Computer Simulation of Strain Energy and Surface- and Interface-Energy on Grain Growth in Thin Films

1994 ◽  
Vol 343 ◽  
Author(s):  
R. Carel ◽  
C. V. Thompson ◽  
H. J. Frost
Keyword(s):  
Thin Films ◽  
Grain Growth ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Driving Forces ◽  
Interface Energy ◽  
Orientation Dependence ◽  
Surface And Interface ◽  
Elastic Regime ◽  
Strained Films

ABSTRACTWe have simulated strain energy effects and surface- and interface-energy effects on grain growth in thin films, using properties of polycrystalline Ag (p-Ag) on single crystal (001) Ni on (001) MgO for comparison with experiments. Surface- and interface-energy and strain energy reduction drive the growth of grains of specific crystallographic orientations. The texture that will result when grain growth has occurred minimizes the sum of these driving forces. In the elastic regime, strain energy density differences result from the orientation dependence of the elastic constants of the biaxially strained films. In the plastic regime, strain energy also depends on grain diameter and film thickness. In p-Ag/(001) Ni, surface- and interface-energy minimization favors Ag grains with (11) texture. In the absence of a grain growth stagnation, the texture at later times is always (111). However, for high enough strains and large enough thicknesses, the strain energy driving force can favor a (001) texture at early times, which reverts to a (111) texture at later times, once the grains have yielded.

Texture Maps for Orientation Evolution During Grain Growth in Thin Films

1995 ◽  
Vol 403 ◽  
Author(s):  
Steven C. Seel ◽  
Roland Carel ◽  
Carl V. Thompson
Keyword(s):  
Thin Films ◽  
Grain Growth ◽  
Strain Energy ◽  
Driving Forces ◽  
Chemical Vapor ◽  
Interface Energy ◽  
Fcc Metals ◽  
Surface And Interface ◽  
Different Temperatures ◽  
Energy Anisotropy

AbstractOrientation selective grain growth in thin films arises due to anisotropy in materials properties. For continuous thin films, there are at least two orientation dependent driving forces for grain growth: (i) surface and interface energy anisotropy; (ii) strain energy anisotropy (both elastic and plastic). In fcc metals, the preferred growth of grains with (111) texture occurs due to their low surface and interface energy. Stresses in thin films arise during deposition and as a result of post-deposition annealing. A texture dependence of strain energy density arises in biaxially strained thin films due to anisotropy of elastic properties and/or orientation-dependent yield stresses. For most fcc metals, the strain energy driving force promotes the growth of (001) grains due to minimization of the combined elastic and plastic strain energy. The magnitudes of the orientation dependent driving forces for grain growth depend on the characteristics and processing conditions of the film and substrate. We have performed grain growth experiments for Ag films on single crystal Ni on MgO; Ag films on plasma-enhanced chemical vapor deposited (PECVD) SiO2 on MgO; Ag films on oxidized Si; and Ni films on oxidized Si. The texture resulting from grain growth in films of different thicknesses and deposited at different temperatures were determined, and the results are presented in the form of texture maps. The texture which dominates as a result of grain growth can be understood through the use of texture maps and compares well with analytic models for texture development during grain growth in thin films.

Grain Growth in Polycrystalline Thin Films

1994 ◽  
Vol 343 ◽  
Author(s):  
Carl V. Thompson
Keyword(s):  
Thin Films ◽  
Grain Growth ◽  
Energy Minimization ◽  
Film Formation ◽  
Interface Energy ◽  
Surface And Interface ◽  
Grain Sizes ◽  
Thermal Expansion Coefficients ◽  
Average Grain Size ◽  
Strain Energy Minimization

ABSTRACTThe performance and reliability of polycrystalline films are strongly affected by the average grain size and the distribution of grain sizes and orientations. These are often controlled through grain growth phenomena which occur during film formation and during subsequent processing. Abnormal rather than normal grain growth is most common in thin films, and leads to an evolution in the distribution of grain orientations as well as grain sizes, often leading to uniform or restricted crystallographic orientations or textures. Surface and interface energy minimization and strain energy minimization can lead to development of different textures, depending on which is dominant. The final texture resulting from grain growth depends on the film thickness, the deposition temperature, the grain growth temperature, the thermal expansion coefficients of the film and substrate, and the mechanical properties of the film, as well as other factors.

Finite Element Modeling of Grain Aspect Ratio and Strain Energy Density in a Textured Copper Thin Film

1996 ◽  
Vol 436 ◽  
Author(s):  
R. P. Vinci ◽  
J. C. Bravman
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Aspect Ratio ◽  
Finite Element Modeling ◽  
Strain Energy Density ◽  
Driving Force ◽  
Strain Energy ◽  
Interface Energy ◽  
Element Modeling ◽  
Grain Aspect Ratio

AbstractWe have modeled the effects of grain aspect ratio on strain energy density in (100)-oriented grains in a (111)-textured Cu film on a Si substrate. Minimization of surface energy, interface energy, and strain energy density (SED) drives preferential growth of grains of certain crystallographic orientations in thin films. Under conditions in which the SED driving force exceeds the surface- and interface-energy driving forces, Cu films develop abnormally large (100) oriented grains during annealing. In the elastic regime the SED differences between the (100) grains and the film average arise from elastic anisotropy. Previous analyses indicate that several factors (e.g. elimination of grain boundaries during grain growth) may alter the magnitude of the SED driving force. We demonstrate, using finite element modeling of a single columnar (100) grain in a (111) film, that changes in grain aspect ratio can significantly affect the SED driving force. A minimum SED driving force is found for (100) Cu grains with diameters on the order of the film thickness. In the absence of other stagnation mechanisms, such behavior could cause small grains to grow abnormally and then stagnate while large grains continue to grow. This would lead to a bimodal grain size distribution in the (100) grains preferred by the SED minimization.

scholarly journals Increasing the mean grain size in copper films and features

2008 ◽  
Vol 23 (3) ◽  
pp. 642-662 ◽  
Author(s):  
K. Vanstreels ◽  
S.H. Brongersma ◽  
Zs. Tokei ◽  
L. Carbonell ◽  
W. De Ceuninck ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Growth ◽  
Driving Forces ◽  
Texture Evolution ◽  
Deposition Process ◽  
Interface Energy ◽  
Growth Mode ◽  
Copper Films ◽  
Mean Grain Size ◽  
The Mean

A new grain-growth mode is observed in thick sputtered copper films. This new grain-growth mode, also referred to in this work as super secondary grain growth (SSGG) leads to highly concentric grain growth with grain diameters of many tens of micrometers, and drives the system toward a {100} texture. The appearance, growth dynamics, final grain size, and self-annealing time of this new grain-growth mode strongly depends on the applied bias voltage during deposition of these sputtered films, the film thickness, the post-deposition annealing temperature, and the properties of the copper diffusion barrier layers used in this work. Moreover, a clear rivalry between this new growth mode and the regularly observed secondary grain-growth mode in sputtered copper films was found. The microstructure and texture evolution in these films is explained in terms of surface/interface energy and strain-energy density minimizing driving forces, where the latter seems to be an important driving force for the observed new growth mode. By combining these sputtered copper films with electrochemically deposited (ECD) copper films of different thickness, the SSGG growth mode could also be introduced in ECD copper, but this led to a reduced final SSGG grain size for thicker ECD films. The knowledge about the thin-film level is used to also implement this new growth mode in small copper features by slightly modifying the standard deposition process. It is shown that the SSGG growth mode can be introduced in narrow structures, but optimizations are still necessary to further increase the mean grain size in features.

Energy Minimization During Epitaxial Grain Growth: Strain VS. Interfacial Energy

1993 ◽  
Vol 317 ◽  
Author(s):  
J. A. Floro ◽  
R. Carel ◽  
C. V. Thompson
Keyword(s):  
Grain Growth ◽  
Interfacial Energy ◽  
Energy Minimization ◽  
Strain Energy ◽  
Elastic Anisotropy ◽  
Interface Energy ◽  
Growth Strain ◽  
Free Energies ◽  
Film Substrate ◽  
Epitaxial Grain Growth

ABSTRACTWe have investigated Epitaxial Grain Growth (EGG) in polycrystalline Ag films on Ni (001) substrates. EGG is driven by minimization of crystallographically anisotropie free energies such as the film/substrate interfacial energy and the film strain. Under some conditions EGG results in the preferred growth of the (111) epitaxial orientations that are predicted to minimize the interfacial energy. However, when Ag films are deposited on Ni (001) at low temperature, EGG experiments consistently find that (111) oriented grains are consumed by grains with (001) orientations predicted to have much higher interface and surface energy. The large elastic anisotropy of Ag can account for this discrepancy. The film thickness and the deposition temperature (relative to the grain growth temperature) determine whether strain energy or interface energy minimization dominates orientation evolution during grain growth.

Lateral grain growth in poly-Si films by gas flame high temperature annealing

1996 ◽  
Vol 441 ◽  
Author(s):  
W. F. Qu ◽  
A. Kitagawa ◽  
Y. Masaki ◽  
M. Suzuki
Keyword(s):  
High Temperature ◽  
Tensile Stress ◽  
Compressive Stress ◽  
Grain Growth ◽  
Strain Energy ◽  
Driving Forces ◽  
Stress Distributions ◽  
High Temperature Annealing ◽  
Gas Flame ◽  
Si Films

AbstractPoly-Si films with the preferential orientation to a random, a (100) and a (110) texture were annealed using a flat gas flame. Remarkable lateral grain growth of (111) grains was observed for poly-Si films with a random and a (110) texture, while in (100) texture films the growth of (100) grains predominated over other grains. There existed tensile stress in as-prepared films. Grains with different orientation were under a different tensile stresses, and such stress distributions on the orientation of grains were different for different textures. The tensile stress was found to become larger in grown grains after high temperature annealing, while the stress on shrunken grains decreased or turned to compressive stress after annealing. These results indicate that strain energy stored in grains is one of the important driving forces in secondary grain growth.

Competition between strain and interface energy during epitaxial grain growth in Ag films on Ni(001)

1994 ◽  
Vol 9 (9) ◽  
pp. 2411-2424 ◽  
Author(s):  
J.A. Floro ◽  
C.V. Thompson ◽  
R. Carel ◽  
P.D. Bristowe
Keyword(s):  
Surface Energy ◽  
Grain Growth ◽  
Interfacial Energy ◽  
Elastic Anisotropy ◽  
Interface Energy ◽  
Orientation Dependence ◽  
Embedded Atom ◽  
Strain Energy Minimization ◽  
Film Substrate ◽  
Epitaxial Grain Growth

Epitaxial Grain Growth (EGG) is an orientation-selective process that can occur in polycrystalline thin films on single crystal substrates. EGG is driven by minimization of crystallographically anisotropic free energies. One common driving force for EGG is the reduction of the film/substrate interfacial energy. We have carried out experiments on polycrystalline Ag films on Ni(001) substrates. The orientation dependence of the Ag/Ni interfacial energy has been previously calculated using the embedded atom method. Under some conditions, EGG experiments lead to the (111) orientations calculated to be interface- and surface-energy-minimizing. However, when Ag films are deposited on Ni(001) at low temperature, EGG experiments consistently find that (111) oriented grains are consumed by grains with (001) orientations predicted to have much higher interface and surface energy. The large elastic anisotropy of Ag can account for this discrepancy. Strain energy minimization favors growth of (001) grains and can supersede minimization of interfacial energy if sufficient strain is present and if the film is initially unable to relieve the strain by plastic deformation.

The Correlation of Fatigue Crack Growth Rates in Rubber Subjected to Multiaxial Loading Using Continuum Mechanical Parameters

2007 ◽  
Vol 80 (1) ◽  
pp. 169-182 ◽  
Author(s):  
W. V. Mars ◽  
A. Fatemi
Keyword(s):  
Energy Density ◽  
Crack Growth ◽  
Growth Rates ◽  
Test Piece ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Driving Forces ◽  
Mechanical Parameters ◽  
Small Cracks ◽  
Crack Growth Rates

Abstract Although both the crack nucleation and growth stages of the fatigue failure process in rubber are manifestations of the same characteristic material behavior, the nucleation stage deserves special attention. In this case, continuum mechanical parameters may be used to characterize the driving forces of small cracks, without reference to the geometry of the test piece. The ability to estimate crack driving forces from continuum mechanical parameters during the growth process of small cracks has been investigated by correlating three different parameters (maximum principal strain, strain energy density, and cracking energy density) to rates of crack growth observed photographically during fatigue tests on initially uncracked specimens. Significant scatter in crack growth rates was observed resulting from high crack density and crack interactions. These results are also compared to crack growth measurements made on a pure shear (planar tension) test piece. The difference between continuum parameters that refer to a specific material plane, and those that do not is emphasized. Generally, the maximum principal strain and cracking energy density parameters provided similar levels of correlation. The strain energy density parameter consistently gave the poorest correlation. An advantage of the cracking energy density is that it considers the experiences of specific planes embedded in the material (i.e. it is a plane-specific parameter).

scholarly journals Effect of Annealing on Microstructure and Mechanical Properties of Magnetron Sputtered Cu Thin Films

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shiwen Du ◽  
Yongtang Li
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress ◽  
Grain Size ◽  
Strain Energy ◽  
Texture Coefficient ◽  
Elastic Strain Energy ◽  
Interface Energy ◽  
Cu Films ◽  
Si Substrates

Cu thin films were deposited on Si substrates using direct current (DC) magnetron sputtering. Microstructure evolution and mechanical properties of Cu thin films with different annealing temperatures were investigated by atomic force microscopy (AFM), X-ray diffraction (XRD), and nanoindentation. The surface morphology, roughness, and grain size of the Cu films were characterized by AFM. The minimization of energy including surface energy, interface energy, and strain energy (elastic strain energy and plastic strain energy) controlled the microstructural evolution. A classical Hall-Petch relationship was exhibited between the yield stress and grain size. The residual stress depended on crystal orientation. The residual stress as-deposited was of tension and decreased with decreasing of (111) orientation. The ratio of texture coefficient of (111)/(220) can be used as a merit for the state of residual stress.

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