The dissociation of an ammonia molecule on a cluster of Si atoms simulating the 100 silicon crystal structure with two Si dimers has been investigated by means of the DFT and an approximate instanton methods. The model corresponds to the low coverage limit of the surface. Absolute rate constants of two different dissociation paths are evaluated together with deuterium isotope effects. It is demonstrated that, even at room temperatures, the process is dominated by tunneling and that dissociation to a silicon atom of the adjacent dimer, rather than a silicon within the same dimer, is the prevailing mechanism. This leads to creation of a metastable structure which will slowly decay through a two-step hydrogen atom migration towards the absolute minimum on the potential energy surface corresponding to the NH2 group and the hydrogen atom residing in the same dimer.