Several alternative models have been proposed for the much-studied $\text{Si}\left(111\right)\text{−}(2\times 1)$ surface structure, including: A reverse-tilted $\pi$-bonded chain model [Zitzlsperger et al. Surf. Sci 377, 108 (1997)]; a three-bond scission model [by Haneman, Phys. Rev. 121, 1093 (1961)]; and a $\pi$-bonded chain model with enhanced vibrations (present work). These models are compared here to the generally accepted modified $\pi$-bonded chain model [Himpsel et al., Phys. Rev. B. 30, 2257 (1984)], by analyzing low-energy electron diffraction (LEED) intensity–voltage curves measured earlier. Using the efficient automated tensor LEED technique, the models can be refined to a much greater degree than with earlier methods of LEED analysis. This study distinctly favors the earlier modified $\pi$-bonded chain model, but with strongly enhanced vibrations. To compare models that have different numbers of adjustable free parameters, a Hamilton ratio test is used: It can distinguish between improvement due to a better model and improvement due only to more parameters.

• Received 9 March 2004

DOI:https://doi.org/10.1103/PhysRevB.70.045307