374558 Stabilization of the Surface Morphology of Stressed Solids Using Electric Fields and Thermal Gradients
Stressed crystalline conducting materials are commonly found in micro-electronic devices and are involved in nanofabrication techniques. The surface morphological instability of these materials limits the functionality and durability of the devices. Failure of these materials is commonly mediated by the well-known Asaro-Tiller/Grinfeld (ATG) instability, which results from the competition between surface energy and strain energy and leads to the formation of cusp-like surface features with deep grooves and, eventually, the surface cracking of the material.
We have examined the surface morphological stability of electrically and thermally conducting crystalline elastic solids in uniaxial tension under the action of a temperature gradient, as well as under the simultaneous action of a temperature gradient and an electric field. For the analysis, we used linear stability theory and self-consistent dynamical simulations based on a fully nonlinear surface mass transport model that accounts for surface thermomigration and electromigration induced by the externally applied fields, surface diffusional anisotropy, and the Arrhenius temperature dependence of the surface diffusivity.
We found that a properly directed higher-than-critical thermal gradient alone can stabilize the planar surface morphology against the ATG instability. Under conditions typical of metallic thin-film interconnects, the required critical thermal gradient was found to be on the order of 100 K/cm. We also found that electric fields and thermal gradients, if properly directed, can work synergistically to achieve a strong effective external field, which, if higher than critical, can stabilize the planar surface morphology. The temperature dependence of the surface diffusivity does not change the criticality criterion but only affects the rate of growth or decay of the surface morphological perturbation from the planar state. In case of failure due to the ATG instability, we characterized the super-exponential growth of the surface perturbation amplitude and derived a scaling relationship for the amplitude evolution near failure. Our study sets the stage for an effective, practical solution to inhibit surface cracking of crystalline solids due to the ATG instability through simultaneously applied multiple external fields.