Single photons and photon pairs are typically generated by spontaneous parametric down conversion or quantum dots; however, spontaneous four-wave mixing (SFWM) in silicon microring resonators [1] is also an appealing source of entangled photons, offering a strong cavity-enhanced nonlinear interactions while maintaining features, such as compact, simple to fabricate, and allowing for thermal tuning. However, silicon ring-resonators usually suffer from a trade-off between providing a high pair generation rate (PGR) and high extraction efficiency. To achieve high PGR, devices are generally operated with the signal and idler photons in the undercoupling regime and pump photons at the critical coupling point, while high extraction rates require the converted photons to be overcoupled. Therefore, the optimal conditions for achieving maximal output photon pair flux are critical coupling for the pump photons and overcoupling for the converted photons [2,3]. However, it is not easy to approach such optimal coupling conditions with traditional single-bus waveguide-coupled resonators and double-bus resonators because they do not allow the coupling conditions for the pump and converted photons to be controlled independently.Herein, we propose to use dual asymmetric Mach-Zehnder *Corresponding authors (YueChan Kong,