Deriving mobility-lifetime products in halide perovskite films from spectrally and time-resolved photoluminescence

Abstract

Lead-halide perovskites are semiconductor materials with attractive properties for photovoltaic and other optoelectronic applications. However, determining crucial electronic material parameters, such as charge-carrier mobility and lifetime, is plagued by a wide range of reported values and inconsistencies caused by interpreting and reporting data originating from different measurement techniques. Here, we propose a method for the simultaneous determination of mobility and lifetime using only one technique: transient photoluminescence spectroscopy. By measuring and simulating the decay of the photoluminescence intensity and the redshift of the photoluminescence peak as a function of time after the laser pulse, we extract the mobility, lifetime, and diffusion length of halide perovskite films. With a voltage-dependent steady-state photoluminescence measurement on a cell, we relate the diffusion length to the external voltage and quantify its value at the maximum power point.

Fig. 1.. Schematic illustration of carrier diffusion and spectral shift process based on simulated results.

(A) After the laser pulse hits the sample, the generated carriers in the film will diffuse from one side of the film to the other, while recombination occurs simultaneously. CB, conduction band; VB, valence band. (B) Time-dependent PL spectra show an obvious redshift with time, which indicates the reabsorption of PL along with carrier diffusion in perovskite. (C) Schematic illustration of the time dependence of the ratio R, from which we can quantify the influence of mobility and diffusion coefficients on the spectral shifts. R is the ratio of the low-energy region to the high-energy region and defined as $R={\int }_{1.45}^{1.58}\mathrm{\varphi }\mathit{dE}/{\int }_{1.68}^{1.80}\mathrm{\varphi }\mathit{dE}$. Note that R(t) may have slightly different shapes than shown in (C) in the presence of, e.g., trapping/detrapping effects (cf. section S2), but it will always show a feature related to the mobility.

Fig. 2.. Tr-PL decay and spectral shift of experimental data for different illumination intensities.

(A) PL spectra at different time delays during the measurement with an illumination intensity of 1.79 μJ/cm² using a logarithmic scale. (B) PL spectra at different time delays during the measurement with an illumination intensity of 1.79 μJ/cm² using a linear scale. (C) PL decay curves at three different fluences. (D) Decay curves of carrier concentration with shifted time axis. The average carrier concentration over volume is used at the initial time (t ≈ 0). (E) Differential decay time versus Fermi-level splitting. (F) Spectral shift ratio versus Fermi-level splitting. The solid lines in [(E) and (F)] indicate trends in the experimental data.

Fig. 3.. Experimental and simulation results.

(A) Experimental results of ΔE_F versus illumination intensity acquired from steady-state PL results and the corresponding simulation results. (B) Experimental differential decay time versus Fermi-level splitting acquired from gated CCD setup and the corresponding simulated results with different carrier mobilities. On the y axis (right side), we calculated $L_{\mathrm{D}}=\sqrt{D{\mathrm{\tau }}_{\text{diff}}}$, where $D=\mathrm{\mu }\mathit{kT}/q$ and μ = 2 cm²/Vs. SC, short circuit; OC, open circuit; MPP, maximum power point. (C) Experimental ratio versus time acquired from gated CCD setup and the corresponding simulated results with different carrier mobilities. Here, we shift the R by subtracting a constant to obtain the same starting value. (D) The corresponding differential ratio value versus time from the experiment and simulations. (E) Experimental results of ΔE_F versus the external bias voltage acquired from the voltage-dependent PL measurement under 1-sun light intensity. (F) The relationship between L_D and external bias voltage, which is acquired from the reverse scan result of (E) and the simulated result (μ = 2 cm²/Vs) of (B). On the y axis (right side), we calculated L_D/d, where d is the thickness of the film.

Fig. 4.. Analysis of factors influencing τ_diff versus ΔE_F plot and corresponding physical processes.

(A and B) Influence of carrier diffusion on the onset value of τ_diff. The carrier mobility was adjusted. (C and D) Influence of electron trapping process on the PDE part of τ_diff. The electron lifetime related to trap 1 is adjusted by changing the electron capture coefficient ${\mathrm{\beta }}_{\mathrm{n}}$ while maintaining a constant trap density $N_{\mathrm{t}}$. (E and F) Influence of the hole capture process on the ODE part of τ_diff. The hole lifetime related to trap 2 was adjusted by changing the hole capture coefficient ${\mathrm{\beta }}_{\mathrm{p}}$ while maintaining a constant trap density $N_{\mathrm{t}}$. We further show the influence of the hole lifetimes related to trap 1 and trap 3 in figs. S11 and S12. E_c, energy level of conduction band edge; E_t, energy level of trap; E_v, energy level of valence band edge.

Fig. 5.. Numerical simulation of device performance.

The simulated power conversion efficiency as a function of (A) diffusion length L_D and (B) exchange velocity S_exc using Eq. 1. The mobility μ in (A) was calculated using $L_{\mathrm{D}}=\sqrt{\frac{k_{\mathrm{B}}T}{q}{\mathrm{\mu \tau }}_{\text{diff}}}$ by assuming τ_diff = 1.3 μs. The purple dashed lines in the figures at (A) L_D = 2.6 μm and (B) S_exc = 2700 cm/s indicate the approximate experimental values of our sample.