Stress-induced Instability Research Articles

Undulatory Delamination of Thin Polymer Films on Gold Surfaces

Using two-dimensional surface plasmon resonance measurements, we have observed the formation of traveling waves in the delamination of thin films of polydimethylsilane (PDMS) exposed to methanol. Films were spin-coated on a gold surface and the methanol was added to the top surface. The stress-induced instability caused by the swelling of the PDMS thin film when its edge is pinned to the gold surface leads to wrinkle formation and propagation at the interface. The periodic pattern is thought to be the result of an Asaro-Tiller-Grinfeld (ATG) instability.

Stress-induced surface instability of an elastic layer

The surface evolution of an elastic layer subjected to a far-field uniform tensile stress is analyzed by using a linear perturbation theory. The atomic transport mechanism controlling the surface evolution is the gradient of chemical potential associated with elastic strain energy and surface curvature. The critical spatial frequency of unstable surface perturbations is a function of the thickness of the elastic layer, surface energy, Young’s modulus of the elastic layer, and the applied tensile stress. For thin films, the critical spatial frequency is inversely proportional to the square root of the film thickness and proportional to the applied stress, while it is proportional to the square of the applied stress and independent of the layer thickness for thick films.

Temperature effect on surface roughening of thin films

The effect of the deposition temperature on the surface roughness and the growth exponent of thin films in the early growth time regime has been studied using a linear continuum model. Surface diffusion and three commonly observed roughening mechanisms, namely, shot noise, the Ehrlich–Schwobel (ES) effect, and the stress-induced instability, are step-by-step incorporated into the model to analyze the temperature effect in different cases. It has been revealed that when the thermal activated surface diffusion is operative, the surface roughness of the films without the stress effect will decrease with deposition temperature. In addition, a rougher film surface caused by the ES effect can also be observed at low temperatures. If stress exists due to a lattice mismatch at the film/substrate interface, however, high deposition temperatures may result in an unstable growth with the roughness increasing with temperature. Our analyses have also found that the growth exponent is strongly temperature dependent, and the film growth may fall into three or four temperature regions depending on whether the stress effect is present or not: (1) low-temperature region with a fixed growth exponent of 0.5 or slightly larger than 0.5 due to the ES effect; (2) a middle crossover temperature region with the growth exponent decreasing with temperature from 0.5 (or slightly larger than 0.5) to 0.25; (3) high-temperature region characterizing by noisy Mullins diffusion equation with a constant growth exponent of 0.25; and (4) if stress exists during film growth, at the high-temperature region where the stress-induced morphology instability begins to operate the growth exponent will be larger than 0.25 and increase with temperature.

Phase-field modeling of stress-induced surface instabilities in heteroepitaxial thin films

A phase-field model for investigating the surface morphological evolution of a film is developed, taking into account the surface energies of film and substrate, the interfacial energy between the film and substrate, and the elastic energy associated with the lattice mismatch between the film and substrate. Using the lattice mismatch and the surface energies for the Ge∕Si heteroepitaxial system, the morphology of islands and the formation of a wetting layer are investigated using two-dimensional simulations. The results show that the wetting angle increases continuously with the increase in the lattice mismatch, and the surface angle of the island on wetting layer varies with the island size. It is demonstrated that the anisotropy of elastic interactions alone is not sufficient to cause surface angle discontinuity or faceting that is observed in experiments.

Molecular architecture of a eukaryotic DNA transposase

Mobile elements and their inactive remnants account for large proportions of most eukaryotic genomes, where they have had central roles in genome evolution. Over 50 years ago, McClintock reported a form of stress-induced genome instability in maize in which discrete DNA segments move between chromosomal locations. Our current mechanistic understanding of enzymes catalyzing transposition is largely limited to prokaryotic transposases. The Hermes transposon from the housefly is part of the eukaryotic hAT superfamily that includes hobo from Drosophila, McClintock's maize Activator and Tam3 from snapdragon. We report here the three-dimensional structure of a functionally active form of the transposase from Hermes at 2.1-A resolution. The Hermes protein has some structural features of prokaryotic transposases, including a domain with a retroviral integrase fold. However, this domain is disrupted by the insertion of an additional domain. Finally, transposition is observed only when Hermes assembles into a hexamer.

Theory of superplasticity in polycrystalline materials: Stress-induced structural instabilities of grain boundaries

Theory of superplasticity in polycrystalline materials: Stress-induced structural instabilities of grain boundaries

Atomic pattern formation at the onset of stress-induced elastic instability: Fracture versus phase change

A systematic theoretical study is presented of the stress-induced structural response of initially cubic single crystals to uniaxial [100] loading based on elastic stability analysis and isostress molecular-dynamics simulations through a classical description of interatomic interactions in model metallic crystals. Special emphasis is placed on the study of the atomic pattern formation characteristics in the crystal's structural response to loading at and beyond the onset of elastic instability. The instability is reached at a rigorously defined critical stress level that occurs in association with the vanishing of a shear modulus, i.e., when ${C}_{22}∕{C}_{23}\ensuremath{-}1=0$, where ${C}_{rs}$ are stress-dependent elastic moduli. Although the atomic mechanism for the onset of instability is invariant, two divergent atomic processes are found to occur beyond the onset of instability, depending on subtle differences in the elastic properties of the crystals. Our analyses and simulations of a crystal model with the relatively small initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.41$ (based on the elastic moduli of copper) reveal an inhomogeneous structural transformation mechanism, through the creation of individual rotating domains that lead to formation of a new hexagonal single crystal without loss of strength. This theoretical result is consistent with what is known experimentally for metals with relatively small values of $({C}_{22}∕{C}_{23}\ensuremath{-}1)$, e.g., certain copper alloys and the alkali metals, which can undergo various cubic-to-hexagonal structural transformations. However, a crystal model based on the elastic moduli of nickel, with the larger initial value of ${C}_{22}∕{C}_{23}\ensuremath{-}1=0.73$, fails to exhibit domain rotation beyond the onset of elastic instability and, as a result, the initial destabilization of the crystal structure then leads to fracture.

Ge dots self-assembling: Surfactant mediated growth of Ge on SiGe (118) stress-induced kinetic instabilities

The ordering of islands on naturally or artificially nanostructured surfaces is one of the most recent objectives among actual nanotechnology challenges. We show in this letter that, by a combination of two approaches, i.e., a two-step molecular beam epitaxy (MBE) deposition process and surfactant-mediated growth, we are able to obtain chains of nicely ordered ultrasmall islands of lateral size below 50 nm. The two-step MBE process consists of vicinal Si(001) surface self-patterning by SiGe growth instability and Ge dot ordering by subsequent Ge deposition on a SiGe template layer. The surfactant-mediated growth consists of submonolayer Sb deposition prior to Ge growth, in order to reduce the island size up to 25 nm. The best ordering of Ge islands is obtained when the island size matches the wavelength of the template layer.

Decreased expression of the DNA mismatch repair gene Mlh1 under hypoxic stress in mammalian cells.

The hypoxic tumor microenvironment has been shown to contribute to genetic instability. As one possible mechanism for this effect, we report that expression of the DNA mismatch repair (MMR) gene Mlh1 is specifically reduced in mammalian cells under hypoxia, whereas expression of other MMR genes, including Msh2, Msh6, and Pms2, is not altered at the mRNA level. However, levels of the PMS2 protein are reduced, consistent with destabilization of PMS2 in the absence of its heterodimer partner, MLH1. The hypoxia-induced reduction in Mlh1 mRNA was prevented by the histone deacetylase inhibitor trichostatin A, suggesting that hypoxia causes decreased Mlh1 transcription via histone deacetylation. In addition, treatment of cells with the iron chelator desferrioxamine also reduced MLH1 and PMS2 levels, in keeping with low oxygen tension being the stress signal that provokes the altered MMR gene expression. Functional MMR deficiency under hypoxia was detected as induced instability of a (CA)(29) dinucleotide repeat and by increased mutagenesis in a chromosomal reporter gene. These results identify a potential new pathway of genetic instability in cancer: hypoxia-induced reduction in the expression of key MMR proteins. In addition, this stress-induced genetic instability may represent a conceptual parallel to the pathway of stationary-phase mutagenesis seen in bacteria.

Stress-induced suppression of piezoelectric properties in PbTiO3:La thin films via scanning force microscopy

Sol-gel derived polycrystalline La-doped PbTiO3 films are investigated by scanning force microscopy (SFM) in a piezoelectric contact mode. The SFM signal proportional to the effective piezoelectric coefficient, deff, is measured inside individual domains as a function of the mechanical force exerted by the SFM tip on the film’s surface. It is found that the piezoelectric signal can be fully suppressed under sufficiently high force (∼20–22 μN). The suppression is qualitatively different for domains of opposite polarities where deff may change its sign depending on the orientation of polarization vector. The piezoelectric hysteresis loops acquired under increasing force gradually shrink with an asymmetric decrease of the piezoelectric coefficients. This leads to a pronounced vertical shift of the loops (deff offset). The obtained results are discussed in terms of the competing electrostatic and piezoelectric contributions to the measured signal and stress-induced polarization instabilities in the vicinity of the SFM tip.

Dislocations and morphological instabilities: Continuum modeling of misfitting heteroepitaxial films

We present a continuum model of nonequilibrium heterogeneous elastic systems, which includes both smooth and singular strains, as well as their coupling to free surfaces, in two spatial dimensions. It accurately includes nucleation, interactions, and dynamics of dislocations. In particular, we demonstrate that the model recovers the well-known Matthews-Blakeslee critical thickness for the nucleation of misfit dislocations. For misfitting heteroepitaxial films above the critical thickness, dislocations compete with the stress-induced instability of the film-vapor interface as a strain-relief mechanism. At early times, the dislocations slow down the initial instability by climbing to the film-substrate interface and relaxing the misfit strain partially. However, the late-time morphology is determined by the strong interaction between the stress concentration at the bottom of the grooves and the singular stresses due to dislocations.

Generic degradation mechanism for 980 nm InxGa1−xAs/GaAs strained quantum-well lasers

We have observed In out diffusion from strained InxGa1−xAs quantum wells into the adjacent GaAs barriers in degraded 980-nm-wavelength strained quantum-well lasers. A previous calculation on misfit stress-induced compositional instability indicates that this material system is stable with respect to misfit strain. Therefore, the out diffusion of In from an InxGa1−xAs quantum well is mainly driven by the compositional discontinuity across the well/barrier heterointerfaces, and is believed to be activated by the nonradiative recombination of injected carriers.

Phase-field modeling of stress-induced instabilities.

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. Using a formulation that is independent of the state of reference chosen for the displacement field, we write down the elastic energy in an unambiguous fashion, thus obtaining an entire class of models. According to the choice of reference state, the particular model emerging from this class will become equivalent to one of the two independently constructed models on which brief accounts have been given recently [J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999); K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999)]. We show that our phase-field approach recovers the sharp-interface limit corresponding to the continuum model equations describing the Asaro-Tiller-Grinfeld instability. Moreover, we use our model to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by reproducing some known results and by comparison with a sharp-interface simulation. We then proceed to investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wave numbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion. In the absence of gravity, the end state of a laterally finite system is a single groove growing at constant velocity, as long as no secondary instabilities arise (that we have not been able to see with our code). With gravity, several grooves are possible, all of which are bound to stop eventually. A laterally infinite system approaches a scaling state in the absence of gravity and probably with gravity, too.

Morphological instability of growth fronts due to stress-induced mobility variations

We report a comparison between theory and experiment for a general stress-induced morphological growth instability that is kinetically rather than energetically driven. Stress variations along a perturbed planar growth front result in variations in interfacial mobility in a manner that is destabilizing under one sign of the stress state and stabilizing under the opposite sign, even for a pure material. Investigation of solid-phase epitaxial growth at a corrugated Si(001) interface under both compression and tension results in good agreement between experiment and theory with no adjustable parameters, demonstrating that this mobility-based mechanism is dominant in determining morphological evolution in this system.

On Kinetically vs. Energetically Driven Growth Instabilities in Solid and Vapor Phase Epitaxy

ABSTRACTA stress-induced kinetically-driven morphological instability is of general applicability to driven systems. The effect of stress on the reaction mobility for incorporation into the growing solid couples to stress variations along a perturbed planar growth front, resulting in amplification or decay of the perturbation depending on the sign of the stress. Experimentally we studied a model system in which stress is applied externally to a chemically pure substance, permitting us to isolate the effect of strain from any possible effects of composition, and found that the new kinetically-driven effect dominates the behavior for solid phase epitaxial growth (SPEG) of Si(001). A linear stability analysis of a sinusoidally perturbed planar growth front, incorporating both the kinetically and the energetically driven effects, has been performed. Stability maps are developed, indicating parameter ranges under which the morphological evolution is dominated by the energetically-driven instability, the kinetically-driven instability, and the kinetically-driven stabilization. Numerical values of the key dimensionless parameters for SPEG and for SiGe/Si(001) Molecular Beam Epitaxy (MBE) are very similar in cases where they are known, indicating that the kinetically-driven effect may be important in determining morphological evolution related to quantum dot formation in MBE as well

SURFACE ROUGHENING OF HETEROEPITAXIAL THIN FILMS

▪ Abstract Heteroepitaxial structures with strained semiconductor thin films are widely used in electronic and optoelectronic devices. One of the more important defect creation processes in these films is related to a stress-induced morphological instability that tends to roughen the film surface by mass diffusion during film growth or annealing. Interestingly, the same mechanism of surface roughening can be utilized for fabrication of quantum dot devices. This article gives an overview of a series of theoretical and experimental studies on surface roughening in heteroepitaxial films. It is shown that the strain caused by lattice mismatch drives the diffusional atomic flux along the film surface in such a way that an initially flat film evolves into an undulating profile with cusp-like surface valleys with singular stress concentration near the cusp tip. The essential features of this evolution process are described by a family of mathematical curves called cycloids. The fundamental length and time scales associated with surface roughening can be obtained from thermodynamic and kinetic considerations. The stress concentration at cycloid-like surface valleys caused by roughening is found to create dislocations of various characters that participate in the overall strain relaxation of a heterostructure.

Novel dislocation structure and surface morphology effects in relaxed Ge/Si-Ge(graded)/Si structures

The defect structure in relaxed graded Ge/GexSi1−x/Si structures grown on (001) exact and (001) off-cut substrates using ultra-high vacuum chemical vapor deposition was characterized using transmission electron microscopy (TEM), atomic force microscopy, and electron beam induced current. The samples grown on off-cut (001) substrates showed a remarkable improvement in surface roughness and dislocation pile-up densities. By applying both a dislocation blocking criterion and surface roughness to graded Si-Ge/Si(001) structures, we can predict the formation of dislocation pile-ups in graded structures. Nonparallel misfit dislocation networks in off-cut wafer samples are not as efficient at blocking perpendicular dislocation motion, leading to a large reduction in dislocation pile-up density. The lower pile-up density on layers grown on off-cut wafers results in less stress-induced surface instability during growth, leading to surfaces with much lower roughness. TEM studies revealed that the array of 60° dislocations, that usually forms to relieve the misfit stress, transforms into a lower energy hexagonal dislocation network consisting of edge dislocations with Burgers vectors of the type 1/2〈110〉, 1/2〈1̄10〉, and 〈100〉. Such reactions were found to be more prevalent in the samples grown on off-cut substrates. Favorable intersections of {111} type planes on the off-cut substrates were found to aid such reactions.

Misfit stress-induced compositional instability in hetero-epitaxial compound semiconductor structures

We have calculated the effect of misfit stress on the compositional stability of strained-layer hetero-epitaxial compound semiconductor structures. For uniformly stressed layers, a simple formula is derived for the change in chemical potential of the lattice atoms diffusing across the hetero-interface. An increase in the total chemical potential indicates that interdiffusion of the specific elements is thermodynamically unfavorable and therefore the composition of the structure is stable with respect to the misfit stress-induced interdiffusion of the specific elements. On the other hand, a decrease in the total chemical potential indicates that the interdiffusion will be driven by the misfit stress and the composition of the heterostructure is unstable. Various strain-layer systems of III–V compound semiconductors such as In1−xGaxAsyP1−y/InP, In1−xGaxAsyP1−y/GaAs, (Al1−xGax)yIn1−yP/GaAs, (Al1−xGax)yIn1−yAs/GaAs, In1−xGaxP/GaAs, In1−xGaxSb/InP, etc., are examined and their stability is discussed.

Some general properties of stress-driven surface evolution in a heteroepitaxial thin film structure

Heteroepitaxial thin films are subjected to very large stresses, typically in the giga-Pascal range, due to lattice mismatch. Their applications in microelectronic devices have drawn a growing research effort which involves, in part, a better understanding of the processes by which defects such as cracks and dislocations are nucleated in a thin layer structure. One of the possible defect mechanisms is related to a stress-induced morphological instability which tends to roughen the film surface by mass diffusion during film growth or annealing. A major objective of this paper is to show that a few invariance properties of the strain energy density and the chemical potential in a heteroepitaxial structure can be utilized to obtain some valuable information concerning the equilibrium profile, the stress concentration and the formation of cusp-like stress singularities without having to resort to full-scale numerical studies. The process of cusp-formation requires a critical film thickness H cr which is independent of the Matthews critical thickness h er for misfit dislocation formation by propagation of threading dislocations within the film. Calculations show that H cr is significantly larger than h cr for a wide range of misfit strain, suggesting that nucleation of threading dislocations via cusp-formation could be critical in the overall process of strain relaxation in this type of film. Finally, a “phase” diagram is constructed to categorize important consequences of the surface evolution based on the instability wavelength and average film thickness.

WELL-BORE INSTABILITY IN THE NORTH WEST SHELF OF AUSTRALIA

Well-bore instability, experienced mainly in shales, has resulted in significant drilling delays and abandonment of wells in the North West Shelf of Australia. Although these problems may be induced by physico-chemical interactions, there is an increasing awareness that instability in this region is principally associated with in situ stresses that are high relative to the strength of the materials.This paper describes the research undertaken by the Australian Petroleum Cooperative Research Centre to assist industry in understanding and managing stress-induced well-bore instability in this region. To conduct such stability analyses the basic information required includes knowledge of the orientation and magnitude of the principal in situ stresses and the strength and deformation response of the materials to stress changes imposed by drilling. The required data can be determined using welllogging, analytical and laboratory techniques.Analytical methods can be used to examine the relationship between well-bore stability and changes introduced through drilling. Spreadsheets based on the analytical methods have been produced and applied to the assessment of drilling alternatives and/or design of some well-bores in the North West Shelf.The application of the critical mud weight contour plots and mud weight stability profiles produced by the spreadsheets in assessing drilling alternatives, selection of optimum well-bore alignment and mud weight design are demonstrated through examples. The analyses showed that counter to intuitive expectations, an inclined well may be more stable than a vertical well depending on the well-bore direction, deviation angle and stress regime.