Equilibrium Configuration of Epitaxially Strained Thin Film Surfaces

1995 ◽  
Vol 399 ◽  
Author(s):  
K. Jagannadham ◽  
J. Narayan ◽  
J.P. Hirth
Keyword(s):  
Strain Relaxation ◽  
Minimum Energy ◽  
Continuous Distribution ◽  
Radius Of Curvature ◽  
Dislocation Model ◽  
Quasi Equilibrium ◽  
Dislocation Generation ◽  
Discrete Dislocation ◽  
Thick Substrate ◽  
Germanium Silicon

ABSTRACTThe formation of convex and concave regions on the surface of a strained thin epitaxial film on a thick substrate is analyzed by minimization of energy associated with the configuration. The strain energy change resulting from the formation of undulations is modelled with the strain in the film represented by a continuous distribution of dislocations along the perturbed surface and the interface. A discrete dislocation model is also used when periodic undulations are formed. Results of energy minimization for germanium or germanium-silicon alloy films on silicon substrate illustrate that convex regions tend to grow. On the other hand, convex regions formed to conserve mass in shape changes associated with concave regions become stable with minimum energy under quasi-equilibrium when the mobility of adatoms is low. We have determined the size and radius of curvature of the undulations at minimum energy and conclude that it is favorable to form atomic steps on the surfaces from which dislocation generation and strain relaxation takes place.

On Source-Limited Dislocations in Nanoindentation

2004 ◽  
Vol 71 (3) ◽  
pp. 433-435 ◽  
Author(s):  
M. X. Shi ◽  
Y. Huang ◽  
M. Li ◽  
K. C. Hwang
Keyword(s):  
Material Behavior ◽  
Source Distribution ◽  
Dislocation Model ◽  
Dislocation Source ◽  
Dislocation Generation ◽  
Discrete Dislocation

The discrete dislocation model is used in this note to investigate the source-limited dislocation generation and glide in nanoindentation. It is shown that once there are enough sources for dislocation generation, the material behavior becomes independent of the dislocation source distribution.

Development of Cross-Hatch Morphology During Growth of Lattice Mismatched Layers

2001 ◽  
Vol 673 ◽  
Author(s):  
A. Maxwell Andrews ◽  
J.S. Speck ◽  
A.E. Romanov ◽  
M. Bobeth ◽  
W. Pompe
Keyword(s):  
Misfit Dislocation ◽  
Film Growth ◽  
Strain Relaxation ◽  
Dislocation Generation ◽  
Force Microscopy ◽  
Step Flow ◽  
Atomic Force ◽  
Subsequent Step ◽  
Step Flow Growth ◽  
Lateral Scale

ABSTRACTAn approach is developed for understanding the cross-hatch morphology in lattice mismatched heteroepitaxial film growth. It is demonstrated that both strain relaxation associated with misfit dislocation formation and subsequent step elimination (e.g. by step-flow growth) are responsible for the appearance of nanoscopic surface height undulations (0.1-10 nm) on a mesoscopic (∼100 nm) lateral scale. The results of Monte Carlo simulations for dislocation- assisted strain relaxation and subsequent film growth predict the development of cross-hatch patterns with a characteristic surface undulation magnitude ∼50 Å in an approximately 70% strain relaxed In0.25Ga0.75As layers. The model is supported by atomic force microscopy (AFM) observations of cross-hatch morphology in the same composition samples grown well beyond the critical thickness for misfit dislocation generation.

Quantitative Infrared Photoelasticity of Silicon Photovoltaic Wafers Using a Discrete Dislocation Model

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
T.-W. Lin ◽  
G. P. Horn ◽  
H. T. Johnson
Keyword(s):  
Residual Stress ◽  
Numerical Modeling ◽  
Strain Energy ◽  
Dislocation Model ◽  
Slip Systems ◽  
Inspection Method ◽  
Crystalline Defects ◽  
Discrete Dislocation ◽  
Stress Mapping ◽  
And Performance

Residual stress and crystalline defects in silicon wafers can affect solar cell reliability and performance. Infrared photoelastic measurements are performed for stress mapping in monocrystalline silicon photovoltaic (PV) wafers and compared to photoluminescence (PL) measurements. The wafer stresses are then quantified using a discrete dislocation-based numerical modeling approach, which leads to simulated photoelastic images. The model accounts for wafer stress relaxation due to dislocation structures. The wafer strain energy is then analyzed with respect to the orientation of the dislocation structures. The simulation shows that particular locations on the wafer have only limited slip systems that reduce the wafer strain energy. Experimentally observed dislocation structures are consistent with these observations from the analysis, forming the basis for a more quantitative infrared photoelasticity-based inspection method.

Approximation of Physical Spline with Large Deflections

2021 ◽  
pp. 3-18
Author(s):  
Viktor Korotkiy ◽  
Igor' Vitovtov
Keyword(s):  
Mathematical Problem ◽  
Minimum Energy ◽  
Internal Stresses ◽  
Radius Of Curvature ◽  
Large Deflections ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Cross Sectional ◽  
Elastic Line ◽  
Average Curvature

Physical spline is a resilient element whose cross-sectional dimensions are very small compared to its axis’s length and radius of curvature. Such a resilient element, passing through given points, acquires a "nature-like" form, having a minimum energy of internal stresses, and, as a consequence, a minimum of average curvature. For example, a flexible metal ruler, previously used to construct smooth curves passing through given coplanar points, can be considered as a physical spline. The theoretical search for the equation of physical spline’s axis is a complex mathematical problem with no elementary solution. However, the form of a physical spline passing through given points can be obtained experimentally without much difficulty. In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered. As known, in the case of small deflections it is possible to obtain a good approximation to a real elastic line by a set of cubic polynomials ("cubic spline"). But as deflections increase, the polynomial model begins to differ markedly from the experimental physical spline, that limits the application of polynomial approximation. High precision approximation of an elastic line with large deflections is achieved by using a parameterized description based on Ferguson or Bézier curves. At the same time, not only the basic points, but also the tangents to the elastic line of the real physical spline should be given as boundary conditions. In such a case it has been shown that standard cubic Bézier curves have a significant computational advantage over Ferguson ones. Examples for modelling of physical splines with free and clamped ends have been considered. For a free spline an error of parametric approximation is equal to 0.4 %. For a spline with clamped ends an error of less than 1.5 % has been obtained. The calculations have been performed with SMath Studio computer graphics system.

Semiconductor Superlattices: Order and Disorder

1987 ◽  
Vol 93 ◽  
Author(s):  
R. Hull ◽  
J. E. Turner ◽  
A. Fischer-Colbrie ◽  
Alice E. Whitea ◽  
K. T. Short ◽  
...  
Keyword(s):  
Lattice Mismatch ◽  
Strain Relaxation ◽  
Multilayer Structures ◽  
Two Dimensional ◽  
Semiconductor Alloys ◽  
Dislocation Generation ◽  
Growth Interface ◽  
Order And Disorder ◽  
Metastable Structures ◽  
Si Ion Implantation

ABSTRACTWe review and discuss the main structural phenomena inherent in epitaxial multilayer semiconductor growth: lattice mismatch, misfit dislocation generation, two-dimensional vs. threedimensional growth, interface abruptness and planarity and the local atomic structure of semiconductor alloys. The prevalence of metastable structures, often a function of crystal growth temperature, is discussed. We also investigate the effect of Si ion implantation and subsequent rapid thermal annealing of AlGaAs/GaAs and InGaAs/GaAs multilayer structures, with reference to strain relaxation, layer planarity and enhanced Al, In and Si diffusion.

Strain Relaxation by Dislocation Arrays in Thin Films

2003 ◽  
Vol 779 ◽  
Author(s):  
Prita Pant ◽  
Shefford P. Baker
Keyword(s):  
Thin Films ◽  
Critical Strain ◽  
Strain Relaxation ◽  
Minimum Energy ◽  
Strain Tensor ◽  
Total Strain Energy ◽  
Dislocation Arrays ◽  
Strain Data ◽  
Shear Strains ◽  
Fcc Metal

AbstractAn analytical model for strain relaxation by misfit dislocation arrays in thin films is presented that takes into account all components of the strain tensor, including shear strains. The model is developed for (001) films and applied to strain relaxation in (011) oriented FCC metal films. Our results show that shear strains strongly influence the total strain energy of the film. Since both the critical strain for dislocation formation, and the equilibrium spacing of dislocations in arrays depend on the minimum energy values, these quantities are found to be different from those predicted by previous models. This model is useful for understanding both critical strain data and strain relaxation in films.

Continuum Mechanics-Discrete Defect Modeling and Bubble Raft Simulation of Cracked Specimen Response in Nanoscale Geometries

2002 ◽  
Vol 740 ◽  
Author(s):  
Michael J. Starr ◽  
Walter J. Drugan ◽  
Maria d. C. Lopez-Garcia ◽  
Donald S. Stone
Keyword(s):  
Fracture Behavior ◽  
Crack Tip ◽  
Crack Size ◽  
Dislocation Model ◽  
Dislocation Emission ◽  
Crack Location ◽  
Discrete Dislocation ◽  
Emission Behavior ◽  
The Continuum ◽  
Continuum Elasticity

ABSTRACTIn a continuation of prior work, a new group of Bragg bubble model experiments have been performed to explore the effects of nanoscale crack size and nanoscale structural geometry on atomically-sharp crack tip dislocation emission behavior. The experiments have been designed to correspond to the theoretical limits that bound the expected crack tip response. Continuum elasticity analyses of these situations have also been carried out, in which the leading-order terms in the Williams expansion (the K and T terms) are determined, and the predictions of these continuum analyses coupled with discrete dislocation theory are compared with the experimental results. The experiments exhibit fascinating changes in crack tip dislocation emission direction with changing crack and structural size, crack location and loading conditions, as well as substantial changes in the magnitude of the resolved shear stress that drives dislocation emission. These changes are predicted well by the continuum elasticity-discrete dislocation model down to extremely small dimensions, on the order of a few atomic spacings. Preliminary experiments were performed with layered and two-atom basis rafts to establish crucial comparisons between theory and experiment that validate the applicability of continuum elasticity theory to make predictions directly related to nanoscale fracture behavior.

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