Grazing incidence wide angle x-ray scattering

The grazing incidence wide angle x-ray scattering (GIWAXS) technique can be used for probing atomic and molecular distances in crystal lattices. It is noteworthy that, the setup of GIWAXS measurements is the same as that of GISAXS measurements except for a much shorter sample-to-detector distance. This shifting allows recording the scattered x-ray beams under larger exit angles with the same detector, which is able to provide structural information on the sub-nanometer scale. In this way, single atoms are the scat-terers for x-ray rather than mesoscopic objects which are considered as form factors in GISAXS. Moreover, the regular arrays of these atoms determine the intensity of the scat-tering signal. When{hkl}lattice planes fulfill Bragg’s law at a certain angle, constructive interference occurs. Compared to XRD, GIWAXS is able to detect the preferred orienta-tion of the crystals in thin films. For example, in terms of the semiconducting polymer P3HT, the orientation distribution of its crystallites either face-on or edge-on can be quan-tified using GIWAXS. In order to better understand the correlation between the crystal orientation and scattering signals, four scenarios of GIWAXS pattern are schematically illustrated in figure 2.16.

If the sample is highly crystalline and with a direction of all crystal planes normal to the substrate (lattice spacing of d), the resulting GIWAXS pattern shows well-defined Bragg

Figure 2.16: Sketches of different lamellar stackings in films with their corresponding 2D GIWAXS data underneath in case of a)ideally vertical lamellar stacks, b)slightly disordered vertical lamellar stacks, c)textured lamellar stacks in horizontal direction and d)completely disordered lamellar stacks. The blue line packings and grey blocks indicate lamellar struc-tures and substrates, respectively. The green backgrounds in a) are guide to the eyes for the vertical lamellar stacks. Adapted from reference [88].

peaks with a distance of 2π/d only in horizontal direction, as shown in figure 2.16a. If crystal planes are not perfectly perpendicular to the substrate but with a small angular perturbation, broadening Bragg peaks in horizontal direction are present in the GIWAXS data (figure 2.16b). If all crystal planes change their direction from vertical to horizontal, the Bragg peaks shift to vertical direction accordingly, as illustrated in figure 2.16c. In the case of all crystal planes without any preferential orientation, Debye-Scherrer rings are observed in the GIWAXS pattern instead of Bragg peaks (figure 2.16d).

Unlike XRD with a specular reflection, the GIWAXS detector records the signals of diffuse scattering. In this case, the k~i is fixed and all k~f lie on an Ewald sphere. As a consequence, especially in the case of high exit angles,qx gives a non-negligible contribu-tion to the k~f. In the GIWAXS measurements, a spherical surface in q-space is projected to a 2D detector, thus the obtained GIWAXS pattern is distorted. In order to extract structural information, the raw 2D GIWAXS pattern requires to be reconstructed into the natural reciprocal space coordinates [89]. Here, qx and qy cannot be decoupled, the x axis in the GIWAXS pattern is qr instead of qx. qr is determined by

q_r =^qq_x²+q_y² (2.36) The GIXSGUI analysis package is used to retrieve the corrected reciprocal space pat-terns in the present thesis, which is based on a number of corrections related to the scattering geometry [89]. These corrections include field correction, efficiency correction, solid-angle correction and polarization correction. The field correction is caused by vari-ous photon sensitivity between different detector pixels. The efficiency correction is done due to the different lengths of traveling paths for the scattered x-rays under different exit angles. The different distances lead to different medium attenuation and absorption prob-ability for different pixels on the 2D array of the detector. Solid-angle correction takes into account that the recorded intensity depends on the solid angle Ω and the pixel area.

X-rays generated at synchrotron beamlines are typically horizontally polarized, which leads to an angular dependent intensity of the scattered beams. This impact on intensity is eliminated via the polarization correction. The detailed description of all corrections can be found in reference [90].

An example of the raw 2D GIWAXS data and the data after reconstruction is shown in figure 2.17. A wedge of missing data is observed in the reconstructed 2D GIWAXS data (figure 2.17b), which is caused by the inaccessible q-range.

Figure 2.17: a) A raw 2D GIWAXS data recorded on the detector. b) The corresponding corrected 2D GIWAXS data retrieved using GIXSGUI. The inaccessible q-range in a wedge shape is denoted by the pink curves.

In the present chapter, various techniques to characterize mesoporous titania films, tita-nia/polymer composite films and solar cells are presented. Different real- and reciprocal-space imaging methods are used to investigate the film form and structure described in section 3.1. Various spectroscopic and electronic characterizations are applied to probe the sample functionality as presented in section 3.2. All the characterization methods are introduced in detail, including instrument specifications, working principles and the principles of data analysis.

3.1 Structural characterizations

Two main types of characterization methods are employed in this work. The first type is categorized as real-space techniques, including height profilometry (section 3.1.1), atomic force microscopy (section 3.1.2) and scanning electron microscopy (section 3.1.3). Nitro-gen adsorption–desorption isotherms are used for characterization of pore size, specific surface area and pore volume (section 3.1.4). The second type comprises reciprocal-space techniques, like x-ray diffraction (section 3.1.5) and grazing incidence scattering (section 3.1.6).