Elastic strain and misfit dislocation density in Si0.92Ge0.08 films on silicon substrates

Thin (less than 1 μm) epitaxial Si_0.92Ge_0.08 films on (100) Si substrates were grown by an UHV evaporation technique at a substrate temperature of 750 °C. The film strain and misfit dislocation density were examined by means of X-ray diffraction and transmission electron microscopy, respectively. The films are shown to be in state of compression, and the misfit dislocation density depends strongly on film thickness. The critical film thickness below which pseudomorphic growth without misfit dislocations occurs is found to be about 0.1 μm. The extrapolation model of van der Merwe's misfit dislocation theory is modified assuming low lattice mismatch and a diamond structure. The misfit dislocation distances thus calculated are compared with the measured distances, and it is found that the former are always smaller than the latter.     

Misfit dislocations and stress in In<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As/GaAs heterostructures

We have estimated the elastic properties of In_{1 − x} Ga _x As/GaAs heterostructures and the characteristics of misfit dislocations in such heterostructures: misfit dislocation spacing, Burgers vector length in various interfaces, surface density of dangling bonds, film/substrate interface energy, critical film thickness below which pseudomorphic growth is possible without misfit dislocations, elastic strain energy of the film-substrate system, average elastic strain of a thin-film island as a function of its radius, thermal stresses induced by the thermal-expansion and lattice mismatches between the layers in contact, and crack length in the film.     

纳米尺度圆孔表面薄膜界面失配位错形核机理

研究了无限大基体内纳米尺度圆孔表面薄膜中界面螺型位错形核的临界条件,薄膜考虑了表/界面效应。运用弹性复势方法,获得了两个区域应力场的解析解答,并导出位错形核能公式,由此讨论了表/界面效应对薄膜界面位错形核的影响规律。算例结果表明,表/界面效应在纳米尺度下对位错形核的影响显著,不同表/界面效应下位错形核的临界薄膜厚度有很大差异,当基体与薄膜的相对剪切模量超过某一值后,只有考虑负的表/界面应力时位错才有可能形核;薄膜厚度在小于某一临界尺寸时负的表/界面应力更容易位错形核,薄膜厚度大于某一临界尺寸时正的表/界面应力更容易位错形核。     

Stability of strained thin films with interface misfit dislocations: A multiscale computational study

The stability of thin single-crystal, internal-defect-free Fe films on Mo(110) and W(110) substrates is investigated through calculations of energetics including contributions from the misfit strain, interfacial misfit dislocations, film surface and interface. The misfit dislocation model is developed through the Peierls-Nabarro framework, employing ab initio calculations of the corrugation potential at the film/substrate interface as an input to the model. The surface and interfacial energies for pseudomorphic films are calculated as a function of film thickness from 1 to 10 layers, employing first-principles spin-polarized density-functional theory calculations in the generalized gradient approximation. First-principles calculations are also employed to obtain the Fe surface stress used in the Peierls-Nabarro model to account for the strain dependence of the surface energy. It is found that the competition between the misfit strain, misfit dislocations, film surface and interfacial energies gives rise to a driving force for solid-state dewetting of a single-crystal, internal-defect-free film, i.e., an instability of a flat film that leads to formation of thicker and thinner regions. The details of the energetics are presented to demonstrate the robustness of the mechanism. Our findings indicate that misfit dislocations and their configurations play a significant role in a morphological evolution of metallic thin films.     

Some features of the behavior of misfit dislocations during diffusion

The misfit between one film and another is often accommodated by misfit dislocations. If the crystals are miscible and are allowed to interdiffuse the misfit dislocations become distributed in the alloyed volume. Frequently, some parts of one dislocation move away from the interface into one crystal and other parts move into the other crystal. The parts in one crystal are connected to those in the other by dislocations that thread the diffusion zone. The density of these threading dislocations depends on the misfit between the two crystals, and may be influenced by the Kirkendall effect and by the misfit accommodated by elastic strain. Interaction between misfit dislocations in the diffusion zone often leads to the creation of new grains. These grains are unusual in that their lattices are curved to accommodate misfit between the upper and lower film surfaces. The boundaries to the grains are approximately perpendicular to the original interface and are made up of misfit dislocations that once occupied the material inside the curved grain. As dislocations and grain boundaries enhance diffusion the threading dislocations, and the boundaries to the curved grains, are expected to contribute to mixing of the films.     

Phase field modeling of flexoelectric effects in ferroelectric epitaxial thin films

The flexoelectric effect which is defined as the coupling between strain gradient and polarization has long been neglected because it is insignificant in bulk ferroelectrics. However, at nanoscale, the strain gradient can be dramatically increased leading to giant flexoelectric effects. In the present study, the flexoelectric effects in epitaxial nano thin films of a 180° multi-domain structure, which are subjected to a compressive in-plane misfit strain, are investigated by the phase field method. Unlike the case of a single domain structure where the strain gradient is mainly attributed to the formation of dislocation which relaxes the misfit strain, in a multi-domain structure, it is attributed to many factors, such as surface and interface effects, misfit relaxation and domain wall structure. The results obtained show that relatively large flexoelectricity-induced electric fields are produced near the domain wall region. The induced field will not only influence the domain structure of the thin film, but also the hysteresis loops when it is under an applied electric field.     

Misfit dislocation sources in epitaxial films part II: Growth of Pd on (111) Au substrates

Direct observations of the epitaxial growth of Pd films on (111) Au substrates in the transmission electron microscope have revealed new misfit dislocation sources. The Pd film grew pseudomorphically up to a mean deposit thickness of about 6 Å, when “trigons” of misfit dislocation comprising three perfect dislocations with Burgers vectors lying in the film plane and meeting in a threefold node nucleated and grew by dislocation climb to relieve misfit strains. In situ results and the dislocation analysis are described; weak-beam electron microscopy is used to show that the trigons are faulted on a fine scale. Mechanisms for the nucleation of dislocation trigons and for subsequent misfit dislocation growth are presented and discussed in detail.     

Transmission electron microscopy observations of misfit dislocations in GaAsP epitaxial films

Transmission electron microscopy observations have been made of misfit dislocation structures in GaAsP epitaxial films in foils both parallel to (1) the interface between the epitaxial film and the substrate and (2) the {1 1 1} glide planes. These observations support a near surface source mechanism of dislocation multiplication for relief of the epilayer misfit. It is also suggested that the recently observed surface reconstruction in the III-V compounds might allow for an easier nucleation of dislocations at the surface than hitherto thought. Furthermore, an efficient Lomer dislocation has been observed forming from two 60° glide dislocations thus supporting the hypothesis that all dislocations found in these foils, including the sessile Lomer type, originate from a glide process.     

Identification of atomic steps at AlSb/GaAs hetero-epitaxial interface using geometric phase method by high-resolution electron microscopy

Geometric phase analysis (GPA) is applied to determining the strain fields in AlSb/GaAs hetero-epitaxial film from high-resolution electron microscopy (HREM) images. The misfit dislocations along the hetero-interface are shown to be predominantly 90° Lomer dislocations. The epitaxial film is almost fully relaxed by a high density of misfit dislocations. The 90° Lomer dislocations are assumed to be formed by either recombination of two 60° mixed misfit dislocations through a glide and climb process or direct nucleation at the interface. The atomic steps (ASs) are visualized in the strain map, providing a new method for identifying the ASs at the interface.     

Configuration and local elastic interaction of ferroelectric domains and misfit dislocation in PbTiO3/SrTiO3 epitaxial thin films

Abstract

We have studied the strain field around the 90° domains and misfit dislocations in PbTiO₃/SrTiO₃ (001) epitaxial thin films, at the nanoscale, using the geometric phase analysis (GPA) combined with high-resolution transmission electron microscopy (HRTEM) and high-angle annular dark field––scanning transmission electron microscopy (HAADF-STEM). The films typically contain a combination of a/c-mixed domains and misfit dislocations. The PbTiO₃ layer was composed from the two types of the a-domain (90° domain): a typical a/c-mixed domain configuration where a-domains are 20–30 nm wide and nano sized domains with a width of about 3 nm. In the latter case, the nano sized a-domain does not contact the film/substrate interface; it remains far from the interface and stems from the misfit dislocation. Strain maps obtained from the GPA of HRTEM images show the elastic interaction between the a-domain and the dislocations. The normal strain field and lattice rotation match each other between them. Strain maps reveal that the a-domain nucleation takes place at the misfit dislocation. The lattice rotation around the misfit dislocation triggers the nucleation of the a-domain; the normal strains around the misfit dislocation relax the residual strain in a-domain; then, the a-domain growth takes place, accompanying the introduction of the additional dislocation perpendicular to the misfit dislocation and the dissociation of the dislocations into two pairs of partial dislocations with an APB, which is the bottom boundary of the a-domain. The novel mechanism of the nucleation and growth of 90° domain in PbTiO₃/SrTiO₃ epitaxial system has been proposed based on above the results.     

Quasicontinuum study the influence of misfit dislocation interactions on nanoindentation

Multiscale simulations using the quasicontinuum (QC) method with the embedded-atom method (EAM) potential are performed to examine the mechanical response of Cu–Ag bilayer film during nanoindentation tests. An attempt is made, from the viewpoint of collective interaction among misfit dislocations on the interface, to account for the strengthening and weakening mechanisms of interface on Cu–Ag bilayer film. The details of misfit dislocation nucleation, motion and collective interaction on Cu/Ag and Ag/Cu interfaces are discussed systematically, respectively. The investigation shows that the property and performance of Cu–Ag bilayer film mainly depend on the mechanical property of upper film. Both the strengthening and weakening effects are closely related to the collective interaction among misfit dislocations on the interface. Due to the pinning effect of interface on misfit dislocation, both the local interface migration and the voids can be observed at the core region of misfit dislocations. For nanoindentation on Cu/Ag bilayer film, the plastic deformation is localized chiefly in the lower Ag substrate and the void will disappear with the redistribution of misfit dislocations, which indicate that there are distinct protective and strengthening effects of the upper Cu film on the lower Ag substrate. While, for nanoindentation on Ag/Cu bilayer film, both the upper Ag film and the lower Cu substrate experience plastic deformation and the voids will not disappear, which imply that there are an obvious weakening effect of the upper Ag film on the lower Cu substrate. In addition, the multiscale simulation results are consistent with the experimental results.     

Energy of a dislocation near an epitaxial interface

The energy of a straight mixed dislocation in a coherent epitaxial layer at a uniform distance t from the interface is calculated. It is shown that, in addition to terms associated with coherency strain and the dislocation energy, there is a term associated with the interaction of the coherency and dislocation strain fields which makes the total energy decrease as the dislocation approaches the interface, but this term is negligible when the dislocation is nearer the epilayer surface than the interface. The result is used to modify a calculation of Jesser and Matthews of the critical thickness of an epitaxial layer at which the introduction of misfit dislocations becomes energetically favourable. The present work reduces the calculated critical thickness by 30–50%.     

Grazing incidence reciprocal space mapping of partially relaxed SiGe films

Epitaxially grown lattice mismatched semiconductor structures are increasingly important for microelectronic and optoelectronic applications. Recently, a great deal of research has been carried out on strain relaxation mechanisms in lattice mismatched epitaxial films. Here, we describe triple-axis x-ray diffraction measurements that were performed to study strain relaxation mechanisms and dislocation formation in Si_1–x Ge _x alloys grown on (0 0 1) Si substrates. At low growth temperature (T_g 600°C) and small lattice mismatch (>2%), two different mechanisms of strain relaxation are observed, depending on the growth temperature and the magnitude of the strain. At Higher growth temperatures or larger lattice mismatch, strain relaxation occurs initially by surface roughening. Subsequently, 60° misfit dislocations nucleate in regions of high strain. At smaller lattice mismatch or lower growth temperature, the surface of the film does not roughen and the 60° misfit dislocations are formed primarily by Frank–Read multiplication. Triple-axis x-ray diffraction reciprocal space maps taken at grazing incidence on very thin epitaxial films can easily distinguish between these two mechanisms. Here, the lattice planes perpendicular to the interface are measured, whereas conventional diffractometry looks either at the planes parallel to the wafer surface or at planes having components both parallel and perpendicular to the surface. In the grazing incidence geometry, thickness broadening of the x-ray peak is eliminated, since the film is essentially infinitely thick parallel to the surface.     

Anisotropy effect on strain-induced instability during growth of heteroepitaxial films

The use of misfit strain to improve the electronic performance of semiconductor films is a common strategy in modern electronic and photonic device fabrication. However, pursuing a favorable higher strain could lead to mechanical instability, on which systematic and quantitative understandings are yet to be achieved. In this paper, we investigate the anisotropy effects on strain-induced thin-film surface roughening by phase field modeling coupled with elasticity. We find that compared with films grown along {111} and {100} surfaces, the instability of {110} film occurs at a much lower strain. Our simulations capture the evolution of interface morphology and stress distribution during the roughening process. Similar characterizations are performed for heteroepitaxial growth from a surface pit. Finally, from 3D simulations, we show that the surface roughening pattern on {110} film exhibits a clear in-plane orientation preference, consistent with experimental observations.     

Use of misfit strain to remove dislocations from epitaxial thin films

Misfit strain can be used to drive threading dislocations out of epitaxial films and thus to improve their perfection. This process is influenced by film thickness, the orientation of the interface, the dimensions of the interface parallel to its plane, and the misfit between film and substrate. A simple theoretical model, and the experimental observations made on deposits of Ga(As, P) on GaAs, suggest that it is desirable for the film thickness to be small. This in turn implies that the misfit should be large. It should not, however, be large enough to cause dislocation nucleation. If the film is face-centered cubic, and the threading dislocations are uniformly distributed over the 〈110〉 {111} slip systems, then the most desirable interface orientations lie near {012} or {013}. If the Burgers vectors of the threading dislocations are not uniformly distributed then other interfaces may become desirable. Multilayers are able to remove threading dislocations more effectively than single films.     

The study of grain boundary density effect on multi-grain thin film under tension

The grain-size effect on the yield strength and strain hardening of thin film at sub-micron and nanometer scale closely relates to the interactions between grain boundary and dislocation. Based on higher-order gradient plasticity theory, we have systematically investigated the size effect of multi-grain thin film arising from the grain boundary density under tensile stress. The developed formulations employing dislocation density and slip resistance have been implemented into the finite element program, in which grain boundary is treated as impenetrable interface for dislocations. The numerical simulation results reasonably show that plastic hardening rate and yield strength are linear to the grain boundary density of multi-grain thin film. The aspect ratio of grain size and orientation of slip system have distinct influence on the grain plastic properties. The research of slip system including homogeneous and nonhomogeneous distribution patterns reveals that the hardening effect of low-angle slip system is greater than that of high-angle slip system. The results agree well with the experimentally measured data and the solutions by discrete dislocation dynamics simulation.     

Equilibrium surface roughness of a strained epitaxial film due to surface diffusion induced by interface misfit dislocations

In recent years, developments in the microelectronics industry have led to extensive studies of the growth and characterization of thin solid films and their implementation in electronic and opto-electronic devices. A goal is to produce thin films with minimal bulk and surface defects. For those systems produced by epitaxial growth of a film on a substrate that has a slightly different lattice parameter, the stress associated with the elastic mismatch strain needed to satisfy the constraint of epitaxy provides a driving force for nucleation and growth of undesirable defects in the film material or on its surface. Among the most common defects are interface misfit dislocations, arranged more or less periodically on the film-substrate interface, which partially relax the elastic mismatch strain in the film. It has been observed that, for some material systems, surface roughness or waviness arises which correlates spatially with the positions of interface misfit dislocations. It is suggested here that the waviness along the surface may be a result of surface diffusion which is driven by a gradient in the chemical potential of the material along the surface. The chemical potential gradient arises from the nonuniform strain field of the interface misfit dislocations, as well as from the unrelaxed elastic mismatch strain. The focus here is on the development of a relatively simple model of this system which leads to an estimate of the magnitude and profile of surface waviness under conditions of thermodynamic equilibrium, i.e., after the material responds to the chemical potential gradient by seeking out a new configuration for which stresses are redistributed and the chemical potential is again uniform. The condition of uniform chemical potential for the final shape leads to an integro-differential equation for the equilibrium surface shape which is solved numerically. For representative values of system parameters, estimates of equilibrium surface roughness are obtained which can vary from less than one percent of film thickness to a significant fraction of film thickness. Although transient aspects of the process are not studied here, the characteristic time for achieving an equilibrium configuration is estimated.     

Anisotropic surface structure in ordered strained InGaP

We have studied the surface structure of ordered In_xGa_1−xP organometallic vapour phase epitaxy (OMVPE)-grown layers using optical microscopy, atomic force microscopy (AFM), and synchrotron topography. The layers were intentionally lattice mismatched (0.388≤x_In≤0.552), and they exhibited a surface structure with three basic features. The first one is a fine island structure with the size of surface features in the range of 10 nm, which is very similar for all layers regardless of their misfit. This fine structure is superposed to surface undulations with lateral dimensions in the micrometer scale. The surface structure of the strained layers (tensile and compressed) follows the dislocation line pattern revealed by synchrotron topography. The change of the dominant misfit dislocation direction from [011] to [0−11] is observed for the layer still under tension with Δa/a=−3.28×10⁻³. The best surface morphology and no misfit dislocations are observed for the slightly compressed layer with Δa/a=+9.42×10⁻⁴. With increased compression in the layers, we observed at first the creation of large (probably metal) precipitates and then the formation of a misfit dislocation net. The third feature observed on the surface of ordered layers is the presence of hillocks. Their density, shape and orientation depend on lattice mismatch.     

Synthesis and strain relaxation of Ge-core/Si-shell nanowire arrays

Analogous to planar heteroepitaxy, misfit dislocation formation and stress-driven surface roughening can relax coherency strains in misfitting core-shell nanowires. The effects of coaxial dimensions on strain relaxation in aligned arrays of Ge-core/Si-shell nanowires are analyzed quantitatively by transmission electron microscopy and synchrotron X-ray diffraction. Relating these results to reported continuum elasticity models for coaxial nanowire heterostructures provides valuable insights into the observed interplay of roughening and dislocation-mediated strain relaxation.