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 DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

The Stress Driven Islands Formation in Epitaxial Films and Solid HE4 Films.

1992 ◽  
Vol 280 ◽  
Author(s):  
Michael A. Grinfeld
Keyword(s):  
Surface Energy ◽  
Shear Modulus ◽  
Film Thickness ◽  
Epitaxial Films ◽  
Morphological Instability ◽  
Thin Solid Films ◽  
Solid Films ◽  
Mismatch Stress ◽  
Critical Film Thickness ◽  
Morphological Patterns

ABSTRACTWe discuss the static and quasi-static problems appearing in the theory of morphological instability of interfaces. The approach has allowed to predict the corrugations in He4 films and to explain the dislocation-free Stranski-Krastanow pattern of epitaxial growth of thin solid films with the critical film thickness H = σμ/τ2 (σ is a surface energy, μ- the shear modulus, and τ - the mismatch stress). In this paper we discuss possible morphological patterns of corrugations and their changes which appear in result of the stress driven “rearrangement” destabilization of originally flat interfaces.

scholarly journals New types of one-dimensional discrete breathers in a two-dimensional lattice

2020 ◽  
Vol 10 (2) ◽  
pp. 185-188
Author(s):  
Alexander Semenov ◽  
Ramil Murzaev ◽  
Yuri Bebikhov ◽  
Aleksey Kudreyko ◽  
Sergey Dmitriev
Keyword(s):  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Discrete Breathers

A modified two-dimensional triangular lattice model under honk environment

2020 ◽  
Vol 31 (06) ◽  
pp. 2050089
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
High Dimensional ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The Stability ◽  
Honk Effect ◽  
Real Traffic

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

Rheed Study of Strain Relaxation in Epitaxial Cds and Sn Overlayers

1990 ◽  
Vol 208 ◽  
Author(s):  
David W. Niles ◽  
Hartmut Höchst
Keyword(s):  
Film Thickness ◽  
Lattice Constant ◽  
Reasonable Agreement ◽  
Critical Thickness ◽  
Strain Relaxation ◽  
Epitaxial Films ◽  
Mechanical Equilibrium ◽  
Lattice Constants ◽  
Critical Film Thickness ◽  
Experimental Findings

ABSTRACTThe relaxation of strain in epitaxial overlayers is studied through an analysis of RHEED patterns. From the separation of the RHEED reflections, we determine the in-plane lattice constants for α-Sn/Cd0.8Zn0.2Te(100), CdS/GaAs(100), and CdS/CdTe(100) heterostructures. The discussion focuses on the critical thickness of the overlayers and the relaxation of the inplane lattice constant (a∥) of epitaxial films which exceed the critical thickness. Predictions based on Matthews and Blakeslee's mechanical equilibrium theory show reasonable agreement with our experimental findings, indicating that the metastability of the epitaxial overlayers does not cause a significant reduction in the critical film thickness.

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