Strain Relaxation Dynamics Research Articles

Anisotropic strain relaxation in epitaxially constrained α -(Al,Ga)2O3 thin films on a-plane Al2O3

Binary α-Ga2O3 and ternary α-(AlxGa1−x)2O3 thin films with x = 0.29 and 0.54 were deposited on a-plane Al2O3 substrates via plasma-assisted molecular beam epitaxy. The strain relaxation dynamics along three orthogonal crystal directions was investigated ex situ and in situ by synchrotron-based high-resolution x-ray diffraction. A pronounced in-plane anisotropy was observed as strain is preferably built up across [1¯1.0] whereas along [00.1] it is effectively relieved. The particular behavior depends on the Al content with almost immediate plastic relaxation for x = 0 and 0.29. For x = 0.54, strain relaxation is elastic within the first monolayers. A dislocation glide on the r-plane slip system has been identified as the dominating plastic relaxation mechanism as layers grow thicker.

Strain in epitaxial high-index Bi2Se3(221) films grown by molecular-beam epitaxy

High-index Bi2Se3(221) film has been grown on In2Se3-buffered GaAs(001), in which a much retarded strain relaxation dynamics is recorded. The slow strain-relaxation process of in epitaxial Bi2Se3(221) can be attributed to the layered structure of Bi2Se3 crystal, where the epifilm grown along [221] is like a pile of weakly-coupled quintuple layer slabs stacked side-by-side on substrate. Finally, we reveal strong chemical bonding at the interface of Bi2Se3 and In2Se3 by plotting differential charge contour calculated by first-principle method. This study points to the feasibility of achieving strained TIs for manipulating the properties of topological systems.

Peculiarities of strain relaxation in linearly graded InxGa1−xAs/GaAs(001) metamorphic buffer layers grown by molecular beam epitaxy

This paper presents a comprehensive study of structural, optical and electrical properties of heterostructures with linearly graded InxGa1−xAs metamorphic buffer layers (MBLs) grown by molecular beam epitaxy on GaAs (001) substrates. The low density of threading dislocations (well below 106cm−2) in 1-μm-thick In0.3Ga0.7As layers grown atop of the linearly graded InxGa1−xAs/GaAs MBLs has been confirmed by using transmission electron microscopy (TEM). X-ray diffraction (XRD) data demonstrate good agreement between the experimentally measured In step-back and its calculations in the frames of existing models. Combining the XRD reciprocal space maps (RSM) of the structures and the spatially-resolved selective area electron diffraction measurements by cross-sectional TEM in depth-profiled RSM diagrams allowed direct visualization of the strain relaxation dynamics during the MBL growth. Strong effect of the azimuth angle and the value of an unintentional initial miscut of nominally (001) oriented GaAs substrate on the strain relaxation dynamics was observed.

Strain dynamics during La2O3/Lu2O3 superlattice and alloy formation

The dynamics of strain relaxation and intermixing during molecular beam epitaxy of La2O3 and Lu2O3 superlattices and alloys consisting of both binaries on Si(111) have been studied by real-time in situ grazing incidence x-ray diffraction and high resolution transmission electron microscopy. The presence of both hexagonal and cubic polymorphs of La2O3 influences the epitaxial formation within the superlattice. The process of strain relaxation is closely related to the presence of a (La,Lu)2O3 alloy adopting a cubic symmetry. It is formed by interdiffusion of La and Lu atoms reducing internal lattice mismatch within the superlattice. An interface thickness dominated by interdiffusion regions of about 3 monolayers is determined by high-angle annular dark field scanning transmission electron microscopy.

Strain and lattice orientation distribution in SiN/Ge complementary metal–oxide–semiconductor compatible light emitting microstructures by quick x-ray nano-diffraction microscopy

This paper presents a study of the spatial distribution of strain and lattice orientation in CMOS-fabricated strained Ge microstripes using high resolution x-ray micro-diffraction. The recently developed model-free characterization tool, based on a quick scanning x-ray diffraction microscopy technique can image strain down to levels of 10−5 (Δa/a) with a spatial resolution of ∼0.5 μm. Strain and lattice tilt are extracted using the strain and orientation calculation software package X-SOCS. The obtained results are compared with the biaxial strain distribution obtained by lattice parameter-sensitive μ-Raman and μ-photoluminescence measurements. The experimental data are interpreted with the help of finite element modeling of the strain relaxation dynamics in the investigated structures.

Dislocation-interaction-based model of strained-layer relaxation

A strained layer relaxes plastically when dislocations propagate within the layer, leaving behind an array of misfit dislocations at the layer interface. We develop an analytical model of this process, based on the idea that relaxation is frustrated when propagating dislocations are trapped or annihilated by encounters with previously created misfit dislocations or other propagating dislocations. The theory characterizes the evolving density of the misfit array and the density of propagating dislocations in terms of a pair of coupled rate equations. The two trapping functions which appear in these equations are evaluated quantitatively by numerically investigating all possible dislocation-dislocation encounters. Fluctuations in the local stress field driving the individual dislocations are explicitly taken into account when evaluating the trapping functions. Analysis of the rate equations shows that there are two regimes in the strain-relaxation dynamics. Initially, the strain decreases rapidly following a universal dependence on time scaled with the initial dislocation density n0. At a (rescaled) crossover time that increases with n0, the strain levels off from the universal relaxation curve and saturates to an asymptotic residual strain level, which decreases with n0. Microscopically, our model reveals that the initial fast strain-relaxation regime is dominated by collisions between propagating dislocations, while the slow saturation regime is dominated by the trapping of propagating dislocations by the misfits. In the end, the self-trapping of the propagating dislocations by the misfit array they themselves have generated leaves the layer in a frustrated state with residual strain higher than the critical strain. The predictions of the theory are found to be in good agreement with experimental measurements and with large-scale numerical simulations of layer relaxation.

Dynamics of strain relaxation studied by in situ x-ray diffraction immediately after layer heteroepitaxy

The temporal development of strain relaxation is monitored during and immediately after heteroepitaxy by x-ray diffraction with high resolution in strain and time. ZnSe layers on (001)GaAs with thicknesses just a little above the onset of plastic relaxation reveal inhomogeneous, partial relaxation which continues with a time constant of 50 s immediately after the stop of layer growth. A model of generation, glide, and blocking of dislocations well explains the observation that the degree of relaxation finally reached after growth stop is determined by the density of dislocations rapidly generated prior to it.

Monitoring of ZnCdSe layer properties by in situ x-ray diffraction during heteroepitaxy on (001)GaAs substrates

The authors demonstrate in situ high-resolution x-ray diffraction applied during heteroepitaxy on (001)GaAs for instant layer characterization. The current thickness, composition, strain, and relaxation dynamics of pseudomorphic layers are precisely determined from qz scans at the (113) reflection measured at a molecular beam epitaxy chamber with a conventional x-ray tube in static geometry. A simple fitting routine enables real-time in situ x-ray diffraction analysis of layers as thin as 20nm. Critical thicknesses for dislocation formation and plastic relaxation of ZnCdSe layers versus Cd content are determined. The strong influence of substrate temperature on heteroepitaxial nucleation process, deposition rate, composition, and strain relaxation dynamics of ZnCdSe on GaAs is also studied.

Manipulation of strain relaxation in metamorphic heterostructures

The authors have discovered that high doping densities in an alloy graded InGaAs buffer have dramatic effects on strain relaxation dynamics and consequently surface and optical qualities in metamorphic heterostructures. Compared with undoped graded buffers, the use of Be doping significantly improves structural, surface, and optical qualities while the use of Si doping deteriorates all these properties. This discovery is significant for the realization of metamorphic optoelectronic devices.

Nonlinear Transient Finite Element Analysis of the Relaxation Mechanisms in Strained Silicon Grown on SiGe Virtual Substrate

AbstractStrained-silicon (ε -Si) is essential for future nanoscale MOSFET devices. In this paper we report on the dynamics of strain relaxation in Si/SiGe heterostructures, investigated by transient nonlinear finite element analysis. The contribution to total misfit strain is found largely plastic in the graded SiGe layer and the top of the Si substrate, while it is mainly elastic in the strained Si layer and part of the SiGe constant layer. The calculated lattice parameter for the strained Si layer is about 5.47Å for Si0.8Ge0.2 and 5.52 Å for Si0.6Ge0.4. Calculated threading dislocation density was about 5.6x105 cm-2 for x=0.20 and 2.17x106cm-2 for x=0.40. A plastic strain rate of 8.4x10-3s-1 for Si0.8Ge0.2 and 4.1x10-2 s-1 for Si0.6Ge0.4 leading to a density of moving dislocations of ~2.2x109 cm-2 and ~ 1010cm-2, respectively, have been obtained. The elastic strain in the strained-Si layer appeared to increase with increasing the cooling rate, while plastic work was found to be independent of cooling rates.

Strain relaxation and interfacial stability in III–V semiconductor strained-layer heteroepitaxy: atomistic and continuum modeling and comparisons with experiments

A systematic study is presented of interfacial stability and strain relaxation through misfit dislocation formation in III–V semiconductor layer-by-layer heteroepitaxy. A multiscale modeling strategy is developed that links continuum elasticity theory with atomistic structural relaxation and Monte Carlo simulations using a valence force field description of interatomic interactions. Results are presented for the energetics of the transition from a coherent to a semicoherent film/substrate interface consisting of a misfit dislocation network, the semicoherent interface structures, the associated strain fields, and the film surface morphological characteristics for InAs epitaxy on GaAs(1 1 1)A. The capability of continuum elasticity theory to provide a satisfactory description of the atomistic simulation results is discussed. In addition, using thin compliant substrates and grading the composition of the deposited film are demonstrated to have beneficial effects on film strain relaxation. Furthermore, the dynamics of strain relaxation is analyzed based on a phenomenological mean-field theoretical framework. Our theoretical results are in very good agreement with our experimental measurements on InAs/GaAs(1 1 1)A samples for films grown by molecular beam epitaxy on thick and thin GaAs buffer layers.

Dislocation dynamics of strain relaxation in epitaxial layers

Many experimental observations have clearly shown that dislocation interaction plays a crucial role in the kinetics of strain relaxation in epitaxial thin films. A set of evolution equations are presented in this article. The key feature of the equations is the incorporation of dislocation interactions into the kinetic process by introducing a resistance term. The resistance to threading dislocation gliding is characterized by a hardening function, which depends only on the relaxed plastic strain. The evolution equations are tested on the GexSi1−x/Si(100) materials system. Existing fundamental parameters are incorporated into the present model. The evolution equations successfully reproduce a wide range of experimental data on strain relaxation in GexSi1−x/Si heterostructures.

Dislocation evolution in epitaxial multilayers and graded composition buffers

This paper presents models to describe the dislocation dynamics of strain relaxation in an epitaxial uniform layer, epitaxial multilayers and graded composition buffers. A set of new evolution equations for nucleation rate and annihilation rate of threading dislocations is developed. The dislocation interactions are incorporated into the kinetics process by introducing a resistance term, which depends only on plastic strain. Both threading dislocation nucleation and threading dislocation annihilation are characterized. The new evolution equations combined with other evolution equations for the plastic strain rate, the mean velocity and the dislocation density rate of the threading dislocations are tested on Ge x Si 1− x /Si(100) heterostructures, including epitaxial multilayers and graded composition buffers. It is shown that the evolution equations successfully predict a wide range of experimental results of strain relaxation and threading dislocation evolution in the materials system. Meanwhile, the simulation results clearly signify that the threading dislocation annihilation plays a vital role in the reduction of threading dislocation density.

Evolution of microstructure and dislocation dynamics in InxGa1−xP graded buffers grown on GaP by metalorganic vapor phase epitaxy: Engineering device-quality substrate materials

This study explores the dislocation dynamics of strain relaxation in graded composition buffers of InxGa1−xP grown on GaP (InxGa1−xP/GaP) by metalorganic vapor phase epitaxy. Transmission electron microscopy, cathodoluminescence imaging, atomic force microscopy, and triple-axis x-ray diffraction are applied to the characterization of InxGa1−xP/GaP with final compositions ranging from x=0.09 to x=0.39 and growth temperatures ranging from 650 to 810 °C. The previously reported escalation of defect density with continued grading of InxGa1−xP/GaP beyond x∼0.3 is discovered to be due to the formation of dislocation pileups. A new defect microstructure with a branching morphology and featuring sharp local strain fields, hereafter referred to as branch defects, is observed to pin dislocations and cause the dislocation pileups. Branch defect morphology varies strongly with growth temperature, becoming significantly stronger with increasing growth temperature and causing severe material degradation above 700 °C. Further experiments show that branch defects evolve during growth and that the onset of branch defect formation is delayed by increasing growth temperature. Comparison with the literature suggests that the evolution of branch defects may control the microstructure of indium-bearing phosphides and arsenides over a very wide range of conditions. In the absence of branch defects at high growth temperatures and low indium compositions near x∼0.1, nearly ideal dislocation dynamics dominated by dislocation glide kinetics are recovered, providing the first experimental proof of a kinetic model for graded buffer relaxation. This new understanding of the evolution of microstructure and dislocation dynamics in InxGa1−xP/GaP suggests that growth temperature must be optimized as a function of composition for optimal material quality. A simple process optimization in InxGa1−xP/GaP graded to x=0.39 results in an overall threading dislocation density of 4.7×106 cm−2, which is the lowest reported value to date for x>0.3. Combining the new observations with earlier findings, we present three basic design rules for producing practical, device-quality graded buffers: branch defects must be avoided or suppressed, growth temperature must be maximized, and surface roughness must be minimized. Using these design rules, we also present optimization strategies for achieving device-quality substrate materials. Applying these design rules and optimization strategies, we hope to achieve threading dislocation densities of <106 cm−2 in InxGa1−xP/GaP over the full range of useful compositions.

Effect of growth conditions on the structural properties of ion beam sputter deposited SiGe epilayers

Structural properties of Si1−xGex layers epitaxially grown on Si(100) by Ion Beam Sputter Deposition were studied as a function of growth temperature and film thickness. It was shown that the structure of defects strongly depends on the growth temperature, Tg. The dislocations cross grid which is observed at the SiGe/Si interface for layers grown at high (700 °C) Tg is missing in layers grown at low (≲550 °C) Tg, while a new type of defects parallel to {001} and {113} lattice planes appear at these temperatures. The optimal Tg for a Ge content of 20-25 at. % was found to be close to 550-625 °C. Surface roughness for all the growth temperatures was found to be less than that for such a ‘‘smooth’’ technique as MBE. Photoluminescence studies revealed, to the best of our knowledge for the first time, two peaks on the low energy side in the neighborhood of the Si(TO) peak of the epilayers. The evolution of the intensity of these peaks is strongly correlated with the dynamics of strain relaxation and can be attributed to a set of dislocations at the SiGe/Si interface extending both to the epilayer and to the bulk Si.

Crystallographic tilting of heteroepitaxial layers

Mismatched heteroepitaxial layers generally exhibit a crystallographic tilt with respect to their vicinal substrates, but this phenomenon is poorly understood. Two models have been proposed for tilted epitaxy previously. The Nagai model considers the mismatch at surface steps on vicinal substrates and the misfit dislocation theory considers misfit dislocations with inclined Burgers vectors as the primary cause of tilted epitaxy. Neither of these theories applies in the general case, however. The misfit dislocation theory does not consider the mechanism of the preferential introduction of dislocations with a particular orientation, and therefore does not predict the direction of tilted epitaxy. Here a general theory for tilted epitaxy is proposed, including both contributions cited above. We propose that the preferential glide of certain Burgers orientations is the result of vicinal substrates, commonly used in heteroepitaxy, which create an assymetry in the stresses for the various active slip systems. If the substrate inclination is about an axis of symmetry, then the tilt of the epitaxial growth is about the same axis, and its sign is determined by the nature of the mismatch: the relief of compressive strain results in negative tilt whereas the relief of tensile strain results in positive tilt. The exact amount of tilt will depend on the dynamics of strain relaxation. Upper and lower limits for the tilt have been derived. The observed tilt angle contains information on how the relaxation process took place.