Oncu Akyildiz

Grain boundary grooving and cathode voiding in bamboo-like metallic interconnects by surface drift diffusion under the capillary and electromigration forces

The process of grain boundary (GB) grooving and cathode voiding in sandwich type thin film bamboo lines are simulated by introducing a mathematical model, which flows from the fundamental postulates of irreversible thermodynamics. In the absence of the electric field, the computer studies on the triple junction kinetics show that it obeys the first order reaction kinetics at early transient stage, which is followed by the familiar time law as t¯1∕4, at the steady state regime. The applied electric field (EF) in constant current experiments modifies this time law drastically above the well-defined electron wind intensity (EWI) threshold, and puts an upper limit for the groove depth, which decreases monotonically with EWI. Below the threshold level, the capillary regime predominates, and EF has little effect on the general kinetics of GB grooving, other than the linear increase in total elapsed time with EWI. An analytical formula for the cathode failure time in constant voltage test is obtained in terms of...

Particle-size and morphology dependence of the preferred interface orientation in LiFePO4 nano-particles

We gain new insights into the equilibrium properties and potential two-phase lithiation mechanisms in LiFePO4 nano-particles by conducting a first-principles investigation of the anisotropic chemical interfacial energy landscape in LiFePO4. The chemical interfacial energy per unit area along the ac plane is found to be remarkably low (7 mJ m−2) with respect to the bc (115 mJ m−2) and ab (95 mJ m−2) chemical interfacial energies. Because chemical interfacial energy and coherency strain energy have different anisotropies, the thermodynamically stable interface orientation is shown to depend both on the particle size and on the particle morphology. In particular, ac interfaces are favored for isotropic particles below 40 nm. This indicates that, if experimentally-relevant nano-particles were to (de)lithiate under a thermodynamic two-phase mechanism, the resulting front would be orientated along the ac plane, and not along the bc plane as is assumed in most lithiation models in the literature.

The thermodynamic stability of intermediate solid solutions in LiFePO4 nanoparticles

Theoretical predictions from first principles and recent advances in in situ electrochemical characterization techniques have confirmed the presence of solid-solution states during electrochemical (de)lithiation of LiFePO4 nanoparticles. Surprisingly, however, such thermodynamically unfavorable solid solution states have been observed at rates as low as 0.1C. Given the high diffusivity of Li in LiFePO4 and the thermodynamic instability of homogeneous solid solution states, spinodal decomposition to a thermodynamically favorable two-phase state is expected to occur on time scales as rapid as 1–100 ms. In this paper, we resolve this apparent paradox by demonstrating that, given the symmetry of the low-energy solid-solution Li/Va orderings and the 1D character of Li diffusion, spinodal decomposition from a solid solution preferentially leads to the formation of a diffuse ac interface with a large intermediate solid-solution region, as opposed to the commonly assumed bc interface. Our first principles predictions not only rationalize the persistence of solid-solution states at low-to-moderate C-rates in high-rate LiFePO4 electrodes, but also explain the observations of large intermediate solid-solution regions at an ac interface in single LixFePO4 particles quenched from a high-temperature solid solution.

Grain boundary grooving induced by the anisotropic surface drift diffusion driven by the capillary and electromigration forces: Simulations

The morphological evolution kinetics of a bicrystal thin film induced by anisotropic surface drift diffusion and driven by the applied electrostatic field is investigated via self consistent dynamical computer simulations. The physico-mathematical model, which is based upon the irreversible thermodynamic treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], provided us with auto-control on the otherwise free-motion of the triple junction at the intersection of the grooving surface and the grain boundary, without having any a priori assumption on the equilibrium dihedral angles. The destruction of the symmetry of the freshly formed grain boundary grooves under the anisotropic surface diffusion driven by the concurrent action of the capillarity and electromigration is observed. After prolonged exposure times the applied electric field above the well defined threshold level modifies Mullins’ familiar stationary state time law as, t¯1/4, and causes the pr...

Morphological evolution of tilted grain-boundary thermal grooving by surface diffusion in bicrystal thin solid films having strong anisotropic surface Gibbs free energies

The variational extremum method is further extended to give the full coverage for the inclined (tilted) grain-boundary (GB) configuration with respect to the sidewalls of a bicrystal thin solid film having strong anisotropic specific surface Gibbs free energy associated with the singular directions (faceting). A set of critical computer simulation experiments is performed on the asymmetrically disposed (inclination) bicrystal thin metallic films having four- and sixfold anisotropic specific surface Gibbs free energies to demonstrate the various GB-groove root topologies. Special computer runs are also designed using the realistic structural and physicochemical properties to simulate the thermal grooving profile of polycrystalline alumina (Lucalox™), and tungsten, which undergone heat treatments for 90 and 120 min at 1650 and 1350 °C in air and vacuum (10−4 Pa), respectively. The simulation profiles almost perfectly agree with the published experimental atomic force microscopy photographs after linewidth m...

Grain boundary grooving in bi-crystal thin films induced by surface drift-diffusion driven by capillary forces and applied uniaxial tensile stresses

Grain boundary (GB) grooving, induced by surface drift-diffusion and driven by the combined actions of capillary forces and applied uniaxial tensile stresses, is investigated in bi-crystal thin films using self-consistent dynamical computer simulations. A physico-mathematical model, based on the irreversible thermodynamics treatment of surfaces and interfaces with singularities allowed auto-control of the otherwise free-motion of the triple junction at the intersection of the grooving surface and the GB, without having any a priori assumption on the equilibrium dihedral angles. In the present theory, the generalised driving forces for stress-induced surface drift-diffusion arise not only from the usual elastic strain energy density (ESED), but also much stronger elastic dipole tensor interactions (EDTI) between the applied stress field and the mobile atomic species situated at the surface layer and in the GB regions. Accelerated groove-deepening kinetics shows that the surface drift-diffusion enhanced by the applied uniaxial tensile stresses through EDTI is dominant over the GB flux leakage at the triple junction. At high uniaxial stress levels (≥500 MPa for a 100-nm thick copper film), a sequential time-frame for micro-crack nucleation and growth is recorded just before specimen failure took place. These non-equilibrium thermokinetics discoveries (kinetics and energetics) contradict or at least do not support the hypothesis of the steady-state diffusive GB micro-crack formation and propagation due to ‘constant’ flux drainage through GB enhanced by tensile stresses acting normal to it.

Thermal Grooving by Surface Diffusion: a Review of Classical Thermo-Kinetics Approach

In polycrystalline materials wherever a grain boundary intersects a free surface and whenever the topographic variation associated with the atomic motion is favored by total free energy dissipation, the material surface grooves. In this review, we focused on the grain boundary grooving by surface diffusion which is an active mechanism at moderate temperatures and for grooves small in size. Starting with a description of the classical thermo-kinetics treatment of the process, we briefly reviewed Mullins’ very first modeling effort with a small slope assumption at the groove root and further considerations regarding finite slopes, different grain geometries, and anisotropic surface free energies. We concluded by giving examples of experimental observations in accord with theoretical calculations. Keywords: Thermal grooving; Grain boundary groove; Surface diffusion DOI: 10.17350/HJSE19030000042 Full Text: Review Article

Morphological Evolution of Intragranular Void under the Thermal-Stress Gradient Generated by the Steady State Heat Flow in Encapsulated Metallic Films: Special Reference to Flip Chip Solder Joints

The morphological evolution of intragranular voids induced by the surface drift-diffusion under the action of capillary forces, electromigration (EM) forces, and thermal stress gradients (TSG) associated with steady state heat flow is investigated in passivated metallic thin films via computer simulation using the front-tracking method. As far as the device reliability is concerned, the most critical configuration for interconnect failure occurs even when thermal stresses are low if the normalized ratio of interconnect width to void radius is less than certain range of values (which indicates the onset of heat flux crowding). This regime manifests itself by the formation of two symmetrically disposed finger shape extrusions (pitchfork shape slits) on the upper and lower shoulders of the void surface on the windward side. The void growth (associated with supersaturated vacancy condensation) on the other hand inhibits anode displacement but enhances cathode and shoulder slit velocities drastically, which causes lateral spreading.

Computer Simulations on the Grain Boundary Grooving and Cathode Edge Displacement in Bamboo-like Metalic Interconnects

The process of grain boundary (GB) grooving and cathode edge displacement in sandwich type thin film bamboo lines are simulated by introducing a new mathematical model. In the absence of the electric field, the computer studies on the triple junction kinetics show that it obeys the first order reaction kinetics at early transient stage, which is followed by the familiar time law as t^1/4, at the steady state regime. The applied electric field (EF) in constant current experiments modifies this time law drastically above the well-defined electron wind intensity (EWI) threshold, and puts an upper limit for the groove depth, which decreases monotonically with EWI. Below the threshold level, the capillary regime predominates, and EF has little effect on the general kinetics of GB grooving, other then the linear increase in total elapsed time with EWI.