Measuring the randomness of micro- and nanostructure spatial distributions: Effects of scanning electron microscope image processing and analysis.

The quantitative characterisation of the degree of randomness and aggregation of surface micro- and nanostructures is critical to evaluate their effects on targeted functionalities. To this end, the methods of point pattern analysis (PPA), largely used in ecology and medical imaging, seem to provide a powerful toolset. However, the application of these techniques requires the extraction of the point pattern of nanostructures from their microscope images. In this work, we address the issue of the impact that Scanning Electron Microscope (SEM) image processing may have on the fundamental metric of PPA, that is, the Nearest Neighbour Index (NNI). Using typical SEM images of polymer micro- and nanostructures taken from secondary and backscattered electrons, we report the effects of the (a) noise filtering and (b) binarisation threshold on the value of NNI as well as the impact of the image finite size effects. Based on these results, we draw conclusions for the safe choice of SEM settings to provide accurate measurement of nanostructure randomness through NNI estimation.

Quantitative characterization of hierarchical multiscale surfaces of micro and nanostructured materials.

Hierarchical surfaces have recently attracted a lot of interest, mainly due to their ability to exhibit multifunctionality combining different properties. However, despite the extensive experimental and technological appeal of hierarchical surfaces, a systematic and thorough quantitative characterization of their features is still missing. The aim of this paper is to fill this gap and build a theoretical framework for the classification, identification and quantitative characterization of hierarchical surfaces. The main questions addressed in the paper are the following: given a measured experimental surface how can we detect the presence of hierarchy, identify the different levels comprising it and quantify their characteristics? Special emphasis will be given on the interaction of different levels and the detection of the information flow between them. To this end, we first use a modeling methodology to generate hierarchical surfaces of a wide spectrum of characteristics with controlled features of hierarchy. Then we applied the analysis methods based on Fourier transform, correlation functions and multifractal (MF) spectrum properly designed to this aim. The results of our analysis reveal the importance of the hybrid use of Fourier and correlation analysis in the detection and characterization of different types of surface hierarchy as well as the critical role of MF spectrum and higher moment analysis, in the detection and quantification of the interaction between hierarchy levels.

One-step control of hierarchy and functionality of polymeric surfaces in a new plasma nanotechnology reactor.

Hierarchical micro-nanostructured surfaces are key components of 'smart' multifunctional materials, used to control wetting, adhesion, tactile, friction, optical, antifogging, antibacterial, and many more surface properties. Hierarchical surfaces comprise random or ordered structures ranked by their length scale spanning the range from a few nanometers to a few micrometers, with the larger microstructures typically embedding smaller nanostructures. Despite the importance of hierarchical surfaces, there have been few studies on their precise and controlled fabrication or their quantitative characterization, and they usually involve multiple and complex fabrication steps. Here, we present a new plasma nanotechnology, which we term 'nanoinhibit', and a new plasma reactor for producing in one facile process-step-controlled hierarchy at will on polymeric surfaces. We couple the new plasma nanotechnology with detailed computational nanometrology based on the analysis of scanning electron microscopy images and targeted to specific functionality. We showcase the potential of 'nanoinhibit' for functional surface fabrication by controlling the wetting and optical functionality of the fabricated hierarchical surfaces and showing its dependence on surface morphology metrics. Finally, we observe that 'nanoinhibit' produces a new class of 'strong hierarchical' surfaces exhibiting spatially separated periodic and fractal-like components.

Optical properties of high aspect ratio plasma etched silicon nanowires: fabrication-induced variability dramatically reduces reflectance.

In this work we investigate both experimentally and theoretically the optical properties of aligned, perpendicular to the substrate, high aspect ratio (AR), plasma etched Si nanowires (SiNWs) with controlled variability. We focus on the role of imperfections in fabrication, which manifest themselves as dimensional variability of SiNW, lattice defects or positional randomization. SiNW arrays are fabricated by e-beam lithography (perfectly ordered array) or colloidal particle self-assembly (quasi-ordered array) followed by cryogenic Si plasma etching, which offers fast etch rate (up to 3 µm min(-1)) combined with clean, smooth, and controllable sidewall profile, but induces some dimensional variability on the diameters of the SiNWs. Sub-200 nm diameter SiNWs having AR as high as 37:1 are demonstrated. The total reflectance of SiNWs is below 2% in a wide range of the optical spectrum. We experimentally demonstrate improved light absorption when moving from a perfectly ordered (after e-beam lithography) to a defective and quasi-ordered (after colloidal self-assembly) SiNW array. In addition our measured reflectivity (for both ordered and quasi-ordered SiNWs) is much lower compared to the one predicted theoretically for a perfect SiNWs array, using full-electrodynamic calculations with the layer-multiple-scattering method. To explain such low reflectivity, we model the influence of disorder using the average T-matrix approximation and show that even small dimensional variability (10-20%) leads to dramatic reduction of the reflectance (matching the experimental results) and increased light trapping inside the SiNW justifying their possible application in photovoltaic devices.

Plasma-assisted nanoscale protein patterning on Si substrates via colloidal lithography.

Selective immobilization of proteins in well-defined patterns on substrates has recently attracted considerable attention as an enabling technology for applications ranging from biosensors and BioMEMS to tissue engineering. In this work, a method is reported for low-cost, large scale and high throughput, selective immobilization of proteins on nanopatterned Si, based on colloidal lithography and plasma processing to define the areas (<300 nm) where proteins are selectively immobilized. A close-packed monolayer of PS microparticles is deposited on oxidized Si and, either after microparticle size reduction or alternatively after metal deposition through the PS close-packed monolayer, is used as etching mask to define SiO2 nanoislands (on Si). C4F8 plasma was used to selectively etch and modify the SiO2 nanoislands while depositing a fluorocarbon layer on the Si surface. The plasma-treated surfaces were chemically characterized in terms of functional group identification through XPS analysis and reaction with specific molecules. Highly selective protein immobilization mainly through physical adsorption on SiO2 nanoislands and not on surrounding Si was observed after C4F8 plasma-induced chemical modification of the substrate. The thickness of the immobilized protein monolayer was estimated by means of AFM image analysis. The method reported herein constitutes a cost-efficient route toward rapid, large surface, and high-density patterning of biomolecules on solid supports that can be easily applied in BioMEMS or microanalytical systems.

Using chaotic dynamics to characterize the complexity of rough surfaces.

In this work, we use the basic ingredients of chaotic dynamics (stretching and folding of phase space points) for the characterization of the complexity of microscopy images of rough surfaces. The key idea is to use an image as the initial condition of a chaotic discrete dynamical system, such as the Arnold cat map, and track its transformations during the first iterations of the map. Since the basic effects of the Arnold map are the stretching and folding of image texture, the application of the map leads to an enhancement of the high frequency content of images along with an increase of discontinuities in pixel intensities. We exploit these effects to quantify the complexity of S type (lying between homogeneity and randomness) of the image texture since the first (enhancement of high frequencies) can be used to quantify the distance of texture from randomness and noise and the second (the proliferation of discontinuities) the distance from order and homogeneity. The method is validated in synthetic images which are generated from computer generated surfaces with controlled correlation length and fractal dimension and it is applied in real images of nanostructured surfaces obtained from a scanning electron microscope with very interesting results.

A consistent approach for the treatment of Fermi acceleration in time-dependent billiards.

The standard description of Fermi acceleration, developing in a class of time-dependent billiards, is given in terms of a diffusion process taking place in momentum space. Within this framework, the evolution of the probability density function (PDF) of the magnitude of particle velocities as a function of the number of collisions n is determined by the Fokker-Planck equation (FPE). In the literature, the FPE is constructed by identifying the transport coefficients with the ensemble averages of the change of the magnitude of particle velocity and its square in the course of one collision. Although this treatment leads to the correct solution after a sufficiently large number of collisions have been reached, the transient part of the evolution of the PDF is not described. Moreover, in the case of the Fermi-Ulam model (FUM), if a standard simplification is employed, the solution of the FPE is even inconsistent with the values of the transport coefficients used for its derivation. The goal of our work is to provide a self-consistent methodology for the treatment of Fermi acceleration in time-dependent billiards. The proposed approach obviates any assumptions for the continuity of the random process and the existence of the limits formally defining the transport coefficients of the FPE. Specifically, we suggest, instead of the calculation of ensemble averages, the derivation of the one-step transition probability function and the use of the Chapman-Kolmogorov forward equation. This approach is generic and can be applied to any time-dependent billiard for the treatment of Fermi-acceleration. As a first step, we apply this methodology to the FUM, being the archetype of time-dependent billiards to exhibit Fermi acceleration.

Plasma nanotextured PMMA surfaces for protein arrays: increased protein binding and enhanced detection sensitivity.

Poly(methyl methacrylate) (PMMA) substrates were nanotextured through treatment in oxygen plasma to create substrates with increased surface area for protein microarray applications. Conditions of plasma treatment were found for maximum uniform protein adsorption on these nanotextured PMMA surfaces. Similar results were obtained using both a high-density plasma (HDP) and a low-density reactive ion etcher (RIE), suggesting independence from the plasma reactor type. The protein binding was evaluated by studying the adsorption of two model proteins, namely, biotinylated bovine serum albumin (b-BSA) and rabbit gamma-globulins (RgG). The immobilization of these proteins onto the surfaces was quantitatively determined through reaction with fluorescently labeled binding molecules. It was found that the adsorption of both proteins was increased up to 6-fold with plasma treatment compared to untreated surfaces and up to 4-fold compared to epoxy-coated glass slides. The sensitivity of detection was improved by 2 orders of magnitude. Moreover, highly homogeneous protein spots were created on optimized plasma-nanotextured surfaces through deposition with an automated microarray spotter, revealing the potential of plasma-nanotextured surfaces as protein microarray substrates.

Plasma directed assembly and organization: bottom-up nanopatterning using top-down technology.

Fabrication of periodic nanodot or nanocolumn arrays on surfaces is performed by top-down lithographic procedures or bottom-up self-assembly methods, which both make use of plasma etching to transfer the periodic pattern. Could plasma etching alone act as an assembly--organization method to create the pattern and then transfer it to the substrate? We present data that support this idea and propose a mechanism of periodicity formation where etching and simultaneous deposition take place.

Modeling of roughness evolution during the etching of inhomogeneous films: material-induced anomalous scaling.

Although a lot of experimental and model results for roughness evolution exhibit anomalous scaling, the origins of such a behavior remain still unclear. In this paper, the possible contribution of material inhomogeneities to the appearance of anomalous scaling behavior in kinetic roughening is investigated by a simple modeling of roughness evolution in the etching of porous and composite films. It is found that the roughness evolution during the etching of both kinds of inhomogeneous films displays anomalous scaling behavior with peculiar features (no expansion of correlations vs time and square-root time increase in surface width roughness) defining a new universality class. Furthermore, the insertion of correlations between film pores or fillers along etching direction leads to roughness instability, i.e., linear increase in surface width roughness. The latter observation may be exploited for the detection of correlations between pores or fillers using roughness evolution as a diagnostic tool.

Rare events and their impact on velocity diffusion in a stochastic Fermi-Ulam model.

A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections.

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of noninteracting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.

Fermi acceleration in the randomized driven Lorentz gas and the Fermi-Ulam model.

Fermi acceleration of an ensemble of noninteracting particles evolving in a stochastic two-moving wall variant of the Fermi-Ulam model (FUM) and the phase randomized harmonically driven periodic Lorentz gas is investigated. As shown in [A. K. Karlis, P. K. Papachristou, F. K. Diakonos, V. Constantoudis, and P. Schmelcher, Phys. Rev. Lett. 97, 194102 (2006)], the static wall approximation, which ignores scatterer displacement upon collision, leads to a substantial underestimation of the mean energy gain per collision. In this paper, we clarify the mechanism leading to the increased acceleration. Furthermore, the recently introduced hopping wall approximation is generalized for application in the randomized driven Lorentz gas. Utilizing the hopping approximation the asymptotic probability distribution function of the particle velocity is derived. Moreover, it is shown that, for harmonic driving, scatterer displacement upon collision increases the acceleration in both the driven Lorentz gas and the FUM by the same amount. On the other hand, the investigation of a randomized FUM, comprising one fixed and one moving wall driven by a sawtooth force function, reveals that the presence of a particular asymmetry of the driving function leads to an increase of acceleration that is different from that gained when symmetrical force functions are considered, for all finite number of collisions. This fact helps open up the prospect of designing accelerator devices by combining driving laws with specific symmetries to acquire a desired acceleration behavior for the ensemble of particles.

Lyapunov instability versus relaxation time in two coupled oscillators.

We consider the relation between relaxation time and the largest Lyapunov exponent in a system of two coupled oscillators, one of them being harmonic. It has been found that in a rather broad region of parameter space, contrary to the common expectation, both Lyapunov exponent and relaxation time increase as a function of the total energy. This effect is attributed to the fact that above a critical value of the total energy, although the Lyapunov exponent increases, Kolmogorov-Arnold-Moser tori appear and the chaotic fraction of phase space decreases. We examine the required conditions and demonstrate the key role of the dispersion relation for this behavior to occur. This study is useful, among other things, in the understanding of the damping of nuclear giant resonances.

Plasma nanotextured polymeric lab-on-a-chip for highly efficient bacteria capture and lysis.

We describe the design, fabrication, and successful demonstration of a sample preparation module comprising bacteria cell capture and thermal lysis on-chip with potential applications in food sample pathogen analysis. Plasma nanotexturing of the polymeric substrate allows increase of the surface area of the chip and the antibody binding capacity. Three different anti-Salmonella antibodies were directly and covalently linked to plasma treated chips without any additional linker chemistry or other treatment. Then, the Ab-modified chips were tested for their capacity to bind bacteria in the concentration range of 10(2)-10(8) cells per mL; the module exhibited 100% efficiency in Salmonella enterica serovar Typhimurium bacteria capture for cell suspensions below 10(5) cells per mL (10(4) cells injected with a 100 µL sample volume) and efficiency higher than 50% for 10(7) cells per mL. Moreover, thermal lysis achieved on-chip from as low as 10 captured cells was demonstrated and shown to compare well with off-chip lysis. Excellent selectivity (over 1 : 300) was obtained in a sample containing, in addition to S. Typhimurium and E. coli bacteria.

Nonhyperbolic escape and changes in phase-space stability structures in laser-induced multiphoton dissociation of a diatomic molecule.

The dependence of photodissociation of a diatomic molecule (vibrating according to the Morse potential) on the frequency of the laser field that induces it, is studied in the context of classical nonlinear dynamics. First, it is observed that as the laser frequency increases towards the harmonic frequency of the potential, a transition from stabilization due to Kolmogorov-Arnold-Moser tori to stabilization caused by the resonance stability island occurs. Then, considering the photodissociation as a nonhyperbolic half-scattering process, we investigate the influence of these changes in the phase space stability structures on dissociation dynamics via the examination of the fractal set of singularities appearing in the time-delay function of the initial state. It is found that the effective fractal dimension of this set (a finite-scale approximation of the exact dimension which is always equal to 1) and the percentage of its singularities provide a link between these changes and the dissociation rate.

Nonperiodic delay mechanism and fractallike behavior in classical time-dependent scattering.

We study the occurrence of delay mechanisms other than periodic orbits in scattering systems with time-dependent potentials. By using as model system two harmonically oscillating disks on a plane, we have found the existence of a mechanism not related to the periodic orbits of the system, that delays trajectories in the scattering region. This mechanism creates a fractallike structure in the scattering functions and can possibly occur in several time-dependent scattering systems.

Scattering off two oscillating disks: dilute chaos.

We investigate the role of the unstable periodic orbits and their manifolds in the dynamics of a time-dependent two-dimensional scattering system. As a prototype we use two oscillating disks on the plane with the oscillation axes forming an angle theta. The phase space of the system is five dimensional and it possesses a variety of families of unstable periodic orbits (UPOs) with intersecting manifolds. We perform numerical experiments to probe the structure of distinct scattering functions, in one and two dimensions, near the location of the UPOs. We find that the corresponding manifolds occur only in a very particular and localized way in the high-dimensional phase space. As a consequence the underlying fractal structure is ubiquitous only in higher-dimensional, e.g., two-dimensional, scattering functions. Both two-dimensional and one-dimensional scattering functions are dominated by seemingly infinite sequences of discontinuities characterized by small values of the magnitude of the projectile's outgoing velocity. These peaks accumulate toward the phase-space locations of the UPOs, with a rate which monotonically depends on the corresponding instability exponent. They represent the intersections of the set of the initial conditions with invariant sets of larger dimensionality embedded in the phase space of the system, which are not directly related with the UPOs. We adopt the term "dilute chaos" to characterize these phenomenological aspects of the scattering dynamics.

Quantum versus classical dynamics in a driven barrier: The role of kinematic effects.

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances, and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. In that frequency region, the classical and quantum transmission coefficients are in optimal agreement. Moreover, the transmission threshold (i.e., the energy above which the transmission coefficient becomes larger than a specific small threshold value) is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well-separated coherent pulses, a phenomenon that admits purely classical kinematic interpretation.

Formation and metrology of dual scale nano-morphology on SF(6) plasma etched silicon surfaces.

Surface roughness and nano-morphology in SF(6) plasma etched silicon substrates are investigated in a helicon type plasma reactor as a function of etching time and process parameters. The plasma etched surfaces are analyzed by atomic force microscopy. It is found that dual scale nano-roughness is formatted on the silicon surface comprising an underlying nano-roughness and superimposed nano-mounds. Detailed metrological quantification is proposed for the characterization of dual scale surface morphology. As etching proceeds, the mounds become higher, fewer and wider, and the underlying nano-roughness also increases. Increase in wafer temperature leads to smoother surfaces with lower, fewer and wider nano-mounds. A mechanism based on the deposition of etch inhibiting particles during the etching process is proposed for the explanation of the experimental behavior. In addition, appropriately designed experiments are conducted, and they confirm the presence of this mechanism.