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To understand the origins of stress in thin films, we have used wafer curvature to measure the stress evolution during electrodeposition of Ni on lithographically patterned Si substrates. The stress is measured as the hemispherical islands grow and impinge upon each other, forming interfacial boundaries between them.We relate the results to a model for polycrystalline films in which the stress is attributed to competing processes occurring where the layers in adjacent grains grow into each other and form new segments of grain boundary. This model predicts that the stress in each layer depends on the rate at which the grain boundary is growing when that layer is incorporated into the film. The calculations agree with the measured stress vs thickness using a single set of fitting parameters for five different growth rates. [ABSTRACT FROM AUTHOR]

During deposition, many thin films go through a range of stress states, changing from compressive to tensile and back again. In addition, the stress depends strongly on the processing and material parameters. We have developed a simple analytical model to describe the stress evolution in terms of a kinetic competition between different mechanisms of stress generation and relaxation at the triple junction where the surface and grain boundary intersect. The model describes how the steady state stress scales with the dimensionless parameter D/LR where D is the diffusivity, R is the growth rate, and L is the grain size. It also explains the transition from tensile to compressive stress as the microstructure evolves from isolated islands to a continuous film. We compare calculations from the model with measurements of the stress dependence on grain size and growth rate in the steady state regime and of the evolution of stress with thickness for different temperatures. [ABSTRACT FROM AUTHOR]

In situ stress measurements during molecular-beam epitaxy growth of InxGa1-xAs/GaAs provide insight into the relaxation behavior of thin films grown on mismatched substrates. Strain relaxation in the materials studied occurs due to the formation and glide of dislocations. Measurements of additional relaxation during growth interruptions show that relaxation is kinetically limited during the early stages of growth. In thicker films, the residual strain is not significantly affected by growth conditions. We find that relaxation in thick layers does not proceed as far as predicted by models which consider the formation of dislocation arrays or dislocation blocking, and we discuss this discrepancy between theory and experiment. We discuss the effect of a nonuniform dislocation array configuration on the overall relaxation behavior. Results from dislocation dynamics simulations are presented which provide evidence that nonuniform dislocation array distributions limit the extent of plastic relaxation. [ABSTRACT FROM AUTHOR]

This article describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, and noncontact technique for the measurement of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 μm) deposited on thin circular silicon wafers (105 μm) of "large" in-plane dimensions (50.8 mm in diameter) subjected to thermal loading histories. The loading and geometry is such that the system experiences deformations that are clearly within the nonlinear range. The discussion is focused on investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and finally, on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch! strain. Results obtained on the basis of both simple models and more-detailed finite-element simulations are compared with the full-field CGS measurements with the purpose of validating the analytical and numerical models. © 2001 American Institute of Physics. This article describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, and noncontact technique for the measurement of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 μm) deposited on thin circular silicon wafers (105 μm) of "large" in-plane dimensions (50.8 mm in diameter) subjected to thermal loading histories. The loading and geometry is such that the system experiences deformations that are clearly within the nonlinear range. The discussion is focused on investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and t! he substrate c... [ABSTRACT FROM AUTHOR]

In the early stage of growth of a metal film on a substrate by the Volmer-Weber mechanism, a tensile stress in the film is observed to arise at about the point in the process when islands of deposited material begin to coalesce. The mechanism commonly proposed as the origin of this tensile stress is that the coalescing islands deform in order to form a relatively low energy grain boundary, at the expense of some surface energy by surface area reduction, and that this proceeds until a stress is generated that has magnitude sufficient to prevent further area reduction. Several models have been proposed for this process, but the inferred tensile stress estimates have been much larger than observed stress magnitudes in many cases. The purpose here is to introduce a model for the process based on the theory of contact of elastic solids with cohesion. A description of the process is developed on this premise for one-dimensional, two-dimensional, and three-dimensional states of deformation of coalescing islands. It is found that the latter case leads to an estimate of film stress generally consistent with observations. The features of the model for different dimensionalities are compared and contrasted with each other, as well as with other models which have been proposed for this process. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A combined analytical and computational model is developed to study the mechanics of strained epitaxial island growth in typical semiconductor systems. Under certain growth conditions in systems with a film/substrate lattice mismatch, deposited material is known to aggregate into islandlike shapes with geometries having arc shaped cross-sections. A two-dimensional model assuming linear elastic behavior is used to analyze an isolated arc shaped island with elastic properties similar to those of the substrate. The substrate is assumed to be much larger than the island. Finite element analysis shows that in order to minimize the total energy, which consists of strain energy, surface energy, and film/substrate interface energy, a coherent island will adopt a particular height-to-width aspect ratio that is a function of only the island volume. It is then shown that for an island with volume greater than a certain critical size, the inclusion of a mismatch strain relieving edge dislocation is favorable. The criterion for the critical size is based on a comparison of the configurational forces acting on the edge of the island in the presence of an edge dislocation. Finally, a finite element calculation combined with an analytical treatment of the singular dislocation fields is used to determine the minimum energy island aspect ratio for the dislocated island/substrate system. The combination of the minimum energy morphology studies for the coherent and dislocated systems with the dislocation nucleation criterion gives a complete model for strained epitaxial island growth which can serve as a basis for interpretation of experiments. [ABSTRACT FROM AUTHOR]

Presents a study which used simple theoretical models to investigate the possible mechanisms of void growth in interconnect lines with a bamboo grain structure. Features of a typical interconnect line; Equations that govern the behavior of the material in the interconnect line; Equations and boundary conditions which determine the stress and deformation in the model of the line.

Analyzes the glide of a dislocation extending from the free surface of the layer to the layer-substrate interface. Information on the driving force on a threading dislocation; Effect of an intersecting misift dislocation; Conclusions.

Studies the role of dislocation blocking in limiting strain relaxation in heteroepitaxial films. Effect of the interactions of parallel dislocations on the residual strain; Analysis of theoretical misfit strains; Discussion of the theory based on the energy of a parallel array of interacting dislocations.

Presents information on a study that used picosecond ultrasonics techniques to examine the vibrations of several nanostructures composed of laterally patterned gold films on fused quartz substrates. Experimental procedure; Results and discussion on the study.

Focuses on a study which proposed a fundamental definition of excess stress as the particular stress measure which is work-conjugate to the Burgers displacement during glide of a threading dislocation in a strained layer. Concept of excess stress; Comparison with definitions of effective stress in kinetic laws of glide in bulk materials.

An integral-equation approach is utilized in numerically determining dispersion relations for guided surface waves on an elastic half space. The surface waveguide problem is first cast as a partial-differential-equation boundary-value problem whereupon an application of the bilateral Laplace transform enables transformed displacement to be determined as a function of transformed stress. By inverting the transformed displacement directly and incorporating the boundary conditions, one can obtain an integral-equation formulation of the boundary-value problem which is analyzed numerically to yield dispersion relations. The problem which is considered assumes that an elastic half space is in contact with two rigid smooth barriers. A waveguide is formed by arranging the barriers so that a strip on the surface of uniform width is traction free. It is demonstrated that a valid simplification in waveguide problems is that body-wave disturbances, localized in the vicinity of each edge of the guide, have negligible effect on the reflection of surface waves at the opposite edge of the guide. [ABSTRACT FROM AUTHOR]

We report on calculations of the formation energies of several [100] and [110] oriented step structures on biaxially stressed Si and Ge (001) surfaces. It is shown that a novel rebonded [100] oriented single-height step is strongly stabilized by compressive strain compared to most well-known step structures. We propose that the side walls of "hut"-shaped quantum dots observed in recent experiments on SiGe/Si films are made up of these steps. Our calculations provide an explanation for the nucleationless growth of shallow mounds, with steps along the [100] and [110] directions in low- and high-misfit films, respectively, and for the stability of the (105) facets under compressive strain. [ABSTRACT FROM AUTHOR]

The physical system under study is a single crystal film grown epitaxially on a substrate of comparable thickness which is constrained to remain flat. In general, the layers are strained due to a mismatch in lattice parameter between the film and substrate materials. The free energy change of the system due to formation of strain-relaxing interface misfit dislocations is estimated, and the discriminating case of zero energy change leads to a critical thickness condition on mismatch strain, film thickness, substrate thickness, and crystallographic slip orientation which is necessary for the spontaneous formation of such dislocations. The condition obtained generalizes the Matthews–Blakeslee (MB) criterion for a thin film on a thick substrate to the case of a complaint substrate/epitaxial film system, and it reduces to the MB criterion when either the film or substrate is relatively thick. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An asymptotic analysis of the grazing-incidence problem is made for the point where the traction-free boundary of an elastic solid intersects the front of the plane pulse propagating parallel to it. [ABSTRACT FROM AUTHOR]

Dynamic self-organization of coherently strained islands during SiGe molecular beam epitaxy on Si(001) is measured in real time using a novel spectroscopic light scattering technique. We show that an array of hut clusters self-orders on a square mesh with increasing areal coverage. Ordering occurs to minimize the repulsive elastic interactions between neighboring islands. Self-organization breaks down when islands coalesce during deposition or during static coarsening. © 1998 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Resonant tunneling measurements are used to probe the inhomogeneous strain in individual SiGe quantum dots. Current–voltage characteristics of strained Si/SiGe resonant tunneling diodes of diameter D≤0.25 μm exhibit additional fine quasi-periodic structure in the resonant peaks. The fine structure is consistent with lateral quantization in the SiGe quantum well due to in-plane confining potentials arising from inhomogeneous strain, which we calculate by finite element techniques for various D. Quenching of the fine structure by a magnetic field is consistent with the effective length scale of the strain-induced potential. © 1998 American Institute of Physics. [ABSTRACT FROM AUTHOR]