Andrew J. Peters

Effects of block copolymer polydispersity and χN on pattern line edge roughness and line width roughness from directed self-assembly of diblock copolymers

This paper addresses two fundamental issues: (1) the connection between block copolymer polydispersity (as measured by a polydisperisty index (PDI)) and pattern LER/ LWR limits and (2) the connection between block copolymer χN value and pattern LER/LWR limits. In this work, we have used coarse grained molecular dynamics (MD) simulations of BCP DSA to study the effect of block copolymer PDI on DSA properties including LER/LWR and patterning capability. It is observed that as PDI increases from 1 to values of ~1.3, there is little effect on pattern LER/LWR, and as PDI increases above ~1.3 the LER/LWR increases slowly with increasing PDI. This suggests that LER/LWR concerns are not a major determinant in terms of specifying block copolymer PDI requirements for DSA processes. Concerning χN and LER/LWR, there is a sharp increase in roughness for χN<30. Because of the sharp increase at such low χN values, it is unlikely that BCP DSA processes for semiconductor manufacturing will be able to operate at low χN values even though microphase separation still occurs at these low χN values.

Detailed molecular dynamics studies of block copolymer directed self-assembly: Effect of guiding layer properties

Detailed molecular dynamics simulations have been performed to explore the effect of guiding layer properties and errors on resulting directed self-assembly pattern properties produced in block copolymer (BCP) thin films. Guiding patterns that are noncommensurate to the natural BCP pitch are considered, as are guiding lines that have correlated or anticorrelated line edge deviations. The process window is detailed for noncommensurate line widths. Guiding lines with various correlated and anticorrelated roughnesses show that under the high χ conditions used here, very significant guiding roughness is required to have any effect on the BCP film, and most of the guiding roughness is damped out within 5 nm of the bottom surface of the BCP film. Also, pitch subdivision patterns (where the BCP natural periodicity is some integer multiple smaller than the guiding pattern periodicity) damp out guiding line roughness more easily than pitch replicating patterns where a guiding pattern exists for each line formed in...

Coarse grained molecular dynamics model of block copolymer directed self-assembly

A model has been developed for the simulation of block copolymer (BCP) directed self-assembly (DSA) based on a coarse grained polymer model that anneals using molecular dynamics. The model uses graphics processing units (GPUs) to perform the calculations; this combined with the coarse graining means simulations times approach the speed of other more commonly used simulation techniques for BCPs. The model is unique in how it treats the pure phase blocks interactions with themselves (i.e. A-A and B-B interactions) and their interactions with each other. This allows for simulations that can potentially more accurately capture the differences between the properties of each block such as density and cohesive energy. The model is fully described and used to examine some of the issues that are unique to DSA lithographic applications of BCPs. We describe a method to calculate χ for the off-lattice MD system based on observation of the order-disorder transitions (ODT) for different degrees of polymerization N. The model is used to examine the transient, complex, non-classical morphologies that can occur through film thickness during a DSA process. During the phase separation process from a mixed initial state, the BCPs first locally phase separate to form small aggregate type structures. These aggregates then coalesce into larger features that approach the size of the equilibrium domain. These features then shift to match the guiding pattern on the underlayer followed by the slow elimination of defects. We also studied how the guiding patterns work in chemo-epitaxy DSA. The guiding patterns have a strong immediate effect on the BCP film nearest the interface and induce locally aligned self-assembly. Over time, this induced pattern tends to propagate up through the thickness of the film until the film is uniformly aligned to the guiding pattern. We also clearly see that the observed morphology at the top of the film gives no indication of the morphology through the depth, especially during the transient portions of the self-assembly process.

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.

PS-b-PHOST as a high χ block copolymers for directed self assembly: optimization of underlayer and solvent anneal processes

Directed self-assembly (DSA) of block copolymers (BCP) could enable high resolution patterning beyond the capabilities of current optical lithography methods via pitch multiplication from lower resolution primary lithographic patterns. For example, DSA could enable dense feature production with pitches less than 80 nm from patterns generated using 193 nm exposure tools without the need for double patterning or other schemes. According to theory, microphase separation of diblock copolymers occurs when the critical condition that χ N >10.5 is met while the pitch of the resulting polymer features scale as ~N 2/3 , where χ is the Flory Huggins interaction parameter and N is the total degree of polymerization for the diblock copolymer. In order to generate patterns with smaller pitches, N must be decreased while maintaining a χ N >10.5 to allow for phase separation. This requires utilization of polymers with higher χ values as N is decreased. Current materials, such as PS-b-PMMA, exhibit a relatively low χ value of ~0.04, which limits the practical pitch of DSA line-space patterns produced using PS-b-PMMA to approximately 20 nm. In this paper, we investigate alternative materials, namely poly(styrene)-b-poly(hydroxystyrene) (PS-b-PHOST), which exhibits a high χ value via hydrogen bonding interactions that can allow for production of sub-20nm pitch DSA patterns. In order to utilize any diblock copolymer for DSA, a neutral underlayer and a method for annealing the block copolymer are required. Here, a random copolymer, poly(styrene-co-hydroxystyrene-co-glycidyl methacrylate), is developed and reported for use as a neutral underlayer for PS-b-PHOST. Furthermore, a solvent annealing method for PS-b-PHOST is developed and optimized using ethyl acetate to allow for uniform microphase separation of PS-b-PHOST.

Investigation of high χ block copolymers for directed self-asssembly: synthesis and characterization of PS-b-PHOST

Directed self assembly (DSA) of block copolymers (BCP) could enable high resolution secondary patterning via pitch multiplication from lower resolution primary lithographic patterns. For example, DSA could enable dense feature production at pitches less than 20 nm from patterns generated using 193 nm exposure tools. According to theory, microphase separation of block copolymers can only occur when the critical condition that χN>10.5 is met, where χ is the Flory Huggins interaction parameter and N is the total degree of polymerization for the block copolymer. In order to generate smaller DSA pattern pitches, the degree of polymerization of the block copolymer is reduced since this reduces the characteristic length scale for the polymer (e.g. radius of gyration). Thus, as N is reduced, the effect of this reduction on χN must be balanced by increasing χ to maintain a given level of phase separation. Currently, most DSA work has focused on the use of poly(styrene)-b-poly(methyl methacrylate) (PS-b-PMMA) copolymers whose low χ value (i.e. ~0.04) limits the practical DSA pitch using such materials to approximately 20nm. The general goal of this work has been to explore new higher χ block copolymer systems, develop DSA patterning schemes based on such materials, and test their ultimate pitch resolution. This paper discusses the synthesis and characterization of poly(styrene)-b-poly(hydroxystyrene) (PS-b-PHOST) copolymers made via nitroxide mediated radical polymerization. The formation of lamellar fingerprint structures in PS-b-PHOST using solvent annealing is demonstrated. Using this fingerprint data, initial estimates of χ for PS-b-PHOST are made which show that it appears to be at least one order of magnitude larger than the χ for PS-b-PMMA . Finally, graphoepitaxy of self-assembled lamellar structures in PS-b-PHOST is demonstrated using SU-8 guiding patterns on cross-linked neutral underlayers.

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.