Jinlu
He
,
Wei-Hai
Fang
and
Run
Long
*
College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China. E-mail: runlong@bnu.edu.cn
First published on 9th September 2019
Understanding nonradiative charge recombination mechanisms is a prerequisite for advancing perovskite solar cells. By performing time-domain density functional theory combined with nonadiabatic (NA) molecular dynamics simulations, we show that electron–hole recombination in perovskites strongly depends on the oxidation state of interstitial iodine and oxygen passivation. The simulations demonstrate that electron–hole recombination in CH3NH3PbI3 occurs within several nanoseconds, agreeing well with experiment. The negative interstitial iodine delays charge recombination by a factor of 1.3. The deceleration is attributed to the fact that interstitial iodine anion forms a chemical bond with its nearest lead atoms, eliminates the trap state, and decreases the NA electron–phonon coupling. The positive interstitial iodine attracts its neighbouring lattice iodine anions, resulting in the formation of an I-trimer and producing an electron trap. Electron trapping proceeds on a very fast timescale, tens of picoseconds, and captures the majority of free electrons available to directly recombine with free holes while inhibiting the recombination of free electrons and holes, delaying the recombination by a factor of 1.5. However, the positive interstitial iodine easily converts to a neutral iodine defect by capturing an electron, giving rise to a singly occupied state above the valence band maximum and acting as a hole trap. The photoexcitation valence band hole becomes trapped by the hole trap state very rapidly, followed by acceleration of recombination with the conduction band free electron by a factor of 1.6. Surprisingly, molecular oxygen interacting with interstitial iodine anion forms a stable IO3−1 species, which inhibits ion migration, stabilizes perovskites, and suppresses the electron–hole recombination by a factor of 2.7. Our simulations reveal the microscopic effects of the oxidation state of interstitial iodine defects and oxygen passivation in perovskites, suggesting an effective way to improve perovskite photovoltaic and optoelectronic devices.
Intrinsic defects are inevitable in low-temperature solution-processed LHPs due to the low stability against thermal and light radiation.22 Dozens of experimental and theoretical works have explored the roles played by a large number of native point defects in LHPs,20,23–30 which found those defects have significant impact on the performance of perovskite solar cells by controlling the quality of films and carrier dynamics.31–34 Sample quality can be directly detected by advanced experimental techniques, such as atomic force microscopy and scanning electron microscopy. However, photoinduced charge dynamics can be only measured via indirect spectroscopy methods, and their nature remains largely elusive.35,36
Interstitial iodine defects are common and active deep traps in MAPbI3,37 easily forming in the presence of excess iodine.37 The impacts of interstitial iodine defects on the electronic structure and charge dynamics of perovskites are under active research and debate. Petrozza and coauthors have shown, using photoluminescence spectroscopy, that a neutral interstitial iodine defect can trap a conduction band (CB) electron, subsequently recombining with a valence band (VB) hole on a surprisingly long timescale and leading to a significantly increased carrier lifetime and an enhanced open-circuit voltage of MAPbI3 perovskite solar cells.32 However, Yang et al. have demonstrated that excess iodine can suppress the formation of interstitial iodide defects and extend the carrier lifetimes.38 On the contrary, Wang et al. have demonstrated that interstitial iodine defects notably decrease carrier lifetimes and lower the photovoltaic performance of MAPbI3 perovskite solar cells.39 The positive and negative effects of interstitial iodine defects on the excited charge carrier lifetime of MAPbI3 perovskite may be related with their oxidation state. First-principles calculations have predicted that positive interstitial iodine (Ii+1) is unstable under light irradiation,37 which tends to trap an electron, resulting in the formation of an neutral interstitial iodine (Ii) that acts as a deep trap state,25 accelerating electron–hole recombination.28,38,40 In addition, the interstitial iodine defects have low migration activation energies (0.1 eV), and they easily diffuse in perovskites, which constitutes the main factor resulting in perovskite material degradation.41,42 In contrast, negative interstitial iodine (Ii−1) is relatively stable,37 while the ion migration, including both MA+ and I−, leads to notable current–voltage hysteresis of a perovskite solar cell.43 Interestingly, theoretical calculations have illustrated that oxygen preferentially interacts with the interstitial iodine anion rather than lattice iodine atom, forming thermodynamically stable IO3− species,44 which potentially stabilizes the MAPbI3 perovskite44 and rationalizes the improved perovskite solar cell performance as well as clarifies the enhanced reversible photoluminescence quantum yield upon material exposure to oxygen in experiments.45–49 Understanding the underlying mechanisms for the impact of oxidation state of interstitial iodine and oxygen passivation effect on the excited-state lifetime of MAPbI3 perovskite calls for a time-domain study of nonradiative electron–hole recombination in real time and at the atomistic level.
Motivated by both the experimental32,38,39,45–49 and theoretical works25,37,44 showing the positive and negative effects of interstitial iodine on the photoexcitation carrier lifetime of MAPbI3, as well as the role played by oxygen passivation, we have investigated the charge trapping and nonradiative electron–hole recombination processes (depicted in Fig. 1) of MAPbI3 in the presence of interstitial iodine defects with different oxidation states, Ii, Ii−1, and Ii+1, as well as oxygen passivation with the stable species IO3−1,44 using a combination of real-time time-dependent density functional theory (TD-DFT)50,51 and nonadiabatic molecular dynamics (NAMD).52–55 Our simulations show that the electron–hole recombination across the conduction band minimum (CBM) and valence band maximum (VBM) (Fig. 1a) in pristine MAPbI3 occurs over several nanoseconds, agreeing well with experimental data.56 The neutral Ii acts as an electron donor, creates a hole trap above the VBM (Fig. 1b), increases NA coupling, and accelerates the electron–hole recombination by a factor of 1.6. The negatively charged Ii−1 defect eliminates the trap state (Fig. 1a) and decreases the electron–hole recombination across the CBM–VBM energy gap by a factor of 1.3 compared to the pristine MAPbI3, arising due to reduced NA electron–phonon coupling. The Ii+1 defect introduces an electron trap below the CBM (Fig. 1c), which acts an electron acceptor. The CB free electrons are highly captured by the trap state, followed by recombining with the holes located in the VBM. The trap-assisted electron–hole recombination between the VBM and the trap state delays by a factor of 1.5 relative to the pristine MAPbI3. Meanwhile, positively charged interstitial iodine is easily converted to a neutral defect by capturing an electron, accelerating electron–hole recombination. Molecular oxygen interacting with Ii−1 defect forms a stable IO3−1 that inhibits ion migration and reduces current–voltage hysteresis. At the same time, oxygen passivation decreases the NA electron–phonon coupling further and suppresses electron–hole recombination across the band gap (Fig. 1a) by a factor of 2.7. This study reveals the impact of oxidation state of interstitial iodine defects on charge dynamics and rationalizes the phenomenon observed in the experiment that oxygen can be responsible for the enhanced perovskite solar cell performance and PLQY45–49 and reduced hysteresis,57 providing valuable guidelines for the design of high-performance perovskite photovoltaic devices.
A 192-atom 2 × 2 × 1 tetragonal73 supercell was used to represent the pristine MAPbI3. The neutral Ii structure is obtained by adding an iodine atom, colored green, into the pristine MAPbI3 system. The Ii−1 and Ii+1 systems are created via adding and removing an electron into/from the Ii structure. By introducing 3/2 O2 into the Ii−1 structure, we obtain the IO3−1 system. Geometry optimization, adiabatic MD, and NA coupling calculations are carried out with the Vienna Ab initio Simulation Package (VASP).74 The electron exchange–correlation effect is described with the Perdew–Burke–Ernzerhof (PBE) functional,75 and the electron–ion core interactions are treated with the projected-augmented wave (PAW) method.76 The energy cutoff of 400 eV is used to converge the total energy during geometry optimization with a Γ-centered 2 × 2 × 2 Monkhorst–Pack k-mesh.77 The adiabatic MD trajectory and NA couplings are obtained at Γ-point because the direct bandgaps for all five systems are at the Γ-point. In order to capture the weak van der Waals interactions within the perovskites, Grimme's DFT-D3 correction approach is used.78
After the geometry is optimized at 0 K, the five systems are heated to 300 K via velocity rescaling to 2 ps. Then, we obtained 6 ps adiabatic MD trajectories within the microcanonical ensemble simulations with a 1 fs atomic time step. In order to study the charge carrier trapping and recombination dynamics in the five systems, the first 4000 geometries of the 6 ps adiabatic MD trajectories were chosen as initial configurations for the NAMD simulations. During the NAMD simulations, the calculated energy gap of 1.65 eV for pristine MAPbI3 is scaled to the experimental value of 1.61 eV (ref. 79) by subtracting a constant. The energy gaps of Ii, Ii−1, Ii+1 and IO3−1 systems are subtracted the same constant. Because electron–hole recombination in perovskites occurs in a typical range from several nanoseconds to microseconds, it is a consuming task to solve the time-dependent Schrödinger equation on these timescales. Therefore, we run short-time NAMD simulations for each pair of states and obtain the rate constant for each process depicted in Fig. 1. Then, we construct the coupled equations, which are shown in ESI,† solve these equations using the obtained the rate constants, and obtain the long time-evolution populations of each state participating in the carrier relaxation. The details of the coupled kinetics equations and their solutions are presented in ESI.†
In addition to the reported I–I and I–Pb distances, we computed the root-mean-square displacement velocity of atoms in the four systems to investigate the influence of oxidation state of the interstitial iodine defect on atomic fluctuations with thermal impact, by separating the atoms into organic (MA) and combined inorganic species (Pb and I). In order to further explore the effect of the defects, we differentiate the interstitial iodine atom from lattice Pb and I atoms in the defective systems (Table 1). The computed data show that interstitial iodine defects in all charged states accelerate the motion of all atoms in the order Ii+1 > Ii−1 > Ii compared to pristine MAPbI3. The sequence of the motions of both organic MA atoms and inorganic Pb/I atoms remains the same for all atoms, attributed to the correlated motions of organic and inorganic parts. The stronger motion in the defective systems than the pristine MAPbI3 indicates that the interstitial iodine defects lower the stability of perovskites; in particular, the instability primarily originates from the distortion of the inorganic I–Pb octahedrons due to their notably increased motions compared to the organic MA cations. The situation becomes stronger in the charged systems (Ii+1, Ii−1) compared to the neutral interstitial iodine system (Ii), rationalizing the larger migrations of iodine ions than iodine atoms.41,43,80–82 The analysis provides an excellent explanation that interstitial iodine defects significantly degrade perovskite films' exposure to light or thermal radiation.39
Totala | MAb | Pb–Ic | Pb–Id | Ie | Of | |
---|---|---|---|---|---|---|
a Averaged on all atoms. b Averaged on atoms in MA. c Averaged on Pb and I atoms. d Averaged on Pb and I atoms except interstitial iodine atom. e Averaged on interstitial iodine atom. f Averaged on O atoms. | ||||||
MAPbI3 | 0.0342 | 0.0469 | 0.0128 | — | — | — |
Ii | 0.0352 | 0.0481 | 0.0141 | 0.0142 | 0.0059 | — |
Ii−1 | 0.0356 | 0.0487 | 0.0140 | 0.0141 | 0.0066 | — |
Ii+1 | 0.0374 | 0.0509 | 0.0152 | 0.0153 | 0.0060 | — |
IO3−1 | 0.0300 | 0.0409 | 0.0130 | 0.0131 | 0.0055 | 0.0061 |
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Fig. 3 PDOSs of (a) pristine MAPbI3, (b) Ii, (c) Ii−1 and (d) Ii+1 systems. The insets show the charge densities of the key electronic states involved in the charge trapping and recombination. |
NA electron–phonon coupling arises due to the interaction between electronic and nuclear vibrational motions. The mixing of two wave functions of initial and final states directly determines the strength of NA coupling, dij. It is because inorganic iodine and lead atoms primarily create the electron–phonon coupling, leading to low electron–hole recombination rate. The organic MA species does not contribute to the band edges, while it simultaneously affects NA coupling in an indirect way and stabilizes the perovskite structure by filling the inorganic cages. The calculated bandgap of pristine MAPbI3 is 1.65 eV (Fig. 3a), agreeing well with the experimental data79 and DFT calculated values.83,84 Introduction of interstitial iodine for all charged states (0, −1, +1) into the pristine MAPbI3 has little influence on the bandgaps of the defective systems (Fig. 3b–d).
The neutral Ii defect creates a half-occupied trap state that is close to the VBM (Fig. 3b). Thus, it can trap holes or electrons, but the two processes cannot happen simultaneously due to the Pauli exclusion principle. Since the trap state is near the VBM that has strong NA coupling between the trap state and VBM due to a small energy gap, hole trapping becomes a major process. The trapped hole is populated, resulting in the Ii acting as a p-type dopant and introducing positive charge carriers near the VBM. As a result, photoexcited CB electrons can recombine with holes residing in both the VB and the trap state. The gap state is mainly localized on the interstitial iodine defect (inset of Fig. 3b). The increased charge density of VBM enhances the overlap between the VBM and CBM, strengthening the NA coupling between them compared to that in the pristine system.
The negatively charged iodine anion creates no gap state in the Ii−1 system (Fig. 3c). The interstitial iodine anion and lead cation form a strong I–Pb chemical bond, eliminating the unsaturated dangling bonds and moving the gap states into the VB. Iodine anion decreases the electron wave functions around itself while leaving the hole wave functions largely unchanged (inset of Fig. 3c) and, therefore, reducing their overlap, lowering NA electron–phonon coupling.
The positively charged iodine cation creates a trap state below the CBM in the Ii+1 system (Fig. 3d). The unoccupied trap state can serve as an electron acceptor, leading the Ii+1 to act as an n-type dopant, and produces negative charge carriers near the CBM. Because interstitial iodine cation and lattice iodine anions attract each other and form an I-trimer, the electron trap state is produced. Apparently, the I-trimer localizes the charge density on itself (inset of Fig. 3d), which also notably disturbs the I–Pb octahedrons and simultaneously decreases the charge densities of VBM and CBM (inset of Fig. 3d), and in particular for the CBM, further lowering the NA coupling between them with respect to the pristine and Ii−1 systems. Consequently, the photoexcited holes can recombine with the electrons located on both the CB and trap state. Because the energy gap between the trap state and the CBM is small, the electron trapping is expected to proceed very fast.
The analysis derived from Fig. 3 demonstrates that iodine chemistry has a significant influence on the electronic structure, and thus, on the charge trapping and recombination dynamics in perovskites.
The pure-dephasing times, summarized in Table 2, are computed using the second-order cumulant approximation of the optical response theory.63 Quantum transition between a pair of states requires formation of coherent superposition states via NA electron–phonon coupling. Short-lived superpositions facilitate slow dynamics, which can be interpreted by quantum Zeno effect in the limit of infinitely fast loss of coherence.87 The ∼10 fs decoherence times are significantly shorter than the electron–hole recombination times that take place over several nanoseconds in the MAPbI3 perovskite.56 Thus, it is essential to consider the decoherence effect during the NAMD simulation.88 The short pure-dephasing times provide a reasonable explanation for the fact that perovskite materials have long excited state lifetimes, rationalizing the high performance of perovskite solar cells.
Energy gap (eV) | NA coupling (meV) | Dephasing (fs) | Rate (×10−3 ps−1) | λ (eV) | ||
---|---|---|---|---|---|---|
Pristine | CBM → VBM | 1.61 | 1.02 | 10.8 | 0.64 | 0.071 |
Ii | CBM → VBM | 1.70 | 2.09 | 8.7 | 1.85 | 0.063 |
VBM → trap | 0.09 | 3.10 | 8.5 | 30.33 | 0.051 | |
CBM → trap | 1.61 | 1.16 | 9.3 | 1.00 | 0.020 | |
Hole trapping | — | — | — | — | 0.083 | |
Electron trapping | — | — | — | — | 0.012 | |
Ii−1 | CBM → VBM | 1.66 | 0.83 | 10.1 | 0.49 | 0.110 |
CBM → VBM | 1.65 | 1.95 | 8.2 | 0.92 | 0.051 | |
Ii+1 | Trap → VBM | 1.21 | 0.56 | 2.6 | 0.44 | 0.031 |
CBM → trap | 0.44 | 2.12 | 3.4 | 23.81 | 0.020 | |
IO3−1 | CBM → VBM | 1.69 | 0.73 | 7.0 | 0.24 | 0.011 |
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Fig. 5 Evolution of populations of the key states for charge trapping and recombination in (a) pristine MAPbI3, (b) Ii, (c) Ii−1 and (d) Ii+1 systems. |
The electron–hole recombination in pristine MAPbI3 occurs in several nanoseconds (Fig. 5a), agreeing well with the experimental data.56 The long lifetime is attributed to the small NA coupling (1.02 meV) and short pure-dephasing time (10.8 fs). The electron–phonon coupling is small because the CBM and VBM are supported by lead and iodine atoms, Fig. 3a. The neutral Ii accelerates electron–hole recombination because the trap state provides new relaxation pathways (Fig. 5b). The trap state is across the Fermi level and above the VBM and is capable of trapping a photoexcited VB hole in tens of picoseconds due to a strong NA coupling of 3.10 meV. Once trapped, the hole can recombine with a CB electron in one nanosecond. Overall, the electron–hole recombination in the Ii system is accelerated by a factor of 1.6 compared with the pristine system. On the other hand, the occurrence of electron trapping is unlikely because the trap state is away from the CBM and the NA coupling between the states is small, 1.16 meV, making the direct recombination of CB electrons with the VB holes a highly impossible event because the process is 15 times slower than the hole trapping (Fig. S14 in ESI†). Therefore, neutral interstitial iodine accelerates the charge recombination via hole trap-assisted carrier relaxation pathways.
The negatively charged Ii−1 and positively charged Ii+1 defect suppress the electron–hole recombination by a factor of 1.3 (Fig. 5c) and 1.5 (Fig. 5d), respectively, operating by different mechanisms. The Ii−1 does not produce a mid-gap state (Fig. 3c) and possesses smaller NA electron–phonon coupling (0.83 meV) and comparable pure-dephasing time with respect to the pristine MAPbI3. A decrease in NA coupling occurs because the negatively charged interstitial iodine induces local geometry distortion and lowers electron wave functions, inset of Fig. 3c. The positively charged Ii+1 creates a trap state below the CBM, which can rapidly trap a CB electron in tens of picoseconds due to the large NA coupling of 2.12 meV. Once trapped, the VB hole can recombine with the trapped electron and a CB electron on a similar time scale of sub-3 nanoseconds. One should note that a direct electron–hole recombination between the CBM and VBM is negligible in the presence of Ii+1 defect because most electrons are trapped by the defect, followed by electron–hole recombination between the trap state and VBM. The deceleration in recombination is because the NA coupling (0.56 meV) reduces and pure-dephasing accelerates (Fig. 3 and Table 2). As a result, both negative and positive interstitial iodine can inhibit charge recombination and extend excited charge carriers' lifetimes. However, previous calculations show that Ii+1 easily captures an electron and converts to a neutral interstitial iodine,37 accelerating charge recombination and decreasing the excited-state lifetime.38,40 As a result, Ii−1 is the most possible interstitial iodine defect responsible for an extended excited-state lifetime and an enhanced solar cell performance.32 However, the mobile MA and I ions lead to unusual phenomena in LHP materials and optoelectronic/photovoltaic devices, such as current–voltage hysteresis and switchable photovoltaic effect, and degenerate the performance of devices.43
The PDOS shows that the IO3−1 defect creates no mid-gap state (Fig. 6b). Oxygen passivation does not change the components of the band edges, while it decreases the electron wave functions, and the hole wave functions remain unchanged (inset of Fig. 6b) compared to the Ii−1 system (inset of Fig. 3c), reducing the NA coupling further (0.73 meV). In Fig. 6c, FTs show that low-frequency modes dominate the spectral density, in agreement with Fig. 4. The dominant peak at 67 cm−1 can be assigned to the I–Pb bending.86 The peak at 155 cm−1 can be attributed to the librations of the organic cations.86 The frequencies in the 200–400 cm−1 range can be associated with the modes of oxygen/iodine product,44 agreeing with the fact that oxygen passivation stabilizes the perovskites, reflected by the almost unchanged I–O chemical bond lengths. Light and fast oxygen generates high-frequency modes and results in short dephasing time compared to the pristine and Ii−1 systems. Fig. 6d shows the time-evolution populations of the CBM and VBM, whose dynamics are depicted in Fig. 1a. The timescales are obtained by fitting the data to an exponent, The recombination is delayed by a factor of 2.7 and 1.8 compared to the pristine and Ii−1 systems, respectively. The deceleration is attributed to the weak NA electron–phonon coupling and short pure-dephasing time. In particular, the NA coupling and pure-dephasing time are 0.73 meV and 7.0 fs in the present case, while they are 1.02 meV/10.8 fs and 0.83 meV/10.1 fs for the pristine and Ii−1 systems, respectively. Smaller electron–phonon coupling and shorter dephasing time favor a longer electron–hole recombination time.
In addition to the above reported NA coupling, reorganization energy, λ, is another important parameter that reflects the charge transfer rate, which characterizes the energy cost due to geometry change experienced by a neutral to a charged system, and vice versa. In general, the lower the reorganization energy, the smaller the geometry relaxation and higher the charge transfer rate. Therefore, we calculated the reorganization energy using constrained DFT because this approach can well describe the unpaired electron, according to the equation:
λ = E(M) − E(M*), | (2) |
The above discussions illustrate that the excited charge carriers' lifetimes can be significantly modulated by the oxidation state of interstitial iodine defects. Despite the ability of positive interstitial iodine to suppress electron–hole recombination, it tends to easily attract an electron to become a neutral defect that accelerates charge recombination. In turn, negative interstitial iodine favors the extension of charge carriers' lifetime, while the significant ion migrations in this case induce significant current–voltage hysteresis. The disadvantage is harmful to perovskite solar cells and even is a common problem in real applications because ion migration degrades perovskite films and devices. Oxygen can passivate negatively charged iodine defects and inhibit ion migration, as well as reduce hysteresis and nonradiative charge and energy losses, providing a mechanistic understanding for the prolonged excited charge carrier's lifetime in the presence of iodine defects and suggesting rational strategies to improve the photovoltaic performance of perovskite solar cells.
This study advances our understanding of the oxidation state of interstitial iodine and the role oxygen plays in the charge dynamics of perovskites, providing valuable insights for the development of high-performance perovskite photovoltaic and optoelectronic devices.
Footnote |
† Electronic supplementary information (ESI) available: Coupled kinetics equations and their solutions; data fitting for the state-to-state transition rates; time-evolution populations of the electron trap-assisted electron–hole recombination in Ii system; the electronic configurations for reactant (initial) and product (final) states of each dynamics process. See DOI: 10.1039/c9sc02353d |
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