Molecular Systems Design & Engineering View Article Online PAPER View Journal | View Issue Self-assembly morphology of block copolymers in This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. sub-10 nm topographical guiding patterns† Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. Cite this: Mol. Syst. Des. Eng., 2019, 4, 175 S. Gottlieb, a B. Rösner,b L. Evangelio,a M. Fernández-Regúlez,a A. Nogales, c M. C. García-Gutiérrez, c T. F. Keller, de J. Fraxedas, f T. A. Ezquerra,c C. Davidb and F. Perez-Murano *a In this paper, we investigate the directed self-assembly of block copolymers in topographical guiding pat- terns with feature sizes in the range of the block copolymer half-pitch. In particular, we present the self- assembly of an 11.7 nm half-pitch block copolymer in sub-10 nm resolution guiding patterns fabricated by the direct e-beam exposure of hydrogen silsesquioxane (HSQ). One result of this analysis is that the block copolymer self-assembles such that the guiding pattern features form part of the 3-D architecture of the film. We are capable of determining a shift in the block copolymer pitch as a function of the guiding pat- tern pitch with sub-nanometer accuracy by means of both real-space (AFM, SEM) and reciprocal-space techniques (GISAXS). An interesting result is that the block copolymer self-assembly in the studied struc- tures depends on the guiding pattern pitch rather than on the trench width as in standard graphoepitaxy. We analyze the structures by means of a free energy model and present both theoretical and experimental Received 27th July 2018, evidence of a narrower processing window for such kind of guiding patterns than for regular directed self- Accepted 1st November 2018 assembly using wide topographical guiding patterns, and discuss the origin of this effect. We argue that chain deformation in the vicinity of the top cap of the guiding pattern feature is responsible for an increase DOI: 10.1039/c8me00046h of the free energy of the ordered state, which leads to a smaller energy difference between the defect-free rsc.li/molecular-engineering and defective self-assembly than that for the observed self-assembly morphology. Design, System, Application Block copolymer lithography has, in the recent years, evolved as a versatile method to pattern surfaces with a resolution from a few tens of nanometers down to a few nanometers. Due to this potential, the technique is at the prospect of gaining importance in semiconductor high-volume manufacturing for sub-10 nm nodes. Currently, the major drawback of block copolymer lithography is the too high defect density as compared with standard lithography techniques. Here, we explore the behaviour of block copolymer self-assembly in topographical guiding patterns with sub-10 nm feature width. We analyse the system with SEM, AFM and GISAXS and reconstruct the molecular structure, i.e. the self-assembly morphology of the block copolymers, based on our measurements and define design rules for such high-resolution guiding patterns. We use a free-energy model to determine the process window for guiding pattern fabrica- tion using the example of an 11.7 nm half-pitch lamellar PS-b-PMMA block copolymer. This work provides new insight into the behaviour of block copoly- mers during directed self-assembly in topographical guiding patterns with feature widths as small as the characteristic block copolymer domain size. Introduction between a few nanometers and a few tens of nanometers.1–6 For this reason, the technique belongs to the group of next- The directed self-assembly (DSA) of block copolymers (BCPs) generation lithography (NGL) techniques under consideration has emerged as a nanopatterning technique with a resolution for high-volume manufacturing in the microelectronics in- dustry for sub-10 nm feature widths as defined by the Inter- a Instituto de Microelectrónica de Barcelona IMB-CNM, CSIC, 08193 Bellaterra, national Technology Roadmap for Semiconductors ITRS.7 Barcelona, Spain. E-mail: Francesc.Perez@csic.es b Laboratory for Micro- and Nanotechnology, Paul Scherrer Institut, 5232 Villigen- Block copolymers consist of two chemically different poly- PSI, Switzerland mer chains connected by a covalent bond.8 Upon heating the c Instituto de Estructura de la Materia IEM-CSIC, 28006 Madrid, Spain material above its glass transition temperature, it self- d Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany assembles into an ordered phase of well-defined structures. e Fachbereich Physik, Universität Hamburg, 22607 Hamburg, Germany f Block copolymers exhibit a complex phase behavior and as a Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Barcelona, 08193, Spain function of the relative and absolute chain lengths, they are † Electronic supplementary information (ESI) available. See DOI: 10.1039/ capable of assembling into diverse morphologies, like spheri- c8me00046h cal, cylindrical, gyroid or lamellar structures.9–12 Due to large This journal is © The Royal Society of Chemistry 2019 Mol. Syst. Des. Eng., 2019, 4, 175–185 | 175 View Article Online Paper Molecular Systems Design & Engineering defect-annihilation energies, a self-assembled film of block Here, we report on the directed self-assembly of a 23.4 nm copolymers will never be free of point defects.13 Lithographi- full-pitch lamellar diblock PS-b-PMMA block copolymer with cally defined structures used to introduce long-range order a low defect density in sub-10 nm resolution topographical into self-assembled block copolymers, i.e. to direct the self- guiding patterns fabricated by the direct exposure of hydro- assembly of block copolymers, are referred to as guiding gen silsesquioxane (HSQ) to an electron beam. The self- patterns. The most frequently used strategies to direct the assembly is characterized by means of GISAXS, SEM and AFM self-assembly of block copolymers are the fabrication of measurements and compared to the morphology that is chemical patterns, referred to as chemoepitaxy,2,14–17 and the known from the directed self-assembly of block copolymers fabrication of topographical patterns, referred to as in wide topographical guiding patterns.5 We apply a free en- This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. graphoepitaxy.5,18–21 ergy model21,30 and compare the fabricated structures with Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. The fabrication of chemical guiding patterns requires pat- respect to the free energy difference between defect-free self- terning techniques with excellent resolution because the assembly and the defective self-assembly. chemically modified areas need to be in the size range of the block copolymer domains.15,17 Works concentrating on very Experimental high-resolution topographical guiding patterns for lamellar block copolymers are sparse.4 This may be because one of The substrates used in the experiments are pieces of 2 × 2 the principal advantages of the use of graphoepitaxy5 is the cm2 cleaved from a p-doped silicon <100> oriented wafer (4– lower required resolution for the guiding pattern fabrication. 40 Ω cm resistance). High-resolution topographic guiding patterns have been used to direct the self-assembly of a spherical PS-b-PDMS block co- HSQ deposition, exposure and development polymer by fabricating HSQ posts subsequently covered with The chip is cleaned in an O2 plasma at 100 W for 20 s. We a PDMS brush.22 In this case, the authors proposed a free en- use flowable oxide FOX 16 by Dow Corning Corporation di- ergy model to explain the orientation of the block copolymer luted 1 : 6 in methyl isobutyl ketone (MIBK) and spin coat template with respect to the guiding pattern as a function of this solution at 1000 rpm for 1 min. This yields a film thick- the guiding pattern pitch. ness of 42 nm. The exposure of HSQ by electron beam in- The investigation of the behavior of block copolymers in duces a cross-linking process,31–34 which converts the ex- high-resolution topographical guiding patterns is of techno- posed areas into an SiO2-like amorphous material. logical interest for at least two reasons. On one hand, the The exposure is performed with Vistec EBPG 5000+ tool need for high-resolution topographical guiding patterns will using a 100 kV electron beam with a beam current of 2 nA. increase substantially as soon as new high-χ block copoly- The exposure dose for the fabrication of sub-10 nm lines mers or other self-assembling materials with significantly varies from 7400 μC cm−2 to 8800 μC cm−2 as a function of smaller pitches are developed.23 On the other hand, the space the pattern pitch, which in this work is between 80 nm and on the chip occupied by guiding pattern features represents 250 nm. The patterns are 512 μm wide and 10 mm long. non-utilizable space for the fabrication of electronic devices After the exposure the non-cross-linked HSQ is removed in on the chip. Therefore, the use of high-resolution topographi- a development step using an alkaline developer (Microposit cal guiding patterns represents a noticeable increase in pat- 351 diluted 1 : 3 in water) for 5 min. Subsequently the sample terning efficiency with respect to systems using large guiding is dipped in H2O for one minute and air-dried. pattern features.24 To our best knowledge there is no work published yet that analyzes the behavior of block copolymers Deposition of neutral brush layer in topographical guiding patterns whose critical feature size A neutral brush layer is spun from a 0.25 wt% solution of PS- has been pushed below the block copolymer domain size. r-PMMA (58 wt% PS and 42 wt% PMMA at a molecular In addition to standard real-space nanocharacterization weight Mbrush = 7.9 kg mol−1 and a polydispersity index methods like SEM and AFM, we use grazing-incidence small- PDIbrush = 1.85) dissolved in PGMEA. The spin coating condi- angle X-ray scattering (GISAXS) as a damage-free, high resolu- tions are 4000 rpm for 30 s, leading to a film thickness of 4 tion characterization technique that is frequently used to an- nm in free surface. An annealing step at 230 °C for 5 min ini- alyze the nanostructure of polymer films.25 tiates a grafting process of the random copolymers to the ac- A significant advantage of GISAXS over common real-space tivated silicon surface. The non-grafted brush layer is re- techniques is that the relatively large sampling volume per- moved by a PGMEA rinsing step. mits the investigation of a statistically meaningful area both on the sample surface and below.26 The low incidence angles used in GISAXS (usually few tenths of a degree), however, Deposition and self-assembly of block copolymers leads to a significantly elongated beam foot print and requires For all the experiments in this work we have used a lamellar sufficiently large guiding patterns. In the last years, GISAXS PS-b-PMMA diblock copolymer (MPS-b-PMMA = 42.3 kg mol−1; has been used to analyze gratings to determine their basic 43 wt% PS, 57 wt% PMMA, PDIBCP = 1.1). The natural pitch geometric properties,27,28 but also more advanced parameters in free surface is 23.4 nm. Spin-coating of a 1.8 wt% solution like the line-edge-roughness (LER) of nanometric structures.29 in PGMEA at 2000 rpm yields a 34 nm thick film in free 176 | Mol. Syst. Des. Eng., 2019, 4, 175–185 This journal is © The Royal Society of Chemistry 2019 View Article Online Molecular Systems Design & Engineering Paper surface. Microphase separation is induced by an annealing rather lamellae perpendicular to the guiding pattern direc- step at 230 °C for 10 min. tion.4,21 On the other hand, the difference in guiding pattern feature width results in a fundamentally different self- Analysis assembly morphology. This difference is indicated in Fig. 1 and will be further explained in the forthcoming paragraphs. The samples are inspected by tapping mode AFM using a Dimension Icon/Nanoscope V by Bruker. The amplitude set- point is 50% of the drive amplitude. The SEM inspection is Directed self-assembly characterization by real-space imaging done with a Zeiss Auriga using the InLens detector. GISAXS techniques This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. measurements, using synchrotron radiation, of representative We analyze results obtained using guiding pattern with sub- Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. samples are conducted at the P03 Micro- and Nanofocus 10 nm width and nominal pitches of 90 nm, 120 nm and 150 X-ray Scattering Beamline at PETRA III in Hamburg, Ger- nm, as depicted in the Fig. 2a)–c). The accuracy of the guid- many.35 The sample-detector distance is set to L = 5800 mm ing patterns in terms of dimensions (pitch and linewidth) and the radiation wavelength to λ = 0.107 nm, respectively. and their low line edge roughness makes them ideal tem- The incidence angle of the beam is αi = 0.4°. The detector plates for DSA. The SEM images depicted in Fig. 2d)–f) dem- that has been used for these experiments is a PILATUS 300k onstrate their excellent ability to direct the self-assembly of pixel detector with a readout time below 3 ms and a pixel size block copolymers. The guiding patterns are capable of of 172 μm × 172 μm. directing the self-assembly of block copolymers without the The estimated uncertainty in lateral size determination formation of defects over areas of various tens of square according to the procedure proposed by Smilgies36 is 0.3 nm. micrometers. Here, we define “defects” as deviation from the Here, the most important contribution to the measurement desired continuous lamella morphology, including point-de- uncertainty originates from the beam divergence, while the fects,13 point-like defects21 and domain wiggling.37 The exam- contribution of the beam band width and geometric ple shown in Fig. 2g) is an SEM image that evidences the smearing is negligibly. defect-free self-assembly in trenches with a 150 nm pitch. The multiplication factor for this pattern is n = 6. This means Results that the density of the block copolymer features in this pat- tern is six times larger than the guiding pattern feature den- The work-flow pursued to fabricate the guiding patterns is sity. An advantage of such small guiding pattern features is a depicted in the top part of Fig. 1 and compared to wide guid- significant increase of the area the can be effectively used on ing pattern fabrication work-flow, which is sketched in the the chip, whereas guiding patterns with wide features widths bottom part of the same figure. The principal difference be- commonly lead to a large proportion of the sample that can- tween the two work-flows is in the guiding pattern feature not be used for patterning. width. The work-flow sketched in the top images is character- Fig. 2h) shows a tapping mode AFM height image of the ized by a guiding pattern feature width below 10 nm, which 150 nm pattern after DSA. Interestingly, we observe that the is in the size range of the block copolymer domain. The lower entire surface is a sequence of PS and PMMA domains, indi- line of images depicts a work-flow using guiding patterns cating that the guiding pattern features are entirely covered with a feature width significantly above the block copolymer by block copolymer molecules. Based on our observations, we domain width. For both alternatives it is particularly impor- conclude that the block copolymer surrounds the guiding tant to deposit a thin 4 nm neutral brush layer (using 0.25 pattern features rather than occupying exclusively the space wt% random copolymer dissolved in PGMEA) to inhibit between them, as it is the case for wide guiding patterns (for grafting of random copolymers to the guiding pattern walls. a reconstruction of the respective structure, see sketch in Otherwise the self-assembly morphology would no longer be Fig. 2i)). A detailed analysis of the AFM image to understand in lamellae parallel to the guiding pattern direction, but the configuration is shown in the ESI.† A similar self- Fig. 1 Sketches comparing the self-assembly morphology in topographical guiding patterns with sub-10 nm guiding pattern width (top part) with the self-assembly morphology in guiding patterns with a width significantly above 10 nm (bottom part).The parameter p indicates the guiding pat- tern pitch, and w the separation between guiding pattern features, so that the guiding pattern width is p–w. This journal is © The Royal Society of Chemistry 2019 Mol. Syst. Des. Eng., 2019, 4, 175–185 | 177 View Article Online Paper Molecular Systems Design & Engineering This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. Fig. 2 SEM images of patterns with different pitches before and after self-assembly. a)–c): SEM images of 90 nm, 120 nm, 150 nm guiding patterns, d)–f): SEM images of 90 nm, 120 nm, 150 nm guiding patterns with self-assembled block copolymer, g): SEM image of defect-free assem- bly on large scale, h): AFM height image of the 150 nm structure, i): single line scan along the green dotted line in h) with a sketch of the self- assembly morphology in the background. assembly morphology has been observed in a study analyzing sion with respect to their equilibrium spacing L0, which can the directed self-assembly of block copolymers based on a be determined by measuring the block copolymer pitch. Al- chemoepitaxy–graphoepitaxy hybrid process, however, other though we get an excellent qualitative understanding of how than in the present study, with only few nanometers of the block copolymers self-assemble in our system, it is diffi- topography.3,38,39 cult to determine deviations in the block copolymer pitch Another interesting observation concerns the different de- with high accuracy by the exclusive use of real-space tech- grees of visibility of the guiding patterns in the AFM height im- niques. Here, we concentrate on the analysis of the block co- age compared to the SEM image. Although the AFM analysis re- polymer pitch as a function of the guiding pattern pitch. An veals that the guiding patterns are entirely covered with block analysis of the correlation length can be found in the ESI† copolymers, the guiding pattern lines produce a strong SEM part. signal. This observation suggests that the block copolymer layer The geometry of the GISAXS experiment is sketched in covering the guiding patterns is only few nanometers thick. Fig. 3a). The samples depicted in Fig. 2a)–f) have been ana- The coverage of the guiding pattern thus results most likely lyzed by GISAXS. The elongated shape of the guiding pattern from an energy minimization process during the self-assembly. (512 μm × 10 mm) is necessary to avoid that a large part of These observations confirm the self-assembly morphology the measured signal originates from block copolymers ori- depicted in Fig. 1 and demonstrate that the self-assembly in ented in fingerprint morphology. At the chosen incidence an- these patterns differs significantly from the directed self- gle of 0.4°, the 50 μm beam has a footprint of slightly more assembly when the guiding pattern feature width is notably than 7 mm in length, which is shorter than the pattern larger than the block copolymer domain. length and therefore allows us to detect scattered photons originating exclusively from the block copolymer in the guid- ing pattern. Analysis of the structures with GISAXS The GISAXS measurement of the samples with guiding An important parameter for understanding the behavior of patterns before the deposition of block copolymer shows the block copolymers under confinement is the strain/compres- characteristic scattering features for such gratings.27 The 178 | Mol. Syst. Des. Eng., 2019, 4, 175–185 This journal is © The Royal Society of Chemistry 2019 View Article Online Molecular Systems Design & Engineering Paper This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. Fig. 3 GISAXS analysis of structures with and without block copolymer. a): Geometry of GISAXS experiments, b): GISAXS pattern for 90 nm pitch guiding pattern, c): GISAXS pattern for 120 nm pitch guiding pattern, d): GISAXS pattern for 150 nm pitch guiding pattern, e): GISAXS pattern for 90 nm pitch guiding pattern with self-assembled block copolymer, f): GISAXS pattern for 120 nm pitch guiding pattern with self-assembled block co- polymer, g): GISAXS pattern for 150 nm pitch guiding pattern with self-assembled block copolymer. patterns depicted in Fig. 3b)–d) represent the results of the tern suggests a deviation from perfect parallelism of merely analysis of the guiding patterns with a nominal pitch of 90 few thousandths of a degree. The semicircle has its center in nm, 120 nm and 150 nm. The GISAXS patterns consist of a the sample horizon (at α = 0°; ω = 0°) and its radius (in de- superposition of the Ewald sphere leading to an arc, and a grees) corresponds to the incidence angle of the beam.28 number of grating truncation rods (GTRs), whose separation In Fig. 3e)–g) we depict the scattering patterns of block co- indicates the pitch of the real space lattice in reciprocal polymers after the directed self-assembly. In comparison to space.26 We can easily extract the lattice pitch with the Bragg the measurements shown before, these patterns show a num- equation, which yields a pitch p1 = 89.9 ± 0.3 nm for Fig. 3b), ber of scattering effects in addition to the GTRs and the p2 = 120.3 ± 0.3 nm for Fig. 3c) and p3 = 150.1 ± 0.3 nm for semicircle we observe in the guiding pattern. These scattering Fig. 3d). These values are mean values of the position of two features are consequently due to the self-assembled block co- GTRs in each pattern and demonstrate the excellent precision polymer. In general terms, the signal intensity in the patterns of the guiding pattern fabrication. decreases notably after the deposition of the block copoly- The semicircular shape of the intersection of the Ewald mer. The reason for this effect is that the scattering probabil- sphere with the detector is very sensitive to the orientation of ity at the interface between two materials is proportional to the pattern with respect to the incident beam.40,41 The nearly the difference in their electron density. The difference in the perfectly semicircular shape of the arc in the observed pat- electron density between air and SiO2 in case of the guiding This journal is © The Royal Society of Chemistry 2019 Mol. Syst. Des. Eng., 2019, 4, 175–185 | 179 View Article Online Paper Molecular Systems Design & Engineering pattern sample, is larger than the difference in electron density of the guiding pattern (red curve), the guiding pattern with between the SiO2 and block copolymer. In each GISAXS pattern block copolymer (black curve) and a block copolymer in free there is one GTR that stands out of the rest due to its enhanced surface (blue curve). Small versions of the respective patterns intensity. For Fig. 3e), the high-intensity GTR corresponds to are depicted in the panel as in-sets and the approximate posi- the 4th order, for Fig. 3f), to the 5th order and for Fig. 3g) to tion of the cut is indicated by the white dotted line. The color the 6th order GTR. While this effect is important in the GISAXS of the respective inset frame corresponds to the color of the pattern of the 90 nm grating, it is rather weak in the 120 nm curve. and the 150 nm grating. An important conclusion from this ob- The GISAXS analysis of the fingerprint pattern sample servation is that the order of the GTR that shows this phenome- yields only one peak (ω = 0.267°), that corresponds to the pe- This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. non corresponds to the multiplication factor n we observed in riodicity of the block copolymer pattern. The peak position Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. the SEM and AFM analysis of our structures (Fig. 2). Additional suggests a natural block copolymer pitch L0 = 23.4 ± 0.3 nm. features that distinguish the GISAXS patterns after block copol- In addition to that, the block copolymer fingerprint pattern ymer deposition from those before deposition is the existence produces a remarkable scattering intensity at small diffrac- of satellite arcs that other authors have previously interpreted tion angles ω, causing a large background intensity in the as a result of line edge roughness in the analyzed pattern but blue curve. will not be made a further subject of discussion in this paper.42 For the black and the red curve, we observe GTRs at the Finally, we notice an intensity modulation in the range of α = same diffraction angles ω before and after the block copoly- {0.1°; 0.15°} which is related to the different material composi- mer deposition. The absence of a peak at ω = 0.267° confirms tion of the sample with block copolymer compared to the one that the amount of illuminated material outside the guiding without block copolymer.43 pattern (e.g. material self-assembled in fingerprint morphol- The overall aspect of the GISAXS pattern is similar to ogy) in this experiment is negligible. Although the overall sig- those that have been taken from block copolymers directed nal declines after the deposition of the block copolymer, we by chemical guiding patterns.44,45 In these works, the authors observe that the black curve has a background intensity also observe the effect of intensity enhancement of the n-th whose shape is very similar to the one measured in the fin- GTR for guiding patterns with a multiplication factor n. The gerprint sample. This phenomenon seems to be an effect similarity between GISAXS measurements of our patterns and caused by block copolymers and results in the misleading im- on samples with block copolymer self-assembly directed by pression that low-order GTRs have a significantly higher scat- chemoepitaxy supports our thesis that (i) the intensification tering intensity than the higher-order GTRs. The conversion of determined GTRs is due to the presence of block copoly- from scattering angle ω into the q-space is done with Bragg's mers, (ii) we can draw conclusions about the block copolymer law using structure based on the position of the intensified GTR and (iii) the topographical guiding pattern actually forms part of 4     the 3D morphology of the block copolymer pattern. q sin   , (1) In the following, we will analyze specific transverse cuts  2 through the GISAXS pattern of the 90 nm pitch grating sam- ple before and after the deposition of block copolymers and where the radiation wavelength λ for our experiments is 0.107 in particular investigate the origin of the enhanced intensity nm. In Fig. 4b) we transform the pattern in the q-space and of the 4th order GTR. compare the 3rd and the 4th order GTR of the 90 nm guiding In Fig. 4a) we compare cuts at α = {0.125° ± 0.025} (i.e. pattern sample after the deposition of the block copolymer. around the Yoneda peak43 of the block copolymer materials) Interestingly, the 4th order GTR needs to be fitted with two Fig. 4 Determination of the block copolymer pitch with sub-nm resolution. a): Cuts through GISAXS patterns depicted on the right at exit angle α = 0.125° ± 0.025° (see white dashed lines) and zoomed into the relevant area, b): 3rd order peak of 90 nm pitch guiding pattern peak and its single-peak fit, and 4th order peak of 90 nm pitch guiding pattern and its double-peak fit. 180 | Mol. Syst. Des. Eng., 2019, 4, 175–185 This journal is © The Royal Society of Chemistry 2019 View Article Online Molecular Systems Design & Engineering Paper Gaussians, while for the 3rd order GTR it is sufficient to fit it high defect density as it can also be found in our experi- with one Gaussian. The center of the two Gaussians (drawn ments for strongly incommensurate pitches.21 In the follow- in grey dashed lines) is qα = 0.28 nm−1 indicating a block co- ing, we will estimate the free energy of the block copolymers polymer pitch of 22.4 ± 0.3 nm. For the conversion from q to self-assembled in sub-10 nm guiding patterns using a further real space periodicity d, we use extension of the previously presented model (Fig. 5a)). The model allows to predict the process window due to variations 2  of the pitch dimensions. d (2) We observe, as a function of the pattern guiding dimen- q sions, alternating regions with successful self-assembly and This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. We would like to clarify at this point that the enhanced regions where the self-assembly shows a large number of de- Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. intensity and the particular shape of the 5th order peak both fects, referred to as defect-loaded state due to incommensura- in the red curve and the black curve in Fig. 4a) originates bility. The self-assembly in samples with guiding patterns from the fact that the arc and the 5th order GTR intersect with 80 nm and 110 nm pitch leads to a very large defect den- precisely in the integration area of the analyzed cut and is sity in the block copolymer template (see images in therefore due to a different phenomenon. This concept be- Fig. 5b) and d)), where images with a red frame are examples comes clear when we look at the in-sets of the GISAXS spectra for self-assembly with a large number of defects and images in Fig. 4a), where the dashed white line represents the area with a green frame represent examples with a defect-free self- where the cut has been realized. Based on this observation, assembly. The guiding patterns with 90 nm and 120 nm on the AFM/SEM analysis presented in Fig. 2 and on the sim- pitch do, however, provide a self-assembly morphology that ilarity of this system to a chemoepitaxy system,44,45 we de- is free of defects (Fig. 5c) and e)). The starting point of the ex- duce that this peak represents a superposition of the 4th tended model to describe the free energy of laterally confined guiding pattern GTR and the 1st order block copolymer GTR. block copolymers is the model derived by Turner to deduce This implies that the pitch of the block copolymer that is de- eT/e0. Here, eT is the free energy of one macromolecule con- posited in the 90 nm guiding pattern area differs from its fined in a trench of width w in consideration of the deforma- natural pitch L0 = 23.4 nm by approximately 4.2% (corre- tion free energy, the polymer–wall interaction and the A/B- sponding to a pattern compression, such that the new pat- interfaces, and e0 corresponds to the free energy per macro- tern full-pitch is 22.5 nm). The distortion of cylindrical block molecule under equilibrium conditions. Despite of the differ- copolymers due to guiding pattern incommensurability has ences in pattern feature width, we find that results elaborated been observed by GISAXS before for minimal topographical for the design of wide guiding patterns are adaptable for the guiding patterns.46 present system if we consider the guiding pattern pitch in- stead of the trench width as independent variable (note the Discussion two different x-axis on top and at the bottom of Fig. 5a)). For this reason, the trench width w from the original equation So far, it has been consensus that graphoepitaxial guiding has been replaced by pattern pitch p to adapt the model to patterns have to be designed such that the space between the the system corresponding to the present guiding pattern mor- guiding patterns is exactly or close to an integer multiple of phology: the natural block copolymer pitch.21,30,47,48 This rule implies that the successful design of eT 1   p  2  n  L0 2    L0  2 graphoepitaxial guiding patterns depends on the interplay of      , (3) e0 3   n  L0  p p  pattern pitch p and pattern width wGP. Based on the analysis   presented in the Results section of this paper, we conclude that the design rule for the successful alignment of block co- where n is the multiplication factor, L0 is the block copolymer polymers in topographical guiding patterns with feature sizes equilibrium pitch in free surface and Γ is a term representing in the range of individual block copolymer domains differs the interaction between the block copolymer and the guiding fundamentally from those for wide topographical guiding pattern features. Changing the independent variable from patterns. Similar to chemoepitaxy, the high-resolution topo- w to p is justified by the existence of a continuous periodicity graphical guiding patterns have to be designed such that in the block copolymer film, as shown in the AFM image of their pitch (and not the space between two guiding pattern Fig. 2h). It enables the interference of scattering signal from features) is in the close vicinity of an integer multiple of the a large area in the GISAXS patterns.50 Then, the repeat unit block copolymer pitch (see Fig. 5a)–e)). of the block copolymer self-assembled inside the pattern is A model to describe the normalized free energy of block dictated by the pattern pitch p and not by the space between copolymers under confinement has been developed by two guiding pattern features w. Turner and successfully used to describe the self-assembly of The material dependent Flory–Huggins interaction param- block copolymers in topographical guiding patterns.30,49 We eter influences the energy level of the molecule in equilib- have recently introduced an extension of this model to ex- rium conditions e0. By normalizing the equation with e0, the plain the free energy of a self-assembly morphology with a material dependence of eqn (3) cancels out for its first two This journal is © The Royal Society of Chemistry 2019 Mol. Syst. Des. Eng., 2019, 4, 175–185 | 181 View Article Online Paper Molecular Systems Design & Engineering This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. Fig. 5 (a) Excess of free energy per block copolymer chain in units of the free energy in unconfined state (eqn (6)). The excess of free energy is calculated as the difference between the free energy of the defective state and the energy of the non-defective state, taking into account the defor- mation of the block copolymer on top of the guiding pattern. (b)–(d): SEM images on trenches defined by high resolution guiding patterns as a func- tion of guiding pattern pitch, p. Images with a red framework indicate patterns with defects, while the green ones indicate non-defective alignment. summands. The third summand still contains the polymer– et eTt e wall-interaction energy. This is a material parameter that in-   (6) e0 e0 e0 creases the free energy level of the system, but does not have any influence on the position of characteristic points on the p-axis. is positive, which occurs when Turner's free energy is larger than We will now add a summand eD/e0 to this equation, which the free energy of the defective state. If the term e/e0 is larger than accounts for the additional free energy introduced into the Turner's free energy (e.g. the result of eqn (6) is negative), the system due to the distortion of the block copolymer features block copolymers omit to form defects and deform to fit the guid- in the direct vicinity of the top cap of the guiding pattern fea- ing pattern dimensions. In general, we obtain that the process tures, so that the equation turns into: window (for pitch) in high resolution guiding patterns is smaller than for low resolution guiding patterns, which is a consequence of the different morphologies that the self-assembly takes. eTt 1   p  2  n  L0 2    L0  eD 2 We determine a distortion parameter that we call eD. The       (4) e0 3   n  L0  p p  e0 determination of eD is based on the assumption that the pen-   alty term ep (previously estimated at 0.007 for the self-assembly We call the expression eTt/e0 because it describes the free of PS-b-PMMA in wide guiding patterns21) is valid for all the energy of the system in thin guiding patterns. With the macromolecules in this system that are not subjected to distor- summand eD/e0 we account for the free-energy caused by tion in the close vicinity of the top cap of the guiding pattern chain deformation in the self-assembled system that is inde- features, as argued in the Results section. To describe our new pendent of the incommensurability.3 system accurately, we introduce the distortion term, which ef- The normalized free energy according to Turner in thin fectively increases the free energy of the defect-free state due to guiding patterns (eqn (4)) is now compared with a term that we the deformation of molecules close to the top cap of the guid- call e/e0 and describes the free energy of the system, when it ing pattern features. The term eD is not a function of the guiding forms defects. This term sums up the normalized free energy pattern pitch, because the said distortion is independent of the in free surface (i.e. 1), the interface free energy contribution (in-)commensurability of the guiding patterns. In that sense, due to the interaction between the block copolymers and guid- this parameter depends on the difference between the width of ing pattern features (i.e. 2 × Γ × L0/3 × p) and a constant energy the guiding pattern feature and the width of the domain of the penalty term accounting for an additional free energy contribu- preferentially wetting block (here PMMA). According to our un- tion (including, for example, the formation of additional inter- derstanding, the domain distortions in the vicinity of the top faces, domain wiggling and chain stretching) called ep/e0 cap of the guiding pattern features would reach a minimum in case the two had the same size. Based on this, we state that the parameter eD is the reason for the observed narrowing of the e 2    L0 ep 1  (5) process window and estimate e0 3 p e0 eD ≈ 0.003 e0 (7) Following the reasoning presented in a previous work,21 we can state that the system forms defects, if the term Δet/e0 We provide a detailed derivation of the model including defined as the distortion parameter eD in the ESI† part. For our 182 | Mol. Syst. Des. Eng., 2019, 4, 175–185 This journal is © The Royal Society of Chemistry 2019 View Article Online Molecular Systems Design & Engineering Paper particular case we derive that part of eD is due to the fact that site for the block copolymer to self-assemble in this the guiding pattern features are smaller than the wetting morphology is that the guiding pattern features are in the PMMA domain, and the PMMA domain is subjected to com- size range of the PMMA domain of the block copolymer. pressive force. This structural change can neither be directly We demonstrate that free energy models describing the observed in the GISAXS nor in the AFM measurements. Using self-assembly in wide guiding patterns are still valid for the the equation proposed by Ohta and Kawasaki,51 we can now description of our system after minor adjustments are intro- estimate that the energy penalty due to the domain distortion duced. Based on the modified model and the experimental in the close vicinity of the guiding pattern features accounts results of this work, we determine that the maximum differ- for about nine thousandths of kT per chain. This free energy ence between the defect-free and the defect-loaded state for This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. component does not exist in the self-assembly of block copol- thin guiding pattern features is generally only about half as Open Access Article. Published on 04 December 2018. Downloaded on 6/7/2019 3:47:25 PM. ymers in wide guiding patterns. Our interpretation of this large as for the directed self-assembly in wide guiding pat- term is that eD represents the reason for the smaller process terns. We report that this is due to the distortion created by window for the successful alignment of block copolymers in the incorporation of the thin guiding pattern features in the thin topographical guiding patterns than in wide topographi- block copolymer thin film. As a result, the process window cal guiding patterns. The smaller process window is particu- for the guiding pattern fabrication is smaller than for regular larly obvious when we compare the 110 nm pitch thin feature wide topographical guiding patterns. However, our results in- guiding pattern with the 110 nm trench width pattern for dicate that the fabrication of efficient, high resolution guid- wide guiding pattern features.21 While the wide guiding pat- ing patterns is durable despite the reduced process window, tern shows defect-free assembly, the thin 110 nm pitch guid- which could be relevant to the upcoming of high-chi (low ing pattern is clearly inside the defective area for the high- pitch) block copolymers. resolution guiding patterns. An investigation of the maxi- The present structures have been analyzed by AFM, SEM mum guiding pattern width able to produce the self- and GISAXS. Detailed peak-analysis of GISAXS measurements assembly morphology presented here would provide informa- reinforce the thesis about the morphology derived from the tion about the tolerance of the guiding pattern dimensions. characterization performed by real-space imaging techniques. The continuity of the block copolymer film on top of the Furthermore, GISAXS enables the determination of the chang- guiding pattern (which is the prerequisite both for the partic- ing block copolymer pitch as a function of the guiding pattern ular block copolymer self-assembly and the successful pitch with sub-nm resolution. We furthermore propose a GISAXS analysis) is certainly only observed in samples where method to qualitatively analyze the defect density of block co- the amount of deposited block copolymer is sufficiently large. polymers in narrow topographical guiding patterns by GISAXS. In a situation where a significantly lower block copolymer thickness is deposited or the guiding pattern features would Conflicts of interest have been significantly higher, it is conceivable that the block copolymer self-assembles in a discontinuous fashion as usu- There are no conflicts of interest to declare. ally observed in wide-guiding pattern feature graphoepitaxy. This finding, furthermore, demonstrates that the maxi- Acknowledgements mum free energy difference between the ordered (i.e. defect- This project is partially funded by the EU project NFFA (Nano- free) and the disordered (i.e. defect-loaded) state in the de- science Foundries and Fine Analysis) (grant agreement no. scribed system merely accounts for 0.004 e0, which is a result 654360) and by MICINN through the Nanointegra project that is in good agreement with calculations done by Garner (TEC2015-69864-R). The ICN2 is funded by the CERCA pro- et al. for chemical guiding patterns.52 The maximum free en- gram/Generalitat de Catalunya. The ICN2 is supported by the ergy difference is here defined as the free energy difference Severo Ochoa program of MICINN (SEV-2013-0295). We would for completely commensurate topographical thin guiding pat- like to acknowledge Christophe Navarro and Celia Nicolet terns. As the distortions only occur close to the top cap of the from Arkema for supplying some of the polymers used in this features, structural fluctuations only occur in a small part of work. We would, furthermore, like to acknowledge the team, the pattern and a reliable pattern transfer may therefore still in particular Dr. Björn Beyersdorff, of the P03 Micro- and be possible.3,38 Nanofocus X-ray Scattering Beamline at PETRA III in Ham- burg, Germany, and thank them for the technical support Conclusions during our GISAXS measurements. We have presented the fabrication of topographical guiding References patterns for the directed self-assembly of block copolymers with sub-10 nm resolution by electron beam exposure of 1 S. O. Kim, H. H. Solak, M. P. Stoykovich, N. J. Ferrier, J. J. De HSQ. During the self-assembly in these guiding patterns, we Pablo and P. F. Nealey, Nature, 2003, 424, 411–414. observe a self-assembly morphology, where the block copoly- 2 R. Ruiz, H. Kang, F. A. 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