrical resistivity as a function of temperature showed that all samples undergo an metal-insulator (M-I) transition having a peak at transition temperature TMI. Y-doping increases the resistivity and the metal-insulator transition temperature (TMI) shifts to lower temperature. The temperature-dependent resistivity for temperatures less than metal-insulator transition is explained in terms the quadratic temperature dependence and for T > TMI, thermally activated conduction (TAC) is appropriate. Variation of frequency dispersion in permittivity and loss pattern due to La-site substitution in LPMO was observed in the dielectric response curve.
Self-organizing Behavior of Y-junctions of Graphene Nanoribbons IJERA Editor
With the help of our molecular dynamics simulation we want to motivate emerging and development of technological methods for building of carbon nanostructure networks. We shall study self-organizing behaviors of graphene nanoribbons in Y-junctions. We determine the conditions for perfect formation of nanotube Yjunctions from parallel nanoribbons. The role of graphene nanolithography in nanoribbon network and nanotube network production is studied. Our simulations show the possibility of nanotube network realization as well.
1994 atomic structure of longitudinal sections of a pitch based carbon fiber ...pmloscholte
1) STM images of longitudinal sections of pitch-based carbon fibers revealed a hexagonal superstructure with a periodicity of 14.9 A, indicating the top graphitic plane was rotated 9.5" from the underlying bulk.
2) Near defects, this superstructure was modulated with a (6 x fi)R30" pattern. The same modulation was found in images showing atomic resolution.
3) Power spectra of modulated regions contained extra peaks corresponding to the (6 x fi)R30" pattern, in addition to the six peaks from the hexagonal graphitic structure. This indicates the atomic structure is disturbed to a depth of at least two layers from the surface.
Carbon nanotubes and their applications are discussed. There are several allotropes of carbon including diamond, graphite, buckminsterfullerene (C60), and single-walled carbon nanotubes. Carbon nanotubes are cylindrical forms of carbon that can be single-walled or multi-walled. They are composed of hexagonal networks of carbon atoms and have remarkable mechanical, thermal, and electrical properties. Common synthesis methods for carbon nanotubes include arc discharge, laser ablation, and chemical vapor deposition using metal catalysts.
1. The document investigates the electrodeposition of FeCoNiCu/Cu and CrFeCoNiCu/Cu multilayered nanowires for applications in magnetic sensing devices. It explores fabrication methods to achieve better sensitivity, low coercivity, and low magnetic saturation.
2. Experiments are conducted to characterize electrolyte compositions and deposition parameters. Constant potential and pulsed potential techniques are used to fabricate multilayers. Composition and magnetic properties are analyzed. Maximum giant magnetoresistance of 10.64% is achieved for optimized layer thickness and saturation field.
3. Adding chromium is expected to further improve properties like reducing coercivity based on prior research on chromium's effects in other material systems.
Polynomials, shape finding procedures and reverse mathematics and graphics are presented here that improve the down time and quality of the manufacturing process.
The growth and assembly of organic molecules and inorganic 2D materials on gr...Akinola Oyedele
The unique properties of graphene have made it a promising material for integration in future electronic applications. The idealized surface of graphene, atomically-flat and without dangling bonds, offers the opportunity to understand the assembly of organic and inorganic molecules to form a wide range of ordered architectures and functional graphene-based heterostructures. In this review, we summarize recent progress in the growth of hierarchical nanostructures on graphene. The self-assembly of organic molecules and inorganic two-dimensional (2D) layers on graphene for the construction of various types of heterostructures are highlighted. Van der Waals interactions between the assembled molecules and graphene are shown to allow the formation of highly-ordered structures with preferred molecular orientations and stacking configurations that circumvent the strict lattice-matching requirements in traditional epitaxial growth. Finally, we briefly discuss representative applications of graphene-based heterostructures in electronic and optoelectronics.
Electron Diffusion and Phonon Drag Thermopower in Silicon NanowiresAI Publications
The field of thermoelectric research has undergone a renaissance and boom in the fast two decades, largely fueled by the prospect of engineering electronic and phononic properties in nanostructures, among which semiconductor nanowires (NWs) have served both as an important platform to investigate fundamental thermoelectric transport phenomena and as a promising route for high thermoelectric performance for device applications. In this report we theoretical studied the carrier diffusion and phonon-drag contribution to thermoelectric performance of silicon nanowires and compared with the existing experimental data. We observed a good agreement between theoretical data and experimental observations in the overall temperature range from 50 – 350 K. Electron diffusion thermopower is found to be dominant mechanism in the low temperature range and shows linear dependence with temperature.
Study of Boron Based Superconductivity and Effect of High Temperature Cuprate...IOSR Journals
This paper illustrates the main normal and Boron superconducting state temperature properties of magnesium diboride, a substance known since early 1950's, but lately graded to be superconductive at a remarkably high critical temperature Tc=40K for a binary synthesis. What makes MgB2 so special? Its high Tc, simple crystal construction, large coherence lengths, high serious current densities and fields, lucidity of surface boundaries to current promises that MgB2 will be a good material for both large scale applications and electronic devices. Throughout the last seven month, MgB2 has been fabricated in various shape, bulk, single crystals, thin films, ribbons and wires. The largest critical current densities >10MA/cm2 and critical fields 40T are achieved for thin films. The anisotropy attribution inferred from upper critical field measurements is still to be resolved, a wide range of values being reported, γ = 1.2 ÷ 9. Also there is no consensus about the existence of a single anisotropic or double energy cavity. One central issue is whether or not MgB2 represents a new class of superconductors, being the tip of an iceberg that waits to be discovered. Until now MgB2 holds the record of the highest Tc among simple binary synthesis. However, the discovery of superconductivity in MgB2 revived the interest in non-oxides and initiated a search for superconductivity in related materials, several synthesis being already announced to become superconductive: TaB2, BeB2.75, C-S composites, and the elemental B under pressure.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
1. Converting the buffer layer to semiconducting graphene and
the role of incommensurate mutual modulation
A Thesis Proposal
Presented to
The Academic Faculty
by
Matthew Conrad
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
School of Physics
Georgia Institute of Technology
May 2016
2. Converting the buffer layer to semiconducting graphene and
the role of incommensurate mutual modulation
Approved by:
Professor Edward Conrad, Chair
Professor Philip First
Professor Martin Mourigal
4. CHAPTER I
INTRODUCTION
In 2004 graphene[1, 2] captured the attention of the condensed matter community and
claimed the Nobel Prize in 2010. It was one of the first truly 2D materials available for
rigourous study and opened up an entirely new field of research. The discovery of graphene
was surprising as 2D materials were long thought to be unstable and the electron transport in
graphene resembled the behavior of massless Dirac fermions [3]. Even more excitement grew
as graphene showed great promise for applications through remarkable electronic properties
like long range ballistic conduction at room temperature and record mobilities[4].
Recently, progress towards graphene-based electronics has halted due to the inability
to develop a viable form of semiconducting graphene. As a result, research has shifted to
other less favorable materials such as 2D metal dichalcogenides. A promising system for
semiconducting graphene is the first graphene layer grown on SiC(0001) (the buffer layer)
due to its strong and ordered interaction with SiC. However, a proper understanding of the
buffer layer has been elusive because theoretical studies were too computationally expensive
and growth methods inhibited comprehensive experimental studies. However, improved
growth methods are now available for detailed electronic and structural measurements.
Such studies are essential to enable a proper theoretical understanding and to assess if
buffer graphene can be tailored into a viable form of semiconducting graphene.
This thesis proposal outlines a path of study for the buffer layer from an experimen-
tal and theoretical perspective. First, a literature review is presented that outlines what
graphene is and how to it semiconducting. Then a review of graphene on SiC and a history
of the buffer layer will be provided. Following the literature review, detailed measurements
of the first surface X-ray diffraction (SXRD) measurements on the buffer layer are coupled
with angle resolved photomession spectroscopy (ARPES) measurements to correlate the
atomic and electronic structure through a simple tight binding model. Finally, an outline
1
5. a
b
τ1
τ2
τ3
a b
ΓK KM
E−EF(eV)
30
20
10
0
-10
c
0.1
0
-0.11.61.7
1.8
-0.5
0
0.5
kx (˚A−1)ky (˚A−1)
E−EF(eV)
-5
0
5
E−EF(eV)
DOS (a.u)
d
a∗
b∗K
Γ K
M
Figure 1.1: (a) Atomic structure of graphene. The gray diamond represents the unit
cell. “A” (“B”) atoms are in gray (gold). The red arrows represent the lattice vectors.
Black arrows represent the vectors for the three nearest neighbors to an atom A atom. (b)
Band structure of graphene π-bands (yellow) and σ-bands (gray) calculated from the tight
binding method. The two π-bands touch at the K-point(and K ) with a linear dispersion
that give rise to a Dirac cone shown in (c). The insert is a schematic of reciprocal space.
The reciprocal lattice vectors in blue, a∗ and b∗, are determined from the lattice vectors in
(a), a and b, respectively. The boundary of the first Brillioun zone is indicated by the gray
hexagon. The band structure was calculated along the path shown in red. (d) density of
states of graphene pi-bands.
of the future work to conduct detailed experimental and theoretical studies of the buffer
will be presented.
1.1 Graphene
Graphene is a planar two-dimensional hexagonal crystal of carbon atoms [see Fig. 1.1(a)].
The positions of the atoms are described by lattice and basis vectors, R = Rm,n + r. The
lattice positions are determined by integer multiples of the lattice vectors, Rm,n = ma + nb
where the lattice vectors are rotated by 2π/3. The magnitude of a and b are equal and
define the graphene lattice parameter, ag ≈ 2.46 ˚A. The hexagonal structure is formed by
having two equivalent basis atoms, where the “A” atom is located at the origin and the “B”
atom at RB = 1/3 a − b .
The reciprocal lattice of graphene is also hexagonal where a∗ and b∗ are rotated by π/3
and have a magnitude of 4π/ag
√
3 as shown in the insert in 1.1(b). The symmetry points
of interest are Γ = 0, M = 1/2a∗, K± = ±1/3(a∗ + b∗).
2
6. Each carbon atom has four valence electrons. Three of the electrons in the 2s, 2px, and
2py orbitals sp2 hybridize to form strong σ-bonds to the three neighboring carbon atoms.
The remaining electron in the 2pz state delocalizes and forms π-bonds with the neighbor-
ing carbon atoms. In perfectly flat graphene the π-bonds can be considered separately
because they are orthogonal to the σ-bonds. Furthermore, the π-electrons are responsible
for the low energy electronic structure and were first studied theortically using the tight
binding method to serve as a building block for understanding the electronic properties
of graphite[5]. Despite its simplicity, the tight binding (TB) model predicts experimental
results[6] and agrees with more rigourous ab initio calculations[7] . For this reason, TB
models are often the starting point for exploring new phenomena in the electronic structure
of graphene systems.
At low energy, the band structure of the π-electrons have two bands (bonding and
anti-bonding) that touch at the K±-points with linear dispersion and azimuthal symme-
try[See Fig. 1.1(b) and (c)]. The band structure is classified as a zero gap semiconductor
or a semimetal since the density of states is minimum where the two bands touch[See Fig.
1.1(d)]. Although the band dispersion is the same at K±-points, pseudospin arises from the
inequivalence of the wavefunctions at K±-points[See the insert in Fig. 1.1(b)]. The pres-
ence of linear dispersion and pseudospin at low energy indicate that the quasiparticles in
graphene behave like massless Dirac fermions and open new methods for studying quantum
electrodynamics in a condensed matter system[3]. As such, the shape of the low energy
dispersion is characterized by a Dirac cone and the two bands touch at the Dirac point.
The reason for this unique gapless electronic structure in graphene is due to sublattice
symmetry, i.e. both A and B atoms are carbon, and hexagonal symmetry. The combination
of these symmetries ensures a degeneracy in energy at the K±-points[8]. The methods
for producing bandgaps in graphene involve breaking both or either of these symmetries.
Symmetry-breaking methods fall into three broad classes: quantum confinement, strain and
functionalization.
Theoretically, defining graphene into certain shapes of sufficiently small size may in-
duce bandgaps. Two notable examples are nanoribbons[9] and antidots[10]. Both quantum
3
7. confinement and edge termination play important roles in these systems. The effects of
quantum confinement are demonstrated by the band gap being inversely proportional to
the ribbon width or size of the antidot. Differences in edge termination effects the size of
the band gap and the presence of zero energy states. The challenge facing nanoribbons
lies in the necessity to fabricate crystallographically defined edges with minimal defects at
small and precise ribbon widths or antidot size. Uniaxial strain can open substaintial band
gaps in graphene, but require large strains beyond the elastic limit and reduces the Fermi
velocity[11]. Other types of local strain show promise of opening gaps[12], but have yet
to be realized experimentally due to similar challenges facing quantum confinement. Func-
tionalization through chemical modification[13] or substrate interaction can open gaps by
breaking sublattice symmetry in graphene. However, insufficiently ordered functionalization
or metallic substrates[14] make the transport studies challenging due to reduced mobility
or substrate conduction. These issues are absent in the buffer layer system as the substrate
interaction is known to be ordered and SiC is an insulator. Furthermore, a band gap opened
from substrate interaction does not require precise control of nanoscale features.
1.2 Graphene on SiC
Graphene was first discovered by Van Bommel et al. in 1975[16] by heating SiC until
silicon sublimated from the surface. Once the SiC cooled, the excess carbon rearranged
into layers with a graphitic lattice constant. Forty years later, graphene growth by thermal
decomposition of SiC is one of the most promising growth methods for graphene based
electronics[17]. The reason for this is that current growth techniques[15] allow for precise
layer control and the graphene is well ordered and crystallographically aligned.
There are many methods for growing graphene on SiC. Most studies of graphene growth
have been on the two polar faces, the SiC(0001) Si terminated face (Si-face) and SiC(000¯1)
carbon terminated face(C-face), of hexagonal 4H and 6H SiC[18, 19, 20]. Note that graphene
growth also occurs on other faces and polytypes such as cubic β-SiC(111)[21]. The crystal
structure of 4H-SiC is shown in Fig. 1.2(a). The earliest growth methods consisted of heat-
ing in ultra high vacuum (UHV)[16, 22]. Growth on the C-face and Si-face were found to be
4
8. ab
c
A
B
C
B
a b c
Si-face
C-face
SiC
induction heater
vacuum
leak
graphite
susceptorSi (vapor)
Si-face
C-face
BG
MG
Figure 1.2: Epitaxial graphene on SiC. (a) Crystal structure of 4H-SiC. Si (C) atoms are
yellow (black). The SiC-bilayer stacking sequence is ABCB. The bulk SiC(0001) surface (Si-
face) terminates with a plane of Si atoms, conversely SiC(000¯1) terminates with C atoms
(C-face). (b) Graphene growth on SiC by confinement controlled sublimation [15]. (c)
Schematic of graphene on SiC. Graphene growth is slower on the Si-face compared to the
C-face. The first layer of graphene in the Si-face is called the buffer layer (BG), the second
layer is called monolayer graphene (MG).
quite different. On the C-face growth occurs more quickly and > 30 layers are possible with
many commensurate rotations between the graphene layers[23, 24]. On the Si-face, growth
is slower and only a few layers of graphene form[6]. Furthermore, the graphene layers are ro-
tationally aligned with the SiC to form the so-called (6
√
3×6
√
3)SiCR30◦ reconstruction[20].
The challenge with UHV graphene growth is that large area layer control is not possible
due to high growth rates. Currently, there are a few improved growth techniques such as
growth in an Ar environment[17], chemical vapor deposition[25] and confinement controlled
sublimation (CCS)[15]. In the CCS method, SiC is inductively heated inside a graphite en-
closure [See Fig. 1.2(b)]. The sublimated Si generates a partial pressure due to confinement
within the enclosure. The partial Si pressure is determined by the temperature, crucible ge-
ometry and leak rate. The increase in Si partial pressure slows the graphene growth process
to near equilibrium and causes growth to occur at higher temperatures. For a particular
enclosure, the number of layers grown is determined by the temperature and time. With
the current design, the first layer of graphene, commonly referred to as the buffer layer
(BG), grows at 1400◦C and the second layer (MG) grows at 1550◦C [See Fig. 1.2(c)]. This
5
9. a∗
Gb∗
G
a∗
SiC
b∗
SiC
a b c
Figure 1.3: The (6
√
3×6
√
3)SiCR30◦ reconstruction on SiC(0001). (a) LEED image of a
buffer layer grown by confinement controlled sublimation. (b) reciprocal space interpreta-
tion of (a). The large red (blue) circles are SiC (graphene) rods, smaller red (blue) circles
are (6×6)SiC satellites about SiC (graphene). The graphene rods appear to be commensurate
with the 6
√
3 reciprocal lattice (black dots). (c) Real space 6
√
3 unit cell. The gray (yellow)
circles represent carbon (Si) in the graphene (bulk-terminated SiC). The black diamond is
the 6
√
3 unit cell and the red diamond is the (6×6)SiC quasi-unit cell. The red and blue
filled hexagons emphasize that the (6×6)SiC is not a true unit cell. The red (blue) hexagons
demonstrate the presence (absence) of a graphene carbon atom at the boundaries of the
quasi-unit cell.
convention was adopted since the buffer layer did not possess the electronic properties of
freestanding graphene due to its interaction with SiC. Only when the second graphene layer
forms do angle resolved photoemission spectroscopy (ARPES) measurements observe the
characteristic linear dispersion[19].
1.3 The buffer layer and the 6
√
3 × 6
√
3 R30◦
reconstruc-
tion on SiC(0001)
The history of experimental studies of graphitization on SiC(0001) is characterized by seem-
ingly opposed results and remains to be fully understood. It has been contested whether
the SiC interface is a 6
√
3 or (6×6)SiC reconstruction, if it is bulk-terminated[26], and if the
topmost carbon layer is a full, partial or defected graphene layer[27, 28].
LEED images always suggest the presence of what appears to be a 6
√
3 reconstruction
on SiC(0001) at all stages of graphitization [16, 29, 30]. As a result, layer estimation from
LEED can be challenging and can depend on the growth procedure[29]. The buffer layer
is regarded to form with the initial formation of the 6
√
3 reconstruction. A typical LEED
image of the 6
√
3 is shown in Fig. 1.3(a). The graphene reciprocal lattice vectors are rotated
6
10. 30◦ from SiC and the magnitude is |a∗
g|/a∗
SiC| = 13/6
√
3, i.e. a∗
g = 13/6(a∗
SiC + b∗
SiC). This
leads to a lattice constant of ag = aSiC 6
√
3/13 = 2.462˚A that is only slightly (0.1%)
expanded from graphite (2.460(2)˚A) [31, 32, 33, 34]. Furthermore, a (13 × 13)g graphene
unit cell is commensurate with the (6
√
3×6
√
3)SiCR30◦ unit cell. How a graphene reciprocal
lattice fits onto the 6
√
3 reciprocal lattice is shown in Fig. 1.3(b) and the corresponding real
space unit cell is shown in Fig. 1.3(c).
In constrast to LEED, STM measurements have not produced a satisfying image of a
6
√
3 reconstruction[29]. The primary reconstruction observed is (6×6)SiC [26, 35]. The
difference between the 6
√
3 and (6×6)SiC unit cells are demonstrated in Fig. 1.3(c). The
two measurements are at odds in the sense that an integer multiple of (6×6)SiC reciprocal
lattice vectors cannot describe the graphene position in Fig. 1.3(a). (6×6)SiC features are
observed in LEED images as “satellites,” i.e. there are diffraction rods that surround the
(1 × 1)SiC and (1 × 1)g reciprocal lattice rods that are described by (6×6)SiC reciprocal
lattice vectors[See Fig. 1.3(a) and (b)]. However, it should be noted that (6×6)SiC satellites
surrounding graphene diffraction rods lie on the 6
√
3 reciprocal lattice.
The interpretation of LEED and STM measurements remains an ongoing research
question[36, 37]. One model is that the SiC is unreconstructed. In this model the satellite
rods in LEED are interpretted as resulting from multiple scattering and the (6×6)SiC pattern
seen in STM measurements results from a moir´e pattern between the SiC layer and the
graphene layer. In constrast, the reconstructed model claims that the satellite rods in
LEED are due to structural changes in the interface between graphene and SiC and the (6×
6)SiC seen in STM is imaging the interface reconstruction. Within the reconstructed model,
bulk-terminated[38] and adatom[26] models have been proposed. The bulk-terminated re-
constructed SiC interface model is supported by XPS and ARPES measurements[19] and
the adatom model is supported by STM. What has become clear is that the buffer layer is
a complete graphene layer without substainial defects or incomplete regions[39]. As growth
methods and experimental techniques have improved, the understanding of the buffer layer
electronic structure has changed. Initial ARPES measurements found the buffer layer to be
a wide gap insulator with two significant surface states within the gap making the buffer
7
11. layer unsuitable for electronic applications[19]. Using improved growth methods, this pic-
ture changed and found the buffer layer to be a true semiconductor with no surface states
and a band gap > 0.5 eV [40]. Furthermore, recent structural measurements raise suspicion
that buffer layer may be incommensurate and not a 6
√
3 or (6×6)SiC reconstruction[41] and
that the SiC interface reconstruction may not be bulk-terminated[42].
Theoretical studies of graphene on SiC are limited and remain inconclusive as well.
Depending on the assumptions and calculation method, qualitatively different properties are
predictied. Initial calculations were performed on a smaller, highly stained, bulk-terminated
√
3 ×
√
3 SiC
R30◦ unit cell. While these calculations were on an unrealistic unit cell, they
predicted a wide gap buffer with a metallic state from unbonded Si[43, 44] that seemingly
agreed with initial APRES measurements[19]. On the other hand, calculations of the full
bulk-terminated 6
√
3 buffer vary in predictions from metallic[45], to supporting the insulator
picture of the (
√
3×
√
3)SiC model[46], or remaining silent on its electronic properties[47, 48].
Furthermore, it is not clear why the bulk-terminated reconstruction should be 6
√
3 as there
are other more energetically favorable interface structures, such as (4 × 4)SiCR24.2◦[48].
From all the theoretical studies conducted, none predict the most recent electronic structure
measurements of an improved buffer layer or STS measurements with a gap ∼1 eV[39, 26].
It is clear that more detailed structural measurements are needed to guide further theoretical
study and clarify previous experimental results.
8
12. CHAPTER II
PRELIMINARY RESULTS
The initial work for this thesis proposal attempts to resolve the contradiction between the
theoretical and experimental buffer layer band structure. Using improved growth methods,
the first high resolution surface x-ray diffraction measurements of the buffer layer system
were obtained. These results show that contrary to the last forty years, the buffer layer
system is not the assumed (6
√
3×6
√
3)SiCR30◦ reconstruction. Rather, the graphene lattice
is incommensurate with bulk SiC and engages in a mutual modulation with the SiC interface.
With this new structural model, the measured band structure can be described with a simple
tight binding model.
2.1 The incommensurate SiC(0001) interface
In the traditional buffer layer picture, the commensurate 6
√
3 structure gives rise to 6th
order diffraction rods around the bulk SiC reciprocal lattice rods [see Fig. 1.3 and the insert
in Fig. 2.1(a)]. However, high resolution SXRD measurements reveal that the satellite rods
are symmetrically shifted away from the commensurate 6th order positions and towards the
bulk SiC rods. The incommensurate rods along k in Fig. 2.1(a) are ±q1 = K − GSiC
0,1 whose
magnitude is q1 = qoa∗
SiC, where qo = 1/6(1 + δ) and δ = 0.037(2).
This behavior is a classical result of an incommensurate system[49]. The contracted
satellite positions are a direct result of the commensurate unit cell positions, R, being
modulated by a function, η(R, q). The modulation can be Fourier expanded so that the
new modulated positions, r, are given by[50],
r = R +
d
j=1
ηj sin (qj · R + φj). (2.1)
Each Fourier component has a corresponding amplitude ηj, wavevector qj, and phase φj.
The number of Fourier components is d. From this description the diffraction condition and
9
13. Figure 2.1: Diffraction results from the incommensurate graphene-SiC(0001) systems. (a)
SXRD radial k scans, (0, k, 0.1), around the SiC (0, 1, l) rod (see schematic in the insert).
The background-subtracted intensity is instrument corrected. Data is for the BGo (blue)
and MG (grey) films. Dashed lines mark the commensurate 5/6th and 7/6thpositions in
reciprocal space (black circles in insert). The buffer satellite rods are contracted relative to
the commensurate positions towards the (0, 1, l) rod while the monolayer rods are nearly
commensurate. (b) Radial scan through the nominal graphene (0, 3, 0.1)G rod for the BGo
(blue ◦) and MG (grey ◦) films. Dashed line marks the expected position for a commensurate
6
√
3 graphene film. Blue arrow shows the expected (0, 3, l)G position from Eq. 2.7. The
monolayer film has a contribution from the MG (red line) and the BGML rods (black line).
The green (red) arrow marks the position for graphite (theoretical graphene). The arrows’
horizontal bar represent their known uncertainties. (c) Radial width of graphene rods as a
function of K for BGo (blue ◦), MG (red ◦), and BGML (grey ◦).
10
14. intensity can be calculated. In the kinematic approximation the scattering amplitude is a
Fourier transfrom of the electron density, which is modeled as a delta function distribution,
A(K) =
r
freiK·r
, (2.2)
where fr is the atomic form factor of the atom at position r. Substituting eq. 2.1 into eq. 2.2
and using the Jacobi-Anger expansion eiZ sin θ = ∞
p=−∞ eipθJp(Z), where Jp(Z) is a Bessel
function of the first kind, gives,
A(K) = F(K)
R
∞
{pj}=−∞
ei(K+ j pjqj)·R
ei j pjφj
d
j=1
Jpj (K · ηj). (2.3)
F(K) = Rb
freiK·Rb is the average structure factor from the basis atoms, Rb and is as-
sumed to be slowly varying in subsequent calculations. The integrated intensity is calculated
from the scattering amplitude by I = dK3|A(K)|2,
I(K)
N2|F(K)|2
=
{pj}{pj }
d
j,j
Jpj (K · ηj)Jpj
(K · ηj )ei(pjφj−pj φj )
. (2.4)
Equation 2.3 describes a set of satellite rods through the diffraction condition,
K = G −
d
j
pjqj, (2.5)
where G is a reciprocal lattice vector of the SiC (G(SiC)) or graphene G(g) unmodulated lat-
tice, pj is an integer for the corresponding qj and {pj}{pj } in eq. 2.4 impose a restriction
of the sums such that,
d
j
pjqj =
d
j
pj qj . (2.6)
What is unique about the buffer system is that the buffer layer and the SiC interface layer
are mutually modulated. This is known from the fact that the spacing between the buffer
G
(g)
1,1 and the SiC G
(SiC)
0,2 is an incommensurate wavevector, i.e. q1 = G
(SiC)
0,2 − G
(g)
1,1. This
behavior occurs when the buffer graphene modulation can be Fourier expanded in SiC
reciprocal lattice vectors and vice versa. The allowed incommensurate wavevectors can be
generalized as,
11
15. {q} = G(SiC)
− G(g)
. (2.7)
Since the graphene lattice constant is incommensurate with the 6
√
3 [see Fig. 2.1(b)], so
is the period of the modulation. The mutual modulation is further confirmed by the excellent
agreement between the measured and expected (G
(g)
0,3 = G
(SiC)
1,1 −q1+q2) position of the buffer
G
(g)
0,3. Note that the incommensurate buffer lattice constant is larger (2.469(3)˚A) than the
expected 6
√
3 value (2.462˚A, vertical dashed line) due to the shift to lower K||. Furthermore,
the lattice constant is larger than graphite (2.460(2)˚A) and theoretically isolated graphene
(2.455(3)˚A)[51, 52, 53].
An increased lattice constant is consistent with stronger interlayer interaction in layered
materials[54] and with the view that some of the carbon atoms bond lengths increase due to
some degree of hybridization with Si in the SiC interface. Also, the incommensurate lattice
constant is consistent with previous measurements[41] although they incorrectly attributed
the expanded lattice constant to a buckled buffer graphene layer to claim the buffer layer
was commensurate with a 6
√
3 unit cell. Rather, in the context of mutual modulation the
buffer in-plane lattice constant is properly understood as being truly incommensurate.
The modulation amplitude in the SiC interface layer and the buffer graphene layer can
be quantified by comparing the measured, instrument corrected[55], integrated intensity of
the incommensurate satellite rods to the calculated intensity. The intensity was numerically
calculated with a large number of lattice points by inserting eq. 2.1 into 2.3. To obtain
a meaningful estimate of the modulation, the number of terms in η(R, q) must be limited.
Experimentally, the satellite rods of significant intensity were first order. The minimum
number of wavevectors needed to reproduce the symmetry of the satellites was found to
be d = 3. The three {q} are shown in Fig. 2.2(a). They are of equal magnitude and
directed along q1 = −qob∗
SiC, q2 = qoa∗
SiC, and q3 = qo(b∗
SiC − a∗
SiC). Note that from the
non-orthongonality of {q}, there are multiple sets of {p} for a given satellite rod that
contribute to the diffraction intensity. For example, −q1 = q2+q3 and satisfies the restriction
{pj}{pj } . From symmetry considerations, the modulation amplitudes, {η}, are assumed
to have the same magnitude, η(SiC) or η(g), and parallel to their respective {q}. Multiple
12
16. Figure 2.2: SXRD derived structure of the buffer-SiC interface. (a) The instrument cor-
rected integrated intensity of the satellite rods around the (01l) rod. Crosses mark the
commensurate 6th order rods. The arrows show the three IC wavevectors. The gold circle’s
area are proportional to the measured intensity of the satellite rods. The red circle’s area
are proportional to the fit intensity described in the text for η(SiC) =0.11aSiC. (b) The η
(SiC)
||
dependence of the calculated intensity for the satellite rods shown in (a). The intensity is
normalized to N2. The vertical blue box shows the range of η
(SiC)
|| that best fit the measured
values of all seven rods. The circles represent the normalized experimental intensity values
for the satellite rods.
orientations for the modulation amplitudes were tested and these choices were found to
provide the best fit. Further, the intensity was found to be insensitive to the choice of {φ}.
Figure 2.2(b) shows how the calculated intensity of the satellite rods around G
(SiC)
0,1 vary
as a function of η(SiC). The intensity was normalized to N2, where N is the number of
lattice points in the numerical calculation. When η(SiC) → 0, I → 0 for all satellite rods
and I → 1 at K = G. As η(SiC) increases, the intensity is not symmetric in η(SiC) about zero
and the satellite intensities develop an asymmetry like the observed experimental pattern
[see Fig. 2.2(a)]. The range of η(SiC) with the proper intensity pattern is highlighted by the
blue box in Figure 2.2(b). The best fit value is η(SiC) =0.11(4)aSiC. The same analysis was
performed on the graphene satellites and found a weak, but non-zero, in-plane modulation
of η(g) < .01aSiC.
The incommensurate modulation can be visuallized by plotting the relative density
change of the SiC interface layer. By considering eq. 2.1 as a coordinate transformation, the
normalized density change relative to the unmodulated system is given by ∆ρ/ρ = J−1 −1,
where J−1 is the inverse of the Jacobian determinant for the transformation of R → r. The
13
17. Figure 2.3: Relative density ∆ρ(x, y)/ρ map of the incommensurate SiC interface using the
measured {q} and best fit η
(SiC)
|| . The grey circles and hexagonal mesh overlay represents
interface Si and graphene, respectively. The commensurate 6
√
3 unit cell is marked in red.
Black arrows show the three incommensurate wavevectors.
colormap in Fig. 2.3 shows that the SiC interface consists of a super-hexagonal network with
a period of λ = 6(1 + δ)aSiC. The boundaries have a higher density than bulk terminated
SiC. Note that while the density modulation is periodic, the atomic positions of both the
SiC interface and the buffer graphene are not periodic. The network is very similar to STM
images of the buffer layer[29, 27, 35, 26].
The exact structure of the SiC interface and the driving force for the incommensurate
phase remains to be determined. It is unlikely that a simple sinusoidal modulation used
to fit the data is the complete picture. Recent work by Emery et al. [42] may provide a
clue. They show that the interface layer below the buffer graphene layer has a lower Si
and higher C concentrations than bulk SiC. Silicon vacancies and/or substitutional carbon
could give rise to different bonding geometries that could produce strains sufficient to drive
the incommensurate modulation. On the other hand, a comparable strength in-plane and
interlayer interaction coupled with subsequent changes in bond length may be sufficient to
drive the incommensuration in a bulk-terminated system.
14
18. 2.2 Semiconducting graphene from interface interaction
Although the exact structure is still unknown, the discovery of an incommensurate mutual
modulation in the buffer-SiC system allows the electronic structure of the buffer layer to
be studied and explained in a new context. As will be shown, a simple tight binding
model can reproduce ab initio calculations and experimental ARPES measurements. First
a description of the tight binding calculations is provided followed by a description of the
model and parameters used to study the buffer-SiC interaction.
Given that η(SiC) η(g) and η(g) is small, the buffer-SiC system is modeled as an
unmodulated graphene layer above a modulated triangular lattice of Si atoms at the SiC
surface for all calculations. The Si lattice is rotated 30◦ from the graphene lattice vectors.
Tight binding calculations require periodicy. As a starting point, a (13×13)g graphene unit
cell is commensurate with a 6
√
3 SiC unit cell. In this model, only the influence of Si on the
buffer graphene is studied. A Si interface atom bonds to its nearest neighbor graphene atom
if the in-plane Si-C distance is within a maximum cutoff radius, rcut. Bonding is modeled
through an onsite potential to the carbon atom in the graphene layer. Using a single orbital
nearest neighbor tight binding model of the graphene π-electron network, the Hamiltonian
reads,
H = −t
R,R i,j rSi
(a†
R+ri
aR +rj
+ V θ (rcut − rSi) a†
R+ri
aR+ri
+ H.c.), (2.8)
where R (R ) specifies the unit cell, r specify the C atom positions within the graphene
unit cell, i, j represent that R + ri and R + rj must be nearest neighbors to the carbon
atom and rSi represents the in-plane nearest neighbor distance for a Si atom in the interface
layer to the graphene C at ri. t ≈ 2.8 eV is the transfer integral between nearest neighbor
C sites and a†
r (ar) are operators that create (annihilate) a carbon π-electron at r. V is
the onsite potential due to bonding from with a Si interface atom. θ (rcut − rSi) is the
Heavyside step function that is 1 if rSi < rcut and 0 otherwise, where rSi is the nearest
neighbor distance of a Si interface atom to a C graphene atom. The Fourier transformation,
ar = 1/
√
N k
eik·rφk
(r) is applied to the Hamiltonian, where φk
(r) is the operator that
annihilates a pz orbital at r. After this transformation, the sums over R and R are identical
15
19. and the Hamiltonian becomes,
H = −t
i,j
eik·ri,j
φ†
k
(ri) φk
(rj) + V θ (rcut − rSi) φ†
k
(ri) φk
(ri) + H.c., (2.9)
where ri,j = (R + ri) − (R + rj). The solution to the Schr¨odinger equation is Ψn(k) =
r Cn
r φ†
k
(r) where the coefficients are obtained from the solution to the eigenvalue prob-
lem, det H(k) − ES(k) = 0. The overlap of the pz orbitals is assumed to be negligible.
Therefore, the elements Sm,n = δm,n. The matrix elements of the Hamiltonian are
Hm,n = −t eik·rm,n
δrm+rm,n,rn + V θ(rcut − rSi)δrm,rn . (2.10)
The method used to compare the calculated band structure with the ARPES measure-
ments in Fig. 2.4 is to project the band structure from the supercell Brillouin Zone (BZ)
to the larger primitive graphene BZ[56]. When unfolding the band structure, a weight is
assigned to each eigenvalue at each k value;
Wn(k) =
1
n
rA,i
Cn
rA,i
(k)
∗
rA,i
Cn
rA,i
(k) +
rB,i
Cn
rB,i
(k)
∗
rB,i
Cn
rB,i
(k)
. (2.11)
Here rA/B refer to C atoms in the larger unit cell that unfold to the A(B) sublattice.
Neglecting effects such as polarization, photoelectron diffraction, etc., the ARPES intensity
can then be approximated as;
I(E, k) =
n
i
Wi(k)δ(E − En(k))dE. (2.12)
Assuming the pz orbitals are sufficiently localized, the wavefunction coefficients can also
be used to model an STM measurement. This is done by calculating the charge density
[See Fig. 2.4(c)] for a given energy[10]
ρ(r, E) =
n,k
|Cn
r (k)|2
δ(E − En(K))dE. (2.13)
Both the ARPES intensity and charge density were broadened in energy by ±0.1 eV to
better represent the experimental measurements.
16
20. Figure 2.4: Comparison of the theoretical the incommensurate graphene band structure
with experimental ARPES data. (a) The commensurate 6
√
3 buffer structure derived from
ab initio calculations in Ref. [45]. Black circles are carbon unbonded to the SiC. Gold circles
are carbon bonded to Si in the interface layer below. The NC regions (blue hexagons) and
the carbon chains are marked. (b) A model structure based on modulated SiC layer using
the experimental value, η(SiC) = 0.11aSiC (same color scheme as (a)). Red dashed hexagon
marks the boundary of an isolated graphene island. (c) The calculated charge density
(arbitrary units) at E =−0.6 eV for the structure in (b). (d) TB bands (red) mapped onto
the graphene BZ from the commensurate structure in (a). The low energy bands from the
ab initio commensurate structure are overlaid (black dashed line). (e) DOS for the TB
bands in (d). (f) TB calculated bands (red) from the modulated structure in (b). The
negative 2nd derivative of the experimental ARPES bands (blue) are overlaid. The π-bands
from a 2% monolayer have been subtracted from the experimental bands. (g) DOS for the
TB bands in (f). The direct 0.8eV bandgap is marked.
17
21. rSi
distance (ag
)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Counts(nSi
)
0
5
10
15
20
25
rcut
1/2acc
a b
Figure 2.5: Bonding geometry from ab initio calculation[45]. (a) shows the bonding con-
figuration of the 6
√
3 × 6
√
3R30◦
SiC or (13 × 13)g unit cell do to an assumed unmodulated
bulk-terminated SiC(0001) interface. The graphene lattice vectors are the black arrows,
the SiC interface lattice vectors are the green arrows. The black (gray) circles are carbon
atoms in the graphene layer bonded (did not bond) to Si. The large (small) yellow circles
are Si atoms bonded (not bonded) to C in the graphene layer. The blue circles around a
pair of C atoms are the same distance from the nearest Si within rcut. The red lines indicate
situations where bonding within rcut did not occur. (b) Histogram counting the number of
Si atoms with a nearest neighbor planar distances between Si in the interface layer and C in
the graphene layer, rSi. The yellow (red) histogram of rSi is for bonded (not bonded) Si to
graphene C atoms. The most notable feature is the overlap near .34ag, which is highlighted
in (a).
In order to properly use this tight binding model, the parameters, V and rcut must be
obtained. To do this, the parameters were determined so that the band structure from the
tight binding calculations reproduced previous ab initio calculations[45]. In their calcula-
tions, a complete graphene layer commensurate with the 6
√
3 rested on a bulk-terminated
SiC interface[45] and was then allowed to relax. Figure 2.4(a) shows a visualization of the
predicted bonding configuration. Not all Si interface atoms bonded the graphene C atoms.
They found that 79% of the interface Si bonded to 25% of the BGo graphene C atoms. The
bonding pattern is divided into two regions: a nearly commensurate (NC) region and the
boundaries between the NC regions. In the NC region, the bonding and atomic positions
are close to previous calculations[43] on a (
√
3 ×
√
3)SiC where the unbonded C reseme-
bles benzene-like rings. At the NC boundaries, incomplete hexagonal chains form and are
responsible for the low energy electronic metallic band structure.
18
22. An analysis of the bonding configuration is presented in Figure 2.5(a). The histogram
in Fig. 2.5(b) shows that when rSi > 0.35ag, the Si atom will not bond. The maximum
bond length does not have a sharp cutoff, i.e. there are a few cases where rSi = 0.35ag
and bonding does and does not occur. These four cases are highlighted by red lines in
Fig. 2.5(a). An additional complication arises when 1/2acc < rSi < 0.35ag (acc is the C-C
bond length in buffer graphene layer). In this case 2 C atoms may be equidistant from
the nearest Si atom. In the ab initio calculations, only one C atom bonds to the interface
Si atom[See the blue circles in Fig. 2.5(a)]. Using this information, a simplifying choice
rcut = 1/2acc is used for the incommensurate system.
The onsite potential, V , was chosen by comparing the TB results to the bands from
the ab initio calculations. This was done by adopting the predicted bonding shown in Fig.
2.4(a). A constant V was assigned to those C atoms in the graphene layer that were bonded
to Si in the SiC surface. A large range of V were tested and the resulting band structure
using those V ’s was compared with the ab initio band structure. Perhaps surprisingly, it
was found that V ≈ (−4±2)t in the TB calculation best reproduced the ab intio bands[See
Fig. 2.4(d)]. The large range in V indicates that the tight binding model is robust and
that the key physics from the ab initio calculations are being represented. The agreement
and simplicity of this model immediately provides insight into the ab initio calculations. It
predicts the interaction between SiC and graphene should be strong, but at the same time
the π-bonds are preserved. Note competing interactions of similar strength is a tell-tale
sign of a possible incommensurate phase. Also, it predicts that effects such as strain in the
buffer graphene layer are at least second order to the Si-graphene interaction in describing
the band structure. While both calculations are in excellent agreement, they clearly do not
predict the ARPES semiconducting experimental bands plotted in Fig. 2.4(f).
The effect of modulation must be considered to describe the experimental band struc-
ture within this tight binding model. The bonding configuration and band structure was
calculated for many values of η(SiC). As may be expected, significant changes in bonding
configuration occur when the Si interface atoms are modulated according to eq. 2.1. As
such, significant changes occur in the band structure due to the strong coupling through
19
23. h(SiC)
=0.09aSiC
h(SiC)
=0.052aSiC
1
0
-1
-2
-3
E(eV)
Г K M
1
0
-1
-2
-3
E(eV)
Г K M
a b
c d
hSiC
(aSiC
)
0.1 0.2 0.3
BandGap(eV)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
e
Figure 2.6: Bonding and band structure dependence on η(SiC). (a) and (b) The large
(small) circles indicate unbonded (bonded) graphene to the Si below. As the modulation in
the SiC interface increases the bonding configuration changes. At η(SiC) = 0.052aSiC shown
in (a) the chain boundary of the unmodulated case broadened and opened a band gap of
0.26 eV shown in (c). At η(SiC) = 0.09aSiC shown in (b) the bonding becomes more like
graphene islands and a larger gap forms as shown in (d). (e) The calculated band gap as
a function of η(SiC). As η(SiC) increases, the graphene “island” develops and the band gap
increases to a value that appears to saturate. Dashed line shows the average value of η(SiC)
that produces a given gap.
20
24. the onsite potential. Figure 2.4(b) shows the bonding configuration using the experimental
η(SiC). The modulation descreases bonding to the graphene layer by nearly 40% compared
to the unmodulated case in Fig. 2.4(a). Half of the NC regions in the unmodulated struc-
ture convert into a large region of unpeturbed graphene “islands” that correspond to low
density regions in the SiC interface layer shown in Fig. 2.3. The graphene between the
islands, aligned with the high density boundaries, have a higher number of bonds to the
interface Si as might be expected.
The calculated semiconducting bands look remarkably similar to the measured ARPES
bands for the experimental η(SiC) = 0.11aSiC[See Fig. 2.4(f)]. The predicted band gap
is 0.8 eV as shown in the density of states (DOS) in Fig. 2.4(g) and is consistent with
previous STS measurements[39, 26]. Also, the predicted charge density from the three
highest occupied bands show weak localization at the island edges [See Fig. 2.4(c)] and give
rise to a charge density that strongly resembles previous STM measurements[29].
When studying a large range of η(SiC), it was found that graphene island formation and
subsequent band gap opening was a robust feature of the modulated system. Figure 2.6
(a)-(d) shows the bonding configuration and band structure for two additional values of
η(SiC) other than the experimental value. When η(SiC) < 0.1aSiC, the structure and band
gap are sensistive to small changes in η(SiC)[See Fig. 2.6(f)]. However, even in this range
graphene island formation is sufficient to open band gaps > 0.25 eV . When η(SiC) exceeds
0.1aSiC, a graphene island is fully formed and no significant change in bonding occurs up
to 0.36aSiC. In this range the band gap is largest and nearly constant.
The fact that the unbonded graphene “island” configuration is present for such a large
range of η(SiC)’s and that the opening of a bandgap is prevalent over this same range
lends a great deal of weight to the idea that the incommensurate system is responsible
for the buffer’s semiconducting properties. Coupling this to the fact that the calculated
band structure, using the experimental value of the modulation, reproduces the important
features of the experimentally measured bands supports the importance of the modulated
interface controlling the buffer’s electronic properties.
21
25. Figure 2.7: The effect of ML graphene growth on the buffer band structure. (a) ARPES
bands at the BGo layer K point (kx is perpendicular to ΓK, hν = 70 eV). A Dirac cone
from a 2%ML graphene layer is also visible. (b) A negative 2nd derivative filter of the BGo
bands in (a). (c) A similar 2nd derivative filter for a MG film. Red dashed lines mark the
approximate 0.4 eV shift of the buffer bands.
2.3 Buffer layer stability
Finally, the stability of the buffer layer is addressed. When a monolayer (MG) of graphene
forms above the buffer layer, there are changes in the buffer’s structure. The buffer with
MG on top is distinguished as BGML from the bare buffer layer BGo. Once the MG forms,
the satellite positions and the lattice constant become nearly commensurate (δ < 0.02) with
the bulk SiC [See Fig. 2.1(a) and (b)]. The MG lattice contracts relative to BGML making
the MG incommensurate with both the BGML and SiC. The lattice constants for the buffer
and MG systems are summarized in Table 2.1. Note that the MG lattice constant is nearly
that of theoretically isolated graphene and contracted from graphite. The contraction from
graphite is due to comparitively reduced interlayer interaction. Also, the MG interacts
with only one layer and the incommensuration reduces the interlayer coupling compared to
Bernal stacking. This contraction is analogous to non-Bernal stacked graphene layers on
C-face SiC [See Table 2.1].
3
This work
5
From Ref. [23].
4
Similar values were measured by Schumann et al., [41].
1
From Ref. [51, 52, 53].
2
From Refs. [31, 32, 34, 33].
22
26. Table 2.1: Comparisons of graphene lattice constants, their relative strain (∆a) compared
to theoretical graphene, RMS strain rms, and long range order
Graphene Form Lattice constant (˚A) ∆a (%) rms (%) Order (nm)
Theoretical MG 2.453(4)1 - - -
Graphite 2.460(2)2 +0.28 - -
BGo 2.469(3)3,4 +0.70 0.2 60
BGML 2.462(3)1,3 +0.40 0.6 43
MG 2.455(3)1,3 +0.10 0.3 43
C-Face multilayer 2.452(3)5 -0.04 - 300
There are two additional changes when the MG forms. First, the system becomes more
disordered (30% decrease in long range order) as evidenced by the broader satellite rods in
Fig. 2.1(a). Also, the BGML develops a large RMS strain, rms. RMS strain presents itself
as K-dependent broadening ( rms ≈ ∆K/K). The plot of ∆K vs. K in Fig. 2.1(c) shows
that BGML has the largest slope, i.e. the largest rms. The RMS strain in MG is smaller,
presumably due to strain relaxation allowed by weaker coupling to BGML. However, BGo
presents the lowest overall RMS strain.
It was assumed that the strong buffer-SiC interaction meant the buffer band structure
did not change significantly once the MG formed. Now that a structure change in the buffer
was demonstrated in Fig. 2.1 upon MG formation, it is prudent to revisit how or if the
BGML differs from BGo. Figure 2.7(a) shows the ARPES spectra from the BGo layer. The
π-bands are broad (∆k ∼ 0.35 ˚A
−1
) consistent with q ∼ 0.38 ˚A
−1
. In order to compare
the BGML bands with the BGo, we have plotted a 2nd derivative spectra of the buffer and
MG bands in Fig. 2.7(b) and (c). This compensates for both the ∆k broadening and the
photoelectron attenuations through the MG.
Figure 2.7(c) shows that the semiconducting π-bands are still present with the MG
above. Although the BGML bands intensity is weak, it is consistent with a complete buffer
layer after correcting for attenuation. There is, however a change in the BGML bands
compared to the BGo bands. The π-bands are pushed to lower binding energy by ∼0.4eV
compared to the BGo bands and the band near EF appears to have less dispersion than
the BGo case. While there is a small energy gap between the BGML layer bands and
EF , the experimental error could also support the BGML layer being metallic. Note that
23
27. η(SiC) < 0.05 aSiC (the uncertainty is due to the increased disorder in the BGML). The
low value of η(SiC) is consistent with a buffer layer structure closer to the commensurate
structure that would give rise to either a small gap or metallic bands. The fact that MG
is incommensurate with BGML provides new insight into why graphene grown on the Si-
face has historically lower mobilities than C-face graphene[4, 57, 58]. The incommensuration
may give rise to a quasi-random network of MG-BGML coupling that act to increase random
scattering and thus lower the mobility.
24
28. CHAPTER III
FUTURE WORK
The discovery of incommensurate mutual modulation in the buffer-SiC system has disrupted
the past forty years of understanding of graphene growth on SiC(0001). Its importance is
highlighted by its role in forming semiconducting graphene and reconciling experimental
and theorectical studies. Furthermore, finding semiconducting graphene in the buffer layer
comes at an appropriate time where many research programs have moved on to other less
favorable 2D materials that intrinsically possess a band gap. Graphene on SiC is an ideal
platform for graphene electronics and the semiconducting buffer provides a crucial missing
element. While significant progress has been made towards understanding and producing
the buffer layer, there are many exciting avenues for further exploration that will improve
our understanding of 2D materials and propel graphene from pure research to applications.
The origin of the incommensurate phase in BGo and why BGML becomes nearly com-
mensurate is unknown and can be explored further by detailed experimental studies. It is
not conclusive from initial SXRD measurements that the SiC interface is a bulk-terminated
reconstruction or one with adatoms, vacancies, or varied atomic concentrations. One tech-
nique available to address this questions is x-ray standing wave enhanced x-ray photoelec-
tron spectroscopy (XSW-XPS) that enables a layer by layer estimate of atomic concentra-
tions. XSW-XPS measurements have already been performed on UHV grown multilayer
graphene samples[42]. However, our measurements show that there is a structural change
when a monolayer forms above the buffer layer. As such, XSW-XPS measurements on a
bare buffer layer and monolayer using improved growth methods will provide insights into
the origin of the structural changes and the nature of the incommensurate phase.
Further detailed SXRD measurements of the buffer layer system can also give insight
into the incommensurate structure. Initial measurements focused on the in-plane modula-
tion period and amplitude. However, since the mutual modulation consists of at least two
25
29. layers, an investigation of out of plane modulation is needed and can be accomplished by l
scans of graphene, SiC and modulation related diffraction rods. Additionally, incommensu-
rate phases are known to have temperature dependence[49]. Characterizing the temperature
dependence through SXRD, ARPES and Raman measurements will provide insights into
the type of incommensurate system and the existence of different phases. STM measure-
ments will complement these studies and help take SXRD measurements beyond 1st order
estimates of density changes. Furthermore, recent STM measurements found substaintial
coverage of small particles above the buffer layer. What these particles are and how to
remove them will be critical towards producing a clean buffer layer for use in electronic de-
vices. The most recent set of SXRD measurements will assist in identifying these particles
by extracting the various bond lengths present in these particles. Chemical identification
will provide assistance in the proper surface treatment required to remove them.
A proper understanding of the buffer-SiC mutual modulation requires theoretical studies
to be carried out in tandem. The current tight binding study shows that SiC modulation can
induce band baps in graphene that are consistent with experimental ARPES bands. Also,
the comparable interaction strengths of graphene in-plane and interface interaction suggest
the possibility of an incommensurate phase. However, the buffer layer still requires more rig-
orous study through ab initio calculations. Currently, only relaxation of a bulk-terminated
SiC interface has been studied, but the SXRD measurements show that relaxation from a
modulated configuration should be considered as well. Unfortunately, ab initio calculations
alone may not be sufficient to understand the incommensuration. Most studies require the
imposition of some periodicity. Tight binding allows for the study of larger periodicities
more similar to the incommensurate structure. Therefore, a refinement of the tight binding
model from ab initio calculations is meritted in order to assist in studying the origin of the
incommensurate phase.
The CCS growth method provides substantial improvement in order and layer uniformity
over UHV growth. However, in the CCS design, the temperature and Si partial pressure are
linked by the crucible design. Developing new growth techniques that allow independent
exploration of temperature and Si partial pressure will allow for optimization of sample
26
30. order, the study of all buffer-SiC phases and potentially a platform for bandgap engineering.
Ultimately, the excitement surrounding the buffer layer is its potential for use in elec-
tronic devices. Key questions remain as to how to contact, gate, or dope the buffer layer and
if these processes changes its properties. For example, it was shown that the incommensu-
rate modulation results from a mutual interaction between graphene and the SiC interface.
It is unknown how sensitive the buffer may be to external influences such as the deposition
of a gate dielectric. The interaction with a gate or contact material may be strong as the
SiC interaction seems to partially sp3 hybridize the buffer. This may cause the buffer to
be more reactive and potential changes in the electronic structure of the buffer layer will
require carefull study. These effects can be characterized through SXRD measurements of a
buffer layer with a gate material deposited on top as well as ARPES if the photon energy is
high enough to penerate the gate or contact material. Whether or not buffer can be doped
can characterized by ARPES after sequential submonolayer depositions of K or Cs atoms
in UHV.
27
31. REFERENCES
[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V.
Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,”
Science 306, 666 (2004).
[2] C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov,
E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin Epitaxial Graphite: 2D
Electron Gas Properties and a Route toward Graphene-based Nanoelectronics,” The
Journal of Physical Chemistry B 108, 19912 (2004).
[3] A. K. Geim and K. Novoselov, “The rise of graphene,” Nature Mater. 6, 183 (2007)
0702595v1.
[4] C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N.
Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic Confinement
and Coherence in Patterned Epitaxial Graphene,” Science 312, 1191 (2006).
[5] P. R. Wallace, “The Band Theory of Graphite,” Phys. Rev. 71, 622 (1947).
[6] C. Coletti, S. Forti, A. Principi, K. V. Emtsev, A. A. Zakharov, K. M. Daniels,
B. K. Daas, M. V. S. Chandrashekhar, T. Ouisse, D. Chaussende, A. H. MacDon-
ald, M. Polini, and U. Starke, “Revealing the electronic band structure of trilayer
graphene on SiC: An angle-resolved photoemission study,” Phys. Rev. B 88, 155439
(2013).
[7] A. Gr¨uneis, C. Attaccalite, L. Wirtz, H. Shiozawa, R. Saito, T. Pichler, and A. Rubio,
“Tight-binding description of the quasiparticle dispersion of graphite and few-layer
graphene,” Phys. Rev. B 78, 205425 (2008).
[8] R. Saito, G. Dresselhaus, M. S. Dresselhaus, and Others, Physical properties of carbon
nanotubesvolume 35 (World Scientific, 1998).
28
32. [9] K. Wakabayashi, K.-i. Sasaki, T. Nakanishi, and T. Enoki, “Electronic states of
graphene nanoribbons and analytical solutions,” Science and Technology of Advanced
Materials 11, 54504 (2010).
[10] M. Vanevi´c, V. M. Stojanovi´c, and M. Kindermann, “Character of electronic states
in graphene antidot lattices: Flat bands and spatial localization,” Phys. Rev. B 80,
45410 (2009).
[11] V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, “Tight-binding approach to
uniaxial strain in graphene,” Phys. Rev. B 80, 45401 (2009).
[12] I. I. Naumov and A. M. Bratkovsky, “Gap opening in graphene by simple periodic
inhomogeneous strain,” Phys. Rev. B 84, 245444 (2011).
[13] D. Haberer, D. V. Vyalikh, S. Taioli, B. Dora, M. Farjam, J. Fink, D. Marchenko,
T. Pichler, K. Ziegler, S. Simonucci, M. S. Dresselhaus, M. Knupfer, B. B¨uchner, and
A. Gr¨uneis, “Tunable Band Gap in Hydrogenated Quasi-Free-Standing Graphene,”
Nano Letters 10, 3360 (2010).
[14] C. E. Horn, Y. S. Kim, A. Bostwick, E. Rotenberg, and K, “The formation of an energy
gap in graphene on ruthenium by controlling the interface,” New Journal of Physics
12, 33014 (2010).
[15] W. A. de Heer, C. Berger, M. Ruan, M. Sprinkle, X. Li, Y. Hu, B. Zhang, J. Hankinson,
and E. Conrad, “Large area and structured epitaxial graphene produced by confinement
controlled sublimation of silicon carbide,” Proc. Nat. Acad. of Sci. 108, 16900 (2011).
[16] A. J. V. Bommel, J. E. Crombeen, and A. V. Tooren, “LEED and Auger electron
observations of the SiC(0001) surface,” Surface Science 48, 463 (1975).
[17] K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney,
T. Ohta, S. A. Reshanov, J. Rohrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B.
Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure
graphitization of silicon carbide,” Nat Mater 8, 203 (2009).
29
33. [18] F. Owman and P. M˚artensson, “The SiC(0001) 6
√
3×6
√
3 reconstruction studied with
STM and LEED,” Surface Science 369, 126 (1996).
[19] K. V. Emtsev, F. Speck, T. Seyller, L. Ley, and J. D. Riley, “Interaction, growth,
and ordering of epitaxial graphene on SiC0001 surfaces: A comparative photoelectron
spectroscopy study,” Phys. Rev. B 77, 155303 (2008).
[20] J. Hass, W. A. de Heer, and E. H. Conrad, “The growth and morphology of epitaxial
multilayer graphene,” Journal of Physics: Condensed Matter 20, 323202 (2008).
[21] M.-H. Tsai, C. S. Chang, J. D. Dow, and I. S. T. Tsong, “Electronic contributions to
scanning-tunneling-microscopy images of an annealed β-SiC(111) surface,” Phys. Rev.
B 45, 1327 (1992).
[22] K. V. Emtsev, T. Seyller, F. Speck, L. Ley, P. Stojanov, J. D. Riley, and R. C. G. Leckey,
“Initial Stages of the Graphite-SiC(0001) Interface Formation Studied by Photoelectron
Spectroscopy,” Mat. Sci. Forum 556-557, 525 (2007).
[23] J. Hass, F. Varchon, J. E. Mill´an-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer,
C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why Multilayer Graphene on
4H-SiC(0001) Behaves Like a Single Sheet of Graphene,” Phys. Rev. Lett. 100, 125504
(2008).
[24] M. Sprinkle, J. Hicks, A. Tejeda, A. Taleb-Ibrahimi, P. L. F`evre, F. Bertran, H. Tinkey,
M. C. Clark, P. Soukiassian, D. Martinotti, J. Hass, and E. H. Conrad, “Multilayer epi-
taxial graphene grown on the SiC(000¯1) surface; structure and electronic properties,”
Journal of Physics D: Applied Physics 43, 374006 (2010).
[25] W. Strupinski, K. Grodecki, A. Wysmolek, R. Stepniewski, T. Szkopek, P. E. Gaskell,
A. Gr¨uneis, D. Haberer, R. Bozek, J. Krupka, and J. M. Baranowski, “Graphene
Epitaxy by Chemical Vapor Deposition on SiC,” Nano Letters 11, 1786 (2011).
30
34. [26] G. M. Rutter, N. P. Guisinger, J. N. Crain, E. A. A. Jarvis, M. D. Stiles, T. Li, P. N.
First, and J. A. Stroscio, “Imaging the interface of epitaxial graphene with silicon
carbide via scanning tunneling microscopy,” Phys. Rev. B 76, 235416 (2007).
[27] W. Chen, H. Xu, L. Liu, X. Gao, D. Qi, G. Peng, S. C. Tan, Y. Feng, K. P. Loh, and
A. T. S. Wee, “Atomic structure of the 6HSiC(0 0 0 1) nanomesh,” Surface Science
596, 176 (2005).
[28] Y. Qi, S. H. Rhim, G. F. Sun, M. Weinert, and L. Li, “Epitaxial Graphene on
SiC(0001): More than Just Honeycombs,” Phys. Rev. Lett. 105, 85502 (2010).
[29] C. Riedl, U. Starke, J. Bernhardt, M. Franke, and K. Heinz, “Structural properties of
the graphene-SiC(0001) interface as a key for the preparation of homogeneous large-
terrace graphene surfaces,” Phys. Rev. B 76, 245406 (2007).
[30] I. Forbeaux, J.-M. Themlin, and J.-M. Debever, “Heteroepitaxial graphite on 6H −
SiC(0001) : Interface formation through conduction-band electronic structure,” Phys.
Rev. B 58, 16396 (1998).
[31] J. B. Nelson and D. P. Riley, “The thermal expansion of graphite from 15◦C. to 800◦C.:
part I. Experimental,” Proceed. Phys. Soc. 57, 477 (1945).
[32] Y. Baskin and L. Meyer, “Lattice Constants of Graphite at Low Temperatures,” Phys.
Rev. 100, 544 (1955).
[33] A. A. Ahmadieh and H. A. Rafizadeh, “Dispersion Curves and Elastic Constants of
Graphite,” Phys. Rev. B 7, 4527 (1973).
[34] A. Bosak, M. Krisch, M. Mohr, J. Maultzsch, and C. Thomsen, “Elasticity of single-
crystalline graphite: Inelastic x-ray scattering study,” Phys. Rev. B 75, 153408 (2007).
[35] P. Mallet, F. Varchon, C. Naud, L. Magaud, C. Berger, and J.-Y. Veuillen, “Electron
states of mono- and bilayer graphene on SiC probed by scanning-tunneling microscopy,”
Phys. Rev. B 76, 41403 (2007).
31
35. [36] C. R. Starke, C. Coletti, and U, “Structural and electronic properties of epitaxial
graphene on SiC(0001): a review of growth, characterization, transfer doping and
hydrogen intercalation,” Journal of Physics D: Applied Physics 43, 374009 (2010).
[37] A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. For-
beaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decom-
position of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. of
Appl. Phys. 92, 5 (2002).
[38] J. Hass, J. E. Mill´an-Otoya, P. N. First, and E. H. Conrad, “Interface structure of
epitaxial graphene grown on 4H-SiC(0001),” Phys. Rev. B 78, 205424 (2008).
[39] S. Goler, C. Coletti, V. Piazza, P. Pingue, F. Colangelo, V. Pellegrini, K. V. Emtsev,
S. Forti, U. Starke, F. Beltram, and S. Heun, “Revealing the atomic structure of the
buffer layer between SiC(0 0 0 1) and epitaxial graphene,” Carbon 51, 249 (2013).
[40] M. S. Nevius, M. Conrad, F. Wang, A. Celis, M. N. Nair, A. Taleb-Ibrahimi, A. Tejeda,
and E. H. Conrad, “Semiconducting Graphene from Highly Ordered Substrate Inter-
actions,” Phys. Rev. Lett. 115, 136802 (2015).
[41] T. Schumann, M. Dubslaff, M. H. Oliveira, M. Hanke, J. M. J. Lopes, and H. Riechert,
“Effect of buffer layer coupling on the lattice parameter of epitaxial graphene on
SiC(0001),” Phys. Rev. B 90, 41403 (2014).
[42] J. D. Emery, B. Detlefs, H. J. Karmel, L. O. Nyakiti, D. K. Gaskill, M. C. Hersam,
J. Zegenhagen, and M. J. Bedzyk, “Chemically Resolved Interface Structure of Epi-
taxial Graphene on SiC(0001),” Phys. Rev. Lett. 111, 215501 (2013).
[43] F. Varchon, R. Feng, J. Hass, X. Li, B. N. Nguyen, C. Naud, P. Mallet, J.-Y. Veuillen,
C. Berger, E. H. Conrad, and L. Magaud, “Electronic Structure of Epitaxial Graphene
Layers on SiC: Effect of the Substrate,” Phys. Rev. Lett. 99, 126805 (2007).
[44] A. Mattausch and O. Pankratov, “Ab Initio Study of Graphene on SiC,” Phys. Rev.
Lett. 99, 76802 (2007).
32
36. [45] S. Kim, J. Ihm, H. J. Choi, and Y.-W. Son, “Origin of Anomalous Electronic Structures
of Epitaxial Graphene on Silicon Carbide,” Phys. Rev. Lett. 100, 176802 (2008).
[46] F. Varchon, P. Mallet, J.-Y. Veuillen, and L. Magaud, “Ripples in epitaxial graphene
on the Si-terminated SiC(0001) surface,” Phys. Rev. B 77, 235412 (2008).
[47] T. Cavallucci and V. Tozzini, “Multistable Rippling of Graphene on SiC: A Density
Functional Theory Study,” The Journal of Physical Chemistry C 120, 7670 (2016).
[48] G. Sclauzero and A. Pasquarello, “Carbon rehybridization at the graphene/SiC(0001)
interface: Effect on stability and atomic-scale corrugation,” Phys. Rev. B 85, 161405
(2012).
[49] H. Z. Cummins, “Experimental studies of structurally incommensurate crystal phases,”
Physics Reports 185, 211 (1990).
[50] J. M. Perez-Mato, G. Madariaga, and M. J. Tello, “Diffraction symmetry of incom-
mensurate structures,” Journal of Physics C: Solid State Physics 19, 2613 (1986).
[51] M. Weinert, E. Wimmer, and A. J. Freeman, “Total-energy all-electron density func-
tional method for bulk solids and surfaces,” Phys. Rev. B 26, 4571 (1982).
[52] H. S¸ahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and
S. Ciraci, “Monolayer honeycomb structures of group-IV elements and III-V binary
compounds: First-principles calculations,” Phys. Rev. B 80, 155453 (2009).
[53] S. Wang, “Studies of Physical and Chemical Properties of Two-Dimensional Hexagonal
Crystals by First-Principles Calculation,” J. Phys. Soc. of Japan 79, 64602 (2010).
[54] G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, “Negative thermal
expansion,” J. Phys: Cond. Mat. 17, R217 (2005).
[55] E. Vlieg, “Integrated Intensities Using a Six-Circle Surface X-ray Diffractometer,”
Journal of Applied Crystallography 30, 532 (1997).
33
37. [56] I. Deretzis, G. Calogero, G. G. N. Angilella, and A. L. Magna, “Role of basis sets on
the unfolding of supercell band structures: From tight-binding to density functional
theory,” EPL (Europhysics Letters) 107, 27006 (2014).
[57] F. Speck, J. Jobst, F. Fromm, M. Ostler, D. Waldmann, M. Hundhausen, H. B. Weber,
and T. Seyller, “The quasi-free-standing nature of graphene on H-saturated SiC(0001),”
Appl. Phys. Lett. 99, (2011).
[58] J. Jobst, D. Waldmann, F. Speck, R. Hirner, D. K. Maude, T. Seyller, and H. B.
Weber, “Quantum oscillations and quantum Hall effect in epitaxial graphene,” Phys.
Rev. B 81, 195434 (2010).
34