GISAXS

update 10/2011

Detlef-M. Smilgies

[home]

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 little brother of Grazing-Incidence Diffraction (scattering geometry and sample goniometer). The technique was originally introduced by Joanna Levine and Jerry Cohen [Levine],[Levine2], but has come to full flourish only in the past 10 years for the study of nanostructured systems.


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 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. 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 of 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, Kim,  Smilgies2, Paik].

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].
 
 

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 example of lamellar films formed by symmetric polystyrene-polybutadiene block copolymers. 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 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, even a morphology change as a function of chain length is possible. This has been indeed observed for PS-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-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] 
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-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 [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. 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". While a fiber is the dual system to a thin film, 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 effect have to be included in a proper interpretation.
 
 

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

GISAXS from the polymer film
shown on the left.
[Smilgies]

The scattering from such a lamellar system with a period of about 800 Å is so strong, that in-situ time-resolved measurements of the swelling of the film in solvent vapor on a timescale of minutes were possible [Smilgies].
 

Often, though, the ordering is not quite so perfect:
 
In thick films 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.


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

sample PSPB-V5

PS-PB sample with a chain length in the intermediate regime.
A mixture of  parallel, perpendicular, and unoriented lamellae
is observed. (Busch, Smilgies, Posselt, Papadakis, unpublished)


Thin films with other block copolymer morphologies than the lamellar phase have been analyzed recently: Du et al. characterized and modelled a monolayer of spherical voids in a matrix [Du] using the IsGISAXS code by [Lazzari]. Xu et al. and Li et al. characterized standing hexagonal cylinders [Xu, Li]. 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 random spherical pores [Lee2].  The Hillhouse group independently  analyzed the gyroid phase [Tate, Urade]. 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]. 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.

In their study of silica surfactant mesophases the kinetics of the formation of various morphologies has been studied by Gibaud et al. [Gibaud]. The groups of Magerl and Zabel studied the absorption of spherical micelles from the liquid onto a silicon substrate with neutron scattering [Wolff]. 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 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 and coworkers studied thermal treatment of polyethylene films in-situ with simultaneous small- and wide-angle scattering [Sasaki]. 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].
 
 

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 cylinders with the cylinder material removed [Li] as well as quantum dot arrays [Metzger]. Below the calculated scattering intensity from a dilute layer of elliptical nanoparticles on a wafer surface is shown in the quasikinematic approximation (left panel).
 
 

elliptical nanoparticles: dilute layer
 

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 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
S(qy)
 
 

form factor
F(qy,qz)
(log scale)
 

Vineyard factor
T(qz)
Contributions to a GISAXS intensity map in the quasikinematic approximation.


In our 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 [Naudon], and is based on the seminal work by [Vineyard] on grazing-icidence diffraction. [Heitsch] and coworkers have recently applied the quasi-kinematic approximation to model full 2D scattering images of monolayers 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].

<add image: Heitsch>


Microstructure characterization

From spot-like diffraction patterns information about the microstructure of soft materials can be obtained. The two basic ingredients of the microstructure are
<add picture: Tang - zone-casting>

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.

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, Wolff, Dourdain, Kim, Narayanan, Paik, Smilgies2, Papadakis2, Hanrath].

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

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

<add pictures: Papadakis - instability, Hanrath - Bain path, Campolongo - lab on a drop>



Oriented monodisperse nanoparticles

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].
 
 

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


<artificial gratings: hofmann - Ocko, Rueda - Ezquerra, ocko - transmission>

<add Hanrath, Brueckel, Fang: site-induced orientation of non-spherical nanoparticles>

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. However, by patterning the substrate, further ordering may be imposed on the film, and structures may show a preferential orientation with respect to the substrate as seen in polymer blends where the surface had been prepared by alternating hydrophobic and hydrophilic stripes [Böltau].

Similarly, regular patterns can be prepared by lithographic techniques [Woll] representing an artificial lamellar system PMMA-air. 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.


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.


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).


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, Dunphy, Hanrath] and binary [Smith] superlattices have be obtained. A key for these latter studies was careful tuning of deposition technique and annealing conditions.

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]. 

Indexation schemes for such complex patterns have been proposed by Smilgies & Blasini [Smilgies3] and Breiby and coworkers [Breiby]. The microstructure of such deposits can be studied using Scherrer grain size analysis [Smilgies4]. 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 elaborate spot patterns.

 <add Figure Crossland>


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.

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]. 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-kinamatic.

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. In this work the case of finite objects on a substrate surface is treated.

 [Lee1, Lee2] and [Busch3] investigated basic DWBA models suitable for polymer thin films, 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 David Babonneau made his program "FitGISAXS" available on the web, which is capable of modelling nanostructures in buried layers [Babonneau]. 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. Interfacial effects at the two film surfaces can also be treated, but are most commonly ignored. Hence scattering from thin film systems features additional complexity and is important to consider in the interpretation of GISAXS scattering data.

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.

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 [Hosemann, 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.
 
 


Summary and Outlook

Mesoscopic systems can display a large range of ordering properties. Each of these has a well-defined signature in its GISAXS 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 scattering geometry  is straightforward and, in many cases, without the need for scanning, making GISAXS very attractive to combine 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. Swelling kinetics in block copolymers happens on the time scale of minutes, and are well matched for the study of polymer kinetics. As area detectors are evolving, the msec time scale has become readily accessible with the Pilatus detector family, opening a new window in the self-organization kinetics of nanostructured materials.

All of these features make GISAXS a very versatile tool to study shape and density correlations in nanoscopic systems in situ and in real time.

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

(last update: 10/2011)

A Final Comment

I am trying to keep this tutorial up to date and I very much appreciate your feedback. Recently the use of GISAXS techniques to characterize nanostructured thin films has strongly accelerated, and many new groups are getting involved. Please do not hesitate to point out papers that I may have missed. And please take a moment to fill out the feedback below. DS


The content of this tutorial is
If somone asks you about GISAXS:
This web page was
Other comments


References

[Alexandrovic] Vesna Aleksandrovic, Denis Greshnykh, Igor Randjelovic, Andreas Frömsdorf, Andreas Kornowski, Stephan Volker Roth, Christian Klinke, and Horst Weller: "Preparation and Electrical Properties of Cobalt-Platinum Nanoparticle Monolayers Deposited by the Langmuir-Blodgett Technique", ACS Nano 2,  1123–1130 ( 2008).
[Als-Nielsen] J. Als-Nielsen and D. McMorrow: "Elements of modern X-ray physics", (John Wiley & Sons, New York, 2001).
[Anastasiadis] S. H. Anastasiadis, T. P. Russell, S. K. Satija, and C. F. Majkrzak: "Neutron reflectivity studies of the surface-induced ordering of diblock copolymer films", Phys. Rev. Lett. 62, 1852-1855 (1989)
[Angelescu]
 Dan E. Angelescu, J. H. Waller, D. H. Adamson, P. Deshpande, S. Y. Chou, R.A. Register, and P. M. Chaikin: "Macroscopic Orientation of Block Copolymer Cylinders in Single-Layer Films by Shearing", Adv. Mater. 16, 1736-1740 (2004).
[Babonneau] David Babonneau: "FitGISAXS: software package for modelling and analysis of GISAXS data using IGOR Pro", J. Appl. Cryst. 43, 929–936 (2010).
[Babonneau2] D. Babonneau, S. Camelio, D. Lantiat, L. Simonot, and A. Michel, "Waveguiding and correlated roughness effects in layered nanocomposite thin films studied by grazing-incidence small-angle x-ray scattering", Phys. Rev. B 80, 155446 (2009).
[Baker]Jessy L. Baker, Asaph Widmer-Cooper, Michael F. Toney, Phillip L. Geissler, and A. Paul Alivisatos: "Device-Scale Perpendicular Alignment ofColloidal Nanorods", Nano Lett. 10, 195-201 (2010).
[Baker2]Jessy L. Baker, Leslie H. Jimison, Stefan Mannsfeld, Steven Volkman, Shong Yin, Vivek Subramanian, Alberto Salleo, A. Paul Alivisatos, and Michael F. Toney: "Quantification of Thin Film Crystallographic Orientation Using X-ray Diffraction with an Area Detector", Langmuir 26, 9146 (2010).
[Bian]
 Kaifu Bian, Joshua J. Choi, Ananth Kaushik, Paulette Clancy, Detlef-M. Smilgies, and Tobias Hanrath: "Shape-anisotropy driven symmetry transformations in nanocrystal superlattice polymorphs", ACS Nano. 5  2815–2823 (2011).
[Breiby]Dag W. Breiby, Oliver Bunk, Jens W. Andreasen, Henrik T. Lemked and Martin M. Nielsen: "Simulating X-ray diffraction of textured films", J. Appl. Cryst. 41, 262–271(2008).
[Böltau] M. Böltau, S. Walheim, J. Mlynek, G. Krausch, U. Steiner, Nature 391, 877 (1998).
[Busch] P. Busch, D.-M. Smilgies, D. Posselt, F. Kremer, and C.M. Papadakis: "Grazing-incidence small-angle x-ray scattering (GISAXS) - Inner structure und kinetics of thin block copolymer films", Macromol. Chem. Phys. 204, F18-F19 (2003). (preprint)
[Busch2]
 P. Busch, D. Posselt, D.-M. Smilgies, F. Kremer and C. M. Papadakis: ''Diblock copolymer thin films investigated by tapping mode AFM: Molar mass dependence of surface ordering'', Macromolecules 36, 8717-8727 (2003).
[Busch3] P. Busch, M. Rauscher, D.-M. Smilgies, D. Posselt, and C. M. Papadakis: "Grazing-incidence small-angle x-ray scattering (GISAXS) as a tool for the investigation of thin nanostructured block copolymer films - The scattering cross-section in the distorted wave Born approximation", J. Appl. Cryst. 39, 433-442 (2006).
[Busch4]
 P. Busch, D. Posselt, D.-M. Smilgies, M.Rauscher, and C.M. Papadakis: "The Inner Structure of Thin Films of Lamellar Poly(Styrene-b-Butadiene) Diblock Copolymers as Revealed by Grazing-Incidence Small-Angle Scattering", Macromolecules 40, 630-640 (2007).
[Busch5]
 Peter Busch, Sitaraman Krishnan, Marvin Paik, Gilman E. S. Toombes, Detlef-M. Smilgies, Sol M. Gruner, and Christopher K. Ober: "Surface induced tilt propagation in thin films of semifluorinated liquid-crystalline side-chain block copolymers", Macromolecules 40, 81-89 (2007).
[Campolongo]
 Michael J. Campolongo, Shawn J. Tan, Detlef-M. Smilgies, Mervin Zhao, Yi Chen, Iva Xhangolli, Wenlong Cheng, and Dan Luo:"Crystalline Gibbs Monolayers of DNA-Capped Nanoparticles at the Air–Liquid Interface", ACS Nano (2011), Article ASAP, DOI: 10.1021/nn202383b
[Choi]
 Joshua J. Choi, Clive R. Bealing, Kaifu Bian, Kevin J. Hughes, Wenyu Zhang, Detlef-M. Smilgies, Richard G. Hennig, James R. Engstrom, and Tobias Hanrath, "Controlling Nanocrystal Superlattice Symmetry and Shape-Anisotropic Interactions through Variable Ligand Surface Coverage", J. Am. Chem. Soc. 2011, 133, 3131–3138.
[Crossland] Edward Crossland, Marleen Kamperman, Mihaela Nedelcu, Caterina Ducati, Ulrich Wiesner, Gilman Toombes, Marc Hillmyer, Sabine Ludwigs, Ullrich Steiner, Detlef-M. Smilgies, and Henry Snaith:  "A bicontinuous double gyroid hybrid solar cell", Nano Lett. 9, 2807-2812 (2009).
[Darko]C. Darko, I. Botiz, G. Reiter, D.W. Breiby, J.W. Andreasen, S.V. Roth, D.-M. Smilgies, E. Metwalli, and C.M. Papadakis: "Multiscale study of crystallization in diblock copolymer thin films at different supercooling", Phys. Rev. E 79, 041802 (2009).
[Di]Zhenyu Di, DorthePosselt, Detlef-M. Smilgies, and Christine Papadakis: "Structural rearrangements in a lamellar diblock copolymer thin film during treatment with saturated solvent vapor",  Macromolecules 43, 418–427 (2010).
[Dourdain]
 S. Dourdain, A. Rezaire, A. Mehdi, B.M. Ocko, A. Gibaud: "Real time GISAXS study of micelle hydration in CTAB
templated silica thin films", Physica B 357, 180–184 (2005).
[Du] Phong Du, Mingqi Li, Katsuji Douki, Xuefa Li, Carlos B.W. Garcia, Anurag Jain, Detlef- M. Smilgies, Lewis J. Fetters, Sol M. Gruner, Ulrich Wiesner, Christopher K. Ober: "Additive-driven Phase Selective Chemistry in Block Copolymer Thin Films:  The Convergence of Top Down and Bottoms Up Processing", Advanced Materials 16, 953-957 (2004).
[Dunphy]Darren Dunphy, Hongyou Fan, Xuefa Li, Jin Wang, and C. Jeffrey Brinker: "Dynamic Investigation of Gold Nanocrystal Assembly Using In Situ Grazing-Incidence Small-Angle X-ray Scattering", Langmuir 24, 10575-10578 (2008).
[Foerster] Forster, S.; Timmann, A.; Konrad, M.; Schellbach, C.; Meyer, A.; Funari, S. S.; Mulvaney, P.; Knott, R. "Scattering Curves of Ordered Mesoscopic Materials", J. Phys. Chem. B 109, 1347–1360 (2005).
[Gibaud] A. Gibaud et al.: "Evaporation-Controlled Self-Assembly of Silica Surfactant Mesophases",  J. Phys. Chem. B 107, 6114-6118 (2003).
[Goodfellow]
 Brian Goodfellow, Reken Patel, Matthew Panthani, Detlef-M. Smilgies, Brian Korgel,"Melting and Sintering of a Body-Centered Cubic Superlattice of PbSe Nanocrystals Followed by Small Angle X-ray Scattering", J Phys Chem C 115, 6397–6404 (2011).
[Hanrath] Tobias Hanrath, Joshua J. Choi, and Detlef-M. Smilgies: "Structure/Processing Relationships of Highly Ordered Lead Salt Nanocrystal Superlattices", ACS Nano 3, 2975–2988 (2009).
[Heitsch] Andrew T. Heitsch, Reken N. Patel, Brian W. Goodfellow, Detlef-M. Smilgies, and Brian A. Korgel: "GISAXS Characterization of Order in Hexagonal Monolayers of FePt Nanocrystals", J. Phys. Chem. C (online, DOI: 10.1021/jp1047979).
[Hosemann]
 Hosemann and Bagchi, ---book---
[Huang]
 Yi-Fang Huang, Chan-Wei Chang, Detlef-Matthias Smilgies, U-Ser Jeng, Anto R. Inigo, Jonathon David White, Kang-Chuang Li, Tsong-Shin Lim, Tai-De Li, Hsiang-Yun Chen, Show-An Chen, Wen-Chang Chen, and Wun-Shain Fann: "Correlating Nanomorphology with Charge-Transport Anisotropy in Conjugated-Polymer Thin Films", Adv. Mater. 21, 1–5 (2009).
[Jiang]Zhang Jiang, Xiao-Min Lin, Michael Sprung, Suresh Narayanan, and Jin Wang: "Capturing the Crystalline Phase of Two-Dimensional Nanocrystal Superlattices in Action", Nano Lett. 10, 799–803 (2010).
[Jiang2]
 Zhang Jiang, Dong Ryeol Lee, Suresh Narayanan, and Jin Wang: "Waveguide-enhanced grazing-incidence small-angle x-ray scattering
of buried nanostructures in thin films", Phys Rev B 84, 075440 (2011).
[Jin] Sangwoo Jin, Jinhwan Yoon, Kyuyoung Heo, Hae-Woong Park, Jehan Kim, Kwang-Woo Kim, Tae Joo Shin, Taihyun Chang, and Moonhor Ree: "Detailed analysis of gyroid structures in diblock copolymer thin films with synchrotron grazingincidence X-ray scattering", J. Appl. Cryst. 40, 950–958 (2007).
[Kim]
 Seung Hyun Kim, Matthew J. Misner, Ling Yang, Oleg Gang, Benjamin M. Ocko, and Thomas P. Russell: "Salt Complexation in Block Copolymer Thin Films", Macromolecules 39, 8473-8479 (2006).
[Lazzari] R. Lazzari: "IsGISAXS: a program for grazing-incidence small-angle X-ray scattering analysis of supported islands", J. Appl. Cryst. 35, 406-421 (2002). 
[Lee1]
 Byeongdu Lee, Jinhwan Yoon, Weontae Oh, Yongtaek Hwang, Kyuyoung Heo, Kyeong Sik Jin, Jehan Kim, Kwang-Woo Kim, and Moonhor Ree: "In-Situ Grazing Incidence Small-Angle X-ray Scattering Studies on Nanopore Evolution in Low-k Organosilicate Dielectric Thin Films", Macromolecules 38, 3395 (2005).
[Lee2]
 Byeongdu Lee, Insun Park, Jinhwan Yoon, Soojin Park, Jehan Kim, Kwang-Woo Kim, Taihyun Chang, and Moonhor Ree: "Structural Analysis of Block Copolymer Thin Films with Grazing Incidence Small-Angle X-ray Scattering", Macromolecules 38, 4311-4323(2005).
[Lee3] Byeongdu Lee, Insun Park, Haewoong Park, Chieh-Tsung Lo, Taihyun Chang, and Randall E. Winans: "Electron density map using multiple scattering in grazing-incidence small-angle X-ray scattering", J. Appl. Cryst. 40, 496–504 (2007).
[Levine]
 J. R. Levine, J. B. Cohen, Y. W. Chung and P. Georgopoulos:" Grazing-incidence small-angle X-ray scattering: new tool for studying thin film growth" , J. Appl. Cryst. 22, 528-532 (1989).
[Levine2] J. R. Levine Parrill, P. Georgopoulos, Y.-W. Chung, and J. B. Cohen:  "GISAXS - Glancing incidence small angle X-ray scattering", J. Phys. IV France 3-C8, 411-417 (1993).
[Li]
 Mingqi Li, Kasuji Douki, Ken Goto, Xuefa Li, Christopher Coenjarts, Detlef M. Smilgies, and Christopher K. Ober: "Spatially Controlled Fabrication of Nanoporous Block Copolymers", Chem. Mater. 16, 3800-3808 (2004).
[Metzger] T. H. Metzger, I. Kegel, R. Paniago, A. Lorke, J. Peisl, J. Schulze, I. Eisele, P. Schittenhelm, and G. Abstreiter: "Shape, size, strain and correlations in quantum dot systems studied by grazing incidence X-ray scattering methods", Thin Solid Films 336,1-8 (1998).
T. H .Metzger, I. Kegel, R. Paniago and J. Peisl: "Grazing incidence x-ray scattering: an ideal tool to study the structure of quantum dots", J. Phys. D: Appl. Phys. 32,  A202–A207 (1999).
[Narayanan]
 Suresh Narayanan, Dong Ryeol Lee, Rodney S. Guico, Sunil K. Sinha, and Jin Wang: "Real-Time Evolution of the Distribution of Nanoparticles in an Ultrathin-Polymer-Film-Based Waveguide", Phys. Rev. Lett. 94, 145504 (2005).
[Naudon] A. Naudon in H. Brumberger (ed.): "Modern Aspects of Small-Angle Scattering", (Kluwer Academic Publishers, Amsterdam, 1995), p. 191.
[Paik]Marvin Y. Paik, Joan K. Bosworth, Detlef-M. Smilgies, Evan L. Schwartz, Xavier Andre, and Christopher K. Ober: "Reversible Morphology Control in Block Copolymer Films via Solvent Vapor Processing: An In-Situ GISAXS study", Macromolecules Macromolecules 2010, 43, 4253–4260.
[Papadakis] C. M. Papadakis, P. Busch, D. Posselt, and D.-M. Smilgies: "Morphological Transition in Thin Lamellar Diblock Copolymer Films as Revealed by Combined GISAXS and AFM Studies ", Advances in Solid State Physics, Vol. 44 (Springer Verlag, Heidelberg, 2004) p. 327-338.
[Papadakis2] Christine M. Papadakis, Zhenyu Di, Dorthe Posselt, and Detlef-M. Smilgies: "Structural Instabilities in Lamellar Diblock Copolymer Thin Films During Solvent Vapor Uptake", Langmuir 24, 13815-13818 (2008). 
[Park-M]
 Miri Park, Christopher Harrison, Paul M. Chaikin, Richard A. Register, Douglas H. Adamson: "Block Copolymer Lithography: Periodic Arrays of 1011 Holes in 1 Square Centimeter", Science 276, 1401-1404 (1997).
[Park-I]
 Insun Park, Byeongdu Lee, Jinsook Ryu, Kyuhyun Im, Jinhwan Yoon, Moonhor Ree, and Taihyun Chang: "Epitaxial Phase Transition of Polystyrene-b-Polyisoprene from Hexagonally Perforated Layer to Gyroid Phase in Thin Film", Macromolecules 38, 10532-10536 (2005).
[Pelletier]
 Vincent Pelletier, Koji Asakawa, Mingshaw Wu, Douglas H. Adamson, Richard A. Register, and Paul M. Chaikin: "Aluminum nanowire polarizing grids: Fabrication and analysis", Appl. Phys. Lett. 88, 211114 (2006).
[Pfeiffer]
 F. Pfeiffer, U. Mennicke and T. Salditt: "Waveguide-enhanced scattering from thin biomolecular films", J. Appl. Cryst. 35, 163-167(2002).
[Pickett] G. Pickett, T. Witten, S. Nagel, Macromolecules 26, 3194 (1993).
[Potemkin]
 Igor I. Potemkin, Peter Busch, Detlef-M. Smilgies, Dorthe Posselt, Christine M. Papadakis: "Effect of the Molecular Weight of AB Diblock Copolymers on the Lamellar Orientation in Thin Films: Theory and Experiment", Macromol. Rap. Commun. 28, 579-584 (2007). (cover)
[Rauscher] M. Rauscher, T. Salditt, and H. Spohn: "Small-angle X-ray scattering under grazing incidence: the cross section in the distorded-wave Born approximation", Phys. Rev. B, 52(23), 16855-16863, (1995).
[Renaud] G. Renaud et al.: "Real-Time Monitoring of Growing Nanoparticles", Science 300, 1416 (2003).
[Rivnay]
 Jonathan Rivnay, Rodrigo Noriega, R. Joseph Kline, Alberto Salleo, and Michael F. Toney: "Quantitative analysis of lattice disorder and crystallite size in organic semiconductor thin films", Phys. Rev. B 84, 045203 (2011).
[Rueda]
 D. R. Rueda, I. Martín-Fabiani, M. Soccio, N. Alayo, F. Pérez-Murano, E. Rebollar, M. C. García-Gutiérrez, M. Castillejo and T. A. Ezquerra: "Grazing-incidence small-angle X-ray scattering of soft and hard nanofabricated gratings", J. Appl. Cryst. 45 (2012).
[Sasaki]
 Sono Sasaki, Hiroyasu Masunaga, Hiroo Tajiri, Katsuaki Inoue, Hiroshi Okuda, Hiromichi Noma, Kohji Honda, Atsushi Takaharad and
Masaki Takata: "In situ investigation of annealing effect on lamellar stacking structure of polyethylene thin films by synchrotron grazing-incidence small-angle and wide-angle X-ray scattering", J. Appl. Cryst. 40, s642–s644 (2007).
[Sendja] B Thiodjio Sendja, R Eba Medjo, J Mane Mane, G Ben Bolie, D Diop and P Owono Ateba: "A GISAXS study of the angular dependence of carbon nanotubes grown on a plain substrate by the dc HF CCVD process", Phys. Scr. 82, 025601 (2010).
[Saunders]
 Aaron E. Saunders, Ali Ghezelbash, Detlef-M. Smilgies, Michael B. Sigman Jr., and Brian A. Korgel: "Columnar Self-Assembly of Colloidal Nanodisks", Nano Letters 6, 2959-2963(2006). Erratum: Nano Letters 7, 541 (2007).
[Schultz]David G. Schultz, Xiao-Min Lin, Dongxu Li, Jeff Gebhardt, Mati Meron, P. James Viccaro, and Binhua Lin: "Structure, Wrinkling, and Reversibility of Langmuir Monolayers of Gold Nanoparticles", J. Phys. Chem. B, 110, 24522-24529 (2006).
[Sinha]
 S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley: "X-ray and neutron scattering from rough surfaces", Phys. Rev. B 38, 2297-2311 (1988).
[Sirringhaus]
[Smilgies] Detlef-M. Smilgies, Peter Busch, Dorthe Posselt, and Christine M. Papadakis: "Characterization of Polymer Thin Films with Small-Angle X-ray Scattering under Grazing Incidence (GISAXS)", Synchrotron Radiation News, Issue 15(5), p. 35-42, 2002. (reprint)
[Smilgies2] Detlef-M. Smilgies, Ruipeng Li, Zhenyu Di, Charles Darko, Christine M. Papadakis, and Dorthe Posselt: "Probing the Self-Organization Kinetics in Block Copolymer Thin Films.", Mater. Res. Soc. Symp. Proc. 1147-OO01-01 (2009). (reprint).
[Smilgies3]D.-M. Smilgies and D. R. Blasini: "Indexation scheme for oriented molecular thin films studied with grazing-incidence reciprocal-space mapping", J. Appl. Cryst. 40, 716-718 (2007).
[Smilgies4]Detlef-M. Smilgies: "Scherrer Grain-Size Analysis Adapted to Grazing-Incidence Scattering with Area Detectors", J. Appl. Cryst. 42, 1030-1034 (2009).
[Smith] Danielle K. Smith, Brian Goodfellow, Detlef M. Smilgies, and Brian A. Korgel: "Self-Assembled Simple Hexagonal AB2 Binary Nanocrystal Superlattices: SEM, GISAXS and Substitutional Defects", J. Am. Chem. Soc. 131, 3281–3290 (2009).
[Stein]
 Gila E. Stein, Edward J. Kramer, Xuefa Li, and Jin Wang: "Layering Transitions in Thin Films of Spherical-Domain Block
Copolymers", Macromolecules 40, 2453-2460 (2007).
[Tang]
 Chuanbing Tang, Adam Tracz, Michal Kruk, Rui Zhang, Detlef-M. Smilgies, Krzysztof Matyjaszewski, Tomasz Kowalewski:"Long-range Ordered Thin Films of Block Copolymers by Zone-Casting and Their Thermal Conversion into Ordered Nanostructured Carbon",  J. Am. Chem. Soc. 127 (Communication), 6918-6919 (2005).
[Tate]
 Michael P. Tate, Vikrant N. Urade, Jonathon D. Kowalski, Ta-chen Wei, Benjamin D. Hamilton, Brian W. Eggiman, and Hugh W. Hillhouse: "Simulation and Interpretation of 2D Diffraction Patterns from Self-Assembled Nanostructured Films at Arbitrary Angles of Incidence: From Grazing Incidence (Above the Critical Angle) to Transmission Perpendicular to the Substrate", J. Phys. Chem. B 110, 9882-9892 (2006).
[Tate2] Michael P. Tate and Hugh W. Hillhouse: "General Method for Simulation of 2D GISAXS Intensities for Any Nanostructured Film Using Discrete Fourier Transforms", J. Phys. Chem. C111, 7645-7654 (2007).
[Urade]
 Vikrant N. Urade, Ta-Chen Wei, Michael P. Tate, Jonathan D. Kowalski, and Hugh W. Hillhouse: "Nanofabrication of Double-Gyroid Thin Films", Chem. Mater. 19, 768-777 (2007).
[Vineyard] G. H. Vineyard: "Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces", Phys. Rev. B 26, 4146-4159 (1982).
[Wolff]
 Max Wolff, Uwe Scholz, Rainer Hock, Andreas Magerl, Vincent Leiner, and Hartmut Zabel: "Crystallization of Micelles at Chemically Terminated Interfaces", Phys. Rev. Lett. 92, 255501 (2004).
[Woll] unpublished. (follow the link to see a pretty picture)
[Xu] T. Xu, J. T. Goldbach, M. J. Misner, S. Kim, A. Gibaud, O. Gang, B. Ocko, K. W. Guarini, C. T. Black, C. J. Hawker, and T. P. Russell: "Scattering Study on the Selective Solvent Swelling Induced Surface Reconstruction", Macromolecules 37, 2972-2977 (2004).
[Yoneda] Y. Yoneda: "Anomalous Surface Reflection of X Rays", Phys. Rev. 131, 2010-2013 (1963).
[Yoon] Jinhwan Yoon, Seung Yun Yang, Byeongdu Lee, Wonchul Joo, Kyuyoung Heo, Jin Kon Kimb, and Moonhor Ree: "Nondestructive quantitative synchrotron grazing incidence X-ray scattering analysis of cylindrical nanostructures in supported thin films", J. Appl. Cryst. 40, 305–312(2007).
[Yoon2] Jinhwan Yoon, Kyeong Sik Jin, Hyun Chul Kim, Gahee Kim, Kyuyoung Heo, Sangwoo Jin, Jehan Kim, Kwang-Woo Kim ,and Moonhor Ree: "Quantitative analysis of lamellar structures in brush polymer thin films by synchrotron grazing-incidence X-ray scattering", J. Appl. Cryst. 40, 476–488 (2007).
[Zhang]
 Jun Zhang, Zhiping Luo, Zewei Quan, Yuxuan Wang, Amar Kumbhar, Detlef-M. Smilgies and Jiye Fang: "Low Packing Density Self-Assembled Superstructure of Octahedral Pt3Ni Nanocrystals", Nano Lett. 11, 2912–2918 (2011).