Resonance Approximation Research Articles

Review of resist-based flare measurement methods for extreme ultraviolet lithography

Flare (stray light) is an important effect impacting extreme ultraviolet lithography (EUVL) imaging system performance. Four flare measurement methods including Kirk, modulation transfer function, double exposure, and zonal ring approximation method are reviewed and analyzed theoretically. The point spread function of an EUV NXE:3100 exposure tool is extracted from the measured Kirk flare (KF) and fitted with a double-fractal model. The KF for this NXE:3100 tool is determined to be 8.5% for a 2-μm diameter absorber pad placed in a 12-mm outer radius bright field, which is larger than the previous 5% KF data measured by ASML and IMEC in 2011. The observation of the increased flare level in the NXE:3100 tool suggests that contamination of EUV optics may be a potential problem for EUVL manufacturing.

Nonlinear Rabi oscillations in a Bose-Einstein condensate

For a Bose-Einstein condensate in a trap with oscillating barriers, in the resonance approximation, evolution equations are derived. Their analytical solution reveals the existence of two fundamentally different types of nonlinear conservative Rabi oscillations: (i) with periodic temporal variation of moduli and phase difference of levels' amplitudes of probability, and (ii) with monotonic temporal variation of the phase difference. It is shown that the two types can be realized for the same parameters of the scheme, but for different initial conditions. Analytical predictions are confirmed by numerical solution to the Gross-Pitaevskii equation.

Light scattering by a 2D electron system with spin-orbit interaction in a strong magnetic field

We theoretically investigate light scattering by electrons of a 2D system in a strong magnetic field perpendicular to the plane of the system (the filling factor is smaller than two, i.e., only the states of the zeroth Landau level are filled). Analysis is carried out in the resonance approximation, in which the frequencies of the incident and scattered light are close to the effective separation between the conduction band and one of the branches of the valence band of the semiconductor. Spin splitting of the Landau level in the conduction band associated with Zeeman and the spin-orbit interactions is taken into account. The dynamic screening effects are considered in the random phase approximation (RPA).

Multiphoton resonant excitations and high-harmonic generation in bilayer graphene

The microscopic theory of bilayer graphene nonlinear interaction with coherent electromagnetic radiation is developed. The Liouville--von Neumann equation for a single-particle density matrix in the multiphoton resonant approximation is solved. We consider low-energy excitations of a Fermi-Dirac sea with THz pump radiation. The obtained solutions disclose Rabi oscillations and resonant multiphoton excitations of a Fermi-Dirac sea in bilayer graphene. On the basis of numerical simulations we examine the rates of high-harmonic radiation at particle-hole annihilation in the field of a strong pump wave. We show that in the THz domain of frequencies one can achieve efficient generation of high harmonics with pump waves of moderate intensities.

Postadiabatic Hamiltonian for low-energy excitations in a slowly-time-dependent BCS-BEC crossover

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate from a Bardeen-Cooper-Schrieffer state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field, our Hamiltonian includes the leading postadiabatic effects that arise because the crossover proceeds at a nonzero sweep rate. We apply a path-integral approach and a stationary phase approximation for the molecular $\mathbf{k}=\mathbf{0}$ background, which is a good approximation for narrow resonances [see, e.g., Diehl and Wetterich, Phys. Rev. A 73, 033615 (2006) as well as Diehl, Gies, Pawlowski, and Wetterich, Phys. Rev. A 76, 053627 (2007)]. We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the $\mathbf{k}\ensuremath{\ne}\mathbf{0}$ molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a postadiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs.

Plasmon excitations in photo- and electron impact ionization of fullerenes

We study collective electron excitations (also referred to as plasmons) in the C60 fullerene in the processes of photoionization and electron inelastic scattering. To reveal the contribution of collective electron excitations, we utilize the plasmon resonance approximation. It is shown that within this framework the photoionization cross section is described as a sum of two contributions, which represent two coupled modes of the surface plasmon. The electron energy loss spectra of C60 are described by three contributions, namely by the two modes of the surface plasmon and the volume plasmon. The results of calculations are in good agreement with experimental data on photoionization and electron inelastic scattering of C60. We show that the collective excitations play a significant role in the ionization process and provide a dominant contribution to the spectra.

Comparison of Quadrature Schemes in DOM for Anisotropic Scattering Radiative Transfer Analysis

The commonly implemented level-symmetric S N quadrature set for the discrete-ordinates method suffers from a limitation in discrete direction number to avoid physically unrealistic weighting factors. This limitation can have an adverse impact for determining radiative transfer, as directional discretization results in angular false scattering errors due to distortion of the scattering phase function in addition to the ray effect. To combat this limitation, several higher-order quadrature schemes with no directional limitation have been developed. Here, four higher-order quadrature sets (Legendre-equal weight, Legendre-Chebyshev, triangle tessellation, and spherical ring approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Heat fluxes obtained at low direction number are compared to the S N quadrature and Monte Carlo predictions to gauge and compare quadrature accuracy. Investigation into the reduction/elimination of angular false scattering with increase in direction number, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. It is found that while the higher-order quadrature sets are able to effectively minimize angular false scattering, the number of directions required is extremely large, and thus it is more computationally efficient to implement proper phase-function normalization to obtain accurate results.

Subgroup method with resonance interference factor table

Subgroup parameters based on the intermediate resonance (IR) approximation are generated by the constrained best fitting method to assure the positivity of the subgroup parameters, and the infinite mass scattering term introduced by the IR approximation is explicitly retained in the subgroup equation. The impact on the heterogeneous problem is investigated. To preserve the reference reaction rates obtained by the subgroup calculation, the Hébert SPH method is adopted. A resonance interference correction factor table is introduced to consider the resonance interference effect. The proposed resonance calculation method is tested on various problems, which cover homogeneous cases, 1D pin cell cases, as well as 2D assembly cases. It is demonstrated that (1) the proposed resonance interference factor table method can significantly reduce the error caused by resonance interference; (2) the SPH method can reduce the error of subgroup collapsing; (3) the infinite mass scattering term can significantly impact the result of a heterogeneous problem. Numerical results also revealed that all the three effects are in the same direction and add up to about 600 pcm reactivity increase, bringing a good consistency between the multi-group calculation and continuous energy Monte Carlo calculation.

Equilibrium of a system of superconducting rings in a uniform gravitational field

To construct a plasma trap with levitating magnetic coils in the thin ring approximation, we derive the expression for the potential energy of a system of several superconducting rings (one of which is fixed) capturing the preset flows in the uniform gravitational field as a function of the coordinates of the free ring (or rings). Calculations performed in the Mathcad system show that the potential energy of such a system has a local minimum for certain values of parameters. Stable levitation of a superconducting ring in the position corresponding to calculations is realized in the field of another superconducting ring, and this leads to the conclusion that a magnetic Galatea trap can be prepared on the basis of a levitating quadrupole.

Jet theoretical Yang-Mills energy in the geometric dynamics of two-dimensional monolayer

Langmuir-Blodgett (LB)-films consist of few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe a structurization into LB-monolayers. Consequently, we develop on the 1-jet space \documentclass[12pt]{minimal}\begin{document}$J^{1}([0,\infty ),\mathbb {R}^{2})$\end{document}J1([0,∞),R2) the single-time Lagrange geometry (in the sense of distinguished (d-) connection, d-torsions, and an abstract anisotropic electromagnetic-like d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer. One assumed that an expansion near singular points for the constructed geometrical Lagrangian theory describes phase transitions to LB-monolayer. Trajectories of particles in a field of the electrocapillarity forces of monolayer have been calculated in a resonant approximation utilizing a Jacobi equation. A jet geometrical Yang-Mills energy is introduced and some computer graphic simulations are exposed.

Permittivity of complex oxide crystals with allowance for spatial dispersion

The temporal and spatial dispersions of the permittivity of complex oxide crystals, which have numerous branches of dipole active oscillations, is considered. Formulas for calculating the susceptibility spectra of complex oxides in the terahertz region with allowance for both types of dispersion are obtained in the resonance approximation of photon-phonon interaction using quantum Green’s functions. The calculation results are used to discuss the well-known experimental data.

Prediction of Burst in Flexible Pipes

Usually when a large internal fluid pressure acts on the inner walls of flexible pipes, the carcass layer is not loaded, as the first internal pressure resistance is given by the internal polymeric layer that transmits almost all the loading to the metallic pressure armor layer. The last one must be designed to ensure that the flexible pipe will not fail when loaded by a defined value of internal pressure. This paper presents three different numerical models and an analytical nonlinear model for determining the maximum internal pressure loading withstood by a flexible pipe without burst. The first of the numerical models is a ring approximation for the helically rolled pressure layer, considering its actual cross section profile. The second one is a full model for the same structure, considering the pressure layer laying angle and the cross section as built. The last numerical model is a two-dimensional (2D) simplified version, considering the pressure layer as an equivalent ring. The first two numerical models consider contact nonlinearities and a nonlinear elastic-plastic material model for the pressure layer. The analytical model considers the pressure armor layer as an equivalent ring, taking into account geometrical and material nonlinear behaviors. Assumptions and results for each model are compared and discussed. The failure event and the corresponding stress state are commented.

A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach

We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self-consistent second-order approaches. We analyze the discrepancy between the noise calculated by our method and the exact Levitov formula for a simple non-interacting quantum dot model. Furthermore, we study the noise of the canyon of current suppression in a two-level dot, a phenomenon that requires the inclusion of electron–electron interaction as well as higher order tunneling processes.

Investigation of dominant states in the collisions of Ar VII and Kr XXIV with H_2 and He targets

In thermal plasma, the ion--atom collisions proceed most probably through resonance processes. One of the important processes is the resonant transfer excitation followed by emission of X-rays (RTEX), which causes self-cooling for plasma. In addition, it is identical to the dielectronic recombination (DR) in electron-ion collisions. The present work deals with the calculation of DR cross-sections (\sigma^{DR}s) and DR rate coefficients (\alpha^{DR}s) as well as RTEX cross-sections (\sigma^{RTEX}s) for Mg-like ions [Ar^{6+} and Kr^{24+}] with L-shell and K-shell excitation for \Deltan = 0 and \Delta n \neq 0. Comparison between the present results and other calculations for the rates are presented. RTEX cross-sections are calculated for the collision of Ar^{6+} and Kr^{24+} ions with He and H_2 targets. The calculations are carried out using the adapted angular momentum average scheme in the isolated resonance approximation.

Representation of spectral functions and thermodynamics

In this paper we study the question of effective field assignment to measured or nonperturbatively calculated spectral functions. The straightforward procedure is to approximate it by a sum of independent Breit-Wigner resonances, and assign an independent field to each of these resonances. The problem with this idea is that it introduces new conserved quantities in the free model (the new particle numbers), therefore it changes the symmetry of the system. We avoid this inconsistency by representing each quantum channel with a single effective field, no matter how complicated the spectral function is. Thermodynamical characterization of the system will be computed with this representation method, and its relation to the independent resonance approximation will be discussed.

The Effective Two-Particle Interaction of Cold Atoms as Derived from Bragg Scattering

We study the dynamic structure function of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We compare our result with the Bragg-scattering measurements in 85Rb by Papp et al. (Phys. Rev. Lett. 101:135301, 2008) and show that these experiments set very strict limits to the shape of the effective two-particle interaction ruling out the contact and hard spheres potentials. Using the Feshbach resonance approximation we derive the effective interaction, which turns out to be very similar to the soft spheres potential in momentum space. At large scattering lengths the interaction becomes universal and could be directly measured by Bragg scattering. We also discuss the experimental conditions needed for the appearance of the maxon-roton structure in the excitation spectrum and finally show that when the scattering length becomes larger than 2000 Bohr radii the uniform gas phase undergoes a phase transition into the density wave state.

Application of inversion techniques for bubble size spectra from attenuation measurements in lab-generated bubble distributions

The size distribution of a bubble population can be estimated from measurements of the frequency-dependent attenuation through the bubble cloud. These attenuation values are the inputs to an inversion method that makes use of a resonant bubble approximation wherein it is assumed that only resonant bubbles contribute to the attenuation at a given frequency, e.g., Caruthers et al., [JASA (1999)]. H. Czerski has shown that power law bubble distributions proportional to (radius)x, where x≤-2, have few enough large bubbles for resonant bubble inversion methods to yield accurate results. In this paper, the Caruthers and Czerski inversion methods are both verified with synthetic data and applied to acoustic measurements in a fresh water tank using lab-generated bubble distributions. Work sponsored by the Office of Naval Research, Code 321US.

Width of the chaotic layer: Maxima due to marginal resonances

Modern theoretical methods for estimating the width of the chaotic layer in the presence of prominent marginal resonances are considered in the perturbed pendulum model of nonlinear resonance. The fields of applicability of these methods are explicitly and precisely formulated. The comparative accuracy is investigated in massive and long-run numerical experiments. It is shown that the methods are naturally subdivided in classes applicable for adiabatic and nonadiabatic cases of perturbation. It is explicitly shown that the pendulum approximation of marginal resonance works well in the nonadiabatic case. In this case, the role of marginal resonances in determining the total layer width is demonstrated to diminish with increasing main parameter λ (equal to the ratio of the perturbation frequency to the frequency of small-amplitude phase oscillations on the resonance). Solely the "bending effect" is important in determining the total amplitude of the energy deviations of the near-separatrix motion at λ≳7. In the adiabatic case, it is demonstrated that the geometrical form of the separatrix cell can be described analytically quite easily by means of using a specific representation of the separatrix map. It is shown that the nonadiabatic (and, to some extent, intermediary) case is most actual, in comparison with the adiabatic one, for the physical or technical applications that concern the energy jumps in the near-separatrix chaotic motion.

Electron impact excitation rate coefficients for P-like Ni XIV

We have calculated the atomic data including electron impact excitations and radiative decays among the lowest 143 fine-structure levels arising from 3s23p3, 3s3p4, 3s23p23d, 3p5, 3s3p33d, and 3s23p3d2 configurations in P-like Ni XIV. Direct excitation collision strengths are calculated employing the relativistic distorted-wave method. Resonances are included via the isolated resonance approximation using distorted-waves. Resonance contributions from S-like [3s23p3, 3s3p4, 3s23p23d,3p5, 3s3p33d,3s23p3d2, 3p43d,3s3p23d2,3s23d3]n′l′ complex series are taken into account. Effective collision strengths are reported over an electron temperature range of 1.0×105–1.0×108 K.

Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation

Nonlinear dynamics of the establishment of electron-hole coherent superposition states in graphene by multiphoton resonant excitation of interband transitions in laser fields is considered. The single-particle time-dependent density matrix for such a quantized system is calculated in the multiphoton resonant approximation. The dependence of Rabi oscillations of the Fermi-Dirac sea in graphene on the time, momentum, and photon number at multiphoton laser excitation is analyzed.