Singular response to a dopant of an evaporating crystal surface

Moving crystal surfaces can undergo step-bunching instabilities when subjected to an electric current. We show analytically that an infinitesimal quantity of a dopant may invert the stability, whatever the sign of the current. Our study is relevant for experimental results [S. S. Kosolobov et al., JETP Lett. 81, 117 (2005)] on an evaporating Si(111) surface, which show a singular response to Au doping, whose density distribution is related to inhomogeneous Si diffusion.