This work proposes a double quantum dot structure as an intermediate-band layer to developing solar cell performance for the first time. The continuity-current equation is coupling with the density matrix equations, which are solved numerically to obtain the quantum efficiency. This modeling will calculate the momentum matrix elements of transitions, consider the orthogonalized plane wave for wetting layer- quantum dot transitions, and covers more characteristics than the rate equations by considering all the possible interactions between the states. The results simulate both the excitonic and nonexcitonic (electron-hole) cases. The work emphasizes adding the double quantum dot layer, which gives flexibility in choosing the energy difference between states controlling the recombination rates. The work refers to the importance of orthogonalized plane-wave in solar cell work. In both models, the band-band recombination is high for slight energy differences between the states, confirms the importance of the double quantum dot system to manipulate transitions between states and obtain higher rates. For the electron-hole model, the leakage is high due to the fast recombination of holes. The discrimination between occupations of states is increasing under the excitonic model due to growing hole occupation. In both models, reducing the quantum dot - quantum dot recombinations and increasing all other recombinations will increase the quantum efficiency. The high quantum dot band-to-band rate increases the quantum efficiency. In the excitonic model, lower rates than in the electron-hole model are enough for high quantum efficiency.