The ideality factor n_id quantifies the deviation of the current-voltage characteristics of a solar cell from the ideal diode equation, excluding the influence of series and shunt resistances. It can be influenced by two effects: the scaling of the electron and hole density with injection level and the scaling of the dominant recombination mechanism with the electron and hole density. In an extrinsically-doped semiconductor in low-level injection (e.g. n << p = N_A), the majority carrier density is independent of the injection level which leads to an ideality factor of n_id = 1, independent of the dominant recombination mechanism. In the case of an intrinsic semiconductor (i.e. high-level injection, n = p), the ideality factor serves as tool to distinguish between recombination mechanisms: n_id = 1 is typically associated with radiative recombination or recombination via shallow traps; n_id = 2 with recombination through deep trap states; n_id = 2/3 with Auger recombination; and interface recombination can span a range of values depending on injection conditions and transport asymmetries.

Lead halide perovskites neither perfectly fall in the doped nor the intrinsic category. They have very low doping densities in the dark but show photodoping effects under illumination due to trapping of charge carriers. This situation is uncommon in semiconductor physics and requires innovative ways of analyzing and understanding charge carrier dynamics in general and ideality factors in particular.

Here, we discuss how photodoping in otherwise intrinsic semiconductors affects the ideality factor. At low injection levels, the trap occupation is limited by minority carrier detrapping. The trap behaves as a shallow trap yielding an ideality factor of n_id = 1, just as in the intrinsic case. At higher injection levels however, we find that the trap occupation is now limited by the majority carrier trapping, interestingly leading to an ideality factor of n_id = 1.5. At very high injection levels, the electron and hole density surpass the trap density, leading to the intrinsic case of a deep trap with n_id = 2. We point out that the ideality factor of n_id = 1.5 is a normal outcome of SRH theory and does not require interface recombination. We discuss the consequence of this effect on the photoluminescence quantum yield in steady state and on the transient photoluminescence behavior and compare the theory to measurements on perovskite thin films.