Raman scattering of nanocrystalline silicon embedded in SiO2

Raman scattering of nanocrystalline silicon embedded in SiO₂ matrix is systematically investigated. It is found that the Raman spectra can be well fitted by 5 Lorentzian lines in the Raman shift range of 100–600 cm⁻¹. The two-phonon scattering is also observed in the range of 600–1100 cm⁻¹. The experimental results indicate that the silicon crystallites in the films consist of nanocrystalline phase and amorphous phase; both can contribute to the Raman scattering. Besides the red-shift of the first order optical phonon modes with the decreasing size of silicon nanocrystallites, we have also found an enhancement effect on the second order Raman scattering, and the size effect on their Raman shift     

Optical properties of nanocrystalline silicon embedded in SiO2

Nanocrystalline silicon embedded SiO₂ matrix has been formed by annealing the a-SiO_x films fabricated by plasma enhanced chemical vapor deposition technique. Absorption and photoluminescence spectra of the films have been studied in conjunction with micro-Raman scattering spectra. It is found that absorption presents an exponential dependence of absorption coefficient to photon energy in the range of 1.5–3.0 eV, and a sub-band appears in the range of 1.0–1.5 eV. The exponential absorption is due to the indirect band-to-band transition of electrons in silicon nanocrys-tallites, while the sub-band absorption is ascribed to transitions between surfaces and/or defect states of the silicon nanocrystallites. The existence of Stokes shift between absorption and photoluminescence suggests that the phonon-assisted luminescence would be enhanced due to the quantum confinement effects.     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

The Inverse Scattering Transform for the Benjamin–Ono Equation

We extend the inverse scattering transform (IST) for the Benjamin–Ono (BO) equation, given by A. S. Fokas and M. J. Ablowitz ( Stud. Appl. Math. 68:1, 1983), in two important ways. First, we restrict the IST to purely real potentials, in which case the scattering data and the inverse scattering equations simplify. Second, we extend the analysis of the asymptotics of the Jost functions and the scattering data to include the nongeneric classes of potentials, which include, but may not be limited to, all N -soliton solutions. In the process, we also study the adjoint equation of the eigenvalue problem for the BO equation, from which, for real potentials, we find a very simple relation between the two reflection coefficients (the functions β(λ) and f (λ)) introduced by Fokas and Ablowitz. Furthermore, we show that the reflection coefficient also defines a phase shift, which can be interpreted as the phase shift between the left Jost function and the right Jost function. This phase shift leads to an analogy of Levinson's theorem, as well as a condition on the number of possible bound states that can be contained in the initial data. For both generic and nongeneric potentials, we detail the asymptotics of the Jost functions and the scattering data. In particular, we are able to give improved asymptotics for nongeneric potentials in the limit of a vanishing spectral parameter. We also study the structure of the scattering data and the Jost functions for pure soliton solutions, which are examples of nongeneric potentials. We obtain remarkably simple solutions for these Jost functions, and they demonstrate the different asymptotics that nongeneric potentials possess. Last, we show how to obtain the infinity of conserved quantities from one of the Jost functions of the BO equation and how to obtain these conserved quantities in terms of the various moments of the scattering data.     

Asymptotics of the scattering phase for the Dirac operator: High energy, semi-classical and non-relativistic limits

In this paper we prove several results for the scattering phase (spectral shift function) related with perturbations of the electromagnetic field for the Dirac operator in the Euclidean space. Many accurate results are now available for perturbations of the Schrödinger operator, in the high energy regime or in the semi-classical regime. Here we extend these results to the Dirac operator. There are several technical problems to overcome because the Dirac operator is a system, its symbol is a 4×4 matrix, and its continuous spectrum has positive and negative values. We show that we can separate positive and negative energies to prove high energy asymptotic expansion and we construct a semi-classical Foldy-Wouthuysen transformation in the semi-classical case. We also prove an asymptotic expansion for the scattering phase when the speed of light tends to infinity (non-relativistic limit).     

Note on Asymptotic Solutions of the Korteweg-de Vries Equation with Solitons

The long time asymptotic solution of the Korteweg-de Vries equation containing both solitons and the dispersive wavetrain is described. It is shown that a soliton interacts elastically both with the dispersive wavetrain and with other solitons. An explicit formula for the phase shift produced upon interaction is given. These ideas also apply to other nonlinear evolution equations solvable by the inverse scattering transform.     

Classical propagators of quadratic quantum systems

A new quantum mechanical formalism based on the probability representation of states is applied to ions in traps and stimulated Raman scattering. Explicit expressions are found for the classical propagators of a free particle, a harmonic oscillator, an ion in the Paul trap, an ion in the Penning trap, and stimulated Raman scattering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 285–296, November, 1999.     

3D FEA of Size Effects in Deformation of Thin Metallic Films

The purpose of this work is to analyze size effects in the deformation occurring during nanoindentation-tests of thin metallic films on ceramic substrates. It is well known that classical phenomenological theories of plasticity are hardly applicable in cases of very small dimensions of a body [1]. Thus, the dependency of the mechanical behavior of thin films on the thickness can not be studied in the framework of classical theories. In order to simulate numerically the deformation, a specific material model has been chosen which is able to account for size effects. It bases on the theory of ”Mechanism Strain Gradient” (MSG) plasticity [2] in conjunction with the deformation theory of plasticity. The material model has been implemented via the user defined element subroutine (UEL) in the commercial FE code ABAQUS/Standard as a ten-node tetrahedron-element. With the developed subroutine the deformation of thin copper films on Si substrates during nanoindentation-tests has been simulated. Different material models of the indentor (rigid and elastic) as well as different friction conditions between the film and the pyramidal indentor were tested. Furthermore, the influence of an additional oxide layer on the films surface has been analysed. In order to verify the numerical investigations, results from nanoindentation experiments have been used for comparison [4]. The FE simulations for different thicknesses in the range of 100-600nm showed a very good agreement with the experiments. In particular, the size dependency of the force-displacement curves, calculated by using the developed subroutine, is in rather good agreement with experiments. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ensemble Monte Carlo study of nonequilibrium carrier dynamics in photo-excited p-i-n structures

Light scattering from conduction electrons (or from valence holes) can give information on the time-resolved velocity distribution of nonequilibrium carriers. The experimental approach utilizes, e.g., Raman scattering from the single particles to ascertain the velocity distribution. Calculation of the distribution function through an ensemble Monte Carlo technique allows a comparison between the experiment and theory. Here, this is demonstrated with studies of a GaAs p-i-n structure embedded within cladding AlAs layers. The calculations are compared with experimental results that have recently been published on the same structure. For time scales of several hundred femtoseconds, the hot carrier transport that is probed by the single-particle Raman scattering is dominated by the transport in the Γ valley, and overshoot velocities 4–5 × 10⁵ cm/sec are observed.     

Recovering asymptotics of metrics from fixed energy scattering data

The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on Rⁿ from fixed energy scattering data is studied. It is shown that if two such metrics, g₁,g₂, have scattering data at some fixed energy which are equal up to smoothing, then there exists a diffeomorphism N 'fixing infinity' such that N^*g₁-g₂ is rapidly decreasing. Given the scattering matrix at two energies, it is shown that the asymptotics of a metric and a short range potential can be determined simultaneously. These results also hold for a wide class of scattering manifolds.     

Structure and magnetic properties of nanocrystalline ferromagnets (I)

The role of effective anisotropy in nanocrystalline ferromagnets is investigated. These alloys are prepared by annealing amorphous ribbons and have excellent soft magnetic properties. A two-phase model is established considering the role of the intergranular amorphous phase. The results indicate a strong dependence of effective anisotropy on the structure and magnetic parameters of the amorphous phase as well as on the size of a grains. In view of the new model, the magnetic hardening beyond the optimally annealing temperature seems to be ascribed to the deterioration in magnetic properties of interfacial amorphous phase.     

Controlling unpredictability in the randomly driven Hénon–Heiles system

Noisy scattering dynamics in the randomly driven Hénon–Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time distributions, how an external perturbation, be it dissipation or periodic forcing with a random phase, can enhance or mitigate the unpredictability of a system that exhibit chaotic scattering. In fact, if basin boundaries have the Wada property, predictability becomes very complicated, since the basin boundaries start to intermingle, what means that there are points of different basins close to each other. The main responsible of this unpredictability is the external forcing with random phase, while the dissipation can recompose the basin boundaries and turn the system more predictable. Therefore, we do the necessary simulations to find out the values of dissipation and external forcing for which the exit basins present the Wada property. Through these numerical simulations, we show that the presence of the Wada basins have a specific relation with the damping, the forcing amplitude and the energy value. Our approach consists on investigating the dynamics of the system in order to gain knowledge able to control the unpredictability due to the Wada basins.     

Microstructure of a-SiOx:H

A set of a-SiO_x:H (0.52 <x< 1.58) films are fabricated by plasma-enhanced-chemical-vapor-deposition (PECVD) method at the substrate temperature of 250°C. The microstructure and local bonding configurations of the films are investigated in detail using micro-Raman scattering, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It is found that the films are structural inhomogeneous, with five phases of Si, Si₂O:H, SiO:H, Si₂O₃:H and SiO₂ that coexist. The phase of Si is composed of nonhydrogenated amorphous silicon (a-Si) clusters that are spatially isolated. The average size of the clusters decreases with the increasing oxygen concentration x in the films. The results indicate that the structure of the present films can be described by a multi-shell model, which suggests that a-Si cluster is surrounded in turn by the subshells of Si₂O:H, SiO:H, Si₂O₃:H, and SiO₂.     

Formation of nanocrystalline Fe73.5Cu1Nb3Si13.5B9 alloy under high pressure

The formation of nanocrystalline Fe_73.5 Cu₁Nb₃Si_13.5 B₉ alloy by annealing an amorphous Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy at a temperature of 823 K under pressures in the range of 1–5 GPa is investigated by using X-ray diffraction, electron diffraction, and transmission electron microscopy. The high pressure experiments are carried out in belt-type pressure apparatus. Experimental results show that the initial crystalline phase in these annealed alloys is a-Fe solid solution (named a-Fe phase below), and high pressure has a great influence on the crystallization process of the a-Fe phase. The grain size of the a-Fe phase decreases with the increase of pressure (P). The volume fraction of the a-Fe phase increases with increasing the pressure as the pressure is below 2 GPa, and then decreases (Pδ2 GPa). The mechanism for the effects of the high pressure on the crystallization process of amorphous Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy is discussed Project supported by the National Natural Science Foundation of China (Grant No. 19674070) and the Natural Science Foundation of Hebei Province.     

Spectral distributions for long range perturbations

We study distributions which generalize the concept of spectral shift function, for pseudo-differential operators on . We call such distributions spectral distributions. Relations between relative scattering determinants and spectral distributions are established; they lead to the definition of regularized scattering phase. These relations are analogous to the usual one for the standard spectral shift function. We give several asymptotic properties in the high energy and semiclassical limits where both nontrapping and trapping cases are considered. In particular, we prove Breit-Wigner formulae for the regularized scattering phases, for semiclassical Schrödinger operators with long-range potentials.     

Microstructure of a-SiOx:H

A set of a-SiO_x:H (0.52 <x< 1.58) films are fabricated by plasma-enhanced-chemical-vapor-deposition (PECVD) method at the substrate temperature of 250°C. The microstructure and local bonding configurations of the films are investigated in detail using micro-Raman scattering, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It is found that the films are structural inhomogeneous, with five phases of Si, Si₂O:H, SiO:H, Si₂O₃:H and SiO₂ that coexist. The phase of Si is composed of nonhydrogenated amorphous silicon (a-Si) clusters that are spatially isolated. The average size of the clusters decreases with the increasing oxygen concentration x in the films. The results indicate that the structure of the present films can be described by a multi-shell model, which suggests that a-Si cluster is surrounded in turn by the subshells of Si₂O:H, SiO:H, Si₂O₃:H, and SiO₂.     

Dark solitons in N-coupled higher order nonlinear Schrödinger equations

By considering the third order dispersion, self-steepening and stimulated Raman scattering effects, we analyse the dark soliton propagation in N-coupled higher order nonlinear Schrödinger equations. Using Painlevé analysis, we prove that this system is completely integrable. The result is confirmed further by the presentation of Lax pair. Using the Hirota method, the construction of soliton solution is discussed.     

The Evolution of a Nonlinear Critical Level

The evolution of inviscid forced Rossby waves on a parallel flow in the presence of a critical layer is discussed. It is shown that the transient critical layer becomes nonlinear after sufficient time has elapsed and that the “? π” logarithmic phase shift is modified accordingly. All harmonics are found to be important in the nonlinear range, even outside the critical layer.