Void evolution in nanocrystalline metal film under uniform tensile stress

A theoretical model to describe the nucleation and growth of voids at triple junctions of nanocrystalline metal film under uniform tensile loading is suggested. The void growth rate controlled by grain boundary diffusion under the combined influence of void surface energy, grain boundary interface energy and elastic energy stored in the solid is evaluated. Stress relaxation during uniform tension deformation is finally discussed; the effective stress relaxation distance is also calculated. The stress relaxation not only suppresses the nucleation of voids and cracks, but also influences the void growth rate.     

Stress relaxation behavior of Cu/Sn/Cu micro-connect after electrical current

The effect of electromigration on stress relaxation behavior of pure tin solder joints was investigated. It was found that the stress relaxation rate was accelerated significantly after the sample was subjected to current stressing. The accelerating effect increased with the current stressing time. Measurements of the activation energy and stress exponent suggested that the dominant mechanism of the stress relaxation of pure tin solder joint went from dislocation climb to grain boundary diffusion after electromigration. As a result of grain boundary diffusion and sliding, grain boundary grooves were observed on the surface of the tin solder joints after electromigration. The groove was associated with the divergence of vacancy concentration at the grain boundaries. The vacancy concentration at the grain boundaries, which increased with the current stressing time, promoted the atomic diffusion along the grain boundaries, resulting in a higher stress relaxation rate.     

Self diffusion studies on cobalt thin films

The study of lateral diffusion in thin metallic films is important from the application point of view, especially in electromigration reliability studies. Lateral self diffusion in cobalt thin films is studied using a non-destructive tracer scanning method. Neutron irradiation is employed to make a well-defined radioactive (⁶⁰Co) region in the middle of a continuous cobalt thin film stripe of width 3 mm. The experimental data are fitted to the appropriate solution of the diffusion equations by means of a non-linear least square fitting procedure using a computer. The diffusion experiments are conducted in the temperature range 300–600°C in argon atmosphere. This thin film data are compared with the diffusion data available on bulk cobalt. The activation energy for surface diffusion obtained (0·14 eV) is very much smaller than the reported activation energy for grain boundary diffusion in cobalt.     

Molecular dynamics study of surface effects on atomic migration near aluminum grain boundary

In this paper, atomic migration near grain boundary of aluminum wiring line in micro-electronic device is analyzed by molecular dynamics (MD) simulation. Interatomic potential used is based on effective-medium theory (EMT). It is shown that junction point composed of grain boundary and surface is a region where active movement of atoms (atomic diffusion) appears. Under tensile loading, not only atomic diffusion but also slip between atomic layers (dislocation movement) is activated in the junction region. If there exists a certain constraint on the surface due to, for example, a passivation film attached on the aluminum line, atomic rearrangement near the junction changes remarkably.     

Temperature-dependent surface diffusion near a grain boundary

Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain–grain–fluid triple intersection, involve a prescribed slope at the groove axis. The well-known similarity reduction is no longer valid when the dihedral angle and surface diffusivity depend on time due to variation of the surface temperature. We adapt a nonlinear fourth-order model that can be discerned from symmetry analysis to be integrable, equivalent to the fourth-order linear diffusion equation. The connection between classical symmetries and separation of variables allows us to develop the correction to the self-similar approximation as a power series in a time-like variable.     

Beading instabilities in thin film lines with bamboo microstructures

Thin film interconnect lines with bamboo grain structures are theoretically analyzed to determine the microstructural conditions under which the line is stable against beading (island formation) induced by surface energy. The equilibrium grain shape is one which meets the substrate at the equilibrium wetting angle, meets other grains at the equilibrium grain boundary groove angle and has a surface of constant curvature. For any initial cross-sectional area, only one grain size satisfied these three conditions. The grain shape, grain size and resistance of the equilibrium thin film interconnect line are derived. Lines with grain sizes less than the equilibrium grain size may adjust by buckling or undergoing grain growth. However, lines with grain sizes in excess of the equilibrium grain size develop breaks or opens. While these changes in line microstructures cannot be prevented, they may be drastically retarded by slowing the rate of surface diffusion.     

激光分子束外延SrTiO3薄膜退火过程中表面扩散的研究

用激光分子束外延研究了SrTiO3同质外延时原位退火中,反射高能电子衍射(RHEED)强度的恢复--驰豫时间,导出了高真空下表面扩散的活化能为0.31 eV,与低真空下的结果相比要小许多,这反映了粒子达到基片时的能量差.对沉积不同厚度的薄膜退火研究,表明当薄膜厚度增加时,表面恢复情况减弱,而导致随后的沉积时RHEED振荡周期的改变.     

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.     

Diffusion size effect

On the basis of the fact that the mean square displacement of atoms in the vicinity of the surface is higher than that in the bulk, a thin film diffusion size effect is introduced. In films of the order of 100 Å thick it leads to a marked increase in the diffusivity as the film thickness decreases. The size effect introduced is used to explain experimental data on the high diffusivity in thin films. The approach developed should also be taken into account when consideration is given to other thermally activated processes in thin films as well as in the vicinity of free surfaces, interfaces and grain boundaries (segregation, vacancy distribution and migration to the surface, phase formation etc.).     

Diffusion and clustering on the titanium (0001) surface

In this paper, we present a study of diffusion and clustering of atoms on the titanium (0001) surface using molecular dynamics and molecular statics methods. The formation energy of each defect cluster is calculated using a combination of annealing and quenching techniques. Diffusion mechanisms of clusters are elucidated by the analysis of atomic trajectories, and are confirmed by calculating energy states along the diffusion path and by fitting the diffusion coefficients to one or more Arrhenius functions. Our simulations show that the clusters diffuse by a sequence of atomic jumps; once an atom moves forward by half an atomic diameter, the others follow it. Such a correlated process involves an activation energy that is comparable to that of an adatom. Atoms in each cluster, especially those in clusters consisting of three and seven atoms, are tightly bound. However, due to high mobility, the clusters are less likely to be the critical nuclei in three-dimensional growth of thin films on the (0001) surface. Even the cluster consisting of seven atoms swaps a linear distance of 60 nm during the growth of one monolayer of thin film under typical deposition conditions and at room temperature, making it ineffective as a critical nucleus above room temperature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chemical Stresses Induced by Boundary Layer Diffusion in a Cylindrical Sandwich Composite

The chemical stresses developed in a cylindrical sandwich composite during radial boundary layer diffusion have been investigated. The system consists of a thin layer A of circular cross section sandwiched between two semi-infinite outer layers B, with the diffusivity of diffusant in A (D_A) being much greater than that in B (D_B). Two boundary conditions, the constant surface concentration and the instantaneous surface concentration, were considered. The concentration distributions were obtained by the Bessel-Laplace transform method. The stress functions were solved analytically based on the linear elasticity. Numerical computations were performed to illustrate the effects of the diffusivity ratio (D_A/D_B) and of the thickness of the central layer A on stress distributions. The results show that the induced stress in layer A increases as the diffusivity ratio, or its thickness, increases, in consistency with the general findings for composites of rectangular geometry.     

The study of grain boundary density effect on multi-grain thin film under tension

The grain-size effect on the yield strength and strain hardening of thin film at sub-micron and nanometer scale closely relates to the interactions between grain boundary and dislocation. Based on higher-order gradient plasticity theory, we have systematically investigated the size effect of multi-grain thin film arising from the grain boundary density under tensile stress. The developed formulations employing dislocation density and slip resistance have been implemented into the finite element program, in which grain boundary is treated as impenetrable interface for dislocations. The numerical simulation results reasonably show that plastic hardening rate and yield strength are linear to the grain boundary density of multi-grain thin film. The aspect ratio of grain size and orientation of slip system have distinct influence on the grain plastic properties. The research of slip system including homogeneous and nonhomogeneous distribution patterns reveals that the hardening effect of low-angle slip system is greater than that of high-angle slip system. The results agree well with the experimentally measured data and the solutions by discrete dislocation dynamics simulation.     

Low temperature interdiffusion in the Au-Pd and Au-Rh thin film couples

Interdiffusion profiles in thin polycrystalline multilayer films of Pd-Au and Ti-Rh-Au at temperatures up to 490°C have been measured by Rutherford backscattering. Room temperature grain boundary diffusion of Au into Rh was observed and analyzed to give D_B = 3.5 × 10^-17 cm² sec^-1. The Whipple analysis is applied to our data for the diffusion of Au in Pd; using the lattice diffusivity of Neukam, an activation energy for grain boundary diffusion of 0.9 eV is found. The diffusion of Pd in Au has also been analyzed using the Whipple model, which gives a grain boundary activation energy of 0.6 eV.     

Grain boundary interdiffusion and stresses in thin polycrystalline films

We consider the kinetics of tensile stress relaxation in thin metal film attached to inert substrate, controlled by chemical interdiffusion along the grain boundaries. We assume that the source of diffusing atoms is located at the surface of the film. We show that the kinetics of stress relaxation in the film can be either accelerated or slowed down if compared with the same kinetics in a single-component film, depending on the difference of intrinsic GB diffusion coefficients of the two components. In the case of faster matrix atoms, the tensile stress in the film significantly increases beyond its initial value at the beginning of interdiffusion process, while in the case of faster diffuser atoms, the compressive stresses develop in the film at the intermediate stages of stress evolution.     

Multiple grain growth events in liquid phase sintering

Sintered tungsten heavy alloys consist of a solidified liquid alloy matrix phase which interpenetrates a solid tungsten skeletal structure. A consequence of liquid phase sintering is considerable grain growth while the compact densifies. The driving force for grain growth is a decrease in the interfacial surface energy, and the process itself is the combined result of liquid diffusion, solid diffusion, and vapor diffusion if porosity is present. In this study, we utilized microgravity sintered samples to avoid solid-liquid segregation to study the multiple diffusion processes. Coupled with the diffusion event through the liquid phase, there is simultaneous solid-state sintering such as coalescence. The dihedral angle determines the contiguity and the grain growth rate. The liquid diffusion grain growth rate constant is at least one order of magnitude larger than the solid diffusion grain growth rate constant. As composition changes, the ratio of grain growth contributions from these three components also changes, which, in turn, causes grain size, grain size distribution, and contiguity variations.     

Simultaneous grain boundary motion,grain rotation,and sliding in a tricrystal

Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.     

SIMS Studies of Tracer Diffusion of Al in Thin Film Nanocrystalline Cu

Diffusion of Al in thin film nanocrystalline Cu(18 nm)has been investigated by means of second ionmass spectroscopy(SIMS).In the experimental temperature ranges from 421 to 773 K,there seem-ingly exists two diffusion mechanisms.The impurity elements O and C are supposed to accumulateto the grain boundaries and inhibit the fast grain boundary diffusion.     

Mesoscopic nonequilibrium thermodynamics treatment of the grain boundary thermal grooving induced by the anisotropic surface drift diffusion

A systematic study based on the self-consistent dynamical simulations is presented for the grain boundary thermal grooving problem by strictly following the irreversible thermodynamic theory of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)]. This approach furnishes us to have auto-control on the otherwise free-motion of the grain boundary triple junction without presuming any equilibrium dihedral (wetting) angles at the edges. The effects of physicochemical properties and the anisotropic surface diffusivity on the transient grooving behavior, which takes place at the early stage of the scenario, were considered. We analyzed the experimental thermal grooving data reported for tungsten in the literature, and compared them with the carried simulation results. This investigation showed that the observed changes in the dihedral angles are strictly connected to the transient behavior of the simulated global system, and manifest themselves at the early stage of the thermal grooving phenomenon.     

Grain boundary interdiffusion in Cd/Te thin film couples

Interdiffusion in Cd/Te thin film couples was studied experimentally through optical measurements and surface analysis. A grain boundary diffusion model was used and the corresponding activation energy was measured and found to be 0.12 ± 0.02 eV.     

Texture competition during thin film deposition – effects of grain boundary migration

In this paper, we describe an implementation of grain boundary migration in the atomistic simulator of thin film deposition (ADEPT), and apply the simulator to study effects of the grain boundary migration on texture evolution. In the implementation, atoms are classified into two categories: those belong to a single grain and those at grain boundaries. An atom is defined as one at a grain boundary if it has more than half of its neighbors occupied and not all of the neighboring atoms are in the same grain. The grain boundary atom is attempted to re-align with neighboring grains to represent the grain boundary migration; the attempt probability is defined by the grain boundary migration coefficient. Our studies show that grain boundary migration does not always assist formation of texture with a top surface of the lowest energy. At the nucleation stage of thin film deposition, high migration coefficient of grain boundaries may enhance the formation of grain nuclei with top surfaces of higher energy, and therefore effectively may suppress formation of textures with a top surface of the lowest energy. This effect may provide an extra dimension to engineer textures of thin films.