High Misfit Research Articles

Stability of shuffle and glide dislocation segments with increasing misfit in Ge∕Si1−xGex(001) epitaxial layers

Using molecular dynamics simulations, based on Tersoff potentials, we show that at typical experimental temperatures high compressive strain regimes suppress the formation of partial glide dislocations, while enhancing the gliding of the shuffle segments. Despite being qualitative in nature, these results suggest that strain relaxation in thin virtual substrates at high misfit may occur with a different modality than in thick graded layers, as indicated by preliminary experimental results by low-energy plasma enhanced chemical vapor deposition.

Various types of growth instabilities in coherent epitaxy

The instability of coherent epitaxial systems Ge/Si(0 0 1) is investigated. The qualitatively different features observed at low misfit (1 or 2%) and at larger misfit (more than 3%) are explained by a different type of nucleation of new terraces. At high misfit they are nucleated on the upper edge of existing steps and this triggers the sudden formation of three-dimensional bumps. At lower misfits, new terraces are nucleated near the centres of existing terraces and growth proceeds as in a pure crystal. The instability takes place at later times as an effect of kinetic roughness.

Strain relaxation and surface roughness of InxAl1−xAs graded buffer layers grown on InP for 6.05Å applications

In this study, metamorphic compositionally graded InxAl1−xAs layers grown on InP by molecular beam epitaxy with a final indium mole fraction of x=1.0(6.05Å) are investigated. To examine the effects of relative growth temperature on strain relaxation and surface morphology at different stages of the buffer layer growth, a series of samples was produced with the indium mole fraction graded from x=0.52tox=0.64, 0.79, and 1.0 with a constant grading rate. The high misfit dislocation velocity in this system allows the grading to be accomplished with a thin layer (∼1μm), complete strain relaxation and low threading dislocation densities. The evolution of the strain relaxation, threading dislocation density, and surface morphology were evaluated by triple axis x-ray diffraction, transmission electron microscopy (TEM), etch pit density (EPD), and atomic force microscopy. Higher growth temperature led to threading densities as low as 106cm−2, as measured by plan-view TEM and EPD. The final surface roughness was controlled by the growth temperature of a constant composition cap layer.

Influence of growth temperature and reactor pressure on microstructural and optical properties of InAlGaN quaternary epilayers

The effects of growth temperature and reactor pressure on the microstructural and optical properties of InAlGaN quaternary epilayers grown on thick GaN buffer by metalorganic chemical vapor deposition were investigated. The addition of Al atoms at the optimized growth temperature of an InGaN layer resulted in deep level emission and in pyramidal shaped surface pits due to island growth caused by the low mobility of the deposited Al atoms in spite of the reduction of in-plane misfit strain and full width at half maximum from high-resolution X-ray diffraction. As the growth temperature increased and reactor pressure decreased, the broad deep level emission and the density of surface pits were greatly reduced and the band-edge emission of InAlGaN epilayers was intense. Surface pits originating from the vertex of threading dislocations under high misfit strain were greatly affected by lowering the growth temperature while the band-edge emission strongly depended on reactor pressure. Therefore, we found that the reduced reactor pressure and the increased growth temperature enhanced lateral growth and were effective in growing the InAlGaN epilayers of optically and microstructurally good quality.

Growth and relaxation of (Zr,Y)O2 epitaxial layers analyzed by XRD reciprocal space mapping

Very thin polycrystalline and epitaxial yttria doped zirconia films have been realized using sol–gel processing. The lattice mismatch between the sapphire substrate and the zirconia crystals induces high misfit strain that we have determined using X-ray diffraction. Epitaxial films made of islands with sizes of several tens of nanometers are under very high stresses which are relaxed by the appearance of structural defects into the cubic zirconia crystals or by structural phase transition from the cubic to tetragonal zirconia form.

SiC voids, mosaic microstructure and dislocations distribution in Si carbonized layers

The defect structure of SiC/Si layers obtained by carbonization of Si is reported by means of transmission electron microscopy in high-resolution (HREM) and conventional (CTEM) modes. 3C–SiC was obtained after a rapid thermal annealing treatment and good interfacial quality is reported in terms of small void dimensions and densities. Moreover, high misfit dislocation densities are observed close to the Si/SiC interface and inside the SiC layer without observable generation of threading dislocations. The mosaic grain structure is also evidenced, with low misorientation with respect to the substrate. These results are encouraging for further growth of III–N alloy heterostructures.

Geometrical Contribution to Yield Strength in Small Volumes

AbstractCritical thickness theory was developed to account for the ability of thin epitaxial metal and semiconductor layers to support high misfit or coherency strain. The thermodynamic equilibrium theory is correct, and is well approximated by a theory based on geometrical arguments. The latter theory is readily extended to arbitrary misfit strain profiles including linearly graded layers, for which a surface layer free of misfit dislocations. This result applies as well to linear strain gradients introduced by deformation, in which case the misfit dislocations are known as geometrically necessary dislocations. We show that a consequence of this surface layer is that the apparent yield strength of the material increases in small structures such as thin wires in torsion. Under large plastic deformation, even if the material is perfectly plastic, critical thickness theory also predicts an apparent work-hardening. The predictions of critical thickness theory are in excellent agreement with experimental data in the literature.

Mechanisms of misfit strain relaxation in epitaxially grown BLT (Bi4-xLaxTi3O12, x = 0.75) thin films

AbstractMechanisms of misfit strain relaxation in epitaxially grown Bi4-xLaxTi3O12 (BLT) thin films deposited on SrTiO3 (STO) and LaAlO3 (LAO) substrates have been investigated by means of transmission electron microscopy (TEM). The misfit strain of 20 nm thick BLT films grown on STO substrate was relaxed by forming misfit dislocations at the interface. However, cracks were observed in 100 nm thick BLT films grown on the same STO. It was confirmed that cracks were formed because of high misfit strain accumulated with increasing the thickness of BLT, that was not sufficiently relaxed by misfit dislocations. In the case of the BLT film grown on LAO substrate, the magnitude of lattice misfit between BLT and LAO was very small (~1/10) in comparison with the case of the BLT grown on STO. The relatively small misfit strain formed in layered structure of the BLT films on LAO, therefore, was easily relaxed by distorting the film, rather than forming misfit dislocations or cracks, resulting in misorientation regions in the BLT film.

Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study.

We study the morphological evolution of strained heteroepitaxial films using kinetic Monte Carlo simulations in two dimensions. A novel Green's function approach, analogous to boundary integral methods, is used to calculate elastic energies efficiently. We observe island formation at low lattice misfit and high temperature that is consistent with the Asaro-Tiller-Grinfeld instability theory. At high misfit and low temperature, islands or pits form according to the nucleation theory of Tersoff and LeGoues.

Steady core flow in an azimuthally drifting reference frame

SUMMARY Flows at the top of the Earth’s core generating the observed geomagnetic secular variation (SV) can be deduced in the frozen-flux approximation with various nonuniqueness-reducing assumptions such as tangential geostrophy and steadiness. Steady flows are attractive because they require only a small number of parameters to explain the gross features of the SV. However, they are unable to reproduce the fine detail contained in the SV, and cannot be used to explain observed decadal changes in the length of day. Here we find flows steady in a local reference frame within the core, but the frame is allowed to rotate relative to the mantle. Previous investigations have studied steady drift with respect to the mantle, introducing just a single extra parameter into the calculation; here we also allow the drift to vary with time. We then minimize a linear combination of the fit to time-varying coefficients expressing the SV, a measure of the complexity of the flow and the drift acceleration. The resulting non-linear inverse problem is solved in a two-stage iterative process—for a given drift, we solve for the best-fitting steady flow, and then adjust the drift to improve the fit. We seek solutions for the intervals 1900–1980 and 1840–1990; over both epochs, allowing the reference frame of a steady flow to drift gives a strikingly improved fit. For flows with a relatively high misfit, the frame drift is westwards at a rate similar to the observed ‘westward drift’ rate of the geomagnetic field at the Earth’s surface (approximately 0.2u yr x1 ). Requiring a tighter fit, and hence a more complex flow, gives rise to two solutions, one with a westward frame drift with respect to the mantle, the other eastward, and the relative drift rates gradually increase to a maximum of 0.9u yr x1 as the misfit decreases. Flows in the mantle reference frame are similar to those deduced previously by any of the nonuniqueness-reducing assumptions. However, in the drifting frame, the flows are almost completely dominated by the drift between the two reference frames. Although the time dependence of the drift is weak and results in only a small additional misfit reduction over a uniform drift, by assuming that the variation in drift reflects variation in solid body rotation of the whole core, it can explain decadal length-of-day changes almost as well as, and prior to 1900 perhaps better than, fully time-dependent tangentially geostrophic flows with vastly more free parameters. We examine the significance of these models in terms of large-scale wave motion in the core.

Structural exploration of thin-film oxide interfaces via ‘simulated amorphisation and recrystallisation’

Realistic atomistic simulation models of interfaces must include a sufficiently large simulation cell to accommodate the incommensurate relationship between the lattice parameters of the two materials, and include misfit-induced defects such as dislocations. In addition, the final structure must not be influenced artificially by the starting structure. Here we present a methodology, which satisfies such demands by performing large-scale atomistic simulations of thin-film oxide interfaces, which approach the meso-scale and involve amorphisation and recrystallisation of the thin film. The methodology is applied to the SrO/MgO(0 0 1) system, which was used as a model system representative of supported materials associated with a high lattice misfit. The final MgO(0 0 1) supported SrO thin-film structures comprise many dislocations (including mixed screw edge and pure edge), defects, reduced interfacial ion densities, commensurate domains and low angle rotated domains.

Properties of InGaN/GaN Quantum Wells Grown by Metalorganic Chemical Vapor Deposition

ABSTRACTOptical and structural properties of InGaN/GaN quantum wells having growth interruption were investigated using high-resolution x-ray diffraction, photoluminescence and transmission microscopy. InxGa1−xN/GaN (x>0.25) six pair quantum wells used in this study were grown on c- plane sapphire by metalorganic chemical vapor deposition. The growth interruption was carried out by closing the group-III metal organic sources before and after growth of InGaN quantum well layers. With increasing the interruption time, the quantum dot-like region and well thickness decreases due to indium re-evaporation or thermal etching effect. As a result, PL peak position is blue-shifted and intensity is reduced. The size and number of V-defect did not vary with interruption time. The interruption time is not directly related with formation of the defect. The V-defect in quantum wells originates at threading dislocations and inversion domain boundaries due to higher misfit strain.

Observation and Mearsurement of Concentration Moments in Rapid Coarsening, Self-Stressed, Au-Ni Thin Plates

Abstract The focus of our study is to demonstrate experimentally how elastic stress effects diffusion behavior and coarsening kinetics in a two-phase binary alloy. This work, based on the theory of Cahn and Kobayashi, focuses on elastic stresses in a thin plate. For the case of phase separation with lattice misfit between solute-rich and solute-poor phases, the diffusion of solute distorts the host lattice and causes elastic stress in the matrix. If the plate is sufficiently thin, the stress can cause the plate to buckle. The buckling stress biases the direction of diffusion, which increases the bending stress even further. Thus, the diffusion and the buckling stress are coupled; each affects the other. The interplay between the two is easiest to observe in a solution in which the solute and solvent have high misfit.

MORPHOLOGY, STRAIN AND MICROSTRUCTURE INTERRELATION IN Si-ON-SAPPHIRE HETEROSTRUCTURE

The interfacial region at the substrate, the morphology of the interface and the surface were studied for a number of Si-on-saphire (SOS) samples using X-ray scattering techniques, transmission electron microscopy (TEM) and scanning electron microscopy (SEM). A strained interfacial layer is formed in this high misfit system. The dislocations created in this layer and at the interfacial steps accommodate the elastic strain buildup. The misfit relaxation is accompanied by the misorientation of the epilayer with respect to the substrate, which itself depends on the substrate miscut parameters and the thickness of the epilayer. The observed azimuthal rotation of the epilayer miscut is attributed to the effect of the anisotropic microtwinning evolving with the increasing epilayer thickness. This azimuthal rotation is reflected by the step morphology on the surface of the epilayers.

High-resolution transmission electron microscopy imaging of misfit-dislocation networks at Cu-MgO and Cu-MnO interfaces

Abstract Misfit dislocation networks at Cu-MgO and Cu-MnO {111}metal//{111}oxide interfaces were studied with high-resolution transmission electron microscopy. Experimental results were compared with image simulations of tentative atomic structures of the interface region derived from lattice statics calculations. The calculations take into account the two-dimensional misfit at the interface, which is necessary given the high misfit and short repeat distances at the interfaces. The lattice statics calculations use simplified potentials across the interface which capture essential characteristics that have emerged from recent experimental results and ab-initio calculations. Trigonal networks of edge misfit locations with Burgers vectors ⅙〈112〉 and line direction 〈110〉 follow from these calculations. These misfit-dislocation networks have associated strain fields in the metal, stretching out from the interface with approximately the repeat distance along the interface. These strain fields show up in image simulations 〈along 〈110〉 and 〈112〉 directions〉 by characteristic but subtle periodic changes in contrast and brightness as well as small displacements of spots. The experimental images, also along 〈110〉 and 〈112〉 directions, showed similar characteristics but they were difficult to detect, especially along 〈112〉 for the Cu-MnO interface, and may easily be missed. Judging from this evidence we conclude that the proposed misfit-dislocation structure is in fact present at these interfaces.

Gold films epitaxially grown by diffusion at the 3C–SiC/Si interface

A thin layer of gold grown epitaxially in a 3C–SiC/Si interface is observed using conventional (CTEM) and high-resolution electron microscopy (HREM) methods. This interlayer was formed after an extended thermal treatment, at 500°C for 500 h, of a 3C–SiC/Si system on which Au was deposited on the surface of SiC for the formation of a Schottky diode. Misfit dislocations are observed in both SiC/Au and Au/Si interfaces having Burgers vectors b= 1 2 〈1̄ 1 0〉 parallel to the interfaces. Such an epitaxy is made in spite of the very high misfit in the Au/Si interface. The net of the misfit dislocations is visible only by cross-section HREM observations. The position of the extra half-planes of the interfacial dislocations is illustrated. An explanation for the mechanism of the Au mass transport through the unaffected SiC film is given. This is attributed to pipe diffusion through the partial dislocations bounding the stacking faults and inversion domain boundaries that pre-exist in 3C–SiC. The same diffusion mechanism allows the transport of Si from the 3C–SiC/Si interface to the top surface of SiC on which islands of Si and Au are formed.

The Nature and Origin of Lateral Composition Modulations in Short-Period Strained-Layer Superlattices

AbstractThe nature and origin of lateral composition modulations in (AlAs)m(InAs)nshort-period strained-layer superlattices grown by molecular beam epitaxy on InP substrates have been investigated by x-ray diffraction, atomic force microscopy, and transmission electron microscopy. Strong modulations were observed for growth temperatures between ≈ 540 and 560° C. The maximum strength of modulations was found for SPS samples with InAs mole fraction x (= n/(n+m)) close to ≈ 0.50 and when n≈m≈2. The modulations were suppressed at both high and low values of x. For x > 0.52 (global compression), the modulations were along the <100> directions in the (001) growth plane. For x < 0.52 (global tension), the modulations were along the two <310> directions rotated ≈ ±27° from [110] in the growth plane. The remarkably constant wavelength of the modulations, between ≈ 20–30 nm, and the different modulation directions observed, suggest that the origin of the modulations is due to surface roughening associated with the high misfit between the individual SPS layers and the InP substrate. Highly uniform unidirectional modulations have been grown by control of the InAs mole fraction and growth on suitably offcut substrates, which show great promise for application in device structures.

Exercising control over the influence of the lattice misfit on the structure of oxide–oxide thin film interfaces

Thin film oxide–oxide interfaces with associated lattice misfits ranging from –20 to +27%, have been ‘grown’ by depositing ions onto a surface in conjunction with dynamics simulation and energy minimisation. Inspection of the resulting interfaces revealed significant structural features within the thin film. These included, for the CaO/MgO(100) system (+13% misfit), the exposure of various CaO surfaces at the interface; grain-boundary formation; the evolution of periodic arrays of misfit induced dislocations; lattice slip, and rotations of the thin film with respect to the support. In each case the driving force to such behaviour was attributed to the reduction in the strain energy generated within the interface which arises from the lattice misfit between the two materials. The implications of employing periodic boundary conditions within interface calculations are also addressed. For those interfaces with high associated lattice misfits: BaO/MgO (+27%), SrO/MgO (+20%) and MgO/SrO (–20%), the deposition procedure yielded thin films with amorphous type structures. In the second part of this study we have explored briefly how one may exercise a degree of control over the influence of the lattice misfit and its implications for the structure and consequently the chemical and physical properties of the thin film. For example, for the SrO/MgO system, by including a CaO buffer layer between the SrO thin film and the MgO support material, it was possible to generate a more coherent and crystalline thin film, contrasting to the amorphous type structures observed without the inclusion of a buffer layer. An alternative approach, in which dopant ions were introduced into the thin film, resulted in pseudomorphic growth. In particular, the dopant ions modified the lattice parameter of the thin film to be commensurate with that of the support.

Clustering and ordering of nitrogen in nuclear grade 316LN austenitic stainless steel

The high misfit strains associated with nitrogen addition and the high chemical affinity with chromium result in a significant driving force for the formation of Cr–N clusters in austenitic steels. The microstructural signatures of cluster formation in nuclear grade 316LN austenitic stainless steel during the early stages of aging at 1123 K are discussed. Aging beyond 25 h results in transformation of fcc clusters to hexagonal Cr 2N precipitates. Strain induced ordering of nitrogen in Cr 2N precipitates due to continued ageing is also highlighted.

Quantitative Transmission Electron Microscopy Investigation of the Relaxation by Misfit Dislocations Confined at the Interface of GaN/Al2O3(0001)

A quantitative transmission electron microscopy (TEM) investigation of the relaxation of GaN grown on Al2O3(0001) has been carried out. Terminating {112̄0}-substrate fringes observed at the interface of the highly mismatched system have been characterized and the efficiency of the relaxation was measured. Wurtzite type GaN was grown by plasma induced molecular beam epitaxy (MBE) on the (0001) basal plane of Al2O3. The in-plane orientation between GaN and substrate reveals a high lattice misfit of f=-13.9% and therefore the critical thickness of dislocation formation is reached when the first monolayer of GaN is grown. An expected interfacial relaxation process is characterized by the results of high resolution transmission electron microscopy (HRTEM) which reveals misfit dislocations confined in the GaN/Al2O3 interface region. The quantitative evaluation of the HRTEM images on the one hand and Moiré pattern on the other hand shows the effectiveness of the observed relaxation process: here a degree of relaxation δ=(-11.8±0.9)% and a residual strain of εr=(-2.1±0.9)% was measured, and it seems that only εr causes a dislocation density of estimately 1010 cm-2 in the GaN epilayer.