Critical step undulation by elastic interaction

Theoretical explanation of the transition from a straight step to a wavy step that was observed on Si(001) is presented. The origin of this transition is the instability developed due to a negative logarithmic divergence of the wavy step elastic self-interaction. Above the critical temperature the straight step is stabilized by the interaction between different steps. The instability results in a second order phase transition with a finite critical wavelength. The predicted mean square fluctuation near the transition point deviates from the wavelength square law predicted by the edge-stiffness theory, and consists of the critical growth of the unstable soft mode, yielding a peaked power spectrum.