  Moving crystal surfaces can undergo step-bunching instabilities, when subject
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.
