The modeling of intermediate band solar cell has been developed since 90's and continued effort is made to facilitate the realization of this novel device. Two formulation has been used to model the generation recombination rate of IBSC including conventionally available modified-Shockley-Reed-Hall formulation or later proposed IBSC formulation (Luque and Marti, PRL 78 5014). This paper proves that these two formulations are actually mathematically equivalent and actually one can be derived from the other. A unified mathematical framework can thus be established and the conventional drift-diffusion model can thus be employed for modeling novel IBSC with the inclusion of new model for intermediate band carrier transport. The debate whether the addition of impurity atoms would decrease the efficiency by shorter recombination lifetime or increase the efficiency by more absorption is studied, and results confirm that the efficient removal of photo-generated carriers from valence and conduction bands and solar concentration is the key to the success of subbandgap photovoltaics.