We performed a systematic investigation on silicon-doped boron clusters BnSi (n = 8-14) in both neutral and anionic states using quantum chemical methods. Thermochemical properties of the lowest-lying isomers of BnSi0/- clusters such as total atomization energies, heats of formation at 0 and 298 K, average binding energies, dissociation energies, etc. were evaluated by using the composite G4 method. The growth pattern for BnSi0/- with n = 8-14 is established as follows: (i) BnSi0/- clusters tend to be constructed by substituting B atom by Si-atom or adding one Si-impurity into the parent B-n clusters with n to be even number, and (ii) Si favors an external position of the B-n frameworks. Our theoretical results reveal that B8Si, B9Si-, B10Si and B13Si- are systems with enhanced stability due to having high average binding energies, second-order difference in energies and dissociation energies. Especially, by analyzing the MOs, ELF, and ring current maps, the enhanced stability of B8Si can be rationalized in terms of a triple aromaticity.