Grain boundary and vacancy diffusion model for electromigration-induced damage in thin film conductors

A theoretical model is proposed to explain the formation of both voids and hillocks in electromigration-induced damage. In this model, grain boundary mass transport is assumed to be responsible for the depletion and accumulation of diffusing atoms.The previously observed high compressive stresses generated in regions of atom accumulation can be explained using this model. In regions of atom depletion, vacancies are created but the expected tensile stresses are not observed because of efficient stress relaxation by the rapid diffusion of the vacancies into the neighboring lattice. The annihilation of these diffusing vacancies at film surfaces causes local film thinning which leads to the formation of electromigration-induced through-voids at grain boundaries.     

A review of crystallographic textures in chemical vapor-deposited diamond films

Diamond is one of the most important functional materials for film applications due to its extreme physical and mechanical properties, many of which depend on the crystallographic texture. The influence of various deposition parameters matters to the texture formation and evolution during chemical vapor deposition (CVD) of diamond films. In this overview, the texture evolutions are presented in terms of both simulations and experimental observations. The crystallographic textures in diamond are simulated based on the van der Drift growth selection mechanism. The film morphology and textures associated with the growth parameters α (proportional to the ratio of the growth rate along the 〈100〉 direction to that along the 〈111〉 direction) are presented and determined by applying the fastest growth directions. Thick films with variations in substrate temperature, methane concentration, film thickness, and nitrogen addition were analyzed using high-resolution electron back-scattering diffraction (HR-EBSD) as well as X-ray diffraction (XRD), and the fraction variations of fiber textures with these deposition parameters were explained. In conjunction with the focused ion beam (FIB) technique for specimen preparation, the grain orientations in the beginning nucleation zones were studied using HR-EBSD (50 nm step size) in another two sets of thin films deposited with variations in methane concentration and substrate material. The microstructures, textures, and grain boundary character were characterized. Based on the combination of an FIB unit for serial sectioning and HR-EBSD, diamond growth dynamics was observed using a 3D EBSD technique, with which individual diamond grains were investigated in 3D. Microscopic defects were observed in the vicinity of the high-angle grain boundaries by using the transmission electron microscopy (TEM) technique, and the advances of TEM orientation microscopy make it possible to identify the grain orientations in nano-crystalline diamond.     

A review of crystallographic textures in chemical vapor-deposited diamond films

Diamond is one of the most important functional materials for film applications due to its extreme physical and mechanical properties, many of which depend on the crystallographic texture. The influence of various deposition parameters matters to the texture formation and evolution during chemical vapor deposition (CVD) of diamond films. In this overview, the texture evolutions are presented in terms of both simulations and experimental observations. The crystallographic textures in diamond are simulated based on the van der Drift growth selection mechanism. The film morphology and textures associated with the growth parameters α (proportional to the ratio of the growth rate along the〈100〉direction to that along the 〈111〉direction) are presented and determined by applying the fastest growth directions. Thick films with variations in substrate temperature, methane concentration, film thickness, and nitrogen addition were analyzed using high-resolution electron back-scattering diffraction (HR-EBSD) as well as X-ray diffraction (XRD), and the fraction variations of fiber textures with these deposition parameters were explained. In conjunction with the focused ion beam (FIB) technique for specimen preparation, the grain orientations in the beginning nucleation zones were studied using HR-EBSD (50nm step size) in another two sets of thin films deposited with variations in methane concentration and substrate material. The microstructures, textures, and grain boundary character were characterized. Based on the combination of an FIB unit for serial sectioning and HR-EBSD, diamond growth dynamics was observed using a 3D EBSD technique, with which individual diamond grains were investigated in 3D. Microscopic defects were observed in the vicinity of the high-angle grain boundaries by using the transmission electron microscopy (TEM) technique, and the advances of TEM orientation microscopy make it possible to identify the grain orientations in nano-crystalline diamond.     

Ion back-scattering analysis of interdiffusion in Cu-Au thin films

Helium ion back-scattering has been used to examine the interdiffusion behavior of the thin film copper-gold system. Techniques for distinguishing bulk diffusion and grain boundary diffusion using back-scattering are presented. At temperatures in the range 200°–500°C, the grain boundary diffusion mechanism is shown to predominate in Cu-Au thin films. The back-scattering results suggest a model in which interdiffusion takes place by very rapid saturation of the grain boundaries in the gold film by copper and a slower filling of the copper grain boundaries by gold. The atoms in the grain boundaries then diffuse into the grains by bulk diffusion. In the parent gold film, we suggest that the amount of Cu Au ₃ formed near the grain boundaries is uniform in depth. In the parent copper film, more Cu₃Au forms near the original Cu-Au interface than further into the copper film. No evidence was found to suggest the formation of a pure layer of CuAu₃ or Cu₃Au. The interdiffusion and compound formation process is found to be characterized by an activation energy of 1.35-1.5 eV.     

Textures and structures of vapor deposits

The texture of vapor deposits (PVD and CVD) changes from the orientation that places the lowest energy lattice plane parallel to the substrate under the condition of low atom or ion concentration adjacent to the deposit, to the orientation that places the higher energy crystal planes parallel to the substrate as the atom or ion concentration adjacent to the deposit increases. However, in the early stage of deposition, the deposit-substrate interface energy and the surface energy constitute the most important energies of the system. Therefore, if the lattice match is established between the substrate and the deposit without generating much strain energy, the epitaxial growth takes place to reduce the interfacial energy. When the epitaxial growth does not take place, the surface energy is dominant in the early stage of deposition and the lowest energy crystal plane tends to be placed parallel to the substrate up to a critical thickness. The critical thickness depends on the deposition conditions. If the deposition condition does not favor placing the lowest energy crystal plane parallel to the substrate, the initial texture will change to that compatible with the deposition condition as the film thickness increases, and the texture turnover thickness will be short. The microstructure and surface topography of deposits are related to their textures.     

Grain boundary migration in Fe-3mass%Si alloy bicrystals with twist boundary

Abstract

The characteristics of grain boundary migration in Fe-3mass%Si alloy bicrystals with ∑3(011), ∑5(001) and ∑9(011) coincidence twist boundaries and random twist boundaries were examined to obtain an information on the development of {110}(001) (Goss) texture. The bicrystals were annealed at 1223 K for an appropriate time and the grain boundary migration speed was evaluated.

The ∑5 001l and ∑9 011l twist boundaries showed higher migration speed than ∑3(011) twist boundaries, and the random twist boundaries migrated faster than other boundaries. The migration speed decreased with increasing annealing time due to an increase in the edge components of the lattice misfits in the migrated boundaries. The grain boundary migration was also sensitive to the deviation angle (?θ) from the ideal orientation relationship for a coincidence boundary. The increase of ?θ accelerated the boundary migration. The motion of the grain boundary was influenced by plastic strain. Migration of the ∑9 twist boundary was more suppressed by plastic strain than that of the random boundary. On the basis of characteristics of the grain boundary migration, the effect of inhibitor on the Goss texture was discussed. © 2000 Elsevier Science Ltd. All rights reserved.     

Synthesis of polyaniline-silver nanocomposite film by unsymmetrical square wave current method

Based on elastic theory strain energy densities of grains with various textures have been calculated in diamond-cubic polycrystalline films. The results show that the strain energy density is anisotropic. The (100) grains have the lowest strain energy density, while the (111) texture corresponds to the highest one. It is the reverse for surface energy density. Therefore, strain energy minimization and surface energy minimization favor different crystalline orientations of grain growth and compete to determine the final texture of thin films. Discussion turns out that such competition in germanium films, as in other diamond-cubic films, results in a (100) texture barely appearing because the strain energy anisotropy can not dominate during grain growths.     

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.).     

Accumulation of coincidence site lattice boundaries during grain growth

Abstract

Monte Carlo simulations were used to investigate the effect of grain growth on the coincidence site lattice (CSL) boundary content of randomly textured polycrystals. Each grain was assigned an orientation, and grain boundary properties were dependent on both the boundary misorientation and the CSL character. While low misorientation angle boundaries (LABs) increase during growth, the fraction of CSL boundaries does not change with time. Decreasing CSL boundary energy and mobility did not alter these results. In contrast with LABs, which are characterised by a scalar misorientation angle, a particular combination of three independent rotation variables is required to create a low energy CSL boundary; thus, these boundaries are unlikely to form or to persist in a random polycrystal. While texture influences boundary formation, a texture that can enhance CSL boundaries is not apparent. Boundary plane effects should not increase CSL fraction during grain growth.     

Abnormal grain growth in thin films not caused by decreased energy of their free surface

We modeled the grain growth process in thin films on substrate. The only driving force for grain growth was a decrease in the total grain boundary energy; possible difference in the energies of the free surface of neighboring grains was not taken into account. The main features of capillarity-driven microstructure evolution qualitatively agree with those observed experimentally. This leads to the conclusion that abnormal grain growth in thin films can develop without assistance of decreased energy of the free film surface.     

Stress behavior of FCC metallic thin films during thermal evaporation

The development of stress in metallic thin films, monitored by in-situ curvature measurements during deposition, is analyzed. Three distinct stress regions including initial compressive, broad tensile, and incremental compressive stress were reported in terms of the film thickness (deposition time) by F. Spaepen. An experimental set-up was assembled for the in-situ curvature measurements utilizing vacuum thermal evaporation and multi-beam laser reflection points arrayed in x- and y-axis. The change in the spacing of laser reflected points was converted to the curvature of specimen, in turn, to instantaneous stress levels in the growing films using Stoney's formula. To investigate the effect on the distinct stress regions, the flux of the depositing metallic atoms was used as an experimental variable in this study. For the lowest flux cases for Cu and Ag, an additional second compressive stress stages after tensile maximum stress was observed in this study. Initial compressive part and tensile maximum stress regions appeared in shorter period of time for the thin films deposited at higher flux of atoms. Thus the flux of depositing atoms may affect the mechanisms of each stage. The initial compressive stress is conjectured to stem from the state of thin film surfaces; dynamic and relaxed surface. A broad tensile region is reported from the fact that the reduction of excess volume associated with grain boundaries and/or the coalescence of grains for high mobility materials. The incremental compressive stress region may be related to surface state and atomic mobilities.     

Energetics of Ti atom diffusion into diamond film

Energetics of Ti atom in metallization of diamond film were studied by calculations using density functional theory (DFT) and a composite basis set. Cluster models consisting of more than 10 C atoms were chosen to simulate the diamond phase with their boundaries saturated with H atoms. When Ti atom diffuses from the surface into the bulk of diamond interstitially, the energy barriers were found to be about 40 eV. Ti was found to favor substitutional sites rather than interstitial sites in diamond crystal. Our results indicate that the high concentration of Ti in chemical vapor deposited diamond films after metallization would occupy the grain boundaries rather than the bulk of diamond grain.     

Structural and morphological investigations on DC-magnetron-sputtered nickel films deposited on Si (100)

Pure nickel thin films were deposited on Si (100) substrates under different conditions of sputtering using direct current magnetron sputtering from a nickel metal target. The different deposition parameters employed for this study are target power, argon gas pressure, substrate temperature and substrate-bias voltage. The films exhibited high density of void boundaries with reduction in <111> texture deposited under high argon gas pressures. At argon gas pressure of 5 mTorr and target power of 300 W, Ni deposition rate was ~40 nm/min. In addition, coalescence of grains accompanied with increase in the film texture was observed at high DC power. Ni films undergo morphological transition from continuous, dense void boundaries to microstructure free from voids as the substrate-bias voltage was increased from −10 to −90 V. Furthermore, as the substrate temperature was increased, the films revealed strong <111> fiber texture accompanied with near-equiaxed grain structure. Ni films deposited at 770 K showed the layer-by-layer film formation which lead to dense, continuous microstructure with increase in the grain size.     

Modeling and visualization of polycrystalline thin film growth

A novel polycrystalline thin film growth simulator, FACET, has been developed. FACET is a multi-scale model with two major components: an atomic level one-dimensional kinetic lattice Monte Carlo (1D KLMC) model and a real time feature scale two-dimensional facet nucleation and growth model.

The 1D KLMC model has been developed to calculate inter-facet diffusion rates. By inputting the diffusion activation energies, the model will calculate the inter-facet atomic flux between {1 0 0}, {1 1 0}, and {1 1 1} facets of FCC materials at any temperature. The results of the 1D KLMC model have been verified by comparison with a full three-dimensional kinetic lattice Monte Carlo (3D KLMC) model.

The feature scale polycrystalline thin film nucleation and growth model is based on describing grains in terms of two-dimensional faceted surfaces and grain boundaries. The profile of the nuclei are described by crystallographically appropriate facets. The position and orientation of the nuclei can be randomly selected or preferred textures can be created. Growth rates are determined from different deposition fluxes and surface diffusion effects. Quantitative microstructural characterization tools, including roughness analysis, average grain size analysis, and orientation distribution analysis, were incorporated into the model, which allows the users to design, conduct and analyze the virtual experiments within one integrated graphical user interface. Users can also visualize the nucleation and growth process of the film and obtain the final film microstructure. The effects of thickness, temperature, and deposition flux on thin film microstructures have been studied by FACET.     

Grain boundary migration in Fe-3mass%Si alloy bicrystals with twist boundary

The characteristics of grain boundary migration in Fe-3mass%Si alloy bicrystals with Σ3〈011〉, Σ5〈001〉 and Σ9〈011〉 coincidence twist boundaries and random twist boundaries were examined to obtain an information on the development of {110}〈001〉 (Goss) texture. The bicrystals were annealed at 1223 K for an appropriate time and the grain boundary migration speed was evaluated.The Σ5〈001〉 and Σ9〈011〉 twist boundaries showed higher migration speed than Σ3〈011〉 twist boundaries, and the random twist boundaries migrated faster than other boundaries. The migration speed decreased with increasing annealing time due to an increase in the edge components of the lattice misfits in the migrated boundaries. The grain boundary migration was also sensitive to the deviation angle (Δθ) from the ideal orientation relationship for a coincidence boundary. The increase of Δθ accelerated the boundary migration. The motion of the grain boundary was influenced by plastic strain. Migration of the Σ9 twist boundary was more suppressed by plastic strain than that of the random boundary. On the basis of characteristics of the grain boundary migration, the effect of inhibitor on the Goss texture was discussed.     

多晶材质电子结构及热电性能的模拟

发展了一种研究多晶体系电子态以及热电性质的计算机模拟方法。首先采用相场动力学方法模拟多晶材质图案，再利用其模型序参量构造晶界的势函数，用近自由电子近似构造体系的哈密顿量。求解薛定谔方程得到体系的本征态。通过电荷密度的分布研究电子的限域特征,分析模拟结果发现对于晶界为势垒的情况，电子的基态出现在最大晶粒中；而对于晶界为势阱的情况，电子更容易限域在多个晶粒交叉的晶界附近，由得到的本征能级和波函数可以计算出温差导致的电位差，即得到赛贝克系数随温度的变化。结果表明具有导电晶界的多晶体的赛贝克系数要高于具有导电晶粒的多晶体。     

The segregation of osmium to grain boundary dislocations in tungsten

Field ion atom probe data is presented which shows that trace amounts of nickel and osmium segregate to grain boundaries in tungsten. The nickel atoms are randomly distributed in the grain boundary plane whereas the osmium is strongly segregated to the core region of a grain boundary dislocation. The differences in behavior of the solute atoms is explained by comparing atomic volumes.