Two-Dimensional Phase Transition Mediated by Extrinsic Defects

We have investigated the $(\sqrt{3}\times \sqrt{3})$ to $(3\times 3)$ phase transition in the α phase of Sn/Ge(111) with variable temperature STM at temperatures between 30 and 300 K. Point defects in the Sn film stabilize localized regions of the $(3\times 3)$ phase, where the size is characterized by a temperature dependent length (exponential attenuation). The inverse of the attenuation length is a linear function of temperature showing that the phase transition occurs at 70 K. At low temperature a density wave mediated defect-defect interaction realigns the defects to be in registry with the $(3\times 3)$ domains.