The intricate nanoscopic morphology of soft materials such as block copolymer and polymer blend system successfully analyzed by small angle X-ray scatterings (SAXS). In thin films, those soft material systems have attracted great attention because of a potential for practical use of functional materials. The morphology has been revealed by grazing-incidence (GI) methods. Recently, advanced grazing-incidence technique for analysis for surface-, volume-, and material-sensitive method (high time, spatial, and/or material resolution) has been reported. Using low X-ray photon energy, tender X-ray (1–4 eV) and soft X-ray near K-edge carbon, allows probing a complex nanomorphology with those sensitivity. In this chapter, recent GI-SAXS with tender X-ray and resonant soft X-ray (GI-RSoX) will be picked up to open for discussion on new possibility of structural analyses.
- grazing-incidence X-ray scattering
- organic thin film
- block copolymer
- tender X-rays
- depth profiling
Block copolymer (BCP) composed of two (more) immiscible polymers form variety structures with the periodicity of several tens nanometer both in bulk and thin films. BCP thin film has attracted great attention as an applicable material to various fields, e.g., solar cell [1–3], nanolithography [4–6], and size-selective separation [7, 8]. In bulk state, microphase-separated structure is predicted by the Flory-Huggins interaction parameter, the degree of polymerization, and the volume fraction of blocks , whereas in thin film, film thickness [10, 11] and substrate-polymer interaction and/or also polymer-air interaction must be taken into consideration. Controlling morphology, orientation and size of the structures are necessary for practical use although phase-separation behavior of BCP in thin film becomes more complicated. This has motivated numerous orientation control methodology studies that have examined the influence of film thickness [10, 11, 13, 14], surface/or interfacial free energy [14–17], surface topology [15, 18, 19], external applied fields (shear-induced [4, 20], electric field , magnetic field , and light-driven [23, 24]), solvent vapor or thermal annealing[25–30], and directional solidification [31–33]. Since functionality and physical property are also strongly related to the structure and the mobility in the vicinity of interface, revealing structure in detail is required. Suitable characterization techniques are required to monitor the structures of BCP both laterally and in-depth. Several approaches have been used to find BCP structures. Atomic force microscopy (AFM), electron microscopy, dynamic secondary ion mass spectrometry (DSIMS), X-ray photoelectron spectroscopy (XPS), grazing incidence small angle X-ray or neutron scattering (GISAXS, GISANS), X-ray or neutron reflectivity (XRR, NR), etc. have been used to study the structure of BCP thin films. AFM can enable an access of the information only near the surface although the surface structure can be directly observed and easily understandable. Electron microscopy is a powerful tool for visually examining a cross-sectional view of polymeric thin films in two-and three-dimensional real space . DSIMS can elucidate the BCP morphology and the self-diffusion of polymer chains in thin films along a depth direction . Time-of-flight (ToF) SIMS using ion cluster beam was reported to be a particularly well-suited technique that enables the in-depth profiling of polymers [36, 37]. X-ray photoelectron spectroscopy depth profiling with C60+ sputtering revealed the ion distribution in lithium salt-doped BCP thin films [38, 39]. Electron microscopy, DSIMS, and XPS techniques are essentially accompanied by the destruction of specimen because of processing such as sectioning or etching for analysis. In particular, it is important to take into account the deformation and losing of a precise original spatial coordinate induced by sectioning and chemical reactions induced by etching in the analysis of results obtained by these techniques. In contrast, neutron reflectivity (NRR) measurements enable a practically nondestructive analysis of depth profiles and ordering of microphase-separated structure in BCP thin films [40, 41]. However, the NRR provides structural information (density profile) only in the vertical direction to the sample surface and lateral information of the structure is inaccessible. In addition, accuracy of the density profile (depth-resolved information) perpendicular to the surface becomes worse when the film thickness is large for analyzing periodicity of microphase-separated structure. Generally, NRR depth profiling is suited for very thin film (less than 100 nm) as in the above case. GISAXS is another very powerful tool for understanding the nanostructure in both vertical and lateral directions of organic thin film (BCP thin film). And GISAXS is essentially nondestructive method under the condition of the no radiation damage of X-rays [42–47]. Commonly, SAXS and GISAXS methods have been conducted using hard X-rays with energy range of 6–14 keV. However, under these conditions, the penetration depth of X-rays rapidly reaches the thickness scale of the organic materials in the vicinity of the critical angle of total reflection at the polymeric surface, which is making depth-resolved GISAXS measurements with hard X-rays totally impractical. A depth-sensitive GISAXS method using tender X-ray (1.77 keV) was first reported for the BCP thin film by Okuda et al.  and Wernecke et al. . They investigated the structural relaxation near the surface and the dynamic heterogeneity of polymer chains in thin films. At even lower X-ray photon energies, near the adsorption
In this chapter, recent advanced GISAXS experiment utilizing low-energy X-rays will be introduced. GISAXS probes the complex nano- and microphase-separated structure in polymer thin films. Especially, tuning the energy of GISAXS in the tender and soft X-ray regime allows to the tailoring of X-ray penetration depth and contrast and thereby the probing of more complex morphologies in polymer thin films. GI-RSoXS 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
2. Grazing-incidence small angle X-ray scattering
Incident X-ray beam goes into the sample surface at a very shallow angle (normally less than 1°). Scattering is measured with a two-dimensional detector as a function of the exit angle (out-of-plane angle) and the in-plane angle . The magnitude of the scattering vector is given by
As shown in Figure 1, typical sample-to-detector distances (SSD) for GISAXS are of the order of 1–2 m. In the case of small angle scattering, the two-dimensional detector probes mainly the
3. Depth-resolved structure analysis of microphase-separated structures in block copolymer thin film by grazing-incidence small angle X-ray scattering utilizing tender X-ray
3.1. Cylindrical microdomain in block copolymer thin film 
In this section, GISAXS measurement with low energy (tender) X-ray (2.40 keV) is introduced in order to precisely elucidate the depth profile of a microphase-separated structure (hexagonally packed cylinders) of a polystyrene-b-poly (2-vinylpyridine (S2VP) thin film on a silicon wafer with the cylindrical microdomains (poly (2-vinylpyridine): P2VP) oriented parallel to the substrate after the appropriate thermal annealing in vacuum. The cylindrical domains in the S2VP thin film were 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
S2VP thin film (number average molecular weight
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 where X-rays in a wide energy range from 2.1 to 15 keV (energy resolution is 2 × 10−4) is available. In this study, the energy of X-ray was set at 2.40 keV (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 c.a.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 (Hamamatsu Photonics) detectors with SDD of 2.3 m. All detectors were calibrated using lead stearate prepared in-house (
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 (wavelength λ), the critical angle, , of total reflection, and the incident angle . Surface roughness influences practically the penetration depth of X-rays because various 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. Under experimental conditions with the ideally flat surface, is given by
where is the imaginary part of the complex refractive index. The critical angle is specified as where δ is deviation from the real part of the refractive index, and are given by
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 in Figure 4. All spots were assigned to parallel oriented hexagonally packed cylinders. GISAXS patterns at approximately
The observed peak broadening can be interpreted by the change in the penetration depth. While generally such broadening can be understood by either the grain size effect and/or disordering of the crystal lattice, the FWHM in the
where 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. The FWHM of the Bragg spots of the T (11) plane in
When , X-rays travel on the surface of the film and cannot propagate in the film. Only the evanescent wave can penetrate from the sample surface into the film. In this situation, the scattering peak along the
Using above relation, the true
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 the area 2D plane detector. Yamamoto et al.  discussed the effect of the Ewald sphere curvature and performed model calculations using DWBA . At the lower energy of 1.77 keV, while the interparticle interference peaks extended and bent inward at large
The lattice constant
3.2. Orientation and relaxation behaviors of lamellar microdomains of poly(methyl methacrylate)-b-poly(n-butyl acrylate) thin film 
In this section, we investigated the phase-separation behavior of poly (methyl methacrylate-b-n-butyl acrylate) (PMMA-PnBA) forming a lamellar structure aligned parallel to the substrate after appropriate thermal annealing with GISAXS measurement. The structure development through such as degree of the lamellar orientation and relaxation of the lamellar domain spacing was inquired. Also, the GISAXS with tender X-ray for depth-sensitive analysis was conducted to reveal that the difference of the lamellar domain spacing near the surface from the bulk.
To obtain a thin film of the block copolymer PMMA-b-PnBA (
2D GISAXS (hard X-ray) patterns with various annealing times were shown in Figure 9. The pattern of as-spun sample (Figure 9a) was shaped like an ellipse, which might arise from kinetically frozen or poorly ordered structure. Partially intense scattering was observed at
As is well known, preferential wetting of surface and substrate interfaces plays an important role of orientation in thin film [12, 17]. In this case, surface energies of PMMA, PnBA, and Si substrate are 41.1, 33.7, and 77.4 ± 0.5 mJ/m2, respectively . According to the surface free energies, it will be predicted that PMMA segregates to the surface of the silicon substrate, whereas PnBA segregates to air surface. As a result of preferential wetting, the parallel orientation of lamellar structure is induced at the surface and/or the polymer/substrate interfaces and the oriented lamellae propagate into the entire film . In fact, XPS measurement proved that surface molar fractions of PnBA (within a few nanometers) were 80 mol% (repeat unit) in as-cast film and the PnBA component perfectly covered on the surface after thermal annealing with only 60 s. The segregation of each component, orientation of the lamellae, and relaxation of the domain spacing occurred in different time scale. It can be concluded that the PnBA first segregated at air surface within a minute after annealing (PMMA may segregated at the interface), second the microphase-separated structure aligned parallel to the surface, followed by relaxation of the domain spacing.
The polymer thin films have reported to have different mobility dependent on the local region, i.e., near the surface, inside, or near the polymer/substrate interface. It is quite intriguing to investigate that the depth dependence of structure difference exists, in other words, whether there are difference between the structure (orientation, morphology, d-spacing, etc.) in the vicinity of the surface and inside of the film, or not. The GISAXS measurements of PMMA-b-PnBA thin film thermally annealed for 2 h with tender X-ray was performed with various incident angles. As shown in Figure 11(a) and (b), in the case of αi < αc, the scattering (marked arrows) of the lamellar structure oriented parallel to the substrate was considerably diffuse and broaden, while in the case of αi > αc, the scattering became clear and sharp. The FWHM values of scattering peak (parallel lamellar domains) in the one-dimensional GISAXS profile obtained vertically cut at various incident angles can be simulated as the same manner of the size effect of measured region as discussed in the previous section (modified the Laue function). Thus, the penetration depth was controlled by changing the incident angle. At near the critical angle, the surface-sensitive measurement is possible as predicted from Eq. (2). The true
3.3. Evaluation of mesogen orientation in thin films of polyacrylate with cyanobiphenyl side chain 
Understanding the orientation behavior of polymer chain in the vicinity of interfaces (both substrate and free surfaces) is of practical importance in organic thin film technologies such as coating and photoresisting processes. Thus, a large amount of fundamental knowledge has been ever accumulated. It has been broadly recognized that diverse physical properties of polymeric materials in ultrathin film state are very different from those in the bulk state. Compared with the vast amount of studies for amorphous and crystalline (LC) polymers, studies on the anomaly in structure and orientation of side chain liquid crystalline polymers in ultrathin film states are rather unexplored. A large number of data related to mesogen orientation have been reported [72–78]. Accordingly, the side chain LC polymers are mostly aligned homeotropically [23, 79–81] The significant effect of the sample surface is apparent from the fact that the mesogen orientation changes to a planer orientation as the sample surface is covered by another layer or material [23, 82–84]. A cyanobiphenyl(CB)-containing polymethacrylate (PCBMA) exceptionally indicated the planar orientation regardless of the fact that the homologous polyacrylate (PCBA) oriented homeotropically . This unexpected orientation behavior is responsible for the difference in the main chain rigidity (but still no rational explanation). In these contexts, the investigation to reveal in detail the orientation of PCBA is proceeded by the GISAXS measurements by systematically changing the film thickness. Additionally, GISAXS with hard (8.05 keV) and tender (2.30 keV) X-rays were carried out.
The side chain LC polymer PCBA (chemical structure shown in Figure 12,
Figure 13 indicates GI-SAXS data measured with hard X-rays (λ = 0.154 nm) for 30 nm thick at 80 °C. For 140 nm thick film, the scattering peaks corresponding to
GI-SAXS measurements with synchrotron tender X-rays (λ = 0.539 nm, 2.30 keV) were achieved at various αi. Figure 14 shows the 2D GI-SAXS images for 30 nm thick film at room temperature. The CB mesogens at this thickness as mentioned before are oriented both in the homeotropic and planar directions (coexistence). The αc in this sample was estimated at about 0.54° for this X-ray energy. Under conditions of αi < αc (αc is about 0.54° for 2.30 keV), the scattering signals in the thin film was observed only the out-of-plane direction as shown in Figure 14a and b, where Λ is estimated as in the range less than 10–20 nm in these experimental conditions. It is apparently indicated that the CB mesogens adopt homeotropic orientation in the free surface region. When αi > αc, the out-of-plane scatterings were split into double peaks in the
From the overall data of UV-vis absorption spectroscopic  and the GISAXS measurements utilizing hard and tender X-rays, the orientation structural models of CB mesogens in PCBA thin films are schematically illustrated in Figure 15. In thick films with 140 nm, the CB mesogens are almost aligned homeotropically. However, a considerable number of the CB mesogens planarly anchored exist near the substrate (polymer/substrate interface) as revealed by GI-SAXS measurements with hard X-rays (Figure 13). At a thickness of 30 nm, the amounts of homeotropically and planarly oriented CB mesogens is comparable, where depth-resolved information is obtained by GI-SAXS with tender X-ray experiments (Figure 14). In the film thickness of 10–15 nm, the CB mesogens adopt almost planar alignment. When the film becomes further thinner from the critical level of 7 nm, the planar alignment near the surface disappears where the liquid crystal structuring (antiparallel packing of the CB mesogens) is lost.
4. Grazing-incidence resonant soft X-ray scattering 
The GI-RSoXS is a novel technique, which is in particular suited for more complex system such as multicomponent block copolymer and polymer blend films. Resonant soft X-ray scattering has already been successful for probing morphology and spatial structure in organic photovoltaic (OPV) systems [85, 86] and triblock copolymer system . GI-RSoXS allows for detecting near surface and inner structure separately at fixed incident angle by tuning X-ray photon energy because the penetration depth of the X-ray beam is drastically affected by the change in X-ray photon energy across the adsorption edge. Adsorption
GI-RSoXS measurements with soft X-ray were conducted at the synchrotron beamline 220.127.116.11 of the advanced light source (ALS) at the LBNL in Berkeley (USA) [88, 89]. Due to the high adsorption of soft X-ray in air, full setup (sample and X-ray detector) was kept in high vacuum. The energy of X-ray was used in the range of 280–320 eV (λ: 4.4–3.9 nm). Sample-to-detector was 18.5 cm that was sufficient for detecting length scale in the range from 21 nm to a few micron meters. An incident angle αi = 2°, which is near the critical angle αC of 2.3° for 280eV and 1.5° for 283 eV. The both polymers (P3HT and MEH-CN-PPV) were dissolved in chloroform. The thin film of polymer blend was prepared by spin coating from the solution; the thickness was controlled to be about 70 nm. The films were annealed at 200 °C for 10 min in air without degradation. The NEXAFS spectroscopy measurement was conducted for taking the wavelength dependent refractive index (
Figure 16a shows the X-ray energy dependence of the dispersion δ and the adsorption β of P3HT and MEH-CN-PPV homopolymer. The spectra of respective homo polymers are different. NEXAFS spectra of the blend system with different blend ratio can be obtained by a linear superposition of the spectra of P3HT and MEH-CN-PPV homopolymer weighted with the corresponding blend ratio. The dispersion δ spectra of P3HT and MEH-CN-PPV reveal positive and negative values and differ strongly depending X-ray energy. Therefore, the scattering contrast depends on the X-ray energy. Using the adsorption β spectra, the penetration depth Λ of the soft X-rays into the blend film is calculated as shown in Figure 16b. Figure 17 indicates the GI-RSoXS patterns of as spun P3HT/MEH-CN-PPV bulk heterojunction films with a P3HT content of 70 wt% for different energies from 280 to 289 eV (wavelength of X-rays from 4.43 to 4.29 nm). Although the wavelength is varied by only 3%, the scattering patterns significantly change. For energy below 284 eV, an intensity oscillation in vertical direction is observed, which comes from the correlated roughness originating from the interference of scattered X-rays from different interfaces. The correlated roughness vanishes with increasing energies of the X-rays. It indicates no scattering signal from the substrate interface is detected and X-ray penetrates near the surface as shown in Figure 17. The low scattering intensity of GI-RSoXS at 284 eV (Figure 17c) is due to the very low incident intensity at this energy. The reduction of the intensity at 286 eV (Figure 17e) can be ascribed to the significant low contrast between P3HT and MEH-CN-PPV at this energy. Thus, the surface structure is accessible at 286 eV. The change in the total scattered intensity was attributed to the changed contrast conditions from the contrast variation.
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