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 in epitaxial films III. Theory

Observations on the growth of Pd on (001)Au and (111)Au substrates have shown that Pd deposits grow pseudomorphically up to a few monolayers thickness, whereupon misfit dislocations nucleate at the Pd surface and grow into the Pd-Au interface to relieve misfit strains. In this paper the critical thicknesses for coherency loss in Pd/(001)Au and Pd/(111)Au films are measured accurately using an X-ray microanalysis technique. The nucleation and growth of the observed misfit dislocation sources, described in previous papers, is examined in detail theoretically, and the results are compared with experiment. It is shown that misfit dislocation sources in Pd/(001)Au and Pd/(111)Au films nucleate at different deposit thicknesses in excellent quantitative agreement with experiment and are the most energetically favourable sources.     

Initial epitaxial growth of (111) Au/(111) Cu and (111) Cu/(111) Au

The room temperature modes of growth of Au/(111) Cu and Cu/(111) Au are described. For the former growth mode initial deposits (2.4 Å) of gold on copper form smooth flat islands delineated by coincidence lattice misfit dislocations. For 6.0 Å of gold deposit, both thick and thin gold areas were observed with almost complete substrate coverage. For a 10 Å deposit, surface coverage was complete. Strain measurements and dislocation densities obtained on the (111) Au/(111) Cu films suggest the presence of two separate misfit dislocation networks at the interface. The coincidence lattice networks were large enough for transmission electron microscopy observation but contributed little to total overlayer strain. The (van der Merwe) natural lattice misfit dislocations were too closely spaced for direct observation but their presence was inferred because of the strain measurements. The initial epitaxy of Cu/(111) Au was similar to the Stranski-Krastanov model: the initial monolayer of copper (also delineated by coincidence misfit dislocations) grew smoothly on the gold; additional copper formed essentially stress-free “nuclei” on top of the initial copper layer.     

Dislocation wall formation during interdiffusion in thin bimetallic films

Transmission electron microscopy observations are described of the diffusion-induced behaviour of misfit dislocations originally present in the interface of thin bimetallic films. Experiments were carried out with specimens consisting of a layer of approximately 500 Å Cu vapour deposited onto an electropolished Ni substrate approximately 1000 Å thick. Diffusion anneals were performed in situ in the electron microscope at annealing temperatures in the range 450–600°C. The dislocation behaviour in Cu/Ni bicrystals with originally a (100) interface was photographed and video-recorded. A cross-grid of misfit dislocations parallel to 〈110〉 directions was present in the original interface. The Burgers vectors were of type $\text{1}\text{2}$a〈110〉 lying in the interface. During diffusion the misfit dislocations became distributed in the diffusion zone. When $\text{2Dt}$ (where D is the diffusion coefficient and t is the annealing time at a given temperature) exceeded a value of 40–50 Å, the dislocations started to align vertically forming dislocation walls along 〈110〉 directions parallel to the original interface. This resulted in a dislocation cell structure. Lengthwise the dislocation walls grew with shocks. The elastic strain energy of a finite edge dislocation array was estimated. Using this result an energy criterion for the formation of dislocation walls was derived. From this criterion it followed that dislocation wall formation may start to occur when $\text{2Dt}$≈ 45 Å, in good correspondence with the experimental results. Some additional observations of recrystallization phenomena during interdiffusion are reported.     

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.     

Heteroepitaxy of chalcogenide compounds II. Monolayer overgrowth process accompanied by lattice transformation

The growth processes of orthorhombic SnSe and rhombohedral GeTe on NaCl-type PbSe, PbTe and SnTe have been studied by still and in situ electron microscopy, with the following results. (i) Growth proceeds in the monolayer overgrowth mode, as for the substrate-deposit combinations of chalcogenides of the same NaCl-type structure reported in Part I. (ii) Lattice recovery of the overgrown films from the initial pseudomorphic structure to the natural structure proceeds by the development of sets of differently spaced misfit dislocations in appropriate directions, with the formation of doubly positioned regions. (iii) The growth of GeTe on PbTe shows a different aspect from that observed for all other cases in Parts I and II, which exhibit straightforward monolayer overgrowth. Initially, bundles of closely spaced short-segmented misfit dislocations are formed into many island-like patches, suggesting that overgrowth proceeds in the nucleation and growth mode. At a later stage, however, generation and extension of the patches takes place, piloted by a singly extending misfit dislocation; this suggests the monolayer overgrowth mode, which is confirmed by Auger electron spectroscopy. (iv) Climb plays a primary role in the formation of misfit dislocations. For SnSe growth on (001) PbSe, PbTe and SnTe, however, misfit dislocations are glissile along the interface and their rearrangement by slip during growth leads to a well-defined configuration of doubly positioned regions in the later stages, with the overgrown lattices in the two regions in coherent twin contact with each other at the boundaries.     

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.     

Surface strains and measurements of misfit dislocation density by diffraction methods in thin films on substrates

In-plane strain variations near the free surface of an epitaxial thin film containing misfit dislocation shave been calculated. It is shown that strain distribution under the surface of the film is not constant and this distribution also depends on film thickness even for constant misfit dislocation density. The strain derived from diffraction measurements must therefore be corrected to obtain the true misfit dislocation density.     

Fully strained low-temperature epitaxy of TiN/MgO(001) layers using high-flux, low-energy ion irradiation during reactive magnetron sputter deposition

Epitaxial TiN layers, 0.3 μm thick, are grown on MgO(001) in the absence of applied substrate heating using very high flux, low-energy (below the lattice atom displacement threshold), ion irradiation during reactive magnetron sputter deposition in pure N₂ discharges. High-resolution x-ray diffraction, reciprocal lattice maps, and transmission electron microscopy analyses reveal that the TiN(001) films grow with an (001)_TiN||(001)_MgO and [100]_TiN||[100]_MgO orientation relationship to the substrate. The layers are fully coherent with no detectable misfit dislocations. For comparison, TiN/MgO(001) films grown at temperatures of 700-850 °C under similar conditions, but with no intentional ion irradiation, are fully relaxed with a high misfit dislocation density. Thus, the present results reveal that intense low-energy ion irradiation during film growth facilitates high adatom mobilities giving rise to low-temperature epitaxy, while the low growth temperature quenches strain-induced relaxation and suppresses misfit dislocation formation.     

Thermodynamic modeling of the initial microstructural evolution of oxide films grown on bare copper

A thermodynamic model is presented that predicts the initial growth of either a (semi-) coherent crystalline oxide phase or an amorphous oxide phase (with a subsequent amorphous-to-crystalline transition) on a bare metal as function of the substrate orientation, growth temperature and film thickness. The model accounts for possible relaxation of growth stresses by plastic deformation. The direct formation and growth of semi-coherent, crystalline Cu₂O is predicted by application of the model to oxide overgrowth on bare Cu{111}, Cu{100} and Cu{110}. For oxide overgrowths on Cu{111} and Cu{110}, a square grid of misfit dislocations with a dislocation distance of about six Cu₂O unit cells would occur on the basis of the model calculations, which agrees with experimental observations reported for Cu{111} in the literature. On Cu{100} an array of misfit dislocations is formed along the single direction of high lattice mismatch.     

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.     

Transition from a disordered to a crystalline state in II–VI and III–V films

The initial stages of HgCdTe growth on Al₂O₃, GaAs, CdTe, and KCl substrates have been studied by electron diffraction. HgCdTe films were produced by pulsed laser deposition and isothermal vapor phase epitaxy. InGaAs films were grown by isothermal chloride epitaxy on GaAs substrates. In the initial stages of the growth process, we observed a transition from an amorphous to a textured polycrystalline phase and then to a mosaic single-crystal structure. We have calculated the critical size of crystalline grains below which amorphization occurs in II-VI and III-V compounds. The critical grain size agrees with the grain size of the disordered (amorphous) phase that forms in the initial stage of epitaxy. We have determined some characteristics of the heterostructures: critical film thickness below which pseudomorphic growth is possible without misfit dislocation generation, elastic stress in the epitaxial system, surface density of dangling bonds at dislocations, and the critical island radius above which no interfacial misfit dislocations are generated.     

The annealing of misfit dislocations in the (111) Cu/(111) Cu2O system

Recent work on the early stages of the epitaxial oxidation of (111) Cu at 350 °C and in oxygen pressures between 10^-7 and 10^-4 Torr has resulted in the determination of the growth modes that occur and the accompanying elastic strains. Initially a hexagonal 3 × 3 oxide superlattice is formed which continues to grow by a layer growth mechanism up to a theoretically estimated thickness of approximately five monomolecular layers. Subsequent oxidation occurs by the formation of lamellar islands containing misfit dislocations which reduce the coincidence lattice misfit strain. In the present work these (111) Cu/(111) Cu₂O bilayers were annealed and examined in situ in the transmission electron microscope in the temperature range 25–350 °C. The misfit dislocation density decreased as the temperature was increased. The annealing effects are complex and interdiffusion phenomena can be observed even at 60 °C.     

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.     

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.     

Transformation of c-oriented nanowall network to a flat morphology in GaN films on c-plane sapphire

The work significantly optimizes growth parameters for nanostructured and flat GaN film in the 480–830 °C temperature range. The growth of ordered, high quality GaN nanowall hexagonal honeycomb like network on c-plane sapphire under nitrogen rich (N/Ga ratio of 100) conditions at temperatures below 700 °C is demonstrated. The walls are c-oriented wurtzite structures 200 nm wide at base and taper to 10 nm at apex, manifesting electron confinement effects to tune optoelectronic properties. For substrate temperatures above 700 °C the nanowalls thicken to a flat morphology with a dislocation density of 10¹⁰/cm². The role of misfit dislocations in the GaN overlayer evolution is discussed in terms of growth kinetics being influenced by adatom diffusion, interactions and bonding at different temperatures. The GaN films are characterized by reflection high energy electron diffraction (RHEED), field emission scanning electron (FESEM), high resolution X-ray diffraction (HRXRD) and cathodoluminescence (CL).     

Morphological transformations of thin heteroepitaxial films

The features of two-and three-dimensional growth of thin heteroepitaxial films are analysed with allowance for the energy of misfit dislocation (MD) networks. Criteria for distinguishing between Frank-van der Merwe, Stranski-Krastanov and Volmer-Weber growth modes are suggested. For the Stanski-Krastanov mode the transition from layer to island growth is considered to be associated with an increase in the interface energy owing to MD formation. The critical thickness of the pseudomorphic film in the case of the formation of dislocated islands is much less than that in the case of the introduction of MDs into the continuous film and depends on an average migration length of the adatoms. Some theoretical results are compared with experimental results for germanium films obtained by molecular beam epitaxy on Si(001) and Si(111) substrates.     

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.