About 8 year electron density profile (EDP) data from the COSMIC/FORMOSAT-3 satellites radio occultation technique were used to investigate the additional stratification of the F2 (the so-called F3 layer) layer over the equatorial and low-latitude ionosphere on a global scale for both the bottomside and topside ionosphere. The F3 layer was recognized through the altitude differential profile featured by two maxima existing from the selected EDP profile. There were~37,000 (bottomside) and 25,000 (topside) cases of F3 layer selected out of~1.27 million occultation events at equatorial and low-latitude areas during the period of April 2006 to August 2014. The statistical results for the bottomside ionosphere resemble that reported in Zhao et al. (2011a), while in the topside the highest occurrence of F3 layer shows a 3-4 h delay depending on the altitude range of the stratification. The magnetic latitude distribution shows different dependence with a tendency to form a single crest toward high altitude. Also, the seasonal variation is weaker in the topside ionosphere compared to the bottomside one, especially in the high altitude. Then we build up an empirical model of the F3 layer occurrence using the bottomside statistics based on empirical orthogonal function (EOF) decomposition as it gets the inherent characters inside the data set and converges quickly. The model well grasps the main features of the F3 occurrence, e.g., the F3 occurrence's sensitivity on the magnetic latitude. Further, in order to accommodate the ground observation a corrected factor was introduced. As F3 layer is an important phenomenon in the low-latitude ionosphere, we have made an attempt to describe its feature with a consecutive function although future work needs to be done for an overall expression of this structure.