We demonstrate the preferential formation and self-assembly of monodisperse Si magic clusters $\left(X_4\right)$ of size $\sim 13.5\pm 0.5\text{Å}$ on $\text{Si}\left(111\right)\text{−}\left(7\times 7\right)$ surface using scanning tunneling microscope. The growth process is observed to occur via a stepwise assembly of planarized Si tetramers $\left(X_1\right)$ formed from Si adatoms deposited at room temperature, leading to Si tetraclusters $\left(X_2\right)$ (size $\sim 4.6\pm 0.5\text{Å}$) and culminating in tetracluster dimer $\left(X_3\right)$ and trimer $\left(X_4\right)$ formations as the surface is being annealed progressively to $150°\text{C}$. The respective cluster species density distribution at each annealing temperature also shows the preferential formation of $X_1\to X_2\to X_3\to X_4$ at higher temperatures, which we describe using surface reaction schemes; $X_1\to X_2$, $X_2+X_2\to X_3$, and $X_2+X_3\to X_4$. We determine the activation and formation energies for respective cluster species and elucidate the formation energetics and dynamics of tetraclusters which function unequivocally as fundamental building blocks in the self-assembly of stable Si magic clusters. Finally, we resolve the structure of the Si magic cluster to comprise three tetraclusters or $n=12$ Si atoms taking into consideration (i) cluster symmetry and alignment, (ii) close packing, and (iii) minimization of dangling bonds.

• Received 11 February 2009

DOI:https://doi.org/10.1103/PhysRevB.79.235439