Characterizing the Interface Scaling of High χ Block Copolymers near the Order–Disorder Transition

Abstract

Advancements in the directed self-assembly of block copolymers (BCPs) have prompted the development of new materials with larger effective interaction parameters (χ_e). This enables BCP systems with phase separation at increasingly small degrees of polymerization (N). Very often these systems reside near the order–disorder transition and fit between the weak and strong segregation limits where the behavior of BCP systems is not as thoroughly understood. Utilizing resonant soft X-ray reflectivity (RSoXR) enables both the BCP pitch (L₀) and interface width (w_M) to be determined simultaneously, through a direct characterization of the composition profile of BCP lamellae oriented parallel to a substrate. A series of high χ_e BCPs with χ_e ranging from ≈0.04 to 0.25 and χ_eN from 19 to 70 have been investigated. The L₀/w_m ratio serves as an important metric for the feasibility of a material for nanopatterning applications; the results of the RSoXR measurement are used to establish a relationship between χ_e and L₀/w_m. The results of this analysis are correlated with experimentally established limits for the functionality of BCPs in nanopatterning applications. These results also provide guidance for the magnitude of χ_e needed to achieve small interface width for samples with sub-10 nm L₀.

Graphical abstract

INTRODUCTION

Block copolymers (BCPs) offer intriguing possibilities¹ as templates for patterning membranes,^2–4 metal oxides,^5,6 and other lithographically useful structures.^7–10 The most commonly studied BCPs offer accessibility to feature size and domain period (pitch) length scales between 20 and 100 nm.^11,12 The demonstration of directed self-assembly (DSA) of BCPs as a viable lithographic approach for the semiconductor industry has spurred the development of new BCPs with full pitches below 20 nm and larger inherent etch contrasts.^13–23 Smaller pitches have been achieved by the development of BCPs with large effective Flory–Huggins interaction parameters (χ_e), enabling ordered nanostructures where the degree of polymerization (N) is less than 50 monomer units.²⁴ Most predictions of the interface or pitch (L₀) scaling assume a sufficiently large N to neglect the effects of chain size.^25–28 As a result, these new high χ_e, low N materials reside in a parameter space that has received relatively little exploration. Most studies on high χ_e BCPs have focused on characterizing L₀, the order–disorder transition (ODT) temperature, and χ_e but have neglected to examine the interface width, which is a potentially limiting factor in the process. Here, we examine the interface width and L₀ scaling of a series of high χ_e silicon-containing BCPs which are currently being explored as candidates for high throughput patterning at sub-20 nm pitch (i.e., sub-10 nm features sizes).²⁹

BCP structure, including domain period and morphology, has generally been described by self-consistent field theory (SCFT) where the properties are a function of the volume faction (f_i), statistical segment lengths (b), and the segregation strength χ_eN (N is the volumetric degree of polymerization calculated according to eq 1 using a common reference volume v₀ = 118 ų where M_n is the number-average molecular mass, ρ is the polymer density, and N_A is Avogadro’s constant). SCFT predicts that for an AB diblock copolymer with f_A = 0.5 the ODT occurs at (χ_eN)_ODT ≅ 10.5.^25,26, This result may not be accurate for materials with a large χ_e and low N, both due to potential deviations from Gaussian chain behavior and due to the impact of composition fluctuations. Several efforts have been made to develop theories which better reflect the behavior of BCPs under these conditions. For example, Fredrickson–Helfand theory introduces a correction to the ODT prediction which results in an increase in (χ_eN)_ODT for shorter polymer chains to account for fluctuation effects.³⁰ The renormalized one-loop theory (ROL) was developed in an attempt to model BCP behavior over a wide parameter space. Unlike the earlier theories which depend on N, predictions made by this theory depend on the invariant degree of polymerization, $\overline{N}(\overline{N}=N{b}^6/{v_0}^2)$.^24,31,32 ROL predicts that composition fluctuations result in an upward shift of (χ_eN)_ODT according to eq 2, which is an empirical relationship derived by analyzing the results of multiple simulation models. The L₀ scaling of lamellar BCPs depends on whether the system is in the weak-segregation-limit regime (WSL, χN near the ODT), where L₀ ≈ N^1/2 or the strong-segregation-limit regime (SSL, χN ≫ 10.5) where L₀ ≈ χ_e ^1/6N^2/3. A crossover regime where L₀ ≈ N^4/5 has also been observed while transitioning between the WSL and the SSL.^33–36

$$N=\frac{M_{\mathrm{n}}}{\rho v_0{N}_{\mathrm{A}}}$$ (1)

$${\left({\chi }_{\mathrm{e}}N\right)}_{\text{ODT}}=10.495+41{\overline{N}}^{-1/3}+123{\overline{N}}^{-0.56}$$ (2)

In addition to the pitch scaling, there has also been significant investigation into the interface between the two components of a BCP.^37–40 In the WSL the BCP profile is expected to take a sinusoidal shape and show incomplete segregation of the two blocks. In the SSL the two blocks are expected to show a square wave profile with an interface width being inversely proportional to χ_e^1/2. The interface width between BCP components is typically measured using specular X-ray or neutron reflectivity, which measures the scattering length density (SLD) profile as a function of depth in the film.^40–44 The SLD profile can then be transformed into a composition profile, allowing direct investigation of the composition of a BCP with lamella orientated parallel to the substrate. Historically, neutron reflectivity was the primary tool for these measurements, as the contrast between organic materials for hard X-rays was typically insufficient for accurate structural determination. The drawback to this technique is that it generally requires one of the blocks to be deuterated to enhance the contrast and reduce the incoherent background. This can be synthetically challenging for some materials and can influence the thermodynamics between the blocks.⁴⁵ Resonant soft X-ray reflectivity (RSoXR) has emerged recently as a method for enhancing contrast of the native materials based on the type and density of chemical functional groups in the blocks.^46–50 In the soft X-ray region (100–3000 eV) there are absorption edges for the atoms which are the primary constituents of most polymers, carbon (≅285 eV), nitrogen (≅400 eV), and oxygen (≅540 eV). In the vicinity of the absorption edge, the complex refractive index (n = 1 − (λ²/2π)[ρ_R − iρ_Im], where λ is the wavelength, ρ_R is the real, or dispersive, component, and ρ_Im is the imaginary, or absorptive, component in terms of SLD) will vary sharply. The magnitude of this change depends on the proximity of the beam energy to the absorption edge location (which will shift depending on the exact chemistry) and density of the functional groups. The measured interface width from this composition profile (w_M) is determined by modeling the interface as an error function, and the width of the error function (σ) is then converted to w_M using eq 3.

$$w_{\mathrm{M}}=\sigma \sqrt{2\pi }$$ (3)

Accurate characterization of the interfacial width is important for lithographic materials as it is potentially a limiting factor in the performance of a BCP as an etch mask.⁵¹ Polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) is the most commonly explored material for lithographic applications, but it suffers from a number of limitations. Recent results have shown that while the material will form regular patterns down to L₀ ≅ 18 nm, the pattern will not effectively transfer to the underlying substrate at that length scale.¹¹ Additionally, PS-b-PMMA generally requires enhanced etch selectivity through an additional process such as sequential infiltration synthesis.^52–54 The combination of these two challenges has prompted the development of new BCPs capable of achieving smaller pitches and/or with inherently larger etch contrast. Larger χ_e are generally achieved by increasing the difference in polarity between the two blocks. For example, the addition of a tert-butyl group to the PS block of PS-b-PMMA enables L₀ as small as 14 nm and a significant shift in the temperature dependence of χ_e.²⁰ Sub-10 nm domains have been achieved using this approach with poly(cyclohexylethylene)-b-PMMA²¹ and recently feature sizes as small as 3 nm have been fabricated.⁵⁵ There is also some evidence that higher χ_e will lead to a reduction in the line edge roughness (LER).⁵¹ LER values above a tolerable threshold will lead to a deterioration in the electrical properties of the integrated circuit. The degree to which the interface width correlates directly to changes in LER is still unknown.

Silicon-containing BCPs can achieve small pitches and have the advantage of inherently high etch contrast. Block copolymers with poly(dimethylsiloxane) are capable of achieving small feature sizes and good etch transfer to the underlying substrate.^14,17,56,57 In addition to polymers with silicon in the backbone, a series of BCPs with silicon-containing pendant groups have recently been synthesized and studied for DSA applications.^15,58–60 These include (in order of increasing χ_e) PS-b-poly(trimethylsilylstyrene) (PS-b-PTMSS), PS-b-poly-(pentamethyldisylilstyrene) (PS-b-PDSS), poly(4-methoxystyrene)-b-PTMSS (PMOST-b-PTMSS), PMOST-b-PDSS, and poly(5-vinyl-1,3-benzodioxole)-b-PDSS (PVBD-b-PDSS). DSA of PVBD-b-PDSS was recently demonstrated with half-pitches of 5 nm on a hybrid chemo/graphoepitaxial template.

In this study we examine the interface width and L₀ scaling for a series of BCPs with χ_e ranging from ≅0.04 (a similar magnitude to that of PS-b-PMMA)⁶¹ to ≅0.25 (as determined by SAXS measurements on materials in the disordered phase). The interface widths are characterized using RSoXR to enhance the scattering contrast between the two blocks. Limits on the ratio of w_M/L₀ are explored as a function of χ_eN, which helps explain experimental results demonstrating lower pitch limits on BCP etch transfer.

MATERIALS AND METHODS

Sample Preparation

Block copolymers were prepared via anionic polymerization using the techniques described by Durand et al.¹⁵ Block copolymer solutions (3–5 wt % in methyl isobutyl ketone) were spin coated between 1500 and 3000 rpm to create smooth films on a silicon wafer with native oxide. In this study, it is generally observed that the silicon-containing block prefers to wet the air interface while the other block prefers to wet the substrate surface. The film thicknesses were (n + 0.5)L₀ where n is an integer. Films were annealed at 180 °C for 10 min and inspected by optical microscopy to confirm that no topography formed during the annealing process.

RSoXR

RSoXR measurements were performed at the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory using beamline 6.3.2. Measurements at the carbon edge (260–300 eV) were conducted using a 600 mm⁻¹ grating, a 600 nm Ti filter, and a Burle CEM detector.⁶² Measurements at the oxygen edge (520–540 eV) were conducted using a 1200 mm⁻¹ grating, a Cr filter, and the Burle CEM detector. The data were fit using the Refl1D program and uncertainties determined using the differential evolution adaptive metropolis (DREAM) algorithm.⁶³

RESULTS AND DISCUSSION

The properties of the BCPs examined in this study are outlined in Table 1. For all samples the interaction parameter was previously determined using SAXS measurements in the disordered state.^15,60

Table 1.

Sample Parameters, χ_e, w_M, and L₀ from RSoXR Measurements

sample name	Mn [kg/mol] (A block)	Mn [kg/mol] (B block)	Na	χe(SAXS)b at 180 °C	χeN (SAXS)	wM (Å)	L0 (Å)
PS-b-PTMSS392	14.0	14.4	392	0.047	19.1	63.9 [−3.9/+9.8]	179 ± 2.7
PS-b-PTMSS478	16.7	17.4	478	0.047	23.3	53.6 [1.3/+5.3]	216 ± 2.6
PS-b-PTMSS656	23.7	23.2	656	0.047	32.0	44.6 [−1.0/+6.9]	264 ± 2.7
PS-b-PDSS426	15.0	14.7	426	0.112	52.3	34.2 [−1.4/+3.8]	195 ± 2.2
PMOST-b-PTMSS369	14.4	13.0	369	0.135	58.7	29.8 [−0.8/+1.3]	189 ± 2.3
PMOST-b-PDSS182	7.4	5.9	182	0.195	38.5	22.0 [−1.3/+2.0]	129 ± 2.3
PMOST-b-PDSS251	9.7	8.5	251	0.195	53.0	22.4 [−1.2/+1.8]	162 ± 2.4
PMOST-b-PDSS345	12.3	12.5	345	0.195	72.7	22.8 [−1.3/+1.8]	208 ± 2.4
PVBD-b-PDSS218	8.9	7.4	218	0.25	65.3	19.0 [−1.1/+1.9]	154 ± 2.1
PVBD-b-PDSS261	11.0	8.6	261	0.25	54.5	20.6 [−1.6/+2.6]	181 ± 2.3

^aN was calculated using eq 1, densities were experimentally determined previously,¹⁵ and a common reference volume of v₀ = 118 ų was used for all samples.

^bAll values were calculated at 180 °C, based on SAXS measurements of disordered materials.¹⁵

The results of the RSoXR measurements on the PMOST-b-PDSS series are shown in Figure 1, where χ_eN ranged from 32 to 60. The reflectivity curves (Figure 1A) show the classic multilayer signature of a BCP oriented parallel to the substrate. The higher frequency fringes correspond to the total thickness of the film, and the longer spacing between the Bragg peaks corresponds to the L₀ of the polymer. The film prepared from the lowest molecular weight sample (PMOST-b-PDSS₁₈₂) has the greatest number of repeating layers in the film (9 full multilayers) and as a result had the sharpest Bragg peaks. The Bragg peak intensity is a function of both the contrast between the layers and the total number of repeating layers. Both the second-order (q ≅ 0.14 Å⁻¹) and third-order (q ≅ 0.24 Å⁻¹) Bragg peaks are clearly visible, showing the slow decay of the Bragg peak intensity. The best fit to this sample results in a w_M = 22.0 [−1.3/+2.0] Å. The samples with larger molecular weights (PMOST-b-PDSS₂₅₁, PMOST-b-PDSS₃₄₅) show similar behaviors, including both the high frequency fringes and the lower frequency Bragg peaks. As the molecular weight increases, the spacing between the Bragg peaks decreases, consistent with the increase in the BCP domain pitch. The magnitude of the Bragg peaks also decreases because of the reduced number of multilayers in the film. All three samples at different M_n show effectively the same w_M at 22.4 [−1.2/+1.8] Å and 22.8 [−1.3/+1.8] Å for PMOST-b-PDSS₂₅₁ and PMOST-b-PDSS₃₄₅, respectively. All samples show asymmetry in the uncertainties for w_M, with the uncertainty in the positive direction being larger than the uncertainty in the negative direction. Shrinking the interface width has a larger impact on the simulated reflectivity than increasing it, and this results in the asymmetry of the uncertainty.

Figure 1.

Experimental (colored ○) and simulated fits (solid lines) for PMOST-b-PDSS for N = 182, 251, and 345. Measurements were collected at either 282 or 282.5 eV. The corresponding SLD (solid lines indicate ρ_R, dashed lines indicate ρ_Im) and SLD/composition plots are shown in B (N = 182), C (N = 251), and D (N = 345). Composition plots exceed 1 at the SiO₂ layer.

In addition to the results shown in Figure 1, RSoXR measurements were conducted on the remainder of the samples outlined in Table 1. The pitch scaling was explored in order to place the results in context with the behavior of previously investigated BCPs with similar χ_eN. The results of those measurements are shown in the Supporting Information. Figure 2 shows a ln–ln plot of L₀ as a function of N for the three series where multiple molecular masses were examined. All three series show L₀ ∼ N^3/4, a stronger scaling than predicted in either the WSL (N^1/2) or SSL (N^2/3). The scaling observed here is closer to previous results which sometimes observed an N^4/5 scaling in samples with similar χ_eN (35–80), a regime which is associated with stretched Gaussian coils.^33–36 The origin of the scaling behavior in this region is unclear, but it is shown here to be consistent among samples with a range of χ_e.

Figure 2.

Plot showing ln(L₀) as a function of ln(N); all sample sets show slopes of ≈0.75.

For high molecular weight BCPs the interface width is generally small relative to the pitch; for systems near the ODT, the interface region can constitute a significant portion of the BCP. Figure 3 shows the ratio of w_M/L₀ as a function of χ_eN. The PS-b-PTMSS series ranges between χ_eN = 15 and 35, and in this region w_M/L₀ can be seen to increase rapidly with decreasing χ_eN, particularly as the ODT is approached (using eq 2 the (χ_eN)_ODT ≈ 13–15 for most systems investigated in this study). For χ_eN > 30 the w_M/L₀ gradually reduces with increasing χ_eN; this effect is well captured by the PMOST-b-PDSS series which spans 40 < χ_eN < 70. The two materials with the largest χ_eN investigated show w_M/L₀ of just above 0.10. There is some spread in the data in this region, which may be caused in part by conformational asymmetry between the two components of the block copolymer which is not captured in this straightforward scaling approach.^64,65 Separating the results into regions above and below χ_eN = 35 allows two different scaling relationships to be extracted from w_m/L₀ ∼ (χ_eN)^ω. In the region below χ_eN = 35, ω ≈ −3/2; above χ_eN = 35, ω ≈ −2/3. Attempting to fit this data with a single power law exponent generally resulted in poor fits to the data below χ_eN = 35; given that the pitch scaling is well-known, this suggests a shift in the scaling of the interface width as the ODT is approached. Experimental results have shown that when w_m/L₀ ≥ 0.27, etch transfer of a DSA patterned BCP results in large numbers of defects; this limit in relation to the samples investigated in this study is marked in Figure 3. The origin of this behavior can be explained by examining the composition profiles as a function of χ_eN.

Figure 3.

Ratio of w_m/L₀ as a function of χ_eN. From these results a scaling relationship can be extracted, w_m/L₀ ∼ (χ_eN)^ω. For χ_eN < 35 ω ≈ −3/2, and for χ_eN > 35 ω ≈ −2/3. For systems with w_m/L₀ above 0.27 (dashed line) experimental results have shown a loss of alignment upon etching one of the components in the polymer.¹¹

The impact of the interface width on the composition profile is captured in Figure 4, which shows the composition profiles for BCP samples with χ_eN ranging from 19.1 to 72.7. The profiles are normalized by the BCP L₀ to compare materials with a wide range of L₀ on the same graph. PS-b-PTMSS₃₉₂ has the lowest χ_eN value (19.1) and shows both a sinusoidal composition profile and evidence of incomplete phase segregation (i.e., significant regions with composition very close to 1.0 or 0.0 are not observed). PS-b-PTMSS₄₇₈ has a slightly larger χ_eN (23.3) and now shows a narrow region of complete phase segregation near the center of the lamella. As χ_eN increases, the composition profile rapidly shows signs of increasing phase separation. Increasing χ_eN to 38.3 (PMOST-b-PDSS₁₈₂) shows a clear transition to the square wave profile associated with the SSL, although the interface still makes up a considerable portion of the profile. PMOST-b-PDSS₃₄₅ has the largest χ_eN examined in this study and results in lamella with a narrow interface. The incomplete phase segregation at χ_eN = 19.1 demonstrates why this represents a lower limit on the patterning ability of BCPs. While the overall structure still results in a lamellar morphology local composition fluctuations are significant enough to result in incomplete phase segregation at many positions along the lamellae. Upon etch transfer these composition fluctuations result in defects. This could be even more problematic near the neutral brush, which likely acts as a compatibilizer and shifts the local (χ_eN)_ODT to a higher value.¹² Both TEM and scattering measurements have suggested that the magnitude of fluctuations increases near the neutral brush.^66,67 It is also possible that this effective patterning limit will shift for BCPs with lower N, where composition fluctuation effects may have a greater impact.

Figure 4.

Composition profile for BCPs with χ_eN = 191 (PS-b-PTMSS₃₉₂), χ_eN = 23.3 (PS-b-PTMSS₄₇₈), χ_eN = 38.5 (PMOST-b-PDSS₁₈₂), and χ_eN = 72.7 (PS-b-PTMSS₃₄₅). The profiles are normalized by L₀ in order to compare the shape of the composition profile for the BCPs on the same scale. They are also shifted in order to account for the small differences in the SiO₂ thickness in the model so that the minima and maxima of the profiles are centered at the same location.

The lower accessible limit of w_M/L₀ for a given L₀ will depend on χ_e and therefore vary depending on the BCP system. This is explored in Figure 5 where w_M/L₀ is shown as a function of L₀. PS-b-PTMSS has the lowest χ_e of the BCPs investigated in this study, at χ_e ≅ 0.04. As a result, when L₀ decreases, w_M/L₀ increases rapidly, reaching 0.35 at L₀ = 179 Å, demonstrating that this system likely has a similar lower accessible pitch limit as PS-b-PMMA, which is consistent with the similar magnitude of χ_e for the two materials. As discussed in the previous paragraph, this sample shows incomplete phase segregation. This sample series demonstrates that for a material with this χ_e there is a clear barrier to achieving smaller L₀ < 100 Å while maintaining a sufficiently small interface width. As χ_e increases, this limit shifts to progressively lower values. PS-b-PDSS has a χ_e ≅ 0.11, and w_M/L₀ was found to be 0.17 at L₀ = 195 Å, a 40% reduction over the expected value for a PS-b-PTMSS sample with identical pitch (w_M/L₀ for PS-b-PTMSS with this pitch as extrapolated from the trend). This trend is continued as the BCPs with higher χ_e are examined, shifting the lower limits of w_M/L₀. A rough extrapolation of the data for PMOST-b-PDSS suggests that this system could reach a lower patterning limit of L₀ ≈ 90 Å. While there is insufficient data to determine the lower limit of the PVBD-b-PDSS series, experimental results have demonstrated patterning and etch transfer down to L₀ ≈ 100 Å, suggesting that the lower limits lie at even smaller L₀. Extrapolating from these results also provides an estimate for the magnitude of χ_e which will be needed to obtain w_M/L₀ < 0.1 and L₀ < 100 Å, which is χ_e ≈ 0.6–0.7. This is on the order of the value reported for a recently synthesized polymer, polydihydroxystyrene-b-PS,⁵⁵ providing additional hope that new BCPs can provide solutions to the patterning needs of next-generation technology nodes.

Figure 5.

w_M/L₀ as a function of L₀ for all BCP samples.

CONCLUSIONS

Block copolymer lithography requires materials with sufficiently low w_m/L₀ so that the composition fluctuations do not result in defects during etch transfer and the resulting LER does not inhibit electrical performance. By use of RSoXR, the composition profile of a series of high χ_e BCPs was characterized and w_m/L₀ was extracted. This value was scaled as a function of χ_eN, demonstrating a rapid increase as the ODT is approached, and below χ_eN = 20 incomplete phase segregation in the composition profile is observed. This coincides with experimental results showing difficulty in obtaining good etch transfer for a system with similar w_m/L₀, which provides strong evidence that composition fluctuations limited the etch transfer and that w_m/L₀ ≈ 0.27 represents an upper limit for effective BCP lithography. w_m/L₀ was also scaled as a function of L₀, demonstrating a shift in the lower accessible L₀ under this limit with increasing χ_e.