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

TL;DR

This study reveals that vibrational entropy significantly influences the thermodynamic stability of Si(111) surface reconstructions, making the 5x5 structure more stable at low temperatures and highlighting the metastability of the 7x7 structure below room temperature.

Contribution

It demonstrates the crucial role of vibrational entropy in determining the stability and phase transitions of Si(111) surface reconstructions through first-principles calculations.

Findings

Vibrational entropy favors the 5x5 structure at low temperatures.

A phase transition from 7x7 to 5x5 is predicted around room temperature.

The 7x7 structure is metastable below room temperature.

Abstract

We investigate the relative thermodynamic stability of the $3\times3$, $5\times5$, $7\times7$, $9\times9$ and infinitely large structures related to the dimers-adatoms-stacking faults 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 $5\times5$ structure is more stable than the $7\times7$ at low temperatures. While a phase transition is anticipated to occur at around room temperature, the $7\times7\rightarrow5\times5$ 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 $7\times7$ structure at elevated temperatures, but also point for its metastable nature below room temperature.