A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (QIm3m), close-packed spheres (CPS), and the bicontinuous cubic network with Ia3d symmetry (QIa3d). The CPS phase exists in narrow regions along the order−disorder transition for χN ≥ 17.67. Results suggest that the QIa3d phase is not stable above χN ∼ 60. Along the L/QIa3d phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (QPn3m) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and compa...

Unifying Weak- and Strong-Segregation Block Copolymer Theories

Directing the self-assembly of block copolymers

The nanometer-scale architectures in thin films of self-assembling block copolymers have inspired a variety of new applications. For example, the uniformly sized and shaped nanodomains formed in the films have been used for nanolithography, nanoparticle synthesis, and high-density information storage media. Imperative to all of these applications, however, is a high degree of control over orientation of the nanodomains relative to the surface of the film as well as control over order in the plane of the film. Induced fields including electric, shear, and surface fields have been demonstrated to influence orientation. Both heteroepitaxy and graphoepitaxy can induce positional order on the nanodomains in the plane of the film. This article will briefly review a variety of mechanisms for gaining control over block copolymer order as well as many of the applications of these materials. Particular attention is paid to the potential of perfecting long-range two-dimensional order over a broader range of length scales and the extension of these concepts to functional materials and more complex architectures.

/pdf/patterning-with-block-copolymer-thin-films-5gldelhkf5.pdf

Patterning with block copolymer thin films

One of the key challenges in nanotechnology is to control a self-assembling system to create a specific structure. Self-organizing block copolymers offer a rich variety of periodic nanoscale patterns, and researchers have succeeded in finding conditions that lead to very long range order of the domains. However, the array of microdomains typically still contains some uncontrolled defects and lacks global registration and orientation. Recent efforts in templated self-assembly of block copolymers have demonstrated a promising route to control bottom-up self-organization processes through top-down lithographic templates. The orientation and placement of block-copolymer domains can be directed by topographically or chemically patterned templates. This templated self-assembly method provides a path towards the rational design of hierarchical device structures with periodic features that cover several length scales.

Templated Self‐Assembly of Block Copolymers: Top‐Down Helps Bottom‐Up

As the size scale of device features becomes ever smaller, conventional lithographic processes become increasingly more difficult and expensive, especially at a minimum feature size of less than 45 nm. Consequently, to achieve higher-density circuits, storage devices, or displays, it is evident that alternative routes need to be developed to circumvent both cost and manufacturing issues. An ideal process would be compatible with existing technological processes and manufacturing techniques; these strategies, together with novel materials, could allow significant advances to be made in meeting both short-term and long-term demands for higher-density, faster devices. The self-assembly of block copolymers (BCPs), two polymer chains covalently linked together at one end, provides a robust solution to these challenges. As thin films, immiscible BCPs self-assemble into a range of highly ordered morphologies where the size scale of the features is only limited by the size of the polymer chains and are, therefore, nanoscopic. While self-assembly alone is sufficient for a number of applications in fabricating advanced microelectronics, directed, self-orienting, self-assembly processes are also required to produce complex devices with the required density and addressability of elements to meet future demands. Both strategies require the design and synthesis of polymers that have well-defined characteristics such that the necessary fine control over the morphology, interfacial properties, and simplicity of processes can be realized. By combining tailored self-assembly processes (a “bottom-up” approach) with microfabrication processes (a “top-down” approach), the ever-present thirst of the consumer for faster, better, and cheaper devices can be met in very simple, yet robust, ways. The integration of novel chemistries with the manipulation of self-assembly will be treated in this article.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0883769400014263

Block Copolymer Lithography: Merging “Bottom-Up” with “Top-Down” Processes

We have studied the ordering dynamics of a two-dimensional system which consists of a single layer of spherical block copolymer microdomains in a thin film. We follow the annealing process after a quench from the disordered state by electron microscopy and time-lapse atomic force microscopy. At late times the orientational correlation length ξ6 of the microdomain lattice exhibits a t1/4 temporal power law. We compare the time evolution of the densities of dislocations, disclinations and the dislocation orientational correlation function. While most disclinations condense into dislocations and most dislocations condense into "grain boundaries", the dynamics appear to involve the interplay of disclinations and lines of dislocations. Rather than isolated grains shrinking, the most frequently observed process is the collapse of a smaller grain which resides on the boundary of two larger grains.

https://iopscience.iop.org/article/10.1209/epl/i2004-10126-5/pdf

Pattern coarsening in a 2D hexagonal system

Correction of distortion due to thermal drift in scanning probe microscopy

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. DOI: 10.1103/PhysRevLett.113.265502

/pdf/static-and-dynamic-aspects-of-black-silicon-formation-2pyk5xj8jr.pdf

Static and dynamic aspects of black silicon formation.

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.

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

Block copolymer nanolithography

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