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Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.

Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Elliptic. --- Green's Function. --- Parabolic. --- Partial Differential Equation.

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As CMOS scaling is approaching the fundamental physical limits, a wide range of new nanoelectronic materials and devices have been proposed and explored to extend and/or replace the current electronic devices and circuits so as to maintain progress with respect to speed and integration density. The major limitations, including low carrier mobility, degraded subthreshold slope, and heat dissipation, have become more challenging to address as the size of silicon-based metal oxide semiconductor field effect transistors (MOSFETs) has decreased to nanometers, while device integration density has increased. This book aims to present technical approaches that address the need for new nanoelectronic materials and devices. The focus is on new concepts and knowledge in nanoscience and nanotechnology for applications in logic, memory, sensors, photonics, and renewable energy. This research on nanoelectronic materials and devices will be instructive in finding solutions to address the challenges of current electronics in switching speed, power consumption, and heat dissipation and will be of great interest to academic society and the industry.

quantum mechanical --- n/a --- neuromorphic computation --- off-current (Ioff) --- double-gate tunnel field-effect-transistor --- topological insulator --- back current blocking layer (BCBL) --- CMOS power amplifier IC --- information integration --- distributed Bragg --- spike-timing-dependent plasticity --- electron affinity --- enhancement-mode --- current collapse --- gallium nitride (GaN) --- band-to-band tunneling --- vertical field-effect transistor (VFET) --- ionic liquid --- luminescent centres --- thermal coupling --- vision localization --- PC1D --- UAV --- ZnO/Si --- dual-switching transistor --- memristor --- field-effect transistor --- higher order synchronization --- shallow trench isolation (STI) --- memristive device --- on-current (Ion) --- low voltage --- reflection transmision method --- dielectric layer --- source/drain (S/D) --- high efficiency --- nanostructure synthesis --- InAlN/GaN heterostructure --- supercapacitor --- high-electron mobility transistor (HEMTs) --- heterojunction --- p-GaN --- recessed channel array transistor (RCAT) --- gate field effect --- charge injection --- saddle FinFET (S-FinFET) --- L-shaped tunnel field-effect-transistor --- conductivity --- energy storage --- hierarchical --- PECVD --- sample grating --- MISHEMT --- bistability --- threshold voltage (VTH) --- bandgap tuning --- oscillatory neural networks --- UV irradiation --- Mott transition --- third harmonic tuning --- topological magnetoelectric effect --- cross-gain modulation --- 2D material --- solar cells --- silicon on insulator (SOI) --- Green’s function --- optoelectronic devices --- semiconductor optical amplifier --- ZnO films --- graphene --- AlGaN/GaN --- polarization effect --- two-photon process --- conductive atomic force microscopy (cAFM) --- 2DEG density --- vanadium dioxide --- interface traps --- potential drop width (PDW) --- pattern recognition --- drain-induced barrier lowering (DIBL) --- atomic layer deposition (ALD) --- normally off power devices --- gate-induced drain leakage (GIDL) --- insulator–metal transition (IMT) --- zinc oxide --- synaptic device --- subthreshold slope (SS) --- landing --- silicon --- corner-effect --- conditioned reflex --- quantum dot --- gallium nitride --- bismuth ions --- conduction band offset --- variational form --- Green's function --- insulator-metal transition (IMT)

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This book of Molecules is dedicated to Professor John B. Goodenough (born July 25, 1922, Jena, Germany), an American physicist, who won the 2019 Nobel Prize for Chemistry for his work on developing lithium-ion batteries.

structure --- bonding --- physical properties --- collective or localized electrons --- exchange integral --- p-magnetism --- boron sub-oxide --- interstitial atoms --- DFT --- DOS --- ELF --- charge density plots --- bifunctional catalyst --- hybrid catalyst --- oxygen reduction reaction --- oxygen evolution reaction --- four-electron pathway --- lithium ionic conductor --- perovskite structure --- solid electrolyte --- oxide --- lithium-sulfur batteries --- tungsten oxide nanowire --- interlayer --- thiosulfate mediator --- Keywords: spin exchange --- magnetic orbitals --- ligand p-orbital tails --- M–L–M exchange --- M–L…L–M exchange --- α-CuV2O6 --- LiCuVO4 --- (CuCl)LaNb2O7 --- Cu3(CO3)2(OH)2 --- spin Hamiltonian --- magnetism --- energy-mapping analysis --- four-state method --- Green’s function method --- magnetic ground state --- spin exchange --- magnetic anisotropy --- molecular anion --- MPS3 --- qualitative rules --- batteries --- positive electrode --- vanadium phosphates --- covalent vanadyl bond --- mixed anion --- density functional theory --- quantum Monte Carlo --- fast Li+ ion conductor --- Li-ion battery --- spinel --- solid-state battery --- cathode-electrolyte interface --- indigo carmine --- solid polymer electrolyte --- solid state battery --- LMP® technology --- organic battery --- layered oxide cathodes --- alkali–alkali interactions --- electronic structure --- Li diffusion --- defect engineering --- perovskite electrolyte --- lithium-ion battery --- migration pathway --- anisotropic response --- cathode --- polyanion --- high-voltage --- n/a --- M-L-M exchange --- M-L...L-M exchange --- Green's function method --- alkali-alkali interactions

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In the last few years, the leading semiconductor industries have introduced multi-gate non-planar transistors into their core business. These are being applied in memories and in logical integrated circuits to achieve better integration on the chip, increased performance, and reduced energy consumption. Intense research is underway to develop these devices further and to address their limitations, in order to continue transistor scaling while further improving performance. This Special Issue looks at recent developments in the field of nanowire field-effect transistors (NW-FETs), covering different aspects of the technology, physics, and modelling of these nanoscale devices.

random dopant --- drift-diffusion --- variability --- device simulation --- nanodevice --- screening --- Coulomb interaction --- III-V --- TASE --- MOSFETs --- Integration --- nanowire field-effect transistors --- silicon nanomaterials --- charge transport --- one-dimensional multi-subband scattering models --- Kubo–Greenwood formalism --- schrödinger-poisson solvers --- DC and AC characteristic fluctuations --- gate-all-around --- nanowire --- work function fluctuation --- aspect ratio of channel cross-section --- timing fluctuation --- noise margin fluctuation --- power fluctuation --- CMOS circuit --- statistical device simulation --- variability effects --- Monte Carlo --- Schrödinger based quantum corrections --- quantum modeling --- nonequilibrium Green’s function --- nanowire transistor --- electron–phonon interaction --- phonon–phonon interaction --- self-consistent Born approximation --- lowest order approximation --- Padé approximants --- Richardson extrapolation --- ZnO --- field effect transistor --- conduction mechanism --- metal gate --- material properties --- fabrication --- modelling --- nanojunction --- constriction --- quantum electron transport --- quantum confinement --- dimensionality reduction --- stochastic Schrödinger equations --- geometric correlations --- silicon nanowires --- nano-transistors --- quantum transport --- hot electrons --- self-cooling --- nano-cooling --- thermoelectricity --- heat equation --- non-equilibrium Green functions --- power dissipation

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In this book, we aim to address the ever-advancing progress in microelectronic device scaling. Complementary Metal-Oxide-Semiconductor (CMOS) devices continue to endure miniaturization, irrespective of the seeming physical limitations, helped by advancing fabrication techniques. We observe that miniaturization does not always refer to the latest technology node for digital transistors. Rather, by applying novel materials and device geometries, a significant reduction in the size of microelectronic devices for a broad set of applications can be achieved. The achievements made in the scaling of devices for applications beyond digital logic (e.g., high power, optoelectronics, and sensors) are taking the forefront in microelectronic miniaturization. Furthermore, all these achievements are assisted by improvements in the simulation and modeling of the involved materials and device structures. In particular, process and device technology computer-aided design (TCAD) has become indispensable in the design cycle of novel devices and technologies. It is our sincere hope that the results provided in this Special Issue prove useful to scientists and engineers who find themselves at the forefront of this rapidly evolving and broadening field. Now, more than ever, it is essential to look for solutions to find the next disrupting technologies which will allow for transistor miniaturization well beyond silicon’s physical limits and the current state-of-the-art. This requires a broad attack, including studies of novel and innovative designs as well as emerging materials which are becoming more application-specific than ever before.

FinFETs --- CMOS --- device processing --- integrated circuits --- silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFETs) --- solid state circuit breaker (SSCB) --- prototype --- circuit design --- GaN --- HEMT --- high gate --- multi-recessed buffer --- power density --- power-added efficiency --- 4H-SiC --- MESFET --- IMRD structure --- power added efficiency --- 1200 V SiC MOSFET --- body diode --- surge reliability --- silvaco simulation --- floating gate transistor --- control gate --- CMOS device --- active noise control --- vacuum channel --- mean free path --- vertical air-channel diode --- vertical transistor --- field emission --- particle trajectory model --- F–N plot --- space-charge-limited currents --- 4H-SiC MESFET --- simulation --- power added efficiency (PAE) --- new device --- three-input transistor --- T-channel --- compact circuit style --- CMOS compatible technology --- avalanche photodiode --- SPICE model --- bandwidth --- high responsivity --- silicon photodiode --- AlGaN/GaN HEMTs --- thermal simulation --- transient channel temperature --- pulse width --- gate structures --- band-to-band tunnelling (BTBT) --- tunnelling field-effect transistor (TFET) --- germanium-around-source gate-all-around TFET (GAS GAA TFET) --- average subthreshold swing --- direct source-to-drain tunneling --- transport effective mass --- confinement effective mass --- multi-subband ensemble Monte Carlo --- non-equilibrium Green’s function --- DGSOI --- FinFET --- core-insulator --- gate-all-around --- field effect transistor --- GAA --- nanowire --- one-transistor dynamic random-access memory (1T-DRAM) --- polysilicon --- grain boundary --- electron trapping --- flexible transistors --- polymers --- metal oxides --- nanocomposites --- dielectrics --- active layers --- nanotransistor --- quantum transport --- Landauer–Büttiker formalism --- R-matrix method --- nanoscale --- mosfet --- quantum current --- surface transfer doping --- 2D hole gas (2DHG) --- diamond --- MoO3 --- V2O5 --- MOSFET --- reliability --- random telegraph noise --- oxide defects --- SiO2 --- split-gate trench power MOSFET --- multiple epitaxial layers --- specific on-resistance --- device reliability --- nanoscale transistor --- bias temperature instabilities (BTI) --- defects --- single-defect spectroscopy --- non-radiative multiphonon (NMP) model --- time-dependent defect spectroscopy --- n/a --- F-N plot --- non-equilibrium Green's function --- Landauer-Büttiker formalism