The structural and electronic properties of an atomically-flat Te-Si(111) surface have been investigated by means of density-functional theory calculations. This system is interesting because it provides a template for the epitaxial growth of inherently 2D materials. A structural model of the surface is devised that is both energetically more favorable than the ideal on-top model proposed in the literature and dynamically stable. The model, characterized by a staggered arrangement of Te-Te dimers in the passivation layer, is a semiconductor with a narrow band gap resulting from the misalignment of the ${\mathrm{Te}}_{2}$ units. As for the on-top case, however, this structure does not fully conforms to the available experimental observations. A finite-temperature model is hence prepared by means of molecular dynamics simulations at 300 K. It turns out that such a model is characterized by a disordered passivation layer consisting of randomly oriented ${\mathrm{Te}}_{2}$ units and Te chains, which makes it effectively compliant with all the experimental structural data at hand. In addition, it is also a narrow-gap semiconductor compatible with the electrical conductance measurements. These findings suggest that this model is a good candidate for representing the Te-Si(111) surface.
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