A Unified microscopic picture of cation and anion migration in MAPbI$_3$

Using molecular dynamics simulations with neural network potentials, this study reveals that rapid ion migration in MAPbI$_3$ is driven by concerted collective motion of MA interstitials and charge-dependent I-related defects, while MA vacancies remain immobile, thereby revising the conventional understanding of ionic transport in hybrid perovskites.

The Gist

Imagine a solar cell made of a special crystal called MAPbI3. Think of this crystal not as a rigid block of stone, but as a soft, squishy sponge made of tiny building blocks. Inside this sponge, there are two main types of blocks: heavy metal blocks (Lead and Iodine) and lighter, organic "molecule" blocks (called MA, which are like little methylammonium molecules).

The problem is that this sponge isn't perfect. Sometimes, blocks go missing (creating vacancies), and sometimes extra blocks get squeezed in where they don't belong (creating interstitials). When these "defects" start moving around, they can cause the solar cell to break down over time.

For a long time, scientists have been trying to figure out exactly how these defects move and how fast they go. The numbers they got from experiments were all over the place, like a group of people guessing the speed of a car and getting answers ranging from "walking pace" to "supersonic."

This paper uses a super-smart computer simulation (powered by Artificial Intelligence) to watch these defects move in real-time, like a high-speed camera filming a dance floor. Here is what they found, explained simply:

1. The "Ghost" vs. The "Heavy Hauler"

In this crystal, the Iodine defects (the halide ions) are like ghosts. They are light and zippy. Whether an Iodine atom is missing (a vacancy) or an extra one is squeezed in (an interstitial), it zips around very easily. The energy needed to get them moving is very low, like pushing a shopping cart on a smooth floor.

2. The Surprising Dancer (The MA Molecule)

The big surprise in this paper involves the MA molecules. These are much bigger and heavier than the Iodine atoms. You might expect them to be slow, lumbering, and hard to move—like trying to push a grand piano across a room.

• The Old Belief: Scientists thought these big molecules were stuck or moved very slowly.
• The New Discovery: The simulation showed that the MA interstitials (the extra molecules) are actually just as fast as the Iodine ghosts!

How is this possible?
The paper explains that these big molecules don't move alone. They move in a group hug. Imagine three people on a dance floor. Instead of one person trying to squeeze past, they all rotate and shift together in a coordinated "concerted" motion. One steps forward, the others rotate to make space, and suddenly the whole group has shifted. This teamwork allows the heavy MA molecules to zip around almost as fast as the tiny Iodine atoms.

3. The One Who Stays Put

There is one exception: MA Vacancies (holes where an MA molecule is missing). The simulation showed that these holes are essentially immobile. Even when the temperature was turned up high in the simulation, these holes didn't move. It's as if the hole is glued to the floor. This suggests that if you see MA moving in a solar cell, it's likely the extra molecules moving, not the empty spots.

4. Why the Numbers Were Confusing

The paper suggests that the reason past experiments gave such different answers (some saying it's slow, some saying it's fast) is because they were measuring different things.

• The fast movement (0.15–0.20 eV energy barrier) is what happens deep inside the crystal (bulk diffusion), which is what this study focused on.
• The slower movement reported in other studies might be happening at the edges of the crystal grains or at the boundaries between them, where things get stuck and move differently.

The Big Picture

This study rewrites the rulebook for how we understand these materials. It tells us that:

1. Teamwork matters: Even big, heavy molecules can move fast if they move together in a coordinated dance.
2. Charge doesn't matter much: Unlike the Iodine defects, whose speed changes depending on their electrical charge, the MA molecules move at the same speed whether they are charged or neutral.
3. The "slow" MA is a myth: The idea that the organic part of the crystal is a slow, sluggish bottleneck is wrong; it's actually quite agile when it moves as a team.

By understanding that these defects are so mobile and move in specific ways, scientists can now better design ways to "passivate" (plug up) these defects or stop them from moving, which should help make solar cells and lights last much longer.

Technical Summary

Technical Summary: A Unified Microscopic Picture of Cation and Anion Migration in MAPbI3

Problem Statement
Defect passivation and the restriction of defect mobility are critical for extending the lifetimes of halide perovskite devices. While experimental studies have extensively measured ion transport in the prototype material MAPbI$_3$ (methylammonium lead iodide), the results exhibit a significant spread in reported migration barriers (ranging from 0.10 to 0.94 eV). Furthermore, the specific nature and composition of the migrating defects—whether they are vacancies, interstitials, or extended defects—remain difficult to identify experimentally. Conventional computational approaches relying on the Nudged Elastic Band (NEB) method struggle in these soft materials due to the existence of multiple competing low-energy pathways and the low symmetry of the methylammonium (MA) cation. Additionally, standard Molecular Dynamics (MD) simulations often lack the accuracy required for reliable barrier extraction due to limitations in classical force fields.

Methodology
To address these challenges, the authors employed Molecular Dynamics (MD) simulations driven by Machine Learned Force Fields (MLFFs) trained on Density Functional Theory (DFT) data.

• Force Field Development: The study utilized the Allegro model, a local E(3)-equivariant graph neural network potential (NNP), implemented via the NequIP package.
• Training Data: The NNPs were trained on DFT data generated using the SCAN+rVV10 functional (including van der Waals interactions) within the VASP package. The datasets were constructed using an "on-the-fly" sampling approach from short-time MD runs, ensuring the inclusion of diverse structures.
• Defect Modeling: The simulations modeled point defects in 2$\times$2$\times$2 supercells (96 atoms) and production runs in 6$\times$6$\times$6 supercells (2592 atoms). The study considered iodide (I) and MA vacancies and interstitials in their most prominent charge states under intrinsic conditions: $I^-_I$, $V^+_I$, $I^0_{MA}$, $I^+_{MA}$, $V^0_{MA}$, and $V^-_{MA}$. Separate NNPs were trained for neutral and charged MA defects by selecting DFT data with Fermi levels near the valence or conduction bands.
• Validation: The accuracy of the NNPs was validated by comparing migration barriers calculated via Climbing Image NEB (CI-NEB) against DFT benchmarks, showing deviations of less than 0.11 eV. Force comparisons yielded a coefficient of determination ($R^2$) of 0.99.
• Simulation Protocol: Three independent 2-nanosecond MD simulations were performed at five temperatures between 500 K and 600 K. Diffusion coefficients were extracted using the Einstein relation, treating all atoms of a specific species to account for kick-out processes rather than tracer diffusion.

Key Results

• Migration Barriers and Mobility: The simulations revealed that iodide interstitials ($I^-_I$) and vacancies ($V^+_I$) are highly mobile, with activation energies ($E_a$) of 0.18 eV and 0.15 eV, respectively. Remarkably, MA interstitials ($I^0_{MA}$ and $I^+_{MA}$) exhibit comparable mobility with activation energies of 0.18 eV and 0.20 eV.
• MA Vacancy Immobile: In contrast to interstitials, MA vacancies ($V^0_{MA}$ and $V^-_{MA}$) were found to be immobile within the simulated temperature and time scales (up to 600 K). This suggests a lower bound for their activation energy of approximately 0.4 eV.
• Migration Mechanisms:
  • Iodide Defects: Migration occurs via a "kick-out" mechanism where a neighboring iodide atom rotates to fill a vacancy, or an interstitial hops between Pb-I-Pb bridges.
  • MA Interstitials: Despite their molecular nature, MA interstitials migrate via a concerted motion involving three neighboring MA ions. Two MA ions in a Pb-I cage and a third neighbor rotate to align their C-N axes, allowing the central ion to migrate to an adjacent cage.
• Charge State Dependence: The diffusion of iodide-related defects shows dependence on charge state, whereas the diffusion of MA-related defects is virtually independent of charge state. This is attributed to the fact that MA interstitials and vacancies create very shallow impurity levels that are ionized at room temperature, leading to delocalized charge that does not significantly hinder motion.
• Consistency with Experiments: The calculated activation barriers (0.15–0.20 eV) align with the lower end of the wide range of experimentally reported values.

Significance and Claims
The paper claims to provide a unified microscopic picture of ion migration in MAPbI$_3$ that reconciles the discrepancies in experimental activation energies. The authors argue that the lower values observed in experiments (0.15–0.20 eV) correspond to intrinsic bulk diffusion dominated by iodide defects and MA interstitials. The higher values reported in other studies likely reflect additional contributions, such as inter-grain transport or the formation of complex defects, rather than intrinsic bulk migration barriers.

A primary contribution is the revision of the conventional understanding that MA migration is intrinsically slow due to its molecular size. The study demonstrates that MA interstitials are nearly as mobile as iodide defects due to a collective, concerted migration mechanism. Furthermore, the work highlights that the A-cation species (MA) does not significantly affect halide motion, as the mobility of halide defects in MAPbI$_3$ is comparable to that in all-inorganic CsPb(I$_x$Br$_{1-x}$)$_3$ perovskites. Finally, the study underscores the importance of collective molecular motion in enabling fast ionic migration in hybrid perovskites.