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The Landauer-Büttiker (LB) formalism is widely used to simulate transport properties at equilibrium. The applications range from 1D conductors such as nanowires, nanotubes, nanoribbons, to 3D conductors such as molecular junctions with two or more contacts. At the ab initio level, this LB formalism is quite practical thanks to the Fisher–Lee relation, which connects the Landauer expression to the Green's function formalism. The transport properties of a given material can be simulated by finding the Green's function of the system within DFT (or even MBPT).
In this appendix the Green's function formalism is briefly reviewed. Section C.1 provides an introduction with a derivation of the trace formula starting from the Lippmann–Schwinger equations, then Section C.2 discusses recursive Green's function techniques, while Dyson's equation is introduced and applied to the case of a disordered system in Section C.3. Finally, Section C.4 is devoted to the implementation of LB formalism in conventional ab initio codes in order to investigate coherent electronic transport in nanoscale devices.
Phase-coherent quantum transport and the Green's function formalism
Green's functions are one of the most useful tools (Economou, 2006) for calculation of different physical quantities of interest such as the density of states or the quantum conductance and conductivity. In the context of phase-coherent quantum transport, they play a crucial role because their relation with the scattering matrix can be exploited to compute the quantum transmission probabilities as needed within the Landauer–Büttiker formalism presented in Section 3.3.
Once deemed impossible to exist in nature, graphene, the first truly two-dimensional nanomaterial ever discovered, has rocketed to stardom since being first isolated in 2004 by Nobel Laureates Konstantin Novoselov and Andre K. Geim of the University of Manchester. Graphene is a single layer of carbon atoms arranged in a flat honeycomb lattice. Researchers in high energy physics, condensed matter physics, chemistry, biology, and engineering, together with funding agencies, and companies from diverse industrial sectors, have all been captivated by graphene and related carbon-based materials such as carbon nanotubes and graphene nanoribbons, owing to their fascinating physical properties, potential applications and market perspectives.
But what makes graphene so interesting? Basically, graphene has redefined the limits of what a material can do: it boasts record thermal conductivity and the highest current density at room temperature ever measured (a million times that of copper!); it is the strongest material known (a hundred times stronger than steel!) yet is highly mechanically flexible; it is the least permeable material known (not even helium atoms can pass through it!); the best transparent conductive film; the thinnest material known; and the list goes on …
A sheet of graphene can be quickly obtained by exfoliating graphite (the material that the tip of your pencil is made of) using sticky tape. Graphene can readily be observed and characterized using standard laboratory methods, and can be mass-produced either by chemical vapor deposition (CVD) or by epitaxy on silicon carbide substrates.
As described in Chapter 1, the sp2 carbon-based family exhibits a great variety of allotropes, from the low-dimensional fullerenes, nanotubes and graphene ribbons, to two-dimensional monolayer graphene, or stacked graphene multilayers. Two-dimensional monolayer graphene stands as the building block, since all the other forms can be derived from it. Graphene nanoribbons can be seen as quasi-one-dimensional structures, with one lateral dimension short enough to trigger quantum confinement effects. Carbon nanotubes can be geometrically constructed by folding graphene nanoribbons into cylinders, and graphite results from the stacking of a very large number of weakly bonded graphene monolayers.
The isolation of a single graphene monolayer by mechanical exfoliation (repeated peeling or micromechanical cleavage) starting from bulk graphite has been actually quite a surprise, since it was previously believed to be thermodynamically unstable (Novoselov et al., 2004, Novoselov et al., 2005b). At the same time, the route for controlling the growth of graphene multilayers on top of silicon carbide by thermal decomposition was reported, and eventually led to fabrication of single graphene monolayers of varying quality depending on the surface termination (silicon or carbon termination) (Berger et al., 2006). Basic electronic properties of graphene were actually well-known since the seminal work by Wallace in the late forties (Wallace, 1947), such as the electron–hole symmetry of the band structure and the specific linear electronic band dispersion near the Brillouin zone corners (Dirac point), but it was after the discovery of carbon nanotubes by Iijima from NEC (Iijima, 1991) that the exploration of electronic properties of graphene-based materials was revisited (for a review see Charlier, Blase & Roche 2007).
Over the last few decades, there has been a significant increase in the use of computational simulation within the scientific community. Through a combination of the phenomenal boost in computational processing power and continuing algorithm development, atomistic scale modeling has become a valuable asset, providing a useful insight into the properties of atoms, molecules, and solids on a scale “often inaccessible” to traditional experimental investigation.
Atomistic simulations can be divided into two main categories, quantum mechanical calculations and classical calculations based on empirical parameters. Quantum mechanical simulations (often referred to as ab initio or first-principles) aims at solving the many-body Schrödinger equation (Schrödinger, 1926). The original reformulation of the Schrödinger equation offered by the DFT provides valuable information on the electronic structure of the system studied.
The very essence of DFT is to deal with noncorrelated single-particle wavefunctions. Many of the chemical and electronic properties of molecules and solids are determined by electrons interacting with each other and with the atomic nuclei. In DFT, the knowledge of the average electron density of the electrons at all points in space is enough to determine the total energy from which other properties of the system can also be deduced. DFT is based on the one-electron theory and shares many similarities with the Hartree–Fock method. DFT is presently the most successful and promising (also the most widely used) approach to computing the electronic structure of matter. In this appendix, the basics of DFT modeling techniques are explained.
We describe a new protocol for testing coating/substrate interfacial failures through compression loading of micro-pillars containing an inclined interface region, experimentally realized in the TiN/Ti/Si(100) system. Interfacial failures were achieved through direct compression loading in the axial direction, which yielded reproducible failure stresses which exhibited little dependence on the pillar diameter. The testing protocol lends itself to high-resolution analysis of failure surfaces, and is conducive to correlating interfacial structure and chemistry with mechanical failures within the coating/substrate interfacial region.
The paper describes a new technique of molten salt synthesis (MSS) that is based on the direct oxidation of halide ions with molecular oxygen in thermally stable halide melts to prepare nanoparticles of complex oxides. Lithium cobaltate (LiCoO2) was chosen as a model compound for testing this method. Synthesis was achieved in LiCl–CoCl2 melts at 600 and 700 °C, respectively, under a dry-air atmosphere. Fourier transform infrared (FTIR) and Raman spectroscopies, x-ray diffraction (XRD), and transmission electron microscopy (TEM) were used to study the products obtained. The route suggested results in the formation of stoichiometric high-temperature (HT) LiCoO2 powders.
Clotrimazole (C22H17ClN2, 1-[(2-chlorophenyl)(diphenyl)methyl]-1H-imidazole) and fluconazole (C13H12F2N6, 2-(2,4-difluorophenyl)-1,3-bis(1H-1,2,4-triazole-1-yl)propan-2-ol) are two active pharmaceutical ingredients commonly used in the treatment and prevention of superficial and systemic fungal infections. The X-ray powder diffraction data and the unit cell parameters of anhydrous clotrimazole [Triclinic, P${\bar 1}$, a = 8.776(1) Å, b = 10.571(2) Å, c = 10.622(3) Å, α = 114.08(2)°, β = 96.87(2)°, γ = 97.61(2)°, V = 875.2(2) Å3, Z = 2] and monohydrated fluconazole [Triclinic, P${\bar 1}$, a = 5.6353(4) Å, b = 11.753(1) Å, c = 12.326(1) Å, α = 71.220(8)°, β = 79.896(9)°, γ = 84.35(1)°, V = 760.13(9) Å3, Z = 2] are reported.
Electron-withdrawing halogen atoms are often bonded to the surface of carbon nanotubes to assist in the conversion from metallic to semiconducting properties. Single-walled carbon nanotubes (SWCNTs) were surface modified using UV photolysis with: (i) a broad band of wave lengths from approximately 250 to 400 nm having a maximum intensity at approximately 300 nm for photolysis of Cl2, (ii) low-pressure Hg lamps emitting 253.7 nm photons for photo-decomposition of HBr, and (iii) low-pressure Hg lamps emitting both 253.7 and 184.9 nm for photo-dissociation of HCl and HBr, respectively, and analyzed by x-ray photoelectron spectroscopy. Chlorine atoms adhered more readily than bromine atoms with the π-conjugation of the SWCNTs. The dominant increase with treatment was observed in the singly bonded chlorine moiety. Chlorine atoms, generated by UV photolysis of Cl2, produced a higher Cl saturation level of approximately 36 at.% than previously observed for multi-walled carbon nanotubes (13 at.%).The degree of chlorination depended on the amount of oxygen on the surface of the SWCNTs. Photo-dissociation of gaseous HCl and HBr showed lower amounts of halogenation on SWCNTs (approximately 5.8 at.% Cl and 2.5 at.% Br, respectively) than photolysis of Cl2.
To date graphene and graphene-derived materials have created an immense research interests due to its extraordinary physical, chemical, and physiochemical properties, which delineated graphene as an outstanding material for future electronics, optics, and energy-harvesting devices. Typically, graphene has high mobility and optical transparency along with excellent mechanical properties and chemical inertness. Single-layer graphene exhibits ultrahigh optical transmissivity (∼98%), which allows passing through wide range of light wave lengths, thus designated as an ever-reported material for an optically conducting window. Furthermore, graphene's optical, electrical, and electrocatalytic properties can be tuned by applying different chemical functionalization protocols, which make it one of the most suitable candidates for advanced applications in optoelectronic and energy-harvesting devices. This review is intended to summarize the most important experimental results from the recent publications concerning the fascinating properties of graphene electrodes and their applications in various types of solar cells. Furthermore, the state of the art of different graphene synthesis processes and functionalization for the applications in solar cells are also discussed in this review.
A theoretical model of nanovoid nucleation at triple junctions in nanocrystalline materials is developed in this article. The sliding of grain boundaries (GBs) meeting at triple junctions, which can be attributed to the gliding of GB dislocations (GBDs), provides the driving force for nanovoid nucleation. The GB sliding is accommodated by the emission of partial dislocations from GBs as well as GB diffusion. The corresponding energy characteristics of the pile-ups of GBDs, the emission of partial dislocations from the GBs, and GB diffusion are calculated, respectively. Furthermore, an energy balance method to calculate the nucleation of nanovoid at triple junctions is studied. The analysis demonstrates that the nucleation of the triple junction nanovoid depends mainly on the applied stress, the GB length (length of the pile-up), the GB structures, and the GB sliding accommodations.
The bulge test was used to investigate the fatigue properties of gold thin films with a thickness between 100 and 300 nm. The membranes were pressurized at a rate of 0.2 Hz up to 105 times, during which their stress and strain states were continuously recorded. Gold films on a silicon nitride substrate were cyclically loaded into tension and compression. Due to the presence of the substrate, no membrane failure was observed, but the residual stress shifted from an initially tensile state to an increasingly compressive one. Typical fatigue damage mechanisms consisting of extrusions were found in some large grains. Freestanding films were cyclically loaded in pure tension until failure occurred. The data acquired during the fatigue tests show a strong ratcheting of the films, which is indicative of cyclic plastic creep. Microstructural investigations clearly show grain boundary sliding in very thin films with columnar grains extending through the thickness.
Barium strontium titanate (BST) glass-ceramics were fabricated via controlled crystallization with different crystallization routes. Effects of the microwave crystallization and microwave treatment on the microstructure and energy storage properties of the glass-ceramics were systematically investigated. Results showed that microwave crystallization can increase the dielectric constant. In addition, it was found that the microwave process had little impact on the crystallinity (about 90 wt%), but preferred the crystallization of SrAl4O7. Most importantly, the dielectric breakdown strength (BDS) of the glass ceramics was significantly improved from 561.3 to 791.4 kV/cm by the microwave crystallization. And it can be further enhanced to 900.0 kV/cm by conventional crystallization combined with microwave treatment. The corresponding energy densities of samples derived from the microwave processes were increased to 1.05 and 1.13 J/cm3, respectively, compared with the sample fabricated by the conventional crystallization route (0.47 J/cm3).
Nanoporous tungsten oxide films were synthesized by an anodic oxidation process in aqueous NaF/HF electrolytes. The tungsten films were deposited by the radio frequency magnetron sputtering method on sapphire substrates, and the anodic oxidation process was conducted in a dual-electrode reaction chamber with graphite electrode. The effects of processing parameters (anodic voltage, time, temperature, and the operation distance) on the morphology and porosity of the synthesized films were investigated experimentally. The samples were characterized by x-ray diffraction and scanning electron microscopy. The results showed that the pore diameter and porosity increased gradually with increasing anodic voltage, whereas the “wall” of the pore was subjected to electric breakdown at 60 V, and the pore diameter and porosity decreased. The pore diameter and porosity showed an early increased and later decreased state as the operation time and distance are increased. The sensitive response in the resistive method is reaction-dominated type and is exhibited as a linear relationship as a function of hydrogen gas concentration. The response toward 500 ppm hydrogen in air is up to 15.1 with a response time of 10 min at 200 °C.
In the present study, we report an activation and enhancement of room temperature ferromagnetism in pure ZnO and V-doped ZnO (Zn0.95V0.05O and Zn0.90V0.10O) thin films by trioctylphosphine (TOP) functionalization. X-ray diffraction patterns show a slight decrease in the intensity of the diffraction peak on TOP functionalization. Atomic force micrographs of pure and V-doped ZnO films reveal no disorder in the film surface on TOP functionalization. The chemical bond formation of TOP on ZnO film surface was examined by x-ray photoelectron spectroscopy measurements. Photoluminescence measurements of TOP-functionalized ZnO films show enhancements of UV emission and quenching of visible emission. TOP-functionalized ZnO films reveal enhanced ferromagnetic behavior as evidenced from vibrating sample magnetometer measurements.
The oxidant peroxo method (OPM) exhibits several advantage and unique characteristics not found in the traditional methods for the synthesis of lead- and bismuth-based oxides. First of all, it is a clean method based on hydrogen peroxide that matches perfectly with the green chemistry approach. Second, the oxidizing local atmosphere provided by the precursor during its crystallization is unique among all the wet chemical techniques of synthesis, which usually result in reducing environment. Besides these advantages, only a few studies have focused on the use of the OPM to obtain better materials, which makes this field of study an excellent opportunity for the development of materials with higher purity and controlled morphologies.
Phonon thermal conduction was explored and discussed through a combined theoretical and simulation approach in this work. The thermal conductivity κ of polycrystalline graphene was calculated by molecular dynamics simulations based on a hexagonal patch model in close consistency with microstructural characterization in experiments. The effects of grain size, alignment, and temperature were identified with discussion on the microscopic phonon scattering mechanisms. The effective thermal conductivity was found to increase with the grain size and decrease with the mismatch angle and dislocation density at the grain boundaries (GBs). The ∼T−1 temperature dependence of κ is significantly weakened in the polycrystals. The effect of GBs in modifying thermal transport properties of graphene was characterized by their effective width and thermal conductivity as an individual phase, which was later included in a predictive effective medium model that showed degraded reduction in thermal conductivity for grains larger than a few micrometers.