D-line sample stage


update 10/2021

Detlef-M. Smilgies

Chance favors the prepared mind. (Louis Pasteur)

AdvMat cover


  1. Scattering geometry

  2. Structure factor

  3. Block copolymer morphologies

  4. Hierarchical order

  5. Preferential lateral ordering

  6. Form factor

  7. Uniformly orientated nanopaticles

  1. Dynamic scattering effects

  2. Full scattering simulations

  3. Indexation of complex scattering patterns

  4. Grazing-Incidence Wide-Angle Scattering

  5. Combined GISAXS and GIWAXS

  6. Microstructure characterization

  7. Spatially resolved studies

  1. Combining GISAXS and tomography

  2. In-situ real-time experiments

  3. Coherence effects

  4. Soft and tender x-ray scattering

  5. Summary and Outlook

  6. Links

  7. References

Scattering geometry

Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a versatile tool for characterizing nanoscale density correlations and/or the shape of nanoscopic objects at surfaces, at buried interfaces, or in thin films. GISAXS combines features from Small-Angle X-ray Scattering (the mesoscopic length scale, incident beam definition by multiple slits, area detector) and diffuse X-ray Reflectivity (the scattering geometry and sample goniometer). Furthermore, GISAXS can be considered as the big brother of Grazing-Incidence Diffraction (scattering geometry and sample goniometer). The technique was originally introduced by Joanna Levine and Jerry Cohen in 1989 [Levine],[Levine2], but has come to full flourish only in the past two decades for the study of nanostructured thin films.

In order to make x-ray scattering surface sensitive, a grazing incidence angle a is chosen between about half the critical angle ac and several times the critical angles of the film material. The actual choice depends on the system to be studied. For free-standing quantum dots, an incident angle below ac may be chosen to make the scattering exclusively surface-sensitive [Smilgies7]. Largest scattering cross sections are achieved when the incident angle is inbetween the critical angles of the film and the substrate, however, multiple scattering effects have to be taken into account to properly model the data. If the incident angle is somewhat above the critical angle of the substrate, dynamic scattering effect are much reduced, and often the data can be modeled well within the quasi-kinematic approximation introduced by [Naudon]. In each of the latter two cases, a full penetration of the sample for several 100 nm is ensured.

The area detector records the scattering intensity of scattered rays over a range of exit angles b and scattering angles y in the surface plane. A beam stop has to be set up to block spill-over direct beam as well as the reflected beam and the intense diffuse scattering in the scattering plane. The scattering geometry is thus relatively simple, and lends itself to study samples in in-situ environments [Renaud, Smilgies]. As the scattering intensity in the forward direction is high, real-time studies have become feasible [Renaud, Dourdain, KimSmilgies2Papadakis2, Paik, Zhang2]. With modern pixel array detectors, one-shot movies of sample kinetics with 100 frames per second [Smilgies6] or better have become feasible.

In the scattering plane the GISAXS intensity distribution corresponds to a detector scan in Diffuse Reflectivity [Sinha]. The intensity distribution parallel to the surface plane corresponds to a line cut through the corresponding transmission SAXS pattern. The full GISAXS intensity map can be theoretically described within the framework of the Distorted-Wave Born-Approximation [Sinha, Rauscher, Lazzari, Lee1, Busch3, Tate, Stein].

GIWAXS is a related scattering technique probing atomic and molecular distances in crystal lattices. It is closely related to Grazing Incidence Diffraction, however, typically area detectors are used as in GISAXS. GIWAXS is typically used to probe the morphology of conjugated molecules and polymers[ Sirringhaus, Breiby, Chabinyc, He, Huang, Osaka]. Combined GISAXS and GIWAXS studies reveal the orientational order of crystalline blocks in polymers [Busch5, Sasaki, Darko] and orientational order of nonspherical nanocrystals on their superlattice sites [Bian, Choi, Choi2].


Structure factor - lateral and normal density correlations

GISAXS provides information both about lateral and normal ordering at a surface or inside a thin film. This shall be illustrated with the archetypical case of lamellar films formed by symmetric polystyrene - polybutadiene block copolymers (PS-b-PB). In a block copolymer two immiscible polymer chains are coupled by a chemical bond. If both chains occupy equal volumes, a lamellar phase is formed. In a thin film, i.e. if the thickness of the film is on the order of the lamellar period, the presence of two interfaces, air-film and film substrate, may induce preferential order in the film as compared to the bulk polymer which forms a 3D powder of micron-sized lamellar domains:

If interfacial energies are the dominant factor, i.e. if one of the block strongly favors the interface, parallel lamellae are formed. If the interfacial energies of the blocks are similar, interfacial entropy will determine the orientation of the blocks. In particular, chain stretching in the vicinity of the bond between the immiscible polymer chains yields a perpendicular orientation of the lamellae, while the chain end effect favors a parallel orientation [Pickett]. As the entropic effects scale with the chain lengths, a thin film morphology change as a function of chain length is possible. This has been indeed observed for PS-b-PB, where parallel lamellae are observed for short chains and perpendicular lamellae for long chains [Papadakis]

What kind of scattering will result from these two extreme cases ?
If one of the blocks strongly favors one of the two interfaces, or even both, the lamellae will be parallel to the substrate. The classic example is PS-b-PMMA on a Si wafer covered with the native oxide [Anastasiadis]. The signature of parallel lamellae in GISAXS are stripes of intensity at regular spacings along the qz direction. In Langmuir-Blodgett films, such stripes in the diffuse reflectivity are referred to as Bragg sheets. The schematic shows the diffuse scattering only (the intense specular reflection from the surface is omitted). 

Strictly speaking, the sketched pattern is obtained within the validity of the Born-Approximation, i.e. if the incident angles and scattering angles are well above the critical angles of film and substrate. For incident angles between the critical angles of film and substrate, scattering patterns may be more complicated, which can be explained within the framework of DBWA theory [Busch3]

The obvious method of choice for this system is specular reflectivity [Anastasiadis]. The modulation in the electron density by the alternating blocks gives rise to extended Kiessug fringes [Kiessig 1932]. Interestingly reflectivity and GISAXS are complementary in this case: for near-perfect ordereing, lamellar Brage peaks are observed in XR while the GISAXS pattern appears featureless, as the diffuse Bragg sheets are hidden behind the beamstop. If lamellae are more disordered and display wavy interfaces, XR may only show the Kiessig fringes corresponding to the average thickness of the polymer film, while GISAXS reveals diffuse Bragg sheets close to the beamstop. For such a measurement it is essential to use a scattering angle between the critical angles of substrate and film and cover both the specular and diffuse reflectivity in the incident plane with a rod-like beamstop [Smilgies, Busch4].

If both blocks have similar interface energies, chain stretching at the interface comes into play. Chain stretching occurs at the link between the immiscible blocks of the polymer. A nematic ordering of this stretched part parallel to the interface may become favorable giving rise to the formation of perpendicular lamellae. As both interactions scale differently with the degree of polymerization [Pickett, Potemkin], there can be a transition from parallel lamellae to vertical lamellae, as we have found for PS-b-PB [Busch]. The signature of perpendicular lamellae are correlation peaks parallel to the interface, with a rod-like shape normal to the surface, similar to the scattering rods in Grazing-Incidence Diffraction of amphiphilic molecules at the air-water interface [Als-Nielsen]. 


Note that perpendicular lamellae still have the freedom to change direction parallel to the surface plane - in fact AFM pictures [Busch, Busch2] show that meandering lamellae are formed (aka "fingerprint patterns"). Such a system constitutes a 2D powder, similar to monolayers at the air-water interface [Als-Nielsen]. Another way of describing thin film samples is that they have uniaxial alignment. Closely related to such scattering patterns is fiber diffraction, and sometimes such images are also refered to as having "fiber texture" [Breiby]. A fiber is the dual system to a thin film, however, it should be kept in mind that fiber diffration is a transmission experiment and well described within the kinematic approximation, while GISAXS works in reflection geometry, and reflection-refraction effects have to be included for a proper interpretation of the scattering patterns.

AFM image of a diblock copolymer film
displaying vertical lamellae [Busch2]

GISAXS from the polymer film
shown on the left.

The scattering from such a lamellar system with a period of about 75 nm is strong and the ordering kinetics sufficiently slow, so that in-situ time-resolved measurements of the swelling of the film in solvent vapor on a timescale of tens of seconds were possible [Smilgies].

Not always does the kinetics of the film formation result in a single morphology. This is particularly important in a system like PS-b-PB [Busch, Papadakis, Busch3, Busch4, Potemkin], where the morphology changes from parallel lamellae to perpendicular lamellae gradually as a function of chain length. At intermediate chain lengths there is only a small preference of one morphology over the other, i.e. the driving force is weak, and the system is hence slow to reach equilibrium. In this case a coexistence of different structures is observed.

sample PSPB-V5

PS-PB sample V5 with a chain length in the intermediate regime.
A mixture of  parallel, perpendicular, and unoriented lamellae
is observed. [Busch4, Smilgies11]

The situation can be even more complex in thick films where the film thickness is considerable larger than the lamellar period.
In thick films on the order of microns the ordering induced at the interfaces may not prevail throughout the film, and the interior of the film may assume the 3D powder bulk structure.

Rings or partial rings in the intensity maps can indicate anything from complete disorder of the lamellar domains to partial ordering, e.g. lamellae with a finite distribution of tilt angles with respect to the interface.

But the story does not end here: For films thicker than the lamellar prevailence length, top and bottom interface are decoupled. Interfacial ordering is still in effect, however, can be different at the air-film and the film-substrate interfaces. So it is possible to have parallel lamellae at one interface and perpendicular lamellae at the other, as dictated by the interplay of interfacial enthalpy and entropy. Such a behavior has been reported in the closely related cylindrical morphology wich can also display a parallel or perpendicular preferential orientation of the cylindrical domains at the interfaces [Singh].


Block copolymer morphologies

block copolymer GISAXS

GISAXS from block copolymer based nanocomposites:
(a) standing hollow cylinders [Li-M]  (b) monolayer of hollow spheres [Du]
(c) lying semicylinders [Pelletier]  (d) titania gyroid nanoscaffold [Crossland]

Apart from the lamellar structures discussed in the previous section, there is a number of other well-known block copolymer structures Again the question arises how these structures are effected by  interfacial effects in thin films. A number of studies has been devoted to this problem:  Du et al. characterized and modelled a monolayer of spherical voids in a matrix [Du] using the IsGISAXS code by [Lazzari] and applying Babinet's theorem. [Xu] and [Li-M] characterized standing hexagonal cylinders. The Ree group investigated lying hexagonally-packed cylinders, hexagonal perforated layers, and gyroid phases [Lee1, Park-I] and modeled the scattering for the cylinder phase within DWBA. In addition they characterized and modelled a film with randomly distributed spherical pores [Lee2].  The Hillhouse and Wiesner groups independently analyzed the gyroid phase [Tate, Urade], [Crossland] as templates for inorganc nanoporous scaffolds. Ed Kramer's group  performed a comprehensive study of thin film ordered spherical phases, from hexagonally packed monolayers to several tens of monolayers that form bcc-packed spheres with a (110) orientation, as expected from the bulk equilibrium phase [Stein]. More recently [Zhang-Q] and collaborators described how to form single gyroid superlattices, Hence most of the regular bulk phases have been characterized, as they occur in thin film morphology, and preferential alignment with regard to the substrate surface could always be achieved. [Ree] has recently provided a comprehensive review on the multitude of scattering patterns observed in block copolymer thin films. 

Early studies of the effect of solvent vapor on the block copolymer thin film morphology were performed by [Smilgies] and [Xu]. In their study of silica surfactant mesophases the kinetics of the formation of various morphologies was studied by [Gibaud] and coworkers. [Wolff] studied the absorption of spherical micelles from the liquid onto a silicon substrate with grazing-incidence neutron scattering . Jin Wang, Sunil Sinha, and collaborators have shown, how nanoparticles trapped between two polymer surfaces diffuse laterally using resonance-enhanced GISAXS [Narayanan]. The Korgel group showed that monodisperse CuS nanodisks can form ordered columnar arrays on drop casting [Saunders]. Many more papers on nanoparticle self-assembly into two and three dimensional superlattices have been published recently, for example [Alexandrovic, Bian, Campolongo, Choi, Dunphy, Goodfellow, Hanrath, Heitsch, Smith, Zhang]


Hierarchical order in block copolymers with liquid-crystalline side-chains

hierarchical ordering in LC BCP

Hierarchical order in a block copolymer. The cylindrical domains are formed by the short polystyrene block, while the matrix is formed
by a polymer block with liquid crystalline side chains. The GISAXS image in the center panel shows the hexagonally packed cylinders at q_par=0.025 invA.
The smectic ordering of the mesogen side chains shows up as the intense reflection at q_perp=0.15 invA. Finally the GIWAXS image in the right panel shows
the side chain packing and tilt demonstrating that the surface-near mesogens form a smectic-C structure.[Busch5].

Hierarchical ordering has been reported by [Busch5] where a block copolymer in the cylindrical phase and with liquid crystalline side chains in the majority block showed ordering on the mesocopic scale (30 nm), the scale of the scale of the smectic layers (3 nm), and the molecular scale of the alkyl chain packing (0.5 nm). [Sasaki] studied thermal treatment of polyethylene films in-situ with simultaneous small- and wide-angle scattering. Simultaneous small and wide angle scattering was also the key to unravel the intricate relation of superlattice symmetry and on-site orientation of individual particles in PbS and PbSe nanocrystal assemblies [Bian, Choi, Choi2].


Preferential lateral ordering and patterning

All examples discussed so far were 2D powders, i.e. had a well-aligned axis perpendicular to the substrate and rotational averaging with respect to the surface normal, resulting in a rotationally homogeneous scattering intensity with respect to the azimuth angle f. However, by patterning the substrate, further ordering may be imposed on the film, and structures may show a preferential lateral orientation with respect to the substrate as seen in polymer blends, where the surface had been prepared by alternating hydrophobic and hydrophilic stripes [Böltau].

Basic scattering angles for a GISAXS experiment. If the structure is anisotropic in the film plane,
the GISAXS intensity map will depend on the sample azimuth f.

Similarly, regular patterns can be prepared in photoresists by lithographic techniques representing artificial lamellar systems. In these cases the GISAXS intensity distribution depends now also on the azimuth angle f of the substrate. The Kowalewski group has developed the method of zone casting, which makes the preparation of laterally oriented block copolymer domains possible, and after calcination, the creation of oriented carbon nanogratings [Tang]. Nanogratings can also be prepared by using oriented block copolymer films as templates for reactive ion etching [Park-M], as shown in the example below. A quantitative description of such in-plane texture for the use with area detectors has been suggested by [Breiby] et al.

laterally oriented nanostructure

Scattering off an ordered array of Al nanowires, prepared by reactive ion etching of an shear-oriented
block copolymer template [Angelescu, Pelletier]. When the sample is rotated by f, the scattering features become weaker.
Note that on the macroscopic scale, i.e. in the illuminated area of about 0.5 mm by 10 mm, the grating is not perfect.
Sample: Pelletier & Chaikin, Princeton. Scattering data: Smilgies & Gruner, CHESS (unpublished) and Pelletier (thesis).

A recent important application of laterally ordered nanostructures is directed self-assembly (DSA) which is of interest to the semiconductor industry, as lithography methods reach their limits around 10 nm and hence bottom-up methods have become of interest. However, achieving microphase separation on such lengthscales is only possible for polymer combination with a high incompatibility as given by the Flory-Huggins parameter χ as the strong segregation limit is only attained at χN > 10, where N is the degree of polymerization [Kennemur]. Lateral ordering has been achieved by chemical patterning [Nealey] as well as by graphoepitaxy [Jeong] where a block copolymer featuring parallel cylinders of perpendicular lamellae is deposited on a nanostructured substrate with elongated troughs. In both cases the order inducing substrate modifications can be several times the domain spacing of the block copolymer. Instead of using mixed top-down and bottom-up methodology, Russell and coworkers have demonstrated that extended ordering can also by achieved on a stepped substrate which resulted from sputtering a high-index plane of silicon [Park-S].


Form factor

Another type of scattering is observed for nano-objects with a narrow size distribution and well-defined shape. Here the form factor dominates the scattering, in particular, if the nano-objects are randomly placed on the surface. Examples are monodisperse voids in a silica film on a wafer surface [Du], molecular sieves based on standing block copolymer cylinders with the cylinder material removed [Li] as well as quantum dot arrays [Metzger]. Below the calculated scattering intensity from a dilute layer of oblate elliptical nanoparticles on a wafer surface is shown in the quasikinematic approximation (left panel).

elliptical nanoparticles: dilute layer

oblate elliptical nanoparticles: dense layer
with in-plane correlations

The characteristic form factor oscillations are clearly to be seen in the parallel and the perpendicular direction. When the exit angle of the scattered beam is close to the critical angle, signal enhancement due to the Vineyard effect [Vineyard] occurs, resulting in a bright band of intensity at the critical angle. This is also referred to as the Yoneda peak [Yoneda]. Below the critical angle the scattering intensity falls quadratically off to zero. For thin films the Yoneda band extends between the critical angles of the film and the substrate, in particular if the former is smaller than the latter, as often encountered in organic thin films.

For a dense layer of nano-objects, particles have more or less well-defined nearest-neighbor distances. This density correlation gives rise to a structure factor with characteristic modulations parallel to the surface, but constant in the perpendicular direction (right panel).  The characteristic intensity streaks are related to the scattering rods in Grazing-Incidence Diffraction [Als-Nielsen], and are modulated by the form factor.


structure factor

form factor
(log scale)

Vineyard factor

Contributions to a GISAXS intensity map in the quasikinematic approximation.

Note that in this simulation, all the structure was produced by the product of just three functions, the form factor F(qy,qz), the structure factor S(qy), and the Vineyard factor T(qz), where the qy and qz components of the scattering vector q are parallel and perpendicular to the substrate surface, respectively. This quasi-kinematic approach was first introduced by [Naudon] for studying the formation of nanoparticles on surfaces and in buried layers, and is based on the seminal work by [Vineyard] on grazing-icidence diffraction. [Heitsch] and [Smilgies5] have recently applied the quasi-kinematic approximation to model full 2D scattering images of monolayers and multilayers of PtFe nanocrystals deposited by the Langmuir-Blodgett and Langmuir-Schaefer techniques. Particle size distribution and deposition techniques were correlated with the degree of order observed in the layers, as modeled by a static Debye-Waller Factor [Foerster].

NC monolayer

GISAXS image from a Langmuir-Blodgett film of FePt nanocrystals (left) and simulation within the quasi-kinematic approximation (right). [Heitsch].


Uniformly orientated nanopaticles

The highest degree of information on nanoparticles is obtained, if these have not only uniform shape, but also uniform orientation. The classic example are pyramid-shaped quantum dots on single crystalline surfaces [Metzger]. In the latter case the scattering intensity of a line scan taken parallel to the surface depends on the relative orientation of the pyramids to the beam as given by the azimuth angle f of the sample. Another spectacular example of very highly oriented monodisperse nanoparticles are the in-situ growth studies by Renaud et al. in an all-vacuum, windowless small-angle scattering set-up [Renaud]. [Tang] created carbon nanogratings based on zone casting of a lamellar block copolymer which resulted in the formation of perpendicular lamellae both to the substrate and the casting direction. Subsequent pyrolysis  removed one block and converted the other to carbon.

Orientation-dependence of the scattering from quantum dots
shaped like three-sided pyramids [Metzger].

GISAXS from lithographic silicon nanoscale gratings were characterized in great detail by [Hofmann] and [Rueda]. [Soltwisch1,2] pushed the envelop further, going beyong DWBA using a finite element Maxwell solver. The precision of this approach is suitable for critical dimension GISAXS, as of interest for the characterization of lithographic silicon nanostructures for the semiconductor industry.

[Lu] introduced a new technique, grazing-incidence transmission where the transmitted beam through the rear edge of the sample is detected. The approach considerably simplifies the scattering theory. [Park-S] showed that laterally highly oriented hexagonal arrays of block copolymer cylinders can be obtained on a miscut surface with regular steps.


Dynamic scattering effects

A well-known feature of grazing incidence scattering is the Yoneda-Vineyard peak which shows up as a bright line of enhanced diffuse scattering intensity on an area detector when the exit angle equals the critical angle of the surface, a result of the Vinyard function introduced in the above section. The origin of the enhancement lies in the fact that at the critical angle incident beam and reflected beam are of similar amplitude and in phase [Vineyard, Als-Nielsen]. The situation is more complex for thin films which feature two critical angles for film and substrate, and the line expands into the Yoneda band of enhanced scattering between the critical angles.

Yoneda band

Block copolymer film featuring standing cylinders.The bright bands between the critical angles of the film and the substrate
are waveguide resonances in the outgoing wavefunction. The region between the critical angles is also known as
the Yoneda band. The number of resonances sustained  is related to the film thickness and the difference
between the critical angles [Smilgies7, Smilgies11].

If the film has lower electron density than the substrate, as is usually the case for organic thin films on silicon wafers, the reflectivity shows pronounced oscillations between the critical angles which are related to the incident wave resonantly coupling to waveguide modes inside the layer [Feng]. At such a resonance, the electric field inside the film is greatly enhanced [Wang-J]. As a consequence, the scattering intensity is also enhanced. If a film has a well-defined thickness such as a spin-coated polymer film, the Yoneda band features bright bands of intensity corresponding to waveguide resonance in the exit wavefunction. If in addition the incident wave is tuned to a waveguide resonance, too, the largest enhancement effect results [Pfeiffer, Narayanan]. Samples may also be engineered to optimize waveguide performance by coating them with a thin metal top layer such as Ti or Al.

Resonant scattering making use of several waveguide modes can also be applied to reconstruct the electron density in the film [Babonneau2, Jiang2]. As the number of nodes of the waveguide mode incleases, the parts of the films at the antinodes are probed, while the parts at the nodes do not contribute much. This provides additional information for the reconstruction of the electron density profile in the film.

Another interesting angle range is when the incident wave is below the critical angle of the film. In this case the wave penetrating into the film is evanescent, i.e. exponentially damped. This can be used to separate information of near-surface structure, using an angle of incidence of about half the critical angle of the film, from the full film scattering at higher angles. Again perfect films are needed, so that the incident angle is well-defined. In addition for a quantitative analysis, care has to be taken to properly include the reflected wave from the interface to the substrate. This calculation can be done withing the framework of the DWBA theory, which describes all 3 scattering regimes in GISAXS - evanescent, dynamic, and quasi-kinematic [Smilgies7].


Full scattering simulations

An exact formulation of the scattering theory has been given by [Rauscher] within the framework of distorted-wave Born approximation (DWBA) [Sinha, Vinyard] which was further elaborated by [Lazzari] for the case of self-organized metal clusters on oxide surfacs [Renaud]. Remi Lazzari's "IsGISAXS" program is available on the web (see links). In this work the case of finite objects on a substrate surface is treated.

 [Lee1, Lee2] and [Busch3] investigated basic DWBA models suitable for porogens, cylindrical block copolymers, and lamellar block copolymers, respectively. [Tate2] presented an approach of combining scattering calculations with electron density models using discrete Fourier transforms. Recently [Babonneau] made his program "FitGISAXS" available (see links), which is capable of modelling nanostructures in buried layers. In these formulations of the DWBA objects embedded in a thin film are treated. The thin film itself gives rise to new phenomena, such as two critical angles for film and substrate, wave guide resonances inbetween the two critical angles, as well as oscillations related to Kiessig fringes above the critical angle of the substrate. Hence scattering from thin film systems features additional complexity and is important to consider in the interpretation of GISAXS scattering data [Busch3].

Detailed modelling of the scattering from block copolymer thin films has been preformed by Ree's group [Lee2, Yoon, Yoon2, Jin] for lying and standing cylinders, lamellar, and gyroid phases, respectively, while [Du] and [Stein] analyzed spherical phases. Finally [Lee3] introduced a phasing method to solve the previously not very well known structure of the hexagonal perforated layer phase. This means that now detailed models of all block copolymer phases exist. A step by step introduction to modelling GISAXS images using IsGISAXS was given by [Müller-B2] as well as a comprehensive review [Müller-B3].

Detailed modelling goes beyond structure simulation - the fading of the intensity at higher q-values is related to the kind of disorder in the system. Disorder models employed so far include the paracrystal model [Lazzari, Lee2] and the static Debye-Waller factor model [Foerster, Heitsch], which describe disorder of the second kind and of the first kind, respectively. More support from theoretical modelling would be highly desireable, in order to quantify which kind of disorder is present in a given sample, and how to best model it.

Indexation of complex scattering patterns

Self-organized nanoparticles synthesized by solution chemistry have attained better and better quality and monodispersity. Some spectacular results have been achieved for monolayers deposited on the air-water interface [Schultz] and on solid substrates  [Alexandrovic, Jiang, Heitsch]. Moreover, highly ordered and oriented unary [Saunders, DunphyHanrath, Zhang] and binary [Smith] superlattices have be obtained. A key for these latter studies was careful tuning of deposition technique and annealing conditions. Indexation schemes for such complex patterns have been described by [Breiby, Smilgies3, Tate].

crystallization of PbS and PbSe nanoparticles

Crystallization of PbSe (top) and PbS (bottom) nanocrystals dropcast onto a Si wafer into an FCC superlattice.
Fast drying (left) yields randomly oriented FCC domains, while slow drying (right) leads to
oriented 3D assemblies with their (111) faces parallel to the substrate [Hanrath].

Other 3D nanostructures than nanoparticle assemblies and block copolymers have been studied with GISAXS as well: Nanotube forests can be grown using metal nanoparticles as nuclei and have been analyzed with GISAXS [Sendja]. Complex 3D nanostructured materials recently studied with GISAXS are block-copolymer templated nanoporous materials [Urade, Crossland] which are of interest for organic solar cells, catalyst scaffolds, and molecular sieves. Such structures a based on bicontinous phases such as the double gyroid and give rise to complex spot patterns.


Grazing-Incidence Wide-Angle Scattering (GIWAXS)

Fused Thiophenes

Structure-function relationship of a family of fused thiophenes.The fused moieties corresponding to the GIWAXS series have 3, 4, and 5 rings, respectively [He].

GISAXS can be extended into the wide-angle region (GIWAXS), the transition is somewhat fluid. GID and GIWAXS are quite similar except for the data collection strategy - GIWAXS uses an area detector without collimation which works reasonably up to about 30deg scattering angle, while in GID typically a point or line detector is used, with appropriate collimation and mounted on a diffractometer detector arm. As such GID has better resolution and access to the full range of scattering angles, while GIWAXS is advantageous because of the simple collection geometry enabling fast experiments [Smilgies6]. Typically semicrystalline polymer films such as conjugated polymers [Sirringhaus, Chabinyc, Osaka] are efficiently studied with GIWAXS. Also full crystal structure determination for conjugated molecules has been shown using large area detectors  [Breiby, Mannsfeld].

.indexation of pyrene

Indexation of pyrene grown from solution onto a glass surface. The polymorph could be identified  as bulk polymorph I
with the (001) plane growing parallel to the surface [Smilgies12]. The image was obtained at former G2 station
using grazing-incidence reciprocal space mapping on a psi-circle diffractometer with a linear diode array detector [Smilgies3].

Small molecules GIWAXS patterns present a particular challenge. Small molecules typically crystallize in low-symmetry lattices such as triclinic and monoclinic. Such low symmetry arragements are associated with a pronounced polymorphism which can depend on processing conditions (temperature, deposition method), interface energy and solvent. If the thin film structure corresponds to one of the bulk polymorph, it is then a matter of identifying the crystallographic plane that grows parallel to the substrate, using the simple indexation tools outlined above. In this case crystallographic software such as CCDC Mercury can be used to identify the orientation of the molecules with respect to the surface. However, often there can be a thin film structures, the classical example being pentacene [Amassian]. If a previously unknown structure is encountered there are now computer-based search routines to identify the unit cell and the indexation [Hailey, Mannsfeld, Savikhin, Kainz]. A full crystal structure determination is often not possible due to the limited number of observable reflections. However, if the assumption can be made that the bulk molecular structure is maintained, the thin film crystal structure can be cracked using the experimentally determined unit cell and the rigid molecule approximation [Mannsfeld, Savikhin].


Combined GISAXS and GIWAXS

Combined GISAXS and GIWAXS studies have been employed by [Sasaki, Darko] to correlate polymer morphology with polymer crystallization. In oriented nanoparticle superlattices, complementary GIWAXS from the crystalline cores provided detailed information of the orientation of non-spherical nanocrystals on their lattice sites [Bian, Choi, Choi2]. The combination of GISAXS and GIWAXS  helped to understand that the complex Bain transition in cuboctahedral PbS and PbSe nanocrystal superlattices is driven by orientational ordering of the nonacrystals within the superlattice. Simultaneous GISAXS/GIWAXS measurements [Weidman, Smilgies10] have provided further proof and have revealed the complex reorganization kinetics of not only the nanocrystals but also the superlattices as a whole [Weidman].

Bain transition

Bain transition in PbS nanocrystal superlattices as a function of drying dynamics. Structures covering the whole Bain path fcc > bct > bcc can be obtained by tweaking the drying kinetics. As structures approach bcc, nanocrystals display increasing relative orientation on their superlattice sites.
nanocrystal superlattices

Orientational ordering of nanocrystals in oriented FCC(111) and BCC(110) superlattices [Choi].
In the FCC lattice nanocrystals behave like spheres and have random orientation on their lattice sites.
In the BCC lattice formed by PbS nanocrystals with reduced ligand density GIWAXS data of the
PbS atomic lattice reveals that particles are highly oriented.


Microstructure characterization

lamellar order

Microstructure of a conjugated polymer derived from GIWAXS (center) correlated with device properties (left) and AFM (right) [Osaka].

From spot-like diffraction patterns information about the microstructure of soft materials can be obtained. The basic ingredients of the microstructure are
geometric smearing

Effect of gemometric smearing illustrated for a pentacene thin film.
Note the increase in spot elongation as the scattering angle increases [Smilgies9].
Sample width 25 mm, detector distance 100 mm.
The microstructure provides may clues about the film formation and may help to optimize process parameter. Moreover the microstructure often can be related to devices performance, for instance mobility in organic thin film transistors or efficiency of organic solar cell materials.


Spatially resolved studies

OFET scanning
Solution Shearing

Left: Scanning GIWAXS to elucidate the morphology of a TIPS-pentacen film in the gate channel of an organic transistor [Li-R].
Right: Scanning the meniscus region during solution shearing of a TIPS-pentacene film [Smilgies6].

Gibbs layers

Scanning a droplet of a solution of DNA-coated gold nanoparticles revealed formation of an ordered Gibbs layer at the apex of the drop [Campolongo].
The x-ray beam was parallel to the substrate (parSAXS).


Combining GISAXS and tomography

The techniques described above require suitable samples for essentially 1D scanning due to the large footprint of the beam on the sample. A different approach to image patterned films has been taken by [Kuhlmann], [Innis-S], and [Ogawa, Ogawa2, Ogawa3] by combining GISAXS and tomography. In this case the sample is scanned through a small x-ray beam. The scan is repeated for many angles around the surface normal, and specific areas of intensity in the scattering images are used to reconstruct the distribution of material on the surface. In this case the long footprint of the grazing-incidence beam becomes an asset for the 2D reconstruction. Beamline stability and precise alignment to keep the incident angle constant during the azimuthal rotation as well as the large number of scattering images are the major challenges of the technique.


In-situ and real-time studies

Recently the focus of GISAXS studies has shifted towards the study of sample processing conditions and in-situ treatment of samples (such as heating, solvent annealing, or thermal quenching as well as the study of deposition techniques in-situ) [Smilgies, Renaud, Gibaud, WolffDourdainKim, Narayanan, Paik, Smilgies2, Papadakis2, Hanrath, Smilgies6].


Instabilities during swelling of block copolymer lamellae [Papadakis2].

Kirkwood-Alder transition

Kirkwood-Alder transition in dropcast PtCu nanoctahedra during drying under
controlled vapor pressure [Zhang2].

nanocube crystallization

Crystallization of nanocubes with competing structures at the substrate-solution interface and the air-solution interface [Choi2].

self-organized Oswald ripening

Self-organized Oswald ripening of 2nm gold nanocrystals during heating. Binary
superlattices of large fused particles and the original small particles are formed [Goodfellow].

A current trend is towards gaining a more detailed understanding of the thermodynamics, the kinetics and the driving forces of self-organization processes in soft materials thin films:

Block copolymers:


Organic electronics:

These discoveries were facilitated by the ability to study nanostructured materials in a well-controlled in-situ sample environment and in real time. It is to be expected that the GISAXS and GIWAXS techniques will unfold their full potential here.


Coherence Effects

At third-generation sources GISAXS can be combined with coherent scattering methods. [Sun] have recently used Coherent Diffraction Imaging in GISAXS mode to reconstruct a nanosized non-periodic test object. By including the incident angle dependence of the scattering images a full 3D reconstruction of the test object was obtained.

[Bicondoa] have combined GISAXS with x-ray photon correlation spectroscopy to study the nanostructuring of a GaSb surface during sputter ablation.

Both approaches show high promise to obtain further insights into model-free structure reconstruction on non-periodic objects (CDI) or nanoscale dynamics and kinetics (XPCS) beyond regular GISAXS measurements.


Soft  and Tender X-ray Scattering

[Wang-C] developed grazing-incidence scattering using soft x-rays in the vicinity of the carbon edge. The pronounced resonant scattering of carbon atoms in different bonding configurations permits to distinguish between different polymer blocks with chemical sensitivity; in addition, contrast matching is possible. Closely related are new studies in the tender x-ray regime of 2-5 keV, which opens up resonant studies at the phosphorus and sulfur edges [Okuda]. This emerging field has recently been reviewed by [Yamamoto].


Summary and Outlook

Mesoscopic systems can display a large variety of ordering properties. Each of these has a well-defined signature in its GISAXS and/or GIWAXS intensity pattern.  Moreover, due to the penetration power of x-rays, not only surface structures, but also the internal structure of thin films and buried interfaces can be studied without any need of elaborate sample preparation, as needed for instance for cross-section transmission electron microscopy.

Hard x-rays can penetrate air, vapor, and small amounts of liquid allowing samples to be studied in-situ [Smilgies]. The GISAXS and GIWAXS scattering geometries  are straightforward and, in many cases, without the need for scanning, making GISAXS and GIWAXS very attractive to combine even with elaborate in-situ chambers [Renaud]. GISAXS scattering intensities are high compared to grazing incidence diffraction, and in combination with the essentially static scattering geometry, make GISAXS an ideal technique to combine with real-time measurements. Typical CCD cameras acquire at 1 frame per 10 sec down to 1 frame per sec; commercially available pixel array detector can acquire data up to 100 frames per second.  While swelling kinetics in block copolymers happens on the time scale of minutes, and thus CCD cameras are already well matched for the study of polymer kinetics, conjugated  molecules crystallize from solution on a msec time scale. As area detectors are evolving, the msec time scale has become readily accessible with the Pilatus pixel array detector family, opening a new window in the self-organization kinetics of nanostructured materials. And the next generation of detectors capable of submillisecond resolution movies are becoming commenrcially available. However, let's keep in mind that each nanoscale system has its own timescale and radiation damage threshold, so the experimenter's challenge is still to find the best combination of single frame exposure and frame rate.

All of these features make GISAXS and GIWAXS versatile tools to study shape and density correlations in nanoscopic systems in situ and in real time and thus follow the kinetics of the self-assembly pathways.

(originally based on a talk given at the Physical Electronics Conference on Cornell Campus in June 2003)



- Tutorials
Wikipedia GISAXS page
GISAXS wiki by Kevin Yager (Brookhaven National Lab0
GISAXS tutorial by Andreas Meyer (Uni Hamburg)
Byeongdu Lee's SAXS and GISAXS pages (Advanced Photon Source)

- DWBA calculation software
IsGISAXS manual by Remi Lazzari (Université Curie)
FitGISAXS page by David Babonneau (Université Poitiers)
Born Again site by the Juelich group
HipGISAXS site by the Berkeley group

- Data analysis software
Fit2D generic executable (Windows, Mac, Linux) for area detectors (ESRF)
GISAXSshop for analysis of 2D detector images in Igor by Byeongdu Lee (Advanced photon Source)
GIXSGUI for analysis of 2D detector images in Matlab by Zhang Jiang (Advanced Photon Source)
SciAnalysis for 2D detectors in Python (CMS group at NSLS-II)
SIIR-kit for GIWAXS data reduction by the Stanford group
GIXSpack for batch data processing and indexing of area detector data by Detlef Smilgies (distributed by the author)

- Software Overviews
SAS Portal: overview of SAXS/GISAXS software
GIXS software overview by Kevin Yager

Some dear memories

When my interest in GISAXS started around 1998, the technique was almost unknown in the soft matter community except for the pioneeing work of Peter Mueller-Buschbaum and his gang on correlated roughness in homopolymer thin films. As it happened, after one of their visits to my beamline at ESRF, a friend from my time in Denmark, Christine Papadakis, showed me one of her AFM images of her block copolymer samples, and I was hooked - how cool would it be, to do GID (my original playground) on a sample with a period of 1000 Angstroem instead of atomic length scales? Other colleagues and users at ESRF, Hartmut Metzger, Gilles Renaud, and Dominique Thiaudiere, had gotten spectacular results from inorganic systems at the same time, but  soft materials remained largely by the wayside. Shortly afterwards in 2000, I moved to CHESS and had the opportunity to work with a 2D detector at D-line - my first crude GISAXS set-up already revealed  the most intriguing and beautiful  scattering images - see the image from Perter Busch's sample V5 above. I am grateful to CHESS director extraordinaire Sol Gruner for giving me the opportunity to explore an obscure technique that I saw a lot of potential in. Many thanks also to my partners in crime, Christine Papadakis, Peter Busch and Dorthe Posselt as well as Chris Ober and Uli Wiesner and their students with whom I started highly successful collaborations on structure and the self-assembly kinetics in block-copolymer thin films. Rui Zhang and Tomek Kowalewski challenged me to get a GIWAXS set-up working for their studies of P3HT and bulk heterojunctions - this resulted in one of my best cited papers and many others. Then I had the opportunity to make the full circle back to my original background in hard materials, when the first nanocrystals arrived at D-line, and I had the opportunity to play with crystallization on the 2-10 nm scale with the groups of Brian Korgel, Tobias Hanrath, James Fang, Will Tisdale and Marie-Paule Pileni gaining amazing insights into the formation of superlattices. And last and definitely not least, my collaboration with George Malliara' group at Cornell as well as Aram Amassian and his crew at KAUST sparked an amazing program in organic electronics, encompassing OLEDs, OFETs, and OPV with the hottest materials at the time. Special thanks to Ruipeng Li, who worked with me for many years, as a student, as a collaborator, and finally as a colleague at CHESS and who contributed much to the development of sample environments, microbeam capability, and the use of fast detectors at D-line. Ruipeng has continued this line of work as scientist at the CMS beamline at Brookhaven Lab. Thank you all who inspired me and kept my interest peaked - it has been a wild journey into the nanoworld!

Detlef at D-line


D-line - the little beamline that could

In the course of the CHESS-Upgrade project, D-line, the beamline that I have worked at for many years, had to be decommissioned and removed in Summer of 2018. Despite the D-line history of pushing the envelope in real-time in-situ multiprobe measurements (see my cover gallery), a successor general user in-situ materials processing beamline was not funded.

By all SAXS standards, D-line was indeed a small beamline: With an experimental hutch of about 5m lengths that housed incident flight path and slits, sample stage, exit flight path, and detector, the maximum sample-detector distance was just 2m. Overall D-line was also a very short beamline, with only 15m from the source point of a CHESS hard-bent dipole magnet to the sample. And this at a 5.2 GeV storage ring! However, in combination with multilayer optics this arrangement provided a great photon flux of 1e12 photons/s/mm2 at 10 keV.

In case this page inspires you to do experiments as described here, I'll be happy to provide advice about real-time experiments, in-situ sample environments, and data analysis. As my many users and collaborators have shown at D-line, even a small station at a bending magnet can be developed into a cutting-edge GISAXS/GIWAXS beamline.    DS

Mirror site

Due to occasional issues with the access to personal web pages at CHESS, I created a mirror site: https://smilgies.github.io/dms79/. Please bookmark in case access problems continue.

A final comment

Starting around 2007 GISAXS and GIWAXS experiments, particularly for the characterization of soft materials thin films, started to experience tremendous popularity and it has become hard to keep this tutorial up to date. Many new user groups and beamlines have gotten involved and are building up their own expertise and publication lists. Please do not hesitate to point out papers describing new applications or technical break-throughs that I may have missed. And please take a moment to fill out the feedback below. DS

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