The effect of distributed series resistance on the dark and illuminated current—Voltage characteristics of solar cells

Distributed series resistance effects in solar cells are analyzed and the correctness of representing these by a lumped parameter is discussed for any conditions of bias and illumination. In addition to a general mathematical methodology, analytical expressions are derived to simplify the estimation of series resistance effects on the dark and illuminated<tex>J-V</tex>characteristics of the cell. The equivalent series resistance (r<inf>s</inf>) in the dark is found to decrease with current density<tex>J</tex>from<tex>r_{b} + r_{e}/3</tex>at small<tex>J</tex>to (<tex>r_{e} r_{b})^{1/2}</tex>at very high<tex>J</tex>, where r<inf>e</inf>and r<inf>b</inf>are the emitter layer and base region resistances, respectively. For illuminated conditions r<inf>s</inf>depends on<tex>J</tex>as well, being maximum near short-circuit and minimum near open-circuit; however, r<inf>s</inf>further depends on the photogenerated current J<inf>L</inf>: its short-circuit value increases with J<inf>L</inf>from<tex>r_{b} + r_{e}/3</tex>to<tex>r_{b} + r_{e}/2</tex>and the open-circuit value decreases with J<inf>L</inf>from<tex>r_{b} + r_{e}/3</tex>to<tex>(r_{e}r_{b})^{1/2}</tex>. The variability of r<inf>s</inf>is therefore related to the relative importance of r<inf>b</inf>and<tex>r_{e};r_{b}</tex>plays the role of attenuating this variability, a situation not well recognized previously. Previous theoretical and experimental work is critically reviewed throughout this paper.