We calculate the equilibrium morphology of a strained layer, for the case where it wets the substrate (Stranski-Krastonow growth). Assuming isotropic surface energy and equal elastic constants in the film and substrate, we are able to calculate two-dimensional equilibrium shapes as a function of the island size and spacing. We present asymptotic results for the equilibrium shape of a thin island where the island height is much smaller than the island width. We also present numerical results of the full equations to describe the island shape when the islands are widely separated. From these solutions we are able to determine the chemical potential of the island as a function of island volume and the strain energy density along the surface of the island for small to medium-sized islands.

The effects of atomic hydrogen (H) on formation of In(Ga)As quantum dots (QDs) by self-organizing process have been investigated. The low size fluctuation and uniform-shaped QDs are obtained at growth temperature above 450°C. The average size of InGaAs QDs are decreased from 40 nm to 20 nm by atomic H irradiation. The InGaAs QDs are formed uniformly on growth surface in with-H condition while preferentially formed and distributed along the step edges in without-H case. The photoluminescence (PL) peak intensities and full width at half maximum (FWHM) are also improved by atomic H irradiation. The waiting time before GaAs cap layer deposition is a important factor on the optical properties of QDs.

In order to understand Ge island nucleation and evolution, we have studied strain relaxation and clustering of Ge grown on Si(111) by molecular beam epitaxy (MBE) with in situ reflection high energy electron diffraction (RHEED), atomic force microscopy (AFM), and Rutherford backscattering spectrometry (RBS). Our goal is to tailor the size and density of the nanocrystals by controlling thermodynamics and kinetics. At low temperature (∼ 450°C), we observe a sharp 2D-3D growth mode transition after 2.5ML ±0.1ML (we define a thickness of 1ML to be one-third the length of the body diagonal of the Ge conventional unit cell), when transmission diffraction features appear in RHEED and the surface lattice constant begins to relax. The mechanisms of island growth and strain relaxation change with growth temperature. At ∼ 700°C, transmission diffraction spots never appear in RHEED for Ge/Si(111) and strain relaxation occurs gradually. After 37ML of growth, the apparent in-plane lattice parameter increases only 1.5% over that of the Si substrate. This behavior is explained by the different manner in which islands initially nucleate and grow in the two temperature regimes. At low temperature, small islands nucleate and grow on a relatively rough wetting layer (which itself provides preferential sites for dislocation introduction). The areal density of the small islands is relatively high. At high temperature, a small number of islands grow very large from the outset. A general model indicates how, at low temperature, the relative difficulty of overcoming the barrier to dislocation formation actually results in an apparent larger degree of strain relief than at high temperature.

The manner in which misfit strain can influence the morphology of heteroepitaxial layers is reviewed. Following a brief consideration of theoretical modelling, examples of experimental observations for two important materials systems, SiGe/Si and InGaAs/GaAs, are given. It is demonstrated that the formation of undulations of specific types is driven by partial elastic stress-relief and a lowering of the system free energy. Under these conditions, islands of deposit can be formed during initial growth and ripples can be produced upon continuous layers. Furthermore, the presence of surface morphological distortions and the accompanying strain fluctuations also can have a significant impact upon misfit dislocation introduction. Relationships between these fluctuations and dislocation source behaviour are described.

Prior to relaxation of misfit strain by formation of misfit dislocations, a growing heteroepitaxial layer can relax elastically by forming surface undulations called ripples. With increasing amplitude of the ripples the misfit strain and thus stress fields grow markedly inhomogeneous, and dislocation formation may thus be triggered in areas of maximum shear stress. The surface directly above such a new dislocation then represents a band of preferential growth and develops into a ridge, which in turn redistributes the strain in the growing layer. This interwoven elastic/plastic relaxation mechanism can comparably easily be deduced from transmission electron and atomic force microscopy studies of SiGe layers grown onto silicon by liquid phase epitaxy. This growth technique exerts only very small driving forces and thus operates very near thermodynamical equilibrium. The local strain tensor and strain energy density are calculated for the actual layer geometries by three dimensional finite element method and provide for quantification of the mechanism.

Two competing strain relaxation mechanisms, namely misfit dislocation generation and surface roughening, have been extensively studied using the GexSi1-x/Si (x< 0.5) system as an example. A predictive model has been developed which accurately describes the nature of misfit dislocation nucleation and growth under non-equilibrium conditions. Using optical and electron microscopy, coupled with a refined theoretical description of dislocation nucleation, it is shown that strain relieving dislocations are readily generated at low misfits with a characteristic activation energy barrier regardless of the growth technique employed (i.e. MBE, RTCVD and UHVCVD). Secondly we have studied the alternative elastic strain relaxation mechanism involving surface undulation; x-ray diffraction, electron and atomic force microscopy have been used to characterize GexSi1-x/Si (x<0.5) structures grown by UHVCVD and MBE at relatively higher temperatures. A theoretical model has been used to model the critical thickness for surface wave generation. The conditions governing the interplay between dislocation formation and surface buckling are described in terms of a "morphological instability diagram".

InAs single layers were grown by Molecular Beam Epitaxy on nominally (001) oriented GaAs substrates at growth temperatures ranging from 350 °C to 500 °C and thicknesses between 1 nm and 6 μm. A systematic study of the influence of growth temperature and thickness on crystal defects and surface morphology is discussed by comparing High Resolution X-Ray Diffraction, Transmission Electron Microscopy and Atomic Force Microscopy investigations.

Surface hexagonal shaped holes were observed to develop at the lowest temperatures starting from an heterolayer thickness of 50 nm. Both misfit and threading dislocations were revealed; moreover the correlation between hexagonal shaped surface holes and mixed dislocations, with the component of the Burgers vector (b) along the growth axis larger than the minimum interatomic distance, is discussed. The holes increase in size and decrease in density by increasing the layer thickness. An almost complete surface planarization is observed at a thickness of 6 μm by increasing the growth temperature up to 500 °C.

In this study CdTe (111)B was grown by molecular beam epitaxy on vicinal Si(001) substrates, with a variety of substrate tilt angles (θ), and tilt directions (φ) relative to [110]. Layer quality, and content of double-domain and microtwin defects were evaluated by double crystal rocking curve (DCRC) full width at half maximum (FWHM) and x-ray diffraction, respectively. Transmission electron microscopy (TEM) was used to study interface quality and the nature of structural defects as a function of epilayer thickness. In the present investigation, substrate preparation and growth conditions, particularly initiation conditions, are correlated with Si (001) tilt. It has been found that oxide desorption processes can depend strongly on θ, especially for larger values of θ (> 4°). Currently, we routinely produce single domain, twin-free CdTe(111)B epilayers on vicinal Si (001) substrates.

We examine the linear stability of a planar, alloy thin film, exposed to a deposition flux from the vapor. The film surface is subject to stresses generated by compositional inhomogeneity, as well as by film-substrate lattice mismatch. In addition to the misfit induced surface instability shown by numerous previous studies, we find that the deposition flux alone can produce instability and that complex interactions occur when both deposition and surface transport processes are present. Solute expansion stresses result in several novel behaviors. Under certain circumstances, the growing film can be completely stabilized by a tensile misfit and destabilized by the same magnitude of compressive misfit. The predictions of this theory are compared to the results of several experimental studies.

An epitaxial material island which has a lattice parameter differing by a small amount for that of its substrate is considered within the framework of continuum mechanics. The strain distribution in the island is determined for a range of aspect ratio, taking into account the compliance of the substrate. It is demonstrated that the total free energy of a strained island is minimum for some value of aspect ratio, and that this value depends on the volume of the island. To consider strain relaxation, the nucleation of a dislocation at the edge of a strained island is examined and the equilibrium aspect ratio of a dislocated island is computed. In particular, it is shown that an island can reduce its free energy by reducing its aspect ratio and, simultaneously, forming an interface misfit dislocation. The simulations are based on the numerical finite element method.

Two dimensional, non-equilibrium molecular dynamics simulations have been performed to examine the microstructures of both homoepitaxial and heteroepitaxial thin films grown on single crystal substrates. The principal microstructural features to develop within these films are small voids and edge dislocations. Voids form near the surface of the growing film as surface depressions between microcolumns pinch off to become closed volumes. These voids often form in such a way as to introduce dislocations into the crystal with their cores positioned within the voids. Dislocations are also formed during heteroepitaxy at the interface between the substrate and film. These dislocations tend to be mobile. When voids are present in the film and when the lattice misfit is low, dislocations tend to be trapped in the voids or pulled toward them due to dislocation image interactions. Once attached to voids, dislocations are effectively pinned there. When voids are absent or when the misfit is high, dislocations are restricted to the film-substrate interface. In the case of heteroepitaxy, dislocations are found to relieve either tensile or compressive misfit stresses. Misfit stresses may also be accommodated, to some extent, merely by the free volume of the voids themselves.

We present a new Volterra dislocation approach in equilibrium theory for strain relaxation in heteroepi-taxial semiconductor structures, one which includes surface relaxation effects and elastic interactions between straight misfit dislocations. The free-surface boundary conditions are satisfied by placing an image dislocation outside the crystal in such a manner that its stress field cancels that of the real interface misfit dislocation at the surface. The effect of the Airy stress function that removes the fictitious shear and normal stresses at the surface are discussed. This image method provides an equilibrium theory which correctly predicts critical strained layer thicknesses and completely describes the elastic and plastic strain relief as well as the phenomenon of work hardening in lattice mismatched epilayers.

The formation of convex and concave regions on the surface of a strained thin epitaxial film on a thick substrate is analyzed by minimization of energy associated with the configuration. The strain energy change resulting from the formation of undulations is modelled with the strain in the film represented by a continuous distribution of dislocations along the perturbed surface and the interface. A discrete dislocation model is also used when periodic undulations are formed. Results of energy minimization for germanium or germanium-silicon alloy films on silicon substrate illustrate that convex regions tend to grow. On the other hand, convex regions formed to conserve mass in shape changes associated with concave regions become stable with minimum energy under quasi-equilibrium when the mobility of adatoms is low. We have determined the size and radius of curvature of the undulations at minimum energy and conclude that it is favorable to form atomic steps on the surfaces from which dislocation generation and strain relaxation takes place.

In this work, we develop a model for ion-assisted molecular beam epitaxy with application to synthesis of epitaxial SnxGe1-x/Ge/Si(001) with compositions up to x=0.34. The model describes the effect of energetic beam deposition on surface segregation during thin film growth. As the value of a Péclet number expressing the ratio of surface ion-mixing rate to growth rate exceeds unity, the segregation coefficient during ion-assisted growth exceeds the value during thermal growth. A comparison of the model with experiments for SnxGei.1-x synthesis is reported. The experimental results are consistent with the model.

The effect of cyclic uniaxial loading applied to surfaces of thin single crystal plates on dislocation structure is analyzed analytically and numerically. This work investigates detailed changes in dislocation structure near surfaces and in size and concentration of dislocation loops inside the crystal. The results may be helpful in choosing the optimum regime for material processing and in predicting material properties.

Molecular Dynamics (MD) simulations are performed on two-dimensional, triangular lattice models. The program used to perform these simulations was based on codes developed by Farid F. Abraham at the IBM-Almaden Research Center in San Jose, CA and by J.M. Haile, but also contained modifications to increase efficiency. These simulation models contain three constrained sides and a free surface, use a Lennard-Jones 6:12 interatomic potential, and initially exist with various amounts (∼ 5 to 10 %) of compressive strain. Our paper studies the formation of dislocations from atomic ledges during relaxation from a compressive state, as well as the subsequent motion of these dislocations. These simulations are particularly relevant to understanding morphological changes on the surface and nucleation of dislocations in heteroepitaxial thin films.

Surface roughening associated with strain relaxation of Si1-xGex films grown epitaxially on (100) Si substrates has been investigated using transmission electron microscopy, atomic force microscopy and x-ray diffraction. Epitaxial films 100 Å in thickness and containing 18% Ge, which are subcritical with respect to the formation of misfit dislocations, show strain relaxation through surface roughening on annealing at 700 °C. Enhanced surface grooves aligned along <100> directions are observed in films annealed at 850 °C. Strain relaxation as measured by x-ray diffraction is significantly greater at the higher temperature. Prolonged anneals at 850 °C also result in islanding. The surface roughening processes have also been studied in subcritical films with 15% Ge at 900 °C. These films also show enhanced grooving aligned along <100> directions. These observations are consistent with an anisotropic elastic analysis which indicates that grooving should occur preferentially along <100> directions. Intermixing effects in these samples have also been investigated through depth profiling using Auger Electron Spectroscopy. In addition to the above subcritical films, other films with 18% and 22% Ge and supercritical thicknesses have also been studied. For these films, surface grooving is observed along <110> directions, which suggests that these grooves are related to the formation of misfit dislocation networks. The role of these surface roughening processes in the nucleation of dislocations has also been explored.

Several Si1-xGex/Si heterostructures were grown at 525°C using a commercially available UHV-CVD reactor. Layers with a germanium fraction ranging from 0.15 to 0.5 were examined by means of cross-sectional transmission electron microscopy and atomic force microscopy. Surface waves were found in layers with a thickness above a critical value which decreases rapidly as the Ge fraction is increased. Both experimental and modeling results show that surface waves are generated before misfit dislocations for Ge fractions above 0.3.

We have investigated the morphological evolution of islanded Ge/Si(100) samples formed by > 3 monolayer (ML) Ge deposition. Ge was deposited onto Si(100) surfaces cleaned by flash desorption of the native oxide at rates near 1/2 ML per minute. Growths were performed in an ultra-high vacuum system with a base pressure of < 10−9 Torr. Substrate temperature during growth was 500 °C. Post-deposition processing ranged from no additional treatment to 1 hour at 560 °C anneals. Samples removed from the growth chamber were processed using standard transmission electron microscopy (TEM) specimen preparation techniques and characterized using plan-view TEM. Micrographs were computer analyzed to generate island size distributions (histograms of island size). These size distributions fall into general classes. First, samples with only coherent Ge islands exhibit relatively narrow size distributions. Secondly samples with both coherent and incoherent islands presented bi-modal size distributions with coherent islands populating the smaller radii. These results will be discussed in the context of a model which includes elastic as well as surface and interface energies as driving forces for ripening.

The residual stress in a 6H-SiC wafer with a 3C-SiC epitaxial overlayer is determined by the technique of Synchrotron white beam x-ray topography (SWBXT). The short wavelength and high energy attributes of synchrotron radiation are exploited to very accurately determine the wafer curvature. Different approaches including absorption edge contour (AEC) mapping, multiple diffraction line (MDL) analysis and diffracted x-ray beam divergence (DXBD) analysis in both transmission and reflection geometry are demonstrated. The residual stress distribution is calculated from the wafer curvature measurement.