Enhancing Charge-Emitting Shallow Traps in Metal Halide Perovskites by >100 Times by Surface Strain

Abstract

The low density of deep trapping defects in metal halide perovskites (MHPs) is essential for high-performance optoelectronic devices. Shallow traps in MHPs are speculated to enhance charges recombination lifetime. However, it is unknown about the shallow trap chemical nature and distribution, and impact on solar cell operation. Herein, we report that shallow traps are much richer in MHPs than traditional semiconductors. Their density can be enhanced by >100 times through local surface strain, indicating shallow traps mainly located at the surface. The surface strain is introduced by anchoring two-amine-terminated molecules onto formamidinium cations, and the shallow traps are formed by the band edge downshifting toward defect levels. The high-density shallow traps temporarily hold one type of charges and increased concentration of the other type of free carrier in working solar cells by keeping photogenerated charges from bimolecular recombination, resulting in reduced open circuit voltage loss to 317 mV.

Metal halide perovskites (MHPs) are beginning to change the photovoltaic landscape with their increasingly mature technologies¹. The efficiency of defective polycrystalline perovskite solar cells already approaches the best single crystalline silicon solar cells^2–5, and the stability is quickly improving^3,6–8. Among all the intriguing physical properties of MHPs, the defect tolerance is unique that makes this thin film technology particularly attractive using both solution and vapor deposition processes^9–11. Density function theory (DFT) calculations show that many bulk point defects in MHPs either form energy states in conduction and valence bands or form shallow traps¹². However these point defects at perovskite film surface and grain boundaries still behave as deep traps, which cause non-radiative recombination¹³. Serval calculations showed that halide interstitials (I_i⁻ and I_i⁺), lead vacancies (V_Pb), and antistites (I_MA) can cause deep traps in methylammonium lead triiodide (MAPbI₃)^14–18, and recent deep-level transient spectroscopy characterizations have implied that negatively charged iodide interstitial (I_i⁻), MA vacancy (V_MA⁻) and MA interstitial (MA_i⁺) are possible origin of deep traps in MAPbI₃¹⁹. FA_I antistites is dominant surface deep traps in FAMA perovskites²⁰. To achieve record efficiency and better stability, various surface passivation strategies have been widely developed to reduced surface trap-mediated recombination to elongate carrier recombination lifetime and increase photoluminescence quantum yield^21–23.

Recent work has shown that there are high-density shallow traps in MAPbI₃ with an energy depth of less than 100 meV, and such shallow energy depth allows shallow traps to trap charges for a period and then re-emit them back to conductive band (CB) or valance band (VB), which is different from deep traps that trap charges and cause non-radiative recombination²⁴. Conventional wisdom believes that charges in the shallow traps behave like free charges which makes the defect tolerance of MHPs. However, the present theory lacks critical proof to close the logistic loop. First of all, the presence of shallow traps was not directly proven in pristine or passivated perovskites, mainly because of lack of an appropriate characterization method, despite that some indirect characterizations. Most existing methods for defect characterization do not work well for shallow traps in working solar cells. The most widely applied defect characterization method for perovskite solar cells, thermal admittance spectroscopy (TAS) or drive level capacitance profiling (DLCP), generally only measures deep traps with a depth larger than 100 meV from the conduction or valence band (CB or VB) edges^25–27. Second, DFT calculation fails in accurate prediction when the defect energy depth is in the order of kT, where k is Boltzmann constant and T is room temperature. Third, there is no study showing whether the charges in shallow traps really behave as free ones or should be treated differently yet.

There are very limited studies about shallow traps in MHPs. Some charge traps were treated as shallow, such as iodine interstitials which was reported to reduce the perovskite stability²⁸, but they were shown to be deep in other studies^14,15,18. Long carrier recombination lifetimes have been occasionally observed using time-resolved microwave conductivity (TRMC), which were often attributed to shallow traps. Early analysis of CH₃NH₃PbI₃ films using TRMC derived an extremely shallow trap depth of 10 meV with low concentration in CH₃NH₃PbI₃ films, which explains the significant suppression of charge recombination²⁹. A relatively long carrier recombination lifetime was observed in the (FA, MA, Cs)Pb(I_1-xBr_x)₃ films, and was reduced notably after light-soaking of the films. It was explained by shallow traps in the initially well-intermixed halide distributions which converted into deep traps due to light-induced phase segregation³⁰. Ultralong carrier lifetime up to 100 μs was observed in formamidinium-caesium (FACs) perovskite film with Na⁺ incorporation³¹, however such long lifetime might be not explained by shallow trap formation. Recently, the presence of shallow traps in typical triple-cation perovskite was evidenced by an extremely long-live time-resolved photoluminescence measurements with a high dynamic range of greater than ten orders of magnitude, and a high density of shallow defects dominates recombination and limits device performance³². However, there is rare of direct study of shallow traps in working devices, and very little is known about the chemical nature, density, distribution, and the impact of solar cells performance of shallow traps, despite that these understandings represent one of the fundamental ingredients to fully understand the shallow trap physics in MHPs, which may also help further improve the performance of perovskite devices.

In this work, we characterized shallow traps in working perovskite solar cell devices, and found that MHPs have much richer shallow traps than traditional semiconductors, and the shallow traps are mainly located at the surface. We demonstrated that shallow trap density can be enhanced by >100 times by the surface stain, which was introduced through the fast surface reaction between formamidinium cation (FA⁺) and molecules with amine at two terminals. We also showed that the high-density shallow trap can temporarily hold one type of charges and increase the density of the other type of charges by keeping them from bimolecular recombination, and reduced the open circuit voltage (V_OC) loss of a very stable formamidinium-caesium (FACs) perovskite solar cell to 317 mV, which is the best among the p-i-n perovskite solar cells.

Charge-emitting shallow trap characterizations

Our recent work demonstrated a high density of shallow traps at grain boundaries and surface of the polycrystalline CH₃NH₃PbI₃ (MAPbI₃) films²⁴, where we developed a method to extract the trapping/detrapping information by directly collecting the detrapped charges in working perovskite devices. Here we continue to develop it to quantify the percentage of charges that are extracted without encountering charge traps, non-radiatively recombining, and trapped and then re-emitted. The measurement system is illustrated in Fig. S1, where a train of picosecond laser pulses with controlled photon number per laser pulse are shined onto perovskite solar cells, generating a known number of electron-hole pairs (N₀), which can be derived from the absorption and reflection/scattering of the devices. The read-out electronics, which include a charge sensitive preamplifier and a shaping amplifier, convert the charges extracted to the electrodes into voltage pulses with pulse amplitude proportional to extracted charge numbers, and the output signal was recorded by an oscilloscope. As shown in Fig. 1A, a portion of charges (N₁) are directly collected by electrodes without encountering any charge traps. Some charges are trapped by deep traps and thus won’t be collected by electrodes within the measurement period. Some charges are temporarily held up by shallow traps with a delay time (Δt), and then reemitted to CB or VB and then collected by electrodes (N₂). The collection of these charges would generate voltage pulses whose height represents the integrated charge numbers.

Fig. 1. Charge-emitting shallow traps characterization.

(A) Schematic diagram of the charge collection process in the presence of charge-emitting shallow traps. (B) An output signal of a perovskite solar cell from the measurement setup. (C) N-A plot derived from 50,000 output signals under laser and in dark. (D) N-Δt plot of a typical perovskite solar cell. (E) N-A plot of a typical perovskite solar cell. (F) An output signal of the S1133 Si diode from the measurement setup. (G) An output signal of a CdTe solar cell from the measurement setup. (H) N-A plot of the S1133 Si diode. (I) N-A plot of a CdTe solar cell.

An output signal of a perovskite solar cell is shown in Fig. 1B. For each laser excitation event, directly collected charges cause a large pulse, followed by multiple much smaller pulses with time delays caused by the detrapping of charges from shallow traps with different depths. The delay time (Δt) is related to the trap depth (E_a) based on a relationship of $\frac{1}{\Delta t}=\left(\frac{\sigma v_{th}}{g}\right)N{e}^{-\frac{\Delta E}{kT}}$, where $\sigma$ is electron (hole) capture cross section, $v_{th}$ is electron (hole) thermal velocity, $g$ is the degeneracy of the trap level, $N$ is the effective density of states in CB (VB), $\Delta E$ is the energy separation between the trap level and CB (VB), $k$ is Boltzmann constant, and $T$ is the absolute temperature^33,34. We record information of each pulse, including amplitude and delay time (A, Δt). After collecting data from 50,000–100,000 laser pulse induced events, we plot the histogram of the pulses in amplitude domain (N-A) and delay time domain (N-Δt) (Fig. 1C and D). It should be noted that the statistical method of large amounts of data can eliminate the influence of random pulses on the results, and only certain fixed delayed pulses will be reflected as peaks in the N-A or N-Δt plots, because the occurrence probability of random pulses in time and amplitude is the same. By subtracting the N-A or N-Δt histograms of the device under laser pulses from those measured in the dark, we can exclude the background noise signal. The area below the curve represents the total number of collected charges. Then we can derive the percentage of charges that are directly collected right after laser excitation (N₁/N₀), and collected after delay (N₂/N₀), and those are lost due to deep traps (1- N₁/N₀- N₂/N₀).

Fig. 1D shows a N-Δt plot of a typical p-i-n perovskite solar cell with a device structure of indium tin oxide (ITO)/ poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA) /Cs_0.08FA_0.92PbI₃/C₆₀/bathocuproine (BCP)/copper (Cu). This perovskite composition has been shown to be very stable with module lifetime over thousands of hours under light soaking at open circuit voltage condition and temperature of 60 ±5°C^3,6. We can observe many pulses after the main extraction peak with delay times of 260±20 ns. The TRPL decay times derived by two-exponential fitting were τ₁=30 ns, τ₂=226 ns (Fig. S2). The τ₁ was too short to be resolved by the shallow trap characterization method, and the consistency of decay time of 226 ns in TRPL and delay time of 260±20 ns in shallow trap characterization validates the shallow trap characterization method. Fig. 1E shows the N-A plot of the same perovskite solar cell, where we can observe a peak with higher amplitude, which represents directly collected charges without delay, and another distinct peak at lower amplitude side, which is attributed by the re-emitted charges with some delay. Under a photogenerated charge concentration of 4.9×10¹² cm⁻³, the percentage of charges that were collected directly, collected after being trapped and reemitted, and lost by nonradiative recombination were calculated to be 38.8%, 1.8%, and 59.4%, respectively. And the density of charges that are re-emitted from shallow traps was estimated to be 9×10¹⁰ cm⁻³ from the total re-emitted charge number and perovskite volume (see method for details). It represents a low limit for the shallow trap density, because many shallow traps may not even encounter a charge. The deep traps density was estimated as 2.4×10¹² cm⁻³ from the total recombination charge number and perovskite volume, which is three orders of magnitude lower than the photogenerated charge concentration used in internal quantum efficiency (IQE) measurement (10¹⁵ cm⁻³). The peak IQE of typical perovskite solar cells can reach >95% in the conventional IQE measurement^35,36.

To examine whether the presence of shallow traps in perovskite devices is general, we also fabricated perovskite devices with different perovskite compositions and hole transport layers, including ITO/PTAA/MAPbI₃/C₆₀/BCP/Cu, ITO/PTAA/Cs_0.2FA_0.8Pb(I_0.8Br_0.2)₃/C₆₀ /BCP/Cu, and FTO/NiO_x/Cs_0.1FA_0.9PbI₃/C₆₀/BCP/Cu, and shallow traps were detected in all these perovskite solar cells (Fig. S3). The MAPbI₃ device showed lower shallow trap density than the CsFA devices, which is consistent with the fact that FA-perovskites have longer carrier recombination lifetime and diffusion length than those of MA-perovskites^37–40. The bromine-containing perovskite device showed much higher shallow trap density and longer trapping time than the pure iodide-based perovskite device, and the device with NiO_x hole transport layer also showed higher shallow trap density and longer trapping time than the device with PTAA hole transport layer, implying that different crystallization processes caused by the difference in compositions and interfaces also impact the shallow trap density and properties. We conducted the same characterizations on a single crystalline silicon PIN diode (Hamamatsu S1133) and an efficient CdTe thin film solar cell⁴¹. In striking contrast, neither the Si diode nor the CdTe solar cell showed any delayed pulses after the strong pulse caused by directly collected charges (Fig. 1F and G), indicating that the absence of shallow charge traps in the Si, CdTe or InGaN (Fig. 1H and I, Fig. S4). This again shows that perovskites are unique with their very rich shallow traps.

Increase charge-emitting shallow trap density by strain engineering

We explored several surface passivators to increase the shallow trap density, including phenethylammonium iodide (PEAI), 3-(decyldimethylammonio)-propane-sulfonate inner salt (DPSI), NaI, thiophene, diphenylphosphine, 2,7-dibromofluorene, dopamine hydrochloride, thiosemicarbazide, and p-toluenesulfonic anhydride (TSA). All devices were fabricated with a structure of ITO/ PTAA/ Cs_0.08FA_0.92PbI₃/ C₆₀/ BCP/ Cu. However, none of them notably increases the emissive shallow trap density (Fig. S5). Interestingly, we discovered that surface treatment of FA-containing perovskites using bilateral amines such as ethylenediamine (EDA) enhanced the shallow trap density. As shown by the N-Δt plot in Fig. 2A, the pristine device showed only one remission peak at 260±20 ns. After being treated with 2 mg ml⁻¹ EDA, the perovskite device had a de-trapping time of 420±20 ns, while the reemission peak at 260±20 ns was almost the same. This is consistent with the new PL decay time of the EDA-treated film of were τ₁=0.47 ns and τ₂=409 ns, validating the shallow trap measurement method again (Fig. S6). For each excitation laser pulse which generated 4.9×10⁶ electron-hole pairs, the number of charges which were first trapped and then collected after reemission were derived from the N-A plots to be 5.6×10³ and 6.2×10⁵ in the pristine and 2 mg ml⁻¹ EDA-treated devices, respectively (Fig. 2B), and the total number of collected charges, including directly collected and re-emitted trapped charges, is 2.0×10⁶ and 2.2×10⁶ in the pristine and 2 mg ml⁻¹ EDA-treated devices respectively. It reveals that the EDA surface treatment increased the shallow trap density by two orders of magnitude times while did not reduce the Shockley-Read-Hall (SRH) recombination. To further verify the effect of EDA in enhancing shallow trap density, we conducted cryogenic thermally stimulated photoemission spectroscopy (C-TSPS) measurement which can also detect ultra-shallow traps⁴². This method is based on creating charge carriers by photoexcitation at low temperature and recording the thermally stimulated photoemission as a function of temperature. It is similar to thermoluminescence (TL) spectroscopy where the emitted photons, due to the recombination of de-trapped electrons with holes in recombination centers, are detected during the temperature sweep⁴³. As shown in Fig. 2C, the TL intensity of re-emitted charges was enhanced by ~75 times after the film was treated by 2 mg ml⁻¹ EDA. This also indicates that shallow traps mainly exist in perovskite film surface, rather than in the charge transport layers of the perovskite solar cells.

Fig. 2. Shallow trap manipulation by microstrain.

(A) N-Δt plots of the pristine and 2 mg ml⁻¹ EDA treated devices, the green and blue lines are the peaks fitting for 2 mg ml⁻¹ EDA-treated devices. (B) N-A plots of the pristine, 2 mg ml⁻¹ PA-treated, and 2 mg ml⁻¹ EDA-treated devices. (C) The cryogenic thermally stimulated photoemission spectra of the pristine and 2 mg ml⁻¹ EDA-treated films. (D) Expansion of the perovskite lattice after EDA treatment. Williamson-Hall plot of (E) pristine, (F) 2 mg ml⁻¹ PA-treated, and (G) 2 mg ml⁻¹ EDA-treated perovskite films at various grazing angles. (H) DFT calculation and band edge downshifting introduced by surface local strain.

It is interesting to find out why EDA can increase the shallow trap density in perovskites. Amines were reported to quickly react with FA⁺ on the surface of FA⁺ containing perovskites even at room temperature⁴⁴. Since EDA has amine groups at both ends, it can react with the two FA⁺ cations in the adjacent lattice cells and generate n’-[2-(aminomethylideneamino)ethyl]methanimidamide (2-EMA). After replacing the FA⁺ cations in two adjacent unit cells with 2-EMA, the unit cells locally expand in the direction perpendicular to the 2-EMA molecular chain (Fig. 2D). The device did not show any degradation after the shallow trap measurement and the surface treatment did not change grain structure (Fig. S7). The shallow traps do not introduce additional electron or hole donors, and thus they might not change the work function or band bending of the perovskite surface. The application of the bilateral amines also makes the surface of perovskite films more hydrophobic by exposing the hydrophobic chains⁴⁵. We hypothesize that the strain is the origin of the new shallow traps based on the observation that devices without strain did not induce new shallow traps. To verify it, we treated the perovskite surface with propylamine (PA) which has a similar molecular structure to EDA but only one amine group at one end. The shallow trap reemission peak did not appear in the device with PA surface treatment (Fig. 2B). We also evaluated five other molecules with only one terminal amine group. The results lead to the same conclusion that the surface treatment using molecules with one amine group at one end did not increase the shallow trap density (Fig. S8).

To verify the contribution of strain to charge-emitting shallow traps, we employed Williamson-Hall method on pristine, PA-treated, and EDA-treated films to quantify the microstrain based on the different scattering vector dependence on the peak broadening in the grazing incidence X-ray diffraction (GIXRD)⁴⁶. At the depth of 10 nm, 20 nm, and 50 nm, corresponding to an X-ray incident angle of 0.2°, 0.4°, and 1°⁴⁷, the pristine and PA-treated film showed a depth-independent uniform compressive strain of −0.05±0.01% and −0.04±0.01% along the out-of-plane directly respectively (Fig. 2E and F). However, the EDA-treated film showed a depth-dependent gradient strain of 0.10% at 10 nm depth, −0.03% at 20 nm depth, and −0.04% at 50 nm depth (Fig. 2G), showing that the PA-treatment did not introduce locally expanded lattice structure, but EDA-treatment inverted the surface strain.

To explore the evolution of electronic properties associated with the tensile effect on the perovskite surface, the local density of states (LDOS) across the transition from the bulk region of the perovskite to its surface were calculated using density-functional theory (DFT). The locally expanded lattice structure on the surface can induce band edge downshifting by 0.15 eV on both the valence band maximum (VBM) and conduction band minimum (CBM) compared to those in the bulk region (Fig. 2H). The band edge downshifting reduces the energy gap between defect levels and CB at the surface, which can reduce energic depth of deep traps on the surface, and thus enable them to reemit the trapped charges and enhances device V_OC.

Combination of deep trap passivation and shallow trap enhancement to increase V_OC

We studied the influence of shallow traps on solar cell device performance. The pristine device had a V_OC of 1.070 V, and the V_OC of 2 mg ml⁻¹ EDA-treated device increased to 1.133 V (Fig. S9A), while the J_SC and external quantum efficiency (EQE) were almost unchanged in these devices (Fig. S9B), excluding the increase in V_OC caused by the increased bandgap (E_g). The pristine and 2 mg ml⁻¹ EDA-treated devices did not show obvious hysteresis under reverse and forward scanning (Fig. S9C and D). We also statistics the V_OC among over 15 devices with and without EDA treatment and it also demonstrates that 2 mg ml⁻¹ EDA surface treatment obviously increased the devices V_OC by enhancing the shallow trap density by 100 times, while the short-circuit current density (J_SC) and fill factor (FF) were comparable (Fig. S9E–H). However the total charge collection efficiency (CCE), defined by the ratio between number of total collected charges (N₁+N₂) and generated charges (N₀), was derived to be only 40.0% and 44.3% for the pristine and 2 mg ml⁻¹ EDA-treated devices, respectively, under excitation intensity of 4.9×10¹² cm⁻³. It is noted this carrier concentration is much lower than that induced by 1 sun light, under which more charges can saturate the deep traps and thus the CCE would be much higher. With increasing excitation light intensity, the proportion of recombination charges decreases and the CCE gradually approaches the internal quantum efficiency (IQE), which is measured under an excited carrier density of ~10¹⁵ cm⁻³ (Fig. S10). Nevertheless, the low CCE under weak light excitation can clearly tell that the deep traps in the perovskite were not passivated by EDA.

Iodine vacancy (V_I) behaves as shallow traps near CB, however Pb-Pb dimers at the surface behave as deep traps⁴⁶. Taking the Pb-Pb dimer in (001) planes of perovskite as example, which has the strongest XRD intensity, the formation of Pb-Pb dimers causes the local interplanar spacing along the out-of-plane [001] direction to decrease from the ideal 6.36 Å to 6.13 Å, which is consistent with the weak compressive strain along the out-of-plane direction in the pristine film. Since the molecular length of the reaction product of EDA and FA⁺ in the adjacent unit cells is slightly smaller than the spacing between the two FA⁺ cations in the two adjacent unit cells, the alkyl chain of the reaction product is almost linear between adjacent lattices and does not rotate or protrude toward the [001] direction, making it unable to separate Pb-Pb dimers (Fig. 3A and B). Therefore, we further explored other bilateral amines with longer alkyl chain molecules which may separate Pb-Pb dimers.

Fig. 3. Passivate deep traps and introduce shallow traps simultaneously.

(A) Atomic scheme of Pb-Pb dimer on (001) plane. (B) Atomic scheme of EDA-treated perovskite (001) plane surface. (C) Atomic scheme of PDA-treated perovskite (001) plane surface. (D) Williamson-Hall plot of the PDA-treated films at various grazing angles. (E) N-A plots of devices with PDA surface treatment with various concentration. (F) A schematic of PDA treatment contribution on shallow trap enchantment and deep traps passivation. (G) Typical J-V curves of devices with PDA surface treatment with various concentration.

The bilateral amine 1,5-pentanediamine (PDA) has an alkyl chain longer than that of EDA. The linear molecular length for the reaction product of PDA and two FA⁺ is 8.83 Å, which is much larger than the distance between the two FA⁺ in adjacent unit cells of 6.36 Å, forcing the alkyl chain in the reaction product to rotate and protrude toward the [001] direction, occupying iodine vacancies and effectively separate the Pb dimers (Fig. 3C). The space torsion configuration increases the local interplanar spacing along the [001] direction from 6.13 Å without PDA treatment to 6.28 Å after processing, corresponding to a tensile strain along out-of-plane direction in (001) planes. To verify this, we measured the strain in the PDA-treated film. As shown in Fig. 3D, the PDA treatment introduces a larger surface tensile strain of 0.76% measured at the top 10 nm, and the tensile strain reduced to 0.17% at the depth of 20 nm. And it was still compressive strain of −0.04% at the depth of 50 nm, which was same with the pristine film. The surface tensile strain is believed to transform the deep traps of Pb-dimer caused by V_I under compressive strain to shallow traps. To verify this, we compared the XPS spectra of I 3d and Pb 4f in the pristine, the EDA-treated and the PDA-treated films. The I 3d peaks in these three films were located at the same binding energy (Fig. S11). The binding energy of Pb 4f peaks in the EDA-treated film was same as that in pristine film, and it shifted toward higher binding energy in the PDA-treated film, demonstrating the electron cloud overlap between Pb ions on the PDA-treated surface decreases. It indicates that the distance between Pb ions on the surface increases and Pb-Pb dimers have been separated after PDA surface treatment⁴⁸.

We conducted the shallow traps characterization on the PDA-treated devices. The N-Δt plots show that the 2 mg ml⁻¹ PDA-treated devices have a new trapping reemission peak centered at 740±20 ns, in addition to the same trapping reemission peak of 260±20 ns in the pristine devices (Fig. S12A). The consistent of the TRPL decay time and the trapped time of films treated with various PDA concentration validates the shallow trap measurement method again (Fig. S12B and C). By integrating the N-A plot in Fig. 3E, the CCE of the PDA-treated device increased to 86.0%, and the percentage of charges collected directly and after being trapped was 37.5% and 48.5% for the PDA treated device, implying that a high density of shallow traps was generated, and the deep traps were simultaneously passivated by PDA treatment (Fig. 3F). The typical J-V curves of PDA-treated solar cells are shown in Fig. 3G. The optimal devices exhibited a highest V_OC of 1.20 V. Since the bandgap of the perovskite derived from EQE was 1.51 eV (Fig. S13A and B), it represents 96.8% of the Shockley-Queisser limit of V_OC (1.24 V) for 1.51 eV bandgap semiconductor. The corresponding V_OC loss (E_g-V_OC) was 317 mV, which is the lowest value reported among p-i-n perovskite solar cells. The 2 mg ml⁻¹ PDA-treated devices did not show obvious hysteresis under reverse and forward scanning (Fig. S13C), and did not show obvious after shallow trap measurement (Fig.S13D). We statistics the Voc among over 15 devices with various PDA treatment concentrations, and it demonstrates that devices V_OC increased as long as increased PDA concentration while the J_SC and FF were comparable (Fig. S13E–H). We also evaluated five other molecules with bilateral or multiple terminal amines that have an alkyl chain longer than that of EDA, and the results come to the same conclusion that these surface treatments can simultaneously passivate deep traps and introduce shallow traps (Fig. S14).

Contribution of charge-emitting shallow traps to V_OC enhancement

We then examined whether the presence of shallow traps would impact the device V_OC by modifying the established carrier dynamics rate equation with a charge trapping term and a charge detrapping term (Fig. 4A)⁴⁹:

$$\frac{d{n}_e}{dt}=G-R_{eh}{n}_e{n}_h-R_{SRH}{n}_e-R_{cap}{(N}_T-n_T)n_e+R_{\mathit{\text{detrap}}}{n}_T-R_{\mathit{\text{Auger}}}\left(n_e^2{n}_h+n_e{n}_h^2\right)$$ (1)

$$\frac{d{n}_T}{dt}=R_{cap}{(N}_T-n_T)n_e-R_{\mathit{\text{detrap}}}{n}_T$$ (2)

$$n_h=n_e+n_T$$ (3)

where $n_e$ is free electron concentration, $n_h$ is free hole concentration, $N_T$ is the shallow trap density, $n_T$ is the population of trapped electrons in shallow traps, G is charge generation rate under continuous AM1.5G illumination, $R_{\mathit{\text{Auger}}}$ is Auger recombination constant, $R_{eh}$ is bimolecular recombination constant, $R_{SRH}$ is deep trap mediated recombination constant (Shockley-Read-Hall recombination, SRH recombination), $R_{cap}$ is trap capture rate constant, and $R_{\mathit{\text{detrap}}}$ is the rate constant of electrons reemitting back to the CB. Here we only consider the electron shallow traps, and these three equations describe the kinetics evolution of free and trapped electron concentration, $n_e$ and $n_T$, respectively. The total concentration of electrons in CB and trap states matches hole concentration $n_h$ to keep the charge neutrality in the perovskite films.

Fig. 4. The impact of shallow traps on device V_OC.

(A) Schematic of a recombination model with trapping and detrapping. (B) Temporal carrier density with and without shallow traps. (C) Schematic diagram of quasi-Fermi level splitting with and without shallow traps under AM1.5G illustration. (D) Equilibrium free electron concentration, (E) Equilibrium trapped electron concentration, (F) Equilibrium free hole concentration, and (G) Quasi-Fermi level splitting for various shallow trap density and detrapping rate constant. (H) Quasi-Fermi level splitting for various shallow trap density and $R_{SRH}$. (I) $R_{SRH}$ dependent quasi-Fermi level splitting without and with shallow traps.

By solving the equations numerically, we can derive the transient and equilibrium carrier concentrations (see method for details). Fig. 4B gives the evolution of free carrier concentration at a given moderate shallow trap density of $N_T$ = 10¹⁵ cm⁻³, a detrapping rate constant of $R_{\mathit{\text{detrap}}}$ = 5×10⁶ s⁻¹ and a deep trap mediated recombination rate of $R_{SRH}$ = 5×10⁶ s⁻¹. When there are no shallow traps, the equilibrium free electron and hole concentration are same as 1.8×10¹⁴ cm⁻³, resulting in a quasi-Fermi level splitting of 1.108 V under AM1.5G illumination. After introducing the electron shallow traps with a density of 10¹⁵ cm⁻³, the equilibrium free electron concentration keeps the same to be 1.8×10¹⁴ cm⁻³, while the equilibrium free hole concentration increases by ten times to 1.2×10¹⁵ cm⁻³ due to the presence of trapped electrons with a concentration of 9.7×10¹⁴ cm⁻³ based on equation (3). It indicates that the electron shallow traps are nearly fully occupied by electrons. Partial electrons are temporally held at the trap states, which leads to the reducing in bimolecular recombination and an increased free hole concentration. Since the recombination rate in the devices is dominated by SRH recombination ($R_{SRH}{n}_e$), the free electrons concentration is the same regardless of emissive shallow traps. The increased free hole concentration shifts the hole quasi-Fermi level toward VB by 48 mV, resulting in an increase of the quasi-Fermi level splitting to 1.156 V under AM1.5G illumination (Fig. 4C). Since the quasi-Fermi levels of electrons/holes have not reached the shallow trap levels, it is unnecessary to consider that the Fermi level pinning caused by the shallow traps. It should be noted that the introduction of shallow traps does not notably affect device short-circuit current density (J_SC), because the trapped electrons can eventually re-emit back to CB after being delayed for somewhile.

To further understand the impact of shallow traps on device V_OC, we first investigate the contribution of shallow trap density (N_T) and trap depth (R_detrap) while fixing the deep trap mediated recombination rate ($R_{SRH}$) as 10⁶ s⁻¹. The equilibrium electron concentration, trapped electron concentration, hole concentration and quasi-Fermi level splitting were shown in Fig. 4D–G. When shallow trap density increases, the equilibrium free electron concentration is unchanged, while the trapped electron concentration and hole concentration increased notably, leading to a gradual increase of quasi-Fermi level splitting until the shallow trap density reaches 2.0×10¹⁶ cm⁻³. The shallow traps are completely occupied by electrons, because the carrier generation rate under AM1.5G illumination is much larger than shallow trap densities we consider here⁵⁰. Therefore, the impact of the detrapping rate constant of trapped charges on carrier concentration and the quasi-Fermi level splitting is negligible. Further increasing the shallow trap density to above 2.0×10¹⁶ cm⁻³ does not further improve quasi-Fermi level splitting. This is because most of the photogenerated electrons are trapped by shallow traps, resulting in a decrease in the free electron concentration. In addition, the increased free hole concentration boosted the Auger recombination and bimolecular recombination which further reduced the free electron concentration. The optimal shallow trap density is around 2.0×10¹⁶ cm⁻³ for perovskite solar cells with a perovskite bandgap of 1.55 eV to reach the largest V_OC of 1.25 V under AM1.5G illumination. The corresponding V_OC loss of 300 mV is better than that in reported record performance of perovskite solar cells^11,44,51,52, even though the deep trap mediated recombination constant is as high as 10⁶ s⁻¹.

Considering that deep trap density in perovskite films can be varied by morphology controlling and passivation, we changed shallow trap density (N_T) and $R_{SRH}$ but fixing the shallow trap detrapping rate constant ($R_{\mathit{\text{detrap}}}$) as 5×10⁶ s⁻¹. The equilibrium quasi-Fermi level splitting mapping is shown in Fig. 4H, and several curves of R_SRH dependent quasi-Fermi level splitting at different shallow trap densities are plotted in Fig. 4I for clarification. When the R_SRH is smaller than 1×10⁵ s⁻¹, the non-radiative charge recombination is so slow that the devices would not need the shallow traps for a large V_OC. With the increase of $R_{SRH}$, shallow traps become more important and induce a larger boost of V_OC. Since most reported perovskite charge recombination lifetime is less than 5 μs, or $R_{SRH}$ > 2×10⁵ s⁻¹, shallow traps are beneficial to boost the device V_OC. For example, the V_OC can be improved by 46 mV by introducing shallow traps with a density of 5×10¹⁵ cm⁻³ for state-of-art perovskites with a non-radiative recombination lifetime of 1 μs.

In conclusion, we directly characterized the shallow traps in perovskite solar cells and found that MHPs are rich in shallow traps, which is different from other traditional semiconductors. The shallow traps are mainly located at the perovskite surface, and shallow trap density was enhanced by > 100 times by introducing surface tensile strain. The shallow traps can temporarily hold electrons and increase free hole concentration in working solar cells by keeping charges from bimolecular recombination, and reduced the V_OC loss of a very stable FACs-perovskite to 317 mV, which is the best among the p-i-n perovskite solar cells. The understanding of the shallow traps in MHPs adds another aspect to the unique defect physics of perovskites, which leads to further improvement of perovskite device performance.

Experimental Procedures

Details regarding the experimental procedures can be found in the Supplemental Experimental Procedures.

Resource availability

Lead contact:

Further information and requests for resources and materials should be directed to and will be fulfilled by the lead contact, Jinsong Huang (jhuang@unc.edu).

Materials availability:

This study did not generate new, unique materials.

Data and code availability:

The authors are willing to share all the data and original code reported in the published paper with the research community. The codes are original prepared using MATLAB.