Disproportionation Phenomena on Free and Strained Sn/Ge(111) and Sn/Si(111) Surfaces

TL;DR

This study investigates the disproportionation phenomena on Sn/Ge(111) and Sn/Si(111) surfaces, revealing how strain influences surface distortions and pseudocharge states through a theoretical phase diagram analysis.

Contribution

It provides a novel theoretical understanding of surface distortions and pseudocharge disproportionation in Sn/Ge(111) and Sn/Si(111) surfaces under strain conditions.

Findings

Positive strain removes distortions at Q=3

Negative strain induces higher pseudocharge states Q=4 and Q=6

Discussion of potential fluctuating phase in unstrained Sn/Si(111)

Abstract

Distortions of the $\sqrt3\times\sqrt3$ Sn/Ge(111) and Sn/Si(111) surfaces are shown to reflect a disproportionation of an integer pseudocharge, $Q$, related to the surface band occupancy. A novel understanding of the $(3\times3)$-1U (``1 up, 2 down'') and 2U (``2 up, 1 down'') distortions of Sn/Ge(111) is obtained by a theoretical study of the phase diagram under strain. Positive strain keeps the unstrained value Q=3 but removes distorsions. Negative strain attracts pseudocharge from the valence band causing first a $(3\times3)$-2U distortion (Q=4) on both Sn/Ge and Sn/Si, and eventually a $(\sqrt3\times\sqrt3)$-3U (``all up'') state with Q=6. The possibility of a fluctuating phase in unstrained Sn/Si(111) is discussed.