Formation Of Misfit Dislocations Research Articles

Strain relaxation in semipolar (202¯1) InGaN grown by plasma assisted molecular beam epitaxy

Strain relaxation in semipolar (202¯1) InGaN layers grown by plasma assisted molecular beam epitaxy (PAMBE) was investigated with high-resolution X-ray diffraction (XRD) reciprocal space mapping, cathodoluminescence (CL), fluorescent light microscopy (FLM), and atomic force microscopy. We find that XRD detects lattice relaxation much later than its actual onset occurs. Other techniques used in this study allowed to detect local footprints of plastic relaxation before it was evidenced by XRD: at the initial stages of strain relaxation, we observed changes in layer morphology, i.e., formation of short trench line segments on the surface along the ⟨112¯0⟩ direction as well as dark lines in CL and FLM. The misfit dislocations formation and glide were observed in two slip systems: initially in basal slip system ⟨112¯0⟩{0001} and for larger amount of strain in non-basal, prismatic slip system ⟨112¯0⟩{11¯00}. Experimentally determined critical thickness for InGaN layers grown by PAMBE on semipolar (202¯1) bulk GaN substrates agrees well with literature data obtained with metalorganic vapor phase epitaxy and follows the Matthews-Blakeslee model prediction. We discuss the impact of substrate structural properties on the strain relaxation onset and mechanisms. We also describe the layer morphology and surface roughness evolution related to the increasing In content and strain relaxation of the semipolar (202¯1) InGaN layers.

Global transition path search for dislocation formation in Ge on Si(001)

Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum energy paths on the energy surface emerging from the atomic interactions in the system. The challenge is to find which intermediate states to include and to construct a path going through these intermediates in such a way that the overall activation energy for the transition is minimal. In the numerical approach presented here, intermediate minima are constructed by heredity transformations of known minimum energy structures and by identifying local minima in minimum energy paths calculated using a modified version of the nudged elastic band method. Several mechanisms for the formation of a 90° misfit dislocation at the Ge–Si interface are identified when this method is used to construct transition paths connecting a homogeneously strained Ge film and a film containing a misfit dislocation. One of these mechanisms which has not been reported in the literature is detailed. The activation energy for this path is calculated to be 26% smaller than the activation energy for half loop formation of a full, isolated 60° dislocation. An extension of the common neighbor analysis method involving characterization of the geometrical arrangement of second nearest neighbors is used to identify and visualize the dislocations and stacking faults.

An atomistically validated continuum model for strain relaxation and misfit dislocation formation

In this paper, molecular dynamics (MD) calculations have been used to examine the physics behind continuum models of misfit dislocation formation and to assess the limitations and consequences of approximations made within these models. Without compromising the physics of misfit dislocations below a surface, our MD calculations consider arrays of dislocation dipoles constituting a mirror imaged “surface”. This allows use of periodic boundary conditions to create a direct correspondence between atomistic and continuum representations of dislocations, which would be difficult to achieve with free surfaces. Additionally, by using long-time averages of system properties, we have essentially reduced the errors of atomistic simulations of large systems to “zero”. This enables us to deterministically compare atomistic and continuum calculations. Our work results in a robust approach that uses atomistic simulation to accurately calculate dislocation core radius and energy without the continuum boundary conditions typically assumed in the past, and the novel insight that continuum misfit dislocation models can be inaccurate when incorrect definitions of dislocation spacing and Burgers vector in lattice-mismatched systems are used. We show that when these insights are properly incorporated into the continuum model, the resulting energy density expression of the lattice-mismatched systems is essentially indistinguishable from the MD results.

Critical thickness investigation of MBE-grown GaInAs/GaAs and GaAsSb/GaAs heterostructures

GaInAs/GaAs and GaAsSb/GaAs heterostructures were grown by molecular beam epitaxy with different In/Sb compositions and thicknesses in order to obtain samples with different amounts of initial strain. High resolution x-ray diffraction was used to extract the alloys composition, specify the presence of dislocations, and determine the extent of relaxation while transmission electron microscopy and x-ray topography were used to observe these dislocations and characterize their type and density. The onset for the formation of misfit dislocations was found to be in agreement with the equilibrium theory. However, the films remained coherently strained for thicknesses far beyond this value. The onset for strain relaxation was found by considering the kinetics of plastic deformation using the approach proposed by Tsao and coworkers [Phys. Rev. Lett. 59, 2455 (1987)]. The mechanism of extended defect creation leading to measurable strain relief is described as a multistage process related with the structural stability and metastability of the epitaxial films.

Critical thickness for the formation of misfit dislocations originating from prismatic slip in semipolar and nonpolar III-nitride heterostructures

We calculate the critical thickness for misfit dislocation (MD) formation in lattice mismatched semipolar and nonpolar III-nitride wurtzite semiconductor layers for the case of MDs originated from prismatic slip (PSMDs). It has been shown that there is a switch of stress relaxation modes from generation of basal slip originated MDs to PSMDs after the angle between c-axis in wurtzite crystal structure and the direction of semipolar growth reaches a particular value, e.g., ∼70° for Al0.13Ga0.87N/GaN (h0h̄1) semipolar heterostructures. This means that for some semipolar growth orientations of III-nitride heterostructures biaxial relaxation of misfit stress can be realized. The results of modeling are compared to experimental data on the onset of plastic relaxation in AlxGa1−xN/GaN heterostructures.

Study of the structure of a thin aluminum layer on the vicinal surface of a gallium arsenide substrate by high-resolution electron microscopy

The results of electron-microscopy studies of a thin epitaxial aluminum layer deposited onto a misoriented gallium-arsenide substrate are reported. It is established that the layer consists of differently oriented grains, whose crystal lattices are coherently conjugated with the substrate with the formation of misfit dislocations, as in the case of a layer on a singular substrate. Atomic steps on the substrate surface are visualized, and their influence on the growth of aluminum crystal grains is discussed.

Relationship between misfit-dislocation formation and initial threading-dislocation density in GaInN/GaN heterostructures

The dependence of the critical thickness for the introduction of misfit dislocations in a GaInN/GaN heterostructure system on the dislocation density in the underlying GaN layer was investigated using in situ X-ray diffraction (XRD), ex situ scanning electron microscopy, and transmission electron microscopy analyses. The critical thickness for the introduction of misfit dislocations in the GaInN layer was found to significantly depend on the dislocation density in the underlying GaN layer. Notably, on the basis of the in situ XRD results, a reliable critical thickness for obtaining misfit-dislocation-free growth was determined.

Epitaxial growth of Ba2YNbO6 films on biaxially-textured NiW substrates as a multifunctional single buffer layer for high Jc epitaxial YBCO film

Abstract

Anisotropy of strain relaxation in heterogeneous GaInNAs layers grown by AP-MOVPE

The structural investigations of thick undoped GaInNAs/GaAs heterostructures grown by atmospheric pressure vapor phase epitaxy (AP-MOVPE) have been performed by transmission electron microscopy (TEM) and X-ray diffraction (XRD) techniques. The cross-sectional view TEM images revealed plainly heterogeneous layer structure, consisting of a few sublayers with different indium and nitrogen contents. On the other hand, planar-view TEM images revealed 2D network of misfit dislocations oriented in two orthogonal 〈110〉 crystallographic directions at the (001) sublayer interface. Moreover, the XRD measurements provide information about gradient profiles of indium and nitrogen contents, as well as distinct anisotropy of strain relaxation in GaInNAs epitaxial layer, evoked by the asymmetry in formation of interfacial misfit dislocation. The obtained results were exploited to calculate the band structure diagram of the investigated GaInNAs/GaAs heterostructure and mean values of the lattice parameters of the distorted epitaxial layer unit cell, respectively.

Role of thermal annealing on SiGe thin films fabricated by PECVD

Amorphous Silicon Germanium (a-SiGe) thin films of 500nm thickness are deposited on silicon substrates using Plasma Enhanced Chemical Vapour Deposition (PECVD). To obtain polycrystalline nature of films, thermal annealing is done at various temperature (450–600°C) and time (1–10h). The surface morphology of the pre- and post-annealed films is investigated using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The crystallographic structure of the film is obtained by X-ray diffraction method. Raman spectroscopy is carried out to quantify the Ge concentration and the degree of strain relaxation in the film. Nano-indentation is performed to obtain the mechanical properties of the film. It is found that annealing reduces the surface roughness of the film and increases the Ge concentration in the film. The grain size of the film increases with increase in annealing temperature. The grain size is found to decrease with increase in annealing time up to 5h and then increased. The results show that 550°C for 5h is the critical annealing condition for variation of structural and mechanical properties of the film. Recrystallization starts at this condition and results in finer grains. An increase in hardness value of 7–8GPa has been observed. Grain growth occurs above this critical annealing condition and degrades the mechanical properties of the film. The strain in the film is only relaxed to about 55% even for 10h of annealing at 600°C. Transmission Electron Microscopy (TEM) observations show that the strain relaxation occurs by forming misfit dislocations and these dislocations are confined to the SiGe/Si interface.

Formation of interfacial misfit dislocation in GaSb/GaAs heteroepitaxy via anion exchange process

We report the formation of interfacial misfit dislocation found in GaSb layers grown on (001) GaAs substrates using anion exchange process at different growth temperatures. An in-situ reflection high-energy electron diffraction (RHEED) in conjunction with transmission electron microscopy (TEM), atomic force spectroscopy (AFM) and X-ray diffraction (XRD) analysis was applied to investigate the relations between substrate temperature, As to Sb anion exchange, the changes in threading dislocation density and the growth kinetics of the GaSb/GaAs heteroepitaxy system. A GaSb layer grown at 450°C exhibited the lowest threading dislocation density. Our results provide further understanding of the dominant substrate temperature-dependent growth mechanisms that can affect threading dislocation in the GaSb on a GaAs heteroepitaxy system, which uses anion exchange process to facilitate the formation of interfacial misfit dislocation.

Cracking the Si Shell Growth in Hexagonal GaP-Si Core-Shell Nanowires.

Semiconductor nanowires have increased the palette of possible heterostructures thanks to their more effective strain relaxation. Among these, core-shell heterostructures are much more sensitive to strain than axial ones. It is now accepted that the formation of misfit dislocations depends both on the lattice mismatch and relative dimensions of the core and the shell. Here, we show for the first time the existence of a new kind of defect in core-shell nanowires: cracks. These defects do not originate from a lattice mismatch (we demonstrate their appearance in an essentially zero-mismatch system) but from the thermal history during the growth of the nanowires. Crack defects lead to the development of secondary defects, such as type-I1 stacking faults and Frank-type dislocations. These results provide crucial information with important implications for the optimized synthesis of nanowire-based core-shell heterostructures.

Electron microscopy of iron chalcogenide FeTe(Se) films

The structure of Fe1 + δTe1 − xSex films (x = 0; 0.05) grown on single-crystal MgO and LaAlO3 substrates has been investigated by transmission and scanning transmission electron microscopy. The study of Fe1.11Te/MgO structures has revealed two crystallographic orientation relationships between the film and substrate. It is shown that the lattice mismatch between the film and substrate is compensated for by the formation of misfit dislocations. The Burgers vector projection is determined. The stresses in the film can partially be compensated for due to the formation of an intermediate disordered layer. It is shown that a FeTe0.5Se0.5 film grown on a LaAlO3 substrate is single-crystal and that the FeTe0.5Se0.5/LaAlO3 interface in a selected region is coherent. The orientation relationships between the film and substrate are also determined for this case.

Effect of piezoelectricity on critical thickness for misfit dislocation formation at InGaN/GaN interface

An analytical study has been carried out to investigate the effect of piezoelectricity and spontaneous polarization on the critical thickness for misfit dislocation formation at the interface of InGaN/GaN layers. Two representative critical thickness prediction formulations given by Matthews (1974) and Freund (1987) have been generalized to include piezoelectricity and spontaneous polarization. Critical thicknesses have been calculated by using the generalized methods and presented for both c-plane and a-plane deposition in hexagonal crystal lattice. Numerical results of the critical thickness for an InGaN epitaxial film on a GaN substrate has been presented and discussed in terms of the indium concentration in the epitaxial layer, the line charge associated with the dislocation core, the spontaneous polarization along c-axis, and the piezoelectric constants of the InxGa(1-x)N film. Here, x stands for indium concentration. The indium concentration determines the misfit strain due to lattice mismatch between the InGaN film and GaN substrate. It is shown that the piezoelectricity and spontaneous polarizations have negligible effect on the critical thickness for the case of InGaN/GaN. Parametric studies were carried out by increasing the piezoelectric properties of the InxGa(1-x)N ten folds. It has been found that the enhanced piezoelectricity reduces the critical thickness so that it becomes easier to form the misfit dislocation. We have investigated the reason for the decrease in the critical thickness due to piezoelectricity by investigating the state of stress and internal energy of the film. Our study shows that the enhanced piezoelectric properties give rise to stiffening of the film which increases its elastic energy. This makes it favorable to form misfit dislocations by increasing the available energy for dislocation formation. It is also shown that spontaneous polarization along c-axis in the InGaN film decreases the critical thickness for c-growth orientation while it increases the critical thickness along a-growth orientation. This occurs because the internal energy of the film increases due to spontaneous polarization for c-growth orientation while it decreases for a-growth orientation. However, the increase or decrease in the critical thickness due to spontaneous polarization is very marginal. A line charge associated with dangling bonds along the dislocation core increases the critical thickness because it increases the required energy to form the dislocation.

Atomic scale strain relaxation in axial semiconductor III-V nanowire heterostructures.

Combination of mismatched materials in semiconductor nanowire heterostructures offers a freedom of bandstructure engineering that is impossible in standard planar epitaxy. Nevertheless, the presence of strain and structural defects directly control the optoelectronic properties of these nanomaterials. Understanding with atomic accuracy how mismatched heterostructures release or accommodate strain, therefore, is highly desirable. By using atomic resolution high angle annular dark field scanning transmission electron microscopy combined with geometrical phase analyses and computer simulations, we are able to establish the relaxation mechanisms (including both elastic and plastic deformations) to release the mismatch strain in axial nanowire heterostructures. Formation of misfit dislocations, diffusion of atomic species, polarity transfer, and induced structural transformations are studied with atomic resolution at the intermediate ternary interfaces. Two nanowire heterostructure systems with promising applications (InAs/InSb and GaAs/GaSb) have been selected as key examples.

High-power low-droop violet semipolar (303¯1¯) InGaN/GaN light-emitting diodes with thick active layer design

Devices grown on nonpolar and semipolar planes of GaN offer key performance advantages over devices grown on the conventional c-plane, including reduced polarization fields. This allows for a wider design space on semipolar planes for light emitting diodes (LEDs) to address the problem of efficiency droop at high current densities. LED structures with very thick (10–100 nm) InGaN single-quantum-well/double heterostructure active regions were grown using conventional metal organic chemical vapor deposition on semipolar (303¯1¯) free-standing GaN substrates and processed and packaged using conventional techniques. Simulated band diagrams showed reduced polarization fields on the (303¯1¯) plane. The calculated critical thickness for misfit dislocation formation is higher on the (303¯1¯) plane than on other semipolar planes, such as (202¯1¯), allowing for thicker active regions than our previous work to further reduce droop. The higher critical thickness was confirmed with defect characterization via cathodoluminescence. A trend is demonstrated in lower efficiency droop for devices with thicker active regions. Thermal droop characteristics of these devices are also presented. These observed results were utilized to demonstrate over 1 W of output power at a current density of 1 kA/cm2 from a single 0.1 mm2 LED device.

Anisotropic-strain-relaxation-induced crosshatch morphology in epitaxial SrTiO3/NdGaO3 thin films

We investigate the strain relaxation and surface morphology of epitaxial SrTiO3 (STO) films grown on (001)O and (110)O planes of orthorhombic NdGaO3 (NGO), and (001) plane of cubic (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates. Although the average lattice mismatches are similar, strikingly regular crosshatched surface patterns can be found on STO/NGO(001)O[(110)O] films, contrary to the uniform surface of STO/LSAT(001). Based on the orientation and thickness dependent patterns and high-resolution x-ray diffractions, we ascribe the crosshatch morphology to the anisotropic strain relaxation with possibly the 60° misfit dislocation formation and lateral surface step flow in STO/NGO films, while an isotropic strain relaxation in STO/LSAT. Further, we show that the crosshatched STO/NGO(110)O surface could be utilized as a template to modify the magnetotransport properties of epitaxial La0.6Ca0.4MnO3 films. This study highlights the crucial role of symmetry mismatch in determining the surface morphology of the perovskite oxide films, in addition to their epitaxial strain states, and offers a different route for designing and fabricating functional perovskite-oxide devices.

Strain accommodation by facile WO₆ octahedral distortion and tilting during WO₃ heteroepitaxy on SrTiO₃(001).

In this work, we demonstrate that WO6 octahedra in tungsten trioxide (WO3) undergo an unusually large degree of distortion and tilting to accommodate interfacial strain. This motion strongly impacts nucleation, structure, and defect formation during the epitaxial growth of WO3 on SrTiO3(001). A metastable tetragonal phase can be stabilized by heteroepitaxy and a thickness-dependent phase transition (tetragonal to monoclinic) is observed. In contrast to misfit dislocation formation, facile WO6 octahedral deformation gives rise to three types of planar defects. The thicknesses of affected regions can range from several to tens of nanometers with graded lattice parameters, allowing the strain from interfacial lattice mismatch to be relieved gradually. These atomically resolved, unique interfacial defects may significantly alter the electronic, electrochromic, and mechanical properties of WO3 epitaxial films.

Photostrictive/Piezomagnetic Core–Shell Particles Based on Prussian Blue Analogues: Evidence for Confinement Effects?

High-quality core–shell particles, which associate a photostrictive core (Rb0.5Co[Fe(CN)6]0.8·zH2O, RbCoFe) and a ferromagnetic shell (Rb0.2Ni[Cr(CN)6]0.7·z′H2O, RbNiCr), were successfully grown by a multistep protocol based on coprecipitation in water. High-resolution transmission electron microscopy shows that well-defined heterostructures are formed and that the core–shell interface is abrupt with the epitaxial relationship [001](001)RbCoFe//[001](001)RbNiCr, confirmed by simulations of the X-ray diffraction line widths. The core particles are monocrystalline, with 50 nm sides, and the shell consists of large platelet-like crystallites, with a height that corresponds to the shell thickness and lateral dimensions comparable to the size of the core particles. Analysis of the diffracted intensities as a function of shell thickness (9–26 nm) shows that the epitaxial shell growth does not lead to a thick pseudomorphic layer at the interface. In contrast, Williamson–Hall plots suggest that a structural relaxation takes place to adapt the mismatched lattices, with the formation of misfit dislocations distributed over the entire shell thickness. This later finding is indicative of an effective mechanical coupling within the heterostructures. However, a magnetization increase by only a few percent was observed under light irradiation for these RbCoFe@RbNiCr particles. We showed from in situ synchrotron X-ray diffraction measurements that these small changes most likely reflect confinement effects as photoswitching of the core phase is partly or completely blocked depending on the shell thickness.

Material Characterization of Ge1−x Sn x Alloys Grown by a Commercial CVD System for Optoelectronic Device Applications

High-quality compressive-strained Ge1−xSnx/Ge films have been deposited on Si(001) substrate using a mainstream commercial chemical vapor deposition reactor. The growth temperature was kept below 450°C to be compatible with Si complementary metal–oxide–semiconductor processes. Germanium tin (Ge1−xSnx) layers were grown with different Sn composition ranging from 0.9% to 7%. Material characterizations, such as secondary-ion mass spectrometry, Rutherford backscattering spectrometry, and x-ray diffraction analysis, show stable Sn incorporation in the Ge lattice. Comparison of the Sn mole fractions obtained using these methods shows that the bowing factor of 0.166 nm (in Vegard’s law) is in close agreement with other experimental data. High-resolution transmission electron microscopy and atomic force microscopy results show that the films have started to relax through the formation of misfit and threading dislocations. Raman spectroscopy, ellipsometry, and photoluminescence (PL) techniques are used to study the structural and optical properties of the films. Room-temperature PL of the films shows that 7% Sn incorporation in the Ge lattice results in a decrease in the direct bandgap of Ge from 0.8 eV to 0.56 eV.