The saturated photovoltage of a p-n junction

Assuming the conventional divisions of the semiconductor into depleted and neutral regions, it is shown that for an abrupt p-n junction with nondegenerate carriers a relation exists between the open circuit photovoltage and the PN product at the junction(PN)₀, which is valid for all signal levels. In the small-signal case this leads to the standard result. At intermediate levels a new relationV = KT/q (1 ± m) logₑ ([(PN)₀]1/2/nᵢ)holds, the upper sign for p+-n junctions, the lower for n+-p junctions;m = (ₑ-ₕ)/(ₑ+ₕ). At very high levels the photovoltage saturates toV = kT/q[logₑ(MₚMₙ/n_{i²}) + m logₑ(ₕMₚ/ₑMN)]. Since Mpand MNare the doping levels in the p and n regions, the first term is the diffusion potential and the second term will be positive for p+-n junctions and negative for n+-p junctions. These results compare satisfactorily with the available experimental data.