Benjamin D. Nation

Simulation study of the effect of differences in block energy and density on the self-assembly of block copolymers

One of the potentially most important issues in accurately modeling directed self-assembly of block copolymers (BCPs) is the fact that the real BCPs often have block energy and/or density asymmetry, meaning that each block has a different homopolymer density and/or cohesive energy density (CED). A simulation of BCP behavior based on molecular dynamics of coarse-grained polymer chains has been developed that can independently parameterize and control the density and the CED of each block to more accurately match this asymmetry. This model was used to study the effect on the order-disorder transition (ODT), domain scaling, and self-assembly of thin films of BCPs. BCPs whose blocks each have a different density show deviations from the mean-field ODT coexistence curve, exhibiting an asymmetric order-disorder transition curve. Self-assembly of thin films of BCPs with mismatches in CED shows significant changes in morphologies compared to BCPs with energetically symmetric blocks, because the lowest CED block has a strong propensity to segregate to and “wet” the free interface. This CED mismatch also gives rise to a large number of deviations from bulk behavior including changing vertical-to-horizontal morphologies through film depth, compression and expansion of domain sizes, and island and hole formations among others.

Understanding defects in DSA: calculation of free energies of block copolymer DSA systems via thermodynamic integration of a mesoscale block-copolymer model

Directed self-assembly (DSA) of block copolymers (BCPs) is a promising method for producing the sub-20nm features required for future semiconductor device scaling, but many questions still surround the issue of defect levels in DSA processes. Knowledge of the free energy associated with a defect is critical to estimating the limiting equilibrium defect density that may be achievable in such a process. In this work, a coarse grained molecular dynamics (MD) model is used to study the free energy of a dislocation pair defect via thermodynamic integration. MD models with realistic potentials allow for more accurate simulations of the inherent polymer behavior without the need to guess modes of molecular movement and without oversimplifying atomic interactions. The free energy of such a defect as a function of the Flory- Huggins parameter (χ) and the total degree of polymerization (N) for the block copolymer is also calculated. It is found that high pitch multiplying underlayers do not show significant decreases in defect free energy relative to a simple pitch doubling underlayer. It is also found that χN is not the best descriptor for correlating defect free energy since simultaneous variation in chain length (N) and χ value while maintaining a constant χN product produces significantly different defect free energies. Instead, the defect free energy seems to be directly correlated to the χ value of the diblock copolymer used. This means that as higher χ systems are produced and utilized for DSA, the limiting defect level will likely decrease even though DSA processes may still operate at similar χN values to achieve ever smaller feature sizes.

Calculations of the free energy of dislocation defects in lamellae forming diblock copolymers using thermodynamic integration

Abstract. State-of-the-art directed self-assembly (DSA) of block copolymer (BCP) methods still yield defect densities orders of magnitude higher than is necessary in semiconductor fabrication. The defect free energy of a dislocation pair or jog defect, one of the most common defects found in BCP-DSA, is calculated via thermodynamic integration using a coarse-grained molecular dynamics model as a function of χ and the degree of polymerization (N). It is found that χN is not the best predictor of defect free energy and that a single χN value can yield vastly different free energies when χ and N are different. Defect free energy was highly dependent on defect location relative to the underlayer, and free energy differences ∼100  kT were found among the three possible defect locations on a 1:3 guiding pattern. It was found that increasing molar mass dispersity (Ð) significantly reduced defect free energy. Extrapolating from Ð up to 1.5 suggests that the defect will occur in equal proportions to the defect free state at a Ð of around 1.6 for this system. It was found that long chains tended to concentrate near the defect and stabilize the defect.

Coarse-grained molecular dynamics modeling of the kinetics of lamellar block copolymer defect annealing

Abstract. State-of-the-art block copolymer (BCP)—directed self-assembly (DSA) methods still yield defect densities orders of magnitude higher than is necessary in semiconductor fabrication despite free-energy calculations that suggest equilibrium defect densities are much lower than is necessary for economic fabrication. This disparity suggests that the main problem may lie in the kinetics of defect removal. This work uses a coarse-grained model to study the rates, pathways, and dependencies of healing a common defect to give insight into the fundamental processes that control defect healing and give guidance on optimal process conditions for BCP-DSA. It is found that bulk simulations yield an exponential drop in defect heal rate above χN∼30. Thin films show no change in rate associated with the energy barrier below χN∼50, significantly higher than the χN values found previously for self-consistent field theory studies that neglect fluctuations. Above χN∼50, the simulations show an increase in energy barrier scaling with 1/2 to 1/3 of the bulk systems. This is because thin films always begin healing at the free interface or the BCP-underlayer interface, where the increased A−B contact area associated with the transition state is minimized, while the infinitely thick films cannot begin healing at an interface.

Coarse-grained molecular dynamics modeling of the kinetics of lamellar BCP defect annealing

Directed self-assembly of block copolymers (BCPs) is a process that has received great interest in the field of nanomanufacturing in the past decade, and great strides towards forming high quality aligned patterns have been made. But state of the art methods still yield defectivities orders of magnitude higher than is necessary in semi-conductor fabrication even though free energy calculations suggest that equilibrium defectivities are much lower than is necessary for economic semi-conductor fabrication. This disparity suggests that the main problem may lie in the kinetics of defect removal. This work uses a coarse-grained model to study the rates, pathways, and dependencies of healing a common defect to give insight into the fundamental processes that control defect healing and give guidance on optimal process conditions for BCP-DSA. It is found that infinitely thick films yield an exponential drop in defect heal rate above χN ~ 30. Below χN ~ 30, the rate of transport was similar to the rate at which the transition state was reached so that the overall rate changed only slightly. The energy barrier in periodic simulations increased with 0.31 χN on average. Thin film simulations show no change in rate associated with the energy barrier below χN ~ 50, and then show an increase in energy barrier scaling with 0.16χN. Thin film simulations always begin to heal at either the free interface or the BCP-underlayer interface where the increased A-B contact area associated with the transition state will be minimized, while the infinitely thick films must start healing in the bulk where the A-B contact area is increased. It is also found that cooperative chain movement is required for the defect to start healing.

Predicting process windows for pattern density multiplication using block copolymer directed self-assembly in conjunction with chemoepitaxial guiding layers

Pattern density multiplication using directed self-assembly (DSA) of block copolymers (BCPs) is a technique capable of producing patterns with small pitches utilizing guiding template patterns printed as larger feature sizes and pitches. One method for achieving this density multiplication is to utilize chemoepitaxy based on a guiding underlayer that is nominally topographically flat but which is composed of a pinning region, or stripe if referring to lamellae, which will chemically prefer one microphase of the BCP, as well as a second region that is often referred to as “neutral” to both phases of the BCP. In most conceptions of such a chemoepitaxial approach for alignment of lamellae patterns, the pinning stripe is typically the width of a single lamellae of the phase separated BCP, while the neutral stripe is some odd number of lamellae widths. In this work, detailed simulation studies have been performed to elucidate the effects of variables such as guiding stripe size, chemical composition of the neutral stripes, and small topography on the process window of DSA pitch sub-division patterning processes. A simple but novel technique has been developed and utilized to quantify the level of alignment of a simulated BCP film to an underlying guiding pattern. Such process windows and lithographic parameters have been studied for different pitch sub-division conditions including 1:3 and 1:5 pinning stripe:neutral stripe width ratios. It is found that the center of the processing window occurs at a composition of the “neutral stripe” such that it is slightly to somewhat strongly preferential to the type of polymer of opposite type to that attracted by the pinning stripe, and that this ideal “neutral stripe” composition becomes more neutral as the density multiplication increases.

Block copolymer directed self-assembly using chemoepitaxial guiding underlayers with topography

Guiding underlayers are used in the directed self-assembly of block copolymers (BCPs) to form large defect free arrays. These underlayers traditionally have divided into two categories: chemoepitaxial underlayers which guide the BCP using regions of differing chemical preference and graphoepitaxial guiding underlayers which guide by topographic features built into the underlayer. However, multiple hybrid approaches have been introduced over recent years using both topographic features and chemical preference to direct the BCP film. In this work, a coarse-grained molecular dynamics model is used to explore both the geometric aspects and the chemical preferences of these hybrid underlayers and the effect these variables have on the defectivity of the BCP film. It is found that hybrid underlayers with vertical sidewalls behave in manners similar to more purely graphoepitaxial guiding underlayers, while hybrid underlayers with sloped sidewalls behave in a manner similar to chemoepitaxial guiding underlayers. ...

Chemoepitaxial guiding underlayers for density asymmetric and energetically asymmetric diblock copolymers

Abstract. Currently, high χ block copolymers (BCPs) are being investigated as a method to extend optical lithography due to their ability to microphase separate on small size scales. Typically, BCPs with larger Flory–Huggin’s χ parameters are composed of more dissimilar homopolymers. However, having dissimilar blocks changes how BCPs interact with their guiding underlayers. Several BCPs are simulated annealing on chemoepitaxial guiding underlayers using a coarse-grained molecular dynamics model to explore the effect that either energetic asymmetry or density asymmetry in the BCP have on the pattern registration. It is found that in varying the background region composition four regimes can be found. Minor variations in pinning stripe width are shown to have little effect on the window where well-aligned vertical lamellae form. For BCPs without an energetic mismatch, incommensurate films have the largest window for well-aligned vertical lamellae. However, with an energetic mismatch, the defectivity has a more complicated dependence on film thickness. Two different mixed lamellae (ML) morphologies can form depending on the film volume fraction and the relative compressibilities of the two blocks. It is found that more preferential background regions can be used when the BCP is transitioning between the two ML morphologies. This transition volume fraction shifts for a density asymmetric BCP, likely due to a difference in compressibilities of the two blocks.

Effect of chemoepitaxial guiding underlayer design on the pattern quality and shape of aligned lamellae for fabrication of line-space patterns

Abstract. Chemoepitaxial guidance of block copolymer directed self-assembly in thin films is explored using a coarse-grained molecular dynamics model. The underlayers studied are 2× density multiplying line-space patterns composed of repeating highly preferential pinning stripes of various widths separated by larger, more neutral, background regions of various compositions. Decreasing the pinning stripe width or making the background region more neutral is found to increase the line edge roughness (LER) of the lines, but these conditions are found to give the straightest sidewalls for the formed lines. Varying these underlayer properties is found to have minimal effect on linewidth roughness. A larger pinning stripe causes the pinned line (PL) to foot (expand near the substrate), and a preferential background region causes the unpinned line (UPL) to undercut (contract near the substrate). A simple model was developed to predict the optimal conditions to eliminate footing. Using this model, conditions are found that decrease footing of the PL, but these conditions increase undercutting in the UPL. Deformations in either the PL or UPL propagate to the other line. There exists a trade-off between LER and the footing/undercutting, that is, decreasing LER increases footing/undercutting and vice versa.

Free energy of defects in chemoepitaxial block copolymer directed self-assembly: effect of pattern density and defect position

Abstract. Block copolymers (BCPs) can phase separate to form periodic structures with small spacings, making BCPs an attractive option for furthering the ability of optical lithography. Chemoepitaxy is a method of directed self-assembly (DSA) that uses preferential pinning stripes to guide the BCP. The periodicity of the underlayers pinning stripe compared to the periodicity of the BCP is defined as the density multiplication. Molecular dynamics simulations are used to explore the effect that density multiplication and pinning stripe position (PSP) have on the free energy difference between a defective and defect-free BCP film. For all defect orders, the highest free energies were obtained when a pinning stripe was located directly under or adjacent to the terminating block. At high-density multiplications, the defects were found to approach the free energy of the same defect on an unpatterned underlayer. For all density multiplications and PSPs, the free energy of defective films is significantly higher than that of defect-free films, suggesting that the presence of defects in experiments is likely due to kinetic entrapment of defects. Free energy initially increases with increasing defect size but was found to level off and even decrease for the largest defects in this work.