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 grows 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.