Identifying Dominant Recombination Mechanisms in Perovskite Solar Cells by Measuring the Transient Ideality Factor

The light ideality factor determined by measuring the open-circuit voltage (V) as a function of light intensity is often used to identify the dominant recombination mechanism in solar cells. Applying this “Suns-V” technique to perovskite cells is problematic since the V evolves with time in a way that depends on the previously applied bias (V), bias light intensity, device architecture and processing route. Here, we show that the dominant recombination mechanism in two structurally similar ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ devices containing either mesoporous ${\mathrm{Al}}_2{\mathrm{O}}_3$ or ${\mathrm{Ti}\mathrm{O}}_2$ layers can be identified from the signature of the transient ideality factor following application of a forward bias, V, to the device in the dark. The transient ideality factor is measured by monitoring the evolution of V as a function of time at different light intensities. The initial values of ideality found using this technique are consistent with estimates of the ideality factor obtained from measurements of photoluminescence vs light intensity and electroluminescence vs current density. Time-dependent simulations of the measurement on modeled devices, which include the effects of mobile ionic charge, reveal that this initial value can be correlated to an existing zero-dimensional model while steady-state values must be analyzed taking into account the homogeneity of carrier populations throughout the absorber layer. The analysis shows that Shockley-Read-Hall (SRH) recombination through deep traps at the charge-collection interfaces is dominant in both architectures of measured device. Using transient photovoltage measurements directly following illumination on bifacial devices, we further show that the perovskite–electron-transport-layer interface extends throughout the mesoporous ${\mathrm{Ti}\mathrm{O}}_2$ layer, consistent with a transient ideality signature corresponding to SRH recombination in the bulk of the film. This method will be useful for identifying performance bottlenecks in alternative variants of perovskite and other mixed ionic-electronic conducting absorber-based solar cells.

Figure 1

Schematics of idealized QFL splitting and fundamental recombination mechanisms in perovskite solar cells. (a) Schematic of idealized quasi-Fermi-level splitting ΔE_F in a zero-dimensional material. Where n = p, the Fermi levels split with equal magnitude from equilibrium E_F0 under bias. Where one carrier is in excess ($p\gg n$ is shown), the shift in the minority carrier Fermi energy dominates the change in ΔE_F. (b) Schematic illustrating different possible recombination pathways within a device.

Figure 2

Device architecture and transient Suns-V_OC experimental timeline. (a) Device stack: the mesoporous layer can be either ${\mathrm{Al}}_2{\mathrm{O}}_3$ or ${\mathrm{Ti}\mathrm{O}}_2$. (b) Transient Suns-V_OC experimental timeline: the cell is preconditioned in the dark at a preset voltage V_pre for >60 s. At t = 0, the bias light is switched on and the cell is simultaneously switched to open circuit. The V_OC is subsequently measured for >30 s. The protocol is cycled at increasing bias light intensity and the ideality factor as a function of time is calculated.

Figure 3

Temporal evolution of the open-circuit voltage and ideality factor in measured and simulated devices. Examples of the evolution of measured V_OC for different incident photon fluxes (φ = 0.2–2 sun equivalents) with time following dark preconditioning with (a) V_pre = 1.2 V and (b) V_pre = 0 V for a mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ cell. (c) The measured V_OC plotted against incident photon flux, φ, at different delay times following illumination for the V_pre = 1.2 V case shown in (a). The ideality factor shows an increase in time. (d) The simulated evolution of the V_OC for different incident photon fluxes (φ = 0.1–25.6 sun equivalents) from a V_pre = 1.1 V dark equilibrium solution and (e) from a V_pre = 0 V dark equilibrium solution. For both preconditioning cases shown in the example, recombination scheme 3 is used in the simulation (Table 2, band-to-band in bulk, and interfacial SRH recombination via midgap states). (f) Simulated V_OC vs incident photon flux, φ, at different delay times following illumination for the dark V_pre = 1.1 V initial conditions case shown in (d) also shows an increase in ideality factor with time.

Figure 4

Example energy-level diagrams and charge-density profiles during the open-circuit-voltage transient simulation. Energy-level diagrams (E_CB and E_VB are the conduction and valence-band energies, while E_Fn and E_Fp are the electron and hole quasi-Fermi-levels, respectively), electron (n), hole (p), and mobile ion densities after simultaneously illuminating and switching to open circuit with φ = 1.6 sun equivalent for a device preconditioned with (a) V_pre = 1.3 V in the dark at t = 1 ms following illumination, (b) V_pre = 0 V in the dark at t = 1 ms following illumination, and (c) at steady state (t = 100 s) for both preconditions at open circuit. (d) A device with the same parameter set without mobile ions. Recombination scheme 3 (Table 2) is used in the simulation results shown. The green and blue shaded regions indicate the respective p and n-type regions of the device.

Figure 5

Measured and simulated evolution of the ideality factor with time following forward biasing. Measured n_id(t) for mp-${\mathrm{Ti}\mathrm{O}}_2$ (light blue curve, triangle markers) and mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ (green curve, circle markers) cells following dark (a) V_pre = 1.2 V (mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ device), V_pre = 1.0 V (mp-${\mathrm{Ti}\mathrm{O}}_2$ device). (b) The simulated transient ideality factor, n_id(t), derived from simulations of V_OC(t) for different incident photon fluxes in a p-i-n structure starting from initial conditions simulated for dark equilibrium with V_pre = 1.3 V. The results from simulations with different dominant recombination mechanisms are shown: band-to-band recombination (black curve, diamond markers), interfacial SRH recombination via shallow traps (gray curve, square markers), interfacial SRH recombination via deep traps (pink curve, circle markers), bulk SRH recombination via shallow traps (yellow curve, inverted triangle markers), and bulk SRH recombination via deep traps (dark blue curve, triangle markers).

Figure 6

Alternative measurements of the initial transient ideality factor using EL and PL. (a) Integrated electroluminescent emission flux density vs time for different injection current densities, J = 107, 213, 426, 533, and 853 mA cm⁻² following the application of V_pre = 1.1 V to a mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ cell. (b) Evaluation of n_id for t = 0–0.02 s from EL emission flux density vs injection current density for the three architectures of the device. (c) Integrated photoluminescent flux density vs time for different excitation intensities following the application of V_pre = 1.2 V to a mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ cell. (d) Simulated integrated band-to-band (BTB, radiative, solid curves) and interfacial SRH recombination (dashed curves) fluxes as a function of time for a cell with recombination scheme 3 for V_pre = 1.3 V.

Figure 7

Transient photovoltage measurements on bifacial devices and band-energy-level schematics for mp-${\mathrm{Ti}\mathrm{O}}_2$ and mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ architectures. Transient photovoltage ΔV measurements for following V_pre = 0 V (see the experimental timeline in Fig. S1 within the Supplemental Material [32]). The mp-${\mathrm{Ti}\mathrm{O}}_2$ device shows an initial negative deflection to ΔV when excited through (a) the TCA side by the 488-nm laser pulse. (b) The change in signal is much smaller when the device is excited through the glass side, implying an inverted electric field is localized to the TCA side as shown in (c) the band schematic. The mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ device shows similar negative initial ΔV responses when illuminated through both (d) TCA and (e) glass sides, implying the inverted field is extended into the electronically insulating mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ region as shown in (f) the device band schematic. mp-${\mathrm{Ti}\mathrm{O}}_2$ and mp-${\mathrm{Al}}_2{\mathrm{O}}_3$ are indicated by the yellow and green shaded areas, respectively. Spiro-OMeTAD, perovskite, and ${\mathrm{Ti}\mathrm{O}}_2$ conduction and bands are shown as red, black, and blue curves, respectively (energies not to scale).

Figure 8

Transient optoelectronic measurement system circuit diagram. Circuit diagram for the transient data-acquisition system. The yellow shaded area is the primary circuit, which allows the cell to be electrically biased and switched between open and closed circuits. The light red shaded area is the laser circuit and the light blue shaded region is the white bias light-emitting diode (LED) circuit. Figure reproduced from Ref. [8] (Creative Commons license).

Figure 9

Optical modeling of the mp-${\mathrm{Ti}\mathrm{O}}_2$ device with TCA electrode used in the transient photovoltage measurements. Optical intensity as a function of position for the mp-${\mathrm{Ti}\mathrm{O}}_2$ device stack incorporating the TCA electrode. Illumination from (a) the FTO-glass side and (b) the TCA side. Blue and red curves indicate wavelengths of 488 nm and 638 nm respectively, while the black curve shows the decay of the AM1.5 spectrum integrated from 300 to 768 nm.