The intrinsic non-linearity in silicon has led to this material being proven to be quite useful in the field of quantum optics. A quantum signal source in the form of single photons is an inherent requirement to the principle of quantum key distribution technology for secure communications, since a message that is encrypted via a quantum source cannot be branched or stolen. Here, we present the numerical simulations of a silicon ring with 6-micron radius side-coupled to the bus waveguide as a source for the generation of single photons by exploring the process of degenerate spontaneous four-wave mixing (SFWM). The free spectral range (FSR) is quite large, which simplifies the extraction of signal/idler pairs. The phase matching condition is considered by studying relevant parameters like dispersion and non-linearity. We optimize the ring to achieve a high quality factor by varying the gap between the bus and the ring waveguide. This is the smallest ring studied for photon pair generation, with a quality factor as high as 10⁵. The width of the waveguides is chosen so that the phase matching condition is satisfied, allowing for the propagation of fundamental modes only. The bus waveguide should be pumped at one of the ring resonances with minimum dispersion (1543.5 nm in our case) so that the principle of energy conservation is satisfied. The photon pair generation rates achieved are already better in the low-pump-power regimes in comparison to those discussed in the literature. Such miniaturized structures will prove beneficial for future on-chip architectures where multiple single photon source devices are required on the same chip.