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Application of Micro- and Nanobeams for Materials Science

  • Gema Martínez-CriadoEmail author
Reference work entry

Abstract

Owing to the spatial resolution and sensitivity (i.e., signal-to-background ratio), nano- and micro-X-ray beams are emerging tools with a strong impact in materials science. Although the optical quality of the X-ray focusing devices has limited the progress of X-ray microscopy, recent advances in fabrication techniques as well as in theoretical approaches have pushed the spatial resolution toward the diffraction limit. As a result, materials research using nano- and micro-X-ray beams has begun to extend toward the atomic domain, with concomitant and continuous developments of multiple analytical tools. The study of micro-/nanoscale objects, small embedded domains with weak signals, and/or heterogeneous structures at the (sub)micrometer scales has required the use of intense X-ray pencil beams. Additionally, stimulated by the great brilliance with reduced emittance of current third-generation synchrotron sources and new developments in X-ray detector technology, today intense (sub)micron X-ray beams are available with a variety of focusing devices. Finally, thanks to the multiple interactions of X-rays with matter, these X-ray probes can be used for manifold purposes, such as ultrasensitive elemental/chemical detection using X-ray fluorescence/X-ray absorption, or for identification of minority phases and/or strain fields by X-ray diffraction with (sub)micron resolution. Here we describe how (sub)micrometer X-ray beams are produced and used today using refractive, reflective, and diffractive X-ray optics. We show that micro- and nano-X-ray beams are key tools for space-resolved determination of structural and electronic properties and for chemical speciation of nanostructured or composite materials. Selected recent examples will range from phase separation in single nanowires to visualization of dislocations and buried interfacial defects to domain distortions and quantum confinement effects.

Keywords

Focusing devices Heterogeneities Nanobeams Space-resolved properties X-ray microscopy 

Glossary

CDI

Coherent Diffraction Imaging

DPC

Differential Phase Contrast

CRL

Compound Refractive Lens

ESRF

European Synchrotron Radiation Facility

EXAFS

Extended X-ray Absorption Fine Structure

FZP

Fresnel Zone Plate

KB

Kirkpatrick-Baez Mirror Arrangement

OSA

Order Selection Aperture

SEM

Scanning Electron Microscope

SXM

Scanning X-ray Microscope

SXD

Scanning X-ray Diffraction

TXM

Transmission X-ray Microscope

XANES

X-ray Absorption Near-Edge Structure

XAS

X-ray Absorption Spectroscopy

XBIC

X-ray Beam-Induced Current

XEOL

X-ray Excited Optical Luminescence

Tr-XEOL

Time-Resolved X-Ray Excited Optical Luminescence

XLD

X-ray Linear Dichroism

XRD

X-ray Diffraction

XRF

X-ray Fluorescence

XRM

X-ray Microscopy

Introduction

Synchrotron radiation instrumentation has contributed actively to the rapid progress of materials science. Recently, X-ray nanofocusing optics has been added to standard analytical methods like diffraction, imaging, and X-ray absorption techniques to study nanosized domains emitting only weak signals, heterogeneous samples, and/or embedded objects at the (sub)micrometer length scales. As a result, not only tabletop X-ray microscopes have been developed (Adam et al. 2005), but several synchrotron radiation nanoprobes are available owing to the advanced fabrication methods of focusing devices and the great brilliance with reduced emittance of current third-generation synchrotron sources. Thus, with high spatial resolution, multiple synchrotron beam properties are exploited in several approaches, such as coherence for quantitative determination of strain maps, penetrating nature for in situ operation, temporal profile for time-resolved experiments, polarization for chemical identification, or high brilliance for ultrasensitive elemental detection and/or localization of minority phases.

Over optical, electron, and neutron probes, synchrotron radiation micro- and nanobeams have several advantages. According to the diffraction limit (Als-Nielsen and McMorrow 2001), sDL = γλ∕NA, with γ equal to 0.61 for two-dimensional focusing by a round lens and 0.5 for a linear (or rectangular) lens, λ the wavelength, and NA the numerical aperture, the ultimate resolution is almost two orders of magnitude better than the one for light microscopy. In comparison to electron microscopes, X-ray microscopes are not limited to very thin sections of samples or surface observations. Because of the large energy tunability and penetrating power of synchrotron radiation X-rays, they can provide noninvasively information from thick or buried specimens even under operating conditions. Moreover, X-ray microscopes offer a variety of image-contrast mechanisms in 2D and 3D (e.g., absorption, chemical state, phase, diffraction, polarization) to obtain images, zoom into regions of interest, and build up large fields of view. Finally, although it shares most of the advantages with neutron microscopy (Beguiristain et al. 2002), this latter potential competitor currently suffers from the lack of sufficiently bright sources.

From a technical perspective, the effective X-ray beam characteristics depend not only on the type and quality of the focusing optics but also on the X-ray wavelength and brilliance of the synchrotron source. In general, the beam size can be reduced by scaling down the source dimension or by increasing the demagnification ratio (sG = S × qp with S the size of the source, q the distance from the focusing element to the focal plane, and p the distance from the source to the focusing element), either by setting up the microscope at a larger distance from the source or by reducing the focal distance. This latter approach is particularly useful since the numerical aperture (\(\mathrm {NA} = n\ \sin \ \theta \) where n is the index of refraction at λ and θ the opening angle) can be increased together with the demagnification ratio, reducing the diffraction limited focus size (sDL = γλ∕NA) and increasing the photon density in the spot. Therefore, the working distance q and, thus, the overall length of the beamline play a key role. Accordingly, several third-generation synchrotron facilities optimize currently their emittance while developing long beamlines (e.g., 150 m–1 km) (Yumoto et al. 2005). Moreover, provided small secondary sources (∼25 μm slit), the source size can be fully exploited in both horizontal and vertical dimensions (Mimura et al. 2007; Somogyi et al. 2010). Although micro- and nanobeams could also be created on a shorter beamline using prefocusing lenses, whenever possible the number of optical elements is kept limited to avoid beam degradation due to mirror slope errors, absorption in refractive elements, thermal/vibration instability, etc.

In this chapter, the formation of micro- and nano-X-ray beams is described, the common experimental schemes of X-ray microscopes are discussed, and recent scientific examples are briefly reported. We cover mostly the use of hard X-ray beams, while soft X-ray (sub)microbeams applied to X-ray tomography are described in a previous chapter by Prof. Carolyn Larabell. Compared to a soft X-ray microscope, the focusing optics for a hard X-ray microscope leads to longer focal lengths (up to more than a meter) and larger depth of field (up to a few millimeters). These characteristics are essential when specific sample environments like furnaces or high-pressure cells are used. Also, a shorter wavelength is favorable for X-ray diffraction studies, including wide- and small-angle X-ray scattering approaches. Lensless imaging methods, like coherent diffraction imaging, are also not reviewed in the present chapter but reported by Henry Chapman and Richard Kirian in a previous section as well.

Experimental Approaches

X-ray microscopes are commonly classified into two categories: full-field X-ray microscopes and scanning X-ray microscopes (Sakdinawat and Attwood 2010). Like a classical light microscope, the layout of a full-field X-ray microscope involves optical elements as objectives to create magnified images of the objects (Guttmann et al. 2009). Its design requires the use of high photon intensities: first a condenser irradiates the sample, while an objective lens located behind amplifies the image into a fast charge-coupled device (CCD) camera. Using projection X-ray microscopy, i.e., changing the sample to focal plane distance, higher magnifications can be obtained. A similar scheme is often used for absorption/phase-contrast imaging to represent the density of electron in three dimensions (3D). From a set of images recorded at different angles, tomographic reconstruction algorithms result in the internal structure representation in 3D (see chapter  “Putting Molecules in the Picture: Using Correlated Light Microscopy and Soft X-Ray Tomography to Study Cells”).

The scheme for a scanning X-ray microscope, on the other hand, is more efficient in terms of X-ray photon doses (i.e., a high trade-off between X-ray photon flux and signal-to-noise ratio). The layout entails a focusing device that generates a (sub)micrometer beam. The sample is raster scanned on pixel-by-pixel base across the microprobe. Such design grants multimodal imaging (e.g., simultaneous acquisition of XRD, XRF, and/or XAS). As a result, it is possible to obtain in parallel the crystallographic orientation and elemental or chemical distribution possible within heterogeneous samples with submicron resolution (Mino et al. 2011). However, such setup involves numerous equipment: for example, multielement fluorescence detector, large-area CCD camera, and XYZ translation stage with continuous rotation about an axis.

In both experimental approaches, the nanofocusing optics is a critical element that governs the effective spatial resolution and performance of the X-ray microscopes.

X-Ray Focusing Optics

Generally X-ray spot sizes from micrometers down to tens of nanometers can be achieved using three sort of focusing devices: refractive, reflective, and diffractive optics. The choice depends on the information desired from the measurement, the experimental arrangement (e.g., sample environment), and the source characteristics. There are no ideal optics with the best resolution, highest photon flux, and easiest alignment, which yield shortest data acquisition time for all samples.

Compound Refractive Lenses

Based on refractive effects, compound refractive lenses (CRLs) consist of many single concave lenses stacked behind one another in order to reach practicable focal length (1 m) (Snigirev et al. 1996). Owing to the tiny deviation of the index of refraction n from unity (∼10−5) according to n = 1 − δ + , the focal length of a single X-ray lens of 2 mm radius of curvature would be about 100 m.

From the Gauss lens formula, 1∕f = 1p + 1q, the diffraction-limited resolution sDL of a biconcave lens with aperture 2R0 = 2(2Rω0)1∕2 with R the minimum radius of the aperture and ω0 the projection in the perpendicular direction of the beam is determined by the effective aperture Aeff of the lens reduced by photon absorption and scattering NA = Aeff(2q) compared to the geometrical aperture 2R0.

Concerning the geometrical shape, the pioneers of the development of CRLs, Snigirev and Snigireva (2008), showed that the introduction of a parabolic lens profile (s2 = 2Rω) made CRLs free of spherical aberrations, with focal lengths given by f = R2Nδ, where N is the number of stacked lenses, R the radius of curvature at the apex of the parabola, and δ the real-part decrement of the index of refraction. Recent simulations performed by del Rio and Alianelli (2012) have suggested that to obtain the ideal Gaussian focus, the use of lenses with a Cartesian oval profile could reduce aberrations in highly demagnifying optics.

The CRLs have several advantages, including easy alignment due to its in-line compact design, reliability, and adaptable focal length. Their robustness (mechanical and thermal) and straight optical path, which enhances the stability as there are no angular changes, make them particularly suited for hard XRM. However, they suffer from chromaticity and poor efficiency owing to the strong absorption. Based on advanced nanofabrication techniques to produce extremely small radii of curvature (e.g., electron-beam lithography and deep reactive ion etching), the use of low-Z materials such as diamond, silicon, lithium, beryllium, or boron has made possible efficient and high-resolution devices (Schroer et al. 2005). For example, with a focal distance of about 10 mm, a 60 nm X-ray beam has been demonstrated at 24.3 keV using parabolic refractive nanofocusing lenses made of Si with a photon flux of about 108 ph/s (Schroer et al. 2011; Lengeler et al. 1999).

Although the smallest X-ray beams achieved so far using compound refractive optics are about 50 nm in diameter, there are paths toward sub-10 nm beams, for example, the adiabatically focusing lenses (Schroer and Lengeler 2005), which present an aperture that is gradually (adiabatically) adapted to the size of the beam as it converges to the focus. This approach overcomes the refractive power per unit length of the optics along the optical axis. As a result, hard X-rays can be focused down to 2 nm, keeping a large number of thin lenses stacked behind each other. The spherical aberrations are avoided by using parabolic shapes for each individual lens.

Reflective Optics

Kirkpatrick-Baez Mirrors

X-ray mirrors rely on grazing-incidence conditions to focus the beam down to nanometer scales. Operating below a critical incidence angle \(\theta _{{C}}< \sqrt {\delta }\), where δ is the deviation from unity of the real part of the refraction index, total external reflection takes place according to Snell’s law. Thus, with angles within the milliradiant range, the entire incident wave is reflected, ensuring wide-bandpass high reflectivity. Since the incident beam also propagates in the reflecting medium as an evanescent wave, its extinction typically occurs within the first nanometers of the mirror surface. Accordingly, the surface quality plays a key role in the performance of the mirrors.

Regarding the geometry, total-reflection mirrors are generally used in crossed configuration as proposed in 1948 by Kirkpatrick and Baez to reduce the astigmatism in an early X-ray microscope (Kirkpatrick and Baez 1948). Based on two orthogonal mirrors, the resulting beam is decoupled along the horizontal and vertical directions. Today, two different systems are available: single-layer total-reflection systems and multilayer-coated mirrors based on Bragg condition.

For a single-layer elliptic-shaped mirror, as well described by Morawe et al. (1999), the critical angle θC varies as sin \(\theta _{{C}}=\sqrt { (2\delta )}\), where δ increases linearly with the X-ray wavelength λ and with the square root of the electron density of the material \(\sqrt {\rho _{e}}\). In the X-ray region, typical values are 10−5 for solid materials and about 10−8 for air. In addition, the mirror surface is often coated with high atomic number materials in order to restrict the mirror length, but the aperture 2q remains limited. Using high atomic number coatings, critical angles larger than 3 can be obtained in the soft X-ray range (< 1 keV), while θC barely reaches 0.5 in the hard X-ray regime (> 8 keV). The resulting performance of single-layer systems are basically determined by the mirror material. An estimation of the diffraction limit sDL (assuming NA ≈ sin θC/4) is \(s_{\mathrm {DL}}\approx {1.76}\ \lambda /\sqrt {(2\delta )} = 1.76\ \sqrt {(\pi /r_{\mathit {0}}\ \rho _{e})}\), where r0 is the classical electron radius. For platinum, for example, sDL is about 25 nm.

For multilayer mirrors, on the other hand, the coating consists of a bilayer periodically (period L) deposited of a lower absorbing material (low atomic number) as a spacer and a highly absorbing layer (high atomic number) with high reflectivity (Morawe et al. 1999). The multilayer period L meets the modified Bragg equation \(\Lambda =\lambda /[2 \sqrt {(n^{2}} - \cos ^{2} \theta )] \) in each point of the mirror. As a consequence, the outcoming radiation interferes coherently, producing a higher reflectivity (up to values higher than 90 %) (Morawe et al. 1999). Moreover, the multilayered spacings Λ can be adapted to fulfill the Bragg condition at a much larger angle θ than the one needed under total-reflection regime θC. Thus, the resulting performance is limited in theory by the lateral gradient of the multilayer spacing, depending on surface curvature and beam divergence. The diffraction limit sDL can be estimated from sDL ≈ 0.88∕(1∕ Λ2 − 1∕ Λ1), assuming NA ≈ λ∕2 (1∕ Λ2 −1∕ Λ1) with Λ12 the multilayer spacings at the respective edges of the mirror. For short-period strong-gradient structures, for example, sDL is about 5 nm. In practice, the resulting quality of the multilayer deposition (chemical stability, interface sharpness, interfacial diffusion and stress, etc.) plays also a key role.

Concerning the bending systems, KB mirrors split into two typologies: static mirrors polished according to a proper figure and dynamic systems based on actuators that bend flat mirrors into elliptical shapes (Eng et al. 1998; Ice et al. 2000).

Static mirrors with excellent characteristics are fabricated today by near-atomic polishing techniques; for example, at SPring-8, 7 nm beams resulted from static high-precision multilayer KB mirrors used in combination with a novel phase-error compensator at 20 keV (Mimura et al. 2010).

The dynamic bending, on the other hand, presents some flexibility in terms of the optical properties for specific beamline geometry and incidence angles. However, the use of bulky mechanical benders reduces the overall thermal/vibrational stability of the focusing system. In addition, the setup and optimization into specific elliptical shapes requires long times. Alternatively, the use of electromechanical methods with segmented bimorph mirrors has been recently proposed (Signorato and Ishikawa 2001). In these active mirrors, each segment is composed of oppositely biased piezoelectric ceramic plates (also called PZT). The plates can be bent into a specific shape, suppressing low-frequency errors and achieving the desired curvature under the application of appropriate voltages. Moreover, they can also adaptively change their profiles for the so-called wavefront correction (Kimura et al. 2009).

The principal advantage of the KB systems compared to CRLs is the intrinsic achromaticity, which makes them excellent devices for wide-bandpass applications, such as X-ray fluorescence analysis, absorption spectroscopies, and Laue diffraction techniques. They work over a wide energy range without changing the position or the spot size. However, the main limitation, if negligible figure error and surface roughness are present, is the small critical angle that restricts beam convergence (divergence) (Morawe et al. 1999).

In conclusion, using static KB systems, an in situ wavefront-correction approach to overcome aberrations due to imperfections allows today the production of an X-ray beam focused down to 7 nm at 20 keV (Mimura et al. 2010).

Montel (or Nested KB) Mirrors

The Montel (or nested KB) system consists of elliptical mirrors located next to one another in a perpendicular arrange in order to focus larger divergences with a shorter focal length (Montel 1957). This configuration gets rid of the different magnifications of sequential geometries (Liu et al. 2012).

Over conventional KB systems, nested mirrors have unique advantages in terms of compactness, geometrical demagnification, and ultimate diffraction limit. At the Advanced Photon Source (APS), for example, Liu et al. produced a 150 × 150 nm (H × V ) beam using Montel mirrors at 15 keV. However, important photon losses are present near the edges, which can result, for instance, in hardly 45 % reflectivity at 11 keV (Liu et al. 2011). So far significant technological efforts are put on mirror cutting from large substrates to avoid errors at mirror edges due to polishing round off. But, there are still some other limitations to be overcome in terms of thermal/vibrational instability, mirror imperfections, and beamline geometrical demagnification.

Diffractive Optics

Fresnel Zone Plates (FZP)

The Fresnel zone plates consist of a series of concentric rings of radius rn2 = n λ f, which are narrower at larger radii up to the last finest zone of width Δrn (Chao et al. 2009). The focusing principle is the constructive interference of the wavefront modified through the introduction of a relative change in amplitude or phase in the beams emerging from two neighboring zones.

In general, there are two different zone plates: an amplitude zone plate where the focusing results from different absorptions between two neighboring zones and a phase zone plate where the phase changes on transmission through a zone.

The diffracted limited resolution of a zone plate is given by its maximum diffraction angle NA = λ∕(2 Δrn), so that sDL = 122 Δrn. Thus, a diffraction-limited focus can be produced under X-ray beam illumination with spatial coherence length equal to or greater than the diameter of the zone plate.

Despite their chromatic nature, the Fresnel zone plates present an important advantage in terms of alignment purposes, thanks to their in-line optical nature. The effective efficiency depends on the phase shift and attenuation introduced by the FZP structures. In the soft X-ray energy regime, the photoelectric absorption restricts the efficiency to about 15 %, whereas for hard X-rays up to 40 %, efficiencies could be achieved. Unfortunately, the extreme aspect ratios (height/width of finest zone) necessary to reach such latter values is the bottleneck. Nevertheless, many efforts have been made lately to overcome such issues. For example, frequency-doubled zone plates based on atomic layer deposition technology (Jefimovs et al. 2007) and multistep zone plates operating in higher diffraction orders are promising techniques (Chao et al. 2005). Both approaches address the practical efficiency problems through adequate zone height and/or optimization of higher-order effects.

Up to now, the best performing zone plate lenses in terms of resolution and efficiency are fabricated by means of electron-beam lithography and pattern transfer techniques; for example, a 10 nm beam has been achieved in a soft XRM (Chao et al. 2012) and 30 nm for hard X-rays at 8 keV (Yin et al. 2006). To increase the zone plate resolution, the lenses are also operated in higher diffraction orders; for instance, Rehbein et al. reached an 11 nm beam using soft X-ray third-order full-field microscopy (Rehbein et al. 2012). Although zone plates are easiest to make for soft X-rays, high aspect ratios (> 20) have also been demonstrated for hard X-rays using a zone-doubling approach (Vila-Comamala et al. 2010).

Multilayer Laue Lenses

The multilayer Laue lenses are composed of one-dimensional zone plates (Kang et al. 2006) based on multilayer coatings deposited by magnetron sputtering with varying d-spacing (Kang et al. 2008). The plates are coated, sectioned, and polished to an equivalent outermost zone width as small as 2.5 nm with several thousand zones and a thickness greater than 10 μm (Conley et al. 2008). Thus, over conventional FZP the multilayer Laue lens structure produced by lithographic methods has better fabrication quality in terms of the outermost zone width and aspect ratio, which defines the efficiency for hard X-rays.

In general, the multilayer Laue lenses can be divided into four groups depending on the diffraction condition (Yan et al. 2009): flat, tilted, wedged, and curved lenses. Under normal incidence (i.e., tilting angle is zero), only the inner parts of the structure diffract markedly. If the lenses are tilted, then outer regions are also involved, but the performance is optimized exclusively at a specific angle. The gradual variation of the zone width from the center to the outermost region limits the performance in the tilted case because the Bragg condition attains only at a given lens location (Koyama et al. 2011). That is the reason why for a wedged lens the zones are progressively tilted with respect to the incident X-rays. From elliptical or parabolic zone profiles, it is possible to ensure the Bragg condition, and the diffracted waves from each zone can be in phase at the focus with size close to the wavelength (Yan et al. 2010). However, so far real multilayer Laue lenses suffer from imperfections like interfacial roughness and small growth error, which produce systematic deviation of the zone position from the zone plate law. In addition, the small numerical aperture limits their applications.

Nowadays, under tilted geometry, side-by-side multilayer Laue lenses deliver high efficiency, producing 16 nm 1D focusing at 20 keV (Conley et al. 2008). Using a second set in orthogonal configuration, a 25 × 27 nm2 FWHM spot has been generated with an efficiency of 2 % at 12 keV (Yan et al. 2011). Higher efficiencies and even better resolutions require tapered d-spacings and curved substrates like kinoforms.

Kinoform Fresnel Lenses

The kinoform lenses are hybrid devices that enhance aperture while reducing absorption combining compound refractive optics and zone plates (Evans-Lutterodt et al. 2007). By removing the passive parts that cause multiples of 2π in phase shifts, high transmission, zero order, and high efficiency are merged. The resulting resolution can be increased by stacking many lenses in series, enlarging the numerical aperture.

Typically, there are two designs of kinoform lenses: a long one and a short kinoform (Yan 2010). In the short configuration, all the elements are folded back into a single plane as a blazed zone plate with zones shaped to match the exact phase change needed for forming a spherical wavefront. Compared to the long case that has only one focus, for a short kinoform, there are several foci. In general, the short-kinoform lenses usually outperform long ones in efficiency and spot size due to the edge diffraction effect. Despite some limitations (material quality, absorption loss, etch depths) (Stein et al. 2008), in principle a crossed pair of kinoform lenses can be used to focus in 2D.

Analytical Methods

Today several synchrotron radiation techniques make use of micro- and nano-X-ray beams. Methods like X-ray imaging, absorption, scattering, and diffraction are applied at the microscopic level (Takahashi et al. 2013; Segura-Ruiz et al. 2014; Chen et al. 2013; Yan et al. 2013; Hrauda et al. 2011; Smilgies et al. 2013; Li et al. 2012). The introduction of nanofocusing optics allows not only to record statistically significant data but also specific local signals from individual microstructures (Li et al. 2012), single nano-objects (Segura-Ruiz et al. 2014), or microscopic embedded domains in 2D and 3D (Takahashi et al. 2013; Hrauda et al. 2011). In a large multi-keV energy range, the use of (sub)micrometer beams has several advantages: (1) surface/deep escape depths; (2) element, site, and orbital selectivity with simultaneous access to K absorption edges and fluorescence emission lines of light, medium, and heavy elements; (3) structural probe with atomic resolution; (4) chemical trace sensitivity owing to the high brilliance of synchrotron sources; and (5) detection of orientational effects by applying polarization selection rules.

As a result, several primary and secondary mechanisms involved in the photon-matter interaction are exploited in X-ray microscopes (Als-Nielsen and McMorrow 2001), like XAS, XRD, XAS, XRF, SAXS, WAXS, XEOL, and X-ray beam-induced current (XBIC). All these analytical methods complement each other and produce a comprehensive picture of the materials properties. For example, imaging methods are complementary to diffraction techniques since they operate directly in real space rather than in reciprocal space. Likewise, in contrast to diffraction, the study of absorption can yield local structural information without requiring the existence of long-range ordering, sometimes missing in nanostructured materials.

X-Ray Imaging

One of the well-established methods in X-ray imaging is computed tomography, which provides the reconstruction of an object in slices or in 3D with high spatial resolutions (Donoghue et al. 2006) (see chapter  “Putting Molecules in the Picture: Using Correlated Light Microscopy and Soft X-Ray Tomography to Study Cells”). In comparison with traditional scanners found in hospitals, the coherence of the collimated synchrotron radiation produces much better image quality.

In addition, X-ray phase-contrast modality is a powerful imaging approach commonly used to produce quantitative maps of the electron density of weakly absorbing materials (Cloetens et al. 1999). The technique is based on transferring the phase shift induced by a material on the incident wave into a measurable intensity signal. In its holography-based scheme, for example, the phase information is recovered by means of a nanoscale reference aperture next to the sample that phases the recorded interference pattern. Mathematical phase-retrieval algorithms are used on the acquired phase-contrast images to indirectly measure or reconstruct the phase shifts imposed on the X-rays by the sample (Stockmar et al. 2012). A new related method called X-ray ptychography has been recently developed (Rodenburg et al. 2007), which combines an X-ray focusing mirror and a spatial filter (a pin hole that is inserted to stress a particular spatial frequency or to suppress high-frequency noise).

X-Ray Absorption

The principle of X-ray absorption relies on the annihilation of a photon during the radiation-matter interaction. The energy of the photon is transferred entirely to a photoelectron. By absorption spectroscopy, one measures the absorption of a material as a function of the incident photon energy (Bunker 2010). Other methods analyze the secondary phenomena which take place directly after the absorption. The study of these processes provides the so-called emission spectroscopy techniques.

X-ray fluorescence (XRF) analysis (the emission of photons) and Auger spectroscopy (the emission of electrons) both utilize the secondary mechanism related to the relaxation processes (return to the equilibrium), which follow from the excitation or ionization of the atoms in the material. After the primary absorption mechanism, the atom having undergone the loss of an electron finds itself in an unstable state corresponding to an excess of energy with respect to its ground state. It falls back to its ground state by giving out the energy originally absorbed.

XRF is a process that allows an atom to return to equilibrium (relaxation) after the absorption of a photon and the ejection of an electron. It occurs by an almost immediate (less than 10−15 s) emission of a photon with an energy inferior to that of the incident beam. The technique is particularly useful for trace analysis, yielding not only a very selective signature of chemical elements but also their concentration (Margui 2013). Today the sensitivity of XRF for trace analysis is in the ppb level, 100 times greater than by other methods.

On the other hand, the Auger effect involves the relaxation of an atom back to its ground state after the ejection of a photoelectron due to the absorption by means of the emission of a second electron from an outer energy shell (Schmidt 1997). Thus, by Auger spectroscopy, the energy of the secondary electron is measured in a similar way as in photoemission, which is directly associated with the ejection of photoelectrons from a material. The mean distance travelled by photoelectrons in a solid is of about 0.5–2 nm. Consequently, photoemission is particularly well suited for surfaces science.

X-Ray Scattering

The phenomenon of X-ray scattering is based on the interaction between the X-rays and the electronic clouds of the atoms (Als-Nielsen and McMorrow 2001). Two phenomena can be distinguished: elastic and inelastic scattering.

In a crystal, elastic scattering is restricted to extremely well-defined directions: Bragg diffraction. In disordered or partially ordered material, other methods need be applied such as diffuse scattering (Pietsch et al. 2004). The irregularities in the crystal lattice or in the unit cell show up in the diffraction pattern as scattering signals, which do not belong to the Bragg spots.

Diffuse scattering is also very useful for soft-condensed matter (polymers, biological material, liquid crystals, etc.), which in principle is non- or imperfectly crystalline (Stribeck 2007). Small-angle scattering (SAXS) and wide-angle scattering (WAXS) are diffuse scattering processes which arise due to a partial ordering in the material. Most macromolecular materials show phenomena of structural order on length scales from a few tens to a few thousands of nm. These structural effects in real space turn up at very small diffraction angles in reciprocal space. Thus, SAXS needs to record data at angles as small as 0.005. For that reason, the incident beam must have a very low divergence and the detector must be placed at several meters from the sample (Stribeck 2007).

WAXS, on the other hand, applies to amorphous materials (liquid, glasses, polymers, etc.), which are globally disordered but with regions of short-range ordering. The technique delivers the chemical composition or phase composition of a film and, as interatomic distances are studied, the scattering appears at large angles in reciprocal space (Stribeck 2007).

Finally, the method of anomalous scattering improves the contrast by increasing the contribution of a particular chemical element to the scattering process (Waseda 2002). At energies near an absorption edge, the theoretical scenario of elastic scattering by a free electron is no longer valid because of the creation of a resonance state. The incident wave is reemitted with a phase difference. By using anomalous scattering, the phase problem faced in protein crystallography can be solved.

X-Ray Diffraction

The principle of X-ray diffraction, a particular case of elastic scattering of X-rays by atoms, applies to a periodic stacking of atoms (Bragg’s law), namely, a crystal with long-range ordering (Cullity 1978). Under X-ray illumination, each atom in a crystal becomes the source of a weak amplitude wave which propagates in all directions, interfering among themselves. The resulting scattering from the whole crystal is cancelled in all, except in certain precise directions where the scattering is much stronger. The examination of the positions and intensities of the diffraction spots in an experimentally obtained diffraction pattern allows the reconstruction of the crystal structure in real space.

As an illustration, the next section presents a few examples of materials-related studies carried out recently using micro- and nano-X-ray beams produced mostly at third-generation synchrotron radiation sources. They are focused mainly on, but certainly not limited to, the following topics: visualization of dislocations, phase separation in single nanowires, field-dependent domain distortions, buried interfacial defects, strain state in individual dots, crystallization of conjugated molecules, quantum confinement effects, and microstructures in fuel cells.

Applications

Novel schemes, which combine multiple analytical methods into new techniques like near-field ptychography (Rodenburg et al. 2007), fluorescence tomography (Golosio et al. 2003), diffraction tomography (Bleuet et al. 2008), and/or X-ray excited optical luminescence microscopy (XEOL) (Martinez-Criado et al. 2006), have been recently applied in materials science. Based on the use of micro- and nanobeams, their goal is to achieve a full picture of the materials properties in 2D and/or 3D. For both academic research and industrial purposes, the microscopic studies are intended to reveal the materials microstructure, defects, failure mechanisms, segregation effects, as well as their behavior under crystallization or in operation at the (sub)micrometer length scales.

Visualization of Dislocations

Dislocations, crystallographic defects or irregularities within crystals, strongly influence many of the properties of materials (Nabarro and Duesbery 1979–2003). In general, they are probed by X-ray topography and transmission electron microscopy (Tanner 1976; Forwood et al. 1991). However, there are limitations in terms of spatial resolution and sample thickness. Recently, the strain fields induced by dislocations in a 1-μm-thick silicon single crystal were visualized at SPring-8 with nanometer spatial resolution by Bragg X-ray ptychography (Takahashi et al. 2013). Based on Bragg coherent diffraction imaging (CDI), in this new scanning X-ray microscopy, the retrieved phase information allows to determine the strain within a strained crystal (Robinson and Harder 2009). Thus, Bragg X-ray ptychography can provide high-resolution 3D images of strain within nanocrystals.

Using total-reflection KB mirrors, X-rays with energy of 11.8 keV were focused to a spot size of about 1 μm. As shown in Fig. 1, the microprobe was scanned across the 1-μm-thick silicon single-crystal membrane located on the focal plane, and the coherent Bragg diffraction pattern from the (220) lattice plane was collected at each beam position on a CCD (Takahashi et al. 2013).
Fig. 1

Schematic of the Bragg X-ray ptychography setup of the RIKEN physics beamline I (BL29XUL) at SPring-8 for strain imaging (Adapted with permission from Takahashi et al. (2013): Copyright (2013) APS)

Whereas the coherent illumination of the ordered single-crystal silicon produces characteristic Bragg diffraction patterns, speckle patterns are observed from the dislocation because of destructive interference of X-rays. At the dislocation core, the Bragg scattering creates a diffraction pattern similar to a concentric circle (see Fig. 2). The phase sharply changes when scanning the region distorted by dislocations. Several simulations corroborated that an X-ray vortex beam can be generated when a focused X-ray beam illuminates the phase singularities (Takahashi et al. 2013).
Fig. 2

(a) Image of phase shift for single-crystal silicon thin film obtained by Bragg X-ray ptychography, (b) magnified view of the boxed region in (a) (Adapted with permission from Takahashi et al. (2013): Copyright (2013) APS)

In short, the measurement also revealed that X-rays with a spiral wavefront (i.e., an X-ray vortex beam) can be generated in a silicon single crystal by the strain fields caused by dislocations. Such vortex beams can carry orbital angular momentum, making them very useful in novel spectroscopy techniques (Van Veenendaal and McNulty 2007). Here a key advantage is that the mode can be switched by selecting dislocation singularity and diffraction index. As a result, strong dichroic effects are induced which can be used to study quadrupolar transitions and the magnetism of 3d transition-metal systems.

In summary, it can be anticipated that this methodology will contribute to a greater understanding of the underlying design concepts of new structural materials. In addition, thin silicon crystals can open up new research opportunities in XFEL vortex optics, where production of an intense coherent X-ray beam with orbital angular momentum has been proposed at the fundamental wavelength of the undulator (Takahashi et al. 2013).

Phase Separation in Single Nanowires

Based on large surface to volume ratios, small active volumes, and quantum confinement effects, semiconductor nanowires are promising materials for advanced nanodevices (Li et al. 2006). In particular, the ternary alloy InxGa1−xN, owing to its large absorption edge, is an excellent candidate for the development of high-efficiency multijunction solar cells, light-emitting diodes, and lasers (Nakamura 1998). However, the growth of defect-free InxGa1−xN nanowires with a high degree of compositional uniformity and structural control is still a very difficult task. Data collected in a nonlocal way, i.e., averaging over many nanowires, have revealed the presence of several defects, for example, metallic In precipitates (Gorczyca et al. 2009), which lower the absorption energy edge apart from the induced strain and compositional changes. Therefore, the investigation of individual InxGa1−xN nanowires is crucial to advance the understanding of the mechanisms driving the performance of the InGaN-based nanodevices.

At the ESRF, single molecular beam epitaxy-grown InxGa1−xN nanowires have been recently studied by a multimodal hard X-ray nanoprobe based on KB mirrors (Fig. 3) (Segura-Ruiz et al. 2014). The composition and short- and long-range structural order were examined using both pink (ΔEE ∼ 10−2, flux of about 5 × 1012 ph/s, 55 × 55 nm2 beam size) and monochromatic beams (ΔEE ∼ 10−4, flux of about 5 × 1010 ph∕s, 105 × 110 nm2 beam size).
Fig. 3

Multi-technique setup of the nanoimaging station ID22NI at the ESRF (Replaced by the upgraded beamline ID16B) (Adapted with permission from Segura-Ruiz et al. (2014): Copyright (2014) ACS)

X-ray fluorescence maps exhibit an axial and radial heterogeneous elemental distribution in the single wires with Ga accumulation at their bottom and outer regions (Fig. 4).
Fig. 4

SEM image (first left), In (second), and Ga (third) Kα XRF maps of representative single dispersed and as-grown nanowires on the Si substrate, taken from the top (Adapted with permission from Segura-Ruiz et al. (2014): Copyright (2014) ACS)

Polarization-dependent nano-X-ray absorption near-edge structure demonstrates that despite the elemental modulation, the tetrahedral order around the Ga atoms remains along the nanowires. Figure 5c displays the X-ray linear dichroism spectra around the Ga K-edge measured at the top and bottom of a single nanowire, as well as the calculated data for wurtzite GaN. Both XLD signals exhibit the strong anisotropy typical of the wurtzite GaN lattice. Nano-X-ray diffraction mapping on single nanowires shows the existence of at least three different phases at their bottom: an In-poor shell and two In-rich phases. The different contributions to the (002) diffraction are observed even in the CCD images (shown in the insets of Fig. 5a, b) and have been attributed to regions with different In and Ga content. The alloy homogenizes toward the top of the wires, where a single In-rich phase is observed. No signatures of In-metallic precipitates are observed in the diffraction spectra. The In content and the single nanowires estimated from X-ray fluorescence and diffraction data are in good agreement.
Fig. 5

InGaN (002) XRD reflections (open circles) acquired at the bottom (a) and top (b) of a single nanowire along with the best multi-Gaussian fits (solid line). Different Gaussian contributions are plotted with dotted lines. The insets show the corresponding CCD images. (c) X-ray linear dichroism spectra around the Ga K-edge measured at the top (squares) and bottom (circles) of a single nanowire, as well as the calculated data (triangles) for wurtzite GaN (Adapted with permission from Segura-Ruiz et al. (2014): Copyright (2014) ACS)

Merging all findings, the scenario of the resulting nanowire could be roughly pictured and partially explained by the growth process. The substrate temperature (525C) of the studied nanowires was well below the lowest limit for GaN diffusion-induced self-organized nanostructures growth on Si (620C) (Gómez-Gómez et al. 2014). Therefore, Ga atoms should have a very limited diffusion on the substrate, whereas a notable diffusion is expected for In atoms, which can explain the spontaneous formation of the Ga-richer shell. After impinging on the sidewalls of the nanowire, the In atoms can either diffuse toward the top or get desorbed, whereas the Ga atoms are expected to be incorporated there, because their diffusion and desorption are highly suppressed.

In summary, the hyperspectral approach has demonstrated to be a powerful tool to investigate multiple properties of single nanowires simultaneously at the nanometer length scale (Segura-Ruiz et al. 2014). On the basis of the temporal structure of the synchrotron source, if time resolving power is added, additional valuable information can be obtained, as shown in some upcoming sections of this paper, calling for further time-resolved studies in materials science.

Field-Dependent Domain Distortion

Within the oxide family with perovskite structure, there are many different typologies: ferroelectrics, metals, ferromagnets and antiferromagnets, superconductors, and dielectric insulators (Eerenstein et al. 2006). Ferroelectric materials are those with a switchable, spontaneous electric polarization, which can be combined with other oxides in a superlattice (SL) structure (Lisenkov and Bellaiche 2007). Thus, for instance, a ferroelectric-dielectric SL consists of alternating layers of a ferroelectric material such as lead titanate (PbTiO3) and a dielectric material such as strontium titanate (SrTiO3) (Chen et al. 2013). As a consequence, the properties of the resulting PTO/STO system can be tailored by exploiting competition between the interacting properties of the component layers. For example, the electrical and structural properties as well as the configuration of polarization domains strongly depend on the coupling of the electrical polarization and the structural distortion between these layers.

Weakly coupled PTO/STO SLs exhibits a striped nanodomain configuration similar to the one observed in ultrathin ferroelectrics (Chen et al. 2013). The nonequivalent distribution of the polarization between both constituents gives rise to the formation of complex nanoscale variations on the basic striped motif, including vortices at the corners of domains (Aguado-Puente and Junquera 2002). An applied electric field distorts the domain structure and ultimately changes the SL to a uniformly polarized state without domains. The evolution of the polarization-domain configuration and of the atomic structure within each component layer as a function of time under an electric field is critical to provide insight into the mechanism of the transformation.

Recently, PTO/STO SLs were probed with a resolution of 100 ps by in situ time-resolved X-ray microdiffraction to study the changes taking place in the domain pattern and atomic structure (Chen et al. 2013). X-rays with photon energy of 10 keV were focused to a 200 nm spot using a Fresnel zone plate at station 7ID-B of the Advanced Photon Source (Jo et al. 2011). The distribution of scattered intensity was collected with an area detector, which was gated to perform measurements with the desired timing relationship to the applied field (i.e., at a specified time before or after the beginning of the electric-field pulse).

The results reveal that both layers responded differently to the applied field in reaching the uniformly polarized state (see Fig. 6). The difference is clear in both the nanoscale structure of striped polarization domains and in the development of piezoelectric strain and field-induced polarization. Initially the domains are distorted to increase the polarization in the STO layer while retaining the striped motif. Afterwards, the subsequent change to the uniform polarization state results in piezoelectric expansion dominated by the field-induced polarization of the STO layers (Jo et al. 2010).
Fig. 6

(a) The striped domains of the SL are represented by pairs of domain-related X-ray diffuse scattering peaks, offset from the intense structural reflections at the center of the plots. The domain-related intensity of the satellites decreases more rapidly for the l = 0 peak under an electric field. (b) The evolution of the domains is reflected by the changes of the domain satellites having different Miller indices. The ratio of the intensities of the m = 2, l = 1 to m = 2, l = 0 domain satellites increases under the application of a 2.12-MV/cm electric field (Adapted with permission from Chen et al. (2013): Copyright (2013) APS)

Buried Interfacial Defects in Fuel Cells

Solid oxide fuel cells (SOFCs) are electrochemical devices that convert hydrogen and oxygen into electrical energy at high temperature (800C) (Srinivasan 2010). A unit cell consists of a three-layer structure: one dense electrolyte between two porous electrodes (a cathode and an anode). The electrodes made of ceramic materials contain Ce, Co, Fe, La, Mn, Ni, Sr, Y, and Zr. The cells have a very high efficiency but suffer from important degradation mechanisms which are principally linked to residual stresses, elements diffusion, or microstructure evolution. Thus, the properties of the electrodes play a key role in the efficiency and durability of the cells.

Quantitative characterization techniques with sufficient elemental, structural, and chemical sensitivity at the nanoscale are crucial tools to understand the connection between the SOFC’s microstructure evolution and its performance. In particular for the investigation of the yttria-stabilized zirconia (YSZ) cermet electrolyte, quantitative analysis using X-ray fluorescence mapping is crucial. At the beamline 26-ID of Advanced Photon Source (APS) at Argonne National Laboratory, a SOFC anode sample, composed of nickel (Ni) and YSZ cermet, was investigated using a scanning X-ray microscope equipped with multilayer Laue lenses (MLL) nanofocusing optics to achieve not only high spatial resolution but also performed quantitative phase imaging (Yan et al. 2013). To measure the phase gradients, the technique, so-called differential phase-contrast imaging (DPC), which analyzes how much the X-ray nanobeam is bent when it propagates through the sample, was used (Hornberger et al. 2007). The robust generic DPC analysis algorithm based on a Fourier-shift fitting process enabled to use MLL optics to perform parallel measurements of X-ray fluorescence, absorption, and phase with spatial resolution better than 50 nm on a SOFC anode.

A monochromatic X-ray beam with photon energy of 12 keV was focused to a spot size of about 30 × 52 nm2 using a pair of MLL optics placed orthogonally with respect to each other (see Fig. 7). An energy dispersive silicon drift detector placed at about 90 to the incident beam was used to collect the X-ray fluorescence signal emitted by the sample positioned at the focal plane. The X-rays transmitted through the specimen were captured by a 2D pixel-array detector positioned about 1.4 m downstream from the sample.
Fig. 7

Schematic drawing of the experimental setup. An incident plane wave is focused to a spot by two crossed MLLs. The fluorescence signal and the far-field diffraction pattern are recorded simultaneously as the specimen is raster scanned (Adapted with permission from Yan et al. (2013): Copyright (2013) NPG)

Figure 8 displays the horizontal phase-gradient maps of the specimen collected by the differential intensity, the moment analysis, and Fourier-shift fitting algorithms, respectively (Yan et al. 2013). Whereas the former two suffer from strong artifacts, making them useless for a quantitative phase reconstruction, the Fourier-shift fitting algorithm gives superior contrast.
Fig. 8

(a) SEM image of the SOFC specimen adhered on a Si3Ni4 window with Pt welding, (bd) are horizontal phase-gradient images obtained by differential intensity, moment analysis, and Fourier-shift fitting algorithms, respectively (Adapted with permission from Yan et al. (2013): Copyright (2013) NPG)

Figure 9 shows Ni and Pt fluorescence maps, as well as the X-ray transmission and reconstructed phase images of the SOFC anode sample. The XRF signal from the YSZ electrolyte suffered from significant absorption, preventing it to be used for quantitative analysis. The measurements of absorption and phase show the integral change of the imaginary and real components of the refractive index along the beam direction, thus allowing the determination of the buried interfacial structures. Both of them show the isolated and connected pores under the surface in the Ni anode and the YSZ electrolyte, which cannot be observed by SEM. The phase image displays even higher levels of structural details due to a higher phase contrast, revealing all structural features both in the Ni anode and the YSZ electrolyte. For example, a crack on the top of the sample, indicated by an arrow in Fig. 9d, can be clearly identified in the phase image but is barely detectable in both the absorption and the XRF images (Yan et al. 2013).
Fig. 9

(a) Ni Kα XRF, (b) Pt Lα XRF, (c) X-ray transmission, and (d) reconstructed phase images (units in radian) of the SOFC sample. The arrow in (d) points to a crack, which is barely seen by SEM (Adapted with permission from Yan et al. (2013): Copyright (2013) NPG)

In summary, the high sensitivity of the phase to structural and compositional variations makes the high-resolution DPC technique extremely powerful in correlating the electrode performance with its buried nanoscale interfacial structures that may be invisible to the absorption and fluorescence contrast mechanisms.

Strain State in Single Quantum Dots

Among semiconductor devices, transistors are key elements typically used to amplify and switch electronic signals (Kaiser 1999). A small signal applied between one pair of its terminals allows control of a much larger signal at another pair of terminals. A basic transistor typically has three terminals: a source, where charge carriers enter; a drain, where the charge carriers exit; and a gate in the middle, which regulates the mobility of the charge carriers. In a field-effect transistor, the conductivity of the channel (an active region through which charge carriers flow from the source to the drain) is a function of the potential applied across the gate and source terminals. A common approach to strengthen transistor performance (e.g., carrier mobility and switching speed) is based on strained channel technology (Dhar et al. 2005). Tensile strain improves electron mobility in n-type transistors, while compressive strain is used for a better hole mobility in p-type devices (Ang et al. 2007). In spite of its importance, the impact of channel stress on the lattice structure is not yet fully understood. The use of stressors sometimes causes problems, which arise because such a 2D layer is not properly relaxed and dislocations or other defects are easily incorporated, degrading the functionality of the device.

At the beamline ID01 of the ESRF (Fig. 10), an n-type field-effect transistor with a strained Si channel, so-called dot-FET (Schmidt and Eberl 2001), was investigated by X-ray nanodiffraction (spot size of 400 nm diameter) (Hrauda et al. 2011). Because of the similarity of the crystal structures of Si and Ge, a buried Ge layer was used to induce tensile strain in the Si channel (lattice mismatch of 4.2 %). A three-dimensional SiGe island with 250 nm diameter and about 50 nm height was grown by molecular beam epitaxy on pre-patterned Si (001) (Jovanović et al. 2010). The islands were then overgrown with a Si capping layer that finally acts as a channel. Thus, the small active area of the transistor is buried underneath several layers such as the gate stack and metal contacts, making it hard to assess the structural properties while preserving its functionality.
Fig. 10

(a) Schematic of the experimental setup used at ID01: a beamstop (BS), a Fresnel zone plate (FZP), and an order-sorting aperture (OSA) are used to focus the incoming X-ray beam; an optical microscope (OM) for rough sample alignment; the precise localization of the sample is executed through the X-ray beam itself by scanning the sample position, while the goniometer is tuned to a characteristic signal (e.g., a Si Bragg peak or the diffuse SiGe signal). The signal attenuation by metal contacts can be used to locate the SiGe island in the center of the transistor. (b) An X-ray diffraction scanning (SDX) map is shown overlaid with a transparent microscope image as guide to the eye. (c) Reciprocal space map including the Si (224) Bragg peak and the diffuse signal from the SiGe island. From the position of this signal in reciprocal space, an average Ge content can be estimated. The crystal truncation rod (CTR) gives us information on the thickness of the Si channel. The detector streak (DS) arises due to enhanced air scattering when the goniometer passes through the intense Si Bragg peak (Adapted with permission from Hrauda et al. (2011): Copyright (2011) ACS)

Tensile strain values up to 1 % along the source-drain direction were estimated in the Si channel (Hrauda et al. 2011). The result shows that in order to further improve transistor characteristic, optimizing the shape and material combinations of the whole gate stack is essential. In general, scattered X-ray intensity distributions are very sensitive to slight deviations in the Ge distribution or to externally applied stress.

In summary, using an X-ray nanobeam, the internal structure of the active region of a fully processed field-effect transistor has been explored by diffraction and diffuse scattering techniques. These investigations are highly valuable for the development of process flows, as samples from different processing steps can be compared for analysis without interference from preparation. These findings open the road for further advanced studies of structural modifications under failure, or in-operando, subjected to high temperatures and/or applied fields.

Crystallization of Conjugated Molecules During Solution Shearing

Organic transistors are being extensively investigated for flexible and inexpensive plastic electronics applications, such as automobile dashboards and smart tags (Bao and Locklin 2007). Using an organic semiconductor in its channel, these transistors can be prepared either by vacuum evaporation of small molecules, by solution casting of polymers or small molecules, or by mechanical transfer of a peeled single-crystalline organic layer onto a substrate (Reese et al. 2004). In order to prepare high-mobility organic thin film transistors, solution shearing and related coating techniques such as knife coating or doctor blading are becoming crucial tools to finely control thin-film morphology to a much higher extent than has been possible with traditional deposition methods like drop casting and spin coating. By reasonable choice of the coating parameters, not only high-quality deposits can be prepared but also laterally oriented films.

The first attempt to monitor in situ the solution-shearing process (see Fig. 11), in which a drop of dissolved material is spread by a coating knife onto the substrate, and thin film formation of the soluble small-molecule semiconductor TIPS-pentacene was carried out at Cornell High Energy Synchrotron Source (CHESS) (Smilgies et al. 2013). The effects of shearing speed, blade-substrate gap, and substrate temperature and solution concentration on the crystallization of the film were investigated in real time using microbeam grazing-incidence WAXS and optical microscopy.
Fig. 11

Schematic of the experimental setup to study deposition of organic semiconducting molecules at high spatial and temporal resolution during the coating process. From right to left: X-ray microbeam, precision coating stage displaying a micrograph of a high-quality film, and high-speed X-ray area detector (Adapted with permission from Smilgies et al. (2013): Copyright (2013) VCH)

A solution of a semiconducting molecule (TIPS-pentacene), a silicon wafer kept at a specific temperature as substrate, and the highly polished edge of a second silicon wafer (shearing blade) were used. A precision instrument was developed to match the tight space and weight restrictions imposed by the sample goniometer and the sample microscope (Smilgies et al. 2013).

By drop casting, if the solution is spread too slowly or the temperature is too low, a liquid film is spread, and upon drying, a low-quality film is obtained. On the other hand, when getting the four critical parameters,– gap, speed, temperature, and concentration right – the film rapidly thins from the gap value of 100 μm to below 100 nm, i.e., 1,000-fold, and then solidifies immediately. All of the action happens under the influence of a viscoelastic shear field. This has the effect that molecular crystallites grow with lateral alignment, despite the fact that the amorphous silicon oxide at the surface of the wafer is isotropic: The shear field breaks the lateral symmetry (Smilgies et al. 2013).

In order to investigate the drying kinetics of the molecules under viscoelastic shear as the solution meniscus sweeps by, the X-ray beam was focused to 20 μm. With shearing speeds close to 1 mm/s and a meniscus region of typically 0.5 mm, the time resolution was 10 msec per frame, which allowed to study the crystallization process. As a consequence, a high-speed X-ray pixel-array detector had to be used.

Previous reports have shown that films grown with solution shearing featured very high mobility, a quality that describes how fast a transistor can switch (Giri et al. 2008). Correlated to the high mobility achieved, the molecular structure appeared to be strained, with Bragg reflections moved away from the positions of equilibrium drop-cast films. The CHESS experiments revealed further intricate detail of deposition process and structure formation (see Fig. 12). The results point to casting parameters favorable for the formation of highly ordered and laterally oriented molecular thin films and demonstrate the advantages of this approach to study solution-based crystal nucleation and growth.
Fig. 12

Effect of slow (a, b) and fast solution (c, d) shearing. The top panels show the detector images and the bottom panels the corresponding microscope images; a scale bar of 0.1 mm is shown in panel (a). Images mark the beginning (a, c) and the end (b, d) of a solution shearing experiment. Initially only the liquid scattering ring is seen, then crystallization sets in, while the liquid scattering fades. The final films (b, d) are fully crystalline. Strong Bragg reflections (circles) show that at slow speed (a, b), the film has a complex diffraction pattern due to various misaligned crystallites. At optimum speed (c, d) there is only a simple pattern indicating high orientational order of the TIPS-pentacene crystallites (Adapted with permission from Smilgies et al. (2013): Copyright (2013) VCH)

In summary, based on microbeam grazing-incidence WAXS technique, the developed experimental arrangement can be used to study crystallization under viscoelastic shear and to identify critical parameters for future roll-to-roll processing of organic electronics materials.

Structural Mapping of Organic Field-Effect Transistors

As shown in previous sections, much remains to be understood about low-temperature solution processing and structural modifications before organic circuitry can go into a mass production technology. There are several factors which adversely affect the mobility of organic transistors: grain boundaries, polymorphism and texture, misorientations, as well as surface coverage and wettability of the substrate (Burke et al. 2009; Amassian et al. 2009).

In particular, for fluorinated 5,11-bis(triethylsilylethynyl) anthradithiophene (diF-TES-ADT), treatment of the bottom Au contacts with pentafluorobenzene thiol (PFBT) drastically changes the surface microstructure (Gundlach et al. 2008). As result, carrier transport is drastically enhanced in bottom-contact organic field-effect transistors (OFETs), making diF-TES-ADT a suitable system for exploring local structural heterogeneities.

Spatially resolved measurements collected recently at CHESS using microbeam grazing-incidence WAXS technique allowed the study of the microstructure, texture, grain size, and orientation distribution of organic semiconductor thin films of diF-TES-ADT in actual bottom-contact OFETs (Li et al. 2012) (see Fig. 13). Based on capillary optics, a beam of 10 μm in diameter impinged on to the transistors at a low angle of 2 and the resulting WAXS patters were collected with a high-resolution 2D camera. Thus, relevant structural features within the transistor channels have been detected and located, allowing the identification of microstructural bottlenecks to charge transport.
Fig. 13

(a) Illustration of the diF-TES-ADT molecule and its packing structure in < 001> and < 111> textures, (b) schematic view of a μGIWAXS beam scanning a bottom-contact OFET device. A fluorescence image shows the footprint of the microbeam with a 100 μm scale bar, (ce) μGIWAXS patterns and simultaneous optical micrographs (insets) showing the diffraction pattern and corresponding microbeam location on a 50 μm-channel device with PFBT-treated gold electrodes. The diameter of the circle around the crosshair is 100 μm. The rectangular vertical boxes in (ce) refer to Bragg peaks associated to the < 001> -textured crystals. The large oval in (c) indicates part of the Au (111) ring. The diffraction peaks circled in (e) correspond to the < 111> texture, which appears on the oxide away from the device. In short, there are three key regions:

In transistors consisting of a heterogeneous film, it was possible to precisely determine the location and content of various polycrystalline textures: the pure < 001> texture of diF-TES-ADT extends to distances of ∼25 μm away from the PFBT-treated electrodes, reaches into the channel, and is capable of bridging channels up to 50 μm in length. Beyond this channel length, formation of the < 111> grains in the central part of the channel acts as a significant bottleneck to carrier transport (Li et al. 2012). By modifying the solution-processing method, extended growth of < 001> -textured domains, such that nucleation and growth of the < 111> -textured grains are inhibited, resulted in a performance boost.

In summary, X-ray microbeam scattering was used to map the microstructure, texture, grain sizes, and grain orientations of the organic semiconductor along the channel length of solution-processed bottom-contact OFET devices. The findings have a strong impact on the ongoing process of designing the perfect organic semiconductor.

Probing Quantum Confinement Within a Core-Shell Nanowire

The emergence of imaging schemes capable of overcoming the diffraction barrier is revolutionizing optical microscopy (Gramotnev and Bozhevolnyi 2010). A promising approach is based on shorter wavelengths than visible light. X-ray microscopy is particularly attractive for noninvasive optical imaging at the nanoscale, owing to the central role of quantum confinement effects in limiting carrier dynamics (Nelson and Braun 2008).

An imaging method that combines XEOL (Martinez-Criado et al. 2006) with simultaneous XRF using a nanometer-sized hard X-ray beam was recently developed at the ESRF (Martinez-Criado et al. 2012) (see Fig. 14). Core/multishell nanowires, which produce a variety of size-dependent phenomena for advanced light-emitting diodes (Lee et al. 2011), were used to demonstrate the mechanisms involved. Theory suggests that the carrier distributions in nanowires exhibit two-dimensional confinements under an hexagonal cross section (radial geometry) (Wong et al. 2011).
Fig. 14

Schematic of the experimental setup. The X-ray nanobeam impinges on the sample, which emits luminescence and X-ray fluorescence photons. XEOL and XRF spectra are recorded with a far-field optics system and a Si drift detector, respectively, for each raster position of the specimen the PFBT-treated Au electrode, the channel, and away from the device. The film is purely < 001> textured on the PFBT/Au electrode, revealing part of the (111) diffraction ring of the Au contact and increased diffuse scattering just above the attenuator (c). The film retained the same pure < 001> texture in the channel (d) in contrast with the oxide region away from the device (e), where the < 001> and < 111> textures coexist (Adapted with permission from Li et al. (2012): Copyright (2012) VCH)

Using a Kirkpatrick-Baez mirror-based X-ray nanoprobe with 60 × 60 nm2 spatial resolution at ESRF’s beamline ID22, evidence of carrier localization phenomena preferentially at the corners of hexagonal single coaxial n-GaN/InGaN multiquantum-well/p-GaN nanowires was shown (Fig. 15). The strong green emission at 2.45 eV at room temperature comes from efficient radiative recombinations in the quantum-well structures, and its 2D projection strongly advocates for the existence of additional carrier confinement effects.
Fig. 15

(a) Spatial distribution of the X-ray fluorescence (Ga intensity). (b) X-ray excited optical luminescence (dominant green emission at 2.45 eV attributed to the radiative transition from the In0.24Ga0.76N/GaN multiquantum wells). (c) Calculated square of the electron wave function of the lowest-energy state of the conduction band (Adapted with permission from Martinez-Criado et al. (2012): Copyright (2012) ACS)

Apart from the Stark shift that arises due to both the small piezoelectric field and the spontaneous polarization, these findings result from the enhanced carrier confinement within the multiquantum wells (MQWs) merging at the corners and have been confirmed through a theoretical investigation of the nanowire system (Fig. 15) (Martinez-Criado et al. 2012). A stronger confinement of the wave function at the hexagon corners is observed in remarkable consistence with the XEOL imaging.

Matching theoretical predictions, the experiment narrows the gap between optical microscopy and high-resolution X-ray imaging and calls for further studies on optoelectronic nanodevices. It represents a step toward not only the validation of theories of quantum confinement but also the realization of nanostructures with spectroscopic properties that could prove advantageous in light-emitting devices. Its great potential could be further enhanced by the addition of time resolution (Martinez-Criado et al. 2014) or by using this technique in conjunction with other methods, such as X-ray absorption spectroscopy and X-ray diffraction at the nanoscale.

Nanoscale Distortions of Si Quantum Wells in Si/SiGe

As mentioned above, devices based on individual quantum states of electrons promise to extend drastically the functionalities of integrated electronics. One potential path to create these quantum structures on silicon is based on coupled quantum dots in which electrons are trapped in a thin silicon layer within a stack of layers of an alloy of silicon and germanium (Friesen et al. 2003).

The resulting properties of such systems based on silicon two-dimensional electron gases depend strongly on their crystal structure. The role of specific defects, including atomic steps and other local sources of distortion, has been predicted theoretically and observed by electrical measurements, but this has been difficult to probe in structural studies. Nanodiffraction studies of Si quantum wells in a Si/SiGe heterostructure (Fig. 16) were carried out at beamline ID01 of the ESRF (Evans et al. 2012).
Fig. 16

(a) Synchrotron X-ray nanodiffraction study of a Si quantum device fully integrated in a circuit. The Si/SiGe heterostructure is located on the Si (001) crystal at the lower left of the photograph. The inset shows a diagram of the diffraction of the focused X-ray beam. (b) Layer sequence of the Si/SiGe heterostructure. (c) Optical micrograph of the lithographically patterned Si QW. The X-ray study is conducted within an area of unprocessed Si/SiGe extending radially from the quantum dot at the center of the image. One such area is highlighted by the shaded region (Adapted with permission from Evans et al. (2012): Copyright (2012) VCH)

The experiment probed the integrated quantum-dot structure and allowed a determination of the structural influence of the epitaxial growth and subsequent lithographic processing of the quantum well (Evans et al. 2012). The orientation, thickness, and other critical structural parameters could be extracted from the results. In particular, the intensity of the 004 reflection of the Si quantum well displayed variations at the 100 nm length scale. Such intensity variations (5–10 %) are consistent with changes of the quantum-well thickness (equal to a single 5 Å Si unit cell), which have been attributed to the de-correlation of steps during epitaxial growth. Strains arising from tilts of the lattice modify the band structure by inducing shifts in energy levels that are comparable to the electron temperature in quantum devices (Fig. 17).
Fig. 17

X-ray nanodiffraction map showing the waviness in a 10 nm-thick buried Si quantum well. Structural effects at the 100 nm length scale are apparent in the total intensity of the 004 Bragg reflection of the quantum well, arising from thickness variations of the order of one Si unit cell (Adapted with permission from Evans et al. (2012): Copyright (2012) VCH)

In summary, nanodiffraction measurements allowed the nondestructive analysis of the quantum-well device integrated on a circuit board. These findings revealed the distortions always believed to be present in such Si/SiGe heterostructures. The knowledge gained will help to improve the fabrication processes and so to make better devices in future (Fig. 17).

References

  1. J.F. Adam, J.P. Moy, J. Susini, Table-top water window transmission x-ray microscopy: review of the key issues, and conceptual design of an instrument for biology. Rev. Sci. Instrum. 76, 091301 (2005); L. De Caro, D. Altamura, F.A. Vittoria et al., A superbright X-ray laboratory microsource empowered by a novel restoration algorithm. J. Appl. Crystallogr. 45, 1228–1235 (2012)Google Scholar
  2. P. Aguado-Puente, J. Junquera, Structural and energetic properties of domains in PbTiO3/SrTiO3 superlattices from first principles. Phys. Rev. B 85, 184105 (2002)ADSCrossRefGoogle Scholar
  3. J. Als-Nielsen, D. McMorrow, Elements of Modern X-Ray Physics (Wiley, London, 2001)Google Scholar
  4. A. Amassian, V.A. Pozdin, T.V. Desai et al., Post-deposition reorganization of pentacene films deposited on low-energy surfaces. J. Mater. Chem. 19, 5580–5592 (2009)CrossRefGoogle Scholar
  5. K.W. Ang, C.H. Tung, N. Balasubramanian et al., Strained n-channel transistors with silicon source and drain regions and embedded silicon/germanium as strain-transfer structure. IEEE Electron. Device Lett. 28, 609–612 (2007)ADSCrossRefGoogle Scholar
  6. Z. Bao, J. Locklin, Organic Field Effect Transistors (CRS, Boca Raton, 2007)Google Scholar
  7. H.R. Beguiristain, I.S. Anderson, C.D. Dewhurst et al., A simple neutron microscope using a compound refractive lens. Appl. Phys. Lett. 81, 4290–4292 (2002)ADSCrossRefGoogle Scholar
  8. P. Bleuet, E. Welcomme, E. Dooryhée et al., Probing the structure of heterogeneous diluted materials by diffraction tomography. Nat. Mater. 7, 468–472 (2008)ADSCrossRefGoogle Scholar
  9. G. Bunker, Introduction to XAFS: A Practical Guide to X-Ray Absorption Fine Structure Spectroscopy (Cambridge University Press, Cambridge/New York, 2010)CrossRefGoogle Scholar
  10. S.A. Burke, J.M. Topple, P. Grütter, Molecular dewetting on insulators. J. Phys.: Condens. Matter 21, 423101 (2009)Google Scholar
  11. W. Chao, D.B. Harteneck, J.A. Liddle et al., Soft X-ray microscopy at a spatial resolution better than 15 nm. Nature 435, 1210–1213 (2005)ADSCrossRefGoogle Scholar
  12. W. Chao, J. Kim, S. Rekawa et al., Demonstration of 12 nm resolution Fresnel zone plate lens based soft x-ray microscopy. Opt. Express 17, 17669–17677 (2009)ADSCrossRefGoogle Scholar
  13. W. Chao, P.P. Fischer, T. Tyliszczak et al., Real space soft x-ray imaging at 10 nm spatial resolution. Opt. Express 20, 9777–9783 (2012)ADSCrossRefGoogle Scholar
  14. P. Chen, M.P. Cosgriff, Q. Zhang et al., Field-dependent domain distortion and interlayer polarization distribution in PbTiO3/SrTiO3 superlattices. Phys. Rev. Lett. 110, 047601 (2013)ADSCrossRefGoogle Scholar
  15. P. Cloetens, W. Ludwig, J. Baruchel et al., Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl. Phys. Lett. 75, 2912–2914 (1999)ADSCrossRefGoogle Scholar
  16. R. Conley, C. Liu, J. Qian et al., Wedged multilayer Laue lens. Rev. Sci. Instrum. 79, 053104 (2008)ADSCrossRefGoogle Scholar
  17. B.D. Cullity, Elements of X-Ray Diffraction (Addison-Wesley, Reading, 1978)Google Scholar
  18. M.S. del Rio, L. Alianelli, Aspherical lens shapes for focusing synchrotron beams. J. Synchrotron Radiat. 19, 366–374 (2012)CrossRefGoogle Scholar
  19. S. Dhar, H. Kosina, V. Palankovski, Electron mobility model for strained-Si devices. IEEE Trans. Electron Devices 52, 527–533 (2005)ADSCrossRefGoogle Scholar
  20. P.C.J. Donoghue, S. Bengtson, X. Dong, Synchrotron X-ray tomographic microscopy of fossil embryos. Nature 442, 680–683 (2006)ADSCrossRefGoogle Scholar
  21. W. Eerenstein, N.D. Mathur, J.F. Scott, Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006); R. Ramesh, N.A. Spaldin, Multiferroics: progress and prospects in thin films. Nature Mater. 6, 21–29 (2007)Google Scholar
  22. P.J. Eng, M. Newville, M.L. Rivers et al., Dynamically figured Kirkpatrick Baez x-ray microfocusing optics. Proc. SPIE 3449, 145–156 (1998)ADSCrossRefGoogle Scholar
  23. P.G. Evans, D.E. Savage, J.R. Prance et al., Nanoscale distortions of Si quantum wells in Si/SiGe quantum-electronic heterostructures. Adv. Mater. 24, 5217–5221 (2012)CrossRefGoogle Scholar
  24. K. Evans-Lutterodt, A. Stein, J.M. Ablett et al., Using compound kinoform hard-X-ray lenses to exceed the critical angle limit. Phys. Rev. Lett. 99, 134801 (2007)ADSCrossRefGoogle Scholar
  25. C.T. Forwood, L.M. Clarebrough, Electron Microscopy of Interfaces in Metals and Alloys (Adam Hilger, London, 1991)Google Scholar
  26. M. Friesen, P. Rugheimer, D.E. Savage et al., Practical design and simulation of silicon-based quantum-dot qubits. Phys. Rev. B 67, 121301 (2003)ADSCrossRefGoogle Scholar
  27. G. Giri, E. Verploegen, S.C. Mannsfeld et al., Tuning charge transport in solution-sheared organic semiconductors using lattice strain. Nature 480, 504–508 (2008)ADSCrossRefGoogle Scholar
  28. B. Golosio, A. Simionovici, A. Somogyi et al., Internal elemental microanalysis combining X-ray fluorescence, Compton and transmission tomography. J. Appl. Phys. 94, 145–156 (2003)Google Scholar
  29. M. Gómez-Gómez, N. Garro, J. Segura-Ruiz et al., Spontaneous core–shell elemental distribution in In-rich InxGa1-xN nanowires grown by molecular beam epitaxy. Nanotechnology 25, 075705 (2014)ADSCrossRefGoogle Scholar
  30. I. Gorczyca, S.P. Łepkowski, T. Suski et al., Influence of indium clustering on the band structure of semiconducting ternary and quaternary nitride alloys. Phys. Rev. B 80, 075202 (2009)ADSCrossRefGoogle Scholar
  31. D.K. Gramotnev, S.I. Bozhevolnyi, Plasmonics beyond the diffraction limit. Nat. Photon. 4, 83–91 (2010)ADSCrossRefGoogle Scholar
  32. D.J. Gundlach, J.E. Royers, S.K. Park et al., Contact-induced crystallinity for high-performance soluble acene-based transistors and circuits. Nat. Mater. 7, 216–221 (2008)ADSCrossRefGoogle Scholar
  33. P. Guttmann, X. Zeng, M. Feser, Ellipsoidal capillary as condenser for the BESSY full-field x-ray microscope. J. Phys. Conf. Ser. 186, 012064 (2009)CrossRefGoogle Scholar
  34. B. Hornberger, M. Feser, C. Jacobsen, Quantitative amplitude and phase contrast imaging in a scanning transmission X-ray microscope. Ultramicroscopy 107, 644–655 (2007)CrossRefGoogle Scholar
  35. N. Hrauda, J. Zhang, E. Wintersberger et al., X-ray nanodiffraction on a single SiGe quantum dot inside a functioning field-effect transistor. Nano Lett. 11, 2875-2880 (2011)ADSCrossRefGoogle Scholar
  36. G.E. Ice, J.S. Chung, J.Z. Tischler, A. Lunt et al., Elliptical X-ray microprobe mirrors by differential deposition. Rev. Sci. Instrum. 71, 2635–2639 (2000)ADSCrossRefGoogle Scholar
  37. K. Jefimovs, J. Vila-Comamala, T. Pilvi et al., Zone-doubling technique to produce ultrahigh-resolution X-ray optics. Phys. Rev. Lett. 99, 264801 (2007)ADSCrossRefGoogle Scholar
  38. J.Y. Jo, R.J. Sichel, H.N. Lee, Piezoelectricity in the dielectric component of nanoscale dielectric-ferroelectric superlattices. Phys. Rev. Lett. 104, 207601 (2010)ADSCrossRefGoogle Scholar
  39. J.Y. Jo, P. Chen, R.J. Sichel, Nanosecond dynamics of ferroelectric/dielectric superlattices. Phys. Rev. Lett. 107, 055501 (2011)ADSCrossRefGoogle Scholar
  40. V. Jovanović, C. Biasotto, K.L. Nanver, n-Channel MOSFETs fabricated on SiGe dots for strain-enhanced mobility. IEEE Electron Device Lett. 31, 1083–1085 (2010)Google Scholar
  41. C.J. Kaiser, The Transistor Handbook (C. J. Publishing, Olathe, 1999)Google Scholar
  42. H.C. Kang, J. Maser, G.B. Stephenson et al., Nanometer linear focusing of hard X rays by a multilayer Laue lens. Phys. Rev. Lett. 96, 127401 (2006)ADSCrossRefGoogle Scholar
  43. H.C. Kang, H.F. Yan, R.P. Winarski et al., Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens. Appl. Phys. Lett. 92, 221114 (2008)ADSCrossRefGoogle Scholar
  44. T. Kimura, S. Handa, H. Mimura et al., Wavefront control system for phase compensation in hard X-ray optics. Jpn. J. Appl. Phys. 48, 072503 (2009)ADSCrossRefGoogle Scholar
  45. P. Kirkpatrick, A.V. Baez, Formation of optical images by X-rays. J. Opt. Soc. Am. 38, 766–773 (1948)ADSCrossRefGoogle Scholar
  46. T. Koyama, H. Takenaka, S. Ichimaru et al., Development of multilayer Laue lenses; (2) circular type. AIP Conf. Proc. 1365, 24–27 (2011)ADSCrossRefGoogle Scholar
  47. C.H. Lee, Y.-J. Kim, Y.J. Hong et al., Flexible inorganic nanostructure light-emitting diodes fabricated on graphene films. Adv. Mater. 23, 4614–4619 (2011)CrossRefGoogle Scholar
  48. B. Lengeler, C. Schroer, J. Tummler et al., Imaging by parabolic refractive lenses in the hard X-ray range. J. Synchrotron Radiat. 6, 1153–1167 (1999)CrossRefGoogle Scholar
  49. Y. Li, F. Qian, J. Xiang et al., Nanowire electronic and optoelectronic devices. Mater. Today 9, 18–27 (2006)CrossRefGoogle Scholar
  50. R. Li, J.W. Ward, D.M. Smilgies et al., Direct structural mapping of organic field-effect transistors reveals bottlenecks to carrier transport. Adv. Mater. 24, 5553–5558 (2012)CrossRefGoogle Scholar
  51. S. Lisenkov, L. Bellaiche, Phase diagrams of BaTiO3/SrTiO3 superlattices from first principles. Phys. Rev. B 76, 020102 (2007)ADSCrossRefGoogle Scholar
  52. W.J. Liu, G.E. Ice, L. Assoufid et al., Hard X-ray nano-focusing with Montel mirror optics. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect. Assoc. Equip. 649, 169–171 (2011)ADSCrossRefGoogle Scholar
  53. C.A. Liu, G.E. Ice, W. Liu et al., Fabrication of nested elliptical KB mirrors using profile coating for synchrotron radiation X-ray focusing. Appl. Surf. Sci. 258, 2182–2186 (2012)ADSCrossRefGoogle Scholar
  54. E. Margui, X-Ray Fluorescence Spectrometry and Related Techniques: An Introduction (Momentum Press, LLC, New York, 2013)CrossRefGoogle Scholar
  55. G. Martinez-Criado, B. Alén, A. Homs et al., Scanning x-ray excited optical luminescence microscopy in GaN. Appl. Phys. Lett. 89, 221913 (2006)ADSCrossRefGoogle Scholar
  56. G. Martinez-Criado, A. Homs, B. Alén et al., Probing quantum confinement within single core-multishell nanowire. Nano Lett. 12, 5829–5834 (2012)ADSCrossRefGoogle Scholar
  57. G. Martinez-Criado, J. Segura-Ruiz, B. Alén et al., Exploring single semiconductor nanowires with a multimodal hard X-ray nanoprobe. Adv. Mater. (2014).  https://doi.org/10.1002/adma.201304345
  58. H. Mimura, H. Yumoto, S. Matsuyama et al., Efficient focusing of hard x rays to 25nm by a total reflection mirror. Appl. Phys. Lett. 90, 051903 (2007)ADSCrossRefGoogle Scholar
  59. H. Mimura, S. Handa, T. Kimura et al., Breaking the 10 nm barrier in hard-X-ray focusing. Nat. Phys. 6, 122–125 (2010)CrossRefGoogle Scholar
  60. L. Mino, D. Gianolio, G. Agostini et al., μ-EXAFS, μ -XRF, and μ -PL characterization of a multi-quantum-well electroabsorption modulated laser realized via selective area growth. Small 7, 930–938 (2011)Google Scholar
  61. M. Montel, X-Ray Microscopy and Microradiography (Academic, New York, 1957)Google Scholar
  62. C. Morawe, P. Pecci, J.C. Peffen et al., Design and performance of graded multilayers as focusing elements for x-ray optics. Rev. Sci. Instrum. 70, 3227–3232 (1999)ADSCrossRefGoogle Scholar
  63. F.R.N. Nabarro, M.S. Duesbery, Dislocation in Solids (North Holland, Amsterdam, 1979–2003)Google Scholar
  64. S. Nakamura, The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes. Science 281, 956–961 (1998)CrossRefGoogle Scholar
  65. E.C. Nelson, P.V. Braun, Photonic crystals: photons and electrons confined. Nat. Photon. 2, 650–651 (2008)ADSCrossRefGoogle Scholar
  66. U. Pietsch, V. Holy, T. Baumbach, High Resolution X-Ray Scattering (Springer, New York, 2004)CrossRefGoogle Scholar
  67. C. Reese, M. Roberts, M.M. Ling et al., Organic thin film transistors. Mater. Today 7, 20–27 (2004)CrossRefGoogle Scholar
  68. S. Rehbein, P. Guttmann, S. Werner et al., Characterization of the resolving power and contrast transfer function of a transmission X-ray microscope with partially coherent illumination. Opt. Express 20, 5830–5839 (2012)ADSCrossRefGoogle Scholar
  69. I.K. Robinson, R. Harder, Coherent X-ray diffraction imaging of strain at the nanoscale. Nat. Mater. 8, 291–298 (2009)ADSCrossRefGoogle Scholar
  70. J.M. Rodenburg, A.C. Hurst, A.G. Cullis et al., Hard-X-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007)ADSCrossRefGoogle Scholar
  71. A. Sakdinawat, D. Attwood, Nanoscale X-ray imaging. Nat. Photonics 4, 840–848 (2010)ADSCrossRefGoogle Scholar
  72. V. Schmidt, Electron Spectrometry of Atoms Using Synchrotron Radiation in Part of Cambridge Monographs on Atomic, Molecular and Chemical Physics (Cambridge University Press, Cambridge/New York, 1997)CrossRefGoogle Scholar
  73. O.G. Schmidt, K. Eberl, Self-assembled Ge/Si dots for faster field-effect transistors. IEEE Trans. Electron Devices 48, 1175–1179 (2001)ADSCrossRefGoogle Scholar
  74. C.G. Schroer, B. Lengeler, Focusing hard X rays to nanometer dimensions by adiabatically focusing lenses. Phys. Rev. Lett. 94, 054802 (2005)ADSCrossRefGoogle Scholar
  75. C.G. Schroer, O. Kurapova, J. Patommel et al., Hard x-ray nanoprobe based on refractive x-ray lenses. Appl. Phys. Lett. 87, 124103 (2005)ADSCrossRefGoogle Scholar
  76. C.G. Schroer, A. Schropp, P. Boye et al., Hard X-ray scanning microscopy with coherent diffraction contrast. AIP Conf. Proc. 1365, 227–230 (2011)ADSCrossRefGoogle Scholar
  77. J. Segura-Ruiz, G. Martínez-Criado, C. Denker et al., Phase separation in single Inx Ga1–xN nanowires revealed through a hard X-ray synchrotron nanoprobe. Nano Lett. 14, 1300–1305 (2014)ADSCrossRefGoogle Scholar
  78. R. Signorato, T. Ishikawa, R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8. Nucl. Instrum. Methods A 467, 271–274 (2001)ADSCrossRefGoogle Scholar
  79. D.M. Smilgies, R. Li, G. Giri et al., Look fast: crystallization of conjugated molecules during solution shearing probed in-situ and in real time by X-ray scattering. Phys. Status Solidi RRL 7, 177–179 (2013)CrossRefGoogle Scholar
  80. A. Snigirev, I. Snigireva, High energy X-ray micro-optics. C. R. Phys. 9, 507–516 (2008)ADSCrossRefGoogle Scholar
  81. A. Snigirev, V. Kohn, I. Snigireva et al., A compound refractive lens for focusing high-energy X-rays. Nature 384, 49–51 (1996)ADSCrossRefGoogle Scholar
  82. A. Somogyi, F. Polack, T. Moreno, Status of the nanoscopium scanning nanoprobe beamline of synchrotron soleil. AIP Conf. Proc. 1234, 395–398 (2010)ADSCrossRefGoogle Scholar
  83. S. Srinivasan, Fuel Cells: From Fundamentals to Applications (Springer, New York, 2010)Google Scholar
  84. A. Stein, K. Evans-Lutterodt, N. Bozovic et al., Fabrication of silicon kinoform lenses for hard X-ray focusing by electron beam lithography and deep reactive ion etching. J. Vac. Sci. Technol. B 26, 122–127 (2008)CrossRefGoogle Scholar
  85. M. Stockmar, P. Cloetens, I. Zanette et al., Near-field ptychography: phase retrieval for inline holography using a structured illumination. Sci. Rep. 3, 1927 (2012)CrossRefGoogle Scholar
  86. N. Stribeck, X-Ray Scattering of Soft Matter (Springer, Berlin/Heidelberg, 2007)Google Scholar
  87. Y. Takahashi, A. Suzuki, S. Furutaku et al., Bragg x-ray ptychography of a silicon crystal: visualization of the dislocation strain field and the production of a vortex beam. Phys. Rev. B 87, 121201 (2013)ADSCrossRefGoogle Scholar
  88. B.K. Tanner, X-Ray Diffraction Topography (Pergamon, Oxford, 1976)Google Scholar
  89. M. Van Veenendaal, I. McNulty, Prediction of strong dichroism induced by X rays carrying orbital momentum. Phys. Rev. Lett. 98, 157401 (2007)ADSCrossRefGoogle Scholar
  90. J. Vila-Comamala, S. Gorelick, V.A. Guzenko et al., Dense high aspect ratio hydrogen silsesquioxane nanostructures by 100 keV electron beam lithography. Nanotechnology 21, 285305 (2010)CrossRefGoogle Scholar
  91. Y. Waseda, Anomalous X-Ray Scattering for Materials Characterization (Springer, Berlin/Heidelberg, 2002)CrossRefGoogle Scholar
  92. B.M. Wong, F. Leonard, Q. Li et al., Nanoscale effects on heterojunction electron gases in GaN/AlGaN core/shell nanowires. Nano Lett. 11, 3074–3079 (2011)ADSCrossRefGoogle Scholar
  93. H.F. Yan, X-ray nanofocusing by kinoform lenses: a comparative study using different modeling approaches. Phys. Rev. B 81, 075402 (2010)ADSCrossRefGoogle Scholar
  94. H.F. Yan, J. Maser, A. Macrander et al., X-ray dynamical diffraction from multilayer Laue lenses with rough interfaces. Phys. Rev. B 76, 115438 (2009)ADSCrossRefGoogle Scholar
  95. H.F. Yan, H.C. Kang, R. Conley et al., Multilayer Laue lens: a path toward one nanometer X-ray focusing. X-Ray Opt. Instrum. 1, 401854 (2010)Google Scholar
  96. H.F. Yan, V. Rose, D.M. Shu et al., Two dimensional hard x-ray nanofocusing with crossed multilayer Laue lenses. Opt. Express 19, 15069–15076 (2011)ADSCrossRefGoogle Scholar
  97. H. Yan, Y.S. Chu, J. Maser et al., Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses. Sci. Rep. 3, 1307 (2013)CrossRefGoogle Scholar
  98. G.C. Yin, Y.F. Song, M.T. Tang et al., 30nm resolution x-ray imaging at 8keV using third order diffraction of a zone plate lens objective in a transmission microscope. Appl. Phys. Lett. 89, 221122 (2006)ADSCrossRefGoogle Scholar
  99. H. Yumoto, H. Mimura, S. Matsuyama et al., Fabrication of elliptically figured mirror for focusing hard x rays to size less than 50nm. Rev. Sci. Instrum. 76, 063708 (2005)ADSCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.European Synchrotron Radiation Facility ESRFGrenobleFrance

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