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

Abstract

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.

Kinetics and magnitude of the reversible stress evolution during polycrystalline film growth interruptions

“…33,34 The gradual deepening of the grain-boundary groove by the combination of surface diffusion (on a short time scale) and grain-boundary diffusion (on a larger time scale) is likely influenced by the intrinsic stress state of the film and the surface-shape of the grains. 34,35 It can thus be concluded that an advanced model description of the kinetics of the tensile film-force rise during growth interruptions should incorporate dependencies of the compressive stress relaxation rate on the pre-interruption deposition rate and the average grain size, as resulting from different rates of grain-boundary grooving at the film surface upon growth interruption.…”

Influence of displacement constraints to the surface reconstruction of stressed bicrystal thin films

“…The crucial role of elastic dipole tensor interactions (EDTI) on driving force for surface diffusion was considered previously, under tensile [15] and compressive [16] uniaxial stresses applied to freestanding thin films. As the dimensions of ultrathin films approached, small thicknesses can lead to great stress gradients, which act as a driving force for grain boundary diffusion [17].…”

Hillock formation by surface drift-diffusion driven by the gradient of elastic dipole interaction energy under compressive stresses in bi-crystalline thin films

“…Later, other authors also employed the concept for bulk [19] and grain boundary [20] diffusion. According to our best knowledge, excluding our recent work on the effects of applied uniaxial tension stresses on GB grooving [21], there exists neither gross scale simulation nor analytical work that reflects the dominant effect of long range surface drift-diffusion driven by the stress gradient in the literature. The main reason for this is that the surface is always assumed to be traction free, and thus the Herring's force vanishes identically (see Appendix).…”