Grazing Incidence Small Angle X-Ray Scattering as a Tool for In- Situ Time-Resolved Studies

With the advent of third-generation synchrotron sources and the development of fast two-dimensional X-ray detectors, X-ray scattering has become an invaluable tool for insitu time-resolved experiments. In the case of thin films, grazing incidence small angle X-ray scattering (GISAXS) constitutes a powerful technique to extract morphological information not only of the thin film surface but also of buried structures with statistical relevance. Thus, recently in-situ GISAXS experiments with subsecond time resolution have enabled investigating the self-assembly processes during vacuum deposition of metallic and organic thin films as well as the structural changes of polymer and colloidal thin films in the course of wet deposition. Moreover, processing of thin films has also been investigated in-situ employing GISAXS. In this chapter, we review the current trends of time-resolved GISAXS studies. After an introduction to the GISAXS techni‐ que, we present exemplary results of metallic and organic thin film preparation, wet deposition of polymer thin films and self-assembly of colloidal thin films, as well as examples of thin film modification in, e.g., microfluidic channels and within working devices. Finally, an overview of the future perspectives in the field is provided.


Introduction
Nanostructures have become commonly used in our daily lives because of the novel properties arising at the nanoscale. These are mainly associated to the object size offering a higher surface-to-volume ratio than macroscopic entities and, thus, surface processes become more and more crucial as the material size is reduced. Furthermore, during the last half century several ways of manipulating the materials at the nanometer scale have been developed to control the nanostructure morphology on demand via either building up the nanostructures by atomic manipulation or exploiting self-assembly concepts. The latter presents clear advantages over atomic manipulation such as less demanding fabrication steps and easier scale-up for industrial production. Nevertheless, much is yet to be understood concerning self-assembly. In this sense, apart from the manipulation of materials at the nanoscale, an appropriate and accurate characterization of nanostructures is crucial, especially for studying the kinetics both during fabrication and processing of the nanostructures.
To properly characterize nanostructures, two questions need to bear in mind: what is the size/ shape of the nanostructure and how do they separate from each other. The former is critical since nanostructure geometry strongly influences, e.g., the geometric confinement of the electronic structure [1], the catalytic activity [2,3] or the optical properties [4,5]. The latter is important since different physical properties may arise from particular nanostructure arrangement or in the space confined between the nanostructures, e.g., highly ordered arrays of plasmonic nanostructures present a collective plasmonic behavior [6], an efficient arrangement of the nano-objects may expose higher surface area on a macroscopic level for catalysis applications [7] or polymers within nanostructured media may show different glass transition temperatures and chain mobility due to confinement [8].
Within a non ideal material system, the size of the nanostructures and the spatial arrangement present a distribution over micro/macroscopic regions. Thus, the collective effects of nanostructured objects call for sound statistic evaluation. In this respect, grazing incidence small angle X-ray scattering (GISAXS) is nowadays one of the most interesting techniques for studying the morphology of nanostructured thin films. As its counterpart, transmission SAXS [9], it is sensitive to the size and shape of the nanoparticles and to the correlation distances between them, being capable of resolving objects and distances ranging from few nanometers to several hundreds of nanometers, in real space. In contrast to SAXS, GISAXS inherently presents high surface sensitivity as a consequence of the measurement geometry employed. In GISAXS, the incident X-ray beam impinges the sample at shallow angles, thus total external reflection on the surface may take place. In addition, this implies that the beam footprint on the sample probes macroscopic areas which, together with the nature of reciprocal space techniques, ensure that high sampling statistics is achieved. GISAXS was first demonstrated by Levine et al. using a lab source [10]. However, the full potential of GISAXS is realized when a synchrotron is used as X-ray source. This is due to several reasons. First, a high photon flux is required to probe the surface structures, which may be only present in small amount in comparison to the bulk substrate, thus presenting a weak scattering signal; second, highly collimated beams are demanded to improve the reciprocal space resolution, thus the low emittance, small divergence, and partially coherent beams provided by synchrotron radiation sources are in great favor; third, synchrotron sources provide tunable X-ray wavelength, which may be used to probe the chemical composition in parallel to exploring the morphology.
The high X-ray photon flux of synchrotron sources extremely diminishes the acquisition time of a GISAXS pattern. This fact, along with a high flexibility in sample environments-e.g., vacuum chambers, liquid cells, heating stages, vapor exposure chambers, etc.-makes GISAXS a very powerful tool for acquiring morphological information on kinetic processes, which is extremely relevant to elucidate self-assembly processes. Additionally, the combination of parallel characterization techniques-e.g., optical spectroscopy and microscopy, electrical and magnetic characterization-allows correlating the structural information to the properties of the thin films, of utmost importance for tailoring the thin film functionality.
However, to carry out in-situ GISAXS, the high quality X-ray beam offered by synchrotron sources is not sufficient. The development of the 2D pixel detector, especially single photon counter, has played an important role. The high quantum efficiency and fast read-out time of 2D photon-counting pixel detectors can be translated to lower acquisition times-in comparison with CCD detectors; however, at present, CCD cameras offer small pixel size, implying higher resolution in reciprocal space. The low acquisition time renders a faster capture of the morphological features and the fast detector read-out time and efficiency enable high acquisition rates, thus it is possible to promptly track morphological development and/or modifications.
In this chapter, we will present the current trends of in-situ time-resolved GISAXS investigations during thin film preparation and processing. The chapter is structured as follows. Section 2 briefly introduces the GISAXS theory and analysis of GISAXS patterns. In Section 3, selected examples of in-situ GISAXS studies during the vacuum deposition of metals and organic thin films, as well as in-situ GISAXS investigations of wet deposition processes, are presented. Some exemplary studies of thin film processing and in-operando devices in which the use of in-situ GISAXS has resulted essential are compiled in Section 4. Finally, the conclusions and future perspectives of the field, according to the authors' opinion, are summarized in Section 5.

Grazing incidence small angle X-ray scattering
In this section, the basics of GISAXS will be shortly described. For more detailed information on the GISAXS theory, the readers are referred to [11][12][13].

Geometry, index of refraction and penetration depth
The main particularity of GISAXS lies on the geometry employed. Whereas in SAXS a transmission geometry is used, in GISAXS the X-ray beam impinges on the sample surface under a shallow incident angle, α i , typically of tenths of a degree. The intensity scattered by the sample is then collected with a two-dimensional (2D) detector as a function of the exit, α f , and out-of-plane, ψ, angles being the scattering plane that defined by the incident and specularly reflected X-rays. Typical sample-to-detector distances are in the range of 2-5 m and typical values of the scattering vector modulus q are 1-0.01 nm -1 , i.e., structures in the range of one to several hundred nanometer size in real space are probed by GISAXS.
The coordinate system usually selected in GISAXS presents the x-axis in the direction of the X-ray beam, the y-axis parallel to the sample surface and the z-axis along the surface normal. 1 The scattering geometry is depicted in Figure 1. Figure 1. Sketch of the GISAXS scattering geometry. The sample is inclined by a small angle α i with respect to the incoming X-ray beam and the diffuse scattering is recorded using a 2D detector as a function of the exit angles α f and ψ. Typical sample-to-detector distances range from 2 to 5 m. Experimentally, the specular and the direct X-ray beams are commonly blocked by beamstops (the specular beamstop is the dark blue circle in the GISAXS pattern shown whereas the direct beamstop is not shown) to prevent the detector from oversaturation due to its strong intensity. Within this coordinate system, the scattering vector, q → , i.e., the wave vector transfer due to the scattering event, in the case of monochromatic X-rays with an incident wave vector k → i and wave number k 0 = 2π/λ scattered along the k → f direction is given by Due to the small incident and exit angles involved in the GISAXS geometry a description of the sample based on a mean refractive index is sufficient and basically scattering arises from the variations in refractive index 2 1 For reasons out of our knowledge, the axes of the coordinate system commonly employed, and more often found in the literature, form an inverse trihedral angle-i.e., the axes are defined by the vector product , where, and represent the axis unit vectors-instead of the usual direct trihedral angle. Anyway, since all the angles involved in GISAXS geometry are small, q x is negligible (Eq. (1)) and this axis selection is not particularly relevant.
where δ(λ) and β(λ) represent the dispersion and absorption parts of X-rays, respectively, and are given by the following expressions: in which r e = e 2 /4πε 0 m e c 2 is the classical electron radius, λ the wavelength, ρ the material mass density and M k the atomic mass. f k 0 is the nonresonant term of the atomic scattering factor and can be approximated by the number of electrons Z k whereas f ′ k and f ″ k are the dispersion corrections. The summations are performed over all k atoms within the unit cell, molecule or, in the case of polymers, repeating unit.
Since diffuse scattering can be ascribed to changes in the refractive index any type of surface roughness or electronic contrast variation gives rise to diffuse scattering which contains the morphological information of the probed film.
On the other hand, in the case of X-rays the refractive index is less than unity, implying that total external reflection takes place for angles below the critical angle α c (λ) of the material, which is given by The diffuse scattering at α i,f = α c presents a maximum that is referred to as the Yoneda peak [14] and its position is dependent on the material 3 , as is evident from Eqs. (3) and (5). The X-ray penetration depth varies from several nanometers, for incident angles below α c , to several microns, for incident angles above α c . In the ideal case of a perfectly flat film the penetration depth, Λ, defined as the depth at which the X-ray intensity is attenuated by 1/e, for α i , α c ≪ 1 and α i = α f adopts the following expression 4 [16,17]: where β is the imaginary part of the refractive index. Thus, by varying the incident angle different film depths can be probed (Figure 2).
From the scattering geometry alone, two major advantages of GISAXS over standard microscopic techniques are easily inferred. First, due to the small incident angle used, scattering comes from all the illuminated area within the X-ray footprint-in the order of several mm even for microfocus GISAXS (μGISAXS), i.e., GISAXS performed with X-ray beam sizes of few tenths of microns or lower in both the horizontal and vertical directions-thus providing information of statistical relevance. Second, information not only from the surface but also from buried structures is accessible simply by tuning the incident angle of the X-ray beam with respect to the sample surface normal.

Scattering intensity: form factor and structure factor
The fact that GISAXS is performed at incident angles close to the critical angle implies that reflection on the surface can occur and thus multiple scattering effects take place. As a consequence the Born approximation (BA) is no longer valid and the diffuse scattering is typically analyzed within the framework of the distorted-wave Born approximation (DWBA) to account for reflection/refraction effects. Nevertheless, the basic concepts from the analysis of transmission scattering still apply, namely the use of a form factor and a structure factor. At present, several software packages are available for modeling of GISAXS data employing the DWBA [18][19][20][21].
In the simple BA, the form factor is the Fourier transform of the shape function of the scattering object In the DWBA, for the case of a simple object located on a solid substrate, this form factor is replaced by the coherent sum of four terms to take into account different scattering events that involve the reflection of the incident or scattered X-ray beam on the substrate. 5 Thus, the form factor adopts the following expression a a = - being R(α i ) and R(α f ) the Fresnel reflection coefficients of the substrate. These four terms are schematically represented in Figure 3. In this case-where the BA is valid and reflection/refraction effects can be neglected-the socalled effective layer approximation can be used and the differential cross-section for diffuse scattering can be written as [24,25]: where C is the illuminated surface area, λ the wavelength, T i,f the Fresnel transmission functions and P(q → ) is the diffuse scattering factor. Within this simplification, the diffuse scattering factor can be expressed in terms of the product of a form factor F (q → ) of individual scattering objects and a structure factor S(q → || ) that accounts for the spatial arrangement of the scattering objects on the substrate surface and the interference between individual scattering events. 6 The structure factor is the Fourier transform of the so-called pair correlation 5 In the more general case, transmission has to be taken into account and the Fresnel transmission coefficients appear also in the expression of the form factor. See, e.g., [22,23]. 6 For this reason, the structure factor, S(q → || ), is also often called interference function.
function g(r) that describes the spatial arrangement of scattering entities in real space and several ad hoc pair correlation functions can be used to analyze the GISAXS data. 7 The diffuse scattered intensity I (q → ) for a lateral electron density fluctuation on the surface can be then expressed as In highly diluted systems S(q → || ) tends to 1 since there is no interference between the scattered photons. In these cases, the scattering pattern-being only proportional to F (q → ) reflects the shape of the scattering objects. Opposite, in the case of concentrated systems F (q → ) and S(q are strongly correlated.

Coupling of form and structure factors: approximations
Although sometimes useful for the analysis of horizontal line cuts-i.e., the intensity distribution as a function of q y at constant q z extracted from the 2D scattering pattern-the expression derived for the diffuse scattering intensity in the previous section (Eq. (10)) is a crude simplification since small angle scattering is comprised of a coherent term, which is the product of the form factor and structure factor, and an incoherent one that appears as a consequence of polydispersity in the size distribution of the scattering objects. The incoherent term weaves the form and structure factors and is very difficult to evaluate analytically, thus several approximations have been developed to consider the correlation between the scattering objects and their spatial positions.
The simplest one is the so called decoupling approximation (DA) that assumes that there is no correlation between the kind of scattering object and its position. This approximation is usually applied when the size polydispersity is small or the surface density of scattering entities is low (Figure 4(a)).
Opposite to DA, when the polydispersity is high, a full correlation of the size of the scattering object and its position is assumed in the local monodisperse approximation (LMA). LMA considers that within the coherence length of the X-ray beam neighboring objects present the same size and shape, i.e., the polydisperse scattering objects are clustered in monodisperse domains whose scattering intensities are incoherently summed up (Figure 4(b)).
In between these extreme cases, the size-spacing correlation approximation (SSCA) [26] was developed to account for more realistic correlations between the size and separation of the scattering entities. Its formalism is derived from the paracrystal theory and introduces a partial correlation of sizes and positions in a probabilistic way. Shortly, within the SSCA, given a scattering object of distinct size and position and a description of the size polydispersity by a statistical function, the probability of finding neighboring objects of particular size and positions with respect to the first scattering object is obtained, considering a particular probability distribution. Thus, both size-dispersion and position disorder are propagated statistically along the arrangement of scattering entities and long-range order is gradually destroyed in a probabilistic way (Figure 4(c)).

In-situ GISAXS during deposition processes
During the last decade or so, GISAXS has been established as a very powerful technique to reveal the kinetics of deposition processes for thin film preparation employing different approaches. In particular, GISAXS is strongly contributing to reveal the mechanism of thin film growth and self-assembly both for vacuum and wet deposition processes that are relevant not only from a fundamental point of view but also for technological development. GISAXS presents two decisive advantages over standard microscopic techniques for the investigation of the growth kinetics and self-assembly: first, it provides averaged information over a large sample area-the beam footprint on the sample-thus the information acquired is of statistical significance; second, time resolutions down to several milliseconds are accessible due to the high X-ray intensities offered by third-generation synchrotron sources and the development of fast 2D X-ray detectors, thus fast kinetic processes can be studied.
In this section, exemplary results will be presented illustrating the strong capabilities of in-situ time-resolved GISAXS for the investigation of the stages governing the kinetics of thin film growth and self-assembly, both phenomena of high importance to gain control over the processes so as to tune the thin film properties to the required functionality.

Vacuum deposition of nanostructured metallic thin films
Vacuum deposition of nanostructured metallic films constitutes a very important technological and research field with applications ranging from coatings for antibacterial activity and catalysis to plasmonics, optoelectronics and sensors. In most cases, the morphology is closely related to the functionality of the film. Therefore, it is extremely important to achieve a deep understanding of the growth mechanism and morphological development of the nanostructures so as to allow for tailoring the nanostructured metallic thin film to the desired application.
In order to investigate in-situ vacuum deposition processes using GISAXS, deposition chambers have been specifically designed to be installed at synchrotron beamlines [27][28][29]. In addition, a growing amount of systems have been investigated during the last years-some examples can be found in [30][31][32][33] -from which, in the following, only some selected results will be discussed.
In-situ μGISAXS has been applied to study the sputter deposition process of both Au and Ag on SiO x with time resolutions of 15 and 100 ms, respectively [34,35]. The growth kinetics of these two systems has been probed to proceed in a similar way and in-situ μGISAXS has contributed to elucidate the growth regimes and the associated kinetic thresholds of the systems. The analysis of the temporal evolution of the main scattering features -namely the position and full-width-at-half-maximum (FWHM) of the out-of-plane scattering peak (line cuts of the 2D scattering pattern along q y at constant q z ) together with the evolution of the scattering profile of the so-called detector cuts and off-detector cuts (line cuts of the 2D scattering pattern along q z at q y = 0 and at constant q y ≠ 0, respectively) -led to identify four different growth stages dominating the morphological development of Au and Ag thin films, from the nucleation phase to the formation of a complete layer ( Figure 5). . The evolution of the out-of-plane scattering peak from large q y toward lower values is related to an increase in the mean distance between Ag nanoclusters as a consequence of the increase in clusters size. When the percolation threshold is reached, the peak gets arrested at a nearly constant value. A quantitative analysis of the mean distance D between nanoclusters can be performed from the peak maximum applying q y ≈ 2π/D. (c) Off-detector (along q z ) line cuts versus sputtered thickness at q y = 0.112 nm −1 . As the deposition proceeds, the maximum intensity changes from the Si Yoneda peak to the Ag Yoneda peak and vertical modulations related to the formation of Ag layers appear. The growth kinetics of Au during sputter deposition, apart from being of industrial and technological relevance, is of significant importance from a basic point of view. To simulate the complete 2D μGISAXS patterns along the deposition process, a geometrical model based on the 2D hexagonal paracrystalline arrangement of hemispherical clusters was developed [34] allowing for extracting important parameters such as the surface coverage, film porosity or cluster density, thus enabling to predict morphology-dependent properties of the thin film such as the optoelectronic response.
Since the growth of Ag on SiO x proceeds in a similar manner, the geometrical model proposed by Schwartzkopf et al. [34] has been also successfully applied to the deposition of nanostructured Ag thin films on SiO x for surface enhanced Raman spectroscopy (SERS) (Figure 5(d)) [35]. A key point in SERS, whose underlying main mechanism is the enormous enhancement of the local electromagnetic field in the vicinity of nanostructured noble metal surfaces due to localized surface plasmons, is the gap between nanostructures. At the nanostructure gapsthe so-called "hot-spots" -the electromagnetic enhancement is maximum. In this case, in-situ μGISAXS during sputter deposition of Ag allowed not only identifying the main growth regimes and thresholds but also to correlate the developed morphology to the SERS activity. By modeling the full 2D μGISAXS patterns within the DWBA and the SSCA, a maximum SERS enhancement was found for a mean gap of 1 nm between Ag nanoclusters, corresponding to an effective film thickness of 5.6 nm.
On the other hand, the deposition kinetics of Au on a quasi-regular hexagonal array of selfassembled cadmium selenide (CdSe) quantum dots has also been investigated by in-situ μGISAXS [36]. Opposite to the growth of Au and Ag on SiO x , in the early deposition stage the out-of-plane peak did not change in position but remained fairly constant. The deposition of Au only led to an increase in electronic contrast, thus, of the diffuse scattering intensity produced by the underlying array of CdSe quantum dots. This implies that the quantum dots act as nucleation sites for Au growth. Subsequently, lateral growth and coalescence of Au/ CdSe-dot clusters were observed forming a compact Au/CdSe-dot layer. Finally, Au growth proceeded in the surface normal direction developing a capping layer on the CdSe quantum dots array.
In-situ GISAXS has also contributed to shed light on an intriguing issue during the growth of metallic thin films, namely the influence of the chemical affinity between the metal and the substrate on the deposition kinetics and thin film morphology. This is highly important in the case of, e.g., the deposition of metallic electrodes on organic solar cells or light emitting diodes where, in some cases, the electrodes represent the limiting factor in device performance. The great capabilities of in-situ GISAXS studies for this purpose has been demonstrated during the sputter deposition of Al and Ag on tris(8-hydroxyquinolinato)aluminum (Alq3), a key material in organic light emitting diodes. Alq3 presents a strong chemical interaction with Al whereas it interacts weakly with Ag, which translates into different growth mechanisms. In the case of Al deposition, three different stages of growth were identified and modeling of the 2D patterns revealed the formation of Al nanopillars after diffusion of Al in Alq3 and subsequent metal complex agglomeration [37]. On the other hand, without diffusing into the Alq3 thin film, Ag presents a morphological transition from truncated sphere clusters to cylindrical nanostruc- tures upon surpassing the Ag percolation threshold at an effective film thickness of 5.0 nm (Figure 6), which was attributed to the different Ag-Ag and Ag-Alq3 interactions [38]. The differences in metal interaction and nanocluster diffusion coefficient on different materials can be exploited to tailor the thin film morphology. In this sense, an interesting approach consists in employing polymer thin films as templates in the nanoscale, given the known ability of block copolymers to spontaneously form nanostructures due to phase segregation. In general, when employing vacuum deposition of metals on organic thin films, in a first deposition stage, the metal diffuse into the film which influences the subsequent growth kinetics and, in the case of block copolymers, a selective wetting of the metal on one of the domains is commonly observed, which is ascribed not only to the different metal-polymer interaction but also to the differences in metal diffusion in each of the blocks. From in-situ μGISAXS measurements, the surface diffusion coefficient of Au on polystyrene (PS) has been extracted and a correlation of the developed Au morphology with the optical properties of the film could be achieved by combining μGISAXS with real-time UV-Vis spectroscopic measurements during the growth [39].
On the other hand, Metwalli et al. [40] have taken advantage of the selective wetting of Co on spontaneously nanostructured polystyrene-block-poly(ethylene oxide) (PS-b-PEO) to prepare ordered Co nanoclusters along highly oriented PS domains. The morphology of the polymer thin film consisted of alternating highly oriented crystalline PEO and PS domains with a periodicity of around 30 nm and the in-situ GISAXS experiments demonstrated that selective wetting occurred below the Co thin film percolation threshold. They also elucidated the growth kinetics of Co on the block co-polymer nanostructured template.
A thorough study on the nanostructure development of transition metals on a PS-b-PEO template has also been recently reported [41]. It has been clearly revealed that the growth of Au, as a fairly inert element, was not influenced by the template, whereas Ag demonstrated slightly improved wetting on the PS domain, forming clusters. In the case of reactive metals, e.g., Fe, Ni, and Pt, well-defined and uniform nanocluster patterns were grown selectively on the PS domains. Additionally, by performing in-situ GISAXS experiments, it has been found that the substrate temperature plays an important role in shaping the metal clusters, showing that above the glass transition temperature, T g , of PS, Ag clusters become more irregular. In addition, for Fe, flat nanodots with a low surface-to-volume ratio morphology were grown at substrate temperatures above T g whereas a higher surface-to-volume ratio morphology is obtained for a substrate at room temperature during deposition. This is ascribed to the changes in diffusion coefficient with temperature, so that above T g a higher diffusion coefficient of metal atoms and clusters during the deposition led to a lower surface-to-volume ratio cluster morphology.
The complicated growth kinetics of hierarchical anisotropic gold nanostructures on polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) thin films has been also studied with insitu GISAXS [42]. An anisotropic shape of the deposited metal clusters was achieved by employing a glancing angle deposition (GLAD) geometry. In GLAD, the deposition plume is positioned at an oblique angle regarding the sample surface, which produced nonsymmetric Au clusters and its anisotropic shape manifested as nonsymmetric 2D scattering patterns with respect to the scattering plane (q y = 0). In addition, a hierarchical ordering of the anisotropic Au was achieved benefiting from the selective wetting of Au on the PS domains. The anisotropy of this hierarchical nanostructure was also reflected in the anisotropic optical response of the system.

Vacuum deposition of organic thin films
Organic thin films are especially important since they are increasingly used in devices. In particular, organic semiconductors are employed in organic light emitting diodes (OLEDs), organic field-effect transistors (OFETs), and organic solar cells (OSCs). However, the basic processes of molecular thin film growth are still far from being understood and connecting molecular and nanoscopic/microscopic processes such as molecular diffusion and island size evolution, remains a major challenge. To this purpose in-situ GISAXS, being a non-invasive technique, is increasingly contributing.
As in the case of vacuum deposition of metals, several organic deposition chambers have been designed and built so as to perform in-situ X-ray scattering and/or diffraction measurements at synchrotron beamlines [43,44].
To study these particular systems, in-situ grazing incidence X-ray diffraction (GIXD) and insitu X-ray reflectivity (XRR) are most commonly applied [45][46][47][48], though the information provided by in-situ GISAXS is also very valuable since the dimensions probed are different. Whereas GIXD provides access to the crystal structure and molecular arrangement, GISAXS gives complementary information on the island shape and island-island distances as well as on the island electron density. Therefore, the combination of both techniques provides the necessary information to make a link between the molecular and micrometer size crystallite regimes.
These systems are usually investigated in the so called anti-Bragg geometry, i.e., at incident angles so that the specular peak corresponds to the anti-Bragg point of a given (h k l) permitted Bragg reflection of the molecular crystalline structure. The anti-Bragg points correspond to | q → anti−Bragg | = 1 2 | q → Bragg | and are especially surface sensitive 8 [17]. From a practical point of view, for a selected (h k l) Bragg reflection, α i is chosen so that at α i = α f and ψ = 0 − i.e., the specular peak position-the following relationship is satisfied Note that in Eq. (11) only q z is involved since for specular reflection q x = q y = 0 (Eq. (1)).
At this particular geometry, the specular intensity presents an oscillatory behavior during the growth-the so-called growth oscillations-which arises from destructive interference between neighboring odd and even monolayers (MLs) -lattice planes-so that the scattering from the first, third, fifth ML is cancelled by the growth of the second, fourth, sixth ML, etc. [49]. In the common case of (initial) layer-by-layer growth in organic heteroepitaxy, the periodicity of the oscillations consists in 2 MLs although interference between reflections at the growing surface, the substrate and the interfaces between different film layers can lead to more complex oscillatory behavior. 9 Through correct modeling of the growth oscillations, more complicated epitaxy growth models can be derived making assumptions about the intralayer and interlayer diffusion [50]. Therefore, additional information for the refinement of these models is very useful and can be obtained by performing GISAXS at the anti-Bragg geometry, which allows concurrently following the changes in the specular intensity-the growth oscillations-and the diffuse scattering [51][52][53][54].
The abovementioned geometry has been applied to investigate, e.g., the growth of multilayers of fullerene C 60 molecules on mica in real time [55]. From the growth oscillations, a layer-bylayer growth was deduced whereas from the in-situ μGISAXS data the mean island distance was extracted and converted into surface island density assuming a hexagonal island arrangement. Interestingly, the GISAXS out-of-plane peaks present intensity oscillations with a period of 1 ML, in contrast to the 2 ML period of the specular intensity at the anti-Bragg point (Figure 7). This is due to the fact that diffuse scattering occurs only for uncomplete layers since this is the situation where a lateral variation in electron density-or, in other words, in refractive index-is present, whereas the growth oscillations are due to interference from the reflections at layer interfaces-plus at the substrate and at the growing layer-i.e., diffuse scattering is probing lateral contrast whereas the specular peak probes the structures in the surface normal direction. Through kinetic Monte Carlo simulations and a comparison to the experiments, values of the energy barriers were obtained-namely, the diffusion barrier and lateral binging energy for intralayer events and an Ehrlich-Schwoebel barrier for interlayer diffusion-and, more importantly, this set of parameters was demonstrated to be sufficient to describe the growth of a C 60 layer on underlying C 60 layers, of crucial importance so as to predict the growth dependence on the deposition rate and substrate temperature. The simultaneous acquisition of the specular intensity and GISAXS signal has also been applied to in-situ investigate the molecular diffusion and island evolution during the growth of diindenoperylene (DIP, C 32 H 16 ) on SiO x [56]. Opposite to the C 60 molecule, DIP presents shape anisotropy imposing additional degrees of freedom-tilting and bending-which increases the complexity of the growth process. In this case, above a surface coverage of 3 MLs the GISAXS out-of-plane peak oscillations vanished and the peak position remained constant, meaning a constant island center-to-center distance. This is a clear signature of a transition between a layer-by-layer to a three dimensional (3D) growth, i.e., formation of molecular islands with a fixed surface island density. Additionally, effective activation energies for island nucleation of DIP on SiO x and of DIP on DIP could be extracted from the mean island diameter -derived from the diffuse scattering peak position-at 0.5 ML and 1.5 ML surface coverage, respectively, by varying the deposition substrate temperature.
Another organic semiconductor with rod-like morphology whose growth has been in-situ investigated performing GISAXS using the anti-Bragg geometry is N,N'-dioctyl-3,4,9,10perylene tetracarboxylic diimide (PTCDI-C 8 , C 40 H 42 N 2 O 4 ) [57]. It has been shown that PTCDI-C 8 , as is the case for DIP, underwent a transition from a layer-by-layer growth to a 3D growth but in a smoother fashion. This manifested both as a slow increase in the mean roughness of the completed MLs-derived from the growth oscillations-as well as in a smooth leveling off of the island density-derived from the out-of-plane GISAXS peak position by assuming a hexagonal arrangement of islands. Moreover, the island density extracted from the diffuse scattering at different substrate temperatures, allowed demonstrating higher molecular mobility of PTCDI-C 8 on PTCDI-C 8 than that of PTCDI-C 8 on SiO x , which is responsible for the decreased island density observed in upper MLs.

Wet deposition of polymer and colloidal thin films
Wet deposition encompasses a collection of different methods for the fabrication of thin solid films from a liquid solution and/or suspension as precursor. All of them exploit self-assembly concepts to prepare thin films such as colloidal crystals, thin polymer films and nanocomposites with applications ranging from photonic crystals to polymer solar cells and superhydrophobic or superhydrophilic coatings. During wet deposition, the interaction between the suspended particles-or the dissolved compounds-together with the liquid flow-responsible of internal mass transport-govern the drying kinetics and self-assembly. Hence, tuning these parameters makes it possible to control the self-assembly, thus adjusting the morphology of the dried thin film (ideally) on demand.
Grazing incidence X-ray scattering (GIXS) techniques has been applied to study wet deposition processes such as solution casting [58,59], spin-coating [60], dip-coating [61,62], and blade coating [63]. Nevertheless, although these deposition methods are very useful for device fabrication at research scale, they are not easily scaled-up and/or they are restricted to specific substrate geometries. In this sense, it is important to explore other wet deposition methods of potential industrial relevance.
In recent years, spray coating is gaining interest due to its easy scale-up and integration into production lines as well as to its lack of substrate geometry/size constrains. Moreover, it has already been successfully applied to fabricate operating devices such as polymer solar cells [64][65][66]. Nevertheless, although there are evident similarities to, e.g., solution casting, the drying kinetics present some particularities still not well understood. To this respect, GISAXS has been used to study the self-assemble of colloidal particles during spray coating [65,67,68]. In particular, Herzog et al. [67] were able to identify three different stages during the spray deposition of polystyrene (PS) nanoparticles and subsequent drying corresponding to the formation of a structureless thin liquid film, which subsequently breaks up into small droplets allowing for possible transient nanoparticle ordering and a final freezing of a self-assembled colloidal nanostructure once the solvent is fully evaporated, respectively. These three stages were revealed in the in-situ μGISAXS patterns as first, a decrease in the overall scattered intensity due to the homogeneous liquid film right after a 100 ms spray shot; second, an increase and broadening of the Yoneda peak ascribed to the homogeneity loss of the liquid film that breaks into small droplets as the solvent evaporation proceeds and last, the emergence of well-defined out-of-plane symmetric peaks regarding the scattering plane (Figure 8). In addition, controlling the evaporation rate by adjusting the substrate temperature the assembly process of the nanocolloids can be managed to achieve different film morphologies, what has been investigated in-situ by μGISAXS as well [68]. Apart from spray coating, another interesting approach for large scale low-cost production of organic photovoltaic (OPV) devices is inkjet printing, a method that has drawn considerable attention from an industrial point of view as the field of organic flexible electronics is maturing. As in the case of spray coating, GIXS has been applied to in-situ investigate the structure development during inkjet printing of, e.g., conductive polymer thin films widely used as electrodes in OPV devices [69] as well as of the active layer in bulk-heterojunction (BHJ) polymer solar cells [70]. The film morphology in OPV devices has a direct relationship with its performance and the combination of in-situ wide-and small angle scattering (GIWAXS/ GISAXS) allowed developing qualitative models of the structural evolution of the semicrystalline polymer thin films morphology.
Finally, although it does not present the current large-scale production promises of spray coating and inkjet printing, an interesting approach for wet deposition consist in employing microfluidics, which may be critical for lab-on-chip applications. Here, the peculiarity lies in the nondrying nature of the deposition, i.e., the self-assembly process on the substrate does not take place during solvent evaporation but at the liquid-solid interface during liquid flow. In order to in-situ follow deposition processes using microfluidics by GISAXS-among others; see Section 4-special flow cells have been designed [71]. In this kind of experiments, it is extremely important to adjust the X-ray beam footprint on the substrate to the size of the fluidic channel so as to prevent an overillumination of the sample not in contact with the fluid, thus minimizing undesired signal that could obscure the accessible information. Therefore, the use of μGISAXS becomes essential [72]. This specific setup has been used to investigate the attachment of Au nanoparticles to a polymer thin film (Figure 9) and different stages could be identified, namely the dried polymer film before the liquid inlet was opened (denoted as 1 in Figure 9), a wetted film by the liquid vapor once the liquid inlet was opened (denoted as 2 in Figure 9) and the attachment of Au nanoparticles once the liquid flow reached the probed thin film position (denoted as 3 in Figure 9). Moreover, the increase in intensity of the out-of-plane peak as the experiment proceeded indicated a cumulative deposition of the Au nanoparticles from which it is possible to analyze the deposition kinetics.

In-situ GISAXS during thin film processing
In addition to the aforementioned deposition processes, a different kind of studies in which in-situ GIXS is increasingly contributing consist in thin film processing. GIXS has been performed during thin film nanostructuring in order to gain insight into the morphology transformation processes, e.g., metal nanocluster formation through high temperature annealing induced dewetting [73,74], dewetting of organic multilayer films [75], or refinement of block co-polymer thin film morphology during solvent vapor annealing [76]. Furthermore, working devices have also been investigated by in-situ GIXS so as to identify the structural changes that the active thin film undergo during operation with the aim of improving the device design and final performance, e.g., catalysis on nanoparticles [77], roughening of surfaces during electrodeposition [78], electrochemistry in ionomer matrices of interest in fuelcell devices [79], or BHJ polymer solar cells [80,81]. As in the previous section, the development of specific environmental cells to be installed at synchrotron beamlines commonly constitutes a prerequisite to conduct this kind of experiments. In the following, we will shortly describe some recent exemplary results of in-operando and in-situ GISAXS during thin film processing.
As mentioned in the previous paragraph, a well-known way of producing -or modifying the morphology of-metal nanoclusters on a surface consists in the thermal induced dewetting of metallic thin films. This process has been in-situ investigated by GISAXS for the case of Au on Si (1 1 1) up to the bulk eutectic point T e of the Au/Si system [82]. After the deposition of Au thin nanostructured films by thermal evaporation, a linear increase of the mean distance between Au nanoclusters was observed-associated to an increase in cluster size-together with an increase in the mean cluster height as the temperature approached T e , which jointly translated to an increase in the contact angle of the nanoclusters. More interestingly, from the Au nanoclusters contact angle at T e , the liquid-solid interface tension of nanometer-sized Au clusters was calculated and it was found to be larger than that of macroscopic Au droplets on Si (1 1 1). Additionally, the work of adhesion of an Au nanodroplet at the system eutectic point was derived.
In the case of semiconductor materials, ion beam bombardment is a very useful process to induce surface nanostructuring. During the erosion of a surface by accelerated ions, the produced instabilities can lead to the formation of self-assembled patterns of nanostructures and different surface topographies can be obtained as a function of the ion mass, ion energy and bombardment geometry. In-situ GISAXS with partially coherent X-ray beams (Co-GISAXS) has been employed to study the nanodot formation on a gallium antimonide (GaSb) (0 0 1) surface by normal incidence bombardment of 500 eV Ar ions [83]. The use of partially coherent beams allows not only accessing the kinetic phenomena but also the dynamics. Under a coherent illumination, the scattered intensity consists of a speckle pattern (Figure 10) and the speckle distribution and speckle intensity fluctuations reflect the underlying dynamics of the surface morphology [84]. From a kinetic point of view-GISAXS analysis-the mean size and distance of the nanodots as a function of time was extracted and the kinetic regimes and onsets derived. More interestingly, though the characteristic GISAXS signal remained stable after saturation of the nanostructuring process, the dynamics showed that ageing-slow down of the dynamics-was occurring, mainly ascribed to hindered mass redistribution phenomena. The dynamics was extracted from the speckle analysis through the so-called two-time correlation function that accounts for the fast variation of intensity redistribution within the scattering peak with respect to the averaged intensity distribution over time. Finally, a dynamical transition to a regime dominated by the build-up of stress at the surface was identified. On the other hand, nanostructuring of polymer thin films is an intense field of research and different strategies are being employed, e.g., nanoimprint lithography, porous anodic aluminum oxide (AAO) templating or, as mentioned in Section 3.1, the design of block co-polymer morphologies. An interesting approach consists in the formation of nanostructured surfaces by the so-called laser-induced periodic surface structure (LIPSS) formation, a technique that has been used for years to nanostructure metals and semiconductors but has only recently been applied to polymers [85,86]. In LIPSS, a pulsed laser of a definite polarization is shined on the material at fluences (optical energy per surface area) well below the ablation threshold and the material surface gets nanostructured by interference of the incoming and scattered electromagnetic wave through a feeding mechanism not yet well understood. In the common case of linearly polarized incident light the process induces ripple formation on the surface with a periodicity resembling the wavelength of the laser employed. By performing in-situ GISAXS measurements while irradiating a poly(trimethylene therephthalate) (PTT) thin film the onset of ripple formation at different laser repetition rates and fluences has been revealed [87]. Moreover, the results support a feeding mechanism based on a local heating of the polymer thin film so that LIPSS formation becomes more efficient the shorter is the laser pulse separation, whereas for long enough laser pulse separation heat dissipation takes place between pulses hindering the ripple formation.
A different way in which polymer thin films are processed does not consist in the promotion of structuring to tailor the material properties but in the processes that polymeric materials undergo during operation. For instance, in several applications the polymeric material is in contact with fluids, e.g., in the case of polymeric materials used in human implants. Here, the combination of μGISAXS and microfluidics offers unique capabilities for investigating the morphological changes of polymer thin films in contact with a fluid flow.
A model system comprising of a thin film of sodium alginate with embedded dispersed PS nanoparticles have been investigated by in-situ μGISAXS during water flow in a microfluidic device [88]. This system served as a model to investigate the detachment of thin films and nanoparticle aggregates therein by a fluid flow, both with and without additional sodium alginate cross-linking. More interestingly, the combination of in-situ μGISAXS and a microfluidic cell have resulted in the accurate description of the swelling behavior of the thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) polymer, a well-known hydrogel when cross-linked [89]. An important feature observed in the GISAXS pattern of soft thin films deposited on rough surfaces is the correlated roughness of the film, i.e., the soft matter thin film present a roughness that replicates that of the substrate. Thus, the film shows X-ray waveguiding effects producing scattering with partial coherence and resonant diffuse scattering is observed [13]. In this case, the diffuse scattering with partial phase coherence coming from the different interfaces concentrates into narrow sheets parallel to the q x direction and appear in the 2D GISAXS pattern as intensity modulations in the scattering plane (along q z at q y = 0). These modulations enable a direct determination of the distance between the correlated surfaces by q z = 2π/d corr (Figure 11(a) and (b)). It is important to calculate d corr for large q z values so that the Yoneda peak intensity does not introduce an additional signal that could distort an accurate determination of d corr . From the in-situ μGISAXS measurements, neither the thickness nor the topography of the PNIPAM thin film was observed to change during exposure to highly undersaturated water vapor. However, as early as the film is brought in contact with liquid water it starts swelling mostly in a 1D manner, i.e., mainly an increase of film thickness occurs, being the restructuration of the surface topography (surface flattening) slightly retarded but obviously correlated to the swelling process (Figure 11(c)). Other polymeric thin films that have been investigated by in-situ GISAXS during operation are the active layers of BHJ polymer solar cells (Figure 12). In general, although polymer solar cells hold the promise of future low-cost flexible solar cells, a major problem of these OPV devices is the performance loss during operation. In this sense, in-operando μGISAXS studies have revealed that the active layer suffer from morphological changes during operation [90]. These morphological changes are directly related to the decrease in short-circuit current density (SCCD) that was derived from the simultaneous measurement of current-voltage curves while the device was illuminated by a solar simulator. In order to demonstrate this unequivocal relationship between performance loss and morphological transformation, Monte Carlo (MC) simulations of the SCCD were performed using the structural parameters extracted from modeling of the μGISAXS patterns. The agreement between the MC simulations and the measured SCCD was excellent (Figure 12(c)) concluding that an increase in P3HT domain size and separation during illumination is responsible for the decrease of effective light harvesting area, thus decreasing the exciton splitting events, whereas the PCBM domain size and distance remained fairly constant. Moreover, a temperature effect was ruled out since the solar cell did not exceed 45°C during the experiments due to Peltier cooling.

Conclusions
In this chapter, we have reviewed the current trends in the application of time-resolved GISAXS for in-situ and in-operando studies during thin film formation and processing. It has been shown that GISAXS presents unique capabilities as a noninvasive technique with intrinsic statistical relevance and time resolutions down to the millisecond regime. Moreover, GISAXS constitutes a very versatile technique that can be applied to a large variety of materials with a vast range of applications, and the relative easiness of combining it with other characterization techniques for simultaneous measurements offers the possibility of correlating the film structure to its properties, of utmost importance in most of the applications of thin films.
In the near future, the present developments for the next generation of 2D X-ray photon counting pixel detectors will allow investigating even faster processes since frame rates higher than 10 kHz with large detector dynamic ranges are foreseen. Additionally, the application of present technique improvements to in-situ studies will further contribute to gain deeper knowledge of thin film fabrication and processing. In this sense, the present advances in grazing incidence resonant soft X-ray scattering (GI-RSoXS), with its inherent material contrast through tuning the incident beam energy to one of the absorption edges of the materials under investigation, will certainly help in understanding, e.g., alloying, blending or phase segregation phenomena in-situ with adequate time resolution. Furthermore, the decrease in beam emittance at synchrotrons is currently enabling longer sample to detector distances-up to several tens of meters-which translates in access to lower q ranges (of the order of 0.001 nm −1 or even lower, i.e., real space sizes in the micron range) by performing grazing incidence ultra-small angle X-ray scattering (GIUSAXS) experiments. Thus, through the combination of in-situ GIWAXS (q ≈ 1-50 nm −1 ), GISAXS (q ≈ 0.01-1 nm −1 ) and GIUSAXS (q ≈ 0.01-0.0001 nm −1 ) real space structures from 1 Å to 10 μm will be accessible, which will provide a complete morphological description of the processes from the atomic structure to the microscopic regime allowing to establish an extremely important link between atomic, nanoscopic and macroscopic ordering, which is not yet fully developed.
Finally, the development of new magnet arrays in storage rings is currently taking place and diffraction-limited sources are not far from becoming available. This will provide an enhanced coherence of the X-ray beams and therefore, it is not difficult to anticipate a growth in the application of time-resolved coherent GISAXS (Co-GISAXS). So far, most of the GISAXS experiments are noncoherent, thus the scattered photon phase is lost making modeling indispensable during data analysis. On the contrary, in Co-GISAXS the phase information can be directly retrieved via mathematical algorithms so that, to some extent, the morphology of the scattering entity can be directly reconstructed from the experimental data. Furthermore, as already known from other X-ray coherent techniques such as X-ray photon correlation spectroscopy (XPCS), not only kinetics but also dynamics of the nano-objects may be probed. However, a good resolution of the speckles is necessary to guarantee an accurate determination of the dynamical processes. This requires a high q resolution that corresponds to small detector pixel size and for fast dynamic processes 2D X-ray photon counting pixel detectors with pixel sizes comparable to those of CCD detectors will be indispensable.