The theoretical efficiency of a quantum dot intermediate-band solar cell is estimated from a mathematical model based on the Kronig-Penney equation. The spectrum solutions for the two lowest energy states are calculated numerically using Wolfram Mathematica software. These energies determine the boundaries of the intermediate band produced by GaAs. With these results, the energy conversion efficiency is calculated. The behavior of the efficiency is analyzed based on the concentration of As, the dimensions of the quantum dot and the separation distance between them. The results obtained show an improvement in efficiency.