We propose a natural two-speed model for the phase dynamics of Si(111) 7$times$7 phase transition to high temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated resul
ts show that a 7$times$7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. LEEM experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.
We propose a two-dimensional phase-field-crystal model for the (2$times$1)-(1$times$1) phase transitions of Si(001) and Ge(001) surfaces. The dimerization in the 2$times$1 phase is described with a phase-field-crystal variable which is determined by
solving an evolution equation derived from the free energy. Simulated periodic arrays of dimerization variable is consistent with scanning-tunnelling-microscopy images of the two dimerized surfaces. Calculated temperature dependence of the dimerization parameter indicates that normal dimers and broken ones coexist between the temperatures describing the charactristic temperature width of the phase-transition, $T_L$ and $T_H$, and a first-order phase transition takes place at a temperature between them. The dimerization over the whole temperature is determined. These results are in agreement with experiment. This phase-field-crystal approach is applicable to phase-transitions of other reconstructed surface phases, especially semiconductor $ntimes$1 reconstructed surface phases.
