Effect of internal strain fields on the controllability of nanodimensional ferroelectric films in a plane capacitor

Nanodimensional ferroelectric heteroepitaxial Ba_0.8Sr_0.2TiO₃ films grown by the layer-by-layer mechanism on MgO(100) substrates are examined by the X-ray diffraction and transmission electron microscopy methods. It is established that, when the thickness of the film changes, the stress relaxation proceeds via generation of misfit dislocations at the film-substrate interface. There exists a critical thickness (≈40 nm) of the film below and above which the film possesses tensile and compression stresses, respectively. Examples of how the stresses influence the insulating properties of the films are given.     

Microstructural assessment of InN-on-GaN films grown by plasma-assisted MBE

The structural properties of InN thin films, grown by rf plasma-assisted molecular beam epitaxy on Ga-face GaN/Al₂O₃(0001) substrates, were investigated by means of conventional and high resolution electron microscopy. Our observations showed that a uniform InN film of total thickness up to 1 μm could be readily grown on GaN without any indication of columnar growth. A clear epitaxial orientation relationship of , was determined. The quality of the InN film was rather good, having threading dislocations as the dominant structural defect with a density in the range of 10⁹–10¹⁰ cm⁻². The crystal lattice parameters of wurtzite InN were estimated by electron diffraction analysis to be a=0.354 nm and c=0.569 nm, using Al₂O₃ as the reference crystal. Heteroepitaxial growth of InN on GaN was accomplished by the introduction of a network of three regularly spaced misfit dislocation arrays at the atomically flat interface plane. The experimentally measured distance of misfit dislocations was 2.72 nm. This is in good agreement with the theoretical value derived from the in-plane lattice mismatch of InN and GaN, which indicated that nearly full relaxation of the interfacial strain between the two crystal lattices was achieved.     

Role of long-range shear stresses in the plastic deformation of epitaxial films

The dependence of elastic energy on relaxation parameters ρ _x and ρ _y varying in limits from 0 to 1 is analyzed for near-surface layers of an In_0.1Ga_0.9As epitaxial film on a GaAs (001) substrate whose thickness exceeds the distance between neighboring misfit dislocations.     

Edge misfit dislocations in GexSi1 ? x/Si(001) (x ～ 1) heterostructures: role of buffer GeySi1 ? y (y < x) interlayer in their formation

The structure of dislocations in Ge _x Si_{1 − x} (x ∼ 0.4–0.8) films grown by molecular beam epitaxy on Si(001) substrates tilted by 6° toward the nearest (111) plane has been studied. The epitaxy of GeSi films on substrates deviating from the exact (001) orientation has allowed us to establish the main mechanism of formation of edge misfit dislocations (MDs), which most effectively (for heterostructures of the given composition) relieve stresses caused by the mismatch between lattice parameters of the film and substrate. Despite the edge MDs being defined as immobile (sessile) dislocations, their formation proceeds according to the gliding mechanism proposed by Kvam et al. [J. Mater. Res. 5, 1900 (1990)]. A comparative estimation of the propagation velocities of the primary and induced 60° dislocations, as well as the resulting 90° MDs, has been performed. It has been established that the condition providing for the most effective edge MD formation by the induced nucleation mechanism is the appearance of 60° MDs in a stressed film immediately after it reached a critical thickness. A source of these dislocations can be provided by a preliminarily grown buffer GeSi layer that occurs in a metastable state at the initial stage of plastic relaxation.     

Accommodation of the Lattice Mismatch at the VCx-WC Interface

A VC doped WC-Co alloy is investigated using high resolution transmission electron microscopy. The VC grain growth inhibitor induces the presence of a thin layer on the surfaces of the WC grains in contact with Co and precipitates in the corners of Co pockets. These (VW)C_x compounds adopt an epitaxial orientation relationship with regards to the (0001) base facets of the WC crystals. Due to the small difference in lattice parameters, misfit dislocations are expected in the interfaces. Unlike the thin layers where no defects are observed, two kinds of dislocations are pointed out for larger precipitates. 1/6〈112〉_VC interfacial dislocations are sometimes present while more often 1/2〈1¯10〉_VC dislocations lying above the interface in the (VW)C_x phase are visible.     

Generation of dislocation loops in strained quantum dots embedded in a heterolayer

The generation of prismatic dislocation loops in strained quantum dots is investigated. The quantum dots are embedded in a film-substrate heterostructure with mechanical stresses caused by the difference between the lattice parameters of the film (heterolayer) and the substrate. The intrinsic plastic strain ?_m of a quantum dot arises from the misfit between the lattice parameters of the materials of the quantum dot and the surrounding matrix. The interface between the heterolayer and the substrate is characterized by a misfit parameter f. The critical radius of a quantum dot R _c at which the generation of a dislocation loop in the quantum dot becomes energetically favorable is analyzed as a function of the intrinsic plastic strain ?_m and the misfit parameter f.     

The defect structure of AlGaN/GaN superlattices grown on sapphire by the MOCVD method

High-resolution x-ray diffractometry and electron microscopy are used to study the defect structure and relaxation mechanism of elastic stresses in AlGaN/GaN superlattices grown by the MOCVD method on sapphire covered with a preliminarily deposited GaN and AlGaN buffer layer. Based on an analysis of the half-widths of three-crystal scan modes of x-ray reflections measured in different diffraction geometries, the density of different dislocation families is determined. For all the dislocation families, the density is shown to increase with the Al concentration in the solid-solution layers and depend only weakly on the superlattice period. From the electron-microscopic patterns of planar and cross sections, the types of dislocations and their distribution in depth are determined. It is shown that, in addition to high-density vertical edge and screw dislocations, which nucleate in the buffer layer and propagate through the superlattice layers, there are sloped intergrowing dislocations with a large horizontal projection and bent mixed dislocations with a Burgers vector $\left\langle {11\overline 2 3} \right\rangle $ at the interface between individual superlattice layers. The former dislocations form at the interface between the buffer layer and the superlattice and remove misfit stresses between the buffer and the superlattice as a whole, and the latter dislocations favor partial relaxation of stresses between individual superlattice layers. In samples with a high Al concentration (greater than 0.4) in AlGaN layers, there are cracks surrounded by high-density chaotic horizontal dislocations.     

The structure of a propagating MgAl2O4/MgO interface: linked atomic- and μm-scale mechanisms of interface motion

To understand how a new phase forms between two reactant layers, MgAl₂O₄ (spinel) has been grown between MgO (periclase) and Al₂O₃ (corundum) single crystals under defined temperature and load. Electron backscatter diffraction data show a topotaxial relationship between the MgO reactant and the MgAl₂O₄ reaction product. These MgAl₂O₄ grains are misoriented from perfect alignment with the MgO substrate by ~2–4°, with misorientation axes concentrated in the interface plane. Further study using atomic resolution scanning transmission electron microscopy shows that in 2D the MgAl₂O₄/MgO interface has a periodic configuration consisting of curved segments (convex towards MgO) joined by regularly spaced misfit dislocations occurring every ~4.5 nm (~23 atomic planes). This configuration is observed along the two equivalent [1 0 0] directions parallel to the MgAl₂O₄/MgO interface, indicating that the 3D geometry of the interface is a grid of convex protrusions of MgAl₂O₄ into MgO. At each minimum between the protrusions is a misfit dislocation. This geometry results from the coupling between long-range diffusion, which supplies Al³⁺ to and removes Mg²⁺ from the reaction interface, and interface reaction, in which climb of the misfit dislocations is the rate-limiting process. The extra oxygen atoms required for dislocation climb were likely derived from the reactant MgO, leaving behind oxygen vacancies that eventually form pores at the interface. The pores are dragged along by the propagating reaction interface, providing additional resistance to interface motion. The pinning effect of the pores leads to doming of the interface on the scale of individual grains.     

Molecular dynamic simulation of the CsCl–Al2O3 interface

The interface between solid cesium chloride and α-aluminum oxide was simulated by molecular dynamics technique. It was shown that due to a misfit between lattices of the components the interfacial contact may be presented as a small-angle boundary saturated with dislocations. Also a domain structure is formed. The dislocations and interdomain boundaries act as a source of defects and give rise to the total ionic mobility along the interface and boundaries. According to the calculation at a temperature of nearly 70% of the melting point, the diffusion coefficients of ions along misfit dislocation cores and domain walls, ∼ 10^– 6 cm²/s, are only an order of magnitude lower than the corresponding values for molten salts.     

Strain analysis of misfit dislocations in α-Fe2O3/α-Al2O3 heterostructure interface by geometric phase analysis

The α-Fe₂O₃/α-Al₂O₃ heterostructure interfaces have been studied using transmission electron microscopy (TEM). The interface exhibited coherent regions separated by equally spaced misfit dislocations. The misfit dislocations were demonstrated to be edge dislocations with dislocation spacing of ∼4 nm. The strain fields around the misfit dislocation core were mapped using a combination of geometric phase analysis and high-resolution transmission electron microscopy images. The strain measurement results were compared with the Peierls–Nabarro dislocation model and the Foreman dislocation model. These comparisons show that the Foreman model (a = 2) is the most appropriate theoretical model to describe the strain fields of the dislocation core.     

Specific features of plastic relaxation of a metastable Ge x Si1 − x layer buried between a silicon substrate and a relaxed germanium layer

Heterostructures Ge/Ge _x Si_{1 ? x} /Si(001) grown by molecular beam epitaxy have been investigated using atomic scale high-resolution electron microscopy. A germanium film (with a thickness of 0.5–1.0 μm) grown at a temperature of 500°C is completely relaxed. An intermediate Ge_0.5Si_0.5 layer remains in a strained metastable state, even though its thickness is 2–4 times larger than the critical value for the introduction of 60° misfit dislocations. It is assumed that the Ge/GeSi interface is a barrier for the penetration of dislocations from a relaxed Ge layer into the GeSi layer. This barrier is overcome during annealing of the heterostructures for 30 min at a temperature of 700°C, after which dislocation networks having different degrees of ordering and consisting predominantly of edge misfit dislocations are observed in the Ge/GeSi and GeSi/Si(001) heteroboundaries.     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Determination of the positions of impurity centers in a dislocation core in a NaCl crystal from magnetoplasticity spectra

The spectra of the mean free paths l(ν) of edge dislocations have been studied in NaCl crystals exposed in the electron paramagnetic resonance scheme to the crossed magnetic fields: the Earth’s field (50 μT) and the pump field (2.5 μT, 5–440 kHz). The spectra have been measured for a series of angles θ = 0°–5° of rotation of the sample around its edge [100] with respect to the Earth’s field. The fine structure of the spectra contains a series of peaks whose resonance frequencies are described by the empirical expression v _i ^± = Asin(θ ± Δθ _i ) ≈ A(θ ± Δθ _i ). The parameters Δθ _i are independent of the angle θ within the experimental errors. Within the model of “frozen” magnetic moments associated with impurity center Ca⁺-Cl⁰, the angles Δθ _i characterize the deviation of the axis of the center from the 〈100〉 direction in the core of a dislocation. These angles can be expressed in terms of the spectra obtained: Δθ _i = (? _i ⁺ ? v _i ^? )/2A. The computer simulation of the edge dislocation core provides the set of the angles Δθ _i close to the measured values. The spin-lattice relaxation time of the center on dislocation has been estimated from the low-frequency edge of the spectrum l(ν) as τ _{s ? l} ～ 10^?4 s.     

Initial stages of misfit stress relaxation through the formation of prismatic dislocation loops in GaN–Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> composite nanostructures

The initial stages of misfit stress relaxation through the formation of rectangular prismatic dislocation loops in model composite nanostructures have been considered. The nanostructures are either spherical or cylindrical GaN shells grown on solid or hollow β-Ga²O₃ cores or planar thin GaN films on β-Ga²O₃ substrates. Three characteristic configurations of prismatic dislocation loops, namely, square loops, loops elongated along the GaN/Ga²O₃ interface, and loops elongated along the normal to the GaN/Ga²O₃ interface, have been analyzed. The generation of prismatic dislocation loops from the interface into the bulk of the GaN shell (film), from the free surface into the GaN shell (film), and from the interface into the β-Ga²O₃ core (substrate) has been investigated. It has been shown that, for the minimum known estimate of the lattice misfit (2.6%) in some of the considered nanostructures, no any prismatic dislocation loops can be generated. If the generation of prismatic dislocation loops is possible, then in all the considered nanostructures, the energetically more favorable case corresponds to prismatic dislocation loops elongated along the GaN/Ga²O₃ interfaces, and the more preferred generation of prismatic dislocation loops occurs from the GaN free surface. The GaN/Ga²O₃ nanostructures that are the most and least resistant to the formation of prismatic dislocation loops have been determined. It has been found that, among the considered nanostructures, the planar two-layer GaN/Ga²O₃ plate is the most resistant to the generation of prismatic dislocation loops, which is explained by the action of an alternative mechanism for the relaxation of misfit stresses due to the bending of the plate. The least resistant nanostructure is the planar three-layer GaN/Ga²O₃/GaN plate, in which GaN films have an identical thickness and which itself as a whole does not undergo bending. The critical thicknesses of the GaN shells (films), which must be exceeded to ensure the growth of these shells (films) so as to avoid the formation of prismatic dislocation loops, have been calculated for all the studied nanostructures and three known estimates of the lattice misfits (2.6, 4.7, and 10.1%).     

GaSb layers with low defect density deposited on (001) GaAs substrate in two-dimensional growth mode using molecular beam epitaxy

We report on the growth of fully relaxed and smooth GaSb layers with reduced density of threading dislocations, deposited on GaAs substrate. We prove that three parameters have to be controlled in order to obtain applicable GaSb buffers with atomically smooth surface: interfacial misfit (IMF), the etch pit density (EPD) and the growth mode.The GaSb/GaAs interfacial misfit array and reduced EPD ≤1.0 × 10⁷ cm^?2 were easily obtained using As-flux reduction for 3 min and Sb-soaking surface for 10 s before the GaSb growth initiation. The successive growth of GaSb layer proceeded under the technological conditions described by the wide range of the following parameters: r_G ∈ (1.5 ÷ 1.9) Å/s, T_G ∈ (400 ÷ 520)°C, V/III ∈ (2.3 ÷ 3.5). Unfortunately, a spiral or 3D growth modes were observed for this material resulting in the surface roughness of 1.1 ÷ 3.0 nm. Two-dimensional growth mode (layer by layer) can only be achieved under the strictly defined conditions. In our case, the best quality 1-μm-thick GaSb buffer layer with atomically smooth surface was obtained for the following set of parameters: r_G = 1.5 Å/s, T_G = 530 °C, V/III = 2.9. The layer was characterized by the strain relaxation over 99.6%, 90° dislocations array with the average distance of 5.56 nm, EPD ～8.0 × 10⁶ cm^?2 and 2D undulated terraces on the surface with roughness of about 1 ML. No mounds were observed. We belive that only thin and smooth GaSb layer with reduced EPD may be applied as the buffer layer in complex device heterostructures. Otherwise, it may cause the device parameters deterioration.     

Nucleation of misfit dislocations and plastic deformation in core/shell nanowires

During fabrication of metal nanowires, an oxide layer (shell) that surrounds the metal (core) may form. Such an oxide-covered nanowire can be viewed as a cylindrical core/shell nanostructure, possessing a crystal lattice mismatch between the core and shell. Experimental evidence has shown that, in response to this mismatch, mechanical stresses induce plastic deformation in the shell and misfit dislocations nucleate at the core/shell interface. As a result, the mechanical, electrical and optoelectronic properties of the nanowire are affected. It is therefore essential to be able to predict the critical conditions at which misfit dislocation nucleation at the nanowire interface takes place and the critical applied load at which the interface begins deforming plastically. Two approaches are explored in order to analyze the stress relaxation processes in these oxide-covered nanowires: (i) energy considerations are carried out within a classical elasticity framework to predict the critical radii (of the core and shell) at which dislocation nucleation takes place at the nanowire interface; (ii) a strain gradient plasticity approach is applied to estimate the flow stress at which the interface will begin deforming plastically (this stress is termed “interfacial-yield” stress). The interfacial-yield stress, predicted by gradient plasticity, depends, among other material parameters, on the radii of the core and shell. Both approaches demonstrate how the geometric parameters of nanowires can be calibrated so as to avoid undesirable plastic deformation; in particular, method (i) can give the radii values that prevent misfit dislocation formation, whereas method (ii) can provide, for particular radii values, the critical stress at which interface deformation initiates.     

Microstructure of bulk GaN layer grown on sapphire substrates with amorphous buffer

The structure of bulk GaN layers grown on (0001) sapphire substrates by vapor-phase epitaxy has been studied by x-ray diffraction and transmission electron microscopy (TEM). It is found that these layers contain grown-in and screw dislocations. The dislocation density decreases away from the interface. The effect of an amorphous buffer layer on the formation of the initial GaN layer and, thus, on the degree of perfection of gallium nitride layers is elucidated. A model of generating grown-in dislocations and the relaxation mechanism of misfit stresses are proposed.     

Formation of Ge self-assembled quantum dots on a SixGe1−x buffer layer

Ge self-assembled quantum dots (SAQDs) grown on a relaxed Si_0.75Ge_0.25 buffer layer were observed using an atomic force microscopy (AFM) and a transmission electron microscopy (TEM). The effect of buried misfit dislocations on the formation and the distribution of Ge SAQDs was extensively investigated. The Burgers vector determination of each buried dislocation using the g·b = 0 invisibility criterion with plane-view TEM micrographs shows that Ge SAQDs grow at specific positions related to the Burgers vectors of buried dislocations. The measurement of the lateral distance between a SAQD and the corresponding misfit dislocation with plane-view and cross-sectional TEM images reveals that SAQDs form at the intersections of the top surface with the slip planes of misfit dislocations. The stress field on the top surface due to misfit dislocations is computed, and it is found that the strain energy of the misfit dislocations provides the preferential formation sites for Ge SAQDs nucleation.     

X-ray photoelectron spectra and composition of YBa2Cu3O7 − δ films prepared by laser ablation

The Y3d, Ba3d _5/2, Cu2p _3/2, and O1s X-ray photoelectron spectra of thick (600 nm) superconducting YBa₂Cu₃O_{7 ? δ} films deposited on textured Ni-W substrates with Y₂O₃ + ZrO₂ and CeO₂ buffer layers have been studied. It has been established that, after the mechanical removal of surface layers with a diamond scraper (and as the analyzed region of the film approaches the interface), a decrease in the oxygen content leads to a decrease of the orthophase fraction and an increase of the tetraphase and Cu⁺ ion fractions. This is caused by the presence of elastic stresses in the superconducting film due to the lattice misfit between the phases making up a composite sample. These stresses prevent oxygen diffusion involved in oxidizing annealing. The spectra of the superconducting film have not revealed signals generated by elements of the substrate and buffer layers.     

Strained germanium films in Ge/InGaAs/GaAs heterostructures: Formation of edge misfit dislocations at the Ge/InGaAs interface

Heterostructures of the “strained Ge film/artificial InGaAs layer/GaAs substrate” type have been grown by molecular beam epitaxy. A specific feature of these structures is that the plastically relaxed (buffer) InGaAs layer has the density of threading dislocations on a level of 10⁵–10⁶ cm⁻². These dislocations penetrate into the strained Ge layer to become sources of both 60° and 90° (edge) misfit dislocations (MDs). Using the transmission electron microscopy, both MD types have been found at the Ge/InGaAs interface. It has been shown that the presence of threading dislocations inherited from the buffer layer in a tensile-strained Ge film favors the formation of edge dislocations at the Ge/InGaAs interface even in the case of small elastic deformations in the strained film. Possible mechanisms of the formation of edge MDs have been considered, including (i) accidental collision of complementary parallel 60° MDs propagating in the mirror-tilted {111} planes, (ii) induced nucleation of a second 60° MD and its interaction with the primary 60° MD, and (iii) interaction of two complementary MDs after a cross-slip of one of them. Calculations have demonstrated that a critical layer thickness (h _c ) for the appearance of edge MDs is considerably smaller than h _c for 60° MDs.