Anisotropy driven interrupted coarsening of the Asaro-Tiller-Grinfeld instability

We investigate the effects of surface energy anisotropy on the coarsening dynamics of the Asaro-Tiller-Grinfeld instability at stake in thin semiconductor films. We consider a continuum model which accounts for wetting interactions between the film and its substrate, elasticity driven mass currents and surface energy anisotropy. We derive an explicit non-linear, non-local evolution equation for the film height that we solve numerically. Anisotropy, which dictates the island shapes, impacts the growth kinetics by weakening the possible elastic relaxation, which can lead during annealing to an interruption of Ostwald ripening. The resulting stationary state is characterized by square-based pyramids separated by a wetting layer. It is found that the instability onset is delayed when the film thickness decreases above the critical thickness for the instability to occur. We characterize the influence of the growing flux used for the film deposition on the stationary state reached during subsequent annealing, and find that the density of the resulting self-organized islands increases with the flux.     

Simulation of microstructural evolution in materials with misfitting precipitates

To predict the behavior of directional coarsening and the temporal evolution of the shape of coherent precipitates in two-phase materials, a dislocation-free model is proposed, based on a combination of statistical mechanics and linear elasticity. This model takes elastic anisotropy and isotropic interfacial energy into account. Based on an example of isolated precipitates under plane strain condition, the influence of particle size, inhomogeneity, direction and sign of external loads on the equilibrium shape will be discussed in terms of a generalized thermodynamic force acting on the interface. To simulate the morphological diffusion process of typical microstructures with several random distributed misfitting inclusions, a computational technique in form of a finite element Monte Carlo simulation is presented. Within this numerical technique, no restrictions on the particle shape or the elastic anisotropy of both phases are made.     

The role of atomic mobility during film growth in the structural and magnetic properties of CoCr

We have studied the morphological, crystallographic, and magnetic properties of CoCr thin films sputtered at different substrate temperatures and pressures. Conditions which produce high adatom mobility on the surface of the growing film lead to good c-axis orientation and magnetic anisotropy normal to the substrate, while low mobility leads to poor c-axis orientation and anisotropy. These results are explained in terms of van der Drift's model of the evolutionary growth of vapor-deposited films. The perpendicular coercivities of our samples depend only on the substrate temperature and we find no correlation with the film morphology or grain size.     

The critical layer number of Stranski-Krastanov growth mode epitaxial growth for bcc metallic thin films

Based on the classical elastic theory and a thermodynamic model for surface energy, the critical layer number n_c of Stranski-Krastanov growth mode epitaxial growth for bcc metallic thin films is calculated. n_c is determined by the consideration that the sum of the surface energy of a film and the lattice mismatch elastic energy between a substrate and the film is equal to the surface energy of the substrate. When the film layer number n is larger than n_c, a flat growth of the film on the substrate will transform to an island growth. Our predictions on several metallic films are in agreement with experimental results.     

Effects of elastic anisotropy on the surface stability of thin film/substrate system

The surface stability of thin film/substrate system is an important problem both in the film synthesis and reliability of micro electrical and mechanical system (MEMS). In this work, the elastic anisotropy effect on surface stability of thin film/substrate system was considered. The theoretical analysis indicates that elastic anisotropic influence could play an important role in the surface stability of thin film/substrate system. And the anisotropy effect should be considered both in the thin film synthesis process and its service reliability. In addition, there exists an nondimensional parameter k for cubic crystalline thin film materials in evaluating the anisotropic effect. When k is larger than one unit, the surface stability will be weakened by anisotropic effect; vice versa. The method used in present work could be easy extended to multi-layered thin film/substrate system and help us to consider the elastic anisotropy effect.     

ANALYSIS OF FAILURE MECHANISMS IN THE INTERCONNECT LINES OF MICROELECTRONIC CIRCUITS

Interconnect lines are thin wires inside microelectronic circuits. The material in an interconnect line is subjected to severe mechanical and electrical loading, which causes voids to nucleate and propagate in the line: microelectronic circuits often fail because an interconnect is severed by a crack. Many of the mechanisms of failure are believed to be associated with diffusion of material through the line; driven by variations in elastic strain energy and stress in the solid, by the flow of electric current, and by variations in the free energy of the solid itself. With a view to modelling interconnect failures, we have developed a finite element method that may be used to compute the effects of diffusion and deformation in an electrically conducting, deformable solid. Our analysis accounts for large changes in the shape of the solid due to surface diffusion, grain boundary diffusion, and elastic or inelastic deformation within the grains. The methods of analysis is reviewed in this paper, and selected examples are used to illustrate the capabilities of the method. We compute the rate of growth of a void in an interconnect by coupled grain boundary diffusion and creep; we investigate void migration and evolution by electromigration-induced surface diffusion; we study the influence of electromigration and stress on hillock formation in unpassivated interconnects, and compute the distribution of stress and plastic strain induced by electromigration in a passivated, polycrystalline interconnect line.     

Evolution of two-dimensional crystal morphologies by surface diffusion with anisotropic surface free energies

The Wulff shape of a crystal surface in equilibrium under anisotropic surface free energy has been widely reported and a typical differentiable anisotropic free energy functional form has been used in illustrations. Here we study the evolution of an arbitrary initial two-dimensional crystal shape to equilibrium and we classify the anisotropy in three cases. We find that when the typical surface free energy is critically anisotropic, multiple equilibrium states exist and the evolved equilibrium shape depends on the initial crystal configuration. Numerical simulations show that corners and planar facets develop on the surface in evolution. In cases of severe anisotropy, small surface facets and coarsening can occur. In contrast, when the typical surface free energy is mildly anisotropic, the evolving surface is smooth and the equilibrium shape is unique for a variety of the initial crystal shapes.     

Advanced resonant ultrasound spectroscopy for measuring anisotropic elastic constants of thin films

This paper presents an advanced resonant ultrasound spectroscopy (RUS) method to determine the elastic constants C_ij of thin films. Polycrystalline thin films often exhibit elastic anisotropy between the film growth direction and the in‐plane direction, and they macroscopically show five independent elastic constants. Because all of the C_ij of a deposited thin film affect the mechanical resonance frequencies of the film/substrate layer specimen, measuring resonance frequencies enables one to determine the C_ij of the film with known density, dimensions and the C_ij of the substrate. Resonance frequencies have to be measured accurately because of low sensitivity of the C_ij of films to them. We achieved this by a piezoelectric tripod. Mode identification has to be made unambiguously. We made this measuring displacement–amplitude distributions on the resonated specimen surface by laser Doppler interferometry. We applied our technique to copper thin film and diamond thin film. They show elastic anisotropy and the C_ij smaller than bulk values of C_ij. Micromechanics calculations indicate the presence of incohesive bonded regions.     

Self-organised growth on strained substrates: the influence of anisotropic strain, surface energy and surface diffusivity

The morphological stability of coherent thin films subjected to unequal in-plane biaxial strains is investigated to determine how non-uniform strain states can be used to influence the growth of self-organised island nanostructures. The evolution via surface diffusion is modelled analytically using a small perturbation approach and allows for anisotropies in the surface energy and the surface diffusivity. It is shown that conventional uniform biaxial epitaxy does not provide a driving force towards a particular wavelength as is popularly assumed. This reduces the potential for highly self-organised growth. It is predicted that improvements in island size, shape and spatial distributions can be obtained under certain conditions of anisotropic strain, surface energy and surface diffusivity. This increase in uniformity would be beneficial to the construction of practical devices. Enhancing surface diffusivity anisotropy via the application of an applied strain could offer the most realistic opportunity for controlling the growth of self-assembled structures this way.     

The Kinetics of Pore Shape Evolution in Alumina

The kinetics of shape evolution of a completely faceted crystal/internal void by surface diffusion was modeled. Arrays of micron-sized cavities were generated in sapphire substrates with known surface orientations using microlithography and ion beam etching and converted to internal intragranular pores of nonequilibrium shape by diffusion bonding of the etched substrate to an identical-orientation unetched sapphire substrate. Pore shape evolution rates during high-temperature anneals were monitored and found to be highly sensitive to the orientation of the substrate surface. The observed evolution rates were compared with the predictions of the kinetic model using diffusivity values for alumina that span the range from the highest to the lowest diffusion constants reported in the literature. The comparison suggests that surface-attachment-limited kinetics (SALK) play a major role in surface mass transport on stable low-index planes of alumina.     

Combinatorial approach to the edge delamination test for thin film reliability—adaptability and variability

We have demonstrated the adaptability and variability of a newly developed combinatorial edge delamination test. This was accomplished through studying the effect of substrate surface energy on the adhesion of thin films. In this combinatorial approach, a library (a single specimen) was fabricated with a polymethyl methacrylate (PMMA) film on a silicon substrate. The film has thickness gradient in one direction and the substrate has an orthogonal surface energy gradient. The thickness gradient was produced with a flow coating technique, and the surface energy gradient was controlled by partial oxidation of an alkylsilane layer on a silicon wafer. Applying a constant temperature to the specimen, interfacial debonding events were observed and a distribution of failure was constructed. Our results demonstrate the proposed combinatorial methodology for rapidly and efficiently evaluating the adhesion of general film/substrate systems as a function of many controllable parameters. In addition, this methodology can be used to predict the reliability distributions of the adhesion for practical parameters.     

Thin-film profile on a heterogeneous surface

We derive the shape of the interface between vapor and a physisorbed film on a substrate composed of two media. This represents a simple example of adsorption on a heterogeneous surface. The results are explained in terms of competition between the surface energy and potential energy due to the substrate. Applications to superfluid onset and third sound attenuation are considered.     

Evolution of hole size and shape in {100}, {110} and {111} monocrystalline thin films of gold

Monocrystalline thin films of gold, containing controlled distributions of small holes, were produced by an epitaxial flash deposition process on heated {100}, {110} and {111} monocrystalline substrates of sodium chloride. These films, ranging from 10 to 20 nm in thickness, were then removed from their substrates, annealed for various periods at temperatures ranging from 180 to 290 °C and subsequently examined by transmission electron microscopy in order to record the evolution of hole size and shape as a function of crystallographic orientation and annealing conditions. During annealing, these holes either grow or shrink, depending on the ratio of hole diameter to film thickness, with growing holes developing clearly defined crystallographic facets aligned normal to the film surface. The evolution of hole size is in satisfactory agreement with a kinetic analysis based on atomic surface mobility, whereas the evolution of hole shape is consistent with anisotropy of the surface energy, as computed from a nearest neighbor bond model.     

Deposition and modification of titanium dioxide thin films by filtered arc deposition

Thin films of titanium dioxide have been deposited on glass substrates and conducting (100) silicon wafers by filtered arc deposition (FAD). The influence of the depositing Ti⁻ energy, substrate types and substrate temperature on the structure, density, mechanical and optical properties have been investigated. The results of X-ray diffraction (XRD) showed that with increasing substrate bias, the film structure on silicon substrates changes from anatase to amorphous and then to rutile phase without auxiliary heating, the transition to rutile occurring at a depositing particle energy of about 100 eV. However, in the case of the glass substrate, no changes in the structure and optical properties were observed with increasing substrate bias. The optical properties over the range of 300–800 nm were measured using spectroscopic elliosometery, and found to be strongly dependent on the substrate bias, film density and substrate type. The refractive index values of the amorphous, anatase and rutile films on Si were found to be 2.56, 2.62 and 2.72 at a wavelength of 550 nm, respectively. The hardness and elastic modulus of the films were found to be strongly dependent on the film density. Measurements of the mechanical properties and stress also confirmed the structural transitions. The hardness and elastic modulus range of TiO₂ films were found to be between 10–18 and 140–225 GPa, respectively. The compressive stress was found to vary from 0.7 to 2.6 GPa over the substrate bias range studied. The composition of the film was measured to be stoichiometric and no change was observed with increasing substrate bias. The density of the film varied with change in the substrate bias, and the density ranged between 3.62 and 4.09 g/cm³.     

电场对Au/SiO_2及Au-Ag/SiO_2表面结构与原子迁移特性的影响

利用扫描俄歇微探针（SAM）和原子力显微镜（AFM）研究了SiO2衬底上在外加直流电场作用下沉积的Au薄膜及Au－Ag复层薄膜的表面形貌、结构变化及电迁移扩散行为。结果表明：①在衬底表面施加水平方向电场辅助沉积制备的Au薄膜其表面显示出平整的椭球形晶粒，并沿外电场方向呈织构取向。与未加电场的热蒸发沉积膜相比，具有较为均匀、有序的表面微观结构。②SiO2表面Au-Ag复层薄膜在直流电场作用下，Au，Ag物种同时向负极方向作走向迁移扩散，这与Au－Ag复层薄膜在Si（111）表面电迁移时Au，Ag分别向两极扩散的特点不同，反映了衬底性质对表面原子电迁移的影响。③Au－Ag复膜在电迁移过程中还发生了表面原子聚集状态的变化，原来沉积排布的细小晶粒在电迁移扩散过程中出现不均匀长大，导致薄膜表面粗糙度显著增加。     

Modeling of electromechanically-induced failure of passivated metallic thin films used in device interconnections

A theoretical analysis is presented of the failure of metallic thin films used for device interconnections in integrated circuits. Failure is mediated by void dynamics, which is driven by surface electromigration and processing related residual thermal stresses in the films. The analysis is based on surface mass transport modeling coupled strongly with the electrostatic and elastic deformation problems in the metallic films. Special emphasis is placed on the combined effects on void dynamics of anisotropy both in surface diffusivity along a void surface and in the applied stress tensor. A systematic parametric study is carried out based on self-consistent numerical simulations of surface morphological evolution. Void dynamics is analyzed and results are presented for void morphological stability in terms of critical stress levels as a function of stress state and surface mobility anisotropy. Finally, the role of plastic deformation is discussed around crack-like features emanating from void surfaces in ductile metallic films based on results of molecular-dynamics simulations in Cu.     

Equilibrium surface roughness of a strained epitaxial film due to surface diffusion induced by interface misfit dislocations

In recent years, developments in the microelectronics industry have led to extensive studies of the growth and characterization of thin solid films and their implementation in electronic and opto-electronic devices. A goal is to produce thin films with minimal bulk and surface defects. For those systems produced by epitaxial growth of a film on a substrate that has a slightly different lattice parameter, the stress associated with the elastic mismatch strain needed to satisfy the constraint of epitaxy provides a driving force for nucleation and growth of undesirable defects in the film material or on its surface. Among the most common defects are interface misfit dislocations, arranged more or less periodically on the film-substrate interface, which partially relax the elastic mismatch strain in the film. It has been observed that, for some material systems, surface roughness or waviness arises which correlates spatially with the positions of interface misfit dislocations. It is suggested here that the waviness along the surface may be a result of surface diffusion which is driven by a gradient in the chemical potential of the material along the surface. The chemical potential gradient arises from the nonuniform strain field of the interface misfit dislocations, as well as from the unrelaxed elastic mismatch strain. The focus here is on the development of a relatively simple model of this system which leads to an estimate of the magnitude and profile of surface waviness under conditions of thermodynamic equilibrium, i.e., after the material responds to the chemical potential gradient by seeking out a new configuration for which stresses are redistributed and the chemical potential is again uniform. The condition of uniform chemical potential for the final shape leads to an integro-differential equation for the equilibrium surface shape which is solved numerically. For representative values of system parameters, estimates of equilibrium surface roughness are obtained which can vary from less than one percent of film thickness to a significant fraction of film thickness. Although transient aspects of the process are not studied here, the characteristic time for achieving an equilibrium configuration is estimated.     

Lanczos and recursion techniques for multiscale kinetic Monte Carlo simulations

We review an approach to the simulation of the class of microstructural and morphological evolution involving both relatively short-ranged chemical and interfacial interactions and long-ranged elastic interactions. The calculation of the anharmonic elastic energy is facilitated with Lanczos recursion. The elastic energy changes affect the rate of vacancy hopping, and hence the rate of microstructural evolution due to vacancy-mediated diffusion. The elastically informed hopping rates are used to construct the event catalog for kinetic Monte Carlo simulation. The simulation is accelerated using a second-order residence time algorithm. The effect of elasticity on the microstructural development has been assessed. This article is related to a talk given in honor of David Pettifor at the DGP60 Workshop in Oxford.     

Micromagnetic study of ultrathin magnetic films

The phenomenon of spin reorientations in ultrathin magnetic films is discussed. A micromagnetic theory is presented which reveals the competition between the in-plane shape anisotropy and the normal surface anisotropy through a finite exchange stiffness. For small surface anisotropy, two continuous transitions in spin orientation are derived as the film thickness is increased: first from the uniform, normal configuration to a nonuniform, canting configuration, and then to the uniform, in-plane configuration. This result is consistent with experimental observations. For large surface anisotropy, it is derived theoretically that only the first spin reorientation occurs and the canting configuration remains stable even at large thickness limit.     

Stability of thin solid films

A small amplitude perturbation analysis is used to determine the conditions under which a solid film several hundred ångströms thick on a substrate will rupture. If the perturbation grows with time the film is unstable and rupture may occur, whereas if the perturbation decays the film is stable. Film rupture is caused essentially by diffusion of atoms along the free interface of the film which can, under certain conditions, amplify a perturbation applied to the film-gas interface. This surface diffusion is generated by a gradient of the chemical potential along the free interface. The chemical potential is affected by the curvature of the interface, by the pre-existing internal stresses normally found in thin films (they generate a strain energy term in the chemical potential) and by interaction forces between the atoms at the gas-solid interface with those of the film and substrate. The thin film is assumed to behave like an elastic body. The difference in the forces which act on a volume element in a film thinner than the range of interaction forces between the atoms of the film and substrate and the forces in a bulk solid is accounted for by introducing a body force into the equations of displacement of an elastic solid. Because of the difficulties in writing boundary conditions at the film-substrate interface, two limiting situations are considered: (1) a thin film on a rigid substrate and (2) a thin free film. A critical internal stress necessary for rupture is identified. The time of rupture is estimated from the inverse of the maximum growth coefficient of the perturbation. The dominant wavelength corresponding to the maximum growth coefficient gives an idea as to the size of the islands formed through rupture.