Silicon Emitting Centers (SEC) constitute promising candidates for quantum telecommunication technologies. Their operation depends on the fabrication of light emitting defect centers such as the tri-interstitial Si complex, the W-Center. In this paper the formation of Si tri-interstitial clusters after Ga ion beam bombardment on pure silicon substrates and a subsequent annealing stage is investigated using molecular dynamics (MD) simulations. This study aims to understand the dynamic formation process of W centers after Ga irradiation and annealing in order to facilitate their creation using focused ion beam and annealing experimental systems. A new tri-interstitial cluster identification method is proposed which considers the configuration of the clusters in the Si lattice in order to identify the defects which will act as candidates for the W center. This method successfully identifies W center defect candidates in an ideal system. The number of tri-interstitial clusters increases and spreads deeper into the Si for higher energies and their probability of generation increases until a limiting Ga fluence. Furthermore annealing can eliminate a lot of the unwanted defects maintaining at the same time the number of the tri-interstitial clusters, leading to isolated clusters with less distorted local environment.