The Critical Thickness of the Dislocation-Free Stranski Krastanow Pattern of Growth.

1992 ◽  
Vol 290 ◽  
Author(s):  
Michael A. Grinfeld
Keyword(s):  
Surface Tension ◽  
Critical Thickness ◽  
Epitaxial Films ◽  
Shear Stresses ◽  
Morphological Stability ◽  
Free Boundaries ◽  
Equilibrium Thermodynamics ◽  
Misfit Stress ◽  
Symmetry Change

AbstractIt was demonstrated earlier [1,2] in the framework of equilibrium thermodynamics that the morphological stability of the free boundaries and interfaces in crystals is extremely sensitive to the presence of shear stresses. Relying on that idea we have established the formula H = μσ/τ2 of a critical thickness of solidifying He4 films and of the dislocation-free Stranski-Krastanow growth of epitaxial films (where σ – the coefficient of surface tension, μ - the shear module of the crystal, τ - the external or misfit stress). In this report we present certain facts pertaining to possible patterns of the growing corrugations and introduce the second critical thickness at which a symmetry change in the patterns has to occur.

Pilgrim Trust Lecture, Molecular layers

1939 ◽  
Vol 170 (940) ◽  
pp. 1-39 ◽  
Keyword(s):  
Surface Tension ◽  
Olive Oil ◽  
Water Surface ◽  
Organic Molecules ◽  
Critical Thickness ◽  
Clean Water ◽  
Oily Contamination ◽  
Molecular Layers ◽  
Modern Work

If fragments of camphor are placed upon a clean water surface they move about vigorously and may even be made to propel toy boats. The late Lord Rayleigh (1890 a, 1890 c) found that these movements stopped rather abruptly if the surface tension of the water was lowered by 21 dynes/cm. by oily contamination of the surface. The amount of olive oil needed for this purpose was surprisingly small, corresponding to a thickness of only 16 A (16 x 10 -8 cm.). Miss Pockels (1891) proved that any amount of olive oil less than enough to give a critical thickness of about 10 A had no effect whatever on the surface tension of water, but above this limit the surface tension decreased rapidly as the amount of oil was increased. Only 5 g. of olive oil would be needed to cover an acre of water surface with a film of this critical thickness. Miss Pockels also showed that accidental contamination of the surface, which had previously complicated nearly all observations of surface-tension phenomena, could be eliminated by using a trough filled to the brim with water, and sweeping impurities off the surface by the motion of barriers which rested on the edges of the trough. This use of movable barriers to confine films, to compress them or to remove them from the surface, laid the foundation for nearly all the modern work with films on water. The early theories of surface tension had been developed by physicists (Thomas Young 1805; Laplace, Gauss, etc.) who either treated liquids as continuous fluids between whose elements of volume forces acted, or considered only spherical molecules which exerted upon one another forces that varied as a function of the distance between molecular centres. Such theories naturally could not take into account the wealth of knowledge that had been accumulated by organic chemists regarding the structures of organic molecules.

Stress Driven Patterning of Epitaxial Films

1993 ◽  
Vol 318 ◽  
Author(s):  
Michael A. Grinfeld
Keyword(s):  
Surface Energy ◽  
Surface Morphology ◽  
Film Thickness ◽  
Critical Thickness ◽  
Epitaxial Films ◽  
Layer By Layer ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Periodic Spacing

ABSTRACTWe study possible morphologies of epitaxial films atop attractive substrates appearing as a result of competition of misfit stresses, van der Waals forces and surface energy. Corresponding formula for the critical thickness of the dislocation-free Stranski-Krastanov pattern is established for the isotropic deformable films and substrates. If the film thickness exceeds the critical magnitude the layer-by-layer pattern switches to islanding. At the first stage the islands have a shape of striae (i.e. long parallel trenches with periodic spacing). We discuss also i)the circumstances in which surface morphology of the film corresponds to a two-dimensional superlattice of islands rather than a one dimensional lattice of striae and ii)the influence of a buffer inter-layer.

scholarly journals Experimental study of the wake behind a surface-piercing cylinder for a clean and contaminated free surface

2000 ◽  
Vol 402 ◽  
pp. 109-136 ◽  
Author(s):  
AMY WARNCKE LANG ◽  
MORTEZA GHARIB
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Turbulent Flows ◽  
Cross Sections ◽  
Surface Deformation ◽  
Surface Condition ◽  
Free Surface Flows ◽  
Shear Stresses ◽  
Surface Contaminants ◽  
A New Technique

This experimental investigation into the nature of free-surface flows was to study the effects of surfactants on the wake of a surface-piercing cylinder. A better understanding of the process of vorticity generation and conversion at a free surface due to the absence or presence of surfactants has been gained. Surfactants, or surface contaminants, have the tendency to reduce the surface tension proportionally to the respective concentration at the free surface. Thus when surfactant concentration varies across a free surface, surface tension gradients occur and this results in shear stresses, thus altering the boundary condition at the free surface. A low Reynolds number wake behind a surface-piercing cylinder was chosen as the field of study, using digital particle image velocimetry (DPIV) to map the velocity and vorticity field for three orthogonal cross-sections of the flow. Reynolds numbers ranged from 350 to 460 and the Froude number was kept below 1.0. In addition, a new technique was used to simultaneously map the free surface deformation. Shadowgraph imaging of the free surface was also used to gain a better understanding of the flow. It was found that, depending on the surface condition, the connection of the shedding vortex filaments in the wake of the cylinder was greatly altered with the propensity for surface tension gradients to redirect the vorticity near the free surface to that of the surface-parallel component. This result has an impact on the understanding of turbulent flows in the vicinity of a free surface with varying surface conditions.

An estimation of mechanical stress on alveolar walls during repetitive alveolar reopening and closure

2015 ◽  
Vol 119 (3) ◽  
pp. 190-201 ◽  
Author(s):  
Zheng-long Chen ◽  
Yuan-lin Song ◽  
Zhao-yan Hu ◽  
Su Zhang ◽  
Ya-zhu Chen
Keyword(s):  
Surface Tension ◽  
Respiratory Rate ◽  
Inflation Rate ◽  
Mechanical Stresses ◽  
Normal Lung ◽  
Shear Stresses ◽  
Fluid Viscosity ◽  
Small Airways ◽  
Protective Ventilation Strategy ◽  
Elevated Surface

Alveolar overdistension and mechanical stresses generated by repetitive opening and closing of small airways and alveoli have been widely recognized as two primary mechanistic factors that may contribute to the development of ventilator-induced lung injury. A long-duration exposure of alveolar epithelial cells to even small, shear stresses could lead to the changes in cytoskeleton and the production of inflammatory mediators. In this paper, we have made an attempt to estimate in situ the magnitudes of mechanical stresses exerted on the alveolar walls during repetitive alveolar reopening by using a tape-peeling model of McEwan and Taylor (35). To this end, we first speculate the possible ranges of capillary number ( Ca) ≡ μU/ γ (a dimensionless combination of surface tension γ, fluid viscosity μ, and alveolar opening velocity U) during in vivo alveolar opening. Subsequent calculations show that increasing respiratory rate or inflation rate serves to increase the values of mechanical stresses. For a normal lung, the predicted maximum shear stresses are <15 dyn/cm2 at all respiratory rates, whereas for a lung with elevated surface tension or viscosity, the maximum shear stress will notably increase, even at a slow respiratory rate. Similarly, the increased pressure gradients in the case of elevated surface or viscosity may lead to a pressure drop >300 dyn/cm2 across a cell, possibly inducing epithelial hydraulic cracks. In addition, we have conceived of a geometrical model of alveolar opening to make a prediction of the positive end-expiratory pressure (PEEP) required to splint open a collapsed alveolus, which as shown by our results, covers a wide range of pressures, from several centimeters to dozens of centimeters of water, strongly depending on the underlying pulmonary conditions. The establishment of adequate regional ventilation-to-perfusion ratios may prevent recruited alveoli from reabsorption atelectasis and accordingly, reduce the required levels of PEEP. The present study and several recent animal experiments likewise suggest that a lung-protective ventilation strategy should not only include small tidal volume and plateau pressure limitations but also consider such cofactors as ventilation frequency and inflation rate.

Relaxation in Sub-Micron Si-1-xGex Strain-Layer Mesas

1991 ◽  
Vol 239 ◽  
Author(s):  
Dawei Luo ◽  
David J. Howard ◽  
David C. Paine
Keyword(s):  
Finite Element ◽  
Finite Element Modelling ◽  
Strain Energy ◽  
Critical Thickness ◽  
Thick Layer ◽  
Si Substrate ◽  
Misfit Stress ◽  
Plan View ◽  
Element Modelling ◽  
Strain Layer

ABSTRACTFinite element modelling of strain-layer mesa structures shows that edge effects can contribute to the relaxation of in-plane misfit stress. Calculations were performed for a 200 nm thick layer of Si90Ge10 grown epitaxially on an <001> Si substrate which was patterned into 400-nm-high mesas ranging in diameter from 0.6 to 7 μm. These calculations were experimentally investigated using plan-view TEM to study relaxation in patterned and unpatterned material. This composition and film thickness exceeds the critical thickness predicted using simple strain energy considerations. In one experiment, an initially defect-free 200-nm-thick Si90Ge10 layer was annealed at 960°C for 1 hr to create a nearly fully relaxed layer which was then lithographically patterned into an array of sub-micron mesas. The wafer was then annealed for a second time and changes in the character of die pre-existing dislocations were studied.

Homoepitaxial Growth of Si at Low Temperature (325 °C)

1999 ◽  
Vol 570 ◽  
Author(s):  
J. Platen ◽  
B. Selle ◽  
I. Sieber ◽  
U. Zeimer ◽  
W. Fuhs
Keyword(s):  
Cyclotron Resonance ◽  
Critical Thickness ◽  
Abrupt Change ◽  
Electron Cyclotron Resonance ◽  
Lattice Structure ◽  
Chemical Vapor ◽  
Epitaxial Films ◽  
Film Structure ◽  
Homoepitaxial Growth ◽  
Smooth Interface

ABSTRACTElectron cyclotron resonance chemical vapor deposition (ECR-CVD) is used to grow to prepare epitaxial films on Si(100), Si(111), and Si(311) at 325 °C with a growth rate of 10…12 nm/min. On Si(100) up to a layer thickness of more than 300 nm the films exhibit a well defined and smooth interface and a perfectly ordered lattice structure. Beyond a critical thickness of about 500 nm the formation of conically shaped, amorphous regions was observed. At a thickness of 1.6 µm only 10… 15 % of the surface consists of these amorphous cones. On Si(311), Si(111), and Si(011) the critical epitaxial thicknesses hepi depends on the crystallographic orientation of the substrate in the sequence hepi(311) > hepi(111) > hepi(011) with an abrupt change of the film structure from crystalline to amorphous

The effect of anisotropic surface tension on the morphological stability of planar interface during directional solidification

2009 ◽  
Vol 18 (4) ◽  
pp. 1691-1699 ◽  
Author(s):  
Chen Ming-Wen ◽  
Lan Man ◽  
Yuan Lin ◽  
Wang Yu-Yan ◽  
Wang Zi-Dong ◽  
...  
Keyword(s):  
Surface Tension ◽  
Directional Solidification ◽  
Planar Interface ◽  
Morphological Stability ◽  
Anisotropic Surface

Thermodynamics of Thin Film Epitaxy

2002 ◽  
Vol 69 (4) ◽  
pp. 415-418 ◽  
Author(s):  
R. C. Cammarata ◽  
K. Sieradzki
Keyword(s):  
Thin Film ◽  
Critical Thickness ◽  
Epitaxial Film ◽  
Free Energies ◽  
Equilibrium Thermodynamics ◽  
Direct Identification ◽  
Equilibrium Volume ◽  
Variation Approach ◽  
Thin Film Epitaxy ◽  
Volume Stress

The mechanics of thin film epitaxy is developed using an equilibrium thermodynamics formalism and linear elasticity. A virtual variation approach is employed that leads to a direct identification of the important volume and surface thermodynamic parameters characterizing mechanical equilibrium. In particular, the equilibrium volume stress state of an epitaxial film as a function of the film thickness, surface free energies, and surface stresses is obtained. It is shown how this formalism can be used to determine the critical thickness for epitaxy.

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