arXiv subjects

Vladimir M. Kaganer

Publications and source records attributed to Vladimir M. Kaganer.

17 recordsLinked to original sources

arXiv2025

Dislocation correlations in GaN epitaxial films revealed by EBSD and XRD

Correlations between dislocations in crystals reduce the elastic energy via screening of the strain by the surrounding dislocations. We study the correlations of threading dislocations in GaN epitaxial films with dislocation densities of $5\times10^{8}$ cm$^{-2}$ and $1.8\times10^{10}$ cm$^{-2}$ by X-ray diffraction (XRD) in reciprocal space and by high-resolution electron backscatter diffraction (HR-EBSD) in real space, where the strain is derived from a cross-correlation analysis of the Kikuchi patterns. The measured XRD curves and HR-EBSD strain and rotation maps are compared with Monte Carlo simulations within one and the same model for the dislocation distributions. The screening of the dislocation strains is modeled by creating pairs of dislocations with opposite Burgers vectors, with the mean distance between dislocations in a pair equal to the screening distance. The pairs overlap and cannot be distinguished as separate dipoles. The HR-EBSD-measured autocorrelation functions of the strain and rotation components follow the expected logarithmic law for distances smaller than the screening distances and become zero for larger distances, which is confirmed by the Monte Carlo simulations. The kink in the plot of the autocorrelation function allows a robust and accurate determination of the screening distance without making any simulation or fit. Screening distances of 2 $μ$m and 0.3 $μ$m are obtained for the samples with low and high dislocation densities, respectively. The dislocation strain is thus screened by only 4 neighboring dislocations. In addition, an anisotropic resolution of the HR-EBSD measurements is observed and quantified. In this version, an error in the processing of the HR-EBSD maps of the Si wafer is specified.

cond-mat.mtrl-sci↗

arXiv2024

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 towards 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 ratios.

cond-mat.mtrl-sci↗

arXiv2023

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

X-ray diffraction from dislocation half-loops consisting of a misfit segment and 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 an epitaxial film is studied. Diffraction from dislocations with edge and screw threading arms is considered and the contributions of both types of dislocations are compared.

cond-mat.mtrl-sci↗

arXiv2022

X-ray scattering study of GaN nanowires grown on Ti/Al$_{2}$O$_{3}$ by molecular beam epitaxy

GaN nanowires (NWs) grown by molecular beam epitaxy on Ti films sputtered on Al$_{2}$O$_{3}$ are studied by X-ray diffraction (XRD) and grazing incidence small-angle X-ray scattering (GISAXS). XRD, performed both in symmetric Bragg reflection and at grazing incidence, reveals Ti, Ti$_{3}$O, Ti$_{3}$Al, and TiO$_x$N$_y$ crystallites with in-plane and out-of-plane lattice parameters intermediate between those of Al$_{2}$O$_{3}$ and GaN. These topotaxial crystallites in Ti film, formed due to interfacial reactions and N exposure, possess fairly little misorientation with respect to Al$_{2}$O$_{3}$. 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 modeled by the Monte Carlo method taking into account the orientational distributions of NWs, a variety of their cross-sectional shapes and sizes, and roughness of their side facets. The cross-sectional size distributions of the NWs and the relative fractions of $(1\bar{1}00)$ and $(11\bar{2}0)$ side facets are determined.

cond-mat.mtrl-sci↗

arXiv2022

Nanoscale mapping of the full strain tensor, rotation and composition in partially relaxed In$_x$Ga$_{1-x}$N layers by scanning X-ray diffraction microscopy

Strain and composition play a fundamental role in semiconductor physics, since they are means to tune the electronic and optical properties of a material and hence develop new devices. Today it is still a challenge to measure strain in epitaxial systems in a non-destructive manner which becomes especially important in strain-engineered devices that often are subjected to intense stress. In this work, we demonstrate a microscopic mapping of the full tensors of strain and lattice orientation by means of scanning X-ray diffraction microscopy. We develope a formalism to extract all components of strain and orientation from a set of scanning diffraction measurements and apply the technique to a patterned In$_x$Ga$_{1-x}$N double layer to study strain relaxation and indium incorporation phenomena. The contributions due to varying indium content and threading dislocations are separated and analyzed.

cond-mat.mtrl-sci↗

arXiv2021

Carrier diffusion in GaN -- a cathodoluminescence study. I: Temperature-dependent generation volume

The determination of the carrier diffusion length of semiconductors such as GaN and GaAs by cathodoluminescence imaging requires accurate knowledge about the spatial distribution of generated carriers. To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity profiles measured across single quantum wells embedded in thick GaN and GaAs layers. Thin (Al,Ga)N and (Al,Ga)As barriers, respectively, prevent carriers diffusing in the GaN and GaAs layers to reach the well, which would broaden the profiles. The experimental cathodoluminescence profiles are found to be systematically wider than the energy loss distributions calculated by means of the Monte Carlo program CASINO, with the width monotonically increasing with decreasing temperature. This effect is observed for both GaN and GaAs and becomes more pronounced for higher acceleration voltages. We discuss this phenomenon in terms of both, the electron-phonon interaction controlling the energy relaxation of hot carriers, and the shape of the initial carrier distribution. Finally, we present a phenomenological approach to simulate the carrier generation volume that can be used for the investigation of the temperature dependence of carrier diffusion.

cond-mat.mtrl-sci↗

arXiv2021

Carrier diffusion in GaN -- a cathodoluminescence study. II: Ambipolar vs. exciton diffusion

We determine the diffusion length of excess carriers in GaN by spatially resolved cathodoluminescence spectroscopy utilizing a single quantum well as carrier collector or carrier sink. Monochromatic intensity profiles across the quantum well are recorded for temperatures between 10 and 300 K. A classical diffusion model accounts for the profiles acquired between 120 and 300 K, while for temperatures lower than 120 K, a quantum capture process has to be taken into account in addition. Combining the diffusion length extracted from these profiles and the effective carrier lifetime measured by time-resolved photoluminescence experiments, we deduce the carrier diffusivity as a function of temperature. The experimental values are found to be close to theoretical ones for the ambipolar diffusivity of free carriers limited only by intrinsic phonon scattering. This agreement is shown to be fortuitous. The high diffusivity at low temperatures instead originates from an increasing participation of excitons in the diffusion process.

cond-mat.mtrl-sci↗

arXiv2021

Carrier diffusion in GaN -- a cathodoluminescence study. III: Nature of nonradiative recombination at threading dislocations

We investigate the impact of threading dislocations with an edge component (a or a+c-type) on carrier recombination and diffusion in GaN(0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a GaN(0001) layer with a deeply buried (In,Ga)N quantum well. Varying the acceleration voltage of the primary electrons and comparing the signal from the layer and the quantum well enables us to probe carrier recombination at depths ranging from the close vicinity of the surface to the position of the quantum well. Our experiments are accompanied by fully three-dimensional Monte Carlo simulations of carrier drift, diffusion, and recombination in the presence of the surface, the quantum well, and the dislocation, taking into account the dislocation strain field and the resulting piezoelectric field at the dislocation outcrop. Near the surface, this field establishes an exciton dead zone around the dislocation, the extent of which is not related to the carrier diffusion length. However, reliable values of the carrier diffusion length can be extracted from the dipole-like energy shift observed in hyperspectral cathodoluminescence maps recorded around the dislocation outcrop at low acceleration voltages. For high acceleration voltages, allowing us to probe a depth where carrier recombination is unaffected by surface effects, we observe a much stronger contrast than expected from the piezoelectric field alone. This finding provides unambiguous experimental evidence for the strong nonradiative activity of edge threading dislocations in bulk GaN and hence also in buried heterostructures.

cond-mat.mtrl-sci↗

arXiv2020

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 studied experimentally and modeled by means of Monte Carlo simulations. It is shown that the scattering intensity at large wave vectors does not follow Porod's law $I(q)\propto q^{-4}$. 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, as a reminiscence of the surface truncation rod scattering. At large wave vectors $q$, the scattering intensity is found to be decreased by surface roughness. A root mean square roughness of 0.9~nm, which is the height of just 3--4 atomic steps per micron long facet, already gives rise to a strong intensity reduction.

cond-mat.mtrl-sci↗

arXiv2019

Determination of the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations: fallacies and opportunities

We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 to 200 K. Contrary to common belief, the cathodoluminescence intensity contrast is only weakly affected by exciton diffusion, but is caused primarily by exciton dissociation in the piezoelectric field at the dislocation outcrop. Hence, the extension of the dark spots around dislocations in the luminescence maps cannot be used to determine the exciton diffusion length. However, the cathodoluminescence energy contrast, reflecting the local bandgap variation in the dislocation strain field, does sensitively depend on the exciton diffusion length and hence enables its experimental determination.

cond-mat.mtrl-sci↗

arXiv2018

Piezoelectric field, exciton lifetime, and cathodoluminescence intensity at threading dislocations in GaN{0001}

The strain field of a dislocation emerging at a free surface is partially relaxed to ensure stress free boundary conditions. We show that this relaxation strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric volume charge. The electric field produced by this charge distribution is strong enough to dissociate free excitons at distances over 100 nm from the dislocation line. We evaluate the impact of this effect on cathodoluminescence images of dislocations.

cond-mat.mtrl-sci↗

arXiv2018

Self-Assembled formation of long, thin, and uncoalesced GaN nanowires on crystalline TiN films

We investigate in detail the self-assembled nucleation and growth of GaN nanowires by molecular beam epitaxy on crystalline TiN films. We demonstrate that this type of substrate allows the growth of long and thin GaN nanowires that do not suffer from coalescence, which is in contrast to the growth on Si and other substrates. Only beyond a certain nanowire length that depends on the nanowire number density and exceeds here 1.5 μm, coalescence takes place by bundling, i.e. the same process as on Si. By analyzing the nearest neighbor distance distribution, we identify diffusion-induced repulsion of neighboring nanowires as the main mechanism limiting the nanowire number density during nucleation on TiN. Since on Si the final number density is determined by shadowing of the impinging molecular beams by existing nanowires, it is the difference in adatom surface diffusion that enables on TiN the formation of nanowire ensembles with reduced number density. These nanowire ensembles combine properties that make them a promising basis for the growth of core-shell heterostructures.

cond-mat.mtrl-sci↗

arXiv2016

Elastic vs. plastic strain relaxation in coalesced GaN nanowires: an x-ray diffraction study

The coalescence in dense arrays of spontaneously formed GaN nanowires proceeds by bundling: adjacent nanowires bend and merge at their top, thus reducing their surface energy at the expense of the elastic energy of bending. We give a theoretical description of the energetics of this bundling process. The bending energy is shown to be substantially reduced by the creation of dislocations at the coalescence joints. A comparison of experimental and calculated x-ray diffraction profiles from ensembles of bundled nanowires demonstrates that a large part of the bending energy is indeed relaxed by plastic deformation. The residual bending manifests itself by extended tails of the diffraction profiles.

cond-mat.mtrl-sci↗

arXiv2014

Investigating the origin of the nonradiative decay of bound excitons in GaN nanowires

We investigate the origin of the fast recombination dynamics of bound and free excitons in GaN nanowire ensembles by temperature-dependent photoluminescence spectroscopy using both continuous-wave and pulsed excitation. The exciton recombination in the present GaN nanowires is dominated by a nonradiative channel between 10 and 300 K. Furthermore, bound and free excitons in GaN NWs are strongly coupled even at low temperatures resulting in a common lifetime of these states. By solving the rate equations for a coupled two-level system, we show that one cannot, in practice, distinguish whether the nonradiative decay occurs directly via the bound or indirectly via the free state. The nanowire surface and coalescence-induced dislocations appear to be the most obvious candidates for nonradiative defects, and we thus compare the exciton decay times measured for a variety of GaN nanowire ensembles with different surface-to-volume ratio and coalescence degrees. The data are found to exhibit no correlation with either of these parameters, i. e., the dominating nonradiative channel in the GaN nanowires under investigation is neither related to the nanowire surface, nor to coalescence-induced defects for the present samples. Hence, we conclude that nonradiative point defects are the origin of the fast recombination dynamics of excitons in GaN nanowires.

cond-mat.mtrl-sci↗

arXiv2014

Statistical analysis of the shape of one-dimensional nanostructures: determining the coalescence degree of spontaneously formed GaN nanowires

Single GaN nanowires formed spontaneously on a given substrate represent nanoscopic single crystals free of any extended defects. However, due to the high area density of thus formed GaN nanowire ensembles, individual nanowires coalesce with others in their immediate vicinity. This coalescence process may introduce strain and structural defects, foiling the idea of defect-free material due to the nanowire geometry. To investigate the consequences of this process, a quantitative measure of the coalescence of nanowire ensembles is required. We derive objective criteria to determine the coalescence degree of GaN nanowire ensembles. These criteria are based on the area-perimeter relationship of the cross-sectional shapes observed, and in particular on their circularity. Employing these criteria, we distinguish single nanowires from coalesced aggregates in an ensemble, determine the diameter distribution of both, and finally analyze the coalescence degree of nanowire ensembles with increasing fill factor.

cond-mat.mes-hall↗

arXiv2012

Correlation between In content and emission wavelength of InGaN/GaN nanowire heterostructures

GaN nanowire ensembles with axial InGaN multi-quantum wells (MQWs) were grown by molecular beam epitaxy. In a series of samples, we varied the In content in the MQWs from almost zero to about 20%. Within the nanowire ensemble, the MQWs fluctuate strongly in composition and size. Statistical information about the composition was obtained from x-ray diffraction and Raman spectroscopy. Photoluminescence at room temperature was obtained in the range from 2.2 eV to 2.5 eV depending on In content. Contrary to planar MQWs, the intensity increases with increasing In content. We compare the observed emission energies with transition energies obtained from a one-dimensional model, and conclude that several mechanisms for carrier localization affect the luminescence of these three-dimensional structures.

cond-mat.mes-hall↗

arXiv2007

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability.

cond-mat.other↗