The factor of 2 multiplying the outgoing flux is needed because photons are emitted from both sides, but the incoming flux is assumed to come from just one side. Although the analysis was done for photovoltaic cells under illumination, it applies also when the illumination is simply background thermal radiation, provided that a factor of 2 is then used for this incoming flux as well. The analysis gives a more rigorous expression for ideal diodes in general, except that it assumes that the cell is thick enough that it can produce this flux of photons. When the illumination is just background thermal radiation, the characteristic is