Structure-transport correlation reveals anisotropic charge transport in coupled PbS nanocrystal superlattices

Semiconductive nanocrystals (NCs) can be self-assembled into ordered superlattices (SLs) to create artificial solids with emerging collective properties. Computational studies have predicted that properties such as electronic coupling or charge transport are determined not only by the individual NCs but also by the degree of their organization and structure. However, experimental proof for a correlation between structure and charge transport in NC SLs is still pending. Here, we perform X-ray nano-diffraction and apply Angular X-ray Cross-Correlation Analysis (AXCCA) to characterize the structures of coupled PbS NC SLs, which are directly correlated with the electronic properties of the same SL microdomains. We find strong evidence for the effect of SL crystallinity on charge transport and reveal anisotropic charge transport in highly ordered monocrystalline hexagonal close-packed PbS NC SLs, caused by the dominant effect of shortest interparticle distance. This implies that transport anisotropy should be a general feature of weakly coupled NC SLs.Comment: 49 pages, 20 Figure

Theroy of Photoelectron Emission From an X-Ray Interference Field

In this chapter, we will present the theory for the photoelectronemission from an X-ray interference field. The dipole approximationholds astonishingly well, even for hard X-rays, as far as the magnitudeof the transition matrix element is concerned. However, the forward–backward asymmetry caused already by higher order multipole termscannot be neglected when the photoelectron is emitted by the coherentaction of two X-ray waves travelling in different directions. We willexplicitly elaborate the underlying theory and how corresponding dataare analyzed. Furthermore, we will briefly describe the theory behind theX-ray standing wave excited photoemission of valence band electrons

Coherent X-ray Diffraction Imaging of Nanostructures

We present here an overview of Coherent X-ray Diffraction Imaging (CXDI) with its application to nanostructures. This imaging approach has become especially important recently due to advent of X-ray Free-Electron Lasers (XFEL) and its applications to the fast developing technique of serial X-ray crystallography. We start with the basic description of coherent scattering on the finite size crystals. The difference between conventional crystallography applied to large samples and coherent scattering on the finite size samples is outlined. The formalism of coherent scattering from a finite size crystal with a strain field is considered. Partially coherent illumination of a crystalline sample is developed. Recent experimental examples demonstrating applications of CXDI to the study of crystalline structures on the nanoscale, including experiments at FELs, are also presented

Phase of transmitted wave in dynamical theory and quasi-kinematical approximation

Variation of the phase of the beam transmitted through a crystalline material as a function of the rockingangle is a well-known dynamical effect in x-ray scattering. Unfortunately, it is not so easy to directly measurethese phase variations in a conventional scattering experiment. It was recently suggested that the transmittedphase can be directly measured in ptychography experiments performed on nanocrystal samples. Results of suchexperiment for different crystal thickness, reflections, and incoming photon energies, in principle, can be fullydescribed in the frame of dynamical theory. However, dynamical theory does not provide a simple analyticalexpression for the further analysis. Here we develop a quasi-kinematical theory approach that allows one tocorrectly describe the phase of the transmitted beam for the crystal thickness less than extinction length that isbeyond applicability of the conventional kinematical theory

Coherent X-ray Diffraction Imaging of Nanostructures

We present here an overview of Coherent X-ray Diffraction Imaging (CXDI) with its application to nanostructures. This imaging approach has become especially important recently due to advent of X-ray Free-Electron Lasers (XFEL) and its applications to the fast developing technique of serial X-ray crystallography. We start with the basic description of coherent scattering on the finite size crystals. The difference between conventional crystallography applied to large samples and coherent scattering on the finite size samples is outlined. The formalism of coherent scattering from a finite size crystal with a strain field is considered. Partially coherent illumination of a crystalline sample is developed. Recent experimental examples demonstrating applications of CXDI to the study of crystalline structures on the nanoscale, including experiments at FELs, are also presented

Coherence properties of focused X-ray beams at high-brilliance synchrotron sources

An analytical approach describing properties of focused partially coherent X-ray beams is presented. The method is based on the results of statistical opticsand gives both the beam size and transverse coherence length at any distancebehind an optical element. In particular, here Gaussian Schell-model beams andthin optical elements are considered. Limiting cases of incoherent and fullycoherent illumination of the focusing element are discussed. The effect of thebeam-defining aperture, typically used in combination with focusing elements atsynchrotron sources to improve transverse coherence, is also analyzed in detail. As an example, the coherence properties in the focal region of compoundrefractive lenses at the PETRA III synchrotron source are analyzed

Structural analysis by x-ray intensity angular cross correlations

This chapter reviews the topic of angular intensity correlations in X-ray diffraction. A basic theoretical description of quantities related to angular correlations in a simple X-ray scattering description in the far-field, or Fraunhofer, limit of diffraction in the kinematic approximation is discussed. The chapter reviews the applications of the cross-correlation functions (CCFs) in X-ray studies of materials divided into two major groups. The first part of applications is related to the problem of a single-particle structure recovery in the fluctuation X-ray scattering (FXS) experiments. The second part is related to the studies of structural properties of disordered and partially ordered systems, such as colloids, metallic glasses, liquid crystals, and polymers. The chapter demonstrates that X-ray beams focused to small sizes in combination with cross-correlation analysis can indeed provide valuable information about the structure of partially ordered materials, complementary to the results of conventional small-angle X-ray scattering (SAXS) or grazing-incidence X-ray diffraction (GIXD) analysis