Two-dimensional light diffraction from thin opal films

This paper reports on experimental and theoretical investigations of light diffraction from thin films of synthetic opal. The diffraction patterns have been studied visually and recorded in different scattering geometries with the films illuminated with white unpolarized light. The diffraction pattern obtained with the film illuminated with a light beam along the [111] axis, which is normal to the film surface, has C ₆ symmetry and consists of six strong reflections arranged symmetrically with respect to the incident beam. This pattern becomes substantially more complicated when the film is illuminated by white light at an arbitrary angle to the [111] axis. An experimental study of the spectral response and angular relations of the diffraction patterns has established a fairly full pattern of transformation of diffraction reflections obtained under variation of the angle of light incidence on an opal film. The remarkably good matching of experimental and calculated data provides compelling evidence for light diffraction from thin opal films being two-dimensional.     

Self-consistent inhomogeneity of quantum wells in II–VI semiconductors

An X-ray diffraction method that uses a slightly diverging (3′) beam and maximally attainable diffraction angles ? _B (as large as 77°) was developed to study quantum wells (QWs) with widths of 5–8 nm separated by wide (100–220 nm) barrier layers. The advantage of this method compared to the use of a parallel beam is an increase by two orders of magnitude in the intensity of the beam incident on the sample and an increase in the probability of diffraction for all QWs as a unified single crystal. It is found that the growth on GaAs substrates misoriented by 10° from the (001) plane in the [111]_II direction brings about monoclinization of crystal lattices of the QW layers and barrier layers in opposite directions. Inhomogeneity of composition over the thickness of each well is observed. In the case of growth of a ZnSe/ZnMgSSe structure in which the layers have a crystal-lattice period close to the lattice period of the GaAs substrate, the QWs are inhomogeneously doped with elements from the composition of the barrier layers. The inhomogeneity of QW composition observed in the growth of mismatched layers in ZnCdSe/ZnSSe and ZnCdS/ZnSSe structures is caused by the fact that mismatch between the lattice parameters of QWs and barriers stimulates the growth of self-consistent compositions; this occurs due to a decrease in the Cd concentration in the Zn_1?x Cd _x Se QW in the initial stages of growth compared to the Cd concentration in the flow of gases and an increase in the Zn concentration in the Cd_1?x Zn _x S QW at small values of x up to the concentration matching GaAs (x = 0.4). The mismatch stresses are partially relaxed via dislocations with the (111)_II glide planes, as a result of which is observed the combination of rotation of the crystal planes of the layers and QW around the [1\(\overline 1 \)0] axis and almost cylindrical bending of the entire sample around the perpendicular [110] axis. Mismatch between lattice parameters of the ZnMgSSe barrier layers and the substrate brings about decomposition of these layers into two phases; this decomposition is caused by thermodynamic instability of the alloy.     

Spectroscopy of the photonic stop band in synthetic opals

The photonic band gap of opals has been studied experimentally from their optical transmission spectra as a function of the incident beam orientation in the opal crystal lattice. The measurements were carried out for all high-symmetry points on the surface of the Brillouin zone of an fcc lattice. The experimental dependence of the energy position of the photonic band gap on the light wave vector direction is well described by the set of theoretical relations developed for the stop bands originating from the Bragg diffraction of light on {111}-type planes of the twinned fcc lattice of synthetic opals.     

Optical characterization of synthetic opals

The results of a structural-optical characterization of synthetic opals are presented. Information on the growth-induced features of the opal structure was derived from an analysis of the position and width of the one-dimensional photonic band gap. The structure of the samples was found to vary substantially along the growth axis coinciding with the [111] direction of the fcc lattice. It was shown that the regions corresponding to early stages in the opal structure growth are typically strongly disordered, which manifests itself, in particular, in the crystallites being misoriented relative to the sample growth axis. It was concluded that the regions of synthetic opals most suitable for application as photonic crystals are those corresponding to later growth stages.     

Experimental study of the photonic band structure of synthetic opals at a low dielectric contrast

This paper reports on a comprehensive study of optical transmissivity spectra of synthetic opals as a function of the four major parameters of the observed photonic stop bands, namely, light beam orientation relative to the opal fcc lattice, light polarization, opal-filler dielectric permittivity contrast, and sample thickness. The measurements were performed under low opal-filler dielectric contrast conditions for the principal high-symmetry directions of the twinned fcc lattice of the opals. The experimentally determined dependence of the energy positions of photonic stop bands on the direction of the light wave vector is fitted well by the calculated dispersion relation of Bragg wavelengths in diffraction of light from the (hkl) fcc plane system.     

Multiple Bragg diffraction in low-contrast photonic crystals based on synthetic opals

The phenomenon of multiple Bragg diffraction in low-contrast photonic crystals based on synthetic opals has been studied both experimentally and theoretically. The transmission and reflection spectra of opal films near the K point of the Brillouin zone of the face-centered cubic lattice in s-polarization exhibit the effect of anticrossing of dispersion curves corresponding to the (111) and ([`1]11)(\bar 111) photonic stop bands. The effect of quasi-Brewster suppression of stop bands is clearly pronounced in p-polarization. The experimental data are analyzed using the calculation of the band structure of opal with the inclusion of the polarization of incident light.     

Optical properties of thin films of closely packed SiO2 spheres

Ordered, closely packed, defect-free one-, two-, and three-layer thick films of SiO₂ spheres of diameter D varying from 0.6 to 1.4 μm were obtained. Their optical transmittance and reflectance spectra were measured in the range 0.3–2.5 eV. The one-layer structures reveal a transmittance minimum whose spectral position is described by the Bragg law with the plane separation equal to the sphere radius D/2. As the number of the layers increases, a spectral feature appears which signals the formation of a photonic gap in the 〈111〉 direction of the fcc crystal lattice and is determined by the distance between the {111} planes equal to 0.816D. The spectra of two-and three-layer structures measured with a diverging light beam contain additional lines originating from the formation of photonic gaps by the {111} and {221} planes. __________ Translated from Fizika Tverdogo Tela, Vol. 44, No. 6, 2002, pp. 1026–1031. Original Russian Text Copyright ? 2002 by Bazhenov, Gorbunov, Aldushin, Masalov, Emel’chenko.     

Double diffraction spots in RHEED patterns from clean Ge(111) and Si(001) surfaces

In RHEED patterns from clean Ge(111) and Si(001) surfaces, extra diffraction spots have been observed with superlattice reflection spots due to Ge(111) 2 × 8 and Si(001) 2 × 1 surface structures. The extra spots have not been found out in many previous LEED and RHEED patterns of clean Ge(111) and Si(001) surfaces. When the Ge(111) and Si(001) samples were rotated about an axis normal to the surfaces so as to vary the incident direction of the primary electron beam, the intensity of the extra spots showed a remarkable dependence upon the incident direction and they became invisible in some incident directions, in spite of the experimental condition that an Ewald sphere intersected reciprocal lattice rods of the extra spots. In this study, the extra spots are understood as forbidden reflection spots resulting from double diffraction of superlattice reflections of the surface structures, and the remarkable dependence of their intensity upon the incident direction is explained in terms of excitation of the surface wave of the superlattice reflections. These results suggest that the intensity of diffraction spots in RHEED patterns may be greatly influenced by the surface wave excitation of fundamental and superlattice reflections.     

A Comparison of GaN Epilayers with Multiple Buffer Layers and with a Single Buffer Layer Grown on Si（111） Studied by HRXRD and RBS/Channeling

Two hexagonal GaN epilayers （samples A and B） with multiple buffer layers and single buffer layer are grown on Si （111） by metal-organic vapour phase epitaxy （MOVPE）. From the results of Rutherford backscattering （RBS）/channeling and high resolution x-ray diffraction （HRXRD）, we obtain the lattice constant （a and c） of two GaN epilayers （aA = 0.3190 nm, cA = 0.5184 nm and aB = 0.3192 nm, CB = 0.5179 nm）, the crystal quality of two GaN epilayers （ ХminA=4.87%, ХminB =7.35% along 〈1-↑213〉 axis） and the tetragonal distortion eT of the two samples along depth （sample A is nearly fully relaxed, sample B is not relaxed enough）. Comparing the results with the two samples, it is indicated that sample A with multiple buffer layers have better crystal quality than sample B with a single buffer layer, and it is a good way to grow GaN epilayer on Si （111） substrates using multiple buffer layers to improve crystal quality and to reduce lattice mismatch.     

Selective control of light beams in diffraction experiments on synthetic opals

This paper reports on an experimental and theoretical investigations of the possibility of selectively controlling the intensity of {hkl} diffraction reflections in synthetic opals. The calculations of the photonic stop-band width for low-contrast multi-component photonic crystals argue for a selective pattern of the vanishing of various {hkl} stop bands (and, accordingly, of the various {hkl} diffraction reflections) under variation of the dielectric permittivity of one of the components. Optical diffraction patterns have been studied visually and recorded in various scattering geometries with bulk opal samples illuminated by white unpolarized light. The experiments have made use of immersion spectroscopy, a method reducing essentially to successive measurements of diffraction patterns under variation of the dielectric permittivity of the liquid filler of the opal matrix. The {111} and {220} Bragg reflections have been observed to weaken noticeably at the filler permittivities matching very well with the values derived earlier from an analysis of transmission spectra.     

Photonic Bandgap Deformation in a Nonideal Synthetic Opal Photonic Crystal

The Bragg diffraction in synthetic opal as a 3D photonic crystals has been analyzed using the weak disorder model in various approximations. For a one-domain crystal, the photonic bandgap is calculated in the regime of reflection along the 〈111〉 axis. In the multidomain case, a considerable expansion of the photonic bandgap, the emergence of asymmetry, and the photon band shift to the short-wavelength region are demonstrated. The results are compared with experimental dependences.     

Self-assembly and growth of manganese phthalocyanine on an Au（111） surface

Self-assembly and growth of manganese phthalocyanine (MnPc) molecules on an Au(111) surface is investigated by means of low-temperature scanning tunneling microscopy. At the initial stage, MnPc molecules preferentially occupy the step edges and elbow sites on the Au(111) surface, then they are separately adsorbed on the face-centered cubic and hexagonal closely packed regions due to a long-range repulsive molecule—molecule interaction. After the formation of a closely packed monolayer, molecular islands with second and third layers are observed.     

Anisotropy of light propagation in thin opal films

Thin opal films are prepared by crystallization in a moving meniscus, and their optical transmission spectra are recorded in polarized light and studied. It is shown that the anisotropy of light propagation in the films is unambiguously related to the photonic band structure of opal and depends on the angle of incidence, the orientation of the incidence plane with respect to the opal lattice, and the wavelength and polarization of the incident light. Azimuthal diagrams of transmitted polarized light are constructed in the range of photonic band gaps of three orders for oblique incidence of a light beam. The anisotropy is found to vary with the light wave-length independently in perpendicular polarizations. A model of the band structure of opal wherein opal is represented as an fcc lattice of close-packed spheres adequately describes the optical transmission of opal films only in the range of the first-order photonic band gap.     

A New Method for the Measurement of Thickness in Single Crystals

A new method for thickness determination of single-crystal thin samples at exact zone axis orientation, based on pattern recognition in convergent beam electron diffraction (CBED), is presented. The method is especially well suited to materials with a large unit cell in zone axis directions where the reciprocal lattice is uniformly dense with diffraction points. The new method is based on comparison of a measured CBED zone axis pattern with a set of calculated ones. Its accuracy was estimated to be around 10% in the 5–100 nm thickness range as checked for garnets at the [111] zone orientation.     

Structure of Ultrathin Polycrystalline Iron Films Grown on SiO<Subscript>2</Subscript>/Si(001)

The structure of polycrystalline Fe films grown on an oxidized Si(001) surface at room temperature has been studied by the technique of high-energy electron diffraction. It has been found that the grain orientation in the films depends of the amount of deposited iron. In Fe films less than 5 nm thick, grains have been found to be randomly oriented. Fe films more than 5 nm in thickness exhibit the (111) texture with an axis coinciding with the surface normal. The angular dispersion of the [111] direction in the Fe lattice from the surface normal is ±25°. It has been found that as the Fe films become thicker, the (111) texture changes to the (110) texture.     

A new method of surface structure-analysis by medium energy electron diffraction: distinction between T4 and H3 models for the Si(111)√3 × √3 -In surface

A new method (named GB-MEED) of medium-energy electron diffraction has been invented. This method is used to measure back-scattering medium-energy electron diffraction patterns with a grazing-incident electron beam. It is demonstrated that GB-MEED is sensitive to the structural change of only a few upper layers of the Si(111) surface. A simple model of single-scattering cluster calculation similar to that for X-ray photoelectron diffraction has been applied to analyze presently measured GB-MEED patterns for the Si(111)√3 × √3-In surface. The distinction between T₄ and H₃ models for the Si(111)-√3 × √3-In surface has been made by making the best use of forward focusing of electron-scattering at a medium energy of 1 keV.     

光全息制作的变形面心立方结构光子晶体的带隙

四束激光从空气直接入射到平面结构的感光树脂所制备的面心立方结构实际上是一种不但晶格沿[111]方向拉伸,而且其格点也在[111]方向被拉长的变形面心立方结构。在对这种变形面心立方结构的光子晶体的晶格形状及能带分布的研究中,通过利用麻省理工学院的光子晶体能带计算程序计算了各种参量对此变形面心立方结构的蛋白石和反蛋白石的能带分布的影响,发现在一定条件下该结构的蛋白石会出现完全光子带隙。用激光全息聚合法在正胶的环氧树脂中可制作反蛋白石模板,若用此模板制作硅蛋白石,当晶格沿[111]方向拉伸2.1倍和硅的占空比为13.7%时出现最大的带隙宽度。此最大带隙宽度的结构的制作光路是三角锥形光路,对称地环绕中央光束的三束外围激光束之间夹角为54.0°,三束外围激光束与中央激光束夹角为31.6°。     

Method for Describing the Angular Distribution of Optical Radiation Scattered by a Monolayer of Ordered Spherical Particles (Normal Illumination)

We have developed a method for describing the angular distribution of intensity of radiation scattered by a monolayer of homogeneous spatially ordered monodisperse spherical particles normally illuminated by a plane circularly polarized electromagnetic wave. The method is based on the quasicrystalline approximation (QCA) of the theory of multiple scattering of waves (TMSW) using the multipole expansion of fields and the tensor Green function in vectorial spherical wavefunctions. The method is applied for analyzing the characteristics of radiation scattered by a partially ordered monolayer and a monolayer with a nonideal lattice. The results of calculations are compared with the available experimental data on the position of the first-order diffraction peak on the angular and spectral dependences of the intensity of radiation scattered by a closely packed monolayer with a nonideal triangular lattice of SiO₂ particles. Good conformity of the results has been established.     

On the theory of diffraction of light in photonic crystals with allowance for interlayer disordering

Electrodynamic Green’s functions are used to construct an analytical theory of the Bragg diffraction of polarized light in photonic crystals having a close-packed structure. For opal-based photonic crystals, the Bragg diffraction intensity is calculated with allowance for permittivity periodic modulation and for the presence of an optical crystal boundary and interlayer disordering, which usually appears during sample growth. A comprehensive study is made of the effect of the structure disorder caused by the random packing of growth layers on diffraction. For a random constructed twinned fcc structure, the average structure factor and the scattering (diffraction) cross sections (which are dependent on the linear polarization of the incident and scattered waves) are calculated. Numerical examples are used to show that the theory developed can be applied to analyze and process experimental diffraction patterns of real photonic crystals having a close-packed structure disordered in one direction.     

Design of photonic bands for opal-based photonic crystals

To make a device from an opal—or otherwise—the photonic bands and the optical properties derived from them are needed. Knowing the effects of different parameters defining the opal geometry and different possible modifications of its structure are needed, too. An accurate definition of the device will be required to obtain a good performance. With this aim, the optics of light with a wavevector in the vicinity of the L point in the Brillouin zone and its coupling to bare opals band structure are presented. An important aspect is the transition from finite to infinite crystal and the study of size effects on the bands. It is possible to substantially alter the photonic band structure of an opal-based system, while maintaining the lattice structure, simply by growing layers of other materials with an appropriate refractive index. Here, it is shown how, by the growth of accurately controlled thin layers of silicon and germanium, and further processing, one can induce the opening of two complete photonic band gaps (PBGs) in an opal structure. Finally, the possibility to fabricate a simple device consisting in a planar waveguide will be shown. By means of a very simple and inexpensive procedure, engineered planar defects acting as microcavities have been realized. These can be viewed as a particular case of a much more general class of heterostructures that can be grown by combining opal vertical deposition and chemical vapour deposition of oxides. A further step is made by applying electron beam lithography to provide lateral definition and facilitate three-dimensional structuring.