nanomaterials Article Grain-Boundary-Induced Alignment of Block Copolymer Thin Films Steven Gottlieb, Marta Fernández-Regúlez, Matteo Lorenzoni, Laura Evangelio and Francesc Perez-Murano * Instituto de Microelectrónica de Barcelona (IMB-CNM, CSIC), Bellaterra, 08193 Barcelona, Spain; stgottl@googlemail.com (S.G.); marta.fernandez@imb-cnm.csic.es (M.F.-R.); matteo.lorenzoni@gmail.com (M.L.); lauraevangelioaraujo@gmail.com (L.E.) * Correspondence: francesc.perez@imb-cnm.csic.es; Tel.: +34-935-94-77-00 (ext. 2113)  Received: 3 December 2019; Accepted: 30 December 2019; Published: 4 January 2020  Abstract: We present and discuss the capability of grain boundaries to induce order in block copolymer thin films between horizontally and vertically assembled block copolymer grains. The system we use as a proof of principle is a thermally annealed 23.4 nm full-pitch lamellar Polystyrene-block-polymethylmetacrylate (PS-b-PMMA) di-block copolymer. In this paper, grain-boundary-induced alignment is achieved by the mechanical removal of the neutral brush layer via atomic force microscopy (AFM). The concept is also confirmed by a mask-less e-beam direct writing process. An elongated grain of vertically aligned lamellae is trapped between two grains of horizontally aligned lamellae. This configuration leads to the formation of 90◦ twist grain boundaries. The features maintain their orientation on a characteristic length scale, which is described by the material’s correlation length ξ. As a result of an energy minimization process, the block copolymer domains in the vertically aligned grain orient perpendicularly to the grain boundary. The energy-minimizing feature is the grain boundary itself. The width of the manipulated area (e.g., the horizontally aligned grain) does not represent a critical process parameter. Keywords: nanolithography; block copolymers; directed self-assembly; grain boundaries; AFM; mechanical removal 1. Introduction Block copolymers consist of two or more chemically different polymer chains covalently bonded together [1]. Driven by the repulsive force between chemically different molecules, the chains self-assemble in periodic structures, with characteristic size between few nanometers and few tens of nanometers. These periodic structures can be used as high resolution, bottom-up templates for nanofabrication processes, as for example bit patterned media for hard disk drives [2–4], finFETs [5], and contact holes [6]. A single-crystalline self-assembly morphology (e.g., perfect long-range order) cannot be achieved during the annealing of block copolymer thin films, despite of the fact that single-crystalline morphologies represent the minimal achievable free energy [7]. The formation of a rich variety of defects leads to polycrystalline morphologies and consequently represents limiting factor for the use of block copolymer self-assembly in many applications requiring a low defect density. As of now, this insufficiently low defect density is one of the main problems for the integration of block copolymer lithography in high volume manufacturing (HVM) processes [8]. Chemical and surface patterns defined by top-down lithography are usually used to introduce long-range order and placement accuracy in block copolymer thin films. These patterns are referred to as guiding patterns. The approach of directing the self-assembly of block copolymers by means of topographical patterns is referred to as graphoepitaxy. This principle has been successfully employed Nanomaterials 2020, 10, 103; doi:10.3390/nano10010103 www.mdpi.com/journal/nanomaterials Nanomaterials 2020, 10, 103 2 of 19 by a number of groups, as reported in different works in the last years [9–14]. Very low defect densities can be obtained when the width of the confining trench is exactly or close to an integer multiple of the natural pitch of the block copolymer [15–17]. A suitable guiding pattern design permits it to direct the self-assembly of block copolymers in device-oriented features [5,18], induce long-range order in sub-10 nm half-pitch block copolymers [19] and sub-5 nm half-pitch liquid crystals [20]. The chemoepitaxy approach relies on the introduction of chemical patterns into an underlying polymeric substrate. The orientation of block copolymers can be successfully controlled by the use of self-assembled monolayers [21] and crosslinked polymer mats [22] as underlayers. Common ways to manipulate the surface free energy of a Polystyrene-random-polymethylmetacrylate (PS-r-PMMA) brush layer is to combine a lithography step with the exposure to UV light [23] or to oxygen plasma [24]. The critical dimension of the guiding pattern features has to correspond to (n − 0.5) times the block copolymer pitch [25,26] with n being a positive integer. In contrast to the well-explored approaches of graphoepitaxy and chemoepitaxy, there are only few works that study the use of grain boundaries to introduce order in block copolymer thin films. On the other side, the shape of grain boundaries in block copolymers and the energy minimization process associated to their formation in lamel lar block copolymers have been studied quite extensively for bulk materials, and reported in excellent experimental [27–30] and theoretical [31–34] works. A brief review of grain boundary morphologies in block copolymers can be found in Appendix A.1. The few existing works on 90◦ twist grain boundaries in relation with block copolymer thin films include, for example, experiments with two chemically patterned plates [35], where the grain boundaries are formed parallel to the substrate, and with soft graphoepitaxy, where 90◦ twist grain boundaries have been observed for film thicknesses significantly larger than the guiding pattern feature height [36]. The ordering of block copolymers perpendicular to grain boundaries has recently also been identified as a metastable state in the chemoepitaxial alignment of block copolymers [37] and referred to as “stitch morphology”. Interestingly, in reference [38], the authors are capable of directing the self-assembly of block copolymers by the creation of structures under the formation of 90◦ tilt grain boundaries by mixing the pure block copolymer with a determined ratio of its constituent homopolymers, although it does not represent the energetically most favorable grain boundary morphology for pure block copolymer films [39]. Chemoepitaxy has been used to direct block copolymers into device-oriented features [40]. Despite of few isolated examples, grain boundaries have not been considered as order-inducing features in the directed self-assembly of block copolymers. In this work, we trap one grain of vertically self-assembled block copolymers between two elongated grains of horizontally aligned block copolymers (see Figure 1a). With vertically self-assembled block copolymers we refer to areas where the lamellae are oriented perpendicular with respect to the substrate, while they are oriented parallel to the substrate in case of the horizontal self-assembly morphology. The driving force of the directed self-assembly in this set-up originates from 90◦ twist grain boundaries formed on both sides of the trapped vertically oriented grain. These naturally formed grain boundaries are the reason any other guiding pattern features are redundant. We present grain-boundary-induced alignment (GBIA) as an interesting complementary technique to direct the self-assembly of block copolymers, because it represents a versatile method to align the material on lengths up to its correlation length ξ. The correlation length ξ characterizes the length range where the self-assembly of block copolymers can be successfully directed by grain-boundary-induced alignment. The parameter ξ is inversely proportional to the defect density in the film [41] in fingerprint pattern. Due to the absence of guiding patterns in a stricter sense, grain-boundary-induced alignment does not increase the mean grain size of the material, but rather orients the grains perpendicular to the formed grain boundaries. 2. Results The fabrication of aligned block copolymer patterns via (GBIA) has been realized using two different nano-patterning methods: (i) Atomic force microscopy (AFM) mechanical removal Nanomaterials 2020, 10, x FOR PEER REVIEW 3 of 19 The fabrication of aligned block copolymer patterns via (GBIA) has been realized using3 oftwo Nanomaterials 2020, 10, 103 19 different nano-patterning methods: (i) Atomic force microscopy (AFM) mechanical removal (m- AFM) and (ii) direct e-beam exposure of the underlying neutral brush layer. In block copolymer (m-AFM) lithography, andbrush (ii) direct e-beam layers exposure of are commonly theto used underlying control theneutral brush between free energy layer. In the block copolymer substrate and lithography, brush layers are commonly used to control the free energy between the block copolymer thin film. Most commonly, the brush layer is a random copolymer consisting of the substrate and the block the same two copolymer componentsthin film.used as the Most commonly, block copolymer. the Inbrush case layer is a random the random copolymer copolymer (here: consisting of the same two components as the(PS-r-PMMA)) Polystyrene-random-polymethylmetacrylate used block copolymer. consists Inof case the random the same or similarcopolymer volume (here: fractionPolystyrene-random-polymethylmetacrylate (PS-r-PMMA)) consists of the as the block copolymer (here: Polystyrene-block-polymethylmetacrylate same or similar (PS-b-PMMA)), the volume surfacefraction is wetted as the blocktwo by both copolymer (here: Polystyrene-block-polymethylmetacrylate block copolymer components. A brush layer that favors (PS-b-PMMA)), vertical self- the surfaceinisblock assembly wetted by both two copolymers block copolymer is referred to as neutralcomponents. brush. In the A brush specificlayer casethat of afavors lamellar vertical block self-assembly copolymer asinused blockin copolymers this work, is referred a neutralto as brushneutral brush. leads In the specific to vertically case ofblock standing a lamellar block copolymer copolymer domains. The as used two in this work, workflow a neutralare variations brush leads toinvertically presented standing block the two following copolymer sub-sections anddomains. they are The two workflow depicted in Figure variations are presented 1a. As we will explain ininthethe two following following sub-sections sections, and the selective they are of treatment depicted the brush in Figure layer is1a.used As we will explain in to manipulate thethe following interface sections, energy the selective between the blocktreatment copolymerof theand brushthelayer is used substrate in to manipulate such a way that the weinterface energyofbetween are capable thethe changing block copolymer and self-assembly modetheofsubstrate the block in copolymer such a way from that we are capable vertical of changing the self-assembly mode of the block copolymer from vertical to horizontal. to horizontal. Figure 1. Grain boundary induced alignment principle and work-flow. (a) Work-flow to direct the self-assembly Figure 1. Grainof block copolymers boundary inducedbyalignment grain-boundary-induced alignment; (b) principle and work-flow. (a) Force-dependence Work-flow to direct of the the mechanical self-assemblybrush removal of block while successively copolymers increasing the contactalignment; by grain-boundary-induced force from(b) 0.26Force-dependence µN to 2.34 µN from of the inside to the outside of the spiral. (c) Linewidth (y-axis on left hand side) and line the mechanical brush removal while successively increasing the contact force from 0.26 μN to 2.34 depth (y-axis on right handthe μN from side) as ato inside function of theofapplied the outside force the spiral. (c)extracted Linewidth from the pattern (y-axis shown on left hand in (b). side) and line depth (y-axis on right hand side) as a function of the applied force extracted from the pattern shown in (b). 2.1. Alignment Induced via Mechanical AFM (m-AFM) As depicted 2.1. Alignment in Figure Induced 1a, sketchAFM via Mechanical (2.a),(m-AFM) the fabrication of contact pads in the m-AFM approach relies on the mechanical removal of the neutral brush layer using an AFM tip. The AFM height As depicted in Figure 1a, sketch (2.a), the fabrication of contact pads in the m-AFM approach image depicted in Figure 1b represents a force test to determine the most suitable contact force for relies on the mechanical removal of the neutral brush layer using an AFM tip. The AFM height image the mechanical removal of the neutral brush layer. Here, the contact force has been increased from depicted in Figure 1b represents a force test to determine the most suitable contact force for the 0.26 µN to 2.34 µN in steps of 0.26 µN each segment, where the lowest contact force is applied for the mechanical removal of the neutral brush layer. Here, the contact force has been increased from 0.26 innermost segment of the spiral (see Figure 1b). Based on this experiment, we determine 1.04 µN as μN to 2.34 μN in steps of 0.26 μN each segment, where the lowest contact force is applied for the the minimum required contact force to ensure the complete removal of the neutral brush layer down to Nanomaterials 2020, 10, x FOR PEER REVIEW 4 of 19 Nanomaterials 2020, 10, 103 4 of 19 innermost segment of the spiral (see Figure 1b). Based on this experiment, we determine 1.04 μN as the minimum required contact force to ensure the complete removal of the neutral brush layer down thethe to substrate substrate (see(see Figure 1c), 1c), Figure because because we observe we observethat both that line bothwidth and line line width and depth line enter depthinenter a plateau in a regime where they are no longer a function of the applied force, i.e., plateau regime where they are no longer a function of the applied force, i.e., further increasing the further increasing the contact force further contact does not force further leadnot does to alead larger to aindentation depth. depth. larger indentation For the first set of experiments, we have removedthe For the first set of experiments, we have removed theneutral neutral brush brush layer layerin areas of 500 in areas nm nm of 500 × 5 µm ×5 (Figure 2a). The width of the areas has been chosen so that the resulting μm (Figure 2a). The width of the areas has been chosen so that the resulting structures have a structures have a reasonable size for a later reasonable size characterization. The mechanical for a later characterization. removal uncovers The mechanical removal the underlying uncovers silicon substrate, the underlying silicon is preferentially wetted by PMMA. substrate, which is preferentially wetted by PMMA. During the self-assembly process,block which During the self-assembly process, when the whencopolymer the block is heated above copolymer is heatedits glass above transition its glasstemperature, the formation transition temperature, the of horizontal formation of lamellae horizontal is lamellae induced is in these areas.For block copolymer film thicknesses in the range of L 0 , (where induced in these areas.For block copolymer film thicknesses in the range of L0, (where L0 is the natural L 0 is the natural full pitch of the full lamellar pitch of the block lamellar copolymer), the top material block copolymer), the top is thus PMMA. material is thusOn the other PMMA. On thehand, thehand, other top-layer the consists of top-layer PS when consists thewhen of PS film thickness is in the range the film thickness of 1.5 is in the L0 . of 1.5 L0. range Asthe As them-AFM m-AFMtechnique techniqueisisphysically physicallydisplaces displacesthe therandom randompolymer polymerbrush,brush,pile-ups pile-upsareareformed formed adjacent to the borders of the modified areas. In order to adjacent to the borders of the modified areas. In order to remove pile-ups of removed randomremove pile-ups of removed random copolymer and copolymer and to to be be capable capable of of analyzing analyzingthe the sample sampleappropriately appropriately via via AFM, AFM, the the sample sample undergoes undergoes a Propylene glycol methyl ether acetate (PGMEA) rinsing step a Propylene glycol methyl ether acetate (PGMEA) rinsing step before taking the AFM height imagebefore taking the AFM height image inFigure in Figure2a. 2a.The Thedistance distance d between d between thethe twotwo modified modified zones, zones, as depicted as depicted in Figure in Figure 2a, is2a, 300isnm. 300Thenm. The height step of approximately 7 nm corresponds to the height height step of approximately 7 nm corresponds to the height of the random copolymer layer, which of the random copolymer layer, which has beenhasentirely been entirely removed removed in theintwothe two recessed, recessed, modified modified areas. areas. TheThe two two recessed recessed areasisiswhat areas whatwe we refer to refer to as asguiding guidingpatternpattern forfor thisthis application. application. TheThe result of theofdirected result self-assembly the directed on theseon self-assembly guiding these patterns is depicted in an AFM height image (Figure 2b) and phase image guiding patterns is depicted in an AFM height image (Figure 2b) and phase image (Figure 2c). Profiles (Figure 2c). Profiles revealing the samplethe revealing topography perpendicular sample topography to the modified perpendicular to the areas beforeareas modified and after beforetheanddirected after self-assembly the directed step are presented in Figure 2e,f. The vertically aligned block self-assembly step are presented in Figure 2e,f. The vertically aligned block copolymer copolymer structures havestructures a notably have a notably shallower (and inversed) topography of around 2 nm. The block copolymer adapts shallower (and inversed) topography of around 2 nm. The block copolymer in the trapped grain in the its thickness to the height of the adjacent horizontally self-assembled trapped grain adapts its thickness to the height of the adjacent horizontally self-assembled grains. grains. Additional information concerninginformation Additional the analysis concerning of effect is presented the analysis in Appendix of effect is A.2. presented in Appendix A.2. Figure 2. Figure 2. Results Resultsof ofgrain-boundary-induced grain-boundary-induced alignment via atomic alignment via force atomic microscopy (AFM) mechanical force microscopy (AFM) removal. (a) AFM height image of guiding pattern with two areas treated mechanical removal. (a) AFM height image of guiding pattern with two areas treated by by AFM mechanical removal AFM (m-AFM) without mechanical removal brush layer (corresponds (m-AFM) without brush to sketch 2.a in Figure 1); layer (corresponds (b) AFM to sketch 2.aheight image in Figure 1);of(b) directed AFM self-assembly height image of (DSA) on area directed depicted in self-assembly (a); (c) (DSA) onAFM phase image area depicted in (a);taken simultaneously (c) AFM phase image to image taken (b), showing the self-assembly in horizontal (wide stripes) and vertical simultaneously to image (b), showing the self-assembly in horizontal (wide stripes) and vertical(narrow stripes) lamellae; (d) Zoom-in (narrow the lamellae stripes) central stripe of the AFM ; (d) Zoom-in the phase centralimage stripeof of(c); the(e) single AFM phaselineimage profileofalong (c); (e)blue dashed single line line in (a); (f) average height profile (i.e., average of all line scans) as indicated by profile along blue dashed line in (a); (f) average height profile (i.e., average of all line scans) as the box in (b). indicated by the box in (b). 2.2. Alignment Induced via Electron Beam Direct Exposure Nanomaterials 2020, 10, 103 5 of 19 Nanomaterials 2020, 10, x FOR PEER REVIEW 5 of 19 2.2. Alignment Induced via Electron Beam Direct Exposure The Thesecond secondcasecaseisisthe thesurface surfacemodification modificationby byan anexposure exposureto toan anelectron electronbeam, beam,where wherewe wemake make use of the modification of the neutral brush layer due to interaction with charged use of the modification of the neutral brush layer due to interaction with charged particles. As explained particles. As explained by Evangelioby Evangelio et al.electron et al. [26], high [26], high electron beam beam exposure exposure doses doses (e.g., 256 (e.g.,2 )256 mC/cm mC/cm cause 2 ) cause a change a in the change in the surface free energy of PS-r-PMMA and convert the nominally neutral surface free energy of PS-r-PMMA and convert the nominally neutral brush layer into a brush layer brush layer into athat brush layer that is preferentially is preferentially wetted by PMMA. wetted Asby PMMA. explained Asbefore, explainedthisbefore, this effect, in turneffect, in turn leads leads to to horizontal horizontal self-assembly self-assembly similar to thesimilar one to the oneafter observed observed after theofremoval the removal of the the neutral neutral brush brush layer, layer, but but dispensing dispensing with the physical removal of material. Figure 3 shows the results of self-assembly with the physical removal of material. Figure 3 shows the results of self-assembly in the direct vicinity in the direct vicinity of a 65 nm wide line (Figure 3a) and a 65 nm wide pristine area of a 65 nm wide line (Figure 3a) and a 65 nm wide pristine area Figure 3b. The orientation of the block Figure 3b. The orientation copolymer of the block copolymer perpendicular perpendicular to the grain boundary istoexplained the grain by boundary is explained the energy minimization by the energy inside the minimization inside the grain boundary and occurs as a direct consequence◦ of grain boundary and occurs as a direct consequence of the formation of 90 twist grain boundaries. the formation of 90° twist grain boundaries. Figure 3. Results of grain-boundary-induced alignment obtained by electron beam direct writing. (a) Figure 3. Results of grain-boundary-induced alignment obtained by electron beam direct writing. Horizontal self-assembly on a 65 nm wide stripe; (b) vertical self-assembly (e.g., grain-boundary- (a) Horizontal self-assembly on a 65 nm wide stripe; (b) vertical self-assembly (e.g., grain-boundary-induced induced alignment) alignment) onofstripes on stripes of different different widths widths with with a minimum a minimum of 65 nm. of 65 nm. 2.3. 2.3.Results ResultsofofPattern PatternTransfer TransferofofDirected DirectedFeatures Features into into Silicon Silicon ToTo make make use use ofof grain-boundary-induced grain-boundary-induced alignment alignmentfor forlithography lithographyapplications, applications,ititisisimportant important to to bebe capable capable of transferring of transferring the the defined defined structures structures into into silicon. silicon. As it As it is depicted is depicted in Figurein Figure 4, the 4, the pattern pattern transfertransfer processprocess consistsconsists of twoAfter of two steps. steps.the After the guiding guiding pattern pattern fabrication fabrication (see Figure(see 4a) Figure and4a) the and the self-assembly self-assembly (see Figure(see4b), Figure it is 4b), it is necessary necessary to remove to the remove PMMA, the so PMMA, so remaining that the that the remaining PS can servePS can as anserve etch as an etch mask. This mask. processThis stepprocess step in is displayed is Figure displayed in Figure 4c, where 4c, where the bright the bright lines lines correspond to PS correspond features andtothe PSdark features linesand the darktolines correspond correspond the voids createdtobythe voids created removed PMMA.by Theremoved PMMA PMMA. removal The can PMMA removal effectively be done can using effectively variousbe done using various oxygen-containing oxygen-containing gas mixtures, suchgas mixtures, as Ar/O 2 or such3 /O CHF as2 Ar/O 2 or CHF3/O (see Materials and2 (see Materials Methods partand Methods of this paper for part of this more paper for more information). PS, ininformation). PS, in turn, is relatively turn, more is inert relatively than PMMA more inert than towards PMMA towards oxygen-containing oxygen-containing plasma etch processes, plasma enablingetch processes, an etch selectivityenabling around an3. etch selectivity Secondly, around we use the 3. remaining PS template as an etch mask to transfer the defined features into Secondly, silicon. we use The result thepattern of the remaining PS template transfer of few nm as depth an etchintomask to transfer silicon the defined is depicted in Figure features into 4d. A great silicon. advantageThe result for theoffabrication the patternof transfer devices of with few nmthisdepth into silicon technique is thatisthe depicted in Figure horizontally 4d. A great aligned block advantage copolymersfor the as serve fabrication an etch mask of devices with this and preclude thetechnique is thatofthe chemical attack horizontally Si in this area. Ifaligned blockis the process copolymers conducted on serve as an etch mask and(SOI) a Silicon-on-Insulator preclude thethese wafer, chemicalareasattack of Si in this area. can subsequently If theasprocess be used is electrical conducted on a Silicon-on-Insulator contacts, because the silicon below remains (SOI) wafer, intact.these areas can subsequently This work-flow may representbe used asmethod a simple electrical for contacts, because the fabrication of the densesilicon belowarrays nanowire remains for intact. This work-flow nanoelectronic devices.may represent a simple method for the fabrication of dense nanowire arrays for nanoelectronic devices. Nanomaterials 2020, 10, 103 6 of 19 Nanomaterials Nanomaterials2020, 2020,10, 10,xxFOR FORPEER PEERREVIEW REVIEW 66 of of 19 19 Figure 4.Micrographs Figure4.4. Figure Micrographs Micrographsof ofdifferent of differentfabrication different fabrication fabrication stages stages stages in in thethe inthe pattern pattern pattern transfer transfer transfer process. process. process. (a) (a) image (a)AFM AFM AFM imageimage of of ofm-AFM m-AFM m-AFM treatedtreated treated areaarea area for for grain-boundary-induced for grain-boundary-induced grain-boundary-induced alignment; alignment; alignment; (b) (b) (b) DSA DSA DSA of of block of block copolymers block copolymers copolymers on on the the on the presented presentedguiding presented guidingpattern, guiding pattern, while pattern, while theexcerpt while the the excerptcorresponds excerpt corresponds corresponds toto to area area area surrounded surrounded surrounded by by dashed by dashed dashed lineline line in in (a); in (a); (a); (c) (c)PS (c) PSetch PS etchmask etch maskafter mask afterselective after selectiveremoval selective removalof removal ofPMMA of PMMA via PMMA Reactive via Reactive Reactive Ion Ion Etching Ion Etching (RIE)(area Etching (RIE) (RIE) (areacorresponds (area corresponds to corresponds white to dashed towhite white dashedlineline dashed in (b)); line in (d)(d) in(b)); (b)); pattern (d) pattern patterntransferred transferred transferredinto into intosilicon. silicon. silicon. 3.3. 3.Discussion Discussion Discussion 3.1. 3.1. Surface Energy Modification by by m-AFM 3.1. Surface Surface Energy Energy Modification Modification by m-AFM m-AFM AsAsthe As thesurface the surfaceenergy surface energymodification energy modificationofof modification ofa apolymeric a polymeric polymeric brush brush brush layer layer layerbyby bydirect direct direct e-beam e-beam e-beam exposure exposure exposure hashas hasbeen presented been elsewhere been presented presented elsewhere [26], in elsewhere [26], this section [26], inin this we this sectionwill section we focus we will on the will focus surface focus on on the energy the surface modification surface energy modification by induced energy modification the m-AFM induced induced bystep. by the the m-AFM m-AFMstep. step. The The analysis analysis of of the the wetting The analysis of the wetting behavior wetting behavior behavior of ofaaahomopolymer of homopolymer homopolymer blend blend blend consisting consisting consisting of of thethe of the components components components of of of the the block block copolymer copolymer the block copolymer can serve can serve serve as as aa qualitative qualitative test test for for thethe surface surface energy energy in in micrometric micrometric qualitative test for the surface energy in micrometric areas [26,42]. areas areas [26,42]. [26,42]. Here, Here, Here, wewe weuseuse usethisthis technique thistechnique techniqueto to qualitatively toqualitatively understandthe qualitativelyunderstand thesurface the surfaceenergy surface energyby byobserving observingthe observing thebehavior the behavior of behavior a of of aa PS/PMMA PS/PMMAPS/PMMA blend blend in thein blend the the modified inmodified and in modified andthein and the the non-modified non-modified in non-modified area. area. Phase area. Phase separation Phase separation of PS and separation of of PS and PMMA PS and is PMMA PMMAby induced is induced is the induced annealing by the by theof theannealing annealing film at 230 of of the◦ the film C forfilm at 230 fewatminutes. °C 230 °C To for few for be few minutes. minutes. capable To be capable To be capable of distinguishing of theoftwo distinguishing distinguishing polymers more easilythe two the two polymers in polymers the SEM images,more easily more easily in the SEM in the SEM we subjected images, theimages, samplewe we subjected tosubjected an 18 s oxygen the sample the sample plasma to an to an 18 18 ss treatment atoxygen 500 W plasma oxygen source treatment plasma treatment power. Due atat500 500 WWsource to the higherpower. source power. Due Dueto etch resistivity tothe ofhigher the higher PS with etch etch resistivity resistivity respect of ofPS to PMMA, PSwith we respect with respect the expect to to PMMA, PMMA, we we expect expect the the PMMA PMMA droplets droplets to to be be recessed recessed in in PMMA droplets to be recessed in height. The results are depicted in Figure 5. Figure 5a shows height. height. The The results results are are depicted depicted in in Figure Figurethe 5. 5. Figure Figure 5a 5a shows shows the the behavior behavior of of the the polymer polymer blend blend in in the the close close behavior of the polymer blend in the close vicinity of a 5 µm × 50 µm stripes, where the neutral brush vicinity vicinity of of a a 55 μm μm ×× 50 50 μm μm stripes, stripes, where where the neutral brush layer has been removed by by means of of m-AFM. m-AFM. In Figure Figure 5b 5b we we observe observeofaa the layer hasthe been neutral removed brushby layer means hasof been removed m-AFM. In Figure means5b we observe aInbehavioral difference behavioral behavioral difference difference of the polymer blend between the modified area and the the pristine area in pristine area in more polymer blend betweenofthe themodified polymer blend area and between the modified the pristine area inarea more and detail. more detail. detail. Nanomaterials 2020, 10, 103 7 of 19 Figure 5. Qualitative analysis of PS/PMMA blends on neutral surfaces and on surfaces modified by m-AFM. (a) Overview SEM image of PS/PMMA blend in two modified areas (stripes) and their direct pristine vicinity covered with neutral brush layer, (b) close-up of the part of (a) indicated by the box drawn in light blue, (c) explanatory sketch of the architecture of the droplet sketched on the left side of (b) before and after the oxygen plasma treatment, (d) explanatory sketch of surface on the right side of image (b). The phase-separated PS/PMMA droplet in the pristine area of the sample in Figure 5b is sketched in Figure 5c and provides valuable insight in the behavior of polymer blends on neutral surfaces. The slightly recessed part of the droplet corresponds to a PMMA droplet inside a PS droplet due to the O2 plasma treatment. This indicates that both polymers have very similar interface energies with respect to the neutral brush layer. The surface energy of PMMA (with respect to the air) is slightly higher than of PS [43], which justifies that the PMMA droplet is inside the PS droplet and not vice versa. A similar behavior has been presented before for the investigation of chemical guiding patterns [42,44]. In contrast, we do not observe these characteristic twin-droplets in the modified areas. This behavior is explained by a homogenous coverage of the silicon by PMMA, because the interface energy between the activated silicon and PMMA is significantly lower than between silicon and PS. The PS thus minimizes its surface energy through the formation of droplets surrounded by a continuous PMMA layer. This concept is sketched in Figure 5d. It is concluded that the surface energy is efficiently modified when the neutral brush layer is removed by m-AFM. 3.2. Limits of Grain-Boundary-Induced Alignment An important feature of the ordering of block copolymers via grain-boundary-induced alignment is that it does not require the fabrication of a high-resolution guiding pattern. This comes, however, at the expense of the fact that the maximum alignment length is limited by the correlation length, ξ, of the block copolymer. To estimate a reasonable maximum distance d between the two horizontally aligned grains, we have to know the grain size distribution of the block copolymer finger print after self-assembly. In Figure 6 we present an estimation of the block copolymer correlation length based on the grazing incidence small angle X-ray scattering (GISAXS) pattern depicted in Figure 6a, similar to how it has already been discussed elsewhere (for example in [44,45]). Moreover, we present an analysis of the width of the first order grating truncation rod (GTR) in Figure 6b, and an SEM image indicating the estimated mean grain size in Figure 6c. It is well-known that block copolymer self-assembly is a process based on grain nucleation and subsequent growth, also referred to as coarsening [46]. Characterization techniques like small-angle X-ray scattering (SAXS), depolarized light scattering (DPLS) [47], and grazing-incidence small-angle X-ray scattering (GISAXS) [44] are capable of providing mean values [48] for the grain sizes in block copolymers (e.g., correlation length). Nevertheless, the mean value does not, a priori, contain information about the distribution of the grain sizes. However, the experimental analysis of the grain size in the self-assembly of horizontally aligned diblock copolymers by AFM has been demonstrated to be in excellent agreement with a log-normal distribution function [49]:   2 1  (ln(ξ) − ln(µ))   f (ln(ξ)) = √  ∗ exp − (1)  2 (σ) 2π∗ ln(σ)    2 ∗ ln   with σ being the geometric standard deviation and µ being the number-based geometric mean, equivalent to the mode diameter of the grain. Nanomaterials2020, Nanomaterials 2020,10,10, 103x FOR PEER REVIEW 88ofof1919 Nanomaterials 2020, 10, x FOR PEER REVIEW 8 of 19 Figure 6. Estimating the limits of the directed self-assembly by grain-boundary-induced alignment. (a) Grazing-incidence Figure Figure Estimatingthe 6. Estimating 6. thesmall-angle limits of limits theX-ray of the scattering directed directed (GISAXS) self-assembly self-assembly by pattern by of randomly assembled grain-boundary-induced grain-boundary-induced block alignment. alignment. (a)copolymer (a) features; (b) Grazing-incidence Grazing-incidence estimationX-ray small-angle small-angle of thescattering X-ray full-width(GISAXS) scattering at half maximum (GISAXS) pattern (FWHM) pattern of randomly of randomly of the block copolymer assembled assembled block block grating truncation copolymer copolymer features; rodestimation features; (b) (b) (GTR) to estimate estimation of the of the mean thefull-width full-width atcorrelation at halfmaximum half maximumlength ξ of theof (FWHM) (FWHM) ofsample; theblock the (c)copolymer block SEM image copolymer grating grating truncation of finger-print truncation rod (GTR) pattern rod with to (GTR) estimate atocircle the themean meancorrelation representing estimate the length mean grain correlation ξ ξof size length asofthe thesample; sample;(c) determined by SEM (c)the SEM image analysis imageofof finger-print the GISAXS pattern with pattern. a circle representing the mean grain size as determined of finger-print pattern with a circle representing the mean grain size as determined by the analysis of by the analysis of the GISAXS the GISAXS pattern. pattern. The authors of [49] suggest that the block copolymer grain size can be described by a The authors of Smoluchowski [49] suggestfunction, that the block copolymer grainusually size canused be described by a Smoluchowski The authorscoagulation of [49] suggest thatforthewhich blockσ copolymer = 1.45; grain sizefor cansystems where particle be described by a coagulation trajectories function, are for controlled which by σ = Brownian 1.45; usually motion. If used the for systems correlation where length, ξ particle as trajectoriesbyare determined the Smoluchowski coagulation function, for which σ = 1.45; usually used for systems where particle GISAXS controlled GISAXS lineby Brownian motion. If the correlation length, ξ GISAXS as determined by the GISAXS line trajectories are width analysis, controlled corresponds by Brownian motion.to the If mean correlation the correlation length length, of allas ξGISAXS grains (in this by determined casetheξ= width 900 analysis, nm), we cancorresponds estimate thattothe thegrain meansizecorrelation distributionlength of all grains 𝑓(𝑙𝑛(𝜉)) of our sample case ξ = 900 nm), (in this is: GISAXS line width analysis, corresponds to the mean correlation length of all grains (in this case ξ = we can estimate that the grain size distribution f (ln(ξ)) of our sample is: 900 nm), we can estimate that the grain size 1 distribution  𝑓(𝑙𝑛(𝜉)) (ln(𝜉) −oflnour sample (731.7))  is: 𝑓(ln(𝜉)) = ∗ 𝑒𝑥𝑝 − ( ln ξ 2− ( ) ( )) 2 (2) √2𝜋 ∗11ln(1.45)∗ exp (ln(𝜉) −∗ln 731.7 𝑙𝑛(731.7)) ln (1.45)   ξ  f ( ln ( )) = √ − (2)  𝑓(ln(𝜉)) = (1.45)∗ 𝑒𝑥𝑝  − 2 (2) 𝑙𝑛 (experimentally 1.45)   22 ∗∗ln √2𝜋2π∗ ∗ lnln(1.45) (1.45)    (plotted in Figure 7a). The number 731.7 is selected to obtain the observed value for 𝜉 (plotted (plotted inFigure : in Figure7a).7a).The The number number 731.7 731.7 is selected is selected to obtain to obtain thethe experimentally experimentally observed observed value value for 𝜉for ξ mean : : R ∞ 𝜉 ∗ 𝑓(ln(𝜉))𝑑𝜉 𝜉 = ξ ∗ f (ln(ξ))dξ = 900 𝑛𝑚 (3) ξmean = 0R ∞ 𝜉 ∗ 𝑓(ln(𝜉))𝑑𝜉 = 900 nm (3) 𝜉 = 0 f ( ln ( ξ )) dξ = 900 𝑛𝑚 (3) 𝑓(ln(𝜉))𝑑𝜉 Knowing the approximate grain size distribution of our block copolymer in free surface 𝑓(ln(𝜉)), we Knowing the approximate grain size distribution of our block copolymer in free surface f (ln(ξ)), can estimate Knowing we can estimate the probability the approximate grain the probability p [%], p size that a grain ofofthe [%],distribution that a grain of the oursample is smaller than block copolymer sample is smaller thanin free surface 𝑓(lnvalue a determined a determined (𝜉)), ξwe value ξ 0: 0: can estimate the probability p [%], that a grain ofRthe sample ξ0 𝑓(ln(𝜉))𝑑𝜉 is smaller than a determined value ξ 0: 𝑝(𝜉 ) = 100 ∗ f (ln(ξ))dξ % (4) p(ξ0 ) = 100 ∗ R0∞ 𝑓(ln(𝜉))𝑑𝜉 𝑓(ln(𝜉))𝑑𝜉[%] (4) 𝑝(𝜉 ) = 100 ∗ 0 f (ln(ξ))dξ % (4) 𝑓(ln(𝜉))𝑑𝜉 The particle distribution function in Figure 7a is divided in a red and The particle distribution function in Figure 7a is divided in a red and a blue area. The surface area a blue area. The surface ofareaThe the of redthe reddivided particle part part divided by theby distribution thearea function total total area represents inrepresents Figure 7a the the probability is divided probabilityin a p(ξ p(ξa0an red0 )and that ) blue that an areal area. areal unit Theunit forms surface forms part part area of a grain of thesmaller of a grain smaller red partthan than ξ0 = by divided ξ 450the 0 = 450 nm, nm, total which in areainrepresents which this this case is case the is 4.8%. probability 4.8%. Accordingly, p(ξ0) that Accordingly, 0.3% of 0.3%anofareal the total unit area the total formsarea is is part occupied of a grain occupied by grains smaller by grains with than with the ξ0size the size = 450 ofnm,of 300 300 which nm nm and and in merelymerely this case7 is 7 × × 4.8%. 10 % 10 −10 −10% of the area is occupied by grains Accordingly, of the area is 0.3% of the total occupied area by grains is smaller occupied smaller than than by6565 nm. with the size of 300 nm and merely 7 × 10−10% of the area is occupied by grains grains nm. smaller than 65 nm. Figure7.7.Grain Figure Grain size size analysis analysis in in block copolymer thin block copolymer thin films. films. (a) Grain size Grain distribution size distributionfor forthe theblock block copolymer copolymer in free in surface free surfacefor ξ for mean ξmean == 900 900 nm nm Figure 7. Grain size analysis in block copolymer thin films. (a) Grain size distribution for the block copolymer in free surface for ξmean = 900 nm Nanomaterials 2020, 10, 103 9 of 19 The self-assembly in structures like the ones we fabricate in this work is considered to be successful if there is no defect on the entire length of the grain. We can estimate the probability pd of this event by estimating the probability that all the grains along the grain boundary with the length l are at least as large as the distance d between the two grain boundaries, which is given by the term: l pd = p(ξ0 = d) d (5) In the table presented in Table 1 we present the probability to fabricate a l = 5 µm long array without defects for three different lengths of d. The values for d we worked with in this table are process parameters used in this section. In particular, we have presented the grain boundary-induced alignment with d = 300 nm in Figure 2 fabricated by m-AFM and d = 65 nm in Figure 3 by e-beam direct writing and we observe no defects in these structures—just as predicted by the presented estimation. The fact that a pd (d = 450 nm) yields less than 60% indicates that the probability to find defects in such a structure rather high. An example of a structure with d = 450 nm is depicted in Figure 8a and we observe the formation of defects. Table 1. Results for the probability of defect free self-assembly between two 5 µm grain boundaries for three characteristic distances d between the grains. Average correlation length ξmean is 900 nm. Distance d between Two Grains Probability p of Defect-Free Self-Assembly d 65 nm 99.99999% 300 nm 95.15% 450 nm 57.89% Nanomaterials 2020, 10, x FOR PEER REVIEW 10 of 19 Figure Figure 8.8.Alternative Alternativestructures structures fabricated by by fabricated grain-boundary-induced grain-boundary-induced alignment. (a) Defective alignment. self- (a) Defective assembly due to a too large distance between the two grain boundaries; (b) self-assembly self-assembly due to a too large distance between the two grain boundaries; (b) self-assembly of of multiple arrays of parallel multiple arrays oflamella; (c) lamella; parallel arbitrary(c) shapes fabricated arbitrary shapesbyfabricated mechanical byAFM removal;AFM mechanical (d,e) removal; double- bar cross (d,e) definedcross double-bar by mechanical defined byAFM removal. mechanical AFM removal. 3.3. Fabrication Based on theof Patterns presentedof Arbitrary Geometry analysis, the self-assembly of block copolymers by grain-boundary-induced alignment mainly depends The fabrication on the of patterns correlation to direct length ξ of the the self-assembly of block block copolymer copolymers(material parameter), by grain-boundary- and on the distance d between the two horizontally aligned grains and the length l induced alignment by m-AFM is not limited to trapping one single grain, which has been the onlyof the horizontally aligned grains structure that we(process have parameters). discussed untilFor this now.reason, it is important In Figure 8b–e, we to understand present the mechanisms alternative structures of self-assembly fabricated and defect-annihilation by grain-boundary-induced in detail,such alignment, which has alreadyarray as defect-free beenofsubject to a number nanowires of 200 nmof works [41,44,50,51]. in length and a pitch of 250 nm in Figure 8b. In Figure 8c we show a number of geometric shapes that have been fabricated to demonstrate the versatility of the technique. A double-lined cross of 10 μm × 10 μm with a line width of 500 nm and 250 nm spaces between the lines is depicted in Figure 8d,e. The in-set of Figure 8d shows the Moiré pattern between the two branches of the cross, which indicates the high order of the block copolymer without actually having sufficient measurement points to resolve single block copolymer domains. Moiré patterns are interference patterns [53] that Nanomaterials 2020, 10, 103 10 of 19 The rate at which a block copolymer eliminates defects in the course of the self-assembly process is determined by the energy barrier that has to be overcome in order to annihilate the defect [52]. Here, a smaller energy barrier indicates a faster defect removal mechanism which is expressed by a higher degree of order in the block copolymer. In [52] the authors demonstrate that the energy barrier for the defect removal is inversely proportional to χN. A direct consequence of that is that the correlation length ξ of block copolymers is larger for small-pitch materials (e.g., materials with small χN). This means that an inherent property of grain-boundary-induced alignment is the decreasing number of defects for smaller-pitch materials. Additionally, the influence of different fractions of homopolymer in the block copolymer on both grain boundary energy and correlation length is investigated and presented in Appendix A.3. 3.3. Fabrication of Patterns of Arbitrary Geometry The fabrication of patterns to direct the self-assembly of block copolymers by grain-boundary-induced alignment by m-AFM is not limited to trapping one single grain, which has been the only structure that we have discussed until now. In Figure 8b–e, we present alternative structures fabricated by grain-boundary-induced alignment, such as defect-free array of nanowires of 200 nm in length and a pitch of 250 nm in Figure 8b. In Figure 8c we show a number of geometric shapes that have been fabricated to demonstrate the versatility of the technique. A double-lined cross of 10 µm × 10 µm with a line width of 500 nm and 250 nm spaces between the lines is depicted in Figure 8d,e. The in-set of Figure 8d shows the Moiré pattern between the two branches of the cross, which indicates the high order of the block copolymer without actually having sufficient measurement points to resolve single block copolymer domains. Moiré patterns are interference patterns [53] that occur when a periodic lattice (for example a directed block copolymer pattern) is measured with an imaging technique whose sampling step size is below the step size of the lattice that is supposed to be measured. The existence of the Moiré pattern hence can be understood as a proof for the successfully directed self-assembly of the block copolymers between the two branches of the cross. To verify this thesis, we show a close-up of the center of the fabricated cross in Figure 8e, where we doubtlessly see the directed self-assembly of block copolymers is successful in each one of the four trapped grains. 4. Materials and Methods 4.1. Substrate The substrate are chips cut from a <100> Si wafer. Native oxide is not removed. After cleaning the substrate in isopropyl alcohol and acetone, the substrate undergoes an oxygen plasma treatment for 600 s at 500 W. 4.2. Neutral Brush Layer Deposition The neutral brush layer consists of grafted PS-r-PMMA polymer chains (58 wt% PS, 42 wt% PMMA, Mp = 7.9 kg/mol and polydispersity index 1.85) yielding a film thickness of 6.5. To deposit the neutral brush layer, 1.5 wt% of PS-r-PMMA is dissolved in PGMEA and the solution is spin-coated to the silicon wafer for 30 s at 5000 rpm. To graft the molecules to the surface, the chip is annealed at 230 ◦ C in a nitrogen atmosphere for 300 s. The non-grafted molecules are removed by rinsing the sample in PGMEA. All the polymer materials have been supplied by Arkema (Colombes, France). 4.3. Guiding Pattern Fabrication In this work we use two different methods to fabricate the guiding patterns. The guiding pattern fabrication by AFM consists of removing the neutral brush layer in two elongated rectangular areas of 500 nm × 5 µm separated by a distance d in the range of few hundreds of nanometers. The brush removal is done by mechanical AFM using the contact mode of a Dimension Icon/Nanoscope V AFM (Bruker Corporation, Billerica, MA, USA). The tips used in these experiments (OTESPA, also from Nanomaterials 2020, 10, 103 11 of 19 Bruler, Si-tip with nominal spring constant 42 N/m) have a nominal apex radius of 7 nm in the unused state. We estimate the contact force for the probed deflection set-points to be between 0.26 µN and 2.34 µN. The AFM height image shown in Figure 1b shows the efficiency of the polymeric brush layer removal as a function of the contact force. The contact force has been increased by 0.26 µN for each segment of the spiral going from the inside to the outside. The fabrication of the structures presented in this article has been conducted with nominal contact force of 1.04 µN, because this condition represents the minimum required force to remove the polymer film down to the substrate. The second approach to fabricate the guiding patterns is based on the modification of the brush layer by direct e-beam exposure. The exposure has been performed in a RAITH 150 (TWO) electron lithography tool (Raith Gmbh, Dortmund, Germany) with a nominal beam diameter of 2 nm. We expose lines of 50 µm in length and between 65 nm and 500 nm in width, with separations between 500 nm and 65 nm. We applied the same conditions as used in reference [26]: electron beam with 20 kV acceleration voltage; sample current of 330 pA; exposure dose of 256 mC/cm2 . 4.4. Block Copolymer Deposition The diblock copolymer is a PS-b-PMMA (Arkema (Colombes, France) consisting of 42 wt% PS and 58 wt% PMMA. Upon self-assembly, this material forms 23.4 nm full-pitch lamellar features. Its polydispersity index PDI is 1.1, and the molecular weight is 42.3 kg/mol. A 1.7 wt% solution of the polymer in PGMEA is deposited by spin coating for 30 s at 2500 rpm and subsequently annealed for 600 s in a N2 atmosphere at 230 ◦ C. This process yields a film thickness of 24 nm in free surface. 4.5. Pattern Transfer The pattern transfer consists of two steps. At first, the PMMA block is removed in a selective dry etching step in an Alcatel AMS 110 DE ICP-RIE. (Inductively coupled plasma reactive ion etching). We used etching conditions similar to those previously successfully developed and used by the authors of reference [54]: a gas mixture of 200 sccm Ar and 10 sccm O2 with at 200 W source power and 5 W substrate power. The etch selectivity of PS with respect to PMMA in this process is 1:3 with PS being the more resistant material. The etching time for this step is 21 s. For the subsequent Si etching we use the same RIE tool with a plasma power of 1200 W and a substrate power of 10 W for 12 s. The used gases are 30 sccm SF6 and 25 sccm C4 F8 . We employ an etch process in which both gases are injected in the reaction chamber in a non-pulsed way. 4.6. GISAXS Measurements GISAXS measurements of a representative sample have been conducted at the P03 Micro- and Nanofocus X-Ray Scattering Beamline at PETRA III in Hamburg [55]. The sample-detector distance was 5800 mm and the radiation wavelength 0.107 nm. The incidence angle of the beam was 0.4◦ . The detector that has been used for these experiments is a PILATUS 300k pixel detector (ECTRIS Ltd., Baden-Daettwil, Switzerland) with a readout time t < 3 ms and a pixel size of 172 µm. 5. Conclusions We have shown that the directed self-assembly of block copolymers by grain boundary induced alignment is possible either by the controlled removal of an intermediate polymeric brush layer or its local surface modification. We have shown this concept using both a probe-based mechanical removal approach and an electron-beam direct writing approach. The driving force of the self-assembly is the energy minimization process in the grain boundary between horizontally and vertically assembled block copolymers. This specific grain boundary is referred to as 90◦ twist grain boundary, where the PS/PMMA surface is reduced to a first Scherk surface, which mathematically represents a minimal surface. Because this approach does not require a guiding pattern along the self-assembly direction, the correlation length ξ is the limiting factor for the defect-free alignment. Nanomaterials 2020, 10, 103 12 of 19 For this reason, grain-boundary-induced alignment represents a particularly interesting alternative for early stage testing of new high-χ, low-pitch block copolymers with large correlation lengths. A recent report on the self-assembly of sub-5 nm liquid crystals (with a remarkably high degree of intrinsic order) has shown that the alignment of very small features by the mean of graphoepitaxy may be perturbed by large guiding pattern roughness [20]. Grain-boundary-induced alignment offers one possible solution for upcoming challenges that may be encountered by graphoepitaxy (and also chemoepitaxy), which is the difficulty to provide reliable guiding patterns for very small pitch self-assembling materials. Grain-boundary-induced alignment, in turn, favors the directed self-assembly of materials with small pitches due to their large correlation length. On the down-side, we have to remark that the limited placement accuracy of the block copolymer features may represent an issue that requires improvement. This study presents a straight forward way to direct the self-assembly of block copolymers by taking advantage of the grain boundaries created between two differently oriented areas of block copolymers. Author Contributions: Conceptualization, S.G. and F.P.-M.; validation, S.G., M.L., L.E., M.F.-R., and F.P.-M.; formal analysis, S.G. and F.P.-M.; investigation, S.G.; resources, F.P.-M.; draft preparation, S.G. and F.P.-M.; visualization, S.G., M.L., and F.P.-M.; supervision, F.P.-M.; project administration, F.P.-M.; funding acquisition, F.P.-M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the EU project NFFA, grant number 654360 and by the Spanish project NANOINTEGRA (TEC2015-69865-R) and STARSED (RTI2018-102007-B-I00). Acknowledgments: The authors would like to acknowledge Christophe Navarro and Celia Nicolet from Arkema for supplying some of the polymers used in this work. We would, furthermore, like to acknowledge the team of the P03 Micro- and Nanofocus X-Ray Scattering Beamline at PETRA III in Hamburg, Germany and in particular Björn Beyersdorff for his technical support during the GISAXS measurements. Conflicts of Interest: The authors declare no conflict of interest. Appendix A. Appendix A.1. Overview of Grain Boundary Morphologies in Block Copolymers Two relevant types of grain boundaries are the twist grain boundary at one hand (see Figure A1) and the tilt grain boundary on the other hand (see Figure A2). As for lamellar block copolymers, the grain boundary free energy is a function of the area of the intermaterial dividing surface (IMDS) and the stretching and the compression of molecules in the close vicinity of the grain boundary. The material usually tries2020, Nanomaterials to reduce the 10, x FOR area PEER of the IMDS by stretching and compressing adjacent chains. 13 of 19 REVIEW Figure A1. Different Figure A1. Different types types ofof twist twist grain grain boundaries boundaries and and their their corresponding corresponding inter-material inter-material dividing dividing ◦ surface surface (IMDS). (IMDS). (a) (a) Two Two grains grains of of lamellar lamellar block block copolymers copolymers under under aa twist angle αα  twist angle ≪ 9090°;; the the grey grey areas of the inset represent the IMDS reconstructed in a Scherk surface; (b) two grains areas of the inset represent the IMDS reconstructed in a Scherk surface; (b) two grains of lamellar of lamellar block copolymers underunder block copolymers a twista twist α α90≪◦ ,90°, angleangle thethe inset represent inset representthethe IMDS IMDSreconstructed reconstructedininaahelicoid helicoid shape; (c) two grains of lamellar block copolymers under a twist angle of 90◦ , the grey areas of the inset shape; (c) two grains of lamellar block copolymers under a twist angle of 90°, the grey areas of the represent the IMDS inset represent reconstructed the IMDS in a Scherk reconstructed surface. in a Scherk surface. Figure A1. Different types of twist grain boundaries and their corresponding inter-material dividing surface (IMDS). (a) Two grains of lamellar block copolymers under a twist angle α ≪ 90°; the grey areas of the inset represent the IMDS reconstructed in a Scherk surface; (b) two grains of lamellar block copolymers under a twist angle α ≪ 90°, the inset represent the IMDS reconstructed in a helicoid shape; (c) two grains of lamellar block copolymers under a twist angle of 90°, the grey areas of the Nanomaterials 2020, 10, 103 13 of 19 inset represent the IMDS reconstructed in a Scherk surface. Figure A2. Overview of tilt grain grain boundary boundary morphologies. (a) Two Two grains of lamellar block copolymer tilted under ◦ under an angle well below 90 90°,, (b):two grains of lamellar block copolymer tilted under an angle of 90 ◦ 90°,, (c) 2D-scheme of the IMDS of a low-tilt-angle low-tilt-angle chevron grain boundary, (d) 2D-scheme 2D-scheme of the the IMDS ◦ IMDS of of an anomega omegagrain grainboundary, boundary,(e)(e)2D-scheme 2D-scheme of of thethe IMDS of aofpure IMDS T-junction a pure as observed T-junction in 90in as observed tilt 90°grain boundaries. tilt grain boundaries. anglesα < For ◦ we observe two different reconstruction moduli, which are called helicoid For twist twistangles α 15 < 15° we observe two different reconstruction moduli, which are called interphase and Scherk helicoid interphase andfirst surface Scherk [32,34]. first surface The two morphologies [32,34]. coexist for coexist The two morphologies low angles because for low anglesof their because similar grain of their boundary similar grainenergies boundary (see Figure (see energies A1a,b). FigureTheA1a,b). major Thedifference major between differencethese two between morphologies is the shape of the IMDS. There is no major reconstruction mechanism these two morphologies is the shape of the IMDS. There is no major reconstruction mechanism in the in the formation of helicoid formation grain boundaries of helicoid (see grain shape of the boundaries respective (see shape ofIMDS in inset of IMDS the respective FigureinA1b)). insetInofthe second Figure case, A.1.b)). the first Scherk surface, the IMDS is reconstructed to a distorted chess board In the second case, the first Scherk surface, the IMDS is reconstructed to a distorted chess boardpattern, as described in [31]. The IMDS in these structures can be mathematically described as a first Scherk pattern, as described in [31]. The IMDS in these structures can be mathematically described as a first surface, which forms part Scherkof the familywhich surface, of minimal formssurfaces part of [56]. The insets the family of Figuresurfaces of minimal A1a,c represent [56]. Thea scheme insets ofofFigure the situation A1a,c inside represent a scheme of the situation inside the grain boundary. Here, white and black areas B-B-block the grain boundary. Here, white and black areas represent A-A-block interfaces and represent interfaces, A-A-block respectively. interfaces and The actual IMDS B-B-block is represented interfaces, by theThe respectively. grey areas,IMDS actual whichisrepresent represented A-B-block by the interfaces. The reconstruction of twist grain boundaries in first Scherk surfaces grey areas, which represent A-B-block interfaces. The reconstruction of twist grain boundaries in first has been observed experimentally Scherk surfaces[27,29].has been For better understanding, observed experimentally we have plotted [27,29]. a scheme For better of a first Scherk understanding, we have surface plottedas it ◦ ◦ Figure a occurs schemeinof90a first twistScherk grain boundaries surface as itinoccurs Figurein A1d. 90° For twistlarge twist grain angles (αin boundaries 15 ), the formation A1d. For largeof first Scherk surfaces is energetically favorable when compared to helicoid grain twist angles (α ≫ 15°), the formation of first Scherk surfaces is energetically favorable when compared boundaries. This is at one hand because the helicoid grain boundary massively compresses the to helicoid grain boundaries. This is at one hand because the helicoid grain boundary massively lamellae (and therefore the chains) compresses at large the angles. lamellaeOn thetherefore (and other hand, the firstat the chains) Scherk surface On large angles. is by thedefinition other hand,a minimal the firstsurface Scherk that minimizes the IMDS at large twist angles of α = 90 ◦. surface is by definition a minimal surface that minimizes the IMDS at large twist angles of α = 90°. Tilt grain boundaries represent another grain boundary family commonly observed in bulk block copolymer samples. Schemes of two grains under a low tilt angle θ  90◦ and under a tilt angle θ = 90◦ are represented in Figure A2a,b. Low angle tilt grain boundaries are sub-divided in so-called chevron tilt grain boundaries and omega tilt grain boundaries. While the chevron tilt grain boundary is rather prominent at low tilt angles, the omega grain boundary tends to be the result of energy minimization at larger tilt angles [33]. As we can tell from the two sketches depicted in Figure A2c,d, both morphologies are similar in appearance. The sequence of the omega-layers and semicylinder caps [33] in omega tilt grain boundaries efficiently minimizes the grain boundary energy at higher angles. When the tilt angle increases even more and θ approaches 90◦ (see Figure A2b), the most efficient manner to minimize the free energy of the system is to interrupt the continuity of one of the species and reorganize them in semicylinder caps as shown in Figure A2e. 90◦ tilt and 90◦ twist grain boundary structures, as sketched in Figures A1c and A2b, may form in block copolymer thin films, when a vertically oriented grain is adjacent to a horizontally oriented grain. This situation may occur wherever the surface energy changes abruptly from a neutral surface to a highly preferentially wetted surface. Taking into consideration that the block copolymer features Nanomaterials 2020, 10, 103 14 of 19 on neutral surfaces are upright standing lamellae, the only two structures that may be formed in such grain boundaries are the 90◦ tilt grain boundary and the 90◦ twist grain boundary. In reference [36] the authors argue that the free energy of 90◦ twist grain boundaries is around half of the free energy of 90◦ tilt grain boundaries, which heavily benefits the formation of twist grain boundaries. This calculation is moreover supported by the fact that 90◦ twist grain boundaries, and the resulting tendency to form Scherk’s first surface IMDSs, are also observed in the terraced self-assembly horizontally aligned block copolymers on preferentially wetting substrates [57]. Appendix A.2. Fixed-Height Self-Assembly Transferring the created block copolymer patterns into the underlying substrate is a key step that converts block copolymer lithography into a purposeful technique for semiconductor manufacturing. Here, the pattern transfer process is particularly challenging, because polystyrene and poly(methyl methacrylate) are chemically similar. Despite of PS being chemically relatively inert, it does by far not show etch resistances as large as an inorganic hard mask would do. This leads to fast mask wear and requires exact knowledge about the film thickness of the initial block copolymer film to design a successful pattern transfer process. Nanometric fluctuations of the block copolymer thickness throughout the wafer/chip area due to microscopic impurities or other process-related issues may lead to difficulties in the pattern transfer process. The self-assembly of block copolymers between two grain boundaries is quantized to multiples of 0.5 L0 , because of the adjacent horizontally oriented grains’ quantized height. This concept is clarified in Figure A3, where we present a measurement of the block copolymer height in the horizontally aligned (and previously modified) area. The block copolymer has been removed by m-AFM in an area orthogonal to the long axis of the modified area, and an AFM height image of one part of the sample is depicted in Figure A3a. A single line AFM height profile is shown in Figure A3b. The profile’s precise location and direction is indicated by the white dashed line both in the sketch and in the actual height image. The step height is 35 nm, which corresponds to 1.5 L0 (with L0 being 23.4 nm). Based on the knowledge that the silicon wafer is preferentially wetted by PMMA, we conclude that the top layer must be PS, as sketched in Figure A3c. Nanomaterials 2020, 10, x FOR PEER REVIEW 15 of 19 Figure A3. Measuring Figure A3. Measuring the the height height step step between between substrate substrate and horizontally aligned and horizontally aligned block block copolymer copolymer lamellae. lamellae. (a) AFM height image of prepared sample; (b) single line profile indicated by (a) AFM height image of prepared sample; (b) single line profile indicated by white white dashed dashed line line in in (a); (a); (c) (c) 3D 3D sketch sketch of of the the measurement measurement presented presented in in (a); (a); (d) (d) possible possible self-assembly self-assembly morphologies morphologies with with height quantized to height quantized to from from 0.5 L0–2 0.5 L –2 L L0 in in steps steps of of 0.5 0.5 LL0. . 0 0 0 Figure A3d presents a sketch of four different self-assembly self-assembly heights heights in in steps steps of of 0.5 0.5 L00. We We would like to state stateat atthis thispoint pointthat thatthe the horizontally horizontally aligned aligned areas areas willwill self-assemble self-assemble in a in a quantized quantized state state such such that the film height in the horizontally aligned area is always an integer multiple of that the film height in the horizontally aligned area is always an integer multiple of 0.5 L0 . Interestingly, 0.5 L 0. Interestingly, we observe in we observe all our in all our experiments experiments that that the the self-assembly of self-assembly block copolymers of block in thecopolymers in the vertically aligned vertically aligned trapped grain is few nanometers recessed with respect to the horizontally aligned grains. The opposite has been observed by other authors in a similar experiment [58], where the vertically assembled block copolymer domain is few nanometers higher than the horizontally aligned domain. In both cases the deviation of the vertical lamellae height from the quantized horizontal lamellae height is few nanometers. Nanomaterials 2020, 10, 103 15 of 19 trapped grain is few nanometers recessed with respect to the horizontally aligned grains. The opposite has been observed by other authors in a similar experiment [58], where the vertically assembled block copolymer domain is few nanometers higher than the horizontally aligned domain. In both cases the deviation of the vertical lamellae height from the quantized horizontal lamellae height is few nanometers. Appendix A.3. Grain-Boundary-Induced Alignment with Ternary Blends For the application of grain-boundary-induced alignment it could be favorable to achieve an alignment mode that is not restricted by the correlation length of the block copolymer. One way to do so is to influence the material is such a way that the preferentially formed grain boundary is a 90◦ tilt grain boundary (see Figure A1c) instead of a 90◦ twist grain boundary (see Figure A2b). This is the case when the vertical interface created by the horizontally ordered block copolymer is energetically more attractive to one block than for the other, similar to the energetic situation in graphoepitaxy. Duque et al. [39] calculated the free energy in twist and tilt grain boundaries for a pure diblock copolymer and a ternary blend containing 70% diblock copolymer and a 30% fraction of homopolymers. The calculation yields that 90◦ tilt grain boundaries have the same (or in the concrete case of mixing in 30% homopolymers an almost negligible 2% lower) grain boundary free energy compared to the 90◦ twist grain boundary in case of mixing in homopolymers. The 90◦ twist grain boundary has, in turn, a clear energetic advantage over the 90◦ tilt grain boundary in case of pure diblock copolymers. Moreover, the absolute grain boundary free energy for the ternary blend is reduced heavily to approximately 1/3 of the value for the pure block copolymer. We reproduced this experiment using a blend of the 23.4 nm pitch PS-b-PMMA and different amounts of PS and PMMA with a molecular weight of 39.5 kg/mol with a total accumulated homopolymer fractions between 0% and 45%. In all the experiments, the volume fraction of PS and PMMA is equal. Results of the behavior of the ternary block copolymer/homopolymer blend in the vicinity of a grain boundary is presented in Figure A4. The annotation in the respective SEM images in Figure A4 refers to the accumulated homopolymer fraction, which means that “30% HP” in Figure A4b indicates that the ternary blend contains 15% PS, 15% PMMA, and 70% PS-b-PMMA. We observe two different effects caused by the increasing homopolymer fraction. At one hand, we Nanomaterials 2020, 10, x FOR observe a progressive PEER REVIEW swelling 16 of 19 of the block copolymer features due to the accumulation of homopolymer molecules in the center of the domain (because this is the place where the molecules can avoid the homopolymer molecules in the center of the domain (because this is the place where the molecules energetically unfavorable location close to the IMDS). This effect is accompanied by a decrease of the can avoid the energetically unfavorable location close to the IMDS). This effect is accompanied by a material’s correlation length. decrease of the material’s correlation length. Figure FigureA4. A4.Grain Grain boundary boundary evolution as as function functionof ofhomopolymer homopolymercontent contentinin the the ternary ternary blend. blend. (a)(a) 0% 0% homopolymer, homopolymer, (b) (b) 30%,30%, (c) 45%; (c) 45%; tilt grain tilt grain boundaries boundaries andand the blue the blue areasareas are marked are marked inand in red red twist and twist graingrain boundaries boundaries are marked are marked in blue. in blue. On the other hand, we observe that the proportion of tilt grain boundaries rises upon increasing the homopolymer ratio. Those parts of the grain boundary that correspond to a tilt grain boundary are red shaded, while twist grain boundaries are marked blue (see Figure A4). As a general trend we can state, that the block copolymer is more likely to form tilt grain boundaries at increasing homopolymer fractions. This behavior is explained by the reduction of the free energy difference between the two grain boundary morphologies. The formation of tilt grain boundaries does, Nanomaterials 2020, 10, 103 16 of 19 On the other hand, we observe that the proportion of tilt grain boundaries rises upon increasing the homopolymer ratio. Those parts of the grain boundary that correspond to a tilt grain boundary are red shaded, while twist grain boundaries are marked blue (see Figure A4). As a general trend we can state, that the block copolymer is more likely to form tilt grain boundaries at increasing homopolymer fractions. This behavior is explained by the reduction of the free energy difference between the two grain boundary morphologies. The formation of tilt grain boundaries does, however, not convert into the energetically clearly favorable state. The proportion of tilt grain boundaries and twist grain boundaries for the 45% homopolymer sample is approximately equal, as shown in Figure A4c. This observation indicates that the energetic difference between the two states is very low. The desired situation we describe in the introductory paragraph is, however, only achieved if the formation of a tilt grain boundary is energetically favorable for one particular block, but not for the other one. This effect may be better understood when we consider ref. [59], where the authors observe that added PS-coated Au nanoparticles accumulate particularly in grain boundaries. There, the nanoparticles minimize the A/B interface area of the—in that case—PS-b-PEO block copolymer in favor of the PS-block. The alignment of block copolymers via grain-boundary-induced alignment parallel to the grain boundary can be successful, in case two prerequisites are fulfilled: (i) the total homopolymer fraction in the blend is large enough to lower the tilt grain boundary free energy significantly and (ii) the ratio of the two homopolymers in the blend is sufficiently asymmetric that the tilt grain boundary is reduced significantly more for one block than for the other. 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