Low-energy nuclear recoils induced by elastic neutrino nuclear coherent scattering with nuclei in pure materials have become an important topic of research, in particle physics. We present a detailed model to compute the ionization efficiency for nuclear recoils in silicon (quenching factor) based on original integral equation, which is capable of describing recent measurements at low-energy. We take as case example a silicon based reactor antineutrino experiment and compare the effect of this quenching factor in the calculation of the CE$\nu$NS rate with that of other curves that have been previously used. We are going to discuss the universal applicability of this model to other materials, such as noble liquid TPCs, which in recent years have become relevant for neutrino low energy CENS searches. Finally, a general discussion of the different effects that directly account for the conversion of nuclear recoil energy ($\rm{eV_{nr}}$) into electron equivalent energy ($\rm{eV_{ee}}$) in ionization detectors.