Showing papers on "Brillouin zone published in 1991"

Photonic band structure: The face-centered-cubic case employing nonspherical atoms.

Abstract: We introduce a practical, new, face-centered-cubic dielectric structure which simultaneously solves two of the outstanding problems in photonic band structure. In this new ``photonic crystal'' the atoms are nonspherical, lifting the degeneracy at the W point of the Brillouin zone, and permitting a full photonic band gap rather than a pseudogap. Furthermore, this fully three-dimensional fcc structure lends itself readily to microfabrication on the scale of optical wavelengths. It is created by simply drilling three sets of holes 35.26\ifmmode^\circ\else\textdegree\fi{} off vertical into the top surface of a solid slab or wafer, as can be done, for example, by chemical-beam-assisted ion etching.

Ab initio calculation of phonon dispersions in semiconductors

Abstract: The density-functional linear-response approach to lattice-dynamical calculations in semiconductors is presented in full detail. As an application, we calculate complete phonon dispersions for the elemental semiconductors Si and Ge, and for the III-V semiconductor compounds GaAs, AlAs, GaSb, and AlSb. Our results are in excellent agreement with experiments where available, and provide predictions where they are not. As a byproduct, we obtain real-space interatomic force constants for these materials, which are useful both for interpolating the dynamical matrices through the Brillouin zone, and as ingredients of approximate calculations for mixed systems such as alloys and microstructures. The possibility of studying these systems using the force constants of the pure materials relies on the so-called mass approximation, B i.e., on neglecting the dependence of the force constants upon composition. The accuracy of such an approximation is tested and found to be very good for cationic intermixing in binary semiconductors, while it is less so for anionic substitutions. The situation is intermediate in the case of elemental semiconductors.

The Physics of Phonons

Abstract: Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.

Precise density-functional method for periodic structures

Abstract: A density-functional method for calculations on periodic systems (periodicity in one, two, or three dimensions) is presented in which all aspects of numerical precision are efficiently controlled. Highly accurate and rapidly converging strategies have been implemented for (a) the computation of Hamiltonian matrix elements (by a numerical integration method based on a partitioning of space and application of product Gauss rules), (b) the approximation of integrals over the Brillouin zone (by the quadratic tetrahedron method), (c) the evaluation and processing of the Coulomb potential (via a density-fitting procedure), and (d) the expansion of one-particle states in suitable basis functions (numerical atomic orbitals, Slater-type exponential functions, and plane waves). Absolute precision and convergence are demonstrated for all these aspects and show that the method is a well-suited tool for unambiguous investigations of the density-functional approximation itself. Attention is given, in particular, to basis-set questions. Although the method is of the mixed-basis type, it is demonstrated that plane waves are not necessary; this holds for metals as well as for insulators and semiconductors. By a general prescription, sequences of accurate linear-combination-of-atomic-orbital (LCAO) basis sets can be defined that systematically approach the basis-set limit. This enables the routine application of the inherently efficient LCAO method to all kinds of systems. Exemplary calculations are performed on bulk Si-, g-C (graphite), Na, Ni, Cu, and NaCl, and on a hexagonal monolayer of weakly interacting ${\mathrm{O}}_{2}$ molecules.

Calculated elastic constants and deformation potentials of cubic SiC.

Abstract: The full-potential linear-muffin-tin-orbital method in combination with the local-density-functional theory is used to calculate the equilibrium lattice constant, the cohesive energy, the bulk modulus and its pressure derivative, the elastic constants, the Kleinman internal displacement parameter \ensuremath{\zeta} the zone-center transverse-optical-phonon frequency, its Gr\"uneisen parameter and the corresponding energy-band strain, and optical-mode deformation potentials of cubic SiC. The results for equilibrium properties and the transverse-optical phonon at the center of the Brillouin zone are shown to be in good agreement with the available experimental data and previous first-principles calculations. The elastic constants of 3C-SiC are transformed to a trigonal symmetry tensor along the 〈111〉 direction, which allows a comparison to experimental data on hexagonal SiC. The agreement is found to be good. The elastic constants are also shown to be in good agreement with experimental data on the Young's and shear moduli and the Poisson ratio for polycrystalline SiC and with the Young's modulus of 3C-SiC whiskers along the 〈111〉 direction, which is related to the theoretical cleavage strength. Predictions are also made for the deformation potentials, which have not yet been measured. The discrepancies with previous atomic-sphere-approximation calculations for the trigonal strain and optical-mode deformation potentials indicate the importance of nonspherical terms in the potential for these deformations. The absolute deformation potential of the valence-band maximum is computed by means of a heterojunction calculation between strained and unstrained materials. This procedure is shown to give good agreement with previous calculations for Si.

Phonon attenuation and velocity measurements in transparent materials by picosecond acoustic interferometry

Abstract: A detailed analysis of the method of picosecond acoustic interferometry to study attenuation and velocity of longitudinal acoustic phonons in transparent materials in the Brillouin frequency range with picosecond laser pulses is presented. Experimental results for fused quartz from 90 to 300 K show good agreement with previous Brillouin scattering data. Measurements on a borosilicate glass (Corning 7059) and sapphire have also been made. This method makes these measurements possible under conditions where conventional approaches are not applicable.

Mean-field approach to magnetic ordering in highly frustrated pyrochlores.

Abstract: The metal atoms in the pyrochlore system of compounds ({ital A}{sub 2}{ital B2}O{sub 7}, where {ital A} and {ital B} are metals) form an infinite three-dimensional network of corner-sharing tetrahedra with cubic symmetry. For antiferromagnetic nearest-neighbor interactions and only {ital B} atoms magnetic, there is a very high degree of frustration, and no long-range order is predicted in the absence of further neighbor interactions. A general form of the mean-field theory is developed for dealing with {ital n}-component classical vector spins on any lattice. Calculations for the pyrochlore problem show that the Fourier modes of the system are completely degenerate for all wave vectors in the first Brillouin zone. In some cases further neighbor interactions will select the {bold q}={bold 0} or incommensurate modes. A comparison is made with long-range order known to exist in the pyrochlore form of FeF{sub 3}. The highly degenerate ordered phases of more complicated systems, where both {ital A} and {ital B} atoms are magnetic, will also be discussed. A comparison is made of the corner-sharing tetrahedral lattice and the more familiar stacked triangular antiferromagnets, with regard to the degree of frustration in both systems. Results for the Kagome lattice and the square lattice withmore » crossings, which are the two-dimensional analogs of the corner-sharing tetrahedral lattice, are also briefly discussed.« less

Graphitic interlayer states: A carbon K near-edge x-ray-absorption fine-structure study

Abstract: We have measured the carbon K near-edge x-ray-absorption fine structure of graphite by transmission, electron yield, and fluorescence yield. A rounded and prominent peak is identified in the near-edge spectrum, among the other well-known spectral features. With the aid of a full-potential linearized augmented-plane-wave band calculation, this feature is interpreted as originating from interlayer states in low-symmetry regions of the Brillouin zone. This finding is relevant to interpreting the near-edge structure of graphite intercalation compounds specially of the alkali-metal type.

Phonon dispersion of the bcc phase of group-IV metals. III. bcc hafnium

Abstract: The phonon dispersion of the high-temperature bcc phase of Hf has been measured. The dispersion resembles very much those of the other group-IV metals: bcc Ti and bcc Zr. It is dominated by the low-energy L 2/3(1,1,1) mode and by the low-energy T{sub 1} ({xi}{xi}0) phonon branch with transverse (1{bar 1}0) polarization. These large-amplitude vibrations displace the lattice toward the stacking sequence of the high-pressure {omega} structure and the low-temperature hcp structure, respectively, and are interpreted as dynamical precursor fluctuations toward these low-symmetry phases within the high-symmetry bcc phase.

Electronic structure of the rocksalt-structure semiconductors ZnO and CdO.

Abstract: ZnO, which normally occurs in the hexagonal wurtzite structure, can be transformed to the cubic rocksalt (NaCl) structure by the application of high pressure; this cubic phase has been reported to be metastable at atmospheric pressure. The band structure of this phase is calculated by the ab initio correlated Hartree-Fock method. Not surprisingly, the band structure of rocksalt ZnO is very similar to that of CdO, which has the same crystal structure; we present a band-structure calculation for CdO, which we believe is more accurate than any in the literature. A hallmark of these band structures is that the valence-band maximum is not at the center of the Brillouin zone, in contrast to the situation in tetrahedrally coordinated II-VI semiconductors. We confirm by direct calculation that this peculiarity of the band structure is a consequence of the hybridization of oxygen 2p-derived orbitals with Zn 3d or Cd 4d states, combined with octahedral point symmetry.

Quadratic integration over the three-dimensional Brillouin zone

Abstract: A new method is described to evaluate integrals of quadratically interpolated functions over the three-dimensional Brillouin zone. The method is based on the method of the authors for analytic quadratic integration over the two-dimensional Brillouin zone. It uses quadratic interpolation not only for the dispersion relation epsilon (k), but for property functions f(k) as well. The method allows a 'machine accuracy' evaluation of the integrals and may therefore be regarded as equivalent to a truly analytic evaluation of the integrals. It is compared to other methods of integral approximation by calculating tight-binding Brillouin zone integrals using the same number of k-points for all methods. Also shown are cohesive energy calculations for a number of elements. When the quadratic method is compared to the commonly used linear method, it is found that far fewer k-points are needed to obtain a desired accuracy.

High-energy spin waves in La2CuO4.

Abstract: Time-of-flight spectrocopy using neutrons produced by a spallation source is used to measure the one-magnon scattering throughout the Brillouin zone for La{sub 2}CuO{sub 4} The zone-boundary magnons have an energy {h bar}{omega}{sub ZB}=0312{plus minus}0005 eV and are good eigenstates of the quantum Heisenberg Hamiltonian in that they possess lifetimes {gt}10/{omega} A multiplicative renormalization of the overall frequency scale of classical spin-wave theory accounts for the quantum effects in the one-magnon spectrum

Coherent time-resolved investigation of LO-phonon dynamics in GaAs.

Abstract: The dynamics of coherently excited LO phonons is investigated in GaAs using an infrared time-resolved coherent anti-Stokes Raman scattering technique. The LO-phonon dephasing time is precisely measured as a function of crystal temperature. The results reveal that the relaxation is dominated by the intraband decay into a transverse-acoustic phonon and a LO phonon at the L critical point of the Brillouin zone. The frequently proposed decay route into two longitudinal-acoustic phonons is found to be incompatible with results from our temperature-dependent measurements.

Observation of dissipative superluminous solitons in a Brillouin fiber ring laser.

Abstract: Nonstationary stimulated Brillouin backscattering in a large gain optical-fiber ring cavity laser exhibits superluminous Stokes pulses of quasisoliton type and partial self-induced transparency for the pump. Experimental evidences, comforted by numerical simulation of the three-wave coherent model taking the acoustic-wave dynamics into account, show that this class of long transients occurs even with a cw-coupled pump wave.

Elastic constants and hardness of ion-beam-sputtered tinx films measured by brillouin scattering and depth-sensing indentation

Abstract: TiNx films of various composition have been prepared by reactive‐ion‐beam sputtering at a deposition temperature of 50 °C. Young’s modulus E and hardness H of these films were measured by a depth‐sensing nanoindentation technique, whereas the shear modulus G was obtained by a measurement of the velocity of the acoustic surface wave by Brillouin light scattering. The study was extended over a wide range of stoichiometries, 0≤x≤0.8. A proportionality between E and H has been observed.

An improved impact‐ionization model for high‐energy electron transport in Si with Monte Carlo simulation

Abstract: A new model for impact ionization in Si is presented, which goes beyond the limitations of the Keldysh formula and is based on a more realistic scheme developed starting from a first‐order perturbation theory. This scattering mechanism is modeled by an extended band structure which includes many bands for electrons and one band for holes in a finite Brillouin zone. Some processes have been identified to bring the dominant contribution to the scattering probability, in the present approach, for electron energies ranging up to 3 eV. Expressions for the differential and integrated scattering probabilities have been obtained which are consistent with the band model and can be included in a Monte Carlo simulation of the electron gas. Results for transport quantities are shown for a bulk material in presence of homogeneous and static electric fields under physical conditions where impact ionization influences the carrier dynamics. A comparison with theoretical and experimental data from the literature is also g...

Rotational equilibria and low-order modes of a non-neutral ion plasma.

Abstract: We study rotational equilibria and low-order electrostatic modes of a magnetically confined, non-neutral ion plasma. The plasma rotation rate is controlled with radiation pressure from a laser beam and is continuously varied over the entire allowed range, including Brillouin flow. Excitation of an asymmetric plasma mode by a static field asymmetry is observed. The symmetric quadrupole mode is also studied; its behavior is characteristic of a strongly magnetized plasma at low density, and of an unmagnetized plasma at Brillouin flow.

Quasiparticle properties in ferromagnetic CeRu2Ge2

Abstract: A detailed de Haas-van Alphen study of high-quality crystals of ferromagnetic CeRu2Ge2 (Tc ≈ 8 K) is presented. All expected Fermi surface sheets have been observed, including an extraordinarily large surface with a cross-sectional area bordering on the size of the Brillouin zone itself. A comparison to band structure calculations allows the formulation of a model for the Fermi surface consisting of five spin split sheets. For the first time in one of these systems the completeness of the de Haas-van Alphen data allows a rigorous analysis of the heat capacity and its accountability in terms of the observed quasiparticles. Analysis of the observed spin splitting yields values for the 4f to conduction electron interaction parameters for each sheet and enables a self-consistent understanding of the mass enhancement. A comparison to the related heavy-fermion system CeRu2Si2 provides new insight into the underlying nature of its quasiparticle properties.

Enhanced surface anharmonicity observed in vibrations on Cu(110).

Abstract: Surface anharmonicity has been measured on Cu(110) by examining the temperature dependence of surface phonons with atomic motion normal to the surface using high-resolution electron-energy-loss spectroscopy. At the Brillouin zone center {bar {Gamma}} the energy of the {ital MS}{sub 7} resonance decreases by 3.2 meV and the intrinsic width increased by 8.6 meV as the temperature increases from 21 to 766 K. Energy decrease and width increase are also observed at the Brillouin zone edge {ital {bar Y}} in the {ital S}{sub 3} phonon. The percentage energy decrease is the same in both phonons. Direct comparison with bulk-phonon measurements shows that the anharmonicity at the surface is 4.1--4.8 times greater than in the bulk.

Anharmonic self-energies of phonons in silicon

Abstract: We have carried out a realistic ab initio calculation of the contribution of cubic anharmonicity to the inverse lifetime \ensuremath{\Gamma} and the frequency shift \ensuremath{\Delta} of phonons in silicon. The cubic coupling constants for phonons throughout the Brillouin zone are obtained from an anharmonic Keating-type lattice-dynamical model, which has been fit to a database of results from local-density-approximation frozen-phonon and elastic-modulus calculations. \ensuremath{\Gamma} and \ensuremath{\Delta} have been calculated as a function of temperature T and wave vector. Our results agree reasonably well with experiment, but indicate the need for retention for quartic and higher-order terms, especially at high T.

Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers

Abstract: Recently, stimulated Brillouin scattering in a forward direction (FSBS) in a dual-mode single-core optical fiber was reported by the authors (see Electron Lett., vol.26 p.1195-6, 1990). Frequency shifts on the order of 17 MHz were seen in fiber supporting LP/sub 01/ and LP/sub 11/ modes at 514.5 nm. The phenomenon is examined in detail, and the governing differential equations of the three-wave parametric process, (involving laser pump, Brillouin signal, and acoustic flexural-wave phonon) are derived and solved. FSBS is possible because although the overlap integral between a flexural fiber mode and the light is small, the phonon lifetime is much longer than in conventional stimulated Brillouin scattering (SBS). FSBS may also be the first example of a nonlinear effect which is enhanced by increasing the optical model area at constant pump power. >

Brillouin light scattering on chemical‐vapor‐deposited polycrystalline diamond: Evaluation of the elastic moduli

Abstract: We report on Brillouin light scattering investigations on chemical‐vapor‐deposited polycrystalline diamond films. Besides the longitudinal and two transverse acoustic bulk phonons, a Rayleigh surface mode is observed. From the bulk modes the elastic constants c11, c12, and c44 of 1062±74, 122±8, and 541±22 GPa, respectively, are determined exhibiting the characteristic values of natural diamond. The observed Rayleigh mode sound velocity of 10326±470 m/s is consistent with the (110) texture of the polycrystalline film and the determined elastic constants.

Brillouin scattering by surface acoustic modes for elastic characterization of ZnO films

Abstract: Brillouin scattering from surface phonons was used for determining the dispersion curves of guided acoustic modes propagating along piezoelectric ZnO films. Measurements were performed on films of different thicknesses in the range between 20 and 320 nm, deposited by RF magnetron sputtering on Si and SiO/sub 2/ substrates. Brillouin spectra from Rayleigh acoustic modes are taken in the backscattering geometry at different incidence angles between 30 degrees and 70 degrees . The experimental data for the ZnO/Si films fit the expected theoretical dispersion curves fairly well for film thicknesses greater than 150 nm, while they appreciably depart from the same curves for smaller thicknesses. This behavior is interpreted in terms of a reduction of the effective elastic constants of the film in a layer near the interface, due to the lattice misfit between the film and the substrate. This effect was not observed in the case of ZnO films deposited on fused quartz substrates. >

Suppression of Stimulated Brillouin Scattering and Brillouin Crosstalk by Frequency-Sweeping Spread-Spectrum Scheme

Abstract: Frequency-sweeping spread-spectrum (FS-SS) optical fiber communication system for suppressing the stimulated Brillouin scattering (SBS) is proposed. The Brillouin gain is reduced approximately in proportion to the spreading bandwidth. Measured Brillouin gain is in good agreement with the theory. A preliminary transmission experiment demonstrates that the bit-error rate deteriorated by the SBS crosstalk is recovered by the SS scheme. This fact suggests that the maximum transmission optical power, which is limited by the SBS, can be increased by the spectrum spreading.

Confined LO phonons in GaAs/AlAs superlattices

Abstract: We report the observation of both GaAs and AlAs confined LO phonons in short-period GaAs/AlAs superlattices. The measured GaAs mode frequencies are found to map well onto the bulk dispersion curve with a suitable choice of an effecive wave vector, confirming the validity of this technique for determining bulk phonon dispersions over at least the first half of the bulk Brillouin zone. The frequency separation of confined AlAs LO modes is found to be consistent with a weak dispersion of this branch along the [001] direction, in agreement with recent lattice-dynamic calculations.

Stimulated Brillouin threshold dependence on fiber type and uniformity

Abstract: Stimulated Brillouin scattering sets a limit on the injected power in light-wave systems.1 For single-channel systems of moderate length this effect is the dominant nonlinearity, with a threshold on the order of a few milliwatts.2 As transmitter powers increase, this effect will become an important factor in system design. It is known that the Brillouin gain spectra of fibers are affected by fiber uniformity and type.3,4 Thus, the threshold for stimulated Brillouin scattering should also depend on these parameters.

Mapping the fermi surface of graphite with a display-type photoelectron spectrometer

Abstract: A display spectrometer is used to image the momentum distribution of photoelectrons from the Fermi level in graphite. The Fermi “surface” consists of six points at the corners K of the hexagonal, two-dimensional Brillouin zone, in agreement with band theory. The method is also applied to other equal energy surfaces below the Fermi level, thereby giving the band dispersion of the π-bands.

Phonons on stepped surfaces

Abstract: A simple model of fcc lattice dynamics is studied in the vicinity of a clean, unreconstructed, high-Miller-index (i.e., stepped) surface. Depending on the vibrational modes' spatial extent, they are classified as either bulk phonons, surface phonons, or step phonons. The existence and characteristics of the latter class of vibrational modes are presented throughout the (one-dimensional) step Brillouin zone (BZ). Five classes of stepped surfaces are examined, each differing in the Miller indices of the terrace [(111) or (100)] and step face [(111), (100), or (110)]. All but one of the systems exhibit modes truly localized to the edge. There are many similarities to the study of surface phonons. For instance, when degenerate with the bulk- or surface-phonon bands, the step phonons acquire a finite lifetime and become step resonances. A total of seven step phonons and four step resonances are seen. Most of these are strongly localized to the edge only near the end of the step BZ. Unlike regular surface modes, the step-phonon characteristics (frequency, polarization, and amplitude) depend sensitively on the interatomic potentials near the steps. Two step-phonon measurements have yielded information about these important step parameters. Using a crude estimate of the inelastic-scattering intensity, I propose the possibility for a similar experiment with Ni(755) using existing techniques.

Magnetic properties of Co/Pd multilayers determined by Brillouin light scattering and SQUID magnetometry

Abstract: Co/Pd multilayers with modulation wavelengths between 4 and 220 A have been prepared by magnetically enhanced dc‐triode sputtering on single‐crystal sapphire substrates. Their saturation magnetization and volume and interface anisotropies have been investigated using Brillouin light scattering from collective spin waves and by SQUID magnetometry. The saturation magnetization of Co is found to be independent of the Co layer thickness and reduced by about 20% from the Co bulk value. From the comparison of the results of the two experimental methods, clear evidence for a Pd polarization is found and the polarization depth is estimated. Samples with Co thicknesses of 2 atomic layers and Pd thicknesses ≥5 atomic layers exhibit a perpendicular magnetization due to a large negative out‐of‐plane interface anisotropy. The properties of spin waves in Co/Pd multilayers with the direction of magnetization pointing out‐of‐plane are discussed with respect to an appropriate theoretical model.