ScN/GaN(11Ì 00): A New Platform for the Epitaxy of Twin-Free Metal-Semiconductor Heterostructures.

We study the molecular beam epitaxy of rock-salt ScN on the wurtzite GaN(11̅00) surface. To this end, ScN is grown on freestanding GaN(11̅00) substrates and self-assembled GaN nanowires exhibiting (11̅00) sidewalls. On both substrates, ScN crystallizes twin-free thanks to a specific epitaxial relationship, namely ScN(110)[001]∥GaN(11̅00)[0001], providing a congruent, low-symmetry interface. The 13.1% uniaxial lattice mismatch occurring in this orientation mostly relaxes within the first few monolayers of growth by forming a near-coincidence site lattice, where 7 GaN planes coincide with 8 ScN planes, leaving the ScN surface nearly free of extended defects. Overgrowth of the ScN with GaN leads to a kinetic stabilization of the zinc blende phase, that rapidly develops wurtzite inclusions nucleating on {111} nanofacets, commonly observed during zinc blende GaN growth. Our ScN/GaN(11̅00) platform opens a new route for the epitaxy of twin-free metal-semiconductor heterostructures including closely lattice-matched GaN, ScN, HfN, and ZrN compounds.

X-ray diffraction from dislocation half-loops in epitaxial films.

X-ray diffraction from dislocation half-loops consisting of a misfit segment with two threading arms extending from it to the surface is calculated by the Monte Carlo method. The diffraction profiles and reciprocal space maps are controlled by the ratio of the total lengths of the misfit and the threading segments of the half-loops. A continuous transformation from the diffraction characteristic of misfit dislocations to that of threading dislocations with increasing thickness of epitaxial film is studied. Diffraction from dislocations with edge- and screw-type threading arms is considered and the contributions of the two types of dislocations are compared.

X-ray scattering study of GaN nanowires grown on Ti/Al2O3 by molecular beam epitaxy.

GaN nanowires (NWs) grown by molecular beam epitaxy on Ti films sputtered on Al2O3 are studied by X-ray diffraction (XRD) and grazing-incidence small-angle X-ray scattering (GISAXS). XRD, performed both in symmetric Bragg reflection mode and at grazing incidence, reveals Ti, TiN, Ti3O, Ti3Al and Ga2O3 crystallites with in-plane and out-of-plane lattice parameters intermediate between those of Al2O3 and GaN. These topotaxial crystallites in the Ti film, formed as a result of interfacial reactions and N exposure, possess little misorientation with respect to Al2O3. As a result, GaN NWs grow on the top TiN layer, possessing a high degree of epitaxial orientation with respect to the substrate. The measured GISAXS intensity distributions are modelled by the Monte Carlo method, taking into account the orientational distributions of NWs, the variety of their cross-sectional shapes and sizes, and the roughness of their side facets. The cross-sectional size distributions of the NWs and the relative fractions of the {1100} and {1120} side facets are determined.

Cross-sectional shape evolution of GaN nanowires during molecular beam epitaxy growth on Si(111).

We study the cross-sectional shape of GaN nanowires (NWs) by transmission electron microscopy. The shape is examined at different heights of long NWs, as well as at the same height for NWs of different lengths. Two distinct trends in the evolution of the cross-sectional shape along the NW length are observed. At the top, merging NWs develop common {11̄00} side facets. At the bottom, the NWs acquire roundish shapes. This observation is explained by the entirely different NW environments at the top and the bottom of the NWs. At the top, NWs are exposed to the Ga and N atomic fluxes giving rise to axial growth, resulting in the equilibrium growth shape with zero growth rate at the {11̄00} facets. At the bottom, NWs are shadowed from the impinging fluxes and are only annealed, allowing them to eventually approach the equilibrium crystal shape. The study of identical samples by grazing incidence small-angle X-ray scattering independently confirms these trends in the shape evolution of the sidewall facets.

Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon.

The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent-crystal spectrometers for the hard X-ray free-electron laser sources.

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law.

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q-4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3-4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction.

X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses.

The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.

Diffraction properties of a strongly bent diamond crystal used as a dispersive spectrometer for XFEL pulses.

Self-amplified spontaneous emission (SASE) enables X-ray free-electron lasers (XFELs) to generate hard X-ray pulses of sub-100 fs duration. However, due to the stochastic nature of SASE, the energy spectrum fluctuates from pulse to pulse. Many experiments that employ XFEL radiation require the resolution of the spectrum of each pulse. The work presented here investigates the capacity of a thin strongly bent diamond crystal to resolve the energy spectra of hard X-ray SASE pulses by studying its diffraction properties. Rocking curves of the symmetric C*(440) reflection have been measured for different bending radii. The experimental data match the theoretical modelling based on the Takagi-Taupin equations of dynamical diffraction. A uniform strain gradient has proven to be a valid model of strain deformations in the crystal.

Influence of strain relaxation in axial [Formula: see text] nanowire heterostructures on their electronic properties.

We present a systematic theoretical study of the influence of elastic strain relaxation on the built-in electrostatic potentials and the electronic properties of axial [Formula: see text] nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the [Formula: see text] disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the built-in electrostatic potential in comparison to a planar system of similar layer thickness and In content. In this case, the ground state transition energies approach constant values with increasing thickness of the disk and only depend on the In content, a behavior usually associated to that of a quantum well free of built-in electrostatic potentials. We show that the structures under consideration are by no means field-free, and the built-in potentials continue to play an important role even for ultrathin NWs. In particular, strain and the resulting polarization potentials induce complex confinement features of electrons and holes, which depend on the In content, shape, and dimensions of the heterostructure.

Nucleation, Growth, and Bundling of GaN Nanowires in Molecular Beam Epitaxy: Disentangling the Origin of Nanowire Coalescence.

We investigate the nucleation, growth, and coalescence of spontaneously formed GaN nanowires in molecular beam epitaxy combining the statistical analysis of scanning electron micrographs with Monte Carlo growth models. We find that (i) the nanowire density is limited by the shadowing of the substrate from the impinging fluxes by already existing nanowires, (ii) shortly after the nucleation stage, nanowire radial growth becomes negligible, and (iii) coalescence is caused by bundling of nanowires. The latter phenomenon is driven by the gain of surface energy at the expense of the elastic energy of bending and becomes energetically favorable once the nanowires exceed a certain critical length.

Piezoelectric potential in axial (In,Ga)N/GaN nanowire heterostructures.

We derive analytic expressions for the built-in electrostatic potential arising from piezo- and pyroelectricity in a cylindrical axial In(x)Ga(1-x)N/GaN nanowire (NW) heterostructure. Our simulations show that, for sufficiently thin NWs, a significant reduction of the built-in potential is reached in comparison to the planar heterostructure of the same In content, thickness, and orientation. This specific feature of axial NW heterostructures makes the aspect ratio of the embedded In(x)Ga(1-x)N/GaN disks an important additional degree of freedom to control the recombination energies. We furthermore show that the magnitude of the polarization potential decreases again above a certain value of the aspect ratio and that the extrema of the potential move from the central axis of the NW towards the side facets when the thickness of the disk is increased.

Strain distributions and diffraction peak profiles from crystals with dislocations.

Diffraction profiles for different models of dislocation arrangements are calculated directly by the Monte Carlo method and compared with the strain distributions for the same arrangements, which corresponds to the Stokes-Wilson approximation. It is shown that the strain distributions and the diffraction profiles are in close agreement as long as long-range order is absent. Analytical calculation of the strain distribution for uncorrelated defects is presented. For straight dislocations, the Stokes-Wilson and the Krivoglaz-Wilkens approximations give the same diffraction profiles, with the Gaussian central part and ∝ q(-3) power law at the tails.

Strain engineering of nanowire multi-quantum well demonstrated by Raman spectroscopy.

An analysis of the strain in an axial nanowire superlattice shows that the dominating strain state can be defined arbitrarily between unstrained and maximum mismatch strain by choosing the segment height ratios. We give experimental evidence for a successful strain design in series of GaN nanowire ensembles with axial InxGa1-xN quantum wells. We vary the barrier thickness and determine the strain state of the quantum wells by Raman spectroscopy. A detailed calculation of the strain distribution and LO phonon frequency shift shows that a uniform in-plane lattice constant in the nanowire segments satisfactorily describes the resonant Raman spectra, although in reality the three-dimensional strain profile at the periphery of the quantum wells is complex. Our strain analysis is applicable beyond the InxGa1-xN/GaN system under study, and we derive universal rules for strain engineering in nanowire heterostructures.

Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy.

We investigate the axial and radial growth of GaN nanowires upon a variation of the Ga flux during molecular beam epitaxial growth. An increase in the Ga flux promotes radial growth without affecting the axial growth rate. In contrast, a decrease in the Ga flux reduces the axial growth rate without any change in the radius. These results are explained by a kinetic growth model that accounts for both the diffusion of Ga adatoms along the side facets toward the nanowire tip and the finite amount of active N available for the growth. The model explains the formation of a new equilibrium nanowire radius after increasing the Ga flux and provides an explanation for two well-known but so far not understood experimental facts: the necessity of effectively N-rich conditions for the spontaneous growth of GaN nanowires and the increase in nanowire radius with increasing III/V flux ratio.

Delayed crystallization of ultrathin Gd2O3 layers on Si(111) observed by in situ X-ray diffraction.

We studied the early stages of Gd2O3 epitaxy on Si(111) in real time by synchrotron-based, high-resolution X-ray diffraction and by reflection high-energy electron diffraction. A comparison between model calculations and the measured X-ray scattering, and the change of reflection high-energy electron diffraction patterns both indicate that the growth begins without forming a three-dimensional crystalline film. The cubic bixbyite structure of Gd2O3 appears only after a few monolayers of deposition.

X-ray diffraction peaks from correlated dislocations: Monte Carlo study of dislocation screening.

X-ray diffraction peak profiles are calculated by the Monte Carlo method for arbitrarily correlated dislocations without making any approximations or simplifications. The arrangement of dislocations in pairs with opposite Burgers vectors provides screening of the long-range strains. Moreover, any screening can be modeled by appropriate distribution of the dislocation pairs. Analytical description of the peak profiles is compared with the Monte Carlo results. Symmetric peaks due to screw dislocations and asymmetric peaks due to edge dislocations are simulated and analyzed.

Kinetic optimum of volmer-weber growth.

We find that the molecular beam epitaxy of Fe3Si on GaAs(001) observed by real-time x-ray diffraction begins by the abrupt formation of 3 monolayer (ML) high islands and approaches two-dimensional layer-by-layer growth at a thickness of 7 ML. A surface energy increase is confirmed by ab initio calculations and allows us to identify the growth as a strain-free Volmer-Weber transient. Kinetic Monte Carlo simulations incorporating this energy increase correctly reproduce the characteristic x-ray intensity oscillations found in the experiment. Simulations indicate an optimum growth rate for Volmer-Weber growth in between two limits, the appearance of trenches at slow growth and surface roughening at fast growth.