Dwaipayan Dasgupta

Surface morphological stabilization of stressed crystalline solids by simultaneous action of applied electric and thermal fields

We examine the surface morphological stability of electrically and thermally conducting crystalline elastic solids in uniaxial tension under the simultaneous action of an electric field and a temperature gradient. We use linear stability analysis of a surface mass transport model that accounts for surface electromigration and thermomigration induced by the applied fields and for surface diffusional anisotropy. We find that a properly oriented applied thermal gradient can reduce the critical electric-field strength requirement for stabilization of the planar surface morphology. The temperature dependence of the solid material’s properties does not affect the critical strength requirement of the applied fields.

Stabilization of the surface morphology of stressed solids using thermal gradients

We examine the surface morphological stability of thermally conducting crystalline elastic solids in uniaxial tension under the action of a temperature gradient. We use linear stability theory and self-consistent dynamical simulations based on a surface mass transport model that accounts for surface thermomigration induced by the applied thermal gradient, surface diffusional anisotropy, and the temperature dependence of surface diffusivity. We find that a properly directed thermal gradient of magnitude higher than a critical value can stabilize the planar surface morphology. Under conditions typical of metallic thin-film interconnects, the required critical thermal gradient is on the order of 100 K/cm.

Surface nanopatterning from current-driven assembly of single-layer epitaxial islands

We report numerical simulation results on an approach to surface nanopatterning based on the current-driven assembly of single-layer epitaxial islands on crystalline substrates. We focus on the evolution of pairs of different-size islands driven to coalescence and explore the effects of three key geometrical parameters: the sizes of the two islands of the pair and their center-to-center line misalignment with respect to the electric-field direction. We discover various patterns ranging from equal- and different-size stable steady island-pair configurations to many-island patterns that can be tailored by controlling the initial-pair geometrical parameters and the duration of application of the electric field.

The effect of a thermal gradient on the electromigration-driven surface morphological stabilization of an epitaxial thin film on a compliant substrate

We report a theoretical analysis on the surface morphological stability of a coherently strained thin film that has been grown epitaxially on a deformable substrate and is simultaneously subjected to an external electric field and a temperature gradient. Using well justified approximations, we develop a three-dimensional model for the surface morphological evolution of the thin film and conduct a linear stability analysis of the heteroepitaxial films planar surface state. The effect of the simultaneous action of multiple external fields on the surface diffusional anisotropy tensor is accounted for. Various substrate types are considered, but emphasis is placed on a compliant substrate that has the ability to accommodate elastically some of the misfit strain in the film due to its lattice mismatch with the substrate. We derive the condition for the synergy or competition of the two externally applied fields and determine the optimal alignment of the external fields that minimizes the critical electric fie...

Current-driven nanowire formation on surfaces of crystalline conducting substrates

The formation and precise manipulation of nanoscale features by controlling macroscopic forces is essential to advancing nanotechnology. Toward this end, we report here a theoretical study on formation of nanowires with precisely controlled widths, starting from single-layer conducting islands on crystalline conducting substrates under the controlled action of macroscopic forcing provided by an externally applied electric field that drives island edge electromigration. Numerical simulations based on an experimentally validated model and supported by linear stability theory show that large-size islands undergo a current-induced fingering instability, leading to nanowire formation after finger growth. Depending on the substrate surface crystallographic orientation, necking instabilities after fingering lead to the formation of multiple parallel nanowires per island. In all cases, the axis of the formed nanowires is aligned with the direction of the externally applied electric field. The nanowires have const...

Weakly nonlinear theory of secondary rippling instability in surfaces of stressed solids

Numerical simulations of the surface morphological evolution of uniaxially stressed elastic crystalline solids have demonstrated that in addition to Asaro-Tiller/Grinfeld (surface cracking) instabilities, long-wavelength perturbations from the planar surface morphology can trigger a tip-splitting instability that causes formation of a pattern of secondary ripples, which cannot be explained by linear stability theory. In this study, we develop a weakly nonlinear stability theory, which can explain the occurrence of such secondary rippling instabilities and predict the number of secondary ripples that form on the surface as a function of perturbation wavelength. The theory shows that this type of surface pattern formation arises entirely due to the competition between surface energy and elastic strain energy, regardless of surface diffusional anisotropy or the action of externally applied fields. The origin of secondary rippling is explained through nonlinear terms included in the analysis which generate su...

Stabilization of the surface morphology of stressed solids using simultaneously applied electric fields and thermal gradients

We analyze the surface morphological stability of bulk conducting face-centered cubic (fcc) crystalline solids in uniaxial tension under the simultaneous action of an electric field and a temperature gradient. The analysis is based on self-consistent dynamical simulations, in conjunction with linear stability theory, according to a well validated fully nonlinear surface mass transport model that accounts for surface electromigration and thermomigration induced by the externally applied fields, surface diffusional anisotropy, and the Arrhenius temperature dependence of surface diffusivity. Our simulation results validate the findings of linear stability theory and establish that the electric field and the thermal gradient, if properly directed, can work synergistically to stabilize the planar surface morphology against the Asaro-Tiller/Grinfeld (ATG) instability when the strength of the resulting effective external field is higher than a critical level. We also show that the temperature dependence of the surface diffusivity does not change the criticality criterion for surface stabilization but only affects the rate of growth or decay of the surface morphological perturbation from its planar state. Furthermore, we establish that, in fcc crystals, the morphological response of ⟨111⟩-oriented surfaces is superior to that of differently oriented surfaces. In case of failure due to ATG instability, the super-exponential growth of the surface perturbation amplitude exhibits a logarithmic singularity as the time to failure is approached. Our study provides an effective practical solution to inhibit the surface cracking of crystalline conducting solids based on the optimal combination of the simultaneous action of externally applied electric fields and thermal gradients.

Surface nanopattern formation due to current-induced homoepitaxial nanowire edge instability

Physical nanopatterning based on a precise control of macroscopic forcing is an essential tool of nanoscale science and technology. Using an externally applied electric field as the macroscopic force, we report here a computational study on the formation of surface nanopatterns consisting of single-layer homoepitaxial islands as a result of a morphological instability that can occur under edge electromigration conditions on the straight edge of a single-layer nanowire grown epitaxially on a crystalline substrate. Direct dynamical simulations based on a model that has been validated experimentally for the Ag/Ag system show that the current-induced nanowire edge instability causes the breakup of the nanowire and leads to the formation of uniformly distributed islands, arranged in linear or V-shaped arrays, which are uniformly sized with nanoscale dimensions. The simulation results are supported by linear stability theory and demonstrate that the geometrical features of the island patterns and the island siz...

Electromigration-driven complex dynamics of void surfaces in stressed metallic thin films under a general biaxial mechanical loading

We report results of a systematic computational study of the electromigration-driven complex surface dynamics of voids in mechanically stressed thin films of face-centered cubic metals with 〈100〉-oriented film planes. The films are subjected to an external electric field simultaneously with biaxial mechanical loading, which can be either purely compressive, ranging from purely isotropic to strongly anisotropic including uniaxial, or a mixed type of loading with both tensile and compressive stress components in the applied stress tensor. Our analysis is based on self-consistent dynamical simulations of driven void surface morphological evolution following a well validated, two-dimensional, and fully nonlinear model. We find that depending on the electromechanical conditions, void size, and surface diffusional anisotropy, two types of asymptotic states can be stabilized in the void surface dynamical response, namely, morphologically steady or time-periodic traveling voids, and film failure can be caused by ...