Grain Boundary Groove Research Articles

Technique for Monitoring the Etching Rate of Alumina

AbstractThe effect of chemical and thermal treatments on the grains and grain boundaries of polycrystalline μ-Al2O3has been examined using a combination of microscopy techniques. Commercially available alumina samples (Lucalox™) were chemically etched in phosphoric acid at 200°C in increments of 15 min. Thermal treatments were carried out at 1650°C before chemical treatments. Using maps obtained by visible-light microscopy (VLM) as a guide, the same regions were re-examined using atomic force microscopy (AFM) after subsequent treatments. Variations in the dissolution rates of different grains and grain boundaries could then be studied using AFM. The geometry of the grain-boundary grooves was compared after thermal and chemical treatments. Electron backscattered diffraction (EBSD) patterns recorded in the scanning electron microscope (SEM) were used to obtain crystallographic orientations of the grains which enabled variations in dissolution rates between grains to be correlated to orientation.

The monitoring of grain-boundary grooves in alumina

The geometry of grain-boundary grooves in polycrystalline alumina has been studied using a combination of visible-light microscopy (VLM) and atomic force microscopy (AFM). Samples were heat treated in air to induce thermal grooving. A VLM map was made from the central region of each sample. Profiles of grooves located within the VLM maps were measured using AFM. Using again VLM maps, the same regions were re-examined using AFM after an additional heat treatment. This approach allowed the geometries of grooves which formed at migrating grain boundaries to be directly compared with those at stationary boundaries. The groove profiles measured were asymmetric at migrating grain boundaries and more nearly symmetric at stationary grain boundaries.

Molecular-dynamics analysis of grain-boundary grooving in interconnect films with underlayers

Molecular-dynamics analysis of grain-boundary grooving in interconnect films with underlayers

Surface Energy Anisotropy of SrTiO3 at 1400°C in Air

Geometric and crystallographic measurements of grain‐boundary thermal grooves and surface faceting behavior as a function of orientation have been used to determine the surface energy anisotropy of SrTiO3 at 1400°C in air. Under these conditions, thermal grooves are formed by surface diffusion. The surface energy anisotropy was determined using the capillarity vector reconstruction method under the assumption that Herring's local equilibrium condition holds at the groove root. The results indicate that the (100) surface has the minimum energy. For surfaces inclined between 0° and 30° from (100), the energy increases with the inclination angle. Orientations inclined by more than 30° from (100) are all about 10% higher in energy and, within experimental uncertainty, energetically equivalent. A procedure for estimating the uncertainties in the reconstructed energies is also introduced. Taken together, the orientation dependence of the surface‐facet formation and the measured energy anisotropy lead to the conclusion that the equilibrium crystal shape is dominated by {100}, but also includes {110} and {111} facets. Complex planes within about 15° of {100} and 5° of {110} are also part of the equilibrium shape.

Morphological stability of copper-silver multilayer thin films at elevated temperatures

The kinetics of breakdown of Cu-Ag polycrystalline multilayers during aging at elevated temperatures was investigated. Microlaminates with Cu:Ag layer thicknesses of 2:2, 1:4, 4:1, and 4:0.1 µm were aged for 10 minutes to 192 hours (t), at temperatures ranging from 700 to 900 K. The asdeposited microlaminates had a fine-grained columnar microstructure with well-defined interfaces. Upon annealing, the morphology evolved over three time regimes. In the first regime, the grains in each phase grew quickly to an apparent terminal size, which depended on both the layer thickness and annealing temperature. Next, grooves formed at the intersections of grain boundaries and layer interfaces and grew with a t0.25 dependence. The groove growth appeared to be independent of layer thickness and was approximately equal in Cu and Ag. The microlaminates started to break down in the third regime, as grain-boundary grooves on opposite sides of a layer bridged its thickness. Models for grain growth and grooving in thin films were modified for multilayer microlaminates and were shown to fit the experimental data reasonably well. This suggests that the terminal grain size is reached when groove drag overcomes the capillary forces driving grain growth, and that grooving kinetics are dominated by interfacial diffusion.

Grain-boundary grooving by surface diffusion with strong surface energy anisotropy

A vertical grain boundary intercepting a horizontal free surface forms a groove to reduce the combined surface energy of the system. The groove grows with time and is commonly used for measuring surface diffusion coefficients. This work studies grooving by capillarity-driven surface diffusion with strong surface energy anisotropy and finds that faceted grooves still grow with time t as t 1/4. However, an anisotropic groove can be smooth if the groove surface does not cross a facet orientation. The groove has the same shape as the corresponding isotropic groove, but the growth rate is reduced by a factor that depends on the degree of anisotropy. This reduction induces an error in the surface diffusion coefficient if the isotropic model is applied to a smooth, but anisotropic groove. We show how to correct for this error.

A model of migrating grain-boundary grooves with application to two mobility-measurement methods

Grain-boundary migration controls grain growth and is important in materials processing and synthesis. The mobility of grain boundaries is usually measured by the “quarter-loop” and Sun–Bauer methods. In these methods, a grain boundary migrates and its tip position along a free surface is recorded to infer the mobility. At the tip, a groove develops to reduce the combined surface energy. The groove is small and adjusts quickly. Thus, in both methods, the groove can be treated at each instant as migrating at constant speed. We study this quasi-steady groove formed via surface diffusion, and find that the groove turns the grain boundary (by angle θ) away from being perpendicular to the free surface. We add this tilting effect into both measurement methods by solving the migrating grain-boundary profiles for arbitrary θ. Computed profiles agree well with two Sun–Bauer experiments in which θ=18 and 30°.

Effect of faceting on the thermal grain-boundary grooving of tungsten

Abstract The grain-boundary grooving of electropolished surfaces of polycrystalline tungsten annealed at 1350°C has been studied. Atomic force microscopy images of grooves were taken in the same locations after different annealing times. The profiles of the grooves developed between unfaceted grains were in qualitative agreement with the predictions of Mullins' theory of grooving by surface diffusion mass transport. In particular, the predicted secondary maxima next to the main groove maxima were often observed. Surface faceting strongly affected the grooving kinetics and groove shapes. Grooves developed between faceted and unfaceted grains were often asymmetric with unusual growth kinetics. Our observations suggest that certain faceted grains exhibited a negligible surface diffusion coefficient and that the surface fluxes at the associated groove root were non-zero. Numerical simulations assuming anisotropy of the surface diffusion coefficient (i.e. high diffusion coefficient on the unfaceted side, and negligible diffusion coefficient on the faceted side of the groove) were performed. The qualitative agreement between the simulated and observed groove shapes shows that the groove asymmetry can be explained by surface diffusion anisotropy.

Effect of faceting on the thermal grain-boundary grooving of tungsten

Abstract The grain-boundary grooving of electropolished surfaces of polycrystalline tungsten annealed at 1350°C has been studied. Atomic force microscopy images of grooves were taken in the same locations after different annealing times. The profiles of the grooves developed between unfaceted grains were in qualitative agreement with the predictions of Mullins' theory of grooving by surface diffusion mass transport. In particular, the predicted secondary maxima next to the main groove maxima were often observed. Surface faceting strongly affected the grooving kinetics and groove shapes. Grooves developed between faceted and unfaceted grains were often asymmetric with unusual growth kinetics. Our observations suggest that certain faceted grains exhibited a negligible surface diffusion coefficient and that the surface fluxes at the associated groove root were non-zero. Numerical simulations assuming anisotropy of the surface diffusion coefficient (i.e. high diffusion coefficient on the unfaceted side, and negligible diffusion coefficient on the faceted side of the groove) were performed. The qualitative agreement between the simulated and observed groove shapes shows that the groove asymmetry can be explained by surface diffusion anisotropy.

Energetics and kinetics of surfaces and interfaces in the Fe-Pb system

The energy and the diffusivity of interfaces in the solid Fe-liquid Pb system have been investigated in the temperature range 650-900°C. Grain-boundary grooves are formed at the solid Fe-liquid Pb interface and these have been studied by atomic force microscopy. From the topography of the grooves the relative interfacial energies and interfacial diffusivities are obtained. It is found that liquid Pb does not wet the grain boundaries in Fe. Possible mechanisms for the growth of the grain-boundary grooves are discussed.

Investigation of Surface Grooves from Migrating Grain Boundaries

ABSTRACTVisible-light microscopy (VLM) and atomic-force microscopy (AFM) were used to study the progression of grain-boundary grooving and migration in high-purity alumina (Lucalox™). Groove profiles from the same grain boundaries were revisited using AFM following successive heat-treatments. The grooves measured from migrating grain boundaries were found to have asymmetric partial-angles compared to those measured from boundaries that did not migrate during the experiment. For a moving boundary, the grain with the larger partial-angle was consistently found to grow into the grain with the smaller partial-angle. Migrating boundaries were observed to leave behind remnant thermal grooves. The observations indicate that the boundary may be bowing out during the migration process.

Effect of annealing on the surface microstructural evolution and the electromigration reliability of electroplated Cu films

This paper presents the effects of annealing, performed over a temperature range from 200°C to 400°C, on the surface microstructural evolution and the electromigration reliability of electroplated Cu films. After annealing, a substantial increase in surface roughness was observed, while variations in mean grain size and nanoindentation hardness were minor. Given the annealing temperature, the surface roughness was larger for the films annealed in forming gas, due to the existence of hydrogen. In particular, the films annealed at 400°C in forming gas demonstrated severe grain-boundary grooving and surface voiding. The defective nature of the annealed surface can be alleviated by chemical-mechanical polishing (CMP), when annealing is conducted prior to the CMP. However, it appears that a sequential thermal excursion at relatively high temperatures re-aggravates the integrity of the Cu surface. This argument may be supported by the electromigration-test results on dual-damascene interconnects fabricated using two different thermal profiles. The electromigration lifetimes were longer by more than a factor of two for the interconnects that skipped a post-passivation anneal at 400°C. The experimental evidence presented in this work suggests that controlling the integrity and quality of the Cu surface is an important step in ensuring good electromigration reliability.

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.

Level set modeling of transient electromigration grooving

A numerical investigation of grain-boundary (GB) grooving by means of the level set (LS) method is carried out. GB grooving is emerging as a key element of electromigration (EM) drift in polycrystalline microelectronic (ME) interconnects, as evidenced by a number of recent studies. The purpose of the present study is to provide an efficient numerical simulation, allowing a parametric study of the effect of key physical parameters (GB and surface diffusivities, grain size, current density, etc.) on the EM drift velocity as well as on the morphology of the affected regions. An idealized polycrystalline interconnect which consists of grains separated by parallel GBs aligned normal to the average orientation of interconnect's surface is considered. Surface and GB diffusions are the only diffusion mechanisms assumed. The diffusion is driven by surface curvature gradients and by an externally applied electric field. The corresponding mathematical system is an initial boundary value problem for a two-dimensional Hamilton–Jacobi type equation. To solve the electrostatic problem at a given time step, a full model based on the solution of Laplace's equation for the electric potential is employed. The resulting set of linear algebraic equations (from the finite difference discretization of the equation) is solved with an effective multigrid iterative procedure. The details of transient slit and ridge formation processes are presented and compared with theoretical predictions on steady-state grooving [E. Glickman, M. Nathan, J. Appl. Phys. 80 (1996) 3782; L. Klinger, E. Glickman, V. Fradkov, W. Mullins, C. Bauer, J. Appl. Phys. 78(6) (1995) 3833; L. Klinger, X. Chu, W. Mullins, C. Bauer, J. Appl. Phys. 80(12) (1996) 6670]

Experimental and simulated grain boundary groove profiles in tungsten

Grain-boundary grooving has been studied on polished surfaces of polycrystalline tungsten annealed at 1350°C. Atomic force microscopy images were taken in the same area for each groove after different annealing times. Secondary oscillations next to the main groove maxima (predicted for grooving by surface diffusion) were observed, to our knowledge for the first time. The agreement between experimental and calculated groove profiles (using the surface diffusion model of Mullins (1957, J. appl. Phys., 28, 333)) improved when grain-boundary fluxes were introduced.

Effects of grain growth on dynamic surface scaling during the deposition of Al polycrystalline thin films

Evolution of surface structure during the growth of sputter-deposited polycrystalline Al films is studied by means of atomic force microscopy and dynamic scaling by power spectral density and image variography analyses. We incorporate the effects of grain growth based on quantitative measurements of grain size, morphology, and texture orientation through transmission electron microscopy and x-ray diffraction pole figure texture measurements. Temporal regimes of early surface smoothing followed by roughening are explained by the effects of grain-boundary grooves and grain growth during deposition. Three distinct surface morphologies described as flat grains, hillocks, and ridges develop during film growth. The ridges are periodic structures with constant spacing during growth that form along 〈110〉 directions on vicinal (111)-oriented grains and are due to spontaneous development and growth of steps along 〈110〉 directions induced by the Schwoebel-barrier mechanism. The spacing of ridge structures and the well-characterized median grain size correspond to characteristic dimensions that define transitions between regimes of combinations of physical processes responsible for surface evolution. We found a surface-diffusion-dominated anomalous scaling growth mode $(\ensuremath{\alpha}g1)$ at short length scales and a nonlinear KPZ type mode $(\ensuremath{\alpha}\ensuremath{\approx}0.35)$ at longer length scales.

Preparation of nickel substrates for coated conductors

Polycrystalline Ni has been used as a substrate for high-current, coated YBa/sub 2/Cu/sub 3/O/sub x/ superconductors. For many conductors, Ni is rolled to large deformation and annealed to produce a cube texture. In this study, Ni was rolled to >95% reduction and annealed in 5% H/sub 2//95% He at 300-1000/spl deg/C for various times. The resulting substrates were examined by scanning electron microscopy, X-ray and electron diffraction, and surface interferometry. Key determinations for the Ni were extent of in-plane and out-of-plane texture, surface smoothness, and grain size. The extent of texture was approximately independent of annealing temperature and increased slightly with annealing time. Annealing at temperatures >600/spl deg/C increased surface roughness, primarily due to grain-boundary grooving. Grain growth was fastest at 1000/spl deg/C and was proportional to time to the 0.1 power.

A comparison of theoretical and experimental profiles for thermally-induced grain-boundary grooving

Thermally-induced grain boundary grooving has typically been characterized experimentally by either (1) optical interferometry (OI) or (2) reference line (RL) technique. For the OI technique, groove angle and groove width are reported and for the RL technique, groove angle, width and depth are reported. Even recent Atomic Force Microscope (AFM) studies of grain boundary grooving report their results in terms of groove angle, width, and depth exclusively. These measurements have been interpreted in terms of Mullins' 1957 theory on grain boundary grooving, which includes a derivation of the grain boundary groove profile. However, analyzing the groove depth, width, and angle uses only a small fraction of the groove profile information provided by Mullins' theory. In contrast to the literature, this study uses AFM data from thermal grooving in polycrystalline alumina to make a detailed comparison between Mullins' equation (and a modified form of Mullins' equation) for the entire groove profile rather than just the groove width or groove angle, thus providing a more rigorous and comprehensive test of theory. In addition, despite the wider and deeper grooves produced by microwave annealing, the modified form of Mullins' equation fits well both the microwave and conventionally annealed groove profiles.

Crack-like grain-boundary diffusion wedges in thin metal films

Constrained grain-boundary diffusion in polycrystalline thin metal films on substrates is studied as a strongly coupled elasticity and grain-boundary diffusion problem in which no sliding and no diffusion are allowed at the film/substrate interface. Surface diffusion and grain-boundary grooving are neglected in the present analysis. We show that such a diffusion process leads to the formation of crack-like grain-boundary wedges which cause the normal traction along the grain boundary to decay exponentially with time. A rigorous mathematical analysis is performed to derive and calculate the transient solutions for diffusion along a single grain boundary and along a periodic array of grain boundaries. An approximate closed-form solution is also given as a simple description of constrained grain-boundary diffusion. A most remarkable feature of the solution is that the diffusion wedges induce crack-like singular stress concentrations which could also enhance dislocation plasticity processes in a metal film.

On the kinetic mechanism of grain boundary wetting in metals

The thermodynamic condition characteristic of grain boundary wetting (GBW) causes an imbalance between grain boundary (GB) and solid–liquid interphase surface tensions γGB and γSL. This creates in turn a force acting at the root of the GB groove, and pointing into the solid. The “indentation” action of this force is suggested to cause stress-driven self-diffusion into the GB. This process removes the solid atoms from the groove cavity and causes their deposition along the GB (“internal solution”). Assuming that the GB acts as a perfect sink, this “self-indentation-internal solution” mechanism can account for a number of GBW features: the non-Mullins grooving morphology and linear kinetics, the origin of the singular stress field at the wetting front, the expansion of the solid under GBW, the influence of external stress on GBW, the GBW transitions with temperature, and the fast atomic penetration of the liquid metal ahead of the groove root.