Theoretical study of pure (Si n ) and doped silicon (AlSi n-1 and PSi n-1 ) clusters (n=2–13) using ab initio molecular orbital theory

Abstract

The geometric and electronic structures of Si_n, ${Si}_{n}^{+}$ , ${Si}_{n}^{-}$ , $Al {Si}_{n - 1}$ and $P {Si}_{n - 1}$ clusters ( $2 ⩽ n ⩽ 13$ ) has been investigated using the ab initio molecular orbital theory under the density functional theory formalism. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy ( $Δ^{2} E$ ) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si_n clusters shows similar structural growth. The geometries of the ${Si}_{n}^{+}$ and $Al {Si}_{n - 1}$ are similar to those of the Si_n, but with small distortions. The ground state geometries of the $Al {Si}_{n - 1}$ clusters shows that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si_n cluster. However for ${Si}_{n}^{-}$ , $n = 6$ , 8, 11, and 13, significant changes have been observed in the ground state geometries of the negatively charged clusters as compared to their neutral counterparts. In general the geometries of the P substituted silicon clusters remain similar to that of negatively charged Si_n clusters with small local distortions. In general, the average binding energy of charged clusters is found to be higher than that of neutral Si_n clusters. However, significant differences have been observed in the electronic structure of neutral and charge cluster leading to their different stability pattern. While for neutral clusters, the Si₁₀ is magic, the extra stability of the ${Si}_{11}^{+}$ cluster over the ${Si}_{10}^{+}$ and ${Si}_{12}^{+}$ bears evidence for the magic behavior of the ${Si}_{11}^{+}$ cluster, which is in excellent agreement with the recent experimental observations (ref. [29]). Similarly for $Al {Si}_{n - 1}$ clusters, which is iso-electronic with ${Si}_{n}^{+}$ clusters show extra stability of the AlSi₁₀ cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. For iso-electronic $P {Si}_{n - 1}$ clusters, it is found that although for small clusters ( $n < 4$ ) substitution of P atom improves the binding energy of Si_n clusters but for larger clusters ( $n > 4$ ), the effect is opposite. The fragmentation behavior of all these clusters shows that while small clusters prefers to evaporate monomer, the larger ones dissociates into two stable clusters of smaller size. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.