Optimizing self-consistent field theory block copolymer models with X-ray metrology.

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

Characterizing the Interface Scaling of High χ Block Copolymers near the Order-Disorder Transition.

Advancements in the directed self-assembly of block copolymers (BCPs) have prompted the development of new materials with larger effective interaction parameters (χe). This enables BCP systems with phase separation at increasingly small degrees of polymerization (N). Very often these systems reside near the order-disorder transition and fit between the weak and strong segregation limits where the behavior of BCP systems is not as thoroughly understood. Utilizing resonant soft X-ray reflectivity (RSoXR) enables both the BCP pitch (L0) and interface width (wM) to be determined simultaneously, through a direct characterization of the composition profile of BCP lamellae oriented parallel to a substrate. A series of high χe BCPs with χe ranging from ≈0.04 to 0.25 and χeN from 19 to 70 have been investigated. The L0/wm ratio serves as an important metric for the feasibility of a material for nanopatterning applications; the results of the RSoXR measurement are used to establish a relationship between χe and L0/wm. The results of this analysis are correlated with experimentally established limits for the functionality of BCPs in nanopatterning applications. These results also provide guidance for the magnitude of χe needed to achieve small interface width for samples with sub-10 nm L0.

Advancing X-ray scattering metrology using inverse genetic algorithms.

We compare the speed and effectiveness of two genetic optimization algorithms to the results of statistical sampling via a Markov chain Monte Carlo algorithm to find which is the most robust method for determining real space structure in periodic gratings measured using critical dimension small angle X-ray scattering. Both a covariance matrix adaptation evolutionary strategy and differential evolution algorithm are implemented and compared using various objective functions. The algorithms and objective functions are used to minimize differences between diffraction simulations and measured diffraction data. These simulations are parameterized with an electron density model known to roughly correspond to the real space structure of our nanogratings. The study shows that for X-ray scattering data, the covariance matrix adaptation coupled with a mean-absolute error log objective function is the most efficient combination of algorithm and goodness of fit criterion for finding structures with little foreknowledge about the underlying fine scale structure features of the nanograting.

Design rules for self-assembled block copolymer patterns using tiled templates.

Directed self-assembly of block copolymers has been used for fabricating various nanoscale patterns, ranging from periodic lines to simple bends. However, assemblies of dense bends, junctions and line segments in a single pattern have not been achieved by using sparse templates, because no systematic template design methods for achieving such complex patterns existed. To direct a complex pattern by using a sparse template, the template needs to encode the key information contained in the final pattern, without being a simple copy of the pattern. Here we develop a set of topographic template tiles consisting of square lattices of posts with a restricted range of geometric features. The block copolymer patterns resulting from all tile arrangements are determined. By combining tiles in different ways, it is possible to predict a relatively simple template that will direct the formation of non-trivial block copolymer patterns, providing a new template design method for a complex block copolymer pattern.

Sacrificial-post templating method for block copolymer self-assembly.

A sacrificial-post templating method is presented for directing block copolymer self-assembly to form nanostructures consisting of monolayers and bilayers of microdomains. In this approach, the topographical post template is removed after self-assembly and therefore is not incorporated into the final microdomain pattern. Arrays of nanoscale holes of different shapes and symmetries, including mesh structures and perforated lamellae with a bimodal pore size distribution, are produced. The ratio of the pore sizes in the bimodal distributions can be varied via the template pitch, and agrees with predictions of self consistent field theory.

Optimizing topographical templates for directed self-assembly of block copolymers via inverse design simulations.

An inverse design algorithm has been developed that predicts the necessary topographical template needed to direct the self-assembly of a diblock copolymer to produce a given complex target structure. The approach is optimized by varying the number of topographical posts, post size, and block copolymer volume fraction to yield a template solution that generates the target structure in a reproducible manner. The inverse algorithm is implemented computationally to predict post arrangements that will template two different target structures and the predicted templates are tested experimentally with a polydimethylsiloxane-b-polystyrene block copolymer. Simulated and experimental results show overall very good agreement despite the complexity of the patterns. The templates determined from the model can be used in developing simpler design rules for block copolymer directed self-assembly.

Inverse Design of Topographical Templates for Directed Self-Assembly of Block Copolymers.

A computational inverse design algorithm is presented that predicts the necessary topographical template to direct the self-assembly of a diblock copolymer thin film into a desired complex morphology. This topographical template is determined from the spatial configuration of a template that results in an energy minimum for the system. Degenerate solutions are accounted for by performing multiple simulations with random starting configurations of the topographical template and making a statistically weighted template that is tested using self-consistent field theory simulations. The final template is, thus, the inverse design solution of the desired block copolymer morphology. The results also yield nonintuitive post-configuration design principles.

Morphology control in block copolymer films using mixed solvent vapors.

Solvent vapor annealing of block copolymer thin films can produce a range of morphologies different from the equilibrium bulk morphology. By systematically varying the flow rate of two different solvent vapors (toluene and n-heptane) and an inert gas, phase maps showing the morphology versus vapor pressure of the solvents were constructed for 45 kg/mol polystyrene-block-polydimethylsiloxane diblock copolymer films of different thicknesses. The final morphology was correlated with the swelling of the block copolymer and homopolymer films and the solvent vapor annealing conditions. Self-consistent field theory is used to model the effects of solvent swelling. These results provide a framework for predicting the range of morphologies available under different solvent vapor conditions, which is important in lithographic applications where precise control of morphology and critical dimensions are essential.

Rectangular symmetry morphologies in a topographically templated block copolymer.

Using an array of majority-block-functionalized posts makes it possible to locally control the self-assembly of a block copolymer and achieve several morphologies on a single substrate. A template consisting of a square symmetry array of posts produces a square-symmetry lattice of microdomains, which doubles the areal density of features.

Aligned sub-10-nm block copolymer patterns templated by post arrays.

Self-assembly of block copolymer films can generate useful periodic nanopatterns, but the self-assembly needs to be templated to impose long-range order and to control pattern registration with other substrate features. We demonstrate here the fabrication of aligned sub-10-nm line width patterns with a controlled orientation by using lithographically formed post arrays as templates for a 16 kg/mol poly(styrene-block-dimethylsiloxane) (PS-b-PDMS) diblock copolymer. The in-plane orientation of the block copolymer cylinders was controlled by varying the spacing and geometry of the posts, and the results were modeled using 3D self-consistent field theory. This work illustrates how arrays of narrow lines with specific in-plane orientation can be produced, and how the post height and diameter affect the self-assembly.

Hierarchical nanostructures by sequential self-assembly of styrene-dimethylsiloxane block copolymers of different periods.

Poly(styrene-block-dimethylsiloxane) (PS-b-PDMS) block copolymers with a period as low as 13 nm have been self-assembled on a template formed from PS-b-PDMS of a 34­40 nm period, which is itself templated by micron-scale substrate features prepared using conventional lithography. This hierarchical process provides a simple method for directing the self-assembly of sub-10 nm features and registering them on the substrate.