Comparative Study of Energy Quantization Approaches in Nanoscale MOSFETs

An analytical model has been developed to study inversion layer quantization in the ultra thin oxide MOS （metal oxide semiconductor） structures using variation and triangular well approaches.Accurate modeling of the inversion charge density using the continuous surface potential equations has been done.No approximation has been taken to model the inversion layer quantization process.The results show that the variation approach describes inversion layer quantization process accurately as it matches well with the BSIM 5 （Berkeley short channel insulated gate field effect transistor model 5） results more closely compared with triangular well approach.

Quantization of light energy directly from classical electromagnetic theory in vacuum

It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.

Quantization of the Kinetic Energy of Deterministic Chaos

In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.

Analytical Modeling of Source-to-Drain Tunneling in Nanoscale Silicon MOSFET

Sub-10-nm bulk n-MOSFET （metal-oxide -semiconductor field effect transistor） direct source-to- drain tunneling current density using Wentzel- Krammers-Brillouin 0NKB） transmission tunneling theory has been simulated. The dependence of the source-to-drain tunneling current on channel length and barrier height is examined. Inversion layer quantization, band-gap narrowing, and drain induced barrier lowering effects have been included in the model. It has been observed that the leakage current density increases severely below 4 nm channel lengths, thus putting a limit to the scaling down of the MOSFETs. The results match closely with the numerical results already reported in literatures.

Analytical Modeling of Quantum Mechanical Tunneling in Germanium Nano-MOSFETS

A simple analytical model has been developed to study quantum mechanical effects （QME） in a germanium substrate MOSFET （metal oxide semiconductor field effect transistor）, which includes gate oxide tunneling considering the energy quantization effects in the substrate. Some alternate high dielectric constant materials to reduce the tunneling have also been studied. By comparing with the numerically reported results, the results match well with the existing reported work.

Coulomb Interaction between Electrons and a New Concept of Atom

It is shown that the approximation of a strong Coulomb interaction between electrons results in a new model of the atom with a spatial quantization of electrons accompanied by their quantization in energy. This model implies that electrons rotate in circular orbits centered outside the atomic nucleus and only orbit axes pass through it. The Coulomb interaction between electrons leads to a spherically symmetric distribution of their orbits on the surfaces of equipotential spheres of a spherically symmetric electrostatic field of the nucleus. The distribution is similar to “inscribing” electron orbits into faces of regular nucleus-centered polyhedra so each polyhedron corresponds to a certain electron state (s, p, d, f), and a certain set of polyhedra corresponds to a certain period of the Mendeleev Table. It is shown that a spherically symmetric distribution of electron orbits gives rise to the formation of electron pairs in which electron orbits with a common axis are located symmetrically with respect to the nucleus and the orbital magnetic moments of the electrons are oppositely directed. The physical meaning of the electron spin concept becomes clear. The spin turns out to be related to the orbital magnetic moment of an electron and reflects the fact that two electrons of a pair rotate in opposite directions relative to their common axis. So the spin is one of characteristics of the electron state in the atom associated with electron rotation in the orbit centered outside the nucleus. The atomic model gives an insight into the periodicity of changes in the atomic properties with increasing nuclear charge and the reasons for an electron double energy quantization associated with different states and periods. The model shows that the atomic structure and properties can be explained by using concepts of classical mechanics and classical electrodynamics which regard the electron as a particle.

Stochastic Chaos of Exponential Oscillons and Pulsons

An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the Helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagonal, and external group oscillons, a random energy pulson, random internal, diagonal, and external energy oscillons, and a random cumulative energy pulson.

Quantization for an evolution equation with critical exponential growth on a closed Riemann surface

In this paper, we analyze the concentration behavior of a positive solution to an evolution equation with critical exponential growth on a closed Riemann surface, and particularly derive an energy identity for such a solution. This extends a result of Lamm-Robert-Struwe and complements that of Yang.

Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects

Quantum effects are predominant in tri-gate MOSFETs, so a model should be developed. For the first time, this paper presents the analytical model for quantization effects of thin film silicon tri-gate MOSFETs by using variational approach. An analytical expression of the inversion charge distribution function（ICDF） or wave function for the tri-gate MOSFETs has been obtained. This obtained ICDF is used to calculate the important device parameters, such as the inversion charge centroid and inversion charge density. The results are validated against with the simulation data.

Modeling and simulation of centroid and inversion charge density in cylindrical surrounding gate MOSFETs including quantum effects

An analytical model for surrounding gate metal-oxide-semiconductor field effect transistors （MOS- FETs） considering quantum effects is presented. To achieve this goal, we have used a variational approach for solving the Poisson and Schrodinger equations. This model is developed to provide an analytical expression for the inversion charge distribution function for all regions of the device operation. This expression is used to calculate the other important parameters like the inversion charge centroid, threshold voltage and inversion charge density. The calculated expressions for the above parameters are simple and accurate. The validity of this model was checked for the devices with different device dimensions and bias voltages. The calculated results are compared with the simulation results and they show good agreement.

Modified Nonlinear Model of Arcsin-Electrodynamics

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed.We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.