Figure 1a shows the chemical structures of the PDMS-b-PMPCS diblock copolymer and PDMS-b-PS-b-PMPCS triblock terpolymer, and Table 1 summarizes the properties of the materials used in this study including molecular weight (Mn), degree of polymerization N, polydispersity (PDI), volume fraction f, acetone:heptane A:H ratio used for solvent vapor annealing (SVA), and period L0 with D, M and S subscripts representing PDMS, PMPCS and PS respectively. Syntheses of the diblock copolymer and triblock terpolymer were described in our previous work.25,26 The molecular weight of the PDMS block Mn(D) was fixed while its volume fraction fD ranges from 33–11%. Figure 1b demonstrates the fabrication steps used to convert films of DM or DSM into in-plane SiOx line patterns on flat and patterned silicon substrates (See Supplementary Information). The surfaces of the substrates were chemically functionalized by a 3 nm PS brush layer or a 3 nm PDMS brush layer. According to the Hildebrand solubility parameters of the PDMS (δPDMS = 15.3 MP1/2), PS(δPS = 18.5 MP1/2) and PMPCS (δPMPCS = 20.7 MP1/2) 33−35 the solubility parameter of PS lies approximately midway between those of PMPCS and PDMS suggesting that the PS brush will not be strongly preferential to either block in the DM. In contrast, the PDMS brush is highly preferential to the PDMS block. BCP films with thickness 30–100 nm were subsequently spin-coated and solvent vapor annealed36,37 using an acetone/heptane mixture at room temperature. The BCP films were etched by a two-step reactive ion etching to leave behind oxidized PDMS patterns.
Table 1
Molecular characteristics of the block copolymers, solvent annealing conditions and the structural parameters of in-plane cylinders
Sample | ND:NM or ND:NS:NM | Mn(D) a (g/mol) | Mn(PMPCS) a (g/mol) | PDI b | fD a (%) | fM a (%) | SVA (A:H) | L0 c (nm) | Line/ space ratio |
D4KM12K | 58:30 | 4,300 | 11,700 | 1.07 | 33 | 66 | 8:1 | 16.5 | 1.2:1 |
D4KM17K | 58:44 | 4,300 | 17,500 | 1.07 | 25 | 75 | 8:1 | 18.7 | 1:1.2 |
D4KM21K | 58:52 | 4,300 | 21,100 | 1.05 | 22 | 79 | 7:1 | 20.8 | 1:1.6 |
D4KM34K | 58:85 | 4,300 | 34,300 | 1.05 | 15 | 85 | 4.5:1 | 24.8 | 1:3 |
D4KS7KM40Kd | 58:70:100 | 4,300 | 40,500 | 1.07 | 11 | 73 | 5:1 | 30.9 | 1:4 |
a Determined from 1H NMR results of the macroinitiator and the block copolymers. b Determined from GPC using linear polystyrene standards. cDetermined from SEM of etched films. fD is the volume fraction of PDMS and fM is the volume fraction of PMPCS. dIn ref. [24] this polymer was named D58S70M100 representing its degree of polymerization. |
Line-space patterns with a wide range of fill factors
Solvent vapor annealing in mixed acetone/heptane vapors with appropriate composition produced in-plane cylindrical morphologies for all the BCPs. The etched top-view and cross-section SEM images of the films in Fig. 1c demonstrate highly ordered cylindrical PDMS microdomains on PS-functionalized substrates; similar results were produced on PDMS-functionalized substrates (Supplementary Information, Fig. S1). The preferential wetting of PDMS at the film/air surface (and at the film/substrate interface on PDMS-functionalized substrates) promotes the in-plane orientation. The acetone/heptane mixture ratio (A:H) that yielded well-ordered cylinders was 8:1 for D4KM12K, 7:1 for D4KM17K and D4KM21K, and 4.5:1 for D4KM34K, i.e. a greater amount of heptane was required as the PDMS volume fraction decreased, presumably because heptane selectively swells the PDMS to obtain an effective volume fraction consistent with forming a cylindrical morphology. Acetone constitutes the majority of the vapor, and the sum of the partial pressures of all solvent mixtures used here approached 30 kPa.26
Line-space patterns consisting of a monolayer of cylindrical microdomains were characterized from top-view SEM images of films (Fig. 1c). The DSM triblock terpolymer presents in-plane PDMS core-PS shell cylinders26 L0 is relatively small for these rod-coil BCPs compared with that of typical coil−coil block copolymers with similar molecular weight, due to the interdigitation of the rod block in the matrix,25,26 and the domain size of the PMPCS block is expected to scale almost linearly with the PMPCS molecular weight.21 The fill factor r varies between 0.20 and 0.55, covering a wide range that is advantageous for nanolithographic pattern generation. Cylindrical morphology BCPs typically form arrays with r ~ 0.5, though the range of r can be extended by annealing in selective solvents.38
Lines with spontaneous kinks and Y-junctions
The most dramatic difference between the line patterns formed by the rod-coil BCPs and coil−coil BCPs is the spontaneous formation of zig-zag bends in the former, in contrast to the fingerprint patterns seen in the latter.39 The zig-zag morphology is shown in Fig. 2a for D4KM34K and in Fig. S2-3 for all of our BCPs. The cylinders formed sharp kinks or chevrons (V) and bends with a Y-junction structure or arrow (Y-bend),26 which are indicated by yellow and green circles, respectively. When the bending angle decreased to a small value, the bend is no longer continuous, and the cylinders form line segments (LS), indicated by light pink circles. The morphology therefore changes from chevrons to Y-bends to line segments as the bend angle became more acute.
The critical bending angles at which the chevrons transition to Y-junctions (θY) and the Y junctions to line segments (θLS) are plotted as a function of volume fraction of PDMS (fSi) for all the block copolymers in Fig. 2b. A higher volume fraction of the rod-block, hence narrower PDMS cylinders, correlates with a wider range of existence of the Y-bends. The segment length at the Y-bends, Lb, (Fig. 2a inset and Fig. S4a) is plotted vs θ for D4KM21K, D4KM34K and D4KS7KM40K in Fig. S4g. The segment becomes longer as θ decreases because there is a larger spacing Lcp between the cylinders at the bend. Figure 2c shows the data normalized to L0, revealing that Lb/L0 increases with the volume fraction of PMPCS at fixed θ.
Zig-zag morphologies have been observed in several lamellar rod-coil BCPs16,20,21,23 and their energetics and internal structure have been examined theoretically.40–42 The zig-zag occurs in lamellar structures in which the rod block forms a liquid crystal smectic C arrangement, with the rods oriented at an angle to the intermaterial dividing surface (IMDS). The zig-zag represents a defect in which the tilt angle of the rods with respect to the IMDS is reversed. The tilting of the rods leads to a higher interface area but enables greater relaxation of the coil blocks, therefore it is stabilized by entropy of the coil block, and is promoted by annealing conditions that screen the block repulsion, e.g. the presence of a good solvent. The formation of zigzag lamellae is therefore process-dependent.21 In contrast, coil-coil BCPs lack the driving force provided by rod alignment, but sharp bends, kinks or zig-zags can be created by DSA43 and can occur at the grain boundaries between lamellae in bulk coil-coil BCPs.44–46 The Y-bend appears analogous to the omega structures observed in tilt boundaries of lamellar coil-coil BCPs.44,46 However, such omega or Y-bend structures have not been reported for cylindrical coil-coil BCPs, in which the cylinders at grain boundaries tend to form bends rather than junctions.47
Our findings therefore extend the morphologies observed in cylindrical rod-coil BCPs to include both zig-zags and Y-junctions. The change in bend morphology with angle may be understood by considering both the origin of zig-zags in rod-coil BCPs and the chevron-to-omega transition in lamellar tilt boundaries. We first comment that the energetics of bending of microdomains in coil-coil BCPs is described in terms of the interfacial and chain stretching energies.48–50 The bending free energy per chain at a radius of curvature Rc is described in the Supplementary Information and Fig. S5, and scales with bending angle θ as:
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1597931345.png)
where W is the bending boundary width as shown in Fig. 2b.46 This energy increases dramatically for sharp bends (i.e. low θ and low W), explaining why coil-coil BCPs favor the gradual bends seen in fingerprint patterns. Therefore, the formation of the sharp bends in the DM and DSM clearly indicates that an additional factor is stabilizing the sharp bends, namely the rod-rod interaction. It is significant that the zig-zag morphology was not seen in thermally-annealed cylindrical DM,29 which instead formed a fingerprint pattern. This supports the assumption that the solvent annealing plays a key role in reducing the interfacial energy so that the morphology is dominated by the rod-rod interactions. Thermal annealing at 200 oC causes a nematic orientation and more extended chain conformation for the PMPCS (L0,thermal anneal = 22 nm, L0,solvent anneal = 18.7 nm) in D4KM17K compared to the less rigid chain conformation and presumed locally smectic orientation formed during the solvent anneal. Under the solvent annealing, in which the PMPCS is swollen and the chains may form an interdigitated arrangement, the tilt of the rods could relieve the overcrowding, favoring bends and zig-zags.
The transition from chevron to Y-bend occurs with decreasingθ analogously to the chevron-to-omega transition in lamellar coil-coil BCPs: the additional line segment in the Y-bend reduces the stretching of the chains of the majority block required to fill the volume corresponding to increasing Lcp. The width W of the bent region (Fig. S4a) is larger for the chevron bends than for the Y-bends, e.g. in Fig. 2a, W = 54 nm for the chevron with θ = 137o, W = 26 nm at the transition from chevrons to Y-bends at θ = 120o, and W = 12 nm for the Y junction with θ = 90o. For small θ the Y-bend cannot form because there is insufficient volume to enclose the additional branched cylinder between the two straight sections of the cylinders, and the structure transitions to line segments; conformational asymmetry also favors the formation of line segments compared to bent continous microdomains, as observed in star copolymers.51 These considerations determine the angular range over which the Y-bend is stable.
Directed Self-Assembly of Bends
We now show how the locations and angles of the bends in the DM and DSM block copolymers can be determined by directed self-assembly using a template etched into the substrate. The templates were prepared by electron beam lithography on silicon substrates, then functionalized with a ∼3 nm thick PS or PDMS brush (see Supplementary Information). The sidewalls present a topographical guide and the polymer brushes provide a chemical guide for DSA. The as-cast film thicknesses were 30–50 nm, and during solvent vapor annealing the BCP on the mesas flowed into the trenches, which resulted in 50–100 nm thick films in the 100 nm deep trenches and at most a wetting layer of BCP on the mesas.
The solvent vapor annealed DM and DSM films present in-plane cylindrical morphologies within both PS and PDMS-coated templates, with orientation dominated by the brush. PS-brushed trenches led to cylinders oriented transverse to the trench shown in Fig. 3a for 120 nm wide trenches, and Fig. S6 for larger defect-free areas. The cylinder to cylinder distance is the same as that on the flat substrate. Transverse orientation is also produced for wide trenches (Fig. S7a) and in trenches with gradually changing width, Fig. 3b. In contrast, PDMS-brush functionalized trenches lead to parallel orientation of the cylindrical patterns of all the BCPs. D4KM12K, D4KM21K, D4KM34K and D4KS7KM40K present 7, 6, 4, and 3 cylinders in 120 nm wide trenches, respectively, Fig. 3c, and Fig. S8. This orientation occurred for narrow trenches, e.g. the D4KM34K presents a single cylinder in 30 nm wide trenches transitioning to two cylinders in 50 nm wide trenches (Fig. 3d). Figure 3e plots the number of transverse cylinders along a 625 nm long 120 nm wide PS-brushed trench, and the number of parallel cylinders in 120 wide PDMS-brushed trenches as function of BCP molecular weight.
The wetting behaviors of BCP films in PS-brush and PDMS-brush coated trenches are compared schematically in Fig. 3 f. In both cases, the top surfaces of the films form PDMS wetting layers because PDMS has a lower surface energy than PMPCS, implying that the morphological difference is a result of the wetting behaviors at the trench walls. PS brush coated templates preferentially adsorb the PS block of the DSM triblock terpolymer but are not strongly preferential to either block in the PDMS-b-PMPCS, because the solubility parameter of PS lies approximately midway between those of PMPCS and PDMS.33–35 The adsorption of both PMPCS and PDMS at the sidewalls for DM copolymers and the preferential adsorbtion of the middle block PS for DSM terpolymer favors the orientation of the PDMS cylinders perpendicular to the sidewalls, as schematically shown in Fig. 3 f. Metastable transverse orientations of cylinders have been observed due to capillary flow in other BCPs, evolving into a parallel orientation for longer annealing times,52 or by neutralizing the walls,53 but here the conformationally asymmetrical DM and DSM systems appear to form stable transverse cylinders.
In contrast, for the PDMS brush functionalized templates, the PDMS preferentially forms wetting layers at the top, bottom and sides of the film in the trench, and the cylinders are aligned parallel to the film surface and also to the trench walls. The transverse alignment in the PS-brush coated trenches and the parallel orientation in the PDMS-brush coated trenches was found in films with a range of thicknesses, and the polymer brush modified trenches can even guide the orientation and long range ordering of films much thicker than the trench depth, Fig. S9.
In our previous report of directed self-assembly of D4KM17K diblock copolymer in PS-brushed trenches by thermal annealing (200 ˚C, 72 hr),29 ladder morphologies (consisting of transverse cylinders joined to one parallel cylinder adjacent to each sidewall) as well as cylinders parallel to the sidewalls were formed depending on the film thickness and the groove and mesa width. In comparison, the transverse morphologies of the present study were produced consistently in DM and DSM films in PS-brushed trenches. The difference is attributed to the use of solvent annealing in the present study. The mobility of the rod-coil BCP under thermal annealing is lower than that produced by solvent annealing, and for the wider mesas not all the BCP flowed into the trenches during the thermal anneal. For solvent annealing the influence of mobility, wetting behavior and the swelling and LC configuration of the chains differ from the thermal anneal case and the ordering kinetics is faster.
In prior work, a two-step anneal of D4KM21K consisting of solvent annealing followed by thermal annealing produced vertically-aligned lamellae in which the PMPCS exhibited a hexatic columnar nematic LC arrangement.30 The response of D4KM21K cylinders in templates to a subsequent thermal annealing process is shown in Fig. S10. The transverse or parallel orientation of the cylinders imparted by the PS or PDMS brush respectively during solvent annealing was preserved as they transitioned into lamellae, although some regions of in-plane lamellae were also observed. This process therefore provides a route to templating lamellae of different orientations within trenches via the surface chemistry. Lamellae are favored by larger molecular weight of the PMPCS as well as a more symmetric volume fraction.
We now describe the templating of bends by directed self-assembly within V-shaped templates coated with a PS-brush. Figure 4a-b shows the transverse alignment of D4KM34K and D4KS7KM40K in right-angled trenches. Concentric bending occurs at the corners, and the bending angle of the PDMS cylinders θ is expected to be the supplementary angle of the bending angle of the trench (∠V). The D4KM34K and D4KS7KM40K form Y-junctions on flat substrates at a bending angle ∼ 90o, but in the trenches, wide chevrons are observed for both BCPs. The D4KM34K was also templated in 120 nm wide trenches patterned with ∠V = 30, 60, 90, 120 and 150o, Fig. S7b. The chevron bends display θ = 150, 120 and 90o for ∠V = 30, 60 and 90o respectively, but for ∠V = 120˚ and 150o, the cylinders are tilted with respect to the trench wall and Y-junctions are not observed. Figure 4c and Fig. S7c-d show the effect of other trench geometries. For PDMS-brush functionalized trenches, Fig. S11, the cylinders followed the sidewall contour and concentric bending was observed. These results show that in templated bends the chevrons are favored over Y-bends or line segments, and the angle at the bend is lowered by accomodating a tilt of the cylinders so that they are not perpendicular to the sidewalls. The control over transverse and parallel orientations may be useful in fabricating 3D multilayer structures relevant to microelectronic device layouts.
Summary
We demonstrate the formation of a series of grating patterns with scalable periodicity and line/space ratios from solvent annealed thin films of conformationally asymmetrical silicon-containing rod-coil block copolymers and terpolymers. Spontaneous bending leads to chevrons, Y-junctions and line segments, unlike the fingerprint patterns typically found in thin films of cylindrical or lamellar morphology BCPs. Directed self assembly within chemically functionalized topographical substrates produces a range of patterns with control over the cylinder orientation and bending. In particular, the surface chemistry of the patterned substrate yields in-plane cylinders either transverse or parallel to the sidewalls for a range of polymer compositions and film thicknesses. Furthermore, concentric bending of the cylinders occurs in trenches with angles. These results reveal a powerful platform for designing functional 3D nanostructures or device layouts by utilizing conformationally asymmetrical block copolymers.