Morphological instability in epitaxially strained dislocation-free solid films

New Strategies for Engineering Tensile Strained Si Layers for Novel n-Type MOSFET

We report a novel approach for engineering tensely strained Si layers on a relaxed silicon germanium on insulator (SGOI) film using a combination of condensation, annealing, and epitaxy in conditions specifically chosen from elastic simulations. The study shows the remarkable role of the SiO₂ buried oxide layer (BOX) on the elastic behavior of the system. We show that tensely strained Si can be engineered by using alternatively rigidity (at low temperature) and viscoelasticity (at high temperature) of the SiO₂ substrate. In these conditions, we get a Si strained layer perfectly flat and free of defects on top of relaxed Si_1-xGe_x. We found very specific annealing conditions to relax SGOI while keeping a homogeneous Ge concentration and an excellent thickness uniformity resulting from the viscoelasticity of SiO₂ at this temperature, which would allow layer-by-layer matter redistribution. Remarkably, the Si layer epitaxially grown on relaxed SGOI remains fully strained with -0.85% tensile strain. The absence of strain sharing (between Si_1-xGe_x and Si) is explained by the rigidity of the Si_1-xGe_x/BOX interface at low temperature. Elastic simulations of the real system show that, because of the very specific elastic characteristics of SiO₂, there are unique experimental conditions that both relax Si_1-xGe_x and keep Si strained. Various epitaxial processes could be revisited in light of these new results. The generic and simple process implemented here meets all the requirements of the microelectronics industry and should be rapidly integrated in the fabrication lines of large multifinger 2.5 V n-type MOSFET on SOI used for RF-switch applications and for many other applications.

When finite-size effects dictate the growth dynamics on strained freestanding nanomembranes

We investigate the influence of strain-sharing and finite-size effects on the morphological instability of hetero-epitaxial nanomembranes made of a thin film on a thin freestanding substrate. We show that long-range elastic interactions enforce a strong dependence of the surface dynamics on geometry. The instability time-scale τ is found to diverge as (e/H)-α with α = 4 (respectively 8) in thin (resp. thick) membranes, where e (resp. H) is the substrate (resp. nanomembrane) thickness, revealing a huge inhibition of the dynamics as strain sharing decreases the level of strain on the surface. Conversely, τ vanishes as H 2 in thin nano-membranes, revealing a counter-intuitive strong acceleration of the instability in thin nanomembranes. Similarly, the instability length-scale displays a power-law dependence as (e/H)-β , with β = α/4 in both the thin and thick membrane limits. These results pave the way not only for experimental investigation, but also, for the dynamical control of the inescapable morphological evolution in epitaxial systems.

Strain relaxation in InAs heteroepitaxy on lattice-mismatched substrates

Strain relaxation processes in InAs heteroepitaxy have been studied. While InAs grows in a layer-by-layer mode on lattice-mismatched substrates of GaAs(111)A, Si(111), and GaSb(111)A, the strain relaxation process strongly depends on the lattice mismatch. The density of threading defects in the InAs film increases with lattice mismatch. We found that the peak width in x-ray diffraction is insensitive to the defect density, but critically depends on the residual lattice strain in InAs films.

Orientational competition in quantum dot growth in Si–Ge heteroepitaxy on pit-patterned Si(001) substrates

Growth of quantum dots on patterned substrates shows orientation dependent localization.

Consequences of elastic anisotropy in patterned substrate heteroepitaxy

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi-infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film-substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro-Tiller-Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time-scale for this inversion as function of height is analyzed.

Equilibrium and dynamics of strained islands

We focus in this work on the effect of the surface energy anisotropy on an elastically strained semiconductor film and in particular on its role on the coarsening dynamics of elastically strained islands. To study the dynamics of a strained film, we establish a one-dimensional nonlinear and nonlocal partial differential equation which takes into account the elastic, capillary, wetting, and anisotropic effects. We first construct an approximate stationary solution of our model using a variational method and an appropriate ansatz. This stationary solution is used to compute the chemical potential dependence on the island height. In particular, we find that the surface energy anisotropy increases the convexity of the chemical potential and this is shown to have an effect on the driving force for the coarsening. Second, we study the coarsening dynamics of an islands pair by means of numerical simulations. We find that the presence of the surface energy anisotropy may increase or decrease the coarsening time of the system. We show that this phenomenon depends on the initial heights of island pairs. We thus highlight that the driving force for the coarsening is due to the variation of the chemical potential with respect to the islands height and that two different regimes are possible.

New strategies for producing defect free SiGe strained nanolayers

Strain engineering is seen as a cost-effective way to improve the properties of electronic devices. However, this technique is limited by the development of the Asarro Tiller Grinfeld growth instability and nucleation of dislocations. Two strain engineering processes have been developed, fabrication of stretchable nanomembranes by deposition of SiGe on a sacrificial compliant substrate and use of lateral stressors to strain SiGe on Silicon On Insulator. Here, we investigate the influence of substrate softness and pre-strain on growth instability and nucleation of dislocations. We show that while a soft pseudo-substrate could significantly enhance the growth rate of the instability in specific conditions, no effet is seen for SiGe heteroepitaxy, because of the normalized thickness of the layers. Such results were obtained for substrates up to 10 times softer than bulk silicon. The theoretical predictions are supported by experimental results obtained first on moderately soft Silicon On Insulator and second on highly soft porous silicon. On the contrary, the use of a tensily pre-strained substrate is far more efficient to inhibit both the development of the instability and the nucleation of misfit dislocations. Such inhibitions are nicely observed during the heteroepitaxy of SiGe on pre-strained porous silicon.

Modeling elastic anisotropy in strained heteroepitaxy

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Direct Observation of "Pac-Man" Coarsening

We report direct observation of a "Pac-Man" like coarsening mechanism of a self-supporting thin film of nickel oxide. The ultrathin film has an intrinsic morphological instability due to surface stress leading to the development of local thicker regions at step edges. Density functional theory calculations and continuum modeling of the elastic instability support the model for the process.

Shape and coarsening dynamics of strained islands

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elastocapillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two-dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height h_{0} and they sit on top of a flat wetting layer with a thickness h_{w}. We then consider two islands, and we report that they undergo a noninterrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasistatic dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale t_{c} that is a function of the distance d between the islands and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height h_{0}^{*}, its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.

Asymmetric shape transitions of epitaxial quantum dots

We construct a two-dimensional continuum model to describe the energetics of shape transitions in fully faceted epitaxial quantum dots (strained islands) via minimization of elastic energy and surface energy at fixed volume. The elastic energy of the island is based on a third-order approximation, enabling us to consider shape transitions between pyramids, domes, multifaceted domes and asymmetric intermediate states. The energetics of the shape transitions are determined by numerically calculating the facet lengths that minimize the energy of a given island type of prescribed island volume. By comparing the energy of different island types with the same volume and analysing the energy surface as a function of the island shape parameters, we determine the bifurcation diagram of equilibrium solutions and their stability, as well as the lowest barrier transition pathway for the island shape as a function of increasing volume. The main result is that the shape transition from pyramid to dome to multifaceted dome occurs through sequential nucleation of facets and involves asymmetric metastable transition shapes. We also explicitly determine the effect of corner energy (facet edge energy) on shape transitions and interpret the results in terms of the relative stability of asymmetric island shapes as observed in experiment.

Nanoparticle shape, thermodynamics and kinetics

Nanoparticles can be beautiful, as in stained glass windows, or they can be ugly as in wear and corrosion debris from implants. We estimate that there will be about 70,000 papers in 2015 with nanoparticles as a keyword, but only one in thirteen uses the nanoparticle shape as an additional keyword and research focus, and only one in two hundred has thermodynamics. Methods for synthesizing nanoparticles have exploded over the last decade, but our understanding of how and why they take their forms has not progressed as fast. This topical review attempts to take a critical snapshot of the current understanding, focusing more on methods to predict than a purely synthetic or descriptive approach. We look at models and themes which are largely independent of the exact synthetic method whether it is deposition, gas-phase condensation, solution based or hydrothermal synthesis. Elements are old dating back to the beginning of the 20th century-some of the pioneering models developed then are still relevant today. Others are newer, a merging of older concepts such as kinetic-Wulff constructions with methods to understand minimum energy shapes for particles with twins. Overall we find that while there are still many unknowns, the broad framework of understanding and predicting the structure of nanoparticles via diverse Wulff constructions, either thermodynamic, local minima or kinetic has been exceedingly successful. However, the field is still developing and there remain many unknowns and new avenues for research, a few of these being suggested towards the end of the review.

Morphological Evolution in Heteroepitaxial Thin Film Structures at the Nanoscale

The aim of this study is to resolve the phenomenon of formation of mesoscopic structures on the surface of heteroepitaxial thin film system due to surface diffusion by considering the effects of both surface and interface stresses. Elastic stress field caused by curved surface is solved by using the constitutive equations of linear elasticity for the bulk and surface phases. Based on the method of superposition, a boundary perturbation technique, Goursat-Kolosov complex potentials and Muskhelishvili representations, the boundary value problem is reduced to the successive solution of a system of singular and hypersingular integral equations for any order of approximation. This solution and thermodynamic approach allows us to derive a governing equation which gives the amplitude changing of a surface roughness with time.

Interrupted self-organization of SiGe pyramids

We investigate the morphological evolution of SiGe quantum dots deposited on Si(100) during long-time annealing. At low strain, the dots' self-organization begins by an instability and interrupts when (105) pyramids form. This evolution and the resulting island density are quantified by molecular-beam epitaxy. A kinetic model accounting for elasticity, wetting, and anisotropy is shown to reproduce well the experimental findings with appropriate wetting parameters. In this nucleationless regime, a mean-field kinetic analysis explains the existence of nearly stationary states by the vanishing of the coarsening driving force. The island size distribution follows in both experiments and theory the scaling law associated with a single characteristic length scale.

Nonlinear dynamics of island coarsening and stabilization during strained film heteroepitaxy

Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and both perturbation analysis of the system and numerical simulations of the corresponding nonlinear dynamic equation governing the film morphological profile. Three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of island array stabilization, which corresponds to the formation of steady but nonordered arrays of strained quantum dots, occurs at later time for smaller misfit strain. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical studies on quantum dot coarsening and stabilization.

Shape evolution of a core-shell spherical particle under hydrostatic pressure

The morphological evolution by surface diffusion of a core-shell spherical particle has been investigated theoretically under hydrostatic pressure when the shear modulii of the core and shell are different. A linear stability analysis has demonstrated that depending on the pressure, shear modulii, and radii of both phases, the free surface of the composite particle may be unstable with respect to a shape perturbation. A stability diagram finally emphasizes that the roughness development is favored in the case of a hard shell with a soft core.

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and, second, due to an externally applied electric field normal to the film's free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes such as, e.g., spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films; when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and at the free surface.

A Numerical Study of Stress Controlled Surface Diffusion During Epitaxial Film Growth

A two-dimensional numerical simulation is performed to model the morphological evolution of a strained film growing heteroepitaxially on a substrate under simultaneous action of vapor deposition and surface diffusion. To facilitate numerical implementation, a continuum boundary layer model is proposed to account for the influence of film/substrate interface on the film growth pattern. Discussions are focused on the Stranski-Krastanow growth mode, although our model is capable of explaining Frank-van der Merwe and Volmer-Weber growth modes as well. Both first-order perturbation and numerical results are developed to demonstrate that the film surface tends to remain flat during the initial stage of growth and that surface roughening occurs once the film thickness exceeds a critical value, in consistency with experimentally observed patterns of S-K growth. Numerical results further show that, depending on the deposition rate, the surface evolution could lead to a steady state morphology, unstable cusp formation, or growing islands with flattened valleys.

The Stability of Lattice Mismatched Thin Films

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.

Strained Layer Growth: how do 3d Islands Relax Strains?

We study the elastic strain relaxation in highly strained layers deposited on a [001] substrate induced by coherent 3D islanding. We first calculate the elastic strain distribution within several pyramidal 3D islands with different faces (the observed ones being usually [114] or [014]). For this, we use a valence force field (VFF) description. Our calculation includes interactions between islands, which appear to be a key parameter. We study how the shape of the island modifies the strain relaxation which is proved to vary within the island. Very simple considerations on surface tension indicate why pyramidal islands are the most stable.

Continuum Modeling of Stress-Driven Surface Diffusion in Strained Elastic Materials

The free energy of a deformable crystal is assumed to consist of elastic strain energy and surface energy, and the chemical potential for surface diffusion at constant temperature is obtained under this assumption. The result is applied in considering the phenomena of instability of a flat surface in a stressed material under fluctuations in surface shape, and the development of surface roughness due to the proximity of misfit dislocations to the free surface of the material.

Kinetic versus strain formation of self-organized nanoholes in manganite thin films

We report on the formation of self-organized rows of pits in highly epitaxial La(2/3)Sr(1/3)MnO(3) thin films on top of substrates having different structural misfits by rf magnetron sputtering. The best-defined pits form in coherently grown films at a low misfit irrespective of its nature (tensile or compressive stress). It is also found that the pit rows align along the step edges, which indicates in-phase growth instability with the step edges, irrespective of the misfit. However, out-of-phase pit rows are also found when the terrace width increases due to a decrease of the miscut angle. Pit's volume scales inversely with the lattice mismatch suggesting that structural strain alone does not favor the formation of pits. The formation of pits is analyzed within a thermodynamic model.

Morphological evolution and ordered quantum structure formation in heteroepitaxial core--shell nanowires

We have performed three-dimensional dynamic simulations to study strain-driven morphological evolution and the formation of quantum structures on heteroepitaxial core--shell nanowire surfaces. Our simulations show that depending on geometric and material parameters, such as the radius of the wire, the thickness of the shell, and the mismatch strain, various surface morphologies including smooth core--shell nanowire surfaces, nanoring arrays, nanowire arrays, and ordered quantum dot arrays can be obtained by controlling initial surface configurations through prepatterning. It is also shown that these quantum structures may be trapped in a metastable state and may undergo a series of metastable state transitions during subsequent dynamic evolution. Our results identify possible pathways for fabrication of ordered quantum structures on the epitaxial core--shell nanowire surfaces and provide guidelines for achieving smooth core--shell structures.

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

In the present contribution we review basic mathematical results for three physical systems involving self-organizing solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e. time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different systems. First, we discuss the linear stability of homogeneous steady states, i.e. flat films, and second the systematics of non-trivial steady states, i.e. drop/hole states for dewetting films and quantum-dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly unrelated physical systems mathematically, but does allow as well for discussing model extensions in a more unified way.

Ordering of strained islands during surface growth

We study the morphological evolution of strained islands in growing crystal films by use of a continuum description including wetting, elasticity, and deposition. We report different nonlinear regimes following the elastic instability and tuned by the flux. Increasing the flux, we first find an annealinglike dynamics, then a slower but nonconventional ripening followed by a steady regime, while the island density continuously increases. The islands develop spatial correlations and ordering with a narrow two-peaked distance distribution and ridgelike clusters of islands at high flux.

Colloidal model system for island formation

We present model calculations to explore the possibility of colloidal island formation over strained surfaces. Colloids, aggregating due to attractive depletion interactions, are deposited onto a colloidal surface whose lattice constant and geometry can be varied by optical forces. This allows precise control of the strain between the substrate and the colloidal adsorbate. Three different strain fields are considered: fields with either an unidirectional or a hexagonal variation of strain, and fields with a combination of both variations. We find that the unidirectional field induces the formation of infinitely extended ridges, while hexagonal strain fields lead to regular pyramidal island structures which can be distorted in a controlled way by adding the unidirectional strain component. We furthermore study the dependence of island size on strain strength for the hexagonal strain pattern and find that the area occupied by an island is a constant fraction of the strain field's repeat unit.

Mesoscopic and microscopic modeling of island formation in strained film epitaxy

The instability of strained films for island formation is examined through an approach incorporating both discrete microscopic details and continuum mechanics. A linear relationship between the island wave number and misfit strain is found for large strains, while only in the small strain limit is a crossover to the continuum elasticity result obtained. A universal scaling relation accommodating all range of misfit strains is identified. Our results indicate that continuum mechanics may break down even at relatively small misfit stress due to the discrete nature of crystalline surfaces.

Coarsening, mixing, and motion: the complex evolution of epitaxial islands

During heteroepitaxy, misfit strain causes nanoscale islands to form spontaneously, as "self-assembled quantum dots." The growth and evolution of these islands are remarkably complex. We show that continuum modeling reproduces and explains many of the surprising phenomena observed experimentally. The free energy is reduced by both morphological change and alloy intermixing. However, because diffusion occurs only at the surface, the morphological and compositional evolution are strongly coupled. This leads to a complex dynamical response to the rather simple thermodynamic driving forces.

Effect of stress on the diffusion-controlled dissolution of a spherical particle

The diffusion-controlled dissolution of a spherical particle consisting in two epitaxially stressed solid phases of a substitutional binary alloy in contact with an undersaturated solution is investigated. A linear stability analysis of the solid-liquid interface demonstrates that a morphological instability of the particle may occur due to the epitaxial stress generated by the spherical precipitate embedded in the solid matrix, the liquid pressure being neglected. The critical radius of the particle below which the interface is unstable is determined and the conditions for the roughness development are discussed.

Instabilities and coarsening of stressed crystal surfaces in aqueous solution

Strong pattern formation occurs on polished miscut surfaces of sodium chlorate (NaClO3) single crystals that are uniaxially stressed perpendicular to the step edge direction and placed in a saturated aqueous solution. The wavelength lambda of the stress-induced surface instability increased continuously in experiments up to 9 days after placed in the solution. There were three successive regimes of coarsening: (i) one-dimensional step bunching with lambda approximately t(1/4) until an undulation transition was reached, (ii) a two-dimensional coarsening mechanism with lambda approximately t(1/2), and a gradual transition to (iii) Ostwald ripening-like coarsening with lambda approximately t(1/3). The coarsening of the surface patterns towards a stable, flat surface implies the spontaneous formation of a stress-free skin on the surface of the stressed solid.

Shape and composition map of a prepyramid quantum dot

We present a theory for the shape, size, and nonuniform composition profile of a small prepyramid island in an alloy epitaxial film when surface diffusion is much faster than deposition and bulk diffusion. The predicted composition profile has segregation of the larger misfit component to the island peak, with segregation enhanced by misfit strain and solute strain but retarded by alloy solution thermodynamics. Vertical composition gradients through the center of the island due to this mechanism are on the order of 2%/nm for Ge(X)Si(1-X)/Si and 10-15%/nm for In(X)Ga(1-X)As/GaAs.

Influence of pulsed laser heating on morphological relaxation of surface ripples

A continuum (Mullins-type) model is proposed for the nonisothermal, isotropic evolution of a crystal surface on which mass transport occurs by surface diffusion. The departure from constant temperature is assumed induced by incident pulsed radiation. It has been shown experimentally and theoretically [see, e.g., Yakunkin, High Temp. 26, 585 (1988); Yilbas and Kalyon, J. Phys. D. 34, 222 (2001)] that such a heating mode gives rise to the quasistationary regime, in which the surface temperature of a thick solid film oscillates about the mean value with the pulse repetition frequency. The implications of oscillatory driving with high frequency values on relaxation of surface ripples are examined; in particular, the traveling wave solutions with decreasing amplitude are detected numerically. Pulsed heating also results in faster smoothing of the ripple, compared to the case when the surface is at constant temperature which is same as the mean temperature in the pulsed heating mode. Impact on ripple shape is minor for ripple amplitudes considered.

Roughening rates of strained-layer instabilities

We study the evolution of the morphology of Si0.75Ge0.25 strained layers using a wide range of deposition times, 60<tau<2400 s, at 600 degrees C on laser textured substrates with miscuts theta<15 degrees off Si(001). Ripple-shaped morphologies form spontaneously on miscuts along the 110 directions. At the shortest deposition times, roughening is suppressed as predicted by a linear stability analysis that uses previously measured values for the mass transport rate on the surface. The measured time constant of the roughening is approximately 80 s, a factor of 4 larger than predicted by theory.

Origin of apparent critical thickness for island formation in heteroepitaxy

We find that a continuum model of heteroepitaxy exhibits a sharp crossover with increasing coverage, from planar growth to island formation. The "critical thickness" at which this Stranski-Krastanov transition occurs depends sensitively on misfit strain, with a dependence strikingly similar to that seen experimentally. The initial planar growth occurs because of intermixing of deposited material with the substrate. While the transition is strictly kinetic in nature, it depends only weakly on growth rate. The role of surface segregation is also discussed.

Self-organization of quantum dots in epitaxially strained solid films

A nonlinear evolution equation for surface-diffusion-driven Asaro-Tiller-Grinfeld instability of an epitaxially strained thin solid film on a solid substrate is derived in the case where the film wets the substrate. It is found that the presence of a weak wetting interaction between the film and the substrate can substantially retard the instability and modify its spectrum in such a way that the formation of spatially regular arrays of islands or pits on the film surface becomes possible. It is shown that the self-organization dynamics is significantly affected by the presence of the Goldstone mode associated with the conservation of mass.

Faceting of a growing crystal surface by surface diffusion

Consider faceting of a crystal surface caused by strongly anisotropic surface tension, driven by surface diffusion and accompanied by deposition (etching) due to fluxes normal to the surface. Nonlinear evolution equations describing the faceting of 1+1 and 2+1 crystal surfaces are studied analytically, by means of matched asymptotic expansions for small growth rates, and numerically otherwise. Stationary shapes and dynamics of faceted pyramidal structures are found as functions of the growth rate. In the 1+1 case it is shown that a solitary hill as well as periodic hill-and-valley solutions are unique, while solutions in the form of a solitary valley form a one-parameter family. It is found that with the increase of the growth rate, the faceting dynamics exhibits transitions from the power-law coarsening to the formation of pyramidal structures with a fixed average size and finally to spatiotemporally chaotic surfaces resembling the kinetic roughening.

Competing classical and quantum effects in shape relaxation of a metallic island

Pb islands grown on a Si substrate transform at room temperature from a flattop facet geometry into an unusual ring shape. The volume-preserving mass transport is catalyzed by the electrical field from the tip of a scanning tunneling microscope. The ring morphology results from the competing classical and quantum effects in the shape relaxation. The latter is enhanced by the large anisotropy of the effective mass, and leads to a sequential strip-flow growth on alternating strips of the same facet defined by substrate steps, showing its dynamical impact on the stability of a nanostructure.

Facet growth under stress: the limits of strained-layer stability

A crystal facet is metastable under stress, but the process of growth or sublimation roughens the facet and is expected to render it unstable. This poses a fundamental limit for heteroepitaxial growth of planar layers, e.g., in semiconductor devices. An analysis shows that this facet-growth instability can be suppressed to an arbitrary degree by growing slowly. Moreover, the local stress ("force dipole") inherent in atomic steps introduces a new, purely kinetic effect that dominates at low strain and can render planar growth dynamically stable.

Wetting layer thickness and early evolution of epitaxially strained thin films

We propose a physical model which explains the existence of finite thickness wetting layers in epitaxially strained films. The finite wetting layer is shown to be stable due to the variation of the nonlinear elastic free energy with film thickness. We show that anisotropic surface tension gives rise to a metastable enlarged wetting layer. The perturbation amplitude needed to destabilize this wetting layer decreases with increasing lattice mismatch. We observe the development of faceted islands in unstable films.

Enhanced instability of strained alloy films due to compositional stresses

A single-component strained film is known to be unstable to the stress-driven morphological instability. Here, we determine how the instability is modified in an alloy film by considering the effect of compositional stresses due to an atomic size difference. We find that the coupling of composition to stress always makes the film more unstable to the formation of stress-driven surface undulations. The destabilization is greatest over a range of intermediate deposition rates.

Electromigration in Al thin films induced by surface acoustic waves: application to imaging

The propagation of a high amplitude surface acoustic wave in an Al thin film induces a large-scale electromigration phenomenon resulting in a permanent etching of the acoustic field in the film. The etched patterns depend on the time of propagation and on the acoustic characteristics. Preliminary observations of a few grooved structures in Al films have been performed by different techniques. A first explanation of this phenomenon based on dynamical Grinfeld instabilities is proposed. By providing permanent pictures of acoustic fields emitted by transducers, this effect could be used to perform imaging of surface acoustic wave propagation.