Static and dynamic aspects of black silicon formation.

We present a combination of experimental data and modeling that explains some of the important characteristics of black silicon (BSi) developed in cryogenic reactive ion etching (RIE) processes, including static properties (dependence of resulting topography on process parameters) and dynamic aspects (evolution of topography with process time). We generate a phase diagram predicting the RIE parameter combinations giving rise to different BSi geometries and show that the topographic details of BSi explain the metamaterial characteristics that are responsible for its low reflectivity. In particular, the unique combination of needle and hole features of various heights and depths, which is captured by our model and confirmed by focused ion beam nanotomography, creates a uniquely smooth transition in refractive index. The model also correctly describes dynamical characteristics, such as the dependence of aspect ratio on process time, and the prediction of new etching fronts appearing at topographical saddle points during the incipient stages of BSi development--a phenomenon reported here for the first time.

Three-axis correction of distortion due to positional drift in scanning probe microscopy.

Two common sources of distortion in scanning probe microscopy are piezo creep and thermal drift, the latter caused by slow thermal expansions of materials in the sample and microscope due to small changes in temperature over the course of a scan. We present a technique for correcting distortion due to thermal drift along all three spatial axes, along with simultaneous correction of z-axis piezo creep. Our method works by comparing each scanned topographical image to a second, partial scan, taken immediately afterwards, on which the fast and slow scan axes have been reversed. We model the positional distortion as a low-order polynomial function in three dimensions, searching for the set of correctional coefficients that minimizes the root-mean-square difference between the two scans. We demonstrate in a variety of real-world and simulated tests that this technique can routinely reduce distortion from these effects by over 90%, often to a precision of better than a single pixel.

Electrochemical analysis of azurin thermodynamic and adsorption properties at monolayer-protected cluster film assemblies - evidence for a more homogeneous adsorption interface.

Thermodynamic and adsorption properties of protein monolayer electrochemistry (PME) are examined for Pseudomonas aeruginosa azurin (AZ) immobilized at an electrode modified with a networked film of monolayer-protected clusters (MPCs) to assess if nanoparticle films of this nature offer a more homogeneous adsorption interface compared to traditional self-assembled monolayer (SAM) modified electrodes. Specifically, electrochemistry is used to assess properties of surface coverage, formal potential, peak broadening, and electron transfer (ET) kinetics as a function of film thickness. The modification of a surface with dithiol-linked films of MPCs (Au(225)C6(75)) provides a more uniform binding interface for AZ that results in voltammetry with less peak broadening (<110mV) compared to SAMs (>120-130mV). Improved homogeneity of the MPC interface for protein adsorption is confirmed by atomic force microscopy imaging that shows uniform coverage of the gold substrate topography and by electrochemical analysis of film properties during systematic desorption of AZ, which indicates a more homogeneous population of adsorbed protein at MPC films. These results suggest MPC film assemblies may be used in PME to provide greater molecular level control of the protein adsorption interface, a development with applications for strategies to study biological ET processes as well as the advancement of biosensor technologies.

Correction of distortion due to thermal drift in scanning probe microscopy.

A common source of distortion in scanning probe microscope (SPM) images is "thermal drift," the slow thermal expansion of different materials in the sample and microscope due to small changes in temperature over the course of a scan. We describe here a method for correcting this distortion by immediately following each image scan with a rescan of a small, narrow portion of the same area with the slow and fast scan axes reversed. The original, full image is corrected using a low-order polynomial mapping function, with coefficients determined by a pixel-wise comparison between the original full and rescanned partial images. We demonstrate here that this method can correctly remove distortion from a wide range of images with a precision of better than one pixel, and is also robust to common imaging artifacts. We also address some of the programming considerations that have gone into implementing this computationally intensive technique, which can now be performed using standard desktop hardware in times that range between a few seconds and a few minutes.

Distance dependence of electron transfer kinetics for azurin protein adsorbed to monolayer protected nanoparticle film assemblies.

The distance dependence and kinetics of the heterogeneous electron transfer (ET) reaction for the redox protein azurin adsorbed to an electrode modified with a gold nanoparticle film are investigated using cyclic voltammetry. The nanoparticle films are comprised of nonaqueous nanoparticles, known as monolayer-protected clusters (MPCs), which are covalently networked with dithiol linkers. The MPC film assembly serves as an alternative adsorption platform to the traditional alkanethiolate self-assembled monolayer (SAM) modified electrodes that are commonly employed to study the ET kinetics of immobilized redox proteins, a strategy known as protein monolayer electrochemistry. Voltammetric analysis of the ET kinetics for azurin adsorbed to SAMs of increasing chain length results in quasi-reversible voltammetry with significant peak splitting. We observed rate constants (k degrees (ET)) of 12-20 s(-1) for the protein at SAMs of shorter alkanethiolates that decays exponentially (beta = 0.9/CH(2) or 0.8/A) at SAMs of longer alkanethiolates (9-11 methylene units) or an estimated distance of 1.23 nm and is representative of classical electronic tunneling behavior over increasing distance. Azurin adsorbed to the MPC film platforms of increasing thickness results in reversible voltammetry with very little voltammetric peaks splitting and nearly negligible decay of the ET rate over significant distances up to 20 nm. The apparent lack of distance dependence for heterogeneous ET reactions at MPC film assemblies is attributed to a two-step mechanism involving extremely fast electronic hopping through the MPC film architecture. These results suggest that MPC platforms may be used in protein monolayer electrochemistry to create adsorption platforms of higher architecture that can accommodate greater than monolayer protein coverage and increase the Faradaic signal, a finding with significant implications for amperometric biosensor design and development.

Combinatorial mapping of substrate step edge effects on diblock copolymer thin film morphology and orientation.

We have used a combinatorial gradient technique to map precisely how the terrace structure and microdomain lattice alignment in a thin film of a sphere-forming diblock copolymer are affected by both the thickness of the copolymer film and the height of a series of parallel step edges fabricated on the substrate. We find that for film thicknesses slightly incommensurate with integer numbers of sphere layers, the step edges act as nucleation sites for regions with one more or one fewer layers of spheres. We also find that for our system, the hexagonal lattice formed by a single layer of spheres on the low side of a step edge is aligned along the direction of the step edge only where the film on the high side is sufficiently thin to support only a wetting layer of copolymer material. This work will guide the tuning of film thickness and step height in future studies and applications of graphoepitaxy in block copolymer films.

Ordering mechanisms in two-dimensional sphere-forming block copolymers.

We study the coarsening dynamics of two-dimensional hexagonal patterns formed by single microdomain layers of block copolymers, using numerical simulations. Our study is focused on the temporal evolution of the orientational correlation length, the interactions between topological defects, and the mechanisms of coarsening. We find no free disclinations in the system; rather, they are located on large-angle grain boundaries, commonly where such boundaries bifurcate. The correlation lengths determined from the scattering function, from the density of dislocations, and from the density of disclinations exhibit similar behavior and grow with time according to a power law. The orientational correlation length also grows following a power law, but with a higher exponent than the other correlation lengths. The orientational correlation length grows via annihilation of dislocations, through preferential annihilation of small-angle grain boundaries due to poor screening of the strain field around dislocations located on small-angle grain boundaries. Consequently, the patterns are characterized by large-angle grain boundaries. The most commonly observed mechanism of coarsening is the collapse of smaller grains residing on the boundary of two larger grains delimited by large-angle grain boundaries. Simulations agree remarkably well with experimental results recently obtained.

Correction for piezoelectric creep in scanning probe microscopy images using polynomial mapping.

We describe a method for using polynomial mapping to correct scanning probe microscope images for distortion due to piezoelectric creep. Because such distortion varies from image to image, this method can be used when the actual locations of some features within an image are known absolutely, or in a series of images in which the actual locations of some features are known not to vary. While the general case of polynomial mapping of degree N requires the determination of 2(N+ 1)2 matrix elements by regression, we find that by understanding the mechanism by which piezoelectric creep distorts scanning probe microscope images, we can fix most of these coefficients at 0 or 1 a priori, leaving only 2(N+ 1) coefficients to be determined by regression. We describe our implementation of this strategy using the Interactive Data Language (IDL) programming language, and demonstrate our technique on a series of atomic force microscopy (AFM) images of diblock copolymer microdomains. Using our simplified scheme, we are able to reduce the effects of distortion in an AFM image from 5% of the scan width to a single pixel, using only five reference points.