Abstract

Main

Non-radiative recombination via defects is one of the most important loss processes in most photovoltaic technologies^1,2. Thus, a considerable amount of photovoltaic research has been dedicated to suppressing non-radiative recombination as well as characterizing and quantifying its extent^3,4. This is especially true for emerging photovoltaic technologies such as halide perovskites that mostly rely on solution-processed polycrystalline thin films. In lead halide perovskites, non-radiative recombination is much less of a problem compared to other polycrystalline materials used for photovoltaic applications^5,6. The common explanation is that most intrinsic defects are either shallow or unlikely to form⁷. Interestingly, the experimental community has so far worked under the paradigm that deep defects dominate recombination, whereas shallow defects are mostly considered irrelevant^8,9. The only shallow defects considered crucial for device functionality are mobile ions causing field screening and hysteresis in the current–voltage curve^10,11.

Identifying the properties of the defects dominating non-radiative recombination is important for various reasons. Depending on the dominant defect species, different material optimization strategies and characterization approaches are needed. For deep traps, both transient photoluminescence (PL) and PL quantum yields are viable methods to quantify recombination, and the information content of both quantities is basically identical¹². In the presence of deep traps, transient PL measurements lead to monoexponential decays at sufficiently low injection conditions, from which charge carrier lifetimes can be extracted. Those lifetimes must then be consistent with the PL quantum yields obtained from steady-state PL measurements and consequently correlate with the voltage difference E_g/q–V_oc, where E_g, q and V_oc are the bandgap energy, elementary charge and open-circuit voltage, respectively. Figure ​Figure1a1a shows this correlation for a range of perovskite studies^13,14, where the voltage difference was calculated from the solar cell data while the lifetime was obtained from film measurements. While many data points seem to show correlation between lifetime and voltage difference, others (especially the data points (stars) labelled ‘this work’ and ‘ref. ¹⁵’) feature decay times that seem too long for the associated value of E_g/q–V_oc. This raises the question of whether transient PL decay times are always a valid method to quantify recombination and voltage losses in halide perovskites. Moreover, the finding raises doubts regarding the implicit assumption that deep defects dominate recombination losses and transient PL decay.

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Fig. 1

Meta-analysis of reported energy loss and decay time in publications.

a, The voltage difference E_g/q–V_oc as a function of decay time of perovskite films. The lines indicate the relationship between carrier lifetime and energy loss^13,14, which is calculated based on a step function absorptance by taking p₀=0, p_a=0, p_e=0.05, G_ext=5.3×10²¹cm⁻³s⁻¹ and $V_{\mathrm{oc}}^{\mathrm{SQ}}=1.297\mathrm{V}$ (corresponding to a bandgap of 1.57eV), where p₀ is the equilibrium carrier concentration, p_a is parasitic absorption probability, p_e is emission probability, G_ext is the generation rate of electron-hole pairs due to external illumination and $V_{\mathrm{oc}}^{\mathrm{SQ}}$ is the open-circuit voltage in the Shockley-Queisser (SQ) model. Additionally, k_rad is the radiative recombination coefficient. b, Meta-analysis on the dynamic range of tr-PL decay curves in publications. The colours represent the fitting methods of the tr-PL decay curves. More information is in Supplementary Note 5.

Source data

Here we show that typical triple-cation perovskite layers, layer stacks and solar cells are strongly affected by shallow defects that manifest themselves in steady-state and transient PL data. The most convincing evidence for shallow defects is the presence of an extremely long-lived PL signal in time-resolved PL (tr-PL) measurements with a high dynamic range of greater than ten orders of magnitude. Combined with the observation of PL quantum yields in the range of 2% (this means much smaller than unity) in films, we can rule out radiative band-to-band recombination as the reason for the long-lived decay. Consistent with the dominant influence of shallow defects, the decay approximately follows a power law (PL flux ϕt^-α, where t is time and α is a constant) over the investigated time range and never saturates to an exponential decay (Supplementary Fig. 5). The high dynamic range is important to disentangle different mechanisms in large-signal transients¹⁶ and is not typically found in the literature on halide perovskites (Fig. ​(Fig.1b).1b). The differential decay times exceed 100µs at the end of the decay, which implies that these decays may be the longest measured so far in halide perovskites or any other direct semiconductor considered for photovoltaic applications⁶. The high dynamic range combined with the power-law nature of the decay allows us to observe differential decay times that vary over four orders of magnitude spanning tens of nanoseconds at the beginning of a decay up to hundreds of microseconds. This implies that the heavily used concept of a single ‘lifetime’ of charge carriers in halide perovskites can be highly misleading and may have to be replaced by effective recombination coefficients. We note that decay times exceeding tens of microseconds are observed also in films with one or two charge-extracting layers and in full devices. This finding implies that the shallow traps and long lifetimes are consistent with efficient charge extraction in solar cells with fill factors exceeding 80%. The absence of any type of saturation of the decay time to a constant value shows that (1) the halide perovskite films are extremely intrinsic¹⁷ and (2) the Shockley–Read–Hall (SRH) lifetime for recombination via deep defects must be extremely long (in the range of hundreds of microseconds; Supplementary Fig. 7). The latter finding implies a change of the dominant paradigm that reduction of deep defects is crucial for further efficiency improvements. Instead, we show that a high density of shallow defects dominates recombination and limits device performance.

Defect-mediated recombination

Recombination via defects is the most relevant recombination mechanism for thin-film photovoltaics as it reduces the open-circuit voltage of solar cells and often also the fill factor and the short-circuit current. The SRH model is used to identify non-radiative recombination and estimate its effect on device performance. The SRH recombination rate for one species of singly charged defects is given by^18,19

where n, p and n_i represent electron, hole and intrinsic carrier concentrations; τ_p and τ_n are the SRH lifetimes for holes and electrons; n₁=N_Cexp[(E_T–E_C)/k_BT]; and p₁=N_Vexp[(E_V–E_T)/k_BT]. Here n₁ and p₁ are in the unit ‘per cubic centimetre’ and use further variables such as the effective density of states for the conduction and valence bands (N_C and N_V, respectively) and the energy of the trap (E_T), conduction band edge (E_C) and valence band edge (E_V), as well as a Boltzmann constant (k_B) and temperature (T). Given that lead halide perovskites behave like intrinsic semiconductors¹⁷, the equation is typically simplified using the two assumptions n=p and nn_i. Furthermore, n₁ and p₁ are typically considered negligible relative to n and p, implying that detrapping is neglected, which is typically a good approximation for a deep trap. These simplifications lead to R_SRH=n/(τ_p+τ_n), that is, to the situation in which SRH recombination is often considered synonymous with first-order recombination, which has a rate that is linear in n (and p), that is, R_SRHn^δ, where δ=1 is the reaction order. However, this is only a special case, where the trap is between the quasi-Fermi levels under operation²⁰. If a trap dominating recombination is close to either the conduction or the valence band edge, one of the two voltage-independent terms n₁ or p₁ will become comparable to n and p, and hence affect the recombination rate. Without loss of generality, we assume that we have a defect close to the conduction band, implying that n₁p₁. In this case, the rate R_SRH=n²/[(n+n₁)τ_p+nτ_n] can scale linearly with n (for the case of n₁n); it may scale quadratically with n (for n₁n); or it may have a non-integer recombination order if n and n₁ are similar in magnitude. Thus, depending on the trap level and the quasi-Fermi levels, SRH recombination may lead to 1<δ<2, but in consequence, the ideality factor n_id will assume non-integer values over a wide range of Fermi levels, that is, 1<n_id<2.

Equation (1) describes SRH recombination in a steady-state situation relevant for explaining the current–voltage curve, the open-circuit voltage and the steady-state PL. For a transient experiment, the SRH formalism becomes a set of coupled rate equations that can be solved numerically (Supplementary Note 6). Analytical solutions are possible^15,16 but are commonly used only in the absence of detrapping. A perovskite film on glass whose recombination is dominated by a deep trap will exhibit a monoexponential PL decay at sufficiently low excitation conditions, where radiative recombination can be disregarded. In the presence of shallow traps, however, the decay will have additional features related to detrapping and changes in trap occupation due to the movement of the quasi-Fermi levels relative to the trap position during the transient process. Note that increased apparent lifetimes caused by detrapping have previously been reported for multicrystalline Si wafers^21,22 and for kesterite solar cells²³.

PL experiments

To investigate the nature of defects, we prepared Cs_0.05FA_0.73MA_0.22PbI_2.56Br_0.44 triple-cation perovskite films post-treated with n-octylammonium iodide (OAI), with a bandgap of ~1.63eV, and subsequently fabricated ITO/Me-4PACz/perovskite/C₆₀/BCP/Ag inverted solar cells with non-radiative recombination losses as low as ~100mV (ITO, indium tin oxide; Me-4PACz, [4-(3,6-dimethyl-9H-carbazol-9-yl)butyl]phosphonic acid; BCP, bathocuproine). To quantitatively analyse non-radiative recombination, we measured tr-PL decays as a function of light intensity. Figure ​Figure2a2a shows that the initial PL flux ϕ(t=0) of transient PL measurements scales with the square of the laser power and hence with n², suggesting that the electron and hole concentrations are identical just after the pulse (that is, before recombination could have happened) over a range of pulse intensities. Thus, the perovskite film cannot have either a high hole or a high electron density in the dark, as otherwise the initial amplitude should have scaled linearly with laser power, as seen for instance for Sn-based perovskites¹⁷. Thus, we can treat the OAI-modified film as well as an unmodified control (Supplementary Fig. 12) as intrinsic semiconductors—a finding that is consistent with reports on similar triple-cation perovskites²⁴.

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Fig. 2

The tr-PL and steady-state PL results of OAI-modified films.

a, Change of initial amplitude ϕ(t=0) of tr-PL decay curve (time-correlated single-photon counting set-up) for an OAI-modified perovskite film as a function of carrier concentration. The amplitude is proportional to n², indicating the film is intrinsic. b, Measured differential decay time as a function of Fermi-level splitting by both time-correlated single-photon counting (using different optical density (OD) filters) and gated CCD set-ups. Note that the curve for 0 OD is nearly overlapping with the gated CCD curve. The solid line is the simulated result. c, Calculated and simulated results of ΔE_F versus illumination intensity for OAI-modified film. The calculated data are based on the steady-state PL results.

Source data

Furthermore, we measured tr-PL decays with two different methods (single-photon counting and a gated CCD (charge-coupled device) camera) over approximately ten orders of magnitude in dynamic range (Fig. ​(Fig.2b).2b). In Fig. ​Fig.2b,2b, the normalized decay data have been changed to differential decay time versus Fermi-level splitting. The details of the transformation and the figure before transformation can be found in Supplementary Fig. 4. Figure ​Figure2b2b shows that the tr-PL data obtained using the gated CCD camera features a constantly changing decay time that varies from tens of nanoseconds at high Fermi-level splitting (beginning of the decay) to >100µs at a Fermi-level splitting of ~1V. The covered range of ~500meV in Fermi-level splitting corresponds to exp(500meV/k_BT)≘9.5 orders of magnitude dynamic range (k_B, Boltzmann’s constant). Increasing the laser intensity can enhance the signal-to-noise ratio, which can further increase the dynamic range to over ten orders of magnitude. Then a detectable decay time of >280µs was observed (Supplementary Fig. 7). The decay time (τ) is nearly continuously changing with a constant slope, where τexp(–ΔE_F/(θk_BT)), 2≤θ≤3 and E_F is the Fermi energy. This implies that the decay is approximately consistent with a power law of the type ϕt^–2 as expected (Supplementary Fig. 5) for radiative recombination—or shallow defects—in an intrinsic semiconductor. An alternative to the determination of a (constantly changing) decay time is therefore the determination of a differential recombination coefficient k_diff (details in Supplementary Note 1), which would be constant for a recombination quadratic in free carrier density. This would enable the description of the recombination dynamics by a single constant parameter in the case of the absence of deep defects. Such a recombination coefficient has been frequently used in the organic solar cell community^25,26 but is so far uncommon in the description of halide perovskites.

We also note that the single-photon counting data partly overlap with the data from the gated CCD but have additional features. Due to the repetition rate limitation of the single-photon counting method, the decay times shown using the gated CCD are impossible to measure in the absence of a measurement system that can handle repetition rates below a few kilohertz (Supplementary Fig. 4). In addition, we demonstrate that exponential fitting is unable to reliably extract PL decay times (Supplementary Table 1). Finally, we measured the steady-state PL to determine the ideality factor of the films and obtained a non-integer ideality factor of n_id≈1.2 (Fig. ​(Fig.2c2c).

To verify that the data are consistent with shallow traps but inconsistent with recombination being limited by deep traps, we use a rate-equation model to simulate both the tr-PL and the steady-state PL data (equations are shown in Supplementary Note 6). The solid lines shown in Fig. 2b,c represent fits to the data, with the parameters shown in Supplementary Table 2. We use three shallow defects to fit the data, and they have a distance to the nearest band of about 55, 95 and 125meV. Furthermore, we know from Fig. ​Fig.2a2a that the defects cannot dope the layer, that is, they have to be acceptor-like defects close to the conduction band or donor-like defects close to the valence band (as visualized in Supplementary Fig. 17). We note that defect positions closer to mid-gap would lead to substantially different shapes of the tr-PL (Supplementary Fig. 20). Furthermore, the only way to consistently explain decay times of hundreds of microseconds in combination with steady-state PL values that are much lower than the radiative limit is to invoke the presence of shallow traps that release charge carriers at longer times, thereby leading to a delayed luminescence, a power-law decay and, in consequence, extremely long decay times towards the end of the decay. Detrapping effects can cause the peculiar situation of PL decay times that increase with increasing shallow defect density, which is the opposite trend as that observed for deep defects (Supplementary Fig. 23).

Influence of charge-extracting layers

Figure ​Figure3a3a shows the ΔE_F of layer-stack samples acquired from steady-state PL measurements (Supplementary Fig. 30). The ITO/Me-4PACz/perovskite sample shows the highest ΔE_F value. However, interfacing the perovskite layer with C₆₀ substantially lowers ΔE_F, possibly by introducing additional interfacial defects, as suggested by studies^27,28 and consistent with previous reports on steady-state²⁹ and transient PL^15,30,31. OAI modification can effectively passivate the perovskite/C₆₀ interface defects, as samples with the perovskite/C₆₀ interface show a stronger enhancement in ΔE_F after OAI modification than stacks without C₆₀. Figure 3b,c shows the time-dependent tr-PL decay curves and the differential decay time τ_diff as a function of the ΔE_F of different layer stacks. The decay times of different stacks are remarkably similar. While interfaces between perovskite and C₆₀ reduce ΔE_F values, interfaces with only Me-4PACz show an increase in ΔE_F. This indicates that film growth on Me-4PACz improves the bulk properties and suggests that the Me-4PACz/perovskite interface is electronically rather benign. This also contributes to the Me-4PACz/perovskite samples showing the longest τ_diff at high ΔE_F values. While the general shape of the τ_diff versus ΔE_F curves is similar, the samples with charge-extracting interfaces (either electron transport layer ETL or hole transport layer HTL) show a somewhat lower slope at intermediate values of ΔE_F (highlighted by the plateau in the figure). Possible reasons for this feature are Coulomb effects that have previously been shown to lead to an S-shaped decay time versus ΔE_F curves^15,32.

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Fig. 3

PL characteristics of layer-stack samples.

a, Calculated quasi-Fermi-level splitting for control and OAI-modified samples with different layer stacks, which were measured under 1sun equivalent illumination. b, The tr-PL decay curves of OAI-modified samples with different layer stacks measured by the gated CCD set-up. c, Differential decay time as a function of Fermi-level splitting for OAI-modified samples with different layer stacks measured by the gated CCD set-up.

Source data

Device characteristics

Finally, inverted solar cells were fabricated based on the films. Figure ​Figure4a4a shows that the V_oc of the device increases from 1.114 to 1.214V after OAI modification, resulting in an efficiency increase from 19.9% to 21.4%. Figure ​Figure4b4b presents the statistical distribution of open-circuit voltages as a function of the OAI concentration. The best devices reach a V_oc over 1.23V corresponding to a non-radiative recombination loss: ${\mathrm{\Delta }V}_{\mathrm{oc}}^{\mathrm{nonrad}}=V_{\mathrm{oc}}^{\mathrm{rad}}-V_{\mathrm{oc}}\approx 100\mathrm{mV}$ (current density versus voltage (J–V) curves in Supplementary Fig. 36), whereby the open-circuit voltage in the radiative limit is given by $V_{\mathrm{oc}}^{\mathrm{rad}}=1.332\mathrm{V}$. The horizontal lines represent the values of V_oc expected for different PL quantum efficiency ($Q_{\mathrm{e}}^{\mathrm{lum}}$) values. Results show that $Q_{\mathrm{e}}^{\mathrm{lum}}$ increases from ~0.04% to ~2% as a function of OAI concentration. Although the value is lower than the record value of >5% (refs. ^33,34), it is still higher than most triple-cation-perovskite-based inverted devices (Supplementary Fig. 37). More details about device performances as well as the band alignment between absorber and contact layers can be found in Supplementary Note 4. Figure ​Figure4c4c shows the intensity-dependent open-circuit voltages of full devices, from which we derive ideality factors of around 1.4 (control) to 1.5 (OAI-modified device). These ideality factors are considerably lower than 2, as would be expected from an intrinsic absorber layer dominated by a deep defect, and are therefore consistent with the assumption that the existence of shallow traps still dominates the behaviour in the final cell. This observation is further corroborated by the behaviour of the decay times from tr-PL, shown in Fig. ​Fig.4d.4d. The decay times show a rather similar behaviour to the films and layer stacks shown in Fig. ​Fig.3c.3c. At high ΔE_F (for example, 1.3–1.5eV), the high carrier concentration results in strong radiative recombination, leading to the fast variation of τ_diff. In the intermediate region (for example, 1.05–1.3eV), the decay follows a roughly constant slope of approximately exp(–ΔE_F/6k_BT), which is less steep than for the films and layer stacks. At low ΔE_F (for example, <1.05eV), τ_diff sharply increases again. One possible reason could be the capacitance effect caused by the electrodes¹⁵. The single-photon counting data cannot reflect the real variation of τ_diff in the low ΔE_F region because of the limitation of the repetition rate.

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Fig. 4

Device performance.

a, J–V curves of the control and OAI-modified (2mgml^–1) small-area device. The value shown in the figure, from top to bottom, is J_sc, V_oc, FF and efficiency. b, Statistical open-circuit voltage data of control devices and OAI-modified devices with different OAI concentrations in milligrams per millilitre. The solid lines indicate the PL quantum yields. The box contains the values from the upper to lower quartiles. The lines outside the box indicate the ×1.5 interquartile range, and the line inside the box is the median. The open square inside the box is the mean value. The sample size for each group, from left to right, is 12, 12, 14, 26 and 12. c, Open-circuit voltage of control and OAI device as a function of illumination intensity. d, Differential decay time τ_diff as a function of ΔE_F for the OAI-modified device.

Source data

Outlook

We show that typical triple-cation perovskite layers, layer stacks and solar cells are strongly affected by shallow defects that manifest themselves in steady-state and transient PL data. Detrapping from such shallow traps then leads to extremely long decay times of hundreds of microseconds that can only be measured using a technique with an extremely low repetition rate. These shallow traps are less problematic for device performance than deeper traps with given SRH lifetimes of τ_n and τ_p but are still dominating the steady-state properties. Furthermore, the signatures of shallow traps in transient and steady-state experiments are difficult to distinguish from radiative recombination, which may have contributed to the wide spread of reported values for the radiative recombination coefficient in lead halide perovskites^35–40 as well as the frequent reports on non-radiative contributions to the quadratic recombination coefficient^{9,12,38,39,41}. Furthermore, the work highlights that the often used approximations of the SRH recombination rate must be applied with caution and should not be considered as the default recombination model. The work also shows that the absolute value of the PL decay time extracted from single- or multiexponential fits to low dynamic range fractions of the complete datasets can lead to highly misleading values as decay times may vary over orders of magnitude (tens of nanoseconds to hundreds of microseconds) depending on the excitation density and the repetition rate of the PL set-up. Thus, considering the decay time observed from transient experiments on halide perovskites to be a single number is one of the key fallacies the community needs to overcome to gain insights on recombination dynamics in these materials. A possible alternative to effective decay times for decays that rather resemble a power law instead of an exponential decay is the determination of an effective recombination coefficient.

Methods

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41563-023-01771-2.

Acknowledgements

Author contributions

Y.Y., G.Y. and T.K. conceived the idea. Y.Y., G.Y. and J.Y. fabricated the perovskite-based samples and performed the photovoltaic performance characterizations. M.H. built the steady-state and transient PL measurement set-ups. G.Y. and C.D. performed the PL characterizations. B.K. carried out the UPS characterization and analysed the results. T.K. wrote the codes for the simulations. T.R. conducted the grid search for the simulated parameters. T.K., Y.Y. and G.Y. wrote the manuscript. C.D. and U.R. improved the manuscript. U.R. derived the new equations in Supplementary Note 1. T.K. supervised the project. All authors discussed the results and commented on the paper.

Peer review

Funding

Open access funding provided by Forschungszentrum Jülich GmbH.

Data availability

The data used in the paper are available at https://zenodo.org/records/10101259. Source data are provided with this paper.

Code availability

The codes used for the simulation of this study can be accessed at https://zenodo.org/records/10101259.

Competing interests

The authors declare no competing interests.

Footnotes

Contributor Information

Genghua Yan, Email: ed.hcileuj-zf@nay.eg.

Thomas Kirchartz, Email: ed.hcileuj-zf@ztrahcrik.t.

References