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We investigate the relative thermodynamic stability of the $3\times3$,$5\times5$, $7\times7$, $9\times9$ and infinitely large structures related tothe dimers-adatoms-stacking faults family of Si$(111)$ surface reconstructionsby means of first-principles calculations. Upon accounting for the vibrationalcontribution to the surface free energy, we find that the $5\times5$ structureis more stable than the $7\times7$ at low temperatures. While a phasetransition is anticipated to occur at around room temperature, the$7\times7\rightarrow5\times5$ transformation upon cooling is hindered by thelimited mobility of Si atoms. The results not only flag a crucial role ofvibrational entropy in the formation of the $7\times7$ structure at elevatedtemperatures, but also point for its metastable nature below room temperature.

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