Lattice Gas Model of Si(111)

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A lattice gas model which incorporates the Takayanagi mechanism stabilizing the (7×7) structure of the Si(111) surface is proposed. Monte Carlo calculations are carried out on the model to show that it is applicable to the surface both below and above the transition. The phase diagram and diffuse scatterings of electron in the (1×1) phase within the kinematical approximation are presented. The phase transition from the (7×7) state to the (1×1) is shown to be of the first kind, and it is shown that the model can reproduce diffuse spots around the (\sqrt3×\sqrt3) Bragg points just above the transition. The underlying mechanism is also discussed in detail. Moreover, the disappearance of stacking faults in the (1×1) phase is concluded from the calculation. The interrelation between the reconstructions of Si(111) and Ge(111) is discussed in a unified way on the basis of the calculations. The recent real-time STM observation of the surface at the transition performed by Miki et al. is also discussed.

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