Stress-dependent surface reactions and implications for a stress measurement technique

In contact with an environment, a solid may gain or lose mass due to, for example, deposition or etching. As the reaction proceeds, the surface of the solid moves, either extending or receding. If the solid is under stress, the elastic energy adds to the driving force of the reaction, and may cause the surface to roughen. This phenomenon has recently led to a novel experimental technique to determine the stress state in a solid by using an atomic force microscope to scan the surface profiles before and after etching. Stress is also known to change the mobility of a reaction. By this mechanism, the stress may either roughen or stabilize a flat surface. This article describes a linear perturbation analysis of a three-dimensional solid surface evolving under stress, using a general kinetic law. It is found that when the reaction is near equilibrium, the stress effect on driving force dominates; when the reaction is far from equilibrium, the stress effect on mobility dominates. Under these two conditions, the surface profile spectra have different patterns and length scales. The implications for the stress measurement technique are discussed. It is suggested that the same experimental procedure be used to measure surface energy and activation strains.