Revealing the doping density in perovskite solar cells and its impact on device performance
Traditional inorganic semiconductors can be electronically doped with high precision. Conversely, there is still conjecture regarding the assessment of the electronic doping density in metal-halide perovskites, not to mention of a control thereof. This paper presents a multifaceted approach to determine the electronic doping density for a range of different lead-halide perovskite systems. Optical and electrical characterisation techniques comprising intensity-dependent and transient photoluminescence, AC Hall effect, transfer-length-methods, and charge extraction measurements were instrumental in quantifying an upper limit for the doping density. The obtained values are subsequently compared to the charge on the electrodes per unit volume at short-circuit conditions, which amounts to roughly $10^{16}$ cm$^{-3}$. This figure equals the product of the capacitance $C$ and the built-in potential $V_\mathrm{bi}$ and represents the critical limit below which doping-induced charges do not influence the device performance. The experimental results demonstrate consistently that the doping density is below this critical threshold ($<10^{12}$ cm$^{-3}$ which means $<CV_\mathrm{bi}$ per unit volume) for all common lead-based metal-halide perovskites. Nevertheless, although the density of doping-induced charges is too low to redistribute the built-in voltage in the perovskite active layer, mobile ions are present in sufficient quantities to create space-charge-regions in the active layer, reminiscent of doped pn-junctions. These results are well supported by drift-diffusion simulations which confirm that the device performance is not affected by such low doping densities.