(272f) Surface Stabilization of Heteroepitaxial Thin Films Induced by the Combined Action of Electric and Thermal Fields
Stressed elastic solids are known to undergo surface morphological instabilities; inhibiting such instabilities is important in the fabrication of devices. It is well known, for example, that the competition between elastic strain energy and surface energy can destabilize the surface of a stressed elastic solid through the Asaro-Tiller or Grinfeld (ATG) instability. For device fabrication purposes, heteroepitaxial film/substrate systems are of particular interest. Typically, these consist of a coherently strained thin film grown epitaxially on a substrate of a different material; due to lattice mismatch between the two constituent materials, the film is subjected to misfit strain, which can destabilize the planar film surface according to the so-called Stranski-Krastanow (SK) morphological instability that leads to the formation of islands on the film surface. In recent studies, we have shown that, in such a material system, the application of a properly directed and sufficiently strong electric field can inhibit the SK instability and maintain the planar state of the film surface morphology. Furthermore, we have shown that the requirements for the strength of the externally applied electric field can be minimized by the use of substrate engineering techniques, among which most notable is the use of finite-thickness compliant substrates.
In this presentation, we explore the surface morphological response of a coherently strained epitaxial thin film under the simultaneous action of the applied electric field and a temperature gradient; such thermal fields are common in device fabrication and service. We have developed a three-dimensional (3D) fully nonlinear model for the driven mass transport on the surface of a thin film that is electrically conducting, coherently strained, epitaxially grown on an elastically deformable substrate, and subjected simultaneously to the electric and thermal fields. The model accounts for curvature-driven and stress-driven surface diffusion, electromigration and thermomigration fluxes driven by the external fields, as well as surface diffusional anisotropy. We have derived an evolution equation for the film’s height and solved the elastostatic, electrostatic, and thermal boundary-value problems (BVPs) that are coupled with it. Combining the solutions to the BVPs with the evolution equation and linearizing, we have derived the corresponding amplitude evolution equation for the study of surface morphological stability and pursued it using linear stability analysis. We have examined in detail the synergy and competition between the applied electric and thermal fields and determined their proper alignments for optimal stabilization of the planar film surface morphology. For such alignments, we have predicted the critical electric-field strength required for film surface stabilization as a function of material properties, heteroepitaxial system parameters, and the strength of the applied temperature gradient.
We have also analyzed the surface morphological stabilization of heteroepitaxial films on substrates by combining the simultaneous application of the two external fields with well-known strain engineering techniques, including the use of thin compliant substrates; such substrates provide some elastic accommodation of the lattice-mismatch strain in the epitaxial film due to the substrate’s ability to relax parallel to its interface with the epitaxial film. Employing substrate engineering techniques alone is not sufficient for stabilizing the planar morphology of the epitaxial films; for such stabilization, the simultaneous action of the externally applied electric field is required. Our analysis demonstrates that a properly oriented electric field, acting simultaneously with an external thermal field and in combination with the use of a compliant substrate, can reduce the electric-field strength requirement for planar film surface stabilization by several (over three) orders of magnitude compared to that required for a typical thick substrate and without any thermal aid. Our analysis generates experimentally testable hypotheses and motivates experimental measurements that can be compared directly with the theoretical predictions.