Lattice parameter determination of a strained area of an InAs layer on a GaAs substrate using CBED

All the six lattice parameters (a, b, c, alpha, beta and gamma) of a strained area of an InAs layer grown on a GaAs substrate were determined without any assumption of the crystal lattice symmetry from the higher-order Laue zone (HOLZ) lines appearing in one convergent-beam electron diffraction (CBED) pattern. The analysis was performed with three steps. Firstly, the parameters alpha and beta were determined from the deviations of the HOLZ lines from the mirror symmetry perpendicular to the [001] direction. Secondly, the parameter c was determined from the distance between the intersections of the HOLZ lines, which have the same h and k indices but different l indices. Finally, the parameters a, b and gamma were determined simultaneously from several distances between the intersections of the HOLZ lines. The lattice parameters determined for the strained area were a = 0.611(2) nm, b = 0.615(1) nm, c = 0.6119(7) nm, alpha = 89.5(1) degrees, beta = 89.0(2) degrees and gamma = 89.1(2) degrees. This result implies that the cubic lattice of InAs is elongated approximately in the [111] direction and the exact lattice symmetry is triclinic. The same analysis procedure was applied to another two specimen areas. It was found that the areas have orthorhombic distortions with lattice parameters a = 0.607(2) nm, b = 0.604(1) nm and c = 0.6085(7) nm for one area, and with a = 0.607(2) nm, b = 0.605(1) nm and c = 0.6065(7) nm for the other area. It is should be emphasized that the present analysis of lattice distortions is immediately applicable to the other semiconductors, such as Si, SiGe or GaAs layers, without assuming any crystal system.     

Strain analysis of arsenic-doped silicon using CBED rocking curves of low-order reflections

Local lattice strains of semiconductor devices have been so far examined using higher order Laue zone (HOLZ) line patterns of convergent-beam electron diffraction (CBED). Recently, strain analyses in highly strained regions near interfaces have been reported using split HOLZ line patterns. In the present paper, it is demonstrated for arsenic-doped silicon that the use of CBED rocking curves of low-order reflections provides a promising new tool for the determination of strain distributions of highly strained specimen areas. That is, the anomalous intensity increase in the CBED rocking curves of low-order reflections is explained using a model structure with a strain gradient in the electron beam direction, which is similar to the models used for the split HOLZ line patterns.     

HOLZ line analysis of lattice parameters in magnesium alloys.

A method of refining lattice parameters from deficit higher-order Laue zone (HOLZ) line data from large angle convergent beam electron diffraction (LACBED) data is presented, relying on distances between nearest neighbour intersections alone in order to minimize effects of distortion over the field of view. Use is made of a dynamical correction deltak to the fast electron wavevector k for kinematic analysis. This correction term is shown to depend on the specific HOLZ beam under consideration, as well as the zone axis and eigenvalue associated with the branch index of the relevant dispersion surface. This method is applied to analysis of data from magnesium alloys, where momentum filtering induced by the LACBED method facilitates HOLZ contrast from a relatively low index zone axis (where contrast is not detectable with conventional CBED), and contrast is enhanced at elevated temperatures from a higher index zone axis. Although the accuracy of refined lattice parameters from these sets of data is shown to be no better than 0.1%, it is felt that issues arising out of the analysis may be of some interest, particularly since these are non-ideal specimens. Full eigen-state analysis of the fast electron wavefunction is presented, and issues related to the influence of the dispersion surface on deficit HOLZ line behaviour are discussed.     

Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure

We investigate in detail control methods of polarization mode in a two-dimensional square-lattice photonic crystal laser. In order to control the polarization mode using the square lattice, we investigate the eigenmode of the electromagnetic field against the possible symmetry groups of a square lattice. Both the electromagnetic field distributions of lasing oscillation mode and the band diagram are significantly influenced by the symmetry groups. In the case of the square lattice structure, symmetries "p1", "pm", "p2", and "pmm" are suitable for obtaining the unidirectional polarization mode. Among these symmetry groups, the symmetry group "pmm" is especially interesting considering the simplicity of the eigenmode of the electromagnetic field. In order to obtain the symmetry group "pmm", we deform the unit cell structure of a square lattice from circular to elliptical and investigate the properties of symmetry group "pmm" in detail. The elliptical ratio of the unit cell structure can modify the coupling balance of a lightwave propagating in two perpendicular in-plane directions and can control the eigen energy of each band edge.     

Orthogonal and Biorthogonal FIR Hexagonal Filter Banks With Sixfold Symmetry

Recently, hexagonal image processing has attracted attention. The hexagonal lattice has several advantages in comparison with the rectangular lattice, the conventionally used lattice for image sampling and processing. For example, a hexagonal lattice needs less sampling points; it has better consistent connectivity; it has higher symmetry; and its structure is plausible to human vision systems. The multiresolution analysis method has been used for hexagonal image processing. Since the hexagonal lattice has high degree of symmetry, it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry, which is pertinent to the symmetry structure of the hexagonal lattice. The orthogonal or prefect reconstruction (PR) hexagonal filter banks that are available in the literature have only threefold symmetry. In this paper, we investigate the construction of orthogonal and PR finite impulse response (FIR) hexagonal filter banks with sixfold symmetry. We obtain block structures of 7-size refinement (seven-channel two-dimensional) orthogonal and PR FIR hexagonal filter banks with sixfold rotational symmetry. $sqrt{7}$-refinement orthogonal and biorthogonal wavelets based on these block structures are constructed. In this paper, we also consider FIR hexagonal filter banks with axial (line) symmetry, and we present a block structure of FIR hexagonal filter banks with pseudo-sixfold axial symmetry.      

界面残余应变场的会聚束电子衍射测定

用两种会聚束电子衍射(CBED)技术研究了复合材料界面残余应变场.常规正焦CBED方法中,用优化算法使计算的高阶Laue带(HOLZ)线图与实验图达到最佳拟合,进而确定残余应变.给出了一种减少优化计算中可调参数数目的方法.残余应变与表面弛豫引起的界面附近点阵平面面间距的变化、点阵平面的旋转与弯曲使得离焦的大角度会聚束电子衍射(LACBED)图中的衍射线移位、分裂与弯曲.表面弛豫引起的点阵平面的旋转也决定于本征应变.通过使动力学理论计算的LACBED图与实验图达最佳拟合,可以确定本征应变.用该方法研究了颗粒增强复合材料Al2O3/Al与晶须增强复合材料 (K2O@6TiO2) w/Al的界面残余应变场.     

Realizing the Intrinsic Anisotropic Growth of 1T′ ReS2 on Selected Au(101) Substrate toward Large-Scale Single Crystal Fabrication

Low-symmetry 2D materials with strong in-plane anisotropy are ideal platforms for building multifunctional optoelectronic devices. However, the random orientations and easy formation of multidomain structures lead to the single-crystal synthesis of these materials remains a big challenge. Herein, for the first time, the orientation-controlled synthesis of ReS₂, a typical low-symmetry 2D material, is explored via interface engineering based on the strong interaction between the material and Au substrates with different symmetries. It is revealed that the lattice orientation and growth behavior of ReS₂ are closely relevant to the lattice symmetry of Au facets. Single crystal ReS₂ domains with two and even one orientations are acquired on the four-fold symmetry Au(001) facet and the two-fold symmetry Au(101) facet, respectively. Combined with density functional theory calculations, it is demonstrated that the synergy of ultra-strong ReS₂-Au interfacial coupling and reduction of symmetry of Au facet is critical to realizing its intrinsic anisotropic growth. Furthermore, great enhancement of electrical and photoelectrical performances are acquired on the well-aligned single crystal ReS₂ device. The progress achieved in this work provides significant guidance for the controllable synthesis of wafer-scale single crystals of low-symmetry 2D materials for their practical device applications.     

比特交织编码调制(迭代译码)系统标识映射的对称性研究与应用

该文从群论的角度分析了比特交织编码调制(迭代译码)(BICM(-ID))系统中标识映射的对称性。首先给出了标识映射对称性的定义,并指出,二进制标识映射的对称性是BICM(-ID)系统的固有特性,该对称性同构于m阶超立方的对称群。然后基于BICM(-ID)的对称性,提出一种改进的二进制交换算法(IBSA)。该算法的搜索空间为标识映射对称群陪集的代表系。因此,与传统的二进制算法相比,IBSA的搜索效率得到了提高。最后,2维16阶星座图的仿真结果表明,在40000次的运行过程中,IBSA能提高4%的搜索效率;32阶相移键控星座图的仿真结果表明,该算法至少可提高3.5%的搜索效率,单个映射的计算时间缩短了约4000倍。     

High-resolution X-ray diffraction studies of molecular beam epitaxy-grown HgCdTe heterostructures and CdZnTe substrates

Lattice mismatch between substrates and epitaxial layers of different molefractions can create a variety of distortions and defects in Hg_(1−x)Cd_(x)Te epilayers, thus degrading the performance of infrared detectors fabricated from this material. X-ray diffraction is a sensitive nondestructive technique, which allows in-depth characterization of the crystal lattice prior to detector fabrication. We present results of triple-axis diffractometry performed on single- and double-layer HgCdTe films grown on (211)B CdZnTe substrates by molecular beam epitaxy (MBE). In this study, both the ω and 2θ diffraction angles have been recorded absolutely so that the diffraction peaks in the RSMs can be positioned directly in reciprocal space, without requiring reference to a substrate peak. The positions of both surface-symmetric and asymmetric diffraction peaks have been used to extract lattice spacings parallel and perpendicular to the (211) growth direction. The relaxed lattice parameter of each epilayer has been calculated assuming that the layers are elastically strained. The low symmetry of the (211) growth direction, coupled with the anisotropic elasticity of zinc-blende semiconductors, results in monoclinic distortion of the lattice, as observed in these samples. In double-layer samples, the mosaicity of both layers is greater than that observed in single epilayers. Layers subjected to a Hg-saturated anneal show greater lattice distortion than as-grown samples.     

Propagation in periodically loaded waveguides with higher symmetries

A generalization of Floquet's theorem is presented for periodically loaded closed waveguides possessing a certain class of higher symmetries which includes the screw and glide symmetries. These symmetries frequently appear in microwave structures such as filters, traveling-wave tubes, and traveling-wave antennas. The theorem states that the natural modes are eigenvectors of the symmetry operator characterizing the structure. An alternative derivation of the theorem using an equivalent network representation leads naturally to a simple method for constructing the qualitative dispersion (Brillouin) diagrams for structures with screw or glide symmetry.     

Power optimization of multi-level logic circuits utilizing circuit symmetries

The property of circuit symmetry has long been applied to the problem of minimizing the area and timing of multi-level logic circuits. In this paper, we focus on another important design objective, power optimization, utilizing circuit symmetries. First, we analyse and establish the relationship between several types of circuit symmetry and their applicability to reducing power consumption of the circuit, proposing a set of re-synthesis techniques utilizing the symmetries. We derive an algorithm for detecting the symmetries (among the internal signals as well as the primary inputs) on a given circuit implementation. We then propose an effective transformation algorithm to minimize power consumption using the symmetry information detected from the circuit. Unlike many other approaches, our transformation algorithm guarantees monotonic improvement in terms of switching activities, which is practically useful in that user can check the intermediate re-synthesized designs in terms of the degree of changes of power, area, timing, and the circuit structure. We have carried out experiments on MCNC benchmark circuits to demonstrate the effectiveness of our algorithm. On average we reduced the power consumption of circuits by 12% with relatively little increase of area and timing.     

On the origin of HOLZ lines splitting near interfaces: multislice simulation of CBED patterns

Splitting of HOLZ lines on CBED patterns is systematically observed at the proximity of interfaces and prevents local strain measurements by monitoring of line shifts. It was previously suggested that such splitting occurs due to interface-strain relaxation in thin TEM lamella. Here we confirm this model by dynamical simulation of CBED patterns using the multislice algorithm.     

Consequences of symmetry in periodic structures

Periodic guiding or radiating structures at microwave frequencies often possess symmetry properties in addition to their axial periodicity. These include rotation and reflection symmetries, either occurring alone or in conjunction with translations. These symmetries influence the characteristics of the electromagnetic fields associated with the structures. Therefore, useful information concerning the fields can be obtained from the symmetry properties without resorting to detailed field solutions or to equivalent circuits. These symmetry properties are conveniently analyzed by introducing symmetry operators for which the structure is invariant. This paper shows that two symmetry operators, the screw and the glide, are particularly important in determining the dispersion characteristics of the structures. Some of the implications of these symmetries for leaky wave antennas and microwave tube interaction circuits are explored, and their consequences are examined to facilitate the analysis and synthesis of periodic microwave structures.     

Iterative methods for the canonical decomposition of multi-way arrays: Application to blind underdetermined mixture identification

Two main drawbacks can be stated in the alternating least square (ALS) algorithm used to fit the canonical decomposition (CAND) of multi-way arrays. First its slow convergence caused by the presence of collinearity between factors in the multi-way array it decomposes. Second its blindness to Hermitian symmetries of the considered arrays. Enhanced line search (ELS) scheme was found to be a good way to cope with the slow convergence of the ALS algorithm together with a partial use of the Hermitian symmetry. However, to our knowledge, required equations to perform the latter scheme are only given in the case of third and fifth order arrays. Therefore, our first contribution consists in generalizing the ELS procedure to the case of complex arrays of any order greater than three. Our second contribution is another improvement of the ALS scheme, able to profit from Hermitianity and positive semi-definiteness of the considered arrays. It consists in resorting to the CAND first of a third order array having one unitary loading matrix and second of several rank-1 arrays. An iterative algorithm is then proposed alternating between Procrustes problem solving and the computation of rank-one matrix approximations in order to achieve the CAND of the third order array.     

Symmetry Study for Delta- Operator-Based 2-D Digital Filters

The complexity in the design and implementation of two-dimensional (2-D) filters can be considerably reduced if we utilize the symmetries that might be present in the frequency response of these filters. As the delta-operator formulation of digital filters offers better numerical accuracy and lower coefficient sensitivity in narrowband filter designs when compared to the traditional shift-operator formulation, it is desirable to have efficient design and implementation techniques in$gamma$-domain which utilize the various symmetries in filter specifications. With this motivation, we comprehensively establish the theory of constraints for delta-operator formulated discrete-time real-coefficient polynomials and functions, arising out of the many types of symmetries in their magnitude responses. We also show that as sampling time tends to zero, the$gamma$-domain symmetry constraints merge with those of$s$-domain symmetry constraints. We then present a least square error criterion based procedure to design 2-D digital filters in$gamma$-domain that utilizes the symmetry properties of the magnitude specification. A design example is provided to illustrate the savings in computational complexity resulting from the use of the$gamma$-domain symmetry constraints.     

Symmetry study on 2-D complex analog and digital filter functions

The symmetry properties of 2-D complex polynomials are analyzed in this paper. The characteristics of a polynomial possessing different standard symmetries in their magnitude and phase responses are studied. The nature of constraints that are imposed by the defined symmetries on analog and digital polynomials is discussed. The various classes of complex polynomials possessing the different (quadrantal, diagonal, rotational, and octagonal) symmetries and antisymmetries in their magnitude responses and/or phase responses are tabulated.The work reported here was supported by the Center for Manufacturing Research and Technology Utilization, Tennessee Technological University, Cookeville, Tennessee 38505.     

Photonic crystal-based circulators with three and four ports for sub-terahertz region

Three- and four-port circulators based on resonators in 2D photonic crystals with square unit cell possessing a low symmetry are investigated. The three-ports are described by only one specific element named antiplane of symmetry. On the other hand, the four-port circulators formed by cascading these two three-ports can have one of the two symmetries. One of them is described by the antiplane of symmetry, and the other symmetry corresponds to a twofold rotational axis. The theoretical part of our paper concerns scattering matrix analysis of the devices with different symmetries and also the operation of the four-port circulator as a single-pole triple-throw switch. Finally, the calculated frequency responses of two circulators are presented.     

Tunable Magnonic Spectra in Two‐Dimensional Magnonic Crystals with Variable Lattice Symmetry

Tunable magnonic properties are demonstrated in two‐dimensional magnonic crystals in the form of artificial ferromagnetic nanodot lattices with variable lattice symmetry. An all‐optical time‐domain excitation and detection of the collective precessional dynamics is performed in the strongly magnetostatically coupled Ni₈₀Fe₂₀ (Py) circular dot lattices arranged in different lattice symmetry such as square, rectangular, hexagonal, honeycomb, and octagonal symmetry. As the symmetry changes from square to octagonal through rectangular, hexagonal and honeycomb, a significant variation in the spin wave spectra is observed. The single uniform collective mode in the square lattice splits in two distinct modes in the rectangular lattice and in three distinct modes in the hexagonal and octagonal lattices. However, in the honeycomb lattice a broad band of modes are observed. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal collective modes with different spatial distributions with the variation in the lattice symmetry determined by the magnetostatic field profiles. For the hexagonal lattice, the most intense peak shows a six‐fold anisotropy with the variation in the azimuthal angle of the external bias magnetic field. Analysis shows that this is due to the angular variation of the dynamical component of magnetization for this mode, which is directly influenced by the variation of the magnetostatic field on the elements in the hexagonal lattice. The observations are important for tunable and anisotropic propagation of spin waves in magnonic crystal based devices.