Influence of defects on the order-disorder phase transition of a Si(001) surface

We study the influence of surface defects on the order-disorder phase transition of a Si(001) surface using Monte Carlo (MC) simulations based on the asymmetric-dimer model. The transition becomes broad in the system with a low density of the type-C defect. The temperature dependence of the long-range-order parameter (LOP), local-order parameter, and the intensity of the low-energy electron diffraction (LEED) peak is investigated. In order to analyze the local ordering from the scanning-tunneling-microscopy (STM) image quantitatively, the fraction of the site of the asymmetric image, called 'mesoscopic ordering index' (MOI), is introduced. The critical temperatures, defined as the middle point of the transition region of the LOP, the MOI, and the LEED intensity, are almost the same. The experimental temperature dependence of the LEED peak is explained by a combined effect of the defects and the coherence length. The present study offers an answer to the question what actually corresponds to the transitions observed in LEED and STM experiments.