Density Multiplication and Improved Lithography by Directed Block Copolymer Assembly

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Science  15 Aug 2008:
Vol. 321, Issue 5891, pp. 936-939
DOI: 10.1126/science.1157626


Self-assembling materials spontaneously form structures at length scales of interest in nanotechnology. In the particular case of block copolymers, the thermodynamic driving forces for self-assembly are small, and low-energy defects can get easily trapped. We directed the assembly of defect-free arrays of isolated block copolymer domains at densities up to 1 terabit per square inch on chemically patterned surfaces. In comparing the assembled structures to the chemical pattern, the density is increased by a factor of four, the size is reduced by a factor of two, and the dimensional uniformity is vastly improved.

The use of self-assembling materials to define templates for patterning dense features at length scales of 25 nm and below may provide a means to continue to shrink the dimensions of electronic and storage devices as optical lithography, the engine of the semiconductor industry, reaches intrinsic technological and economical limits (1, 2). For magnetic storage devices, the demands for diminishing feature size and spacing outpace those for integrated circuits, particularly as the industry considers introduction of patterned media (3, 4) to extend densities beyond limitations imposed by the onset of the superparamagnetic effect in conventional continuous granular media (5). Self-assembling block copolymers form dense periodic arrays with dimensions and spacing of domains from ∼3 to 50 nm (6, 7). The domain structure of block copolymer thin films has already been used to create templates for defining nanoscale features in metals, semiconductors, and dielectrics for applications as varied as quantum dots and nanoporous membranes for creating insulating air gaps between wires in integrated circuits (8, 9). One entry point for block copolymer thin films in fabrication thus capitalizes on inexpensive creation and processing of dense nanoscale features of roughly uniform dimensions. Although using the domain structure of thin copolymer films to pattern is termed block copolymer lithography, in the applications described above it has only a superficial relation to optical or electron-beam lithography used in the manufacture of high-performance devices. Lithography, as currently practiced for nanomanufacturing, requires essentially defect-free patterns, control over feature dimensions and shapes with molecular-level tolerances, and precise placement of each patterned feature with respect to the features in the same and underlying and overlying layers (1). In this context, for block copolymers to have an impact in lithography, they must demonstrate, as a minimum, the capability to define individual device elements with some advantage over established lithographic techniques.

Hexagonal arrays formed spontaneously by block copolymers may be applied directly for patterned media applications if adequate organization and dimensional uniformity can be achieved in thin-film templates. Methods to impart improved ordering in block copolymer films include chemical prepatterning (10, 11), graphoepitaxy (12), solvent annealing (13), shear (14, 15), electric fields (16), flow (17), thermal gradients (18, 19), and internal fields (20). Whereas all these methods provide orientational ordering, only chemical prepatterning and graphoepitaxy provide additional control over translational ordering and feature registration (9). For patterned media applications, chemical prepatterning does not compromise storage area (as opposed to graphoepitaxy, where topographic features use valuable substrate area) and allows for guidance of the self-assembling system at a sufficient level to address stringent pattern quality requirements, including vanishingly small defect densities and control over feature shapes and dimensions. The prepatterning method (10), however, is disadvantageous in that it introduces a lithographic step, nominally at the same feature density as that achieved by the block copolymer. Even though the block copolymer assembly can perform a substantial pattern quality rectification with respect to the prepattern, creating a template where each and every feature is exposed by e-beam is challenging because of the long writing times required by large-area applications at high densities [defining of a master template for a 95-mm patterned media disk at 1 terabit per square inch (Tb/in2) would take more than a month].

As a viable alternative, we developed a directed assembly method for feature density multiplication and pattern quality rectification. With density multiplication, not only is the resolution increased with respect to the prepattern but also the exposure time is reduced with the decrease in the number of written features. The constraints in defining the dimensions of individual features of the prepattern can be relaxed because of the rectification action by the block copolymer, enabling the use of faster resists and higher e-beam currents.

We use thin films of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) to demonstrate both density multiplication and pattern quality rectification on substrates prepatterned by e-beam lithography. Two copolymers with different lattice constants, L0, are used to generate hexagonal arrays of perpendicularly oriented PMMA cylinders in a PS matrix at two different densities: L0 = 39 nm, and L0 = 27 nm, as described in detail in the supporting online material (SOM). The assembly process is illustrated in Fig. 1. A brush of hydroxyl-terminated polystyrene (21, 22) (Mn = 6 Kg/mol) is deposited on a SiOx substrate. We then apply an e-beam resist layer and use an electron beam to write the closest possible match to a hexagonal pattern (23) with a lattice constant Ls, such that Ls = nL0 with n = 1, 2 (Fig. 1A) over a total area of 100 μm by 100 μm (for Ls = 39 and 78 nm, we made additional patterns covering 3000 μm by 50 μm). Patterns with both n = 1 and n = 2 were written on the same sample. Samples for block copolymer assembly are then subjected to a brief dose of oxygen plasma to generate a chemical contrast on the substrate. We then remove the bulk of the resist (Fig. 1B), spin-coat a block copolymer film (Fig. 1C), and anneal it in vacuum as described in the SOM. The areas of the surface (arrays of spots) exposed to the oxygen plasma are preferentially wet by the PMMA block, and background areas are slightly preferential toward the PS block. (Perpendicular cylinders with defects including short sections of parallel cylinders are observed on areas of the sample adjacent to the patterned regions.) The PMMA domains are then selectively removed (24). We use scanning electron micrograph (SEM) images to quantify the feature size uniformity of both block copolymer and e-beam features (see SOM).

Fig. 1.

Process to create lithographically defined chemically prepatterned surfaces and subsequent directed assembly. (A) Electron-beam lithography patterns at Ls = L0 (left) and Ls = 2L0 (right). (B) Chemical contrast on the substrate after O2 plasma exposure on the e-beam–defined spots above. (C) Block copolymer thin film. (D) Guided self-assembly in registration with the underlying chemical pattern.

The improved quality of patterning afforded by directing the assembly of block copolymer films on lithographically defined chemically patterned surfaces in comparison to the lithographically defined patterns themselves is presented in Fig. 2. Figure 2, A to D, shows top-down SEM images of developed e-beam resist patterned at Ls = 39, 78, 27, and 54 nm, respectively. Figure 2, E to H, shows micrographs of the block copolymer films guided by the prepattern with the corresponding e-beam features above. The polymer pitch on the guided patterns (Lp) is 39, 39, 27, and 27 nm, respectively. In Fig. 2, I to L, we plot the dot size distributions of both the e-beam and the corresponding block copolymer patterns from at least 15,000 dots. For Ls = 39 and 27 nm, the e-beam patterns (Fig. 2, A and C) have a lower quality apparent in variations in distance between rows and dot size distribution. Both of these sources of noise are rectified by the block copolymer (Fig. 2, E and G). At Ls = 39 nm, the e-beam pattern shows an average dot size of As = 276 nm2 with a standard deviation σs = 30 nm2, whereas the block copolymer pattern had an average dot size Ap = 262 nm2 with σp = 23 nm2, rectifying the quality of the e-beam prepattern by narrowing the dot size distribution (Fig. 2I). The e-beam resist pattern at Ls = 27 nm does not have enough resolution (Fig. 2C) to define a useful lithographic mask, nor does it display the necessary statistics on dot size, shape, or placement required for the application. Nonetheless, the block copolymer film (Fig. 2G) maintains a uniform lattice constant and rectifies the dot size distribution of the e-beam prepattern from σs = 26 nm2 down to σp = 11 nm2 (Fig. 2K).

Fig. 2.

(A to D) SEM images of developed e-beam resist with Ls = 39, 78, 27, and 54 nm, respectively. (E to H) SEM images of the block copolymer film on top of the prepattern defined by the corresponding e-beam pattern above. The lattice pitch on the block copolymer samples is Lp = 39, 39, 27, and 27 nm, respectively. (I to L) Dot size distribution of e-beam (dark teal) and guided block copolymer patterns (light green).

Directed assembly may be implemented not only to improve the quality but also to substantially augment the capabilities of the lithographic process beyond current resolution limits. Figure 2B shows the e-beam resist used to prepattern the substrate at Ls = 2L0 = 78 nm. The block copolymer in Fig. 2F registers with the prepatterned sites and, because the lattice is nearly commensurate to the natural lattice of the block copolymer, the self-assembly interpolates the location of the PMMA cylinders in between the prepatterned dots, multiplying the density of features by a factor of four (two in each direction in analogy to heteroepitaxial thin films) in addition to maintaining a constant and uniform feature size. The commensurability tolerance is about ±0.1L0 for the average lattice spacing. The e-beam prepattern at Ls = 2L0 = 78 nm has an average area As = 595 nm2 with σs = 35 nm2. The block copolymer not only multiplies the feature density but also rectifies the dot area size by more than a factor of two to keep it constant at Ap = 260 nm2 with σp = 22 nm2 [basically with the same statistics when Ls = 39 nm (see Fig. 2, I to J)]. For Ls = 2L0 = 54 nm, the polymer also multiplies the feature density to 1 Tdot/in2 (27-nm pitch), as shown in Fig. 2, D and H, while rectifying the size distribution from σs = 39 nm2 on the e-beam pattern down to σp = 13 nm2 on the block copolymer (Fig. 2L).

Long-range order is preserved throughout the entire prepatterned area (100 by 100 μm2 and 3000 by 50 μm2 for some samples), with defect densities that are compatible with data storage requirements. High-resolution SEM image analysis was performed on a sampling set of images comprising ∼15,000 to 20,000 dots total. Based on this sampling, we estimate a defect density <10–4 for patterns with Ls = 39, 78, and 27 nm and <10–3 for patterns with Ls = 54 nm. We project that defect tolerance in bit-patterned media will be on the order of 1 dot in 104 to 106, depending on the algorithms and countermeasures used. Long-range order is shown in larger area images (4 μm long) and even larger (tens of microns long) Moiré interference patterns in figs. S1 and S2, respectively.

The translational order of these patterns is assessed by looking at correlations in the x and y directions separately [as opposed to traditional Voronoi or Delaunay constructions (25), where all directions in the hexagonal lattice are equivalent] because our patterns are formed on rectangular and not hexagonal lattices as a result of e-beam limitations. We quantify placement accuracy by measuring the standard deviation of placement error along the x direction (σx) and the y direction (σy). The results are summarized in Table 1, and details can be found in the SOM. At smaller dimensions, the block copolymer patterns have tighter distributions and the statistics are preserved for the multiplied and nonmultiplied patterns. As a comparison, placement tolerances for patterned media are projected to be σ ∼1 nm.

Table 1.

Standard deviation of dot placement errors along the x direction (σx) and the y direction (σy) on the e-beam–defined patterns and on the block copolymer patterns (in nm). At smaller dimensions, the block copolymer pattern has tighter distribution compared to the e-beam patterns, and the statistics are the same for the density multiplied and nonmultiplied patterns.

View this table:

Metrics of pattern quality that cannot be determined from top-down SEM images relate to the shapes and dimensions of features in the pattern transfer template. Of particular importance is the side-wall profile of the mask (26, 27). Previous research suggests that the three-dimensional (3D) structure of the domains through the film thickness may be very different from plan-view images, or even bulk block copolymer morphologies, and are known to be strong functions of the geometry and strength of interactions between the polymer and the patterned substrate (28, 29). We therefore explore the fundamental physics of assembly in the case of the interpolated structures by resorting to Monte Carlo simulations of a coarse-grain model of the block copolymer. Details of the simulation method can be found in reference (30). Parameters in the simulations were chosen to describe a PS-b-PMMA block copolymer with L0 = 39 nm, a film thickness of ∼1.1L0, a spot pattern with Ls = 2L0, and spot area equal to twice the natural cylinder area (Fig. 3A, left). A simulated system typically contains 60 cylinders. The PMMA block wets the spots and the PS block wets the background of the chemical pattern. The interactions between the patterned spots and the PMMA block (ΛPMMA) and the patterned background and the PS block (ΛPS) play a critical role with respect to the 3D structure of the assembled domains. The interfacial energies between the chemically patterned surface and the blocks of the copolymer are not known quantitatively, but ΛPMMA is expected to be medium or strong and ΛPS is expected to be weak. Four cases are considered to encompass these expectations and are presented in Fig. 3: (I) weak ΛPMMA and weak ΛPS, (II) strong ΛPMMA and weak ΛPS, (III) medium ΛPMMA and medium ΛPS, and (IV) strong ΛPMMA and strong ΛPS. In our model, the strength of interaction between the patterned substrate and a block is quantified by ΛN, where N is the number of beads per copolymer chain. Our weak, medium, and strong interactions correspond to ΛN = 0.125, 0.25, and 0.375, respectively. The nonpreferred block has an equal but repulsive interaction in all cases. Figure 3A (right) shows a representative cross section for all of the cases at half height in the plane of the film, showing the interpolation of cylindrical domains (with diameter comparable to the natural cylinder diameter) at four times the density with respect to the chemical pattern. Figure 3B shows vertical cross sections of the assembled domains through rows of cylinders on chemically patterned spots alternating with interpolated cylinders (left), and vertical cross sections of rows of interpolated cylinders (right). The cross sections represent a long-time simulation that averages over thermal fluctuations but highlight the effect of the pattern on the average cylinder shape. Cases I to III depict equilibrium scenarios for which a perpendicular orientation of the cylinders is achieved through the full thickness of the film, with case I being the most uniform. Medium ΛPMMA causes the noninterpolated cylinders to adopt an undercut profile (case II). For even stronger ΛPMMA, some of those cylinders actually break into two halves (not shown). If ΛPS and ΛPMMA are both increased (case III), then the interpolated cylinders exhibit a slight constriction at their base. Finally, in the limit of strong ΛPMMA and strong ΛPS (case IV), interpolated cylinders do not extend all the way to the substrate and form a complicated 3D network. They end at a distance of ∼8 nm from the substrate and are connected to each other in the plane of the film, forming perimeters of hexagons centered around cylinders extending vertically away from each patterned spot. Interestingly, the pattern observed at the surface of the film is the same as in other cases, namely, a hexagonal array of spots. These simulated scenarios indicate that there is a window of tolerance for density multiplication to work successfully within a range of interaction values. The fact that there exists a window of tolerance suggests the possibility of added room for experimental optimization to generate lower defect densities or even higher orders of density multiplication. For instance, it should be possible to change the brush layer to optimize the brush interactions in density multiplied patterns with Ls = 54 nm in order to reduce the defect density below 10–4 (see Moiré patterns in fig. S2).

Fig. 3.

Simulation of the directed assembly of block copolymer films for density multiplication. (A) The chemical pattern is shown on the left. On the right is a horizontal cross section of the simulated system taken at mid-height of the film. The color map gives the average local composition, with pure PS in yellow and pure PMMA in blue. Black lines correspond to the planes P and P' along which vertical cross sections are taken. (B) Vertical cross sections showing the average local composition for four different polymer-substrate interactions described in the text (cases I to IV)

A technological benchmark for the quality of the patterns is garnered from transferring the pattern to the underlying substrate. The block copolymer film produced by density multiplication has a vertical side-wall profile suitable for pattern transfer. Using a lift-off technique, we fabricated 20-nm-tall Si pillars. We started with a block copolymer film like the one shown in Fig. 2F (Ls = 78 nm, Lp = 39 nm) after removing the PMMA cylinder and cleaned the pores with oxygen plasma. We deposited 7 nm of Cr by e-beam evaporation and removed the PS mask using a piranha solution leaving Cr dots on the surface (Fig. 4A). We used a CF4 reactive ion etch to generate 20-nm Si pillars (Fig. 4B). The pillars were uniform over the entire sample (3 mm long) and otherwise identical to those formed in patterns where Ls = 39 nm. Taken together, molecular simulation and pattern transfer results demonstrate that the degree of perfection, registration, and vertical side-wall profiles of the enhanced-resolution templates provide a path based on e-beam patterning and directed assembly of block copolymers toward bit-patterned media at densities over 1 Tb/in2.

Fig. 4.

Pattern transfer using a directed block copolymer template with density multiplication (Lp = 39 nm, Ls = 78 nm). (A) Cr dots after lift-off. (B) 20-nm-tall Si pillars etched using the Cr mask in (A).

We envision the role of directed assembly to enhance, augment, and advance the performance of lithographic processes rather than to attempt to develop replacement technology. The starting point is a chemical prepattern at or near the limit of current lithographic tools to provide strong thermodynamic driving forces for directed assembly of patterns with perfection, registration, resolution, and quality beyond those possible with traditional materials and processes. In this context, we anticipate that the experiments here with cylindrical-phase diblock copolymers could be extended to higher-density multiplication factors for patterned media and to other classes of block copolymers to achieve striped or more complex patterns such as those required by the semiconductor industry.

Supporting Online Material

Materials and Methods

Figs. S1 and S2


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