Impact of Surface Adsorbates and Dimensionality on Templating of Halide Perovskites

Two-dimensional (2D) halide perovskites (HPs) are promising materials for various optoelectronic applications, yet a comprehensive understanding of their dynamics is still elusive. Here, we offer insight into the dynamics of prototypical 2D HPs based on MAPbI$_3$ as a function of linker molecule and the number of perovskite layers using atomic scale simulations. We show that the layers closest to the linker undergo transitions that are distinct from those of the interior layers. These transitions can take place anywhere between a few tens of Kelvin below to more than 100 K above the cubic-tetragonal transition of bulk MAPbI$_3$. In combination with the thickness of the perovskite layer this enables one to template phase transitions and tune the dynamics over a wide temperature range. Our results thereby reveal the details of an important and generalizable design mechanism for tuning the properties of these materials.

Halide perovskites (HPs) are a promising class of materials for various applications, including, e.g., highefficiency solar cells, [1][2][3] lasers [4] and light emitting diodes [5].The most studied so far are the regular threedimensional HPs with the formula AMX 3 , where A is an organic or inorganic cation, M is a metal cation, such as Pb or Sn, and X is a halogen.One of the drawbacks of these compounds is that they often exhibit relatively low stability.In recent years, so-called two-dimensional (2D) HPs (also referred to as layered, quasi-2D or Ruddlesden-Popper phases) [6] have, however, gained significant attention [7][8][9][10].These materials are composed of inorganic perovskite layers stacked on top of each other and separated by organic cations that act as spacers (Fig. 1) [11][12][13][14][15][16].They have been shown to exhibit improved stability [17][18][19][20][21][22][23][24][25] and distinct quantum and dielectric confinement effects [26][27][28], which modulate their excitonic properties [29][30][31], differentiating them from their 3D counterparts.In combination with their tunability [32,33], this makes 2D HPs highly attractive for various optoelectronic applications [18,[33][34][35][36][37].PEA-based 2D HP phases with the composition PEA2MAn -1Pbn I3n+1 for n = 2, 3 and 4 layers.For n > 2 hydrogen and iodine atoms are omitted for clarity.The structures were rendered using ovito [38].* erhart@chalmers.se The properties of 2D HPs sensitively depend on the number and type of inorganic layers and the organic cations that connect them [10,13,[39][40][41].The inorganic layers are responsible for the electronic structure [42][43][44] and mechanical properties of the material, while the organic cations affect the interlayer spacing as well as the overall stability and structure.Therefore, understanding the interplay of inorganic layers and organic cations is crucial for designing efficient and stable optoelectronic devices based on these materials.This is evident in the so-called "templating" approach [45][46][47][48][49].This strategy relies on the fact that the organic linkers can significantly affect the phase of the inorganic framework beyond the surface layer, which can be used to improve the stability of the desired 3D perovskite phases.To be able to fully exploit the potential of this approach, it is, however, necessary to understand the precise mechanisms by which organic cations influence the inorganic framework.
Here, we offer comprehensive insight into how phase transitions and dynamics in 2D HPs can be steered through the choice of the organic linker molecule and the dimensionality of the material.This is accomplished through atomic scale simulations based on accurate and efficient machine learning potentials (MLPs) trained against density functional theory (DFT) calculations.We first focus on the prototypical combination of the linker molecule phenylethylammonium C 6 H 5 (CH 2 ) 2 NH 3 (PEA) with MAPbI 3 and identify a transition from a high-temperature structure without global octahedral tilting to a lower temperature structure with a global outof-phase octahedral tilting pattern.The perovskite layer in direct contact with the PEA molecules (referred to as "surface layer" below) undergoes a transition already between 450 and 470 K, while the transition in the interior of the perovskite slab occurs at a temperature that is at least 50 K lower.The combination of these two processes yields a rather broad overall transition, which approaches the transition temperature of bulk MAPbI 3 only for relatively thick inorganic layers comprising at least 30 or more perovskite layers.To generalize the effect of the linker molecule on the local phase transitions, we then extend the analysis to additional molecules, including phenylmethylammonium C 6 H 5 (CH 2 )NH 3 (PMA), buty-lammonium CH 3 (CH 2 ) 3 NH 3 (BA) and methylammonium CH 3 NH 3 (MA).We find that for bulkier molecules like PEA and PMA, the surface layer transitions significantly above the bulk MAPbI 3 transition, while with the smallest molecule, MA, this transition occurs at a lower temperature.Our results thereby provide an atomic scale understanding of how linker and dimensionality can be used to template phase behavior and dynamics in 2D HPs.Since octahedral tilting is intimately tied to the electronic structure [50][51][52][53], our results reveal the details of an important and generalizable design mechanism for tuning the optoelectronic properties of 2D HPs.Thermodynamic properties.We consider a series of 2D HPs assembled from inorganic PbI 6 octahedral units with MA counterions and PEA linker molecules with the chemical formula PEA 2 MA n -1 Pb n I 3n+1 , where n is the number of perovskite layers in each inorganic layer (Fig. 1).In the bulk limit (n → ∞) one obtains MAPbI 3 , which is one of the most widely investigated 3D HPs.We only consider systems with n ≥ 2 since in the single perovskite layer limit (n = 1) we do not observe an untilted inorganic layer even at 600 K.
First, we analyze the potential energy, the heat capacity and the lattice parameters during cooling simulations (Fig. 2).The potential energy of MAPbI 3 shows a small but clear step at 370 K, corresponding to the latent heat associated with its first-order transition from a cubic a 0 a 0 a 0 phase to a tetragonal a 0 a 0 c − phase (Fig. 2a) [54].This gives rise to a sharp peak in the heat capacity at the transition temperature (Fig. 2b).Additionally, the transition can be seen as a clear change in the two in-plane lattice parameters (tilting is around the out-of-plane axis; Fig. 2c) and even the out-of-plane lattice parameter (Fig. S4).The simulations yield a transition temperature for MAPbI 3 of 370 K, which is approximately 40 K higher than the experimental value of about 330 K [12,55].
Comparable transitions are observed in the twodimensional HPs.For smaller numbers of inorganic layers, n, the transition is more gradual and occurs at higher temperatures, but it becomes more pronounced as n increases, converging toward the behavior observed in MAPbI 3 as n increases.This shows that the nature of the phase transition evolves from a continuous to a first-order transition.
Octahedral tilting.To obtain a more detailed understanding of the transitions we compute the distribution over octahedral tilt angles P (θ) along the cooling simulations using ovito [38] as done in Ref. 56 (Fig. 3).The tilt angle distribution for a given temperature is averaged over a few snapshots corresponding to a temperature window of about 1 K in order to improve the statistics.
For bulk MAPbI 3 one observes a sharp transition at 370 K from a single Gaussian peak centered around zero corresponding to a cubic phase (a 0 a 0 a 0 ) to a symmetric bimodal distribution indicating the transition to a structure with out-of-phase tilting (a 0 a 0 c − ; Fig. 3, bottom panel).
For the 2D HPs we can resolve the tilt angle distribution for each symmetrically distinct perovskite layer throughout the structure.This analysis reveals that the perovskite layer that is in direct contact with the PEA linker molecules (the "surface layers") undergoes a transition to a tilted structure that for, e.g., n = 8 occurs at around 450 K (Fig. 3; top panel).In contrast, the interior perovskite layers undergo a transition at a much lower temperature, i.e., closer to the bulk MAPbI 3 transition temperature, e.g., at around 400 K for n = 8, .It is worth noting that the transition in the surface layers has almost no impact on the tilting in the neighboring layer (layer 2 in Fig. 3; also compare Fig. 4b and Fig. 5b).We attribute this behavior to the octahedra rotating around the z-axis, leading to a weak correlation between neighboring octahedra in the z-direction [56,57].
Distribution over the octahedral tilt angles P (θz) as a function of temperatures for a 2D HP PEA2MAn -1Pbn I3n+1 with n = 8 as well as the corresponding 3D HP (MAPbI3).For the 2D HP the tilt angle distribution is decomposed by perovskite layer, where layer 1 refers to the perovskite layer closest to the organic linker molecule.
At high temperatures, for which no global tilting pattern occurs, the tilt angle distributions are unimodal and well described by Gaussians with zero mean.The width of the distribution is, however, wider for the surface layers compared to the rest of the layers indicating a softer free energy landscape.Furthermore, at low temperature, for which all octahedra exhibit a tilt, the surface layers show slightly larger tilt (Fig. S5).Both of these observations are consistent with the surface layers exhibiting a higher transition temperature.
Phase diagram.The spatial variation of the evolution of octahedral tilts means that the PEA based 2D HPs internally undergo two transitions that can be observed separately in our simulations.The first one is associated with the tilting of the octahedra in the surface layer, while the second one is related to the tilting of the interior layers.Extending the tilt-angle analysis for n ranging from 2 to 50 allows us to obtain the variation of the two transition temperatures with n (Fig. 4).(For a brief discussion of the uncertainties in the transitions temperatures please see Sect. 3 in the Supplemental Material.)This shows that the transition in the surface layer depends only weakly on n varying from 470 K (n = 2) to about 450 K (large-n limit).The transition in the interior, which can only be identified for n ≥ 4, exhibits a more pronounced dependence on n starting at about 410 K for n = 4 and converging to the bulk MAPbI 3 value of 370 K in the large-n limit.
The different structure of the surface layer compared to the interior resembles surface (interface) phases, also referred to as complexions [58,59].This type of surface phases can be understood from a simplified thermodynamic viewpoint using surface and interface free energies γ [60].In this view, the above observation suggests that the effective interface free energy between the cubic phase and the organic linkers γ cub/PEA is larger than the sum of the interface energy between the tetragonal phase and the organic linkers γ cub/tet , and the tetragonal and cubic phases γ tet/PEA , i.e., γ cub/PEA > γ cub/tet + γ tet/PEA .
In our simulations, the tilting of the two surface layers on the opposite sides of the inorganic slab are not correlated with each other at the upper transition temperature and can thus occur by chance in-phase or outof-phase.For the out-of-phase tilting pattern (a 0 a 0 c − ) to be commensurate with both surface layers, the latter need to tilt out-of-phase or in-phase with respect to each other for an even and odd number of layers, n, respectively.As a result anti-phase boundaries can be expected to appear with 50% probability at nucleation time and are commonly observed in our simulations (Fig. 4).In some cases we observe such defects to anneal out already on the time scale of our simulations.Under experimental settings one can therefore assume that such defects typically anneal out and are only present in small concentrations.
Lastly, we look at the ordering of the linker molecules.The two layers of PEA forming a single organic spacer layer are always rotated 180 • around the z-axis relative to each other (Fig. 1).In addition, we observe that the different spacer layers can take on arbitrary 90 and 180 • rotations around the z-axis (see e.g., Fig. 4).This leads to the in-plane lattice parameters being equal (see Fig. 2).Reorientation and rotation of the spacer layers mainly take places during the equilibration part of the simulations, and appear to occur statistically.The orientation subsequently remains largely unaffected as temperature is reduced.
Extension to other systems.Now that we have seen how PEA templates the phase transition in the perovskite layers, it is instructive to extend the analysis to other linker molecules.To this end, we consider 2D HPs based on PMA and BA as well as MA-terminated surfaces, specifically {001} slabs of MAPbI 3 with MAI 2 termination (Fig. 5).
For PMA the behavior is qualitatively similar to that of PEA (Fig. S6), i.e., a transition of the octahedral tilt- ing pattern occurs in the surface layer at a temperature about 100 K higher than in the interior, albeit with a stronger dependence on the number of layers for the interior transition.Unlike the case of PEA for which we found tilting with respect to the out-of-plane axis (z), with PMA we obtain tilting around one of the in-plane axes (x or y).
For both PEA and PMA we observe that the transition temperature for the interior increases notably with decreasing number of layers, approaching the transition temperature for the surface for the thinnest slabs considered here.This reflects the increasing relative weight of the surface layer compared the rest of the system as n decreases.Similarly in the limit of large n, the interior transition temperature approaches that of bulk MAPI 3 .
We also note that in the case of PMA we observe almost no anti-phase boundaries.We suggest this to be due to the stronger octahedral correlation perpendicular compared to along the rotational axis, as previously reported in bulk HPs [56,57].This likely leads to a stronger driving force for the (re)orientation of perovskite layers which is needed to avoid or anneal out anti-phase boundaries.
By contrast, in the case of BA, we observe no separation in temperature between the onset of tilting at the surface and the interior.Rather, there is just one transition that for the smallest n is barely 10 to 20 K higher than the phase transition temperature for bulk MAPbI 3 with a very weak dependence on the number of layers.Similarly to the case of PMA, for BA the tilting occurs around one of the in-plane axes.We note that one can observe a secondary transition associated with the motion and ordering of the BA linker molecules themselves (Fig. S9).At higher temperatures the BA molecules move much more freely than PEA and PMA [42], and are on average oriented perfectly perpendicular to the perovskite layers.Below 300 K this motion is, however, frozen out and the BA molecules become sig-nificantly stiffer.
For the MAPbI 3 surface we observe two different types of behavior.For thicker slabs (n > 14) the topmost (surface) layer undergoes a transition at a lower temperature than the interior region, thus exhibiting the opposite behavior compared to PEA and PMA.On the other hand, for thinner slabs (n < 14) the surface transition can no longer be separated from the transition in the interior of the slab.This can be at least partly explained by the transition temperature for the interior layers decreasing with the number of layers which causes the surface-to-interior ratio to increase.We also also observes a qualitative difference in the tilt pattern between thicker and thinner slabs as the former exhibit tilting with respect to the out-of-plane axis while for the latter tilting occurs with respect to one of the in-plane axes.This behavior suggests that the balance between surface and bulk energetics plays a key role here.While resolving the mechanism is beyond the scope of the present work it is deserving of a more in-depth analysis in future studies.
To summarize our analysis indicates that tilting behavior of the surface layer in 2D MAPbI 3 -based perovskites, i.e., the softness of the rotational energy landscape of the octahedra, can be altered and controlled through the choice of the organic linker molecule.For the bulkier molecules, PEA and PMA, we find that the surface layer transitions at a considerably higher temperature than bulk MAPbI 3 , whereas for the smallest molecule considered here, MA, we rather observe the surface transition to occur at a lower temperature than in the bulk.This leads to a transition temperature for the interior that decreases and increases with the number of layers for PEA/PMA and MA, respectively.For BA an intermediate behavior is observed, i.e., no separate transition for the surface layer.These results thus provide guiding principles for how both dimensionality (through the number of layers n) and chemistry (through the organic linkers) can be used to systematically tune the structural transitions and consequently the inorganic dynamics of the system.Both of these are directly tied to enhanced electron-phonon coupling, which is at the heart of the outstanding optoelectronic properties of these materials.The present insight is thereby of immediate interest for designing 2D HP materials and devices for specific applications and temperature ranges.Computational Methods.The PEA-based 2D HPs have a composition of PEA 2 MA n -1 Pb n I 3n+1 where n corresponds to the number of perovskite layers.Starting from known prototypes for n = 1 [15,48,61,62], we construct structures with n > 1 by inserting the required number of perovskite layers (Fig. 1).These structures are then equilibrated by molecular dynamics (MD) simulations at 600 K to remove structural bias before the cooling simulations.This approach is also employed for PMA and BA using the prototype structures from Refs.48, 61, 63.
Energies, forces and virials were obtained for the training structures via DFT calculations as implemented in the Vienna ab-initio simulation package [64][65][66] using the projector augmented wave method [67,68] with a plane wave energy cutoff of 520 eV and the SCAN+VV10 exchange-correlation functional [69].The Brillouin zone was sampled with automatically generated k-point grids with a maximum spacing of 0.25 Å −1 .
We constructed a neuroevolution potential (NEP) model using the iterative strategy outlined in Ref. 70 using the gpumd software [71][72][73].Training structures included MD structures at various temperatures up to 600 K for bulk MAPbI 3 , 2D HP structures with varying number of perovskite layers and three different organic linkers, PEA, PMA and BA.Additionally, prototype (primitive) structures with varying volume were included as well as a few dimer configurations.The MD structures were generated via an active learning strategy using earlier NEP model generations and selected according to their uncertainty, which was estimated from the predictions of an ensemble of models.The final NEP was then trained using all available training data.In total the training set consists of 616 structures, corresponding to a total of 120 000 atoms.For the final model, the root mean squared errors obtained by cross validation using 10 folds are 10 meV atom −1 for the energies, 150 meV Å −1 for the forces and 90 meV atom −1 for the virials (Fig. S1).
All MD simulations were carried out with gpumd [73,74] with a timestep of 0.5 fs.The cooling simulations were run in the NPT ensemble by first heating the system up from zero to 600 K over 1 ns, followed by equilibration at 600 K for 1 ns, before finally cooling down to 200 K over 25 ns.Simulations were carried using cells comprising 6 × 6 × 4 repetitions of the 2D prototype structures which for, e.g., n = 12 corresponds to about 50 000 atoms and a cell size of about 50 Å × 50 Å × 350 Å; see Fig. S3 for convergence testing.
The transitions between different perovskite phases were analyzed using the octahedral tilt angles of the PbI 6 octahedra [56,57,75,76].The tilt angles in the perovskite layers during MD simulations were obtained using ovito [38] as implemented in Ref. 56.

FIG. 2 .
FIG.2.Thermodynamic observables as a function of temperature from cooling simulations.(a) Potential energy (with 1.5kBT and arbitrary reference energy subtracted) for the a series of 2D HPs with composition PEA2MAn -1Pbn I3n+1, which yields MAPbI3 in the bulk limit (n → ∞).(b) Heat capacity of the system obtained as Cp = dE/dT .(c) In-plane lattice parameters.For MAPbI3 this corresponds to the a and b lattice parameters and the tilting in the a 0 a 0 c − phase occurs around the z-axis.The potential energy (and heat capacity) shown here are represented by fits to the raw data show in Fig.S2.

FIG. 4 .
FIG. 4. Time-averaged snapshots from the cooling simulations for the 2D HP PEA2MAn -1Pbn I3n+1 with n = 6 at (a) 500 K, (b) 430 K and (c) 330 K visualized using ovito [38].Here, hydrogen atoms as well as the MA counterions inside the perovskite layers are omitted for clarity.The color coding of the octahedra indicates the rotation angle around the z-axis, θz, with red and blue indicating negative and positive tilting (ranging from −20 to 20 • ), respectively, while gray implies tilt angles close to zero.For 330 K a stacking fault (anti-phase boundary) is formed as highlighted by the green ellipsoid.(d) Transition temperatures as a function of number of layers n with the heat capacity (Fig. 2) shown as a heatmap.

FIG. 5 .
FIG. 5. (a) Transition temperatures as a function of the number of layers n for (b) PEA, (c) PMA and (d) BA-based 2D HPs as well as (e) MAPbI3 surfaces.Triangles and circles indicate the transition temperatures for the surface layer and the interior layers, respectively.The star indicates the cubic-tetragonal phase transition temperature for bulk MAPbI3.(b-e) Average atomic configurations at 430 K (top) and 340 K/360 K (bottom).Red and blue octahedra indicate negative and positive tilt angles (ranging from −20 to 20 ), respectively, whereas gray implies tilt angles close to zero.Arrows indicate the tilt axis, which is out-of-plane for PEA and MAPbI3 surfaces with less than 14 layers, and in-plane for the other systems.Lines in (a) serve as a guide to the eye.