Self-assembling morphologies of symmetrical PS-b-PMMA in different sized confining grooves

Abstract

Directed self-assembly (DSA), an emerging lithographic technique, has attracted increasing attention as a result of its advantages of low cost, high throughput and convenient processing. However, DSA still presents some challenges, such as the control of defects, the fabrication of complex patterns and pattern registration. In this work, self-assembling morphologies of the lamellar diblock copolymer poly(styrene-b-methyl methacrylate) were investigated to gain a better understanding of the DSA process and to offer some reference for the pattern transfer process. A quantized number of lines was obtained in the directing grooves, although warps and dislocations appeared when the number of lines jumped from n to (n + 1). Gradational variations in line width were observed near the edge of the confining grooves, which shows the lack of uniformity in the patterns. A novel structure model is proposed to interpret this variation in the block copolymer lines. Valuable information and insights are provided for nanowire patterning by DSA in state-of-the-art semiconductor devices.

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Introduction

As the size of semiconductor devices continues to decrease, conventional optical lithography has almost reached its limits as a result of increasing costs and more complex processes. The international technology road map for semiconductors¹ recommended the directed self-assembly (DSA) of block copolymers (BCPs), extreme ultraviolet lithography,^2–4 nano-imprint lithography^5–7 and mask-less lithography⁸ as lithographic methods that could satisfy the requirements of resolution and pattern quality in 16/14 nm complementary metal oxide semiconductor transistor technology. In this context, the DSA technique using BCPs is emerging as a competitive lithographic technique.⁹

A BCP is a special material composed of two or more chemically distinct and covalently linked blocks. Poly(styrene-b-methyl methacrylate) (PS-b-PMMA), which consists of two monomers (PS and PMMA), is the most popular BCP in semiconductor fabrication as a result of its good compatibility. After annealing, the blocks in the BCP phase separate from each other and self-assemble into the most energetically favorable nanostructures.¹⁰ By orienting these small nanopatterns, uniform long-ordered line/space or hole arrays can be obtained and used as etching masks in nanofabrication techniques.^11–17 This patterning technique is called DSA. It is a novel “bottom-up” lithographic technology¹⁸ that has important differences from conventional “top-down” approaches. DSA uses pre-patterned substrates with chemical heterogeneities^19–21 or topographic features,^22–25 or both,^26,27 to direct the BCP into ordered patterns. The size of the patterns formed by DSA depends on the length of the BCP molecular chains, which is highly uniform and is determined by the volume fractions of the block and the degree of polymerization of the BCP. Chemoepitaxy and graphoepitaxy are the two main ways of directing the BCP. Chemoepitaxy, in which non-neutral stripes/dots embedded in a neutral substrate are used to direct the BCP, can produce high-density pattern arrays with no sacrifice of space,^28,29 but is more complex and challenging to use in fabrication and pattern registration. Graphoepitaxy, in contrast, uses topographic features to direct the BCP from sidewalls with neutral substrates.^30,31 This has the benefits of a simple process, flexibility in pattern placement and a potentially high degree of frequency multiplication.

As an emerging low cost lithographic technology with a high throughput, DSA has attracted much interest. However, there are still many challenges before it can become a usable manufacturing technique. First, the defect density has to be controlled to within a low level.³² Dislocation is one of the most common types of defect in DSA and cannot yet be eliminated. Second, DSA can currently only produce simple periodic patterns, thus the design rules of chip layouts have to be modified to become compatible with DSA techniques.^33–36 Third, pattern placement or registration is a serious concern. In the graphoepitaxy directing method in particular, the morphology of the BCP is closely related to the compatibility between the size of the directing features and the natural bulk period of the BCP (L₀). Some investigations on pattern placement and the elasticity of a cylindrical BCP in nanogrooves have been reported.^37,38 It was shown that the cylindrical BCP patterns are compressed or stretched to conform with the width of the directing groove. Systematic research on the self-assembling morphologies and pattern registration in nanogrooves has rarely been reported for lamellar BCPs.

We report here a systematic investigation into the self-assembling properties in directing grooves of symmetrical PS-b-PMMA. In particular, the compatibility between the size of the directing groove and the self-assembling morphology of the PS-b-PMMA was studied to obtain a better understanding of how PS-b-PMMA behaves when it is constrained to a particular size. Differently sized hydrogen silsesquioxane (HSQ) grooves were prepared on a neutralized substrate by electron beam lithography. HSQ has been shown to be a suitable directing material in DSA^31,39 because it can transform into silica at high temperatures. Silica is a very common material in semiconductors and can be easily removed by a solution of HF.^40,41 After spin-coating the PS-b-PMMA into HSQ grooves and annealing, phase-separated lines were obtained. Scanning electron microscopy (SEM) images of these samples were processed and analysed using a customized Matlab script to obtain detailed information about the BCP lines. This will be valuable for researchers studying the morphologies of the lines for pattern transfer from the BCP layer to the substrate.

Experimental

Materials

A random copolymer, poly(styrene-co-methylmethacrylate-co-hydroxyethyl methacrylate) [denoted as P(S-r-MMA-r-HEMA), M_n = 35 600 kg mol⁻¹, PDI = 1.28, PS mole fraction = 57%, HEMA mole fraction = 2%], and a symmetrical block copolymer, poly(styrene-b-methyl methacrylate) (denoted as PS-b-PMMA, M_n = 22 000-b-22 000 kg mol⁻¹, PDI = 1.09), were purchased from Polymer Source Inc. and used without any further purification. HSQ electron beam spin-on resist (XR-1541) was purchased from Dow Corning and used as received.

Preparation of neutral layer

100 mm bare Si (100) wafers with approximately 1.5 nm thick native oxide were first immersed in piranha solution (30% H₂O₂–H₂SO₄ 1 : 5 v/v) at 120 °C for 15 min, then rinsed with deionized water and dried under a flow of N₂ to remove any organic contamination and to increase the concentration of hydroxyl groups on the surface for the graft of a neutral layer. Random copolymer P(S-r-MMA-r-HEMA) solutions 0.5 wt% in toluene were spin-coated onto the cleaned wafers at 3000 rev per min for 60 s to obtain approximately 25 nm thick RCP layers which are equally preferable chemically to PS and PMMA. Subsequently, the samples were annealed in an oven at 240 °C for 5 min under an N₂ atmosphere to graft the chains of P(S-r-MMA-r-HEMA) onto the hydroxyl functionalized surface. Ungrafted polymers were removed with toluene under ultrasonication for 10 min. The wafers were then dried under an N₂ flow to remove any residual toluene so that a neutral layer of about 5 nm thickness was obtained on the wafer.

Fabrication of directing features

After neutral layer preparation, the HSQ electron beam resist XR-1541 was spin-coated onto the wafers at 3000 rev per min for 60 s to obtain a resist film of 40 nm thickness. Following this, the wafers were annealed on a hot-plate at 100 °C for 3 min and at 200 °C for 3 min in a post-exposure bake process of the resist. The wafers were then exposed to a 10 mC cm⁻² electron beam and developed in MF CD26 + 4% NaCl solutions at 33.5 °C for 60 s, followed by rinsing in deionized water and drying in N₂ to produce grooves with widths varying from 25 to 200 nm at 5 nm intervals.

Preparation of BCP films

Symmetrical PS-b-PMMA solutions of 0.5 wt% in toluene were spin-coated onto the surface of HSQ patterned wafers at 3000 rev per min for 60 s to deposit the BCP into the grooves. The wafers were then annealed in an oven at 240 °C for 5 min under an N₂ atmosphere to evaporate the remaining solvent and to induce phase separation of the PS-b-PMMA.

Characterization

A Hitachi S-5500 scanning electron microscope was used to collect images at an accelerating voltage of 1.5 kV. To obtain the original morphologies of the BCP films, no other process such as plasma etching or metal sputtering was performed on the samples to enhance the contrast. The SEM images were processed by Matlab with the image processing toolbox to obtain the widths of the grooves, the sizes of the BCP lines and the cross-sectional structures of the patterns.

Results and discussion

Fig. 1 is a schematic diagram of the process flow for graphoepitaxial DSA, including the preparation of the neutral layer, patterning of the HSQ resist and DSA of PS-b-PMMA in nanogrooves. First, the random copolymer P(S-r-MMA-HEMA) was spin-coated onto wafers and annealed to graft the polymer chains to the surface. The ungrafted polymers were then removed by washing in toluene to obtain a film that was chemically neutral to both PS and PMMA [Fig. 1(i)–(iii)]. Second, the HSQ resist was spin-coated onto the neutralized substrate and patterned by electron beam lithography to produce nanogrooves as directing features [Fig. 1(iv)–(vi)]. Third, the block copolymer PS-b-PMMA was spin-coated into the HSQ grooves and annealed at a temperature higher than the glass transition temperature of the PS-b-PMMA to induce phase separation of the BCP [Fig. 1(vii) and (viii)].

Fig. 1 Schematic representation of the process flow for graphoepitaxial DSA of PS-b-PMMA. (i) P(S-r-MMA-r-HEMA) film deposition on the Si substrate. (ii) Graft of the random copolymer. (iii) Removal of ungrafted polymers. (iv) HSQ resist deposition on the neutral layer. (v) Exposure of HSQ resist with electron beam. (vi) Development of HSQ resist. (vii) PS-b-PMMA deposition into HSQ grooves. (viii) Phase separation of PS-b-PMMA by annealing.

Thirty-six differently sized grooves varying from 25 to 200 nm were fabricated at intervals of 5 nm. The SEM images of these samples (Fig. 2) show the self-assembling morphologies of PS-b-PMMA in these grooves. Two different morphologies are observed: lines perpendicular to the confining sidewalls in grooves of 25 and 30 nm width; and lines parallel to the confining sidewall in the grooves ≥35 nm. This phenomenon is in good agreement with the theoretical results of Walton et al.⁴² A critical number of layers of the lamellar BCP between the two parallel confining walls is required to achieve the lowest free energy; below this number the morphology can be either perpendicular or parallel to the confining walls depending on the extent of chain deformation. Above this number the parallel morphology is always favored over the perpendicular morphology.

Fig. 2 SEM images of PS-b-PMMA self-assembling morphologies in different sized HSQ grooves. The labels on the images indicate the widths of the grooves designed in the electron beam exposing layout.

Fig. 3a shows the number of lines (n) in each groove plotted against the normalized groove width (W_g/L₀), where W_g is the average width of the groove as determined by the processing method and measured from the SEM images with Canny edge detection in Matlab. L₀ is the natural bulk period, which is 25 nm in the lamellar PS-b-PMMA. The number of lines in the grooves is quantized to achieve a stair-like plot, which indicates that n is stable in each corresponding range of groove width. The BCP lines are compressed or stretched to comply with the groove width. The degree of compression or expansion of the BCP lines can be modelled by considering the normalized period, λ, which is given by eqn (1). Fig. 3b shows λ plotted against the normalized groove width. If the groove width (W_g) is less than an integral multiple of the bulk equilibrium period (nL₀), the BCP is compressed, otherwise it is stretched:

Fig. 3 Variation in three parameters of PS-b-PMMA versus the normalized groove width. (a) Number of lines (n). (b) Normalized period indicating the degree of compression or expansion of the BCP lines. (c) Ratio between the free energy per polymer chain in the confined PS-b-PMMA and that of the unconfined PS-b-PMMA. The black dots represent the grooves with widths near the transition points from n to (n + 1) lines.

Cheng et al.³⁸ reported that, for a cylindrical BCP, a transition in the number of rows from n to (n + 1) occurs when W_g ≈ (n + 0.5)L₀, which can be demonstrated by finding the lowest free energy of the confined polymer system. In the lamellar BCP studied here, similar thresholds of the groove width for the transition from n to (n + 1) lines are also observed. The ratio between the free energy per polymer chain of the confined BCP (F_c) and the free energy per polymer chain of the unconfined bulk BCP (F₀) is approximated as a function of λ in eqn (2) and (3), where γ_AS is the interfacial tension between block A and the confining sidewall and γ_AB is the interfacial tension between block A and block B as proposed by Turner.⁴³ To demonstrate the minimum free energy, these ratios are calculated and plotted in Fig. 3c, which clearly shows that, for each number of lines, the minimum of the ratio is at the integral normalized groove width, while the transition from n to (n + 1) lines occurs when W_g/L₀ is near (n + 0.5):

Another interesting phenomenon observed is that some defects such as warps and dislocations occur when the groove width is near the transition point from n to (n + 1), shown as black dots in Fig. 3. Fig. 4 shows the SEM images of these grooves. These imperfect patterns may be caused by the high free energy of the confined polymer system around the transition point. When the groove width is near the transition point, the free energy of the BCP system is high enough that the BCP lines are sensitive to the edge roughness of the confining sidewalls. As the edge of the sidewall cannot be perfectly smooth, a small bump on the sidewall may induce warps in the BCP lines, which may even develop into dislocations.

Fig. 4 Defects of the BCP in the grooves with widths near the transition points from n to (n + 1) lines.

To obtain more detail about the self-assembling morphology of BCP lines in the confining grooves, higher resolution SEM images were processed in Matlab. Fig. 5 shows a schematic diagram of how an SEM image is processed. Here, an approximately 200 nm wide groove containing eight BCP lines is chosen as an example. First, the specified region of the groove in the SEM image is cut out and then the noise is smoothed by a median filter. A cross-sectional view of the groove is extracted and plotted with the number of pixels as the horizontal axis and the gray level as the vertical axis. Each pixel in the SEM image corresponds to a 0.4960938 nm length at ×200 000 magnification according to the reporting file of the SEM system. The right-hand image in Fig. 5 clearly shows eight full peaks (P1–P8) corresponding to the eight bright lines in the original SEM image. As the width of a peak (W_p) is defined as the distance between the bottoms of the two nearby valleys, the widths of each line can be measured by the data cursor in Matlab, then calculated and recorded (Table 1). It is apparent that the lines at the edge of the groove (lines 1, 2, 7 and 8) are narrower than those in the centre (lines 3, 4, 5 and 6).

Fig. 5 Schematic diagram showing the procedure for SEM image processing in Matlab. In the right-hand image, the horizontal axis is the number of pixels across the groove (0.4960938 nm per pixel) and the vertical axis is the gray level of each pixel. The eight peaks (P1–P8) in the right-hand image correspond to the eight bright lines in the centre and left-hand images.

Table 1 Widths of BCP lines in a 199.4 nm cross-section groove

Line order	1	2	3	4	5	6	7	8
Width (nm)	18.4	25.8	29.3	28.3	30.3	30.8	24.8	13.9

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Considering the randomness of only one sample, a few SEM images were processed and measured to find whether there is a universal law for every groove. Seven SEM images of grooves with designed widths of 75, 100, 125, 150, 175 and 200 nm were chosen and several cross-sections of the grooves were cut out in each image to measure the average values of the line widths. Fig. 6 shows the average widths fitted into smooth curves. It is clearly seen that the lines in the groove centre are generally wider than those near the groove edge. According to the difference in width, these lines can be classified into three levels, as shown by the three red grids in Fig. 6. Lines in level 1 are those closest to the confining sidewalls with widths from 15 to 22 nm. Lines in level 2 are those second closest to the confining sidewalls with widths from 23 to 28 nm. All the other lines in the groove are classified as level 3, with widths in the range 29–32 nm. As the natural bulk period of the PS-b-PMMA in the experiment was 25 nm, it can be concluded with caution that the lines in level 1 are compressed and the lines in level 3 are stretched, whereas the lines in level 2 are slightly compressed or stretched depending on the width of the groove.

Fig. 6 Average widths of lines in different sized grooves. The lines in the confining grooves are classified into three levels. Level 1 lines are those closest to the sidewalls with widths between 15 and 22 nm. Level 2 lines are the second closest to the sidewalls with widths between 23 and 28 nm. All the other lines in the centre are classified as level 3 with widths between 29 and 32 nm.

To ensure that these average values are representative, a statistical analysis was performed on the data points. First, in each SEM image, 10 cross-sections at intervals of 50 nm were chosen to obtain 10 samples for each line. The standard deviations of these samples were calculated and are plotted in Fig. 7a. Fig. 7a shows that the standard deviations of these samples are all in the range 0.8–3.1 nm, which is about equal to the line edge roughness of the commonly used electron beam resists, although some fluctuations appear due to variations in processing and image noise.⁴⁴ Second, the number of samples along each groove was increased from 10 to 20 and 40, at intervals of 25 nm and 12.5 nm respectively. The standard deviations were then compared (Fig. 7b). Three different-level lines in a groove of 200nm width were chosen as examples to observe the variations in standard deviation versus the number of sample data points. As the number of sample data points doubles and quadruples, the standard deviations of the three different levels of lines slightly increases (level 1) or slightly decreases (levels 2 and 3), with negligible variations of 0.1 nm or less. Therefore it can be concluded that no obvious variation in the standard deviation is observed with an increasing number of sample data points, which means that 10 sample data points at intervals of 50 nm along each groove are representative of the average line width characterization.

Fig. 7 Statistical analysis for samples of line widths. (a) Distribution of standard deviations for 10 sample data points along each groove. All the standard deviations are in the range 0.8–3.1 nm. (b) Variations in standard deviations for 10, 20 and 40 sample data points along lines of three different levels. The standard deviations decrease (level 1) or increase (levels 2 and 3) slightly with variations of <0.1 nm.

By analysing the widths of the lines, the structures of the BCP lines can be described using the model illustrated in Fig. 8. When the groove can accommodate only three lines, the pattern structure is 1-3-1, with no lines in level 2 (Fig. 8a). When the groove is wide enough to accommodate four lines, the pattern structure becomes 1-3-3-1 (Fig. 8b). As the groove becomes even wider and can accommodate five lines, two lines at level 2 are added and, as the groove becomes continuously wider to accommodate five lines, six lines and even higher numbers of lines, more lines at level 3 are added into the centre of the groove, with no change in the pattern structure at the edge, which is always the gradient 1-2-3. Therefore there is always an axisymmetrical structure to the BCP lines in the confining groove, where the widths of the lines are gradational near the edge of the groove and approximately equal in the centre of the groove. This phenomenon is similar to that reported by Cheng et al.,³⁷ who observed gradational variations in the domain size and spacing of the cylindrical BCP across the groove, which can be used to realize gradational nanostructures. The reason for the variation in the width of the groove near the edge is that the HSQ sidewalls have stronger affinities to PS than to PMMA,³¹ which decreases the concentration of the PS blocks near the edge. This indicates that the surface chemistry of the confining sidewalls affects pattern formation over several periods.³⁷ Therefore, by adjusting the widths of the confining grooves or tuning the surface chemistry of the sidewalls, gradational nanostructures can be fabricated.

Fig. 8 Models of lamellar BCP line structures between two parellel confining walls. (a) 1-3-1 structure in the groove with three lines. (b) 1-3-3-1 structure in the groove with four lines. (c) 1-2-3-2-1 structure in the groove with five lines. (d) 1-2-3-3-2-1 structure in the groove with six lines. (e) Universal structure in the groove with more than six line; the widths of the lines are gradational at the edge and approximately equal in the centre.

These results have shown the detailed morphology of the lamellar PS-b-PMMA in the confining grooves. This is a non-uniform structure in which the lines in the centre are stretched while the lines at the edge are compressed. This may be caused by the different affinities of the two blocks to the confining sidewall. Further research should be carried out to eliminate the non-uniformity in the BCP lines because the sizes of the lines and spaces need to be highly equal to guarantee only a small variation in the performance of the device, yielding an excellent integrated circuit product.

Conclusions

This work focused on the self-assembling morphologies of the lamellar BCP PS-b-PMMA (22k-b-22k) in directing grooves. Different sized HSQ grooves on a neutralized Si substrate were fabricated for the DSA of the BCP. Phase-separated lines of BCP both perpendicular and parallel to the sidewalls were observed in grooves of different widths.

Several key findings were made: (1) the number of lines in the parallel structures was shown to be quantized in terms of the compatibility between the groove width (W_g) and the BCP bulk period (L₀); (2) around the transition point from n to (n + 1) lines, some defects such as wraps and dislocations occurred in the BCP patterns as a result of the high sensitivity of the patterns to the edge roughness of the confining walls, which is caused by the high free energies of the polymer system in these states; (3) a gradational variation in the line width from the edge to the centre of grooves was observed, which is believed to be the result of interfacial interactions between the blocks and the confining sidewalls.

A novel structure model has been proposed to interpret these findings and to gain a greater understanding of the sizes and positions of the lines in the grooves. This research offers detailed information on the pattern registration of the graphoepitaxial DSA technique, which has particular significance for the subsequent pattern transfer process because the sizes of the lines and spaces in semiconductor devices should be controlled precisely to guarantee only small variations in device performance and thus excellent product yield in integrated circuit technology. More research should be carried out to obtain a greater understanding of the mechanism for the variation in width of the BCP lines in the grooves and to develop the corresponding pattern transfer process for the DSA technique.

Acknowledgements

The authors thank Xiaosa Zhang from the Chanchun Institute of Applied Chemistry, Chinese Academy of Sciences and Pengfei Nan from Fudan University for helpful discussions.

Notes and references

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