Evolution of a surface-roughness spectrum caused by stress in nanometer-scale chemical etching

It is reported that a flat Free surface of a stressed solid is configurationally unstable under chemical etching and the surface roughness groups with different rates for different spatial frequencies. The theory described in this Letter predicts that with a shallow chemical etching the roughness with spatial frequency below a critical value grows while the roughness of higher frequency decays. The theory was verified via an atomic force microscope experiment with aluminum. This study provides a simple experimental method to measure stress in metals and ceramics.