The surface reconstruction phase transition on Sn or Pb adsorbed Si or Ge (111) surface is widely studied because of the interest of the charge density wave (CDW)[1] in the low temperature phase and the many body effects at much lower temperature. There are few studies, however, focusing the short range ordering of the disordered state in the high temperature phase and/or the electronic structure change accompanied with the phase transition. In this paper, we tried to make theoretical analyses of the temperature factor (Debye-Waller factor) on the X-ray diffraction and the temperature dependence of surface electronic states around the transition temperature.
These surface systems have similar characteristics about their √3x√3-3x3 phase transitions. We assume that the phase transition is a kind of order disorder phase transition [2]whose order parameters are the displacements of the adsorbates normal to the surface. [3, 4] The order parameters are considered with the Ising model and the surface electronic states are handled with the tight binding model. We consider that the ordered phase is the CDW state strongly coupled with the atomic displacements of the adsorbates.
To obtain the electronic properties at finite temperatures, we use the combination of the tight binding model calculation and the Monte Carlo method with Metropolis algorithm. The calculated density of state projected into the reciprocal space (RDOS) shows the electronic band structure that can be compared with the photoemission experiments. We also analyzed the anisotropic Debye-Waller factor of this surface.
[1] E. Tosatti and P. W. Anderson, Jpn. J. Appl. Phys. 2 (1974) 381.
[2] J. Avila et al., Phys. Rev. Lett. 82 (1999) 442.
[3] J. Zhang, et al., Phys. Rev. B60 (1999) 2860.
[4] O. Bunk, et al., Phys. Rev. Lett. 83 (1999) 2226.
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