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.     

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.     

Interplay of surface morphology, strain relief, and surface stress during surfactant mediated epitaxy of Ge on Si

Lattice-mismatch-induced surface or film stress has significant influence on the morphology of heteroepitaxial films. This is demonstrated using Sb surfactant-mediated epitaxy of Ge on Si(111). The surfactant forces a two-dimensional growth of a continous Ge film instead of islanding. Two qualitatively different growth regimes are observed. Elastic relaxation: Prior to the generation of strain-relieving defects the Ge film grows pseudomorphically with the Si lattice constant and is under strong compressive stress. The Ge film relieves strain by forming a rough surface on a nm scale which allows partial elastic relaxation towards the Ge bulk lattice constant. The unfavorable increase of surface area is outbalanced by the large decrease of strain energy. The change of film stress and surface morphology is monitored in situ during deposition at elevated temperature with surface stress-induced optical deflection and high-resolution spot profile analysis low-energy electron diffraction. Plastic relaxation: After a critical thickness the generation of dislocations is initiated. The rough phase acts as a nucleation center for dislocations. On Si(111) those misfit dislocations are arranged in a threefold quasi periodic array at the interface that accommodate exactly the different lattice constants of Ge and Si. Received: 1 April 1999 / Accepted: 17 August 1999 / Published online: 6 October 1999     

Nucleation of kink pairs on partial dislocations: A new model for solution hardening and softening

Nucleation and motion of kink pairs on partial dislocations are examined by elasticity theory for materials with a high Peierls stress. Two approaches are used: one considers the change in average stacking-fault energy (SFE) due to alloying elements and the other considers the change in local SFE due to a nearby solute atom. Both approaches highlight the role of SFE on kink nucleation, propagation and annihilation and both furnish strain rate as a function of stress, temperature and SFE. Model predictions are compared with yield stress data for two systems: firstly, an intermetallic, MoSi₂, which softens for alloying elements (V, Nb, Cr and Al) that decrease the SFE and hardens for Re additions that increase the SFE; secondly, a ceramic oxide, MgO-Al₂O₃ spinel, which softens with increasing addition of excess alumina and at the same time exhibits a decrease in SFE. The average SFE approach agrees qualitatively with the data while quantitative agreement is obtained with the local SFE approach. The possibility is considered that the model applies to other materials, such as TiAl, HfV₂ and Fe₃Al, which show softening with certain alloying additions. One requirement is that the dislocations are dissociated more than a few atomic distances; otherwise kink nucleation occurs on the perfect dislocation (or simultaneously on both partials). Hence the model does not apply to materials such as bcc metals which only have a core dissociation. Normal hardening effects of solutes from size and modulus misfits are additive with any softening effects from a decrease in SFE and so may mask the latter, as occurs for W additions to MoSi₂.     

Two groups of misfit dislocations in GaAs on Si

High-resolution cross-sectional and conventional plan-view transmission electron microscope observations have been carried out for molecular beam epitaxially grown GaAs films on vicinal Si (001) before and after annealing as a function of film thicknesses and observation directions between two orthogonal 110 directions. Two groups of misfit dislocations are characterized at the interface regions between GaAs and Si by analyzing whether their extra half planes exist in the film or the substrate side. Group I misfit dislocations due to stress caused by a lattice misfit between GaAs and Si consist of partial dislocations and 60° and 90° complete dislocations in an as-grown state. With an increase in the film thickness, partial dislocations decrease and complete dislocations increase. After annealing, partial dislocations almost completely disappear and 90° perfect dislocations are predominantly observed. Group II misfit dislocations due to thermal-expansion misfit-induced stress are all 60°-type complete dislocations regardless of film thicknesses and annealing treatment.On leave from Central Research Laboratory, Hitachi, Ltd., Tokyo 185, Japan     

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%).     

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.     

Misfit dislocations in gold/Permalloy multilayers

Several groups have reported the misfit dislocation structures in Au/Ni_0.8Fe_0.2 multilayers where the lattice parameter misfit is very large. To explore the factors controlling such structures, molecular dynamics simulations have been used to simulate the vapour-phase growth of (111)-oriented Au/Ni_0.8Fe_0.2 multilayers. The simulations revealed the formation of misfit dislocations at both the gold-on-Ni_0.8Fe_0.2 and the Ni_0.8Fe_0.2-on-gold interfaces. The dislocation configuration and density were found to be in good agreement with previously reported high-resolution transmission electron microscopy observations. Additional atomic-scale simulations of a model nickel–gold system indicated that dislocations are nucleated as the first nickel layer is deposited on gold. These dislocations have an (a/6)?112? Burgers vector, typical of a Shockley partial dislocation. Each dislocation creates an extra {220} plane in the smaller lattice parameter nickel layer. These misfit-type dislocations effectively relieve misfit strain. The results also indicated that the dislocation structure is insensitive to the energy of the depositing atoms. Manipulation of the deposition processes is therefore unlikely to reduce this component of the defect population.     

Nano-islands on a composite substrate with misfit dislocations

Spatial arrangements of nano-islands (quantum dots) on the free surface of a composite two-layer substrate containing misfit dislocations of edge type are theoretically examined. It is shown that the elastic interaction between misfit dislocations and nano-islands is capable of causing coagulation of nano-islands. The coagulation of nano-islands is shown to be favourable when the upper-layer thickness is smaller than a critical thickness, H₀. An analytical form of H₀ is presented for the partial case with four-to-one correspondence between nano-islands and cells of the misfit dislocation network. Received: 5 December 2000 / Accepted: 29 March 2001 / Published online: 20 June 2001     

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.     

Phenomenological description of phase transitions in thin BaTiO<Subscript>3</Subscript> films

Phase transitions in thin epitaxial films of BaTiO₃ are described phenomenologically in terms of Landau potentials with sixth-and eighth-order terms. It is established that the phase diagram depends on the electrostrictive constant Q ₁₂. The phase diagrams calculated for different values of Q ₁₂ available in the literature differ qualitatively. The dependence of the misfit strain of a film on the film tetragonality at room temperature is found, which makes it possible to determine the thermodynamic path in the phase diagram for a specific film. The dependences of the spontaneous polarization and dielectric constant of a film on the misfit strain at room temperature are constructed.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

The peierls energy and kink energy in fcc metals

In fcc crystals, dislocations are dissociated on the {111} glide plane into pairs of partial dislocations. Since each partial interacts individually with the Peierls potential and is coupled to its neighbour by a stacking fault, periodic variations in the separation distance d of the partials occur when dislocations running along closed packed lattice directions are displaced. This can drastically reduce the effective Peierls stress. By using the Peierls model the structure of 0°, 30°, 60° and 90° dislocations in a typical fcc metal with the elastic properties of Cu and a stacking-fault energy γ₀ in the interval 0.04?≤?γ₀?≤?0.05?J/m² was studied, and the magnitude of the Peierls energy ΔE _P and the resulting kink energies E _K were determined. Since the energies involved are of the order of 10^?3?eV/b or less, their magnitude cannot be asserted with high confidence, considering the simplifying assumptions in the model. The difference in the changes of the core configuration during displacement of dislocations of different orientations should, however, be of physical significance. It is found that a dissociated 60° dislocation generally has a higher effective Peierls energy than a screw dislocation, but the reverse is true for the kink energy, at least in Cu.     

Effect of long-range stresses on the structure of semiconductor heterosystems

The dependence between the misfit value of the interface layers f and the structural parameters of the misfit dislocations is obtained for arbitrary orientation of the interface of a semiconductor heterosystem subjected to the complete relaxation of misfit stresses. Such parameters are the distance D _i between neighboring dislocations of the ith family and projection of the edge component of the Burgers vector onto the interface (b _i ^e ). The number of families incorporated into the interface is determined by the orientation of the boundary and occurrence of the relaxation process. The role of specific cases of this expression for experimental and technological applications is discussed using the appearance of long-range shear and normal stresses in films with orientations of (001) and (111) as examples.     

Epitaxial growth of bcc-FexCo100-x thin films on MgO(1 1 0) single-crystal substrates

Fe_xCo_100-x (x=100, 65, 50 at%) epitaxial thin films were prepared on MgO(1 1 0) single-crystal substrates heated at 300 °C by ultra-high vacuum molecular beam epitaxy. The film structure and the growth mechanism are discussed. FeCo(2 1 1) films with bcc structure grow epitaxially on MgO(1 1 0) substrates with two types of variants whose orientations are rotated around the film normal by 180° each other for all compositions. Fe_xCo_100-x film growth follows the Volmer Weber mode. X-ray diffraction analysis indicates the out-of-plane and the in-plane lattice spacings are in agreement with the values of respective bulk Fe_xCo_100-x crystals with very small errors less than ±0.4%, suggesting the strains in the films are very small. High-resolution cross-sectional transmission electron microscopy shows that periodical misfit dislocations are preferentially introduced in the film at the Fe₅₀Co₅₀/MgO interface along the MgO[1 1¯ 0] direction. The presence of such periodical dislocations decreases the large lattice mismatch of about −17% existing at the FeCo/MgO interface along the MgO[1 1¯ 0] direction.     

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.     

Attenuation of interfacial pinning enhancement in YBCO using a PrBCO buffer layer

Numerous experimental results have suggested that the J_c of YBa₂Cu₃O₇ (YBCO) films is significantly higher near the film–substrate interface than in the remainder of the film. We previously proposed that this effect is due to interfacial pinning enhancement caused by stress and the resulting misfit dislocations at the heteroepitaxial interface. To test this hypothesis we have used a non-superconducting PrBa₂Cu₃O_7?δ (PrBCO) buffer layer to minimize the lattice mismatch with YBCO. We find that the PrBCO layers lower J_c of the 0.4 μm YBCO films in a predictable way, and that, if sufficiently thick (～0.5 μm), they eliminate interfacial enhancement altogether. Our interpretation of this result is that the defects responsible for interfacial enhancement of flux pinning originate at the bottom of the non-superconducting PrBCO layer, which screens the pinning centers from vortices in YBCO. This result demonstrates that the pinning enhancement arises from stress at the film–substrate interface.     

Equilibrium configurations of partial misfit dislocations in thin-film heterosystems

The energy characteristics of orthogonal rows of partial misfit dislocations with V-shaped stacking faults in thin-film heteroepitaxial systems are analyzed theoretically. It is shown that they should appear only in very thin epitaxial films of nanoscopic thickness and for high values of the mismatch exceeding a definite value. Under these conditions partial misfit dislocations associated with V-shaped stacking faults are typical elements of the defect structure of nanolayer heterosystems. For smaller mismatches and larger films thicknesses total misfit dislocations should form. Fiz. Tverd. Tela (St. Petersburg) 40, 2059–2064 (November 1998)     

Electronic structure of strained Sin/Gen(001) superlattices

Using the empirical tight binding method we have investigated the electronic properties of the Si_n/Ge_n(001) strained superlattices as a function of the superlattice periodicity and the band misfit. For n ≥ 4 we have found that first and second conduction band states are localized in Si. The hole states localized in Ge appear for n ≥ 4. The difference between the direct and indirect band gaps is reduced from 2.01 eV for bulk Si to 0.01 eV for n=6 which can be considered to be quasi-direct. For the cases n=6 and n=8, the band gap might become direct for large values of band misfit.     

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.