Kostas Ch. Daoulas

Directed Self-Assembly of Block Copolymers for Nanolithography: Fabrication of Isolated Features and Essential Integrated Circuit Geometries

Self-assembling block copolymers are of interest for nanomanufacturing due to the ability to realize sub-100 nm dimensions, thermodynamic control over the size and uniformity and density of features, and inexpensive processing. The insertion point of these materials in the production of integrated circuits, however, is often conceptualized in the short term for niche applications using the dense periodic arrays of spots or lines that characterize bulk block copolymer morphologies, or in the long term for device layouts completely redesigned into periodic arrays. Here we show that the domain structure of block copolymers in thin films can be directed to assemble into nearly the complete set of essential dense and isolated patterns as currently defined by the semiconductor industry. These results suggest that block copolymer materials, with their intrinsically advantageous self-assembling properties, may be amenable for broad application in advanced lithography, including device layouts used in existing nanomanufacturing processes.

Single chain in mean field simulations: quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations.

The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers.

Morphology of multi-component polymer systems: single chain in mean field simulation studies

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies reconstruction on patterned substrates.

Calculating the Free Energy of Self-Assembled Structures by Thermodynamic Integration

We discuss a method for calculating free energy differences between disordered and ordered phases of self-assembling systems utilizing computer simulations. Applying an external, ordering field, we impose a predefined structure onto the fluid in the disordered phase. The structure in the presence of the external, ordering field closely mimics the structure of the ordered phase (in the absence of an ordering field). Self-consistent field theory or density functional theory provides an accurate estimate for choosing the strength of the ordering field. Subsequently, we gradually switch off the external, ordering field and, in turn, increase the control parameter that drives the self-assembly. The free energy difference along this reversible path connecting the disordered and the ordered state is obtained via thermodynamic integration or expanded ensemble simulation techniques. Utilizing Single-Chain-in-Mean-Field simulations of a symmetric diblock copolymer melt we illustrate the method and calculate the free energy difference between the disordered phase and the lamellar structure at an intermediate incompatibility chiN=20. Evidence for the first-order character of the order-disorder transition at fixed volume is presented. The transition is located at chi(ODT)N=13.65+/-0.10 for an invariant degree of polymerization of N=14 884. The magnitude of the shift of the transition from the mean field prediction qualitatively agrees with other simulations.

Single-chain dynamics in a homogeneous melt and a lamellar microphase: A comparison between Smart Monte Carlo dynamics, slithering-snake dynamics, and slip-link dynamics

We investigate the ability of Monte-Carlo algorithms to describe the single-chain dynamics in a dense homogeneous melt and a lamellar phase of a symmetric diblock copolymer. A minimal, coarse-grained model is employed that describes connectivity of effective segments by harmonic springs and where segments interact via soft potentials, which do not enforce noncrossability of the chain molecules. Studying the mean-square displacements, the dynamic structure factor, and the stress relaxation, we show that local, unconstraint displacements of segments via a Smart Monte Carlo algorithm give rise to Rouse dynamics for all but the first Monte Carlo steps. Using the slithering-snake algorithm, we observe a dynamics that is compatible with the predictions of the tube model of entangled melts for long times, but the dynamics inside the tube cannot be resolved. Using a slip-link model, we can describe the effect of entanglements and follow the different regimes of the single-chain dynamics over seven decades in time. Applications of this simulation scheme to spatially inhomogeneous systems are illustrated by studying the lamellar phase of a symmetric diblock copolymer. For the local, unconstraint dynamics, the single-chain motions parallel and perpendicular to the interfaces decouples; the perpendicular dynamics is slowed down but the parallel dynamics is identical to that in a homogeneous melt. Both the slithering-snake dynamics and the slip-link dynamics give rise to a coupling of parallel and perpendicular directions and a significant slowing down of the dynamics in the lamellar phase.

Equilibration of High Molecular Weight Polymer Melts: A Hierarchical Strategy

A strategy is developed for generating equilibrated high molecular weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains features like hard excluded volume interactions and realistic melt densities. The microscopic representation is mapped onto a model of soft spheres with fluctuating size, where each sphere represents a microscopic subchain with Nb monomers. By varying Nb, a hierarchy of CG representations at different resolutions is obtained. Within this hierarchy, CG configurations equilibrated with Monte Carlo at low resolution are sequentially fine-grained into CG melts described with higher resolution. A Molecular Dynamics scheme is employed to slowly introduce the microscopic details into the latter. All backmapping steps involve only local polymer relaxation; thus, the computational efficiency of the scheme is independent of molecular weight, being just proportional to system size. To...

Morphology and Charge Transport in P3HT: A Theorist’s Perspective

Poly(3-hexylthiophene) (P3HT) is the fruit fly among polymeric organic semiconductors. It has complex self-assembling and electronic properties and yet lacks the synthetic challenges that characterize advanced donor–acceptor-type polymers. P3HT can be used both in solar cells and in field-effect transistors. Its morphological, conductive, and optical properties have been characterized in detail using virtually any and every experimental technique available, whereas the contributions of theory and simulation to a rationalization of these properties have so far been modest. The purpose of this review is to take a snapshot of these results and, more importantly, outline directions that still require substantial method development.

Measuring excess free energies of self-assembled membrane structures

Using computer simulation of a solvent-free, coarse-grained model for amphiphilic membranes, we study the excess free energy of hourglass-shaped connections (i.e., stalks) between two apposed bilayer membranes. In order to calculate the free energy by simulation in the canonical ensemble, we reversibly transfer two apposed bilayers into a configuration with a stalk in three steps. First, we gradually replace the intermolecular interactions by an external, ordering field. The latter is chosen such that the structure of the non-interacting system in this field closely resembles the structure of the original, interacting system in the absence of the external field. The absence of structural changes along this path suggests that it is reversible; a fact which is confirmed by expanded-ensemble simulations. Second, the external, ordering field is changed as to transform the non-interacting system from the apposed bilayer structure to two-bilayers connected by a stalk. The final external field is chosen such that the structure of the non-interacting system resembles the structure of the stalk in the interacting system without a field. On the third branch of the transformation path, we reversibly replace the external, ordering field by non-bonded interactions. Using expanded-ensemble techniques, the free energy change along this reversible path can be obtained with an accuracy of 10(-3)k(B)T per molecule in the n VT-ensemble. Calculating the chemical potential, we obtain the free energy of a stalk in the grandcanonical ensemble, and employing semi-grandcanonical techniques, we calculate the change of the excess free energy upon altering the molecular architecture. This computational strategy can be applied to compute the free energy of self-assembled phases in lipid and copolymer systems, and the excess free energy of defects or interfaces.

Effect of Mesoscale Ordering on the Density of States of Polymeric Semiconductors

A multiscale simulation scheme, which incorporates both long-range conformational disorder and local molecular ordering, is proposed for predicting large-scale morphologies and charge transport properties of polymeric semiconductors. Using poly(3-hexylthiophene) as an example, it is illustrated how the energy landscape and its spatial correlations evolve with increasing degree of structural order in mesophases with amorphous, uniaxial, and biaxial nematic ordering. It is shown that the formation of low-lying energy states in more ordered systems is mostly due to larger (on average) conjugation lengths and not due to electrostatic interactions. The proposed scheme is general and can be applied to a wide range of polymeric organic materials.

Phase behaviour of quasi-block copolymers: A DFT-based Monte-Carlo study

We develop a mesoscopic density functional theory (DFT)-based Monte-Carlo approach for studying the phase behaviour of multi-component systems comprised of irreversibly bonded, conventional macromolecules and supramolecular entities. The latter can reversibly associate with each other and the conventional components to “living”, equilibrium polymers. The computational approach can be applied to a broad class of supramolecular systems and we focus here on quasi-block copolymer systems that contain conventional, “dead” AB-copolymers with a supramolecular B-terminus and supramolecular B-units. The simulations show that, by properly selecting the architecture of the “dead” copolymers and by varying the supramolecular association constant and the incompatibility between the segment species, A and B, one obtains a variety of different microphase-separated morphologies and macrophase separations. Two representative phase diagrams are reported as a function of the association constant, Eb, and the Flory–Huggins parameter, χ, quantifying the repulsion between A and B segments. The simulation results are qualitatively rationalised by considering the dependence of the stoichiometry on the systems parameters, and fractionation effects between coexisting phases are illustrated.