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Nov 6, 2015 - ... analysis of a polystyrene-b- poly(2-vinylpyridine) (S2VP) thin film (420 nm thick) was achieved by grazing-incidence small-angle X-r...
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Depth-Resolved Structure Analysis of Cylindrical Microdomain in Block Copolymer Thin Film by Grazing-Incidence Small-Angle X‑ray Scattering Utilizing Low-Energy X‑rays Itsuki Saito,† Tsukasa Miyazaki,‡ and Katsuhiro Yamamoto*,† †

Department of Materials Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan ‡ Nitto Denko Corporation, 1-1-2, Shimohozumi, Ibaraki, Osaka 567-8680, Japan S Supporting Information *

ABSTRACT: Depth-resolved structure analysis of a polystyrene-bpoly(2-vinylpyridine) (S2VP) thin film (420 nm thick) was achieved by grazing-incidence small-angle X-ray scattering (GISAXS) utilizing lowenergy X-rays (“tender” X-rays). In contrast to techniques utilizing hard X-rays, a gradual change of the penetration depth of soft X-rays around the critical angle of total reflection of a polymer surface is anticipated. In this research, X-ray energy of 2.4 keV was chosen to control the penetration depth and achieve depth-sensitive GISAXS measurement. Microphase-separated structure of the annealed S2VP in the thin film was confirmed to be hexagonally packed cylinders (HEX) aligned parallel to the substrate surface. Significant elongation of the Bragg spots in the qz direction was observed for an incidence angle close to the critical angle. The experimental full width at half-maximum (fwhm) values of the (11) HEX diffraction spot was interpreted using the theoretical fwhm values estimated using the Laue function considering an attenuation decay of X-ray intensity. The penetration depth was controlled by changing the incident angle, and depth-resolved structure analysis revealed that the hexagonal lattice deformed along the depth direction with the deformation gradually relaxed toward the surface. The observed relaxation behavior is related to the higher mobility of polymer chains near the surface.

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photoelectron spectroscopy depth profiling with C60+ sputtering revealed the ion distribution in lithium salt-doped BCP thin films.28,29 Electron microscopy is a powerful tool for visually examining a cross-sectional view of polymeric thin films in twoand three-dimensional real space.30 However, these techniques are accompanied by the destruction of specimen because of processing such as etching or sectioning for analysis. In particular, it is important to consider the influence of etching (e.g., chemical reaction) and sectioning (e.g., deformation and losing a precise original spatial coordinate) in the analysis of results obtained by these techniques. In contrast, neutron reflectivity (NR) measurements enable a practically nondestructive analysis of depth profiles and ordering of microphase-separated structure in BCP thin films.31,32 However, NR provides structural information (density profile) only in the qz direction vertical to the surface, and no lateral information on the structure is accessible. Furthermore, accuracy of the density profile (depth-resolved information) perpendicular to the surface becomes worse as the film thickness is large for

INTRODUCTION Block copolymer (BCP) composed of two or more immiscible polymers form a variety of periodic structure at the nanometer scale. BCP thin films with a variety of self-assembled patterns are widely applied for nanofabrication in microelectronics and semiconductor industry and for size selective separation of biomedical molecules and protein nanoparticles. Control of the BCP phase-separated nanostructures’ orientation is important for these potential applications. This has motivated numerous orientation control methodology studies that have examined the effects of film thickness,1,2 surface or interfacial energy,3−5 surface topology,6,7 external applied fields (shear-induced,8,9 electronic field,10,11 magnetic field,12 and light-driven13,14), solvent vapor annealing,15−21 and directional solidification.22−24 Suitable characterization techniques are required to monitor the structures of BCP both laterally and in-depth. Several approaches have been used to examine BCP structures. Dynamic secondary ion mass spectroscopy (SIMS) can elucidate the BPC morphology and the self-diffusion of polymer chains in thin films along a depth direction.25 Recently, time-of-flight (ToF) SIMS using the ion cluster beam was reported to be a particularly well-suited technique that enables the in-depth profiling of polymers.26,27 X-ray © 2015 American Chemical Society

Received: August 26, 2015 Revised: October 21, 2015 Published: November 6, 2015 8190

DOI: 10.1021/acs.macromol.5b01883 Macromolecules 2015, 48, 8190−8196

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preferentially oriented parallel to the surface of the substrate induced by the surface free energies and/or an interfacial interaction between S2VP and the substrate. In GISAXS, the structural parameters of the cylindrical domains in both the lateral and vertical directions are accessible because the diffraction spots appear with the offset in the qy direction. In the case of a parallel oriented lamellar morphology, since the observed diffraction spots (at qy = 0) are typically hidden behind a beam stop in GISAXS and are insufficient for a precise analysis, the NR measurement is well-suited for the structural analysis (depth profiling) of the vertical direction in very thin films. Furthermore, it is relatively simple to analyze the depthresolved structural parameters of hexagonally packed cylinders in comparison with BCC and FCC lattices of spherical domains47 and gyroids35 such as a labyrinth that have been frequently observed in the BCP system. Thus, the parallel S2VP cylinders are an ideal model for the demonstration of the potential of in-depth profiling utilizing soft GISAXS. Depthresolved GISAXS patterns of the annealed thin film were obtained with the resolution from a few to tens of nanometers. It was found that while the lattice distortion of the hexagonal packing was retained in the entire film, the distortion was more relaxed depending on the depth in the vicinity of the surface. This was related to the changes in the mobility of polymer chains which are relatively mobile near the film surface and are confined near the substrate.48−54

analyzing periodicity of microphase-separated structure. In particular, NR depth profiling is suited for very thin film (commonly less than 100 nm) as in the above case. Furthermore, the probing of both real and reciprocal spaces provides a reliable picture of the thin film structure. Grazingincidence X-ray scattering (GISAXS) is another powerful tool for understanding the nanostructure in both vertical and lateral directions of BCP thin films that is essentially nondestructive under the condition of the absence of damage under X-ray irradiation for polymeric materials.33−38 Commonly, SAXS and GISAXS measurements have been conducted using X-ray energies of 8−13 keV (hard X-rays). However, under these conditions, the X-ray penetration depth rapidly reaches the thickness scale of the polymeric materials in the vicinity of the critical angle of total reflection αc at the surface, making depthresolved GISAXS measurements with hard X-rays totally impractical. Recently, Okuda et al.39,40 demonstrated a depthsensitive GISAXS technique using soft X-rays with an energy of 1.77 keV. They investigated structural relaxation near the surface and the dynamic heterogeneity of polymer chains in a thin film. At even lower X-ray photon energies (near the adsorption K edges of the soft material, e.g., the oxygen, nitrogen, and carbon K edges), the fine structure of the adsorption edge can be utilized in GISAXS. The grazing incidence resonant soft X-ray scattering (GI-RSoXS)41 has been applied for polymer blend thin films with low contrast in the real part of the refractive index for the hard X-rays but with significant differences in the soft X-ray regime. Furthermore, the X-ray penetration depth is drastically affected by the changes in the X-ray photon energy across the K-edge. The surface- and volume-sensitive structure of polymer blend films had been analyzed using this technique.41 Similar to the GISAXS, grazing-incidence small-angle neutron scattering (GISANS) has been developed by Müller-Buschbaum and coworkers. GISANS is a perfectly nondestructive approach for structure analysis and has essentially the same capability for surface-sensitive,42 interface-sensitive (structural information near the polymer−silicon interface enabled by the ability of the neutrons to travel through the substrate),43,44 and depthsensitive analysis.45 Moreover, a combination of time-of-flight (ToF) mode and GISANS has been developed to investigate nanostructured polymer films.43,46 In ToF-GISANS, a broad wavelength band is used instead of a single neutron wavelength; i.e., a range of different scattering vectors is directly probed by the measurement under a single angle of incidence. At an appropriate incident angle, it is possible to simultaneously conduct surface- and bulk-sensitive measurements. While GISANS displays several advantages relative to GISAXS, GISANS experiments still remain rare compared to GISAXS experiments because of GISANS’s requirement for high-flux sources to measure the much weaker signals in grazingincidence geometry and the need for deuterium labeling (in some cases, of course, this is beneficial for structure analysis by tuning the contrast). In the present study, we performed GISAXS measurement with low-energy (tender) X-rays (2.40 keV) to precisely investigate the depth profile of a microphase-separated structure (hexagonally packed cylinders) of a polystyrene-bpoly(2-vinylpyridine) (S2VP) thin film on a silicon wafer with the cylindrical microdomains oriented parallel to the substrate after the appropriate thermal annealing in a vacuum. The merits of using the S2VP with parallel cylinders as a model system are as follows. The cylindrical domains in the S2VP thin film were

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EXPERIMENTAL SECTION

Sample Preparation. S2VP thin film (Mn = 25 400, PDI = 1.24, and ϕPS = 76.3 vol %; see Supporting Information for the synthesis and characterization) was prepared by spin-casting from toluene solution (10 wt %) of S2VP onto a silicon wafer substrate at 3000 rpm for 30 s. Subsequently, the S2VP thin film was thermally annealed under vacuum at 170 °C for 48 h. Film thickness and the roughness of the film surface were estimated by X-ray reflectivity measurement to be 420 nm and a few nanometers, respectively (Figure S2). Surface topology and roughness were also estimated by atomic force microscopy (AFM) (Figure S6) and optical white-light interferometer microscopy measurements (Figure S7). These measurements showed a very flat and smooth surface with different length scales, and no specific pattern was found. This implies that either component of S2VP covered the surface. The water contact angle of the annealed thin film was approximately 90°, in agreement with the previous report for the polystyrene (PS) surface.55 Furthermore, XPS measurements detected no more than a trace amount of nitrogen atoms (vinylpyridine unit) on the surface (nitrogen/carbon (N/C) atomic ratio = 0.0030−0.0078). It is noted that the average S2VP atomic N/C ratio is 0.0322. Thus, we find that the outermost film surface was covered by the PS component, as expected based on the comparison of surface free energy values for PS (approximately 33 mN/m) and poly(2-vinylpyridine) (approximately 60 mN/m).56 Synchrotron Grazing-Incidence SAXS. Tender X-ray GISAXS measurement (room temperature) was performed at BL15A2 at the Photon Factory, KEK, Tsukuba in Japan. The BL15A2 is an undulator beamline that offers X-rays in a wide energy range from 2.1 to 15 keV (energy resolution is 2 × 10−4). In this study, the X-ray energy was set at 2.40 keV (corresponding to the wavelength of 5.16 Å) and the sample-to-detector distance (SDD) was 830 ± 5 mm. The accuracy of the camera lengths arises from the scattering vector calibration on a detector with a standard specimen and a footprint of the incident beam on the sample surface (sample size of ca. 1 cm). The X-ray incident angle was varied between 0.290° and 0.620°, and PILATUS 2M designed for usage in vacuum was used as a detector for the 2D scattering pattern. X-ray exposure time of 300 s was sufficient to obtain a clear scattering pattern. Hard X-ray (wavelength 1.0 Å) GISAXS measurements were performed at BL10C in Photon Factory and BL03XU57 in SPring-8, Harima, Japan, using PILATUS 2M and CCD 8191

DOI: 10.1021/acs.macromol.5b01883 Macromolecules 2015, 48, 8190−8196

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Macromolecules (Hamamatsu Photonics) detectors with SDD of 2.3 m. All detectors were calibrated using lead stearate prepared in-house (d = 5.01 nm, calibrated). The magnitude of the scattering vector is given by q = 4π sin θ/λ, where λ is the X-ray wavelength and 2θ is the scattering angle. The scattering vector qz denotes the component perpendicular to the film surface. The qx and qy are the scattering vector components in the sample surface, perpendicular to and directed to the X-ray beam, respectively. For each set I(y,z), the detector pixels were converted into exit angle αf perpendicular to the surface and an angle 2Θ parallel to the surface by simple geometrical consideration. The scattering vector q is composed of qx, qy, and qz, related to the experimental angles by

⎛ qx ⎞ ⎛ cos 2Θ cos αf − cos αi ⎞ ⎟ ⎜ ⎟ 2π ⎜ q q = ⎜ y⎟ = ⎟ ⎜ sin 2Θ cos αf λ ⎜ ⎟ ⎜q ⎟ ⎠ ⎝ z⎠ ⎝ sin αi + cos αf

(1)

Figure 1. Penetration depth calculated for the present S2VP film for different X-ray energies: 12.397 (blue), 8.265 (green), 3.60 (orange), and 2.40 keV (red). Symbols represent the penetration depth at the αc for each energy.

where αi is the incident angle which is defined henceforth as the angle between incident X-ray and the surface for convenience. This data set was further converted into I(q∥,qz). The scattering vector q∥ is defined by q∥ = (qx2 + qy2)1/2. Penetration Depth of X-rays. The X-ray penetration depth Λ is defined as the depth at which the X-ray intensity is attenuated by 1/e. The value of Λ depends on X-ray energy (in other words, wavelength λ), the critical angle, αc, of total reflection, and the angle of incidence, αi. Surface roughness influences practically the penetration depth of Xrays because various αi are provided. The roughness of the surface used here is regarded as sufficiently small to estimate the penetration depth as evidenced by the clear observation of the critical angle in XRR (Figure S2). Under experimental conditions with the ideally flat surface, Λ is given by Λ=

λ 4π

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RESULTS AND DISCUSSION GISAXS measurements of the S2VP thin film (thickness of 420 nm) using tender X-ray were performed at various incident angles and many Bragg spots were measured as shown for large αi in Figure 2a. All spots were assigned to parallel oriented

2 2

2 2

(αi − αc ) + 4β 2 − (αi 2 − αc 2)2

(2)

where β is the imaginary part of the complex refractive index. The critical angle is specified as αc ∼ 2δ where δ is deviation from the real part of the refractive index. δ and β are given by δ = (reλ 2NA /2π )ρM ∑ wZ(f0Z + f Z′ (E))/∑ wA i Z Z

Z

β = (reλ 2NA /2π )ρM ∑ wZf Z″ (E)/∑ wZAZ Z

Z

(3) Figure 2. GISAXS patterns measured with tender X-rays (2.40 keV) at above (a) and below (b) the critical angle. Schematic illustration represents the unit cell of the aligned cylindrical microdomains relative to the substrate in real space.

(4)

where re is the classical electron radius (2.82 × 10−5 Å), NA is Avogadro’s number, ρM is the mass density, wZ is the fraction of element Z, AZ is the relative atomic mass, f 0Z is the nonresonant term of the atomic scattering factor corresponding to the atomic number, and f ′Z(E) and f ″Z (E) are the real and imaginary parts of the anomalous dispersion for the incident X-ray energy E, respectively. For example, here we used 4.1468 × 10−5 for δ and 7.0239 × 10−7 for β of PS at 2.40 keV. Furthermore, we experimentally obtained the S2VP thin film αc value using GISAXS and XRR measurements (see Supporting Information). The expected critical angle for 2.40 keV was 0.5217°, in good agreement with the αc estimated using the value of δ. Figure 1 shows the calculated S2VP penetration depth. It is difficult to precisely control the penetration depth Λ at the nanometer scale for GISAXS experiment conducted using hard X-rays (1.00 or 1.50 Å) because the value of Λ rises abruptly at αc. However, it can be seen that as the Xray energy decreases, Λ changes more gradually near the critical angle and shows decreased depth values at angles greater than the critical angle. Therefore, better control of Λ is expected for depth-resolved GISAXS measurements using tender X-rays (2.40 keV) because of the critical angle and attenuation coefficient values that are much larger than those for the hard X-rays.

hexagonally packed cylinders. GISAXS patterns at approximately q∥ of 0.26 nm−1 are presented in Figure 2b and show a remarkable elongation of the Bragg spots in the qz direction for smaller αi. One-dimensional scattering profiles vertically cut at q∥ = 0.26 nm−1 with various incident angles are shown in Figure 3. Bragg peaks were assigned to the scattering from transmitted (denoted by T) and reflected (denoted by R) beams by the substrate. These two scattering events are typically noticeable in GISAXS measurements.36,37 Spot positions shift with the change in the incidents angle, and several gaps in the data were observed at the same qz in all profiles. These gaps are because of the device array of the PILATUS detector. Unfortunately, the primary peak of the hexagonally packed cylindrical structures arising from the (10) plane overlapped with the gap. Therefore, second-order peaks derived from (11) reflection at qz approximately 0.6 and 0.7 nm−1 were used for structure analysis. The magnitudes of the Bragg spot full widths 8192

DOI: 10.1021/acs.macromol.5b01883 Macromolecules 2015, 48, 8190−8196

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where N is the number of the reflection plane and b is the unit lattice vector associated with z-direction normal to the surface. Here we must consider that the X-ray wave decays exponentially, and considering the attenuation decay, the Laue function can be re-expressed as L(qz) =

∑ N

sin[(N + 1)qzD01/2] sin[qzD01/2]

⎡ ⎢ exp⎢ − ⎢⎣

( 12 + 23 N )D01 ⎤⎥ 2Λ

⎥ ⎥⎦

(6)

where D01 is the periodicity of the (01) plane. Since the scattering intensity is proportional to the square of the Laue function, the fwhm can be calculated simply. Figure 4 shows the change of the FWHM of the Bragg spots of the T (11) plane in the qz direction. As indicated in Figure 3, the FWHM in the qz direction decreased monotonically with increasing incident angle. Therefore, the peak broadening can be used as a measure of the depth sensitivity in GISAXS measurements. Furthermore, the values for fwhm in the qz direction calculated for the penetration depth Λ given by eq 1 are plotted in Figure 4. The calculated width decreases drastically near the critical angle and shows the same trend as the experimental results, indicating that the broadening of the Bragg spots in the direction vertical to the surface can be interpreted by the size effect determined by the depth Λ. Thus, we find that the measured region of GISAXS measurement can be controlled with the incident angle, enabling depth-resolved GISAXS pattern measurements. However, at larger incident angles, the experimental widths still deviated from the calculated values. It is noted that, limited by the GISAXS experimental setup, we reluctantly used the second-order peaks for the analysis. The larger experimental broadening may be attributed to the presence of a degree of lattice disordering. The in-plane FWHM Δq∥ was almost constant, indicating the average grain size and degree of the lattice disordering did not change. When the αi is below the αc, X-ray waves travel on the film surface and cannot propagate into the film. Only the evanescent wave can penetrate from the surface into the film. In this situation, the experimentally obtained scattering spot αz along the qz direction is observed at the position given by the sum of the incident angle and the scattering angle αs derived from the period of the observed structure. Thus, αs can be expressed as follows:

Figure 3. 1D GISAXS profiles along qz direction obtained by vertical cut at q∥ approximately 0.26 nm−1.

at half-maximum (fwhm) varied in the vicinity of the αc, with larger fwhm values observed at smaller incident angles. The observed peak broadening can be explained by the change in the penetration depth. While generally such broadening can be explained by either the size effect and/or disordering of the lattice, the fwhm in the q∥ direction did not significantly change irrespective of the incident angles as shown in Figure 4, eliminating the influence of lattice disordering

αs = αz − αi

Using eq 7, the true qz value of the (11) reflection of the cylindrical structure (lattice parameter b) can be estimated using the experimentally observed peaks. In the case that the value of αi is greater than that of αc, an Xray wave can propagate into the thin film. In this situation, the X-ray refracts at the film surface, travels through the film, is reflected by the interface between the film and substrate (silicon wafer), and finally travels out of the film surface with refraction. Normally, some scattering events in GISAXS experiments occur because of the refracted X-rays at the polymer surface and reflected X-ray on the substrate surface. Consequently, a number of scattering peaks appear for αi > αc. The scattering cross section for GISAXS of the block copolymer thin film has been calculated within the framework of the distorted wave Born approximation (DWBA).58 Ree et al.35,36 and Papadakis et al.37,38 introduced the DWBA (or a

Figure 4. FWHM values of (11) Bragg spots obtained experimentally and calculated using eq 6.

because the broadening was mainly observed in the qz direction and the size effect was considered. Rather, the broadening in this case is because of the reduction in the size of the measured region. The fwhm of a scattering peak depends on the grain size of a crystal, as expressed by the Laue function, L(q) L(q z) =

∑ exp(iN q z·b) = N

sin[(N + 1)q z·b /2] sin[q z·b /2]

(7)

(5) 8193

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the D01 was set to 18.8 nm, the DWBA calculation gave the best representation for all Bragg spots as shown by dashed lines in Figure 5. For GISAXS experiment in the soft-X-ray region, the large curvature of the Ewald sphere may give rise to an apparent distortion of the GISAXS pattern when the measurements are conducted with a fixed angle of incidence and using area detector such as imaging plates, charge coupled devices, or the PILATUS. Okuda60 discussed the effect of the Ewald sphere curvature and performed model calculations using DWBA.58 At the lower energy of 1.77 keV, while the interparticle interference peaks extended and bent inward at large qz (approximately 2.0 nm−1), no bending of the extended peaks was observed using hard X-rays. In the presence of the Ewald sphere curvature, the unmodified equation is no longer valid. In this study, we used eq 9 that had been developed for the hard X-ray regime to explain the experimental GISAXS pattern. We examined whether this equation is valid for the soft X-ray regime (2.40 keV) in the observed q-range. Structural analysis of the film (not depth-resolved) can be performed with hard Xrays (12.4 keV). The same structural parameter D01 = 18.8 nm was obtained by the simulation of the qz positions of (10) and (11) planes dependent on the angle of incidence, as shown in Figure S4. Moreover, the positions of the other Bragg spots obtained with tender X-rays were interpreted almost entirely relying on eq 8 (Figure S5). Thus, it was concluded that eq 8 worked well in the tender X-ray regime within the q-range observed in this study; i.e., the small-angle approximation is valid. The S2VP thin film lattice parameters obtained by the analysis are summarized as a function of depth in Figure 6. The

combination of Bragg and Snell laws, refraction and reflection) to estimate the scattering peak positions. Scattering intensities due to the incident X-ray (transmission) and reflected X-ray (reflection) were remarkable in the GISAXS. Busch et al.44 calculated the Debye−Scherrer rings (GISANS, not only qz but also q∥ in plane) of the block copolymer films with powder-like orientation of lamellar domains. The scattering peaks arising from transmitted and reflected X-rays at the substrate can be calculated following44 ⎡ ⎢ 2π ⎢ qz = sin αi λ ⎢ ⎢ ⎣ 1/2 ⎤ ⎧ ⎤2 ⎫ ⎥ ⎡⎧ 2 ⎫1/2 2 ⎞ ⎛ ⎪ ⎪ q λ ⎪ ⎪ ⎥ ⎢ ⎛ mλ ⎞ + ⎨sin 2 αc + ⎢⎨⎜ ⎟ − ⎜⎜ ⎟⎟ ⎬ ∓ (sin 2 αi − sin 2 αc)1/2 ⎥ ⎬ ⎥ ⎥ ⎪ ⎪⎝ D ⎠ 2 π ⎪ ⎠ ⎝ ⎥⎦ ⎪ ⎢ ⎭ ⎪ ⎥ ⎪ ⎣⎩ ⎭ ⎦ ⎩

(8) 1/2

where m represents the peak order, which is 3 for the (11) plane in our case. The upper (−) and lower (+) branches in the equation indicate the Bragg diffraction of the transmitted and reflected beams, respectively. D is the characteristic length of the given plane. As for the (11) plane, eq 9 can be derived from eq 8 as follows: qz =

1/2 ⎤ ⎡ ⎧ ⎡ 3λ ⎤2 ⎫ 2π ⎢ sin αi + ⎨sin 2 αc + ⎢ ∓ (sin 2 αi − sin 2 αc)1/2 ⎥ ⎬ ⎥ ⎣ 2D ⎦⎭ ⎥ λ ⎢⎣ ⎩ ⎦

(9)

where D corresponds to the D01 (z component). The critical angle for S2VP was obtained from the Yoneda line59 in the GISAXS pattern observed with hard X-rays (Figure S3), X-ray reflectivity measurements, and the simple calculation of S2VP mass density. All values obtained by this estimation were completely consistent and the αc was 0.521° at 2.40 keV. The fact that the scattering from the reflected beam was observed means that the X-ray propagated through the entire film thickness, collecting structural information for the entire film. The experimentally obtained Bragg spots of the (11) plane are plotted as a function of the incident angle in Figure 5. When

Figure 6. Lattice parameters plotted against the penetration depth (left). Right illustration indicates parallel-aligned cylindrical domains in thin film and the unit cell. The spacing Dn corresponds to the vertical distance neighboring planes (01). |an| and |bn| represent the distance between neighboring cylindrical domains. The following relations were obtained by analysis; D1 > D2 > D3 > ... > Dc = ... = Dn. |a0| = |a1| = ... = |an|. |an| > |bn|. Here, Dc means Dn reached constant value.

nanostructure of the thin film deeper than 100 nm (total thickness was 420 nm) was analyzed by DWBA, where αi > αc and Bragg spots from both transmitted and reflected X-ray appeared. The lattice constant b associated with the direction normal to the surface was slightly smaller than the lateral lattice constant a. The hexagonal lattice was slightly deformed; in particular, the nanocylinders were packed into distorted hexagonal lattice that was laterally elongated and/or vertically collapsed. The distorted hexagonal lattice in polymeric films has been often observed during the drying of solvents.61 The vertical shrinkage of a BCP film occurred mainly during drying

Figure 5. qz positions of the Bragg spots from reflected (blue) and transmitted (red) beams as a function of the incident angle. Green line indicated the critical angle. The dashed lines were obtained by DWBA calculations. 8194

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Macromolecules because the motion of polymer chains in lateral direction was restrained due to the adsorption of polymer chains on the substrate. The deformation in this case remained even after thermal annealing at 170 °C for 48 h. The unrelaxed structure may be caused by strong interaction of poly(2-vinylpyridine) with the substrate. The lattice constant a remained almost constant with respect to the depth. In contrast, the constant b and the angle φ between the lattice vectors increased with decreased depth; i.e., approaching the surface, the lattice deformation was relaxed to a normal hexagonal lattice. Polymer chain mobility in a thin film is often reported to be inhomogeneous along the depth direction. A mobile layer exists (low glass transition or reduced viscosity) in the vicinity of the air/polymer interface, and a bottom layer was restricted near the polymer/substrate interface.48−54 While structural relaxation occurred near the surface because of the high mobility of the polymer chains, it was only observed in the vertical direction. The lattice constant in lateral direction was restricted or has already reached stable value in the thin film.

CONCLUSION Low-energy X-ray GISAXS measurement was performed on a BCP thin film with microphase-separated structure comprising hexagonally packed cylinders oriented parallel to the substrate. The nondestructive and low-energy GISAXS method enabled depth-resolved analysis of the periodicity and deformation of the hexagonal packing along both the depth direction and the lateral direction. FWHMs of the Bragg spots at each incident angle can be used for confirming the depth-resolved analysis. The depth dependent theoretical FWHMs were calculated using the Laue function with an attenuation decay of the X-ray intensity. Comparison of the theoretical FWHMs with the experimental values shows that depth-resolved structure analysis was successfully achieved. It was revealed that the hexagonal lattice of the cylindrical microdomains deformed along the depth direction in the bulk of the film and that the deformation of the lattice was more relaxed in the vicinity of the air/polymer surface. The relaxation near the surface is associated with a higher polymer chain mobility near the surface. We have demonstrated that low-energy GISAXS is a useful and effective way to investigate the depth dependent nanostructure of thin films. Depth dependent ordering and orientation behavior related to the dynamics of the microphaseseparated structure will be analyzed in future work, and the mechanism of these phenomena near the surface will be discussed and revealed.

ACKNOWLEDGMENTS

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01883. Figures S1−S7 (PDF)

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This research was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan, Grant-in-Aid for Scientific Research (C) (26410132, 2014). A part of this work was conducted in Nagoya University, supported by Nanotechnology Platform Program (Molecular and Material Synthesis) of MEXT. Authors acknowledge financial support from Tatematsu Foundation and Research Foundation for the Electrotechnology of Chubu. GISAXS measurements were performed at the Photon Factory of High Energy Accelerator Research Organization (approval 2014G169) and at the SPring-8 (approval 2014A7214, 2014B7264, and 2015A7214). Furthermore, authors thank Prof. Noriyuki Igarashi, Prof. Nobutaka Shimizu, and Dr. Hideaki Takagi (KEK) for their kind and dedicated support of low-energy GISAXS at the PF and Prof. Shusaku Nagano for conducting effective discussions and taking XRR and AFM measurements. NIKA package62,63 was used for 2D GISAXS data reduction. The authors thank Enago for the English language review.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (K.Y.). Notes

The authors declare no competing financial interest. 8195

DOI: 10.1021/acs.macromol.5b01883 Macromolecules 2015, 48, 8190−8196

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Macromolecules

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DOI: 10.1021/acs.macromol.5b01883 Macromolecules 2015, 48, 8190−8196