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Study on the Combined Effects of Solvent Evaporation and Polymer Flow upon Block Copolymer Self-Assembly and Alignment on Topographic Patterns Thomas G. Fitzgerald,†,‡ Richard A. Farrell,†,‡,§ Nikolay Petkov,§, Ciara T. Bolger,†,‡ Matthew T. Shaw,†,‡,^ Jean P. F. Charpin,# James P. Gleeson,# Justin D. Holmes,†,‡,§ and Michael A. Morris*,†,‡,§ Materials Chemistry Section, Chemistry Department, University College Cork, Cork, Ireland , ‡Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin, Ireland, §Micro-Nano Centre, Tyndall National Institute, Lee Maltings, Cork, Ireland, Electron Microscopy and Analysis Facility (EMAF), Tyndall National Institute, Lee Maltings, Cork, Ireland, ^Intel Ireland Ltd., Leixlip, Co. Kildare, Ireland, and #Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland )
†
Received May 21, 2009. Revised Manuscript Received October 1, 2009 Microphase separation of a polystyrene-block-polyisoprene-block-polystyrene triblock copolymer thin film under confined conditions (i.e., graphoepitaxy) results in ordered periodic arrays of polystyrene cylinders aligned parallel to the channel side-wall and base in a polyisoprene matrix. Polymer orientation and translational ordering with respect to the topographic substrate were elucidated by atomic force microscopy (AFM) while film thickness and polymer profile within the channel were monitored by cross-sectional transmission electron microscopy (TEM) as a function of time over a 6 h annealing period at 120 C. Upon thermal annealing, the polymer film simultaneously undergoes three processes: microphase separation, evaporation of trapped solvent, and mass transport of polymer from the mesas into the channels. A significant volume of solvent is trapped within the polymer film upon spin coating arising from the increased polymer/substrate interfacial area due to the topographic pattern. Mass transport of polymer during this process results in nonuniform films, where subtle changes in the film thickness within the channel have profound effects on the microphase separation process. The initially disordered structure within the film underwent an orientation transition via an intermediate formation of perpendicular cylinders (nonequilibrium) to a parallel (equilibrium) orientation with respect to the channel base. Herein, we present a time-resolved study of the cylinder reorientation process detailing how changing film thickness during the annealing process dramatically affects both the local and lateral orientation of the observed structure. Finally, a brief mathematical model is provided to evaluate spin coating over a complex topography following a classical asymptotic approximation of the Navier-Stokes equations for the as-deposited films.
1. Introduction Current “top-down” optical lithographic techniques are rapidly approaching their resolution limits, and potential advances in this technology, such as extreme ultraviolet1,2 and X-ray3,4 light sources, are unlikely to cost-effectively overcome the challenges associated with the production of sub-30 nm features.5,6 Molecular scale self-assembly, which involves the organization of components into ordered structures, is one of the few practical solutions for the generation of dense arrays with such small feature sizes.7 The self-assembly of block copolymers (BCPs) is particularly attractive, as it not only provides a route to arrays of nanostructures (feature sizes ca. 5-50 nm)8,9 but also is a *To whom correspondence should be addressed. E-mail:
[email protected]. Fax: þ353 214274097. Telephone: þ 353 214902180.
(1) Chang, S. W.; Ayothi, R.; Bratton, D.; Yang, D.; Felix, N.; Cao, H. B.; Deng, H.; Ober, C. K. J. Mater. Chem. 2006, 16, 1470–1474. (2) Itani, T. Microelectron. Eng. 2009, 86, 207–212. (3) Mappes, T.; Achenbach, S.; Mohr, J. Microelectron. Eng. 2007, 84, 1235– 1239. (4) Chou, M. C.; Pan, C. T.; Wu, T. T.; Wu, C. T. Sens. Actuators, A 2008, 141, 703–711. (5) Xia, Y. N.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 551–575. (6) Lin, B. J. Microelectron. Eng. 2006, 83, 604–613. (7) Whitesides, G. M.; Grzybowski, B. Science 2002, 295, 2418–2421. (8) Segalman, R. A. Mater. Sci. Eng., R 2005, 48, 191–226. (9) Park, C.; Yoon, J.; Thomas, E. L. Polymer 2003, 44, 6725–6760.
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relatively cheap alternative which is compatible with current semiconductor processing conditions. “BCP nanolithography” is envisioned as a complementary addition to photolithography processes rather than a replacement when combined with a “topdown” registration and physical and/or chemical alignment.10-13 Nanowire structures created using BCP nanolithography typically exhibit superior line edge roughness (LER) and smaller dimensions when compared with photolithographic processing.14-16 BCPs are well-known to form a rich variety of nanostructures (e.g., spherical, cylindrical, lamellar, gyroid) both in the bulk and in film upon microphase separation.17,18 Cylinder- and lamellarforming systems are especially attractive as possible templates for (10) Sundrani, D.; Darling, S. B.; Sibener, S. J. Langmiur 2004, 20, 5091–5099. (11) Black, C. T. Appl. Phys. Lett. 2005, 87, 163116. (12) Kim, S. O.; Solak, H. H.; Stoykovich, M. P.; Ferrier, N. J.; de Pablo, J. J.; Nealey, P. F. Nature 2003, 424, 411–414. (13) Stoykovich, M. P.; Muller, M.; Kim, S. O.; Solak, H. H.; Edwards, E. W.; de Pablo, J. J.; Nealey, P. F. Science 2005, 308, 1442–1446. (14) Liu, C. C.; Nealey, P. F.; Ting, Y. H.; Wendt, A. E. J. Vac. Sci. Technol., B 2007, 25, 1963–1968. (15) Ting, Y. H.; Park, S. M.; Liu, C. C.; Liu, X.; Himpsel, F. J.; Nealey, P. F.; Wendt, A. E. J. Vac. Sci. Technol., B 2008, 26, 1684–1689. (16) Jung, Y. S.; Jung, W.; Tuller, H. L.; Ross, C. A. Nano Lett. 2008, 8, 3776– 3780. (17) Matsen, M. W.; Schick, M. Phys. Rev. Lett. 1994, 72, 2660–2663. (18) Hamley, I. W. Development in Block Copolymer Science and Technology, 1st ed.; New York: Wiley: 2004; 0521452449.
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nanolithography applications. Although these structures are often locally ordered when confined in thin films, they lack the long-range order which is an important requisite for many potential applications where precise positioning and registration is required. Indeed, the microdomains composed of the different blocks typically nucleate randomly and grow with polygranular texture, with periodic ordering maintained over distances of several tens of a lattice constant (i.e., a typical grain size of 1-2 μm).9,19 In thin films, the existence of interfaces at the polymer/substrate and polymer/air boundaries imparts further constraint on the BCP which can severely disrupt the microphase separation process.20 A number of different approaches have been proposed to induce long-range order during the BCP microphase separation process such as electric field alignment,21-23 soft molding,24 and chemical patterning.12,13,25 Graphoepitaxy, in particular, has been the subject of intense research since Segalman et al.26 demonstrated that topographically patterned surfaces could be utilized to direct the self-assembly of a sphere-forming polystyrene-block-poly(2-vinyl pyridine) BCP. This technique merges “top-down” and “bottom-up” approaches where confinement effects imposed by topographic features (typically square-wave channels) direct the self-assembly of the BCP. Long-range order has since been achieved in other sphere-forming BCPs following a similar approach,27,28 while Chuang et al.29 have demonstrated control over the lattice structure of polystyrene-block-poly(ferrocenyl dimethylsilane) within V-shaped channels. Arrays of posts, as opposed to traditional linear features with large mesas, have recently been used to direct the packing of spheres in a polystyrene-block-poly(dimethylsiloxane) BCP.30 Sundrani et al.10 adapted this technique to produce arrays of cylinders parallel to the channel side-wall and base with polystyrene-block-poly(ethylene-alt-propylene) (PS-b-PEP) which has since been extended for a variety of other cylinder-forming systems.31-33 This technique is not limited to directing parallel cylinder alignment34,35; Kim et al.36 have demonstrated a marked improvement in the lateral ordering of hexagonal packed perpendicular cylinders in polystyrene-block-poly(ethylene oxide) when prepared on channelled surfaces. Graphoepitaxy has also been used to direct the alignment of lamellar domains in polystyrene(19) Hahm, J.; Lopes, W. A.; Jaeger, H. M.; Sibener, S. J. J. Chem. Phys. 1998, 109, 10111–10114. (20) Fasolka, M. J.; Mayes, A. M. Annu. Rev. Mater. Res. 2001, 31, 323–355. (21) Mansky, P.; DeRouchey, J.; Russell, T. P.; Mays, J.; Pitsikalis, M.; Morkved, T.; Jaeger, H. Macromolecules 1998, 31, 4399–4401. (22) Xu, T.; Zvelindovsky, A. V.; Sevink, G. J. A.; Lyakhova, K. S.; Jinnai, H.; Russell, T. P. Macromolecules 2005, 38, 10788–10789. (23) Crossland, E. J. W.; Ludwigs, S.; Hillmyer, M. A.; Steiner, U. Soft Matter 2007, 3, 94–98. (24) Li, L.; Yokoyama, H. Adv. Mater. 2005, 17, 1432–1436. (25) Cheng, J. Y.; Rettner, C. T.; Sanders, D. P.; Kim, H. C.; Hinsberg, W. D. Adv. Mater. 2008, 20, 3155–3158. (26) Segalman, R. A.; Yokoyama, H.; Kramer, E. J. Adv. Mater. 2001, 13, 1152– 1155. (27) Cheng, J. Y.; Ross, C. A.; Thomas, E. L.; Smith, H. I.; Vancso, G. J. Appl. Phys. Lett. 2002, 81, 3657–3659. (28) Cheng, J. Y.; Mayes, A. M.; Ross, C. A. Nat. Mater. 2004, 3, 823–828. (29) Chuang, V. P.; Cheng, J. Y.; Savas, T. A.; Ross, C. A. Nano Lett. 2006, 6, 2332–2337. (30) Bita, I.; Yang, J. K. W.; Jung, Y. S.; Ross, C. A.; Thomas, E. L.; Berggren, K. K. Science 2008, 321, 939–943. (31) Jung, Y. S.; Ross, C. A. Nano Lett. 2007, 7, 2046–2050. (32) Fitzgerald, T. G.; Borsetto, F.; O’Callaghan, J. M.; Kosmala, B.; Holmes, J. D.; Morris, M. A. Soft Matter 2007, 3, 916–921. (33) Black, C. T.; Bezencenet, O. IEEE Trans. Nanotechnol. 2004, 3, 412–415. (34) Xiao, S. G.; Yang, X. M.; Edwards, E. W.; La, Y. H.; Nealey, P. F. Nanotechnology 2005, 16, S324–S329. (35) Bosworth, J. K.; Paik, M. Y.; Ruiz, R; Schwartz, E. L.; Huang, J. Q.; Ko, A. W.; Smilgies, D. M.; Black, C. T.; Ober, C. K. ACS Nano 2008, 2, 1396–1402. (36) Kim, S. H.; Misner, M. J.; Xu, T.; Kimura, M.; Russell, T. P. Adv. Mater. 2004, 16, 226–231.
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block-poly(methyl methacrylate) films;37 however, these substrates require elaborate fabrication techniques coupled with extreme confinement to reveal high correlation lengths and low defect densities. The alignment mechanism of PS-b-PEP, monitoring the transition from a randomly ordered parallel cylindrical structure to a highly aligned state as a function of time, has previously been reported.38 Upon spin coating a BCP onto a channeled substrate, the resultant film is known to adopt the corrugation of the substrate,39 and upon annealing polymer on the mesas is drawn into the channel via capillary forces.19,40 In this report, we expand on these findings, detailing how the process of graphoepitaxial alignment of cylinder-forming polystyrene-block-polyisopreneblock-polystyrene (PS-b-PI-b-PS), combined with thermal annealing, is strongly dependent on evaporation of trapped solvent from the film as well as on polymer flow from the mesa into the channel. On-substrate TEM cross-sectional data indicate that upon thermal annealing over a period of 6 h the BCP film undergoes a dramatic decrease in volume primarily due to evaporation of toluene trapped at the polymer/substrate interface during the spin coating process. The volume of trapped solvent is greater than initially expected, arising from the increased polymer/substrate interfacial area of the topographic pattern. This film shrinkage coupled with polymer flow from the mesa results in nonuniform film thicknesses across the channel as well as gradual changes in the thickness during the annealing process. As slight changes in film thickness are known to have a dramatic effect on structural orientation within thin films41,42 a structural reorientation is observed from the initially disordered state through a preliminary formation of perpendicular cylinders to the final equilibrium structure of parallel orientated features. Specifically, we show that the alignment process is a combination of three processes: solvent evaporation, polymer mass transport into the channels, and kinetics of microphase separation. We also demonstrate the precise control of feature orientation and long-range order as a function of film thickness across channel widths ranging from 160 to 430 and 30 nm deep. Finally, a brief mathematical model is provided to evaluate spin coating over the complex topography following classical Navier-Stokes equations, and the resulting simulations are compared with experimental observations for ascast films.
2. Experimental Section 2.1. Film Preparation. PS-b-PI-b-PS (Sigma-Aldrich, 17 wt
% PS, and molecular weight = 52 000 g mol-1) thin films were prepared by spin coating (dwell = 25 s, speed = 3000 rpm, ramp rate = 600 rpm/s), using a Specialty Coating Systems G3P-8 spin coater, from toluene solutions at concentrations ranging from 0.2 to 2.0 wt %. As-cast PS-b-PI-b-PS thin films were annealed at 120 C under vacuum for varying periods of time (ranging from 0 to 24 h) to induce microphase separation. 2.2. Planar and Patterned Substrates. The planar substrates used were silicon (100) wafers, which had been sonciated for 1 h in toluene and dried under a stream of nitrogen prior to spin coating. The patterned substrates were fabricated through a series of lithographic and reactive ion etching steps and consisted (37) Park, S. M.; Stoykovich, M. P.; Ruiz, R.; Zhang, Y.; Black, C. T.; Nealey, P. F. Adv. Mater. 2007, 19, 607–611. (38) Sundrani, D.; Darling, S. B.; Sibener, S. J. Nano Lett. 2004, 4, 273–276. (39) Lee, G.; Jo, P. S.; Yoon, B. K.; Kim, T. H.; Acharya, H.; Ito, H.; Kim, H. C.; Huh, J.; Park, C. M. Macromolecules 2008, 41, 9290–9294. (40) Ruiz, R.; Ruiz, N.; Zhang, Y.; Sandstrom, R. L.; Black, C. T. Adv. Mater. 2007, 19, 2157–2162. (41) Krausch, G.; Magerle, R. Adv. Mater. 2002, 14, 1579–1583. (42) Knoll, A.; Lyakhova, K. S.; Horvat, A.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Nat. Mater. 2004, 3, 886–890.
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Figure 1. (a) Schematic of the spin coating of a block copolymer onto a topographically patterned surface followed by subsequent annealing above the glass transition temperature. (b) 70 tilt-SEM image of the square-wave 430 nm wide channel array (scale bar corresponds to 500 nm). (c) 90 cross-sectional SEM image of an individual channel illustrating regular dimensions (scale bar corresponds to 100 nm) as described in the text. of rectangular-wave channels, with widths and corresponding mesas of 160 and 600 nm, 280 and 540 nm, and 430 and 450 nm with a depth of 30 nm etched into silicon (100) wafers, as described in Figure 1. Regions separating the channels are referred to as the mesa. The 200 mm patterned wafers were diced into 20 30 mm2 rectangular sections, consisting of two regions measuring 12 13 mm2 (10 000-15 000 channels depending on lateral dimensions) which contained the patterned arrays. 2.3. Characterization. Patterned substrates were analyzed prior to BCP deposition by tilt and cross-sectional scanning electron microscopy (SEM; Hitachi FEG S4800). Topographic and phase images of film surfaces were recorded simultaneously by atomic force microscopy (AFM; DME DS-50 dual scope) in tapping mode. Fast Fourier transforms (FFT) of the topographic images were used to qualitatively measure the degree of alignment and the presence of defects/nonregular patterns. Cross-sectional images of polymer profiles on patterned topography were obtained via transmission electron microscopy (TEM; JEOL 2000 FX) operating at a voltage of 200 kV. Cross-sectional samples were prepared using a series of grinding and polishing steps and received a finer polish with a precision ion polishing system (GATAN PIPS 691). Prior to TEM cross-sectional preparation, a 25 nm gold layer was electron-beam evaporated (Temescal NFC 2000) onto the BCP films to function as a protective layer during TEM preparation and to provide contrast between the polymer film and epoxy. Consequently, during TEM imaging, the interface between a metal and a polymer film is significantly more pronounced than an interface between an epoxy layer and a polymer film.
3. Results 3.1. PS-b-PI-b-PS Self-Assembly. As-cast PS-b-PI-b-PS thin films deposited on planar silicon (100) surfaces exhibit a phase mixed structure consisting of a random dispersion of PS microdomains in a PI matrix (Figure 2a). When the BCP is spin coated from a volatile solvent (toluene), the observed disordered structure exists because the solvent evaporates relatively quickly and the polymer chains are immobilized in the film before realizing the thermodynamically stable state. Upon thermal (43) Gomez, E. D.; Das, J.; Chakraborty, A. K.; Pople, J. A.; Balsara, N. P. Macromolecules 2006, 39, 4848–4859.
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annealing, the film at 120 C, that is, above the reported glass transition temperature of the system,43 a striped pattern indicative of hexagonally packed PS cylinders in the PI matrix results (Figure 2b). During the thermal annealing process, the polymer components undergo a sudden transition from a hard or brittle condition to a flexible elastomeric condition. In this state, the mobility of the molecules is greatly increased, allowing them to migrate to obtain the most thermodynamically stable state.44 The cylindrical structure formed upon microphase separation is randomly ordered, and there is no preferential long-range alignment of the cylinders on these planar substrates as indicated by the ring structure observed in the corresponding FFT data (inset Figure 2b). The parallel orientation of the cylinders with respect to the substrate is favored by the formation of PI wetting layers at both the polymer/substrate and polymer/air interfaces.45 FFTs of ordered BCP films are known to provide an accurate evaluation of the cylinder center-to-cylinder center spacing (λ),32,33,46 which in this case is 30.0 ( 0.4 nm. Having obtained this value, the intrinsic polymer length scale (L0) of the system is determined to be 26 nm with a PS cylinder diameter (d) of 12.5 ( 0.3 nm following equations outlined by Black and Bezencenet.33 An experimental determination of the bulk L0 value was not undertaken in this work; however, based on previous work,47,48 we believe that it would compare favorably with the value obtained here. 3.2. Effects of Rapid Solvent Evaporation on Film Thickness. Films spin coated onto flat substrates are both uniform in thickness and flat over large areas:49 however, when spin coating onto arrays of channels, there will be variations in thickness across the channels.39 This is of great importance if these systems are to be used in manufacturing where careful design of topography and process conditions will be required if uniform coatings are to be obtained. (44) Green, P. F.; Limary, R. Adv. Colloid Interface Sci. 2001, 94, 53–81. (45) Collins, S.; Hamley, I. W.; Mykhaylyk, T. Polymer 2003, 44, 2403–2410. (46) Niu, S.; Saraf, R. F. Macromolecules 2003, 36, 2428–2440. (47) Olsen, B. D.; Li, X.; Wang, J.; Segalman, R. A. Macromolecules 2007, 40, 3287–3295. (48) Mykhaylyk, T. A.; Collins, S.; Jani, C.; Hamley, I. W. Eur. Polym. J. 2004, 40, 1715–1721. (49) Schubert, D. W. Polym. Bull. 1997, 38, 177–184.
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Figure 2. Two-dimensional tapping mode AFM images of PS-b-PI-b-PS thin films prepared from 1 wt % solutions of block copolymer in toluene (a) prior to thermal annealing and (b) upon annealing at 120 for 3 h. Inset in (b) is the corresponding FFT image.
Figure 3. Cross-sectional TEM images of PS-b-PI-b-PS thin films prepared from 0.7 wt % solutions of block copolymer in toluene
illustrating the location of the block copolymer within individual 430 nm wide channels upon thermal annealing at 120 C for (a, c) 0 h, (d) 1 h, (e) 1.5 h, (f) 2.5 h, (g) 4 h, and (b, f) 6 h. The scale bars shown are 200 nm for (a) and (b) and 100 nm for (c)-(h).
Figures 3 and 4 illustrate the effects of depositing a thin PS-b-PIb-PS film onto topographically patterned substrates consisting of 430 nm wide and 30 nm deep channels as a function of annealing time at 120 C under vacuum. Figure 3 displays cross-sectional TEM images orthogonal to the channel which provides insight into polymer mobility and accumulation during the annealing process. The as-cast film adopts a sinusoidal type variation across the channels, mirroring the corrugation of the underlying substrate (Figure 4). The spin coating process is effective in filling the channels, producing a film ca. 45 nm thick at the channel side-wall and 36 nm at the center with an ca. 18 nm film deposited on the mesa. As the BCP film is annealed, a significant decrease in the volume of the film is clearly observed from the TEM data (Figure 3), where the film thickness decreases from ca. 36 to 24 nm at the channel center, ca. 45 to 30 nm at the side-wall, and ca. 18 to 5 nm on the mesa (Figure 5). Although the BCP film may be expected to undergo some minor contraction/expansion, as the polymer chains compress/stretch to compensate for any 13554 DOI: 10.1021/la9018162
commensurability deviations between film thickness and natural domain spacing8 during self-assembly, it cannot fully account for the results observed here. We suggest that the decrease in film volume is due to two simultaneous processes occurring; evaporation of trapped solvent from within the film and mass transport of polymer from the mesa into the channel via capillary forces.19 The most dramatic volume decrease occurs within the first 2 h of annealing where film thickness decreases by ca. 10 nm at each of the three measured regions (at the center of the channel, at the side-wall, and on the mesa) (Figure 5). This period is dominated by evaporation of trapped toluene from the BCP film. It has previously been demonstrated that as-cast polymer films on flat substrates can undergo thickness shrinkage of up to 10% upon annealing above the glass transition temperature50,51 due to (50) Richardson, H.; Carelli, C.; Keddie, J. L.; Sferrazza, M. Eur. Phys. J. E 2003, 12, 437–440. (51) Mondal, M. H.; Mukherjee, M. Macromolecules 2008, 41, 8753–8758.
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Figure 4. Height profiles obtained from AFM height images across PS-b-PI-b-PS thin films prepared from 0.7 wt % solutions of block copolymer in toluene on topographically patterned substrates (430 nm channel) prior to thermal annealing (O) and upon annealing at 120 C for 6 h (b).
Figure 5. Plot of polymer film thickness at various points on the channeled surface as a function of annealing time (O, thicknesses at the channel side-wall; 4, thicknesses at the channel center, and 0, thicknesses at the mesa).
evaporation of solvent which is trapped within the film during the spin coating process. However, this does not fully account for the extent of volume loss observed here; to fully explain this, we must consider the influence of the substrate topography. Garcia-Turiel and Jerome52 have reported that the relative volume of solvent in as-cast films thinner than 100 nm is significantly greater than that for thicker films, as solvent is mainly retained at the polymer/ substrate interface. The surface area of the patterned substrates, and thus the area of the polymer/substrate interface, is ca. 15% greater than that for similar films prepared on flat substrates, resulting in a significant increase in the relative volume of solvent trapped within the film. As the polyisoprene matrix is a nonglassy polymer, the chains are stretched in the presence of a good solvent, in this case toluene. This flexibility along with high chain mobility when heated above the glass transition temperature allows the trapped toluene to evaporate quickly, accounting for (52) Garcia-Turiel, J.; Jerome, B. Colloid Polym. Sci. 2007, 285, 1617–1623. (53) Tsige, M.; Grest, G. S. J. Phys.: Condens. Matter 2005, 17, S4119–S4132.
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the observed volume decrease within the first 2 h.53 The authors note that it is not possible from the data obtained/presented in this work to obtain an accurate value of drying rate; Tsige and Grest54 have reported that the rate of solvent evaporation from a polymer film is strongly dependent on time and a single approximation would not be appropriate. We propose that it is this solvent evaporation which accounts for the initial perpendicular orientation of the features upon annealing for 1 h (Figure 6b); this is explained in greater detail in a later section. The increased polymer mobility during the annealing process not only facilitates microphase separation but also brings about mass transport of polymer from the mesa into the channel due to capillary forces.19 3.3. Alignment Mechanism of BCP Features. As-cast films on patterned substrates display a random dispersion of PS microdomains in a PI matrix (Figure 6a) similar to that observed for as-cast films on flat substrates (Figure 2a). As previously discussed, the film adopts the corrugation of the substrate with polymer located both on the mesas and in the channels. Upon annealing for 1 h, polymer film within the channel undergoes microphase separation, resulting in the formation of hexagonally packed PS cylinders orientated perpendicular to the channel base (Figure 6b); the hexagonal arrangement is confirmed by six equally spaced spots in the corresponding FFT (inset image 6b). The PS cylinders exhibit excellent lateral order, suggesting that confinement imposed by the channel improves the polymer self-assembly process. Although the perpendicular orientation is not the thermodynamic equilibrium structure, it is believed to arise due to the evaporation of residual solvent from the film commonly seen in solvent evaporation based annealing36,55 of BCPs. It has been proposed that the presence of the evaporating solvent at the polymer/air interface mediates the surface energies of the blocks, allowing components from both blocks to reside at the film surface.55 As the solvent concentration is lowest (i.e., sufficiently high to provide mobility to the polymer chains but low enough that the chains are not solubilized) at the film surface, initial microphase separation occurs here. The hexagonally packed structure adopted by this BCP can only be achieved in the perpendicular direction in this region of the film, as polymer mobility is of insufficient depth at this initial stage to allow a hexagonal structure to form in the parallel direction. This perpendicular orientation is maintained because further loss of solvent yields an ordering front which extends into disordered regions of the film, and further microphase separation is guided by the existing morphology at the polymer/air interface,36 resulting in the observed perpendicular orientation of the cylinders. The structural parameters are in good agreement with data from films prepared on flat substrates; λ = 29.5 ( 0.2 nm and d = 13.1 ( 0.2 nm. The slight decrease in observed PS cylinder size compared with films on flat substrates is consistent with compressive strains originating from the substrate side-wall structure.10,32 “Holes” also present in regions of the inchannel film correspond to areas where film thickness is insufficient to support an ordered structure. The “holes” are present in the film at the center of the channel, indicating that there is a thickness gradient across the channel resulting from BCP flow from the mesas into the channels, where film at the center of the channel is thinner than film along the side-wall. Although an ca. 17 nm thick film on the mesa remains, no microphase separation is observed, as the thickness is insufficient to support a phase separated structure; the film is, therefore, phase mixed. For longer periods, microphase separation due to thermal annealing begins to dominate the self-assembly process and a (54) Tsige, M.; Grest, G. S. Macromolecules 2004, 37, 4333–4335. (55) Hawker, C. J.; Russell, T. P. MRS Bull. 2005, 30, 952–966.
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Figure 6. Two dimensional tapping mode AFM phase images of PS-b-PI-b-PS thin films prepared from 0.7 wt % solutions of block
copolymer in toluene on topographically patterned substrates (430 nm channel) (a) prior to thermal annealing and upon annealing at 120 C for (b) 1 h, (c) 1.5 h, (d) 2.5 h, (e) 4 h, and (f) 6 h. Insets are the corresponding FFT images.
thermodynamically favored parallel orientation begins to form initially at the channel side-wall (Figure 6c). Confinement effects imposed by the side-wall guide the alignment of these reoriented cylinders parallel to the wall; however, the system is still dominated by perpendicular cylinders as indicated by the six-spot pattern in the FFT (inset of Figure 6c). Eventually, the majority of solvent has evaporated, the film adopts a more regular thickness across the channel, and a parallel orientation extends across almost the entire channel width. Cylinders along the side-wall display good registration with the wall; however, parallel cylinders in the center are randomly ordered (Figure 6d), as they are 13556 DOI: 10.1021/la9018162
not immediately confined by the wall structure. Further annealing results in coarsening of the aligned domains from the side-wall across the width of the channel (Figure 6e). Following annealing for 6 h, the majority of the BCP initially on the mesas is drawn into the channels and the PS cylinders are perfectly aligned parallel to the channel side-wall and base (Figure 6f) which is confirmed by the two-spot pattern in the corresponding FFT. Analysis provides a λ value of 27.1 ( 0.2 nm and a cylinder diameter of 12.2 ( 0.2 nm, which is less than that observed for films on flat substrates but is consistent with compressive strains originating from the side-wall.10 Langmuir 2009, 25(23), 13551–13560
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Figure 7. Two dimensional tapping mode AFM phase images of PS-b-PI-b-PS thin films after annealing at 120 C for 6 h prepared on topographically patterned substrates with channel widths of (a, d) 160 nm, (b, e) 280 nm, and (c, f) 430 nm. Films were prepared from solutions of block copolymer in toluene with concentrations of (a, d) 0.55 wt %, (b) 0.5%, (c, f) 0.6 wt %, and (e) 0.7 wt %. Insets are the corresponding FFT images.
An ca. 5 nm film remains on the mesa but is phase mixed, as the thickness is insufficient to support a phase separated structure. 3.4. Effect of Channel Width Constraint and Film Thickness on Orientation. Suh et al.56 have theorized that in cylinderforming BCP thin films a perpendicular orientation is favored for very thin films and parallel for thicker films; essentially a parallel orientation, which can only form when film thickness is commensurate with L0, occurs for relatively thicker films because of the excess elastic strain that would be imposed on the structure at low thicknesses (this strain reduces with increasing thickness). (56) Suh, K. Y.; Kim, Y. S.; Lee, H. H. J. Chem. Phys. 1998, 108, 1253–1256.
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Importantly, they demonstrate that surface energy effects are significant and can perturb this model. In the case of PS-b-PIb-PS, the propensity to form PI interfacial wetting layers45 allows parallel arrangement at these low thicknesses. The majority of work to date has detailed unconstrained films rather than within channelled structures.41,42,57,58 It might be expected that as channel width reduces, orientation dependence may change. (57) Knoll, A.; Horvat, A.; Lyakhova, K. S.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Phys. Rev. Lett. 2002, 89, 035501. (58) Lee, B.; Park, I.; Yoon, J.; Park, S.; Kim, J.; Kim, K. W.; Chang, T.; Ree, M. Macromolecules 2005, 38, 4311–4323.
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patterned surface is a common occurrence, particularly in the directed self-assembly of BCPs, it is desirable to simulate the process steps to eliminate much trial and error work. In this final section, standard models are applied to evaluate the process of spin coating over a periodic topographically patterned surface and the resultant numerical simulations are compared with experimental observations for the as-synthesized case only (0 h anneal). Spin coating over a complex topography may be modeled from the classical Navier-Stokes equations. In the present situation, the film depth is much smaller relative to its length, and the standard lubrication approximation may be applied.59-61 Assuming only the surface tension and centrifugal forces are significant, the equation governing the polymer and solvent mixture thickness, h, may be written Dh DQx DQy þ þ ¼ -E Dt Dx Dy
ð1Þ
where 2 3 ! ðh þ sÞ3 4 D3 h D3 h 2 5 Q ¼ þ Fω x σ þ Dx3 Dx Dy2 3μ x
Figure 8. Two dimensional tapping mode AFM height profiles across channels corresponding to images in Figure 7. The value from the polymer on top of the polymer on the mesa to the polymer located in the base of the trench is highlighted in each profile from (a) to (f).
In an attempt to quantify possible effects, we studied channel widths of 160, 280, and 430 nm as well as unconstrained films. For unconstrained films, the critical thickness for perpendicular orientation, that is, the maximum value at which perpendicularly orientation cylinders could be maintained, is ca. 25 nm, that is, very close to the intrinsic polymer length scale (L0) of the system. Above this value, the thermodynamically stable orientation is parallel (see the Supporting Information, S1). In the case of the constrained films, that is, within a channel, it was found that a stable perpendicular orientation of cylinders could be achieved at significantly greater thicknesses than those observed in the case of unconstrained films. Figures 7 and 8 show image and height data representing the highest and lowest thickness where perpendicular and parallel orientation, respectively, could be achieved (within experimental variation). In all cases, microphase separation resulted in highly ordered and aligned structures. The measured λ value is ca. 30.0 ( 3 nm in all cases, and variations arise from slight incommensurability between the channel width and the optimum cylinder spacing. The polymer features undergo a slight contraction or expansion to maintain a uniform segment density across the channel;10 as PI is softer than PS, it is probable that the PI matrix is more flexible and accepts a greater part of the compliance responsibility. The critical thicknesses for perpendicular orientation were measured as 31, 42, and 39 nm for the 430, 280, and 160 nm wide channels, respectively, which are greater than the previously determined 25 nm critical thickness for a perpendicular orientation. The data suggest that as the channel width decreases the critical thickness increases. We suggest that this is due to the necessity to define PI wetting layers. In the case of unconstrained films, these are required at only upper and lower surfaces; for the constrained films, this also includes wetting layers at the side-walls. Thus, significantly more material is required as the channel width decreases. 3.5. Numerical Simulation of BCP Behavior over the Patterned Substrate. As spin coating over a topographically 13558 DOI: 10.1021/la9018162
2 3 ! ðh þ sÞ3 4 D3 h D3 h 2 5 σ þ Fω y þ Q ¼ Dy3 Dx2 Dy 3μ y
ð2Þ
ð3Þ
and s describes the topography, x and y denote the Cartesian coordinates, and the solid rotates around x = y = 0 at the rotation velocity ω. E is the evaporation rate, and μ, F, and σ are the fluid dynamic viscosity, density, and surface tension, respectively. For simple geometries, this equation may be solved analytically using the Green function. For practical geometries, these equations must be solved numerically: the results given below are obtained using finite difference methods.62 At first, the values for the surface tension, density, and dynamic viscosity (μ, F, and σ) will be very close to the values for pure toluene (see Supporting Information, S2). However, as the simulation progresses, the increasing concentration of polymer in the mixture combined with the nanoscales involved and a potential nonNewtonian behavior of the fluid will make the values vary considerably. Equations 1-3 are therefore nondimensionalized to regroup μ, F, and σ in a single parameter C. The onedimensional governing equation may be written 2 !3 Dh D 4 D3 h 3 þ ðh þ sÞ C 3 þ x 5 ¼ -1 Dt Dx Dx
ð4Þ
where C ¼
σ 3μE 1=3 , L4 Fω2 Fω2
h0 ¼
3μE 1=3 Fω2
ð5Þ
and L is the length scale in the x direction and h0 is the scale in the vertical direction. (59) Ockendon, H.; Ockendon, J. R. Viscous Flows, 1st ed.; New York: CUP: 1995; 9780470843352. (60) Oron, A.; Davis, S. H.; Bankoff, S. G. Rev. Mod. Phys. 1997, 69, 931–980. (61) Kalliadasis, S.; Bielarz, C.; Homsy, G. M. Phys. Fluids 2000, 12, 1889–1898. (62) Thomas, J. W. Numerical Partial Differential Equations. Finite Difference Methods. Texts in Applied Mathematics (22); Springer-Verlag: New York, 1995.
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Figure 9. Polymer fluid mixture height (a) across a set of trenches and (b) above the first two trenches.
Figure 9 displays the height of the polymer solvent mixture over a set of 50 trenches which are 30 nm deep and 430 nm wide separated by a 450 nm wide mesa, with the wafer rotating at ω = 3000 rpm. The first of the trenches is approximately 1 mm from the center of the wafer and L4C = 3.2 10-25. The position of the trenches corresponds to the sharp oscillations between 0 and 45 000 nm. To ease the reading, the axis has been translated and the origin x = 0 corresponds to the start of the trench closest to the center of the wafer. At the beginning of the simulation, the height profile varies, but after a period of time, depending on the initial film thickness, the profile remains constant. The display on Figure 9a corresponds to this later stage. The polymer and solvent mixture height over two trenches is enlarged in Figure 9b. Since the profile remains almost constant during the simulation, it may be shifted so the plot corresponds to the initial value in Figure 4. As may be seen, the two profiles are very close and the shapes are very similar, although there is about a 10% error on the frequency of the oscillations. The height of the fluid in the numerical profile was adjusted using the constant C. For this assumed position of the trenches, the value of the C is much smaller than anticipated. This difference could be due to the assumed position of the trenches and the values of density, viscosity, and surface tension used for the simulation. The numerical curve is calculated using constant parameters which values might not be known precisely, since they vary with the increasing polymer concentration. The fluid may also display the previously mentioned non-Newtonian behavior which would make the viscosity vary significantly with the centrifugal force.63,64 Forces occurring at the molecular level have been neglected, although these forces might become significant due to the small scale of the trenches and this could be another source of error.
4. Conclusions and Discussion We have examined the practicality of spin coating to achieve controlled filling of topographically patterned surfaces while aiming to produce highly ordered nanopatterns. In particular, it was found that the spin coating process yields an uneven distribution of material across the topography that is far from ideal with polymer located in the channel and on the mesa. Annealing above the glass transition temperature, which is required to effect microphase separation, results in evaporation of solvent trapped within the film during spin coating as well as mass transport of polymer from mesas into channels and so realizes almost ideal filling. A significant volume of solvent is trapped at the polymer/substrate interface during spin coating, resulting in a dramatic decrease in film thickness as it evaporates. The volume loss due to solvent evaporation is greater than (63) Chen, H. S.; Ding, Y. L.; Tan, C. Q. New J. Phys. 2007, 9, 367. (64) Charpin, J. P. F.; Lombe, M.; Myers, T. G. Phys. Rev. E 2007, 76, 016312.
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initially expected due to the increased interfacial region provided by the topographic pattern. Although polymer flow from the mesas is observed, a thin layer of polymer persists on the mesa regardless of annealing time. For this PS-b-PI-b-PS system, we identify four distinct stages in the microphase separation process within channels toward forming the thermodynamically stable phase. The first stage is rapid solvent evaporation resulting in a significant decrease in film thickness and in microphase separation into a nonequilibrium orientation of cylinders perpendicular to the channel base. The second stage of the process is the gradual reorientation of features at the channel side-wall from a perpendicular to parallel orientation. The third stage involves reorientation throughout the entire channel, and the final stage appears to be alignment of the cylinders with the topographically defined channel side-walls. Variations in the depth of material within the channels can have a profound effect on the orientation of the structural features. It is seen that for unconstrained (on flat a substrate) films a perpendicular orientation of cylinders is unattainable across the entire film and only occurs at the edges of islands or holes formed where there is a thickness gradient. A perpendicular orientation can be achieved throughout an entire film, and at greater thicknesses, when confined within a topographic structure. The data indicate that as the channel width decreases, this critical thickness increases. A basic mathematical model was presented, and simulations were conducted on the preannealed PS-b-PI-b-PS films. The numerical and experimental results compare very well, and a more complete model could be a valuable tool to better understand the various processes involved for achieving uniform delivery of the polymer into pattern arrays. These preliminary results are very encouraging and show that, with limited modifications, the model could become an extremely valuable tool, leading to a much better understanding of the process. A similar model could be developed for the annealing phase, which would be coupled with a thermal component. This would account for the fluid properties varying with temperature. The work in this paper shows the complexity of obtaining highly ordered microphase separated films on patterned substrates from the spin coating method. In particular, the distribution of material following deposition and subsequent thermal processing will have to be studied in depth if this form of nanopatterning is going to have importance as a potential rival to photolithography, as precise filling of topography will be required to maintain fidelity during pattern transfer. Also, it is highly important to understand the effect of topography not only on the thickness of materials deposited but also on the relative stability of phase separated components and their orientation. Finally, the data also imply that film geometry could be better controlled by minimization of mesa width. DOI: 10.1021/la9018162
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Acknowledgment. The authors would like to acknowledge SFI Grant 03-IN3-I375 and SFI CRANN CSET grant which supported this work. The authors would like to thank Intel Ireland for provision and development of patterned wafers under the Adaptive Grid Substrate CRANN programme. Access to fabrication facilities was partly funded by the SFI National Access Program (NAP) at the Tyndall National Institute
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(Project Number 132). J.P.F.C. and J.P.G. acknowledge the support of SFI Grants 06/MI/005 (MACSI) and 06/IN.1/I366. Supporting Information Available: AFM phase images in tapping mode of PS-b-PI-b-PS thin films; table showing values and properties used for numerical simulations. This material is available free of charge via the Internet at http://pubs.acs.org.
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