Ab initiostudy of thallium nanoclusters onSi(111)−7×7

Abstract

We have studied the stability of a thallium nanocluster of various numbers of atoms $(N=1,2,\dots{},10)$ on a $\mathrm{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ substrate using density functional theory total energy calculations. We have compared it with clusters of other group III elements (Al, Ga, and In). Thallium is found to be unstable with the triangular cluster, which has been known to be stable for other group III elements. Instead, a slightly different structure, in which Si atop atoms are lower than thallium atoms in height by $2.56\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, was found to be quite stable. Such an abnormal structure originates from the inert pair of $6{s}^{2}$ electrons due to the significant spin-orbit interaction. The initial relaxed $N=6$ Tl cluster continues to grow with increasing $N$ up to $N=9$ in the faulted-half unit cell, which is consistent with experimental observations.