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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.

History of engineering & technology --- 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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The many-faceted efforts to understand the structure and interactions of atoms over the past hundred years have contributed decisively and dramatically to the explosive development of physics. There is hardly a branch of modern physical science that does not in some seminal way rely on the fundamental principles and mathematical and experimental insights that derive from these studies. In particular, the drive to understand the singular features of the hydrogen atom--simultaneously the archetype of all atoms and the least typical atom--spurred many of the twentieth century's advances in physics and chemistry. This book gives an in-depth account of the author's own penetrating experimental and theoretical investigations of the hydrogen atom, while simultaneously providing broad lessons in the application of quantum mechanics to atomic structure and interactions. A pioneer in the combined use of atomic accelerators and radiofrequency spectroscopy for probing the internal structure of the hydrogen atom, Mark Silverman examines the general principles behind this far-reaching experimental approach. Fast-moving protons are directed into gas or foil targets from which they capture electrons to become hydrogen atoms moving uniformly at very high speeds. During their rapid passage through the spectroscopy chamber of the atomic accelerator, these atoms reveal by the light they emit fascinating details of their internal configuration and the interactions that created them. Silverman examines the effects of radiofrequency fields on the hydrogen atom clearly and systematically, explaining the details of these interactions at different levels of complexity and refinement, each level illuminating the physical processes involved from different and complementary perspectives. Readers interested in diverse areas of physics and physical chemistry will appreciate both the theoretical and practical implications of Silverman's studies and the personal style with which he relays them. This is a work of not only an outstanding research physicist, but a fine teacher who understands how curiosity underlies all science.

Atomic structure. --- Back-Goudsmit effect. --- Bohr magneton. --- Bohr radius. --- Clebsch-Gordan coefficient. --- Dirac zeta function. --- Doppler broadening. --- Fermi contact interaction. --- Fermi golden rule. --- Gaussian lineshape. --- Green's function. --- Hermitian operator. --- Huygen's principle. --- Laplace equation. --- Pauli spin matrices. --- Ramsay method. --- Stark effect. --- Thomas precession. --- acceleration potential. --- angular distribution function. --- annihilation operator. --- anticommutator. --- antiresonant frequency. --- basis states. --- coherence terms. --- collisional broadening. --- counter-rotating frame. --- density matrix. --- detection operator. --- diamagnetic interaction. --- efficiency matrix. --- eigenvalue problem. --- extraction potential. --- field mode density. --- fine structure constant. --- gas target. --- gyromagnetic ratio. --- helicity. --- impedance mismatch. --- interaction representation. --- level anticrossing. --- lineshape narrowing. --- occupation probabilities. --- optical signal function. --- paraxial ray equation. --- periodic table. --- polarization of the vacuum. --- power saturation curve. --- quantum interference. --- quantum numbers. --- reflection coefficient. --- resonant frequency. --- selection rules.

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This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.

Research & information: general --- Mathematics & science --- fractional derivative --- generalized Mittag-Leffler kernel (GMLK) --- Legendre polynomials --- Legendre spectral collocation method --- dynamical systems --- random time change --- inverse subordinator --- asymptotic behavior --- Mittag–Leffler function --- data fitting --- magnetization --- magnetic fluids --- Gamma function --- Psi function --- Pochhammer symbol --- hypergeometric function 2F1 --- generalized hypergeometric functions tFu --- Gauss’s summation theorem for 2F1(1) --- Kummer’s summation theorem for 2F1(−1) --- generalized Kummer’s summation theorem for 2F1(−1) --- Stirling numbers of the first kind --- Hilfer–Hadamard fractional derivative --- Riemann–Liouville fractional derivative --- Caputo fractional derivative --- fractional differential equations --- inclusions --- nonlocal boundary conditions --- existence and uniqueness --- fixed point --- gamma function --- Beta function --- Mittag-Leffler function --- Generalized Mittag-Leffler functions --- generalized hypergeometric function --- Fox–Wright function --- recurrence relations --- Riemann–Liouville fractional calculus operators --- (α, h-m)-p-convex function --- Fejér–Hadamard inequality --- extended generalized fractional integrals --- Mittag–Leffler functions --- initial value problems --- Laplace transform --- exact solution --- Chebyshev inequality --- Pólya-Szegö inequality --- fractional integral operators --- Wright function --- Srivastava’s polynomials --- fractional calculus operators --- Lavoie–Trottier integral formula --- Oberhettinger integral formula --- fractional partial differential equation --- boundary value problem --- separation of variables --- Mittag-Leffler --- Abel-Gontscharoff Green’s function --- Hermite-Hadamard inequalities --- convex function --- κ-Riemann-Liouville fractional integral --- Dirichlet averages --- B-splines --- dirichlet splines --- Riemann–Liouville fractional integrals --- hypergeometric functions of one and several variables --- generalized Mittag-Leffler type function --- Srivastava–Daoust generalized Lauricella hypergeometric function --- fractional calculus --- Hermite–Hadamard inequality --- Fox H function --- subordinator and inverse stable subordinator --- Lamperti law --- order statistic --- n/a --- Gauss's summation theorem for 2F1(1) --- Kummer's summation theorem for 2F1(−1) --- generalized Kummer's summation theorem for 2F1(−1) --- Hilfer-Hadamard fractional derivative --- Riemann-Liouville fractional derivative --- Fox-Wright function --- Riemann-Liouville fractional calculus operators --- Fejér-Hadamard inequality --- Mittag-Leffler functions --- Pólya-Szegö inequality --- Srivastava's polynomials --- Lavoie-Trottier integral formula --- Abel-Gontscharoff Green's function --- Riemann-Liouville fractional integrals --- Srivastava-Daoust generalized Lauricella hypergeometric function --- Hermite-Hadamard inequality

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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

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The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.Originally published in 1960.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Riemann surfaces. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Surfaces, Riemann --- Functions --- Analytic function. --- Axiom of choice. --- Basis (linear algebra). --- Betti number. --- Big O notation. --- Bijection. --- Bilinear form. --- Bolzano–Weierstrass theorem. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Branch point. --- Canonical basis. --- Cauchy sequence. --- Cauchy's integral formula. --- Characterization (mathematics). --- Coefficient. --- Commutator subgroup. --- Compact space. --- Compactification (mathematics). --- Conformal map. --- Connected space. --- Connectedness. --- Continuous function (set theory). --- Continuous function. --- Coset. --- Cross-cap. --- Dirichlet integral. --- Disjoint union. --- Elementary function. --- Elliptic surface. --- Exact differential. --- Existence theorem. --- Existential quantification. --- Extremal length. --- Family of sets. --- Finite intersection property. --- Finitely generated abelian group. --- Free group. --- Function (mathematics). --- Fundamental group. --- Green's function. --- Harmonic differential. --- Harmonic function. --- Harmonic measure. --- Heine–Borel theorem. --- Homeomorphism. --- Homology (mathematics). --- Ideal point. --- Infimum and supremum. --- Isolated point. --- Isolated singularity. --- Jordan curve theorem. --- Lebesgue integration. --- Limit point. --- Line segment. --- Linear independence. --- Linear map. --- Maximal set. --- Maximum principle. --- Meromorphic function. --- Metric space. --- Normal operator. --- Normal subgroup. --- Open set. --- Orientability. --- Orthogonal complement. --- Partition of unity. --- Point at infinity. --- Polyhedron. --- Positive harmonic function. --- Principal value. --- Projection (linear algebra). --- Projection (mathematics). --- Removable singularity. --- Riemann mapping theorem. --- Riemann surface. --- Semi-continuity. --- Sign (mathematics). --- Simplicial homology. --- Simply connected space. --- Singular homology. --- Skew-symmetric matrix. --- Special case. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Taylor series. --- Theorem. --- Topological space. --- Triangle inequality. --- Uniform continuity. --- Uniformization theorem. --- Unit disk. --- Upper and lower bounds. --- Upper half-plane. --- Weyl's lemma (Laplace equation). --- Zorn's lemma.