Crucial role of vibrational entropy in the Si(111)-7 x 7 surface structure stability

We investigate the relative thermodynamic stability of the 3 x 3, 5 x 5, 7 x 7, 9 x 9, and infinitely large structures related to the dimer-adatom-stacking fault family of Si(111) surface reconstructions by means of first-principles calculations. Upon accounting for the vibrational contribution to the surface free energy, we find that the 5 x 5 structure is more stable than the 7 x 7 at low temperatures. While a phase transition is anticipated to occur at around room temperature, the 7 x 7 -> 5 x 5 transformation upon cooling is hindered by the limited mobility of Si atoms. The results not only flag a crucial role of vibrational entropy in the formation of the 7 x 7 structure at elevated temperatures, but also point to its metastable nature below room temperature.