Dislocation dynamics simulations of dislocation interactions and stresses in thin films

The dislocation interactions that stop threading dislocations (threads) during relaxation at increasing applied strains in single-crystal thin films are investigated using large-scale three-dimensional dislocation dynamics simulations. Threads were observed to stop via interactions with both threads and misfit dislocations (misfits). Both types of interactions were shown to depend on stress inhomogeneity. Low-stress regions enabled threads to stop in weak thread–misfit interactions even at high average film stresses. Threads were also concentrated in low-stress regions, which facilitated their interaction with other threads. Threads accumulated in thread–thread interactions, and stopped only temporarily in thread–misfit interactions. The mean free path for dislocation motion is shown to be accurately predicted from details of the inhomogeneous stress state arising from the applied strain and the misfit structure. These behaviors are analyzed to present a more complete picture of film strength, strain hardening and relaxation.     

Dislocation accumulation and strengthening in Cu thin films

An analysis that addresses the strain-hardening behavior of thin metallic films on substrates is presented. Stress measurements were made on 0.5 μm thick Cu films on Si substrates during thermal cycling, during stress relaxation at room temperature (RT), and after quenching in liquid nitrogen. Significant strengthening was observed in the thermal cycle during cooling. The stress relaxation at RT shows a decrease of the stress from 360 MPa to 290 MPa within 15 months. A theoretical approach to the strengthening phenomenon is made on the basis of the Peach–Koehler dislocation-interaction forces. It shows that adding threading dislocations into a parallel array of dislocations at the film–substrate interface can contribute significantly to the strain hardening of thin films. The calculated strain hardening accounts for a large portion of the observed strengthening.     

Out-of-plane stresses arising from grain interactions in textured thin films

Face-centered-cubic thin films often have mixed (1 1 1)/(1 0 0) fiber texture. These orientations can have very different in-plane stiffnesses, leading to the possibility of significant stress inhomogeneities. Previous X-ray studies appeared to confirm this, reporting much higher stresses in (1 1 1)- than (1 0 0)-oriented grains. In those studies, the stress in the film normal direction was assumed to be zero everywhere, but Poisson effects suggest that out-of-plane stresses may be significant. Here, an X-ray data analysis that allows for out-of-plane stresses is presented and applied to X-ray data taken from a Cu film. The in-plane stress is shown to be homogeneous, and significant out-of-plane stresses arise. This analysis is shown to be more accurate and more consistent with the microstructure than previous methods. Consideration of inhomogeneous triaxial stress states is seen to be critical to understanding mechanical behavior of films with mixed fiber texture. Models for yielding and texture development are discussed.     

On plastic strain recovery in freestanding nanocrystalline metal thin films

In a recent article [J. Rajagopalan, J.H. Han, M.T.A. Saif, Science 315 (2007) 1831–1834], we have reported substantial (50–100%) plastic strain recovery in freestanding nanocrystalline metal films (grain size 50–65 nm) after unloading. The strain recovery was time dependent and thermally activated. Here we model the time evolution of this strain recovery in terms of a thermally activated dislocation propagation mechanism. The model predicts an activation volume of ≈42b³ for the strain recovery process in aluminum.     

Growth kinetics of nanometric dendrites in metal–carbon thin films

Tungsten–carbon films deposited by pulsed-DC reactive magnetron sputtering show the formation of a dendritic structure at the nanometric scale. The structure is formed by a combination of a polycrystalline β-W phase together with a non-stoichiometric WC_1?x phase. The nanodendrites coincide with W-rich zones, whereas C-rich regions are located at the interstices. The characteristics of this nanostructure have been modulated by varying the metal concentration of the films. The composition, structure and morphology were characterized by X-ray photoelectron spectroscopy, electron probe microanalysis, transmission electron microscopy, X-ray diffraction and atomic force microscopy, and the mechanical and tribological properties were evaluated by profilometry, nanoindentation and microscratch. The observed growth pattern is interpreted as the result of nucleation and growth of a W phase into a W–C amorphous matrix, whose growth is controlled by diffusion of carbon. A simulation model based on phase field modelling and presenting similar morphologies is formulated. This special structure combines properties of W and diamond-like carbon films, which enlarges the scope of applications towards self-lubricating hard and low-friction coatings with improved stability.     

Functional nanostructures through nanosecond laser dewetting of thin metal films

Techniques for processing nanoscale metallic structures with spatial order and tunable physical characteristics, such as size and microstructure, are paramount to realizing applications in the areas of magnetism, optics, and sensing. This paper discusses how pulsed laser melting of ultrathin films can be a powerful but simple and cost-effective technique to fabricate functional nanostructures. Ultrathin metal films (1 nm to 1,000 nm) on inert substrates like SiO₂ are generally unstable, with their free energy resembling that of a spinodal system. Such films can spontaneously evolve into predictable nanomorphologies with well-defined length scales. This study reviews this laser-based experimental technique and provides examples of resulting robust nanostructures that can have applications in magnetism and optics.     

Dislocation cross-slip in heteroepitaxial multilayer films

We simulated dislocation dynamics in heteroepitaxial multilayer thin film systems, considering the case where threading dislocations emerging from the substrate replicate themselves into the thin film during the film growth process. In the regime where the thin film layer thickness is tens of nanometers, the strain hardening mechanism involves the glide of single threading dislocation segments in the thin film instead of by dislocation pile-ups. We studied the dislocations’ evolution behavior and their interactions since these then became significant to the strain hardening of the multilayer structure. Cross-slip of threading dislocation segments in multilayer structure was found to be more prevalent compared to a single-layered thin film. This can result in a more complex pattern of interfacial dislocations and may have a significant contribution to the interactions between threading and interfacial dislocations. The simulation was carried out using the level set method incorporating thin film growth.     

Crack nucleation during mechanical fatigue in thin metal films on flexible substrates

The evolution of damage due to mechanical fatigue in thin metal films on flexible substrates was investigated by in situ electrical resistance measurements. A tensile fatigue load was applied to the metal films by subjecting a single edge of the curved samples to repeated linear motion. The change in the resistance of the metal films was monitored in situ. Upon the nucleation of a fatigue-induced crack, the electrical resistance of the metal film began to increase. The resistance subsequently continued to increase with crack propagation. Therefore, in situ electrical resistance measurements can be used to identify the fatigue-induced crack nucleation cycle. The number of cycles required for crack nucleation decreased with the increase in the fatigue-stressed area of the samples. This behavior is attributed to an increase in the crack nucleation probability with increasing sample size. The amount of strain applied also modified the number of cycles required for crack nucleation according to the Coffin–Manson relationship. The increase in the electrical resistivity with respect to the number of fatigue cycles can be accurately predicted when the fatigue cycle is normalized by the nucleation cycle. This indicates that the fatigue lifetime is determined by crack nucleation and not by crack propagation.     

Comparison of mechanical properties of Ni3Al thin films in disordered FCC and ordered L12 phases

We report the results of several experiments isolating the effect of long-range order on mechanical properties of intermetallic compounds. Kinetically disordered FCC Ni₃Al (Ni 76%) thin films were produced by rapid solidification following pulsed laser melting. For comparison, compositionally and microstructurally identical films with ordered L1₂ structure were produced by subsequent annealing at 550°C for 2 h. These FCC and L1₂ Ni₃Al thin films were tested by nanoindentation for hardness and Young's modulus, and the critical strain to fracture was measured by straining the substrate under four-point bending. Ni₃Al thin films in the disordered phase were found to have nearly twice the critical strain to fracture, more than three times the fracture toughness, and about 20% lower hardness than in the ordered counterpart. Blunter crack tips and crack bridging observed in the disordered phase also illustrate increased ductility. The increased plasticity of Ni₃Al due to chemical disorder is manifested both within the grains and at the grain boundaries. Young's moduli of the ordered and disordered materials were found to be indistinguishable.     

Dislocation interactions and low-angle grain boundary strengthening

The transmission of an incoming dislocation through a symmetrical low-angle tilt grain boundary (GB) is studied for {1 1 0}〈1 1 1〉 slip systems in body-centered cubic metals using discrete dislocation dynamics (DD) simulations. The transmission resistance is quantified in terms of the different types of interactions between the incoming and GB dislocations. Five different dislocation interaction types are considered: collinear, mixed-symmetrical junction, mixed-asymmetrical junction, edge junction, and coplanar. Mixed-symmetrical junction formation events are found not only to cause a strong resistance against the incident dislocation penetration, but also to transform the symmetrical low-angle tilt GB into a hexagonal network (a general low-angle GB). The interactions between the incident dislocation and the GB dislocations can form an array of 〈1 0 0〉 dislocations (binary junctions) in non-coplanar interactions, or a single 〈1 0 0〉 dislocation in coplanar interaction. We study how the transmission resistance depends on the mobility of 〈1 0 0〉 dislocations. 〈1 0 0〉 dislocations have usually been treated as immobile in DD simulations. In this work, we discuss and implement the mobility law for 〈1 0 0〉 dislocations. As an example, we report how the mobility of 〈1 0 0〉 dislocations affects the equilibrium configuration of a ternary dislocation interaction.     

Size effects on the mechanical properties of thin polycrystalline metal films on substrates

An analysis of the effects of the thickness and grain size of polycrystalline thin films on substrates is presented with the objective of linking the film mismatch stress to the underlying characteristic size scales. The model is predicated on the notion that the relaxation of mismatch strain in the film is accommodated by the introduction of dislocation loops whose population, dimensions and interaction energies are controlled by the film thickness and microstructural dimensions. The model is capable of capturing the combined effects of these size scales by accounting for the interaction energies of the constrained dislocation structure, and provides quantitative predictions of the evolution of film stress during thermal excursions. The predictions of the analysis are compared with available experimental results for polycrystalline films of face-centered cubic materials on Si substrates. It is shown that the model correctly predicts the observed influence of film thickness and grain size on stress evolution during thermal excursions. Aspects of strain hardening in thin polycrystalline films with high dislocation densities are also discussed.     

Dislocation evolution with rheological forming of metal

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Coefficients of thermal expansion of thin metal films investigated by non-ambient X-ray diffraction stress analysis

Cu, Ni and Pd layers were deposited by DC-magnetron sputtering on Si wafer substrates. The mechanical stresses and the coefficients of linear thermal expansion (CTEs) were investigated by non-ambient (in-situ) X-ray diffraction measurements employing the sin²ψ crystallite group method. It was found that, in the as-produced state, the CTEs were larger than expected on the basis of literature values for the Cu and Ni layers, but not for the Pd layer. Upon annealing of the layers grain growth and decrease of the crystalline imperfection, monitored by in-situ X-ray diffraction measurements of the diffraction line broadening, occurred. The increase of the crystallite size was paralleled by a decrease of the CTE values for the Cu and Ni films. The grain-size dependence of the CTE is discussed in terms of the coordination (state of bonding) of atoms at grain boundaries and surfaces.     

Interfaces and stresses in thin films

A review of the current understanding of the effect of interfaces on the intrinsic stresses in polycrystalline thin films is given. Special attention is paid to the measurement, modeling and application of surface and interface stresses. Mechanisms for generating the compressive and tensile components of the intrinsic stress are assessed. Prospects for future research are presented.     

Grain growth in thin metallic films

Grain growth in thin films deposited on a substrate was studied theoretically. The thrust of the model proposed is the effect of vacancy generation accompanying grain growth on the rate of the process. In addition, the magnitude of a tensile stress developing in the film was considered. It was shown that due to the contribution of vacancies to the free energy of the system, discernible grain growth is preceded by an “incubation” period, during which the grain structure can be considered as stable, as the rate of growth is relatively small over this incubation time. During this time, the vacancy concentration remains nearly constant, staying at a level much higher than the thermal equilibrium concentration. Based on numerical analysis, a simple expression for the incubation time in terms of the vacancy sink spacing, temperature and grain boundary characteristics was derived. With this formula, the stability of the grain structure of a thin film can be assessed for given conditions.     

Applications of texture in thin films

Thin films are important in a variety of applications, including optical, magnetic,and electronic devices. The origin of microstructure in films formed by physical vapor deposition depends primarily on the homologous deposition temperature, which determines the grain structure and substructure. Texture is coupled to grain structure development through several kinetic parameters, principally surface diffusivity and interfacial energy. The representation of such fiber textures is facilitated by simplified pole intensity versus tilt angle plots rather than entire pole figures. The reliability of thin film interconnection materials such as aluminum alloys is heavily leveraged on both texture and grain structure. The properties of thin magnetic films depend on both the crystallographic texture and the grain shape anisotropy.     

Texture transformations in Ag thin films

A thickness-dependent texture transformation during annealing of initially (1 1 1) fiber-textured face-centered-cubic metal thin films is phenomenologically well known: sufficiently thin films retain the (1 1 1) texture, while sufficiently thick films transform to a (1 0 0) fiber texture. This transformation has been explained based on minimization of strain and interface energies, but recent work calls into question the roles of both of these driving forces. A high-throughput experimental method for the study of this texture transformation has been developed and applied to thin silver films with and without Ti adhesion layers. More than 150 individual samples spanning a range of thicknesses and interface conditions were prepared in a single deposition run. The texture evolution of these samples was characterized using X-ray diffraction as a function of time and temperature during annealing. The transformation proceeds despite the fact that the stresses are too low according to the strain/interface energy model. For films with Ti adhesion layers, the transformation kinetics and extent of transformation depend on the film thickness in a surprising way with intermediate thickness films showing initially fast transformations and stable mixed textures, while thicker films show an incubation time but transform fully. The results are consistent with reduction in defect energy (e.g. dislocations or point defects) as the driving force for secondary grain growth in an environment in which only (1 0 0) recrystallization nuclei can form. The driving force increases with film thickness so the nonmonotonic variation in transformation rate implies that the density of (1 0 0) nuclei decreases with thickness.     

Creep and stress relaxation in free-standing thin metal films controlled by coupled surface and grain boundary diffusion

An analytical solution is presented that interprets the effects of grain size, surface and grain boundary diffusivities, surface and grain boundary free energies, as well as grain boundary grooving on the creep rate in free-standing polycrystalline thin metal films. The Coble creep in the film plane is also taken into account; this has a significant effect on the creep rate of the film. The effects of diffusion ratio and free energy ratio between surface and grain boundary on film agglomeration are illustrated as well. A closed-form expression for stress relaxation in films under constrained strain conditions is derived from this solution. An exponential decay in stress is found as a function of the film microstructure. Results predicted by the solution are shown to be in agreement with the experiments.