Absolute Band Gap Research Articles

Scattering in a two-dimensional photonic crystal: An analytical model.

An exact analysis of light propagation in a model two-dimensional photonic crystal is presented. The system displays full and absolute band gaps in its dispersion characteristics. It is shown that global propagation of s-polarized light derives largely from locally evanescent waves.

Photonic bandgap of two-dimensional dielectric crystals

The existence of an absolute photonic bandgap in the near-infrared for two-dimensional periodic dielectric structures is discussed for photons propagating in the plane of such 2D crystals. A special emphasis is put on the influence of the shape and size of the filling pattern on the absolute bandgap formation. A very large absolute photonic bandgap is predicted for 2D crystals formed by etching into a semiconductor slab a periodic array of large vertical cylindric voids of circular cross-section arranged in a triangular lattice. The technological feasibility of such “optimum” air/GaAs 2D crystals by standard processing techniques (electron beam lithography and reactive ion etching) is demonstrated.

Out of Plane Propagation of Electromagnetic Waves in a Two-dimensional Periodic Dielectric Medium

Abstract By the use of the plane wave method we have calculated the dispersion curves (photonic band structure) of electromagnetic waves propagating in a structure consisting of an infinite array of parallel, infinitely long, dielectric rods of arbitrary cross-section, characterized by a dielectric constant εa, embedded in a medium characterized by a dielectric constant εb, when the intersections of the axes of the rods with a perpendicular plane form a two-dimensional Bravais lattice. In contrast with earlier calculations of the photonic band structures of two-dimensional, periodic, dielectric structures, in the present work the electromagnetic waves are assumed to propagate out of the plane perpendicular to the rods. In numerical calculations we study a triangular lattice of air cylinders in a dielectric medium, which has recently been shown to possess a band gap common to waves of both E and H polarization for propagation in the plane perpendicular to the rods. The shifts of the edges of this absolute band gap as k 3, the component of the wave-vector of the electromagnetic waves parallel to the rods, is increased from zero are studied, as is the closing up of this gap. A new absolute band gap is found to open up below the first band as k 3 is increased. Conclusions concerning the filtering behaviour of two-dimensional, periodic, dielectric structures in the case of out-of-plane propagation of electromagnetic waves through them are drawn.

Investigation of Absolute Photonic Band Gaps in Two-dimensional Dielectric Structures

Abstract We examine the photonic band structure of two-dimensional (2D) arrays of dielectric holes using the coherent microwave transient spectroscopy (COMITS) technique. Such 2D hole arrays are constructed by embedding low-index rods (air) in a dielectric background of higher-index Stycast material (n = 3·60). The dispersion relation for electromagnetic wave propagation in these photonic crystals is directly determined using the phase sensitivity of COMITS. We find that both the square and triangular lattice structures exhibit photonic band gaps that are common to both polarizations for all wave-vectors along major symmetry axes. In addition, the connectivity of the high-index dielectric and the opening of a large gap for propagation with E field perpendicular to the hole cylinders are found to be important criteria for generating a large absolute photonic band gap.

Analysis of the Filling Pattern Dependence of the Photonic Bandgap for Two-dimensional Systems

Abstract We investigate in this paper different aspects of the absolute photonic bandgap (PBG) formation for a two-dimensional periodic dielectric structure. In particular we examine how the symmetry of the filling pattern in a periodic dielectric material influences the photonic gap parameters. We present the results of the calculations and discuss the existence of the absolute PBG, the maximization of its width as a function of the parameters of a two-dimensional dielectric crystal as well as the practical technological feasibility of these optimized structures.

Photonic band gaps in periodic elastic composites 2-D hexagonal lattices

The acoustic band structure of periodic elastic composites were calculated using position-dependent density and elastic constant. The specific system investigated is made up of a periodic array of parallel metallic rods of circular cross section whose intersections with a perpendicular plane from a hexagonal lattice. The rods are embedded in a background medium with different elastic constant and density. The transverse polarization was considered—with displacement u(r,t) parallel to the cylinders (and perpendicular to the Bloch wave vectors). The absolute band gaps extending throughout the first Brillouin zone were found in the low-frequency regime. The specific case studied was Cu(Al) cylinders in the Al(Cu) background. A direct comparison of the hexagonal case with the square-lattice pattern (Kushwaha et al., preceding abstract in this session) reveals that the widths of these band gaps are larger in the case of hexagonal lattices. The precise dependence of the gaps on the filling fraction is investigated.

Adsorbate induced enhancement of secondary electron emission from the layered compound VSe 2

It is demonstrated how adsorbates may drastically enhance the photoemission yield at low kinetic energies from VSe 2 surfaces. The reason for this enhancement seems to be that the adsorbate by reducing the work function φ creates a condition closely resembling negative electron affinity (NBA), i.e. the vacuum level is pulled down into an absolute band-gap. In contrast to true NBA systems, there are empty states (predominantly of V3d character) available below the vacuum level, but due to low probability for scattering into these states, the NEA-like behaviour prevails. Since the involved band minimum is located close to the K symmetry point of the Brillouin zone, adsorbate induced diffuse scattering is vital to the observed enhancement.

Photonic band structure investigation of two-dimensional Bragg reflector mirrors for semiconductor laser mode control

A theoretical study that follows the lines of previous photonic band structure investigations has been undertaken in search of a two-dimensional (2D) periodic dielectric structure that exhibits a certain type of photonic band structure for application as an external feedback mirror for laser diode arrays and broad-area devices. Instead of looking for an absolute band gap for a band of frequencies, we are particularly interested in structures that exhibit only stop bands, i.e., bands with a narrow extent in both frequency and angle. This type of reflecting structure, which can also be termed a 2D Bragg reflector, could provide improved mode control for both longitudinal and transverse characteristics of the modes for these devices. Our study, which employed photonic band structure calculational methods, showed that square lattice dielectric structures exhibit such stop bands for both TE and TM waves and could be used as photonic band structure mirrors to induce better mode control.

Photonic band structure of a truncated, two-dimensional, periodic dielectric medium

We calculate the photonic band structure for the propagation of electromagnetic waves through a structure that consists of parallel, identical, dielectric rods of finite length, whose intersections with a perpendicular plane form a two-dimensional crystal. The rods are embedded in a medium with a different dielectric constant, and the composite system is confined between a pair of perfectly conducting plates that are perpendicular to the rods. The electromagnetic waves propagate in a plane perpendicular to the rods. The resulting photonic band structure can display absolute band gaps if the separation between the perfectly conducting plates is sufficiently large or sufficiently small.

Surface State and Direct Transitions on Al (111) Investigated with Angle-Resolved Photoelectron Spectroscopy

Al(111) has been studied with angle-resolved photoelectron spectroscopy. A previously not observed surface state band located around the K point in the surface Brillouin zone is reported. The measured dispersion of the surface state band falls in an absolute electron energy band gap when the three-dimensional band structure from a new LAPW (Linearized-Augmented-Plane-Wave) calculation is projected onto the surface Brillouin zone of the (111) crystal face. The existence of this surface state has been theoretically predicted by several authors.Direct transitions between bulk bands are found to give significant contributions to the photocurrent. Experimentally deduced initial-state energy dispersions of the bulk transitions are compared to the corresponding dispersions obtained from the LAPW band structure calculation.

Characterization and Transferability of Surface States on W{110}

A dominant surface state has been observed on the W{110} surface by photoemission with 16.8, 21.2, and 40.8 eV photons. For the first time an experimental surface band structure is presented covering the entire surface Brillouin zone. Theoretical calculations of the surface density of states on W{110} are found to be in good agreement with experiment, and allow an assignment of the surface state. The calculations show that this state, which has split off a bulk-band edge into an absolute band gap, is transferable to the W{001} plane.

The electronic structure of the (111) surface of silicon

In this letter results are presented of a new study of the electronic structure of semiconductor surfaces. Optical data were used to obtain the Slater-Koster parameters of the tight-binding bandstructure for silicon, and these parameters have been used to study the bulk and (111) surface region of silicon. The main conclusion is the existence of only one surface state per atom concentrated just below the bottom of the absolute bandgap, and with a localization of two atomic layers (a half-length of 2.1 AA), while the competition between the termination of bulk states and the decay of surface states gives rise to lesser features throughout the valence band and lowest conduction band.

Photo-electronic properties of InAs 0.07Sb 0.93 films

The temperature dependent photoconductive and surface barrier photovoltaic spectral responses of InAs 0.07Sb 0.93 films with an impurity density ∼5.5×10 15 cm -3, grown by liquid phase microzone crystallization, are shown to be a function of their fundamental energy bandgaps shifted to values lower than those of InSb. From charge carrier transport measurements their absolute zero bandgap is calculated as ε g0=0.197 eV, in good agreement with theory. In contrast with previously reported data on InAs xSb 1-x solid solution bulk and single crystal layers, the electron mobility of InAs 0.07Sb 0.93 films increases with decreasing temperature reaching a value of ∼1.32×10 5 cm 2/Vs at 77 K.

Electronic and Optical Properties of InAsxSb1−x Films

Solid solution InAsxSb1−x films have been prepared by flash evaporation of mixed InAs and InSb powders onto semi-insulating (100)-oriented single crystal GaAs substrates and glass cover slips. Electron beam microzone crystallization and thermal annealing were used to improve their crystalline perfection and their electrical properties. Recrystallization from the liquid phase was found to be feasible only over the limited range 0≤x<0.3 consistent with the stability criteria for fixed alloy systems developed by Van Vechten. The composition dependence of the absolute zero energy bandgaps, eg0 determined by means of otpical, photoelectric, and galvanomagnetic measurements supports the data obtained by Coderre and Woolley and disagrees with that of Kudman and Ekstrom obtained on bulk crystalline materials. The minimum in the composition dependence of eg0 of the films is between x=0.3 and x=0.6.