We investigate energy barriers and minimum energy paths (MEPs) for transitions from dislocation-pair defects to perfect
lamellae in self-assembly of AB-diblock copolymer plus A- or B-homopolymer blends using self-consistent field theory
(SCFT) and the numerical string method. For neutral substrates, all minimum energy paths discovered by the string
method show two successive energy barriers. The two-barrier qualitative nature of the MEPs appears not to depend on
the presence or absence of small amounts of homopolymer. For the first energy barrier, the barrier height shows
pronounced increase with addition of A-homopolymer due to localization of A-homopolymer on the T-junction core of
the dislocation. For chemo-epitaxially patterned substrates (stripes of A-attractive substrate alternating with neutral
substrate), the presence of A-attractive stripes helps draw the system towards a perfect lamellar configuration, and
energy barriers along the MEP are reduced, in some cases disappearing entirely. Our findings provide guidance on how
the presence of homopolymer and chemo-epitaxial prepatterns affect the stability of defective morphologies.
We investigate the directed self-assembly (DSA) of cylinder-forming block copolymers inside cylindrical guiding templates. To complement and corroborate our experimental investigations, we use field-theoretic simulations to examine the fluctuation-induced variations in the size and position of the cylindrical microdomain that forms in the middle of the guiding hole. Our study goes beyond the usual mean-field approximation and self-consistent field theory simulations (SCFT) and incorporates the effects of thermal fluctuations in the description of the self-assembly process using complex Langevin (CL) dynamics. In addition to CL simulations, we present an efficient SCFT-based approach that can inform about the positional error of the formed cylinders. In this new scheme, an external chemical-potential field is applied to displace the inner cylinder away from its centered, lowest energy configuration. In both our experimental and modeling efforts, we focus on two wall-wetting conditions: (1) minor-block-attractive sidewalls and bottom substrates and neutral top surfaces and (2) neutral sidewalls, substrates, and top surfaces. For both cases, we explore the properties of the formed cylinders, including fluctuations in the center position and the size of the domain, for various prepattern conditions. Our results indicate robust critical dimensions (CDs) of the DSA cylinders relative to the prepattern CD, with a standard deviation <0.9 nm. Likewise, we find that the DSA cylinders are accurately registered in the center of the guiding hole, with deviations in the hole-in-hole distance on the order of ∼0.7 to 1.4 nm, translating to errors in the hole-to-hole distance of ∼1 to 2 nm.
We have investigated the directed self-assembly (DSA) of cylinder-forming block copolymers inside cylindrical guiding templates. To complement and corroborate our experimental study, we use field-theoretic simulations to examine the fluctuations-induced variations in the size and position of the cylindrical microdomain that forms in the middle of the guiding hole. Our study goes beyond the usual mean-field approximation and self-consistent field theory simulations (SCFT) and incorporates the effects of thermal fluctuations in the description of the self-assembly process using complex Langevin (CL) dynamics. In both our experimental and modeling efforts, we focus on minor-block-attractive sidewalls and bottom substrates and neutral top surfaces and explore the properties of the formed cylinders, including fluctuations in the center position and the size of the domain, for various prepattern conditions. Our results indicate robust critical dimensions (CD) of the DSA cylinders relative to the incoming CD, with a sigma CD < 0.9nm. Likewise, we find that the DSA cylinders are accurately registered in the center of the guiding hole, with deviations in the hole-inhole distance on the order of ≈ 0.7-1nm, translating to errors in the hole-to-hole distance of ≈ 1-1.5nm.
We use self-consistent field theory (SCFT) to study shape rectification in overlapped cylindrical and non-cylindrical prepatterns. Specifically, we examine the potential of directed self-assembly (DSA) of block copolymers to not only reduce critical dimensions relative to the template, but also repair defects in the guiding prepatterns and produce defectfree contact holes. In our study over a wide range of prepattern dimensions, we found that defects in the central minorblock domain arise with decreasing center-to-center distance of the prepattern. Increasing the minor-block fraction in the block copolymer was observed to remove some of the defects. We also studied the effect of adding homopolymer to the block copolymer melt and show how blends can successfully eliminate defects and increase the range of the process window relative to the neat diblock case without influencing domain properties such as the critical dimension and the hole-to-hole distance.
The directed self-assembly (DSA) of diblock copolymers in laterally confining channels is a promising avenue to produce line-and-space patterns with a sub-25 nm pitch. In this study, we use self-consistent field theory (SCFT) to investigate the DSA of both cylinder- and lamella-forming diblock copolymers in narrow trenches with corrugated sidewalls. Specifically, we focus on systems that form lying-down cylinder monolayers or standing-up lamellae parallel to the sidewalls of the channel. While previous experimental and computational studies highlighted well-ordered cylinders and lamellae in smooth channels, undesirable defective structures are also observed. In the present study, the wetting sidewalls of the channels are no longer planar surfaces. Rather, we consider undulating sidewalls and investigate the effect of the rough surfaces on defectivity and line edge roughness (LER) in the self-assembled morphologies. We use SCFT to investigate the formation free energy of isolated, meta-stable defects of both cylindrical and lamellar block copolymers inside channels with sinusoidal corrugations along the sidewalls. Parametric studies include the effects of the amplitude and the frequency of the sinusoidal wall shape function, the placement of the defect core, as well as the number of cylinders and lamellae in channels of varying widths. Our simulations indicate that the relative decreases in defect formation energy in rough channels compared to smooth channels are strikingly similar in both cylinder- and lamella-forming melts. Furthermore, using a suitable order parameter and the center-to-center displacement of the self-assembled lines, our complex Langevin (CL) simulations (beyond SCFT) show that the propagation of the LER is sensitive to the amplitude and the wavelength of the sidewall shape function, with an even stronger dependence in the lamellar case compared to the cylindrical case. More broadly, our study reveals the dependence of line edge roughness propagation on a wide range of parameters that must be carefully controlled in order to successfully implement a directed self-assembly process with block copolymers.
We use self-consistent field theory (SCFT) to study the self-assembly of cylinder-forming diblock copolymers confined
in a cylindrical prepattern. This situation arises in contact holes -the hole shrink problem- where the goal is to produce a
cylindrical hole with reduced dimensions relative to a guiding prepattern. In this study, we focus on systems with a
critical dimension (CD) ranging from 50nm to 100nm and which consequently lead to the formation of a single cylinder
in the middle of the hole. We found that different morphologies arise from the self-assembly process and are strongly
governed by the prepattern dimensions, wetting conditions as well as the polymer molecular weight. We also considered
blends of diblock copolymers and homopolymers and determined optimal blending configurations that not only favor the
formation of the desired cylindrical morphology but also extend the processing window relative to the pure diblock case.
We use self-consistent field theory (SCFT) to study the directed self-assembly of cylinder-forming diblock copolymers
laterally confined in narrow channels. The side walls and top/bottom surfaces of the channel are either all major block
attractive, all minor block attractive, or a combination of major block attractive on the top surface and minor block
attractive on the remaining film surfaces. We focus on systems in which the self-assembled cylinders form a monolayer
oriented parallel to the sidewalls in a thin channel. Experimentally and theoretically, well-ordered perfect cylinders are
observed in narrow channels, but undesirable defective structures are also found. We investigate the energetics of
isolated, meta-stable defects and compare them with two types of defects (dislocations and disclinations) recently
investigated in laterally confined lamellar block copolymer systems using SCFT. Our simulation results are also
compared with defect energy estimates for lying down cylinder monolayers extracted from experimental work by Mishra
and coworkers. Parametric studies include the effects of film thickness, domain spacing, χN, and composition on defect
energies with various wall wetting conditions in narrow channels of varying widths. A major finding is that defects of
cylindrical directed self-assembly in a confined channel have a smaller free energy cost (tens of kT) in comparison with
defects in laterally confined, vertically oriented lamellae (many tens of kT). We also discovered a novel vertically
branched cylinder defect in the case of neutral top and bottom surfaces with significantly lower defect energy than a
corresponding dislocation defect. More broadly, this study reveals unexpected dependences of equilibrium defect
densities on a wide range of parameters that must be carefully controlled in order to successfully implement a directed
self-assembly process with block-copolymers.
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