STRESS-CONCENTRATION AT SLIGHTLY UNDULATING SURFACES

THIS PAPER presents a first-order perturbation analysis of the stress concentration effects caused by slightly undulating surfaces. The perturbation approach that we use treats the undulating surfaces as being perturbed from a reference state in which the surface is perfectly flat. The magnitude of the perturbation is assumed to be sufficiently small compared to other length scales of the bulk material so that a half-plane model can be used for simplification. First-order-accurate perturbation solutions have been derived for the stress distribution along a sinusoidally wavy surface and for the attentuation of the stress concentration away from the undulating surface. The interactions among different surface perturbation waves are investigated by comparing the result of stress concentration factor at the trough of a single wave perturbation along an otherwise flat surface to that for periodically wavy surface. We also examine some of the 3-D effects by using the perturbation algorithm to calculate the stress concentration at undulating surfaces of elastic half-spaces. In all cases, it is found that wavy surfaces can magnify the bulk stress easily by a factor of 2 or 3 when the surface profile does not deviate substantially from flatness. This stress concentration effect is significant especially for already highly stressed heteroepitaxial semiconductor thin films, suggesting that the surface morphology of the film surfaces can play an important role in nucleating dislocations and crack-like surface flows before the bulk stress reaches a critical level.