Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.

Measurements of light scattering from glass substrates by total integrated scattering

A total integrated scattering (TIS) measurement was performed to investigate the surface and volume scattering of K9 glass substrates with low reflectance. Ag layers with thicknesses of 60 nm were deposited on the front and back surfaces of the K9 glass substrates by the magnetron sputtering technique. Surface scattering of the K9 glass substrate was obtained by the TIS measurement of the Ag layers on the assumption that the Ag layers and the K9 substrate had the same surface profile. Volume scattering of the substrates was deduced by subtracting the front and back surface scattering from the total scattering of the substrates. (c) 2005 Optical Society of America.

Optimized vertical carbon nanotube forests for multiplex surface-enhanced raman scattering detection

The highly sensitive and molecule-specific technique of surface-enhanced Raman spectroscopy (SERS) generates high signal enhancements via localized optical fields on nanoscale metallic materials, which can be tuned by manipulation of the surface roughness and architecture on the submicrometer level. We investigate gold-functionalized vertically aligned carbon nanotube forests (VACNTs) as low-cost straightforward SERS nanoplatforms. We find that their SERS enhancements depend on their diameter and density, which are systematically optimized for their performance. Modeling of the VACNT-based SERS substrates confirms consistent dependence on structural parameters as observed experimentally. The created nanostructures span over large substrate areas, are readily configurable, and yield uniform and reproducible SERS enhancement factors. Further fabricated micropatterned VACNTs platforms are shown to deliver multiplexed SERS detection. The unique properties of CNTs, which can be synergistically utilized in VACNT-based substrates and patterned arrays, can thus provide new generation platforms for SERS detection. © 2012 American Chemical Society.

Brillouin scattering of cluster-assembled carbon films

The low frequency vibrational spectrum of cluster beam deposited carbon films was studied by Brillouin light scattering. In thin films the values of both bulk modulus and shear modulus has been estimated from the shifts of surface phonon peaks. The values found indicate a mainly sp2 coordinated random network with low density. In thick films a bulk longitudinal phonon peak was detected in a spectral range compatible with the value of the index of refraction and of the elastic constants of thin films. High surface roughness, combined with a rather strong bulk central peak, prevented the observation of surface phonon features. © 1998 Elsevier Science Ltd. All rights reserved.

Dislocation scattering in AlxGa1-xN/GaN heterostructures

The theoretical electron mobility limited by dislocation scattering of a two-dimensional electron gas confined near the interface of AlxGa1-xN/GaN heterostructures was calculated. Based on the model of treating dislocation as a charged line, an exponentially varied potential was adopted to calculate the mobility. The estimated mobility suggests that such a choice can simplify the calculation without introducing significant deviation from experimental data, and we obtained a good fitting between the calculated and experimental results. It was found that the measured mobility is dominated by interface roughness and dislocation scattering at low temperatures if dislocation density is relatively high (>10(9) cm(-2)), and accounts for the nearly flattening-out behavior with increasing temperature.

X-RAY-SCATTERING FROM A ROUGH-SURFACE AND DAMAGED LAYER OF POLISHED WAFERS

Theoretical and experimental investigations were performed to show the application of x-ray crystal truncation rod scattering combined with x-ray reflectivity in the measurements of surface roughness and near-surface damage of mechanochemically polished wafers. By fitting the measured crystal truncation rod curves it has been shown that polished wafers are divided into three parts -irregular steps on the surface, a damaged thin layer beneath the surface and a perfect bulk. The results show that the root mean square of the surface roughness of mechanochemically polished Fe-doped and/or S-doped InP wafers is one to two atom layers, and that the lateral correlation length of the surface roughness is about 3000-7500 Angstrom. The thickness of the damaged region is found to be about 1000 atom layers.

Lateral periodicity in highly-strained (GaIn)As/Ga(PAs) superlattices investigated by X-ray scattering techniques

In this work we investigate the lateral periodicity of symmetrically strained (GaIn)As/GaAs/Ga(PAs)/GaAs superlattices by means of X-ray scattering techniques. The multilayers were grown by metalorganic Vapour phase epitaxy on (001)GaAs substrates, which were intentionally off-oriented towards the [011]-direction. The substrate off-orientation and the strain distribution was found to affect the structural properties of the superlattices inducing the generation of laterally ordered macrosteps. Several high-resolution triple-crystal reciprocal space maps, which were recorded for different azimuth angles in the vicinity of the (004) Bragg diffraction and contour maps of the specular reflected beam collected in the vicinity of the (000) reciprocal lattice point, are reported and discussed. The reciprocal space maps clearly show a two-dimensional periodicity of the X-ray peak intensity distribution which can be ascribed to the superlattice periodicity in the direction of the surface normal and to a lateral periodicity in a crystallographic direction coinciding with the miscut orientation. The distribution and correlation of the vertical as well as of the lateral interface roughness was investigated by specular reflectivity and diffuse scattering measurements. Our results show that the morphology of the roughness is influenced by the off-orientation angle and can be described by a 2-dimensional waviness.

Aggregation-based fabrication and assembly of roughened composite metallic nanoshells: Application in surface-enhanced Raman scattering

This paper reports an aggregation-based method for the fabrication of composite Au/Ag nanoshells with tunable thickness and surface roughness. It is found that the resultant roughened composite Au/Ag nanoshells can attract each other spontaneously to form films at the air-water interface. Importantly, such films can be transferred onto the solid substrates without being destroyed and show excellent surface-enhanced Raman scattering (SERS) enhancement ability. Their strong enhancement ability may stem from the unique two-dimensional structure itself.

Surface roughness characterization of soft x-ray multilayer films on the nanometer scale

The soft x-ray reflectivity of multilayer films is affected by the surface roughness on the transverse nanometer scale. Scanning tunneling microscopy (STM) is an ideal instrument for providing high-lateral-resolution roughness measurements for soft x-ray multilayer films that cannot be obtained with other types of instruments on the transverse nanometer scale. The surface roughnesses of Mo/Si, Mo/C, and W/Si soft x-ray multilayer films prepared by an ion-beam-sputtering technique were measured with a STM on the vertical and transverse attributes. The film roughnesses and average spatial wavelengths added to the substrates depend on the multilayer film fabrication conditions, i.e., material combinations, number of layers, and individual layer thickness. These were estimated to lead to a loss of specular reflectivity and variations of the soft x-ray scattering angle distribution. This method points the way to further studies of soft x-ray multilayer film functional properties and can be used as basic guidance for selecting the best coating conditions in the fabrications of soft x-ray multilayer films. (C) 1996 American Vacuum Society.

INTERPLAY OF CAF2 SUBSTRATE ROUGHENING AND FILM DEPOSITION RATE ON RADIATIVE SCATTERING OF SURFACE-PLASMON POLARITONS FROM AG FILMS

The radiative decay of surface plasmon polaritons has been investigated in an attempt to characterize the surface roughness of Ag films prepared under different conditions. The polaritons were excited by the method of attenuated total reflection of light. The films were deposited on the face of a 60-degrees BK-7 glass prism at a rate that was deliberately fixed in two different ranges (centred on 0.1 and 10 nm s-1) and in some cases a CaF2 underlayer was used to roughen the film surfaces. The intensity of the scattered light emitted from the opposite face of the films was measured as a function of direction for each using the same sensitivity scale and was correlated with the preparation of the film. It was found that on nominally smooth substrates fast-deposited thinner films give out more light and are deduced to have greater short wavelength (300-600 nm) roughness amplitude. There is also evidence for long wavelenth (7 mum) periodic roughness due to the prism substrate itself. On CaF2 roughened surfaces the light output from the films is further increased and the peak intensity is backward directed with respect to the exciting laser beam direction. Here roughness on a lateral scale of 350 nm is responsible. Also, elastic scattering of surface plasmon polaritons at grain boundaries reduces the light output from fast deposited, small grain, films on CaF2 roughened surfaces. Overall, a consistent picture of roughness induced radiative polariton decay emerges for all cases studied.

INFLUENCE OF METAL GRAIN-SIZE ON SURFACE-ENHANCED RAMAN-SCATTERING

The surface roughness of nominally smooth and of randomly roughened thin silver films is characterized using scanning tunneling microscopy and the metal grain size is assessed using transmission electron microscopy. On each type of substrate used, glass or CaF2-roughened glass, the silver films are deposited either very slowly (approximately 0.15 nm s-1) or quite quickly (approximately 2.0 nm s-1). Only silver films deposited on CaF2-roughened glass yield measurable surface-enhanced Raman signals for benzoic acid; the enhancement is brought about by surface field amplification due to the excitation of delocalized surface-plasmon polaritons. However, the surface-enhanced Raman signals obtained from the slow-deposited silver films are significantly better (by about a factor of 3) than those obtained from the fast-deposited silver films on a given CaF2-roughened substrate. The explanation of this observation does not lie with different surface roughness; both types of film yield closely similar data on the scanning tunneling microscope. Rather, it is suggested that the relatively small grain size of the fast-deposited silver films leads to increased elastic scattering of surface-plasmon polaritons at the grain boundaries, with a consequent increase of internal damping. This results in a reduction of the scattered Raman signal.

SURFACE ENHANCED RAMAN-SCATTERING FROM MILDLY ROUGHENED SURFACES - VARIATION OF SIGNAL WITH METAL GRAIN-SIZE

The intensity of surface enhanced Raman scattering from benzoic acid derivatives on mildly roughened, thermally evaporated Ag films shows a remarkably strong dependence on metal grain size. Large grained (slowly deposited) films give a superior response, by up to a factor of 10, to small grained (quickly deposited) films, with films of intermediate grain size yielding intermediate results. The optical field amplification underlying the enhancement mechanism is due to the excitation of surface plasmon polaritons (SPPs). Since surface roughness characteristics, as determined by STM, remain relatively constant as a function of deposition rate, it is argued that the contrast in Raman scattering is due to differences in elastic grain boundary scattering of SPPs (leading to different degrees of internal SPP damping), rather than differences in the interaction of SPPs with surface inhomogeneities.

Sensitivity of radar backscatter to desert surface roughness

Synthetic aperture radar (SAR) data have proved useful in remote sensing studies of deserts, enabling different surfaces to be discriminated by differences in roughness properties. Roughness is characterized in SAR backscatter models using the standard deviation of surface heights (sigma), correlation length (L) and autocorrelation function (rho(xi)). Previous research has suggested that these parameters are of limited use for characterizing surface roughness, and are often unreliable due to the collection of too few roughness profiles, or under-sampling in terms of resolution or profile length (L-p). This paper reports on work aimed at establishing the effects of L-p and sampling resolution on SAR backscatter estimations and site discrimination. Results indicate significant relationships between the average roughness parameters and L-p, but large variability in roughness parameters prevents any clear understanding of these relationships. Integral equation model simulations demonstrate limited change with L-p and under-estimate backscatter relative to SAR observations. However, modelled and observed backscatter conform in pattern and magnitude for C-band systems but not for L-band data. Variation in surface roughness alone does not explain variability in site discrimination. Other factors (possibly sub-surface scattering) appear to play a significant role in controlling backscatter characteristics at lower frequencies.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.