Factors influencing the nucleation and crystal growth of solution-processed organic lead halide perovskites: a review

According to classical theory, the crystallization process can be divided into nucleation and growth steps. These two processes have different sensitivities to the growing environments such as the supersaturation and air/liquid/solid interfaces, which is one of the reasons for the resulting films with very different morphology. For this reason, it is necessary to recapitulate the main points of the basic nucleation theory first.

Nuclei form when the perovskite solution becomes supersaturated, i.e. the solute concentration (C) exceeds its solubility (C_S). However, these nuclei formed by thermal fluctuation are redissolved back if the supersaturation is not high enough for nucleation [41, 81–84]. The nucleation is a thermodynamic process driven by the total Gibbs free energy change (ΔG). For a homogeneous nucleation process with nuclei formed in the bulk of the solution, ΔG is the sum of the bulk free energy change (ΔG_V) and surface free energy change (ΔG_S):

$$\begin{equation}\Delta G = \Delta {G_{\text{V}}} + \Delta {G_{\text{S}}} = \frac{4}{3}\pi {r^3}\Delta {G_{\text{B}}} + 4\pi {r^2}.\end{equation} \tag{ 1 }$$

Here, r is the radius of sphere nuclei, γ is the unit surface energy of the liquid–nuclei interface and the unit bulk free energy (ΔG_B) is proportional to the logarithm of supersaturation ratio (S, defined as S = C/C_S), i.e. ${{\Delta }}{G_{\text{B}}} \propto {\text{ln}}\left( {C/{C_{\text{S}}}} \right)$. Hence, ${{\Delta }}{G_{\text{B}}}$ becomes positive when the solution becomes supersaturated. ${{\Delta }}G$ does not necessarily turn positive with ${{\Delta }}{G_{\text{B}}}$, but depends on whether the ${{\Delta }}{G_{\text{V}}}$ overcomes the ΔG_S. Taking ΔG_S as positive and ΔG_V as negative, a critical nuclei radius (r*) defined by ${\text{d}}\left( {\Delta G} \right)/{\text{d}}r = 0$ can be obtained, as shown in figure 4(a). If its size exceeds r*, the fluctuation-induced clusters will be thermodynamically stable and tend to grow further as nucleation centers [41, 81–84]. According to this mechanism, an energy barrier (${{\Delta }}G_{{\text{Hom}}}^*$) exists at r = r* with a value defined by equation (1) (figure 4(a)), which hinders the spontaneous nucleation. The height of${{ \Delta }}G_{{\text{Hom}}}^*$ decreases when the supersaturation ratio (S) increases.

Zoom In Zoom Out Reset image size

On the other hand, the presence of both liquid/solid and air/liquid interfaces impacts on the energy barrier. In the case of heterogeneous nucleation, perovskite nucleates on liquid/solid interfaces (such as substrates or added nucleation centers) with its ΔG_S part reduced due to the presence of foreign surfaces. As a consequence, heterogeneous nucleation becomes easier than homogeneous nucleation with its energy barrier (${{\Delta }}G_{{\text{Het}}}^*$) reduced:

$$\begin{equation}{{\Delta }}G_{{\text{Het}}}^* = \frac{{\left( {2 + {\text{cos}}} \right){{\left( {1 - \cos } \right)}^2}}}{4}{{\Delta }}G_{{\text{Hom}}}^*\end{equation} \tag{ 2 }$$

where θ is the contact angle, which can vary from 0° to 180°. The energy barrier for heterogeneous nucleation reduces significantly when θ decreases, depending on the wettability of the foreign surface (figure 4(b)).

For a nucleation process with an energy barrier of ${{\Delta }}{G^*}$, its nucleation rate (I) is given by

$$\begin{equation}I{\text{ }}\exp \left( {\frac{{ - {Q_{\text{D}}}}}{{RT}}} \right){\text{exp}}\left( {\frac{{ - \Delta {G^*}}}{{RT}}} \right)\end{equation} \tag{ 3 }$$

where ${{\Delta }}{G^*}$ represents the nucleation energy barrier and Q_D represents the activation energy for the transport of solute 'monomers' to the nucleus/solution interface.

Although both homogeneous and heterogeneous nucleation may take place during the drying process, these two processes have different sensitivities to the supersaturation of the solution due to different ${{\Delta }}{G^*}$ values, as shown in figure 4(c). In the low-S region, for an ideal solution with uniform concentration and temperature, heterogeneous nucleation is the only process due to its lower ${{\Delta }}{G^*}$ value than that of homogeneous nucleation (i.e. lower threshold S). Due to this characterization, the low-S region has been widely employed to form single crystal with introduced seeds [40]. When S increases (e.g. due to faster solvent removal rate or a faster cooling process), homogeneous nucleation takes place and competes with heterogeneous nucleation, as shown in figure 4(c). However, the heterogeneous nucleation rate is limited by the total area of the foreign surface. Hence, in the case of the high-S region (e.g. injecting antisolvent such as chlorobenzene (CB) or ethyl alcohol (EA)) [21, 87], the homogeneous nucleation process becomes dominant [3, 82].

Heterogeneous nucleation was thought to be less common in the fabrication of perovskites a couple of years ago [3]. However, with growing demands on the precise manipulation of perovskite crystallization, the importance of the heterogeneous nucleation mechanism has increased gradually. One example is the emerging strategies for crystallization controlling with seed-containing precursor solution [88, 89]. The external seed method offers better reproducibility in the film quality [90]. Another updated understanding is that the nucleation of perovskite phase is largely determined by the preformed PbI₂-based solvated phase, which triggers heterogeneous nucleation of perovskite on its surface. Moreover, the heterogeneous nucleation of Ruddlesden-Popper (RP)- and Dion-Jacobson (DJ)-type quasi-2D perovskites on 3D-like perovskite have been demonstrated to be efficient during the drying process, which explains the conditional vertical orientation of quasi-2D perovskites [68].

For a certain foreign surface, the heterogeneous nucleation rate can be widely varied depending on its surface treatment and roughness. As the wettability of the surface is influenced by its surface energy (γ), treating the foreign surface with plasma is a feasible method to lower ${{\Delta }}G_{{\text{Het}}}^*$ and therefore promote the heterogeneous nucleation rate [86]. More generally, as modeled by Yang et al, when the introduced surface is rough, the heterogeneous nuclei prefer to form in the concave regions, as shown in figure 4(d) [85], which is attributed to the further reduced surface free energy item. Figure 4(e) plots the dependence of the energy barrier ratio (i.e. $f\left( \beta \right) = {{\Delta G}}_{{\text{Het}}}^*/{{\Delta }}G_{{\text{Hom}}}^*$) on the contact angle (θ) and the local cone angle as schematically shown in figure 4(f). Based on this consideration, the nucleation rate is not uniform on a rough surface and the formation of nuclei on sites at the concave regions is energetically favored. After nuclei preferentially form at substrates, full coverage of the substrate is prospected as the propagation of perovskite growth [85]. Therefore, the heterogeneous nucleation can be promoted by increasing the surface roughness of the substrate. To achieve rough substrates, mesoporous structure or a layer of sparsely distributed nanoparticles are applied for heterogeneous nucleation [91, 92]. However, the limited mass transportation in the rough surface emerges as an influencing factor, which sometimes leads to interfacial cavities if heterogeneous nucleation is not dominant [93].

At the air/liquid interface, the surface tension plays a role in accelerating the nucleation [86]. This is because the surface region of the liquid is under strain due to the surface tension, which causes an increased average intermolecular distance compared with the interior liquid phase (figure 4(g)). The increased average intermolecular distance weakens the binding effect between solvent and solute and hence increases the ΔG_B value in equation (1), which then reduces the energy barrier for nucleation (${{\Delta }}{G^*} - {{\Delta }}G_{\text{S}}^*$) as illustrated in figure 4(h). This accelerated nucleation on the liquid surface increases with the surface tension of the used solution. This effect has been reported to grow large perovskite single crystals on the centimeter scale with the liquid surface function as the high-priority nucleation region, such as MAPbI₃, MAPbBr₃, MASnBr₃ and 2D (PEA)₂PbI₄ perovskites. On the other hand, it should be mentioned that the nucleation rate at the liquid/air interface can be influenced by other factors such as concentration gradient and temperature gradient, which overpass the surface tension effect in the case of fast solvent removal [68, 74, 94, 95].

The antisolvent method appears to be an efficient strategy to quickly improve the supersaturation of perovskite precursor solution [21, 87, 96]. While the substrate is spinning, a nonpolar antisolvent (e.g. toluene, chlorobenzene, or diethyl ether) is dripped onto the substrate (shown in figure 5(a)). It not only drives out the solvent much faster than it would evaporate by itself but also reduces the intrinsic precursor solubility in the remaining solution upon mixing of antisolvent into it, leading to rapid crystallization for uniform, ultra-smooth perovskite thin films. To date, antisolvent engineering has been widely used to fabricate PSCs with high PCE of over 22% due to its high reproducibility in nucleation control [97–100]. A similar approach to solvent engineering applies the antisolvent after film deposition [63]. As shown in figure 5(b), NMP and diethyl ether were used as the solvent and antisolvent, respectively [101]. A similar method was also adopted to prepare low-band-gap FA_0.75Cs_0.25Pb_0.5Sn_0.5I₃ films through immersion in an antisolvent bath [102]. Beyond the antisolvent method, mixture solvents combining volatile noncoordinating solvents (ACN and 2-ME) and low-volatile high-coordinating solvents (DMSO) offer a strategy for fast drying in the early nucleation stage and retarded drying in the lateral growing stage. The fast drying of ACN and 2-ME formed high supersaturation in the bladed wet film and hence formed a high density of nuclei, which enabled a high speed of blading (99 mm s⁻¹) of uniform solid films at room temperature [74]. The strong coordination between DMSO and PbI₂ guaranteed the slow formation of perovskite phase in the bladed film with large perovskite grains [74]. Scanning electron microscopy (SEM) images showed that these films were still compact and uniform, but the grain size increased to 1–2 μm in the lateral directions. Moreover, promoting the volatilization of the solvent by blowing the casted wet film with N₂ flow has been introduced in both spin-coating [103] and blading methods [68, 95], which lead to rapid formation of a supersaturation region located on the top of the wet thin film.

Zoom In Zoom Out Reset image size

In addition to the common methods mentioned above, other analogical methods to accelerate supersaturation of the perovskite solute include gas-assisted deposition, vacuum flash-assisted solution process (VASP) and thermal annealing. Flowing Ar gas was introduced over a semi-wet film during spin-coating to speed up solvent evaporation. The promptly formed supersaturation encouraged rapid formation of more nuclei [103]. As shown in figure 6(a), the VASP method was also used to facilitate rapid supersaturation of the perovskite solute, yielding more homogeneous films with full surface coverage and without pinholes [104]. High-temperature thermal annealing could induce fast removal of the solvent to create a supersaturation environment of the perovskite precursor solute (figure 6(b)). This accelerates the perovskite nucleation [105]. After increasing the thermal annealing temperature, the crystalline grain size improved from an average of 300 nm to 1 μm.

Zoom In Zoom Out Reset image size

As the mechanisms mentioned above accelerate the nucleation rate, methods to suppress the nucleation rate are also highly desirable in many cases when large grain size is pursued. Tuning the supersaturation of solution through temperature or drying process engineering are accessible methods, but bring complexity in uniformity and yield control in large-area fabrication. To date, it is known that the stage of forming PDS in the wet film is prior to the formation of perovskite phase, which actually dominates the formation of perovskite phase at nucleation sites. Hence, manipulation of PbI₂-based solvent phase has become an efficient method of nucleation rate engineering. Using organic molecules with high donor number can form a coordinate complex with PbI₂-based clusters, which helps to retard the precipitation of PbI₂ from solution. However, molecules with high donor number (e.g. DMSO, NMP) form a stable solvated phase with PbI₂, which remains in the solid films until it is heated. Wang et al revealed that using additional AX salts (such as NH₄Cl, MACl, NH₄I, MAI, and MABr) in precursor solution efficiently suppressed the nucleation rate of PbI₂-based solvated phase (figures 7(a) and (b)), which eliminated the needle-like crystals in resulted films and led to greatly enlarged grain sizes of 2D perovskites [68]. Among these AX salts, NH₄Cl is a promising choice for iodine perovskites as it evaporated completely in the post-thermal-annealing process. This NH₄Cl additive method was later applied to doctor-bladed 3D perovskites by Dai et al [106], in which the suppressed nucleation rate was in situ observed by optical microscope (figure 7(c)). The origin of the suppressed nucleation by AX salts still needs to be clarified. A possible reason is the increased charges of the PbI₂-based colloid particles after binding with excessive halide ions offered by additional AX salts, which hinders the aggregation of colloid particles by an electrostatic repelling effect [48]. On the other hand, some bulky zwitterions were also reported to reduce the nucleation rate of perovskites, such as 3-(decyldimethylammonio)-propane-sulfonate inner salt (DPSI) [107] and 3-(1-pyridinio)-1-propanesulfonate (NDSB201) [108].

Zoom In Zoom Out Reset image size

Moreover, for 2D perovskites, the preferential nucleation sites located at the surface of the precursor solution and the subsequent templated growth from heterogeneous nucleation result in the desired crystal orientation, which boosts the efficiency of the resulting solar cells [68, 109]. As shown in figure 8(a), by applying solvents with high boiling point and long chain cations with higher solubility, a low supersaturation was maintained. This further guaranteed the domain heterogeneous nucleation and crystal growth beneath the preformed perovskite crust on the surface instead of homogeneous nucleation in the solution interior [109, 110].

Zoom In Zoom Out Reset image size

Optimizing the precursor solution temperature can also be used to adjust the nucleation density. The precursor solution temperature is closely related to solubility and solvent evaporation rate. As shown in figures 8(b) and (c), a systematic study of the correlation between crystallization and the precursor solution temperature has been conducted for solution-processed CsPbI₂Br film [111]. On one hand, the nucleation step is supposed to be suppressed due to the enhanced solubility of the precursor at elevated temperatures. On the other hand, the supersaturation ratio might increase significantly due to the much faster solvent removal rate. To obtain thick film with a larger crystalline grain size, the temperature and drying procedure of the precursor solution should be carefully adjusted to avoid the formation of a high density of nuclei.

As another strategy to manipulate the concentration of nucleation centers, external nuclei were intentionally introduced into the precursor solution. Taking advantage of the low solubility of cesium (Cs⁺) salts, Cs⁺ salts were reported to be added into PbI₂ precursor in the first step of two-step methods (as shown in figure 8(d)) [88, 90, 112] or into perovskite precursor solutions for one-step methods [89]. The Cs⁺-enriched regions served as seeds to facilitate heterogeneous crystallization and crystal growth of the perovskites. As a result, large grain size and preferential crystallographic orientation of perovskite film were achieved, along with improved efficiency and stability of the resulting solar cells. Similarly, some additives (such as C₆₀ [113], [6,6]-phenyl-C₆₁-butyric acid methyl ester (PCBM) [25], 3,9-Bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2',3'-d']-s-indaceno[1,2-b:5,6-b']dithiophene) (ITIC) [25], 1,3-bis[3,5-di(pyridin-3-yl)phenyl]benzene (BmPyPhB) [114], V₂O_x nanoparticles [115], black phosphorus quantum dots [116] and so forth [39]) were added into perovskite precursor solution or antisolvents [117–119], acting as nucleation sites. A merit of using external nuclei is their controllable nuclei concentration, which is less sensitive to the variable drying process.

Control over the nucleation location is another important route to manipulating the morphology evolution and dominating orientation of resulting perovskite films. During the drying of the wet film, the environment for nucleation is far from equilibrium conditions with imposed concentration and temperature gradient. As shown in figure 9(a) [120], with the evaporation of the solvent at the upper surface, the concentration of precursor solution decreases from the top to the bottom region. Meanwhile, the evaporation of the solvent is an endothermic process, which tends to make the temperature of the precursor solution increase from the top to the bottom region. Generally, the solubility of perovskite raw material PbI₂ in a solvent (e.g. DMF, DMSO, NMP) decreases at lower temperature. Hence, the top region of the wet film with high concentration and low temperature can be the preferential location for nucleation [120]. On the other hand, as introduced above, the substrate can also become a preferential nucleation region due to the lower energy barrier of heterogeneous nucleation than that of homogeneous nucleation [120]. Since the nuclei formed in solution are very small and surrounded by solvents, it is challenging to directly characterize the nucleation region for a given material system and fabrication procedure.

Zoom In Zoom Out Reset image size

The nucleation location can be engineered through controlling the local concentration and temperature with designed deposition methods. In the antisolvent method, the dripping of antisolvent extracts the solvent from the precursor solution in an extremely short time, which is supposed to induce fast nucleation at the upper part of the precursor solution [121, 122]. Unsatisfactorily, it was proposed that the compact perovskite film formed on the upper surface may hinder the penetration of the antisolvent, resulting in the formation of shrinkage voids at the bottom layer (figure 9(b)). A method combining MACl additive and substrate heating was reported by Li et al to tune the nucleation location. The MACl additive was used to retard crystallization and the substrate heating was used to increase nucleation rate. This led the perovskite or solvated phase to form at the bottom substrate, which eventually resulted in growing a compact monolithic MAPbI₃ film with an average grain size of 3.6 µm [121]. In another attempt, frozen substrates were employed to increase the supersaturation around the substrate through the antisolvent method; the crystals nucleated both at top and bottom regions of the wet thin film during the antisolvent method, as shown in figure 9(c) [94].

For the doctor-blading method, the volatilization of DMF solvent at room temperature is much slower than that in the spin-coating method. For this reason, the temperature gradient and concentration gradient along the vertical direction are significantly counteracted by heat transfer and mass transport, and therefore the surface of the solution is not necessarily the dominant nucleation region. As a consequence, methods of controlling the nucleation and crystallization in spin coating have become invalid in doctor blading. For example, in a case of dealing with quasi-2D perovskite, nucleation on top of the solution was intentionally pursued by hot air blowing, which accelerated DMF volatilization on the precursor solution surface, as shown in figure 9(d). The preferred nucleation on top of the solution triggered a downward growth of BA₂MA₃Pb₄I₁₃ perovskite with out-of-plane orientation, which was unavailable for the same devices fabricated without hot air flow due to the possible homogeneous nucleation in the bulk of the solution [68].

On the other hand, when the drying process of doctor-bladed wet thin film is slow, the insufficient supersaturation does not offer uniformly distributed nucleation centers. In this case, the lateral liquid flow driven by the temperature gradient and concentration gradient along the horizontal direction mediates the shape of the liquid phase and the location of its drying fronts. The nucleation may start at the edge of the precursor solution because the drying at the edge of the solution film is relatively faster than that on the surface of the solution film [123, 124]. When the solution edge is not pinned by the solidified perovskite phase, the nucleation region hops with the shrinking of the solution edge, which evenly results in perovskite film featuring many concentric rings from the edge to the center of the domain [125].

Crystal growth occurs immediately after the formation of stable nuclei (figure 10(a)). The growth of crystal is neither a uniform nor steady process, depending on the size of the crystal and the local supersaturation. There are many mechanisms involved in the crystal growth that make the analysis quite complex. For a perovskite precursor solution with multiple components, ionic and hydrogen bond interactions, the complexity is increased further.

Zoom In Zoom Out Reset image size

For a simple description, the change in energy of a dispersed monomer in solution during crystallization can be schematically shown in figure 10(b) [126, 127]. The lowest energy state at the left side (region-I) represents a building monomer incorporated into the crystal surface, usually with the kinks on the surface of the crystal as the most favored sites (figure 10(a)). The isolated nucleation on the compact surface is more difficult (i.e. the 2D nucleus in figures 10(a) and (b)). The line at the right side (region-III) is determined by the average energy of a monomer dispersed in solution. The energy difference for a monomer between liquid and crystal phases is equal to the chemical potential change for crystal and liquid with the same temperature and pressure, defined as $\Delta \mu = {k_{\text{B}}}T{\text{ln}}\left( {C/{C_{\text{s}}}} \right) = {k_{\text{B}}}T{\text{lnS}}$. There is an energy barrier at the phase boundary with a height of $\Delta {E_i}$, which limits the kinetic coefficient of the growing process. The presence of the energy barrier leads to a crystal growth velocity (V) defined as:

$$\begin{equation}V = \frac{{{\text{d}}r}}{{{\text{d}}t}} = K\left( {C - {C_{\text{s}}}} \right) \propto \exp \left( { - \frac{{\Delta {E_i}}}{{{k_{\text{B}}}T}}} \right)\left( {C - {C_{\text{s}}}} \right)\end{equation} \tag{ 4 }$$

where K is the kinetic coefficient. Based on this simplified picture, the crystal growth rate is supposed to be linear with the driving force of $\left( {C - {C_{\text{s}}}} \right)$; see the green line in figure 10(c). It should be mentioned that the equilibrium concentration (C_S) is dependent on the facet of the crystal. For a building monomer incorporated into different facets, $\Delta \mu$ is different due to the varied binding strength of the monomer on different facets, despite the same average energy of a monomer in solution. Hence, the driving force for crystal growth is anisotropic. The $\Delta \mu$ generally reaches its highest value for the facet with the shortest interplanar distance. This is the reason that most of the quasi-2D perovskite grows fast on its (100) or (001) planes but much slower on its (010) planes [7, 128–130]. It should be clarified that, as illustrated in figure 10(a), the growth of the crystal is also determined by the mass transport (induced by $\nabla C$) and heat transport (induced by $\nabla T$) in solution. Hence, its practical growth direction (direction B) can be different from its preferred growth direction (direction A), which results in steps on the grain surface, as frequently observed in lead halide perovskite grains [131].

The energy barrier in the phase boundary regulates the crystal growth rate, which can have different natures in different mechanisms. Generally, it can be the energy required for: (a) a surface chemical reaction, (b) the monomer to break bonds with coordinating solvent molecules for its incorporation (called desolvation), or (c) the monomer to overcome steric effect and occupy a correct orientation. Taking $\Delta {E_i}$ into consideration helps one to understand the growth of perovskite crystal. As mentioned above, in the work carried out by Zhang et al, the growth speed of PbI₂-based solvated phase was reported to increase in the presence of moisture, which was explained as the reduced energy barrier for the desolvation of DMSO from PbI₂–DMSO solvated phase with the assistance of H₂O molecules [72]. In another work carried out by Cui et al, the Rb⁺ ions added to perovskite precursor solution preferred to accumulate at the phase boundary region and introduced an additional energy barrier for the incorporation of MA⁺ cations [132]. Similarly, the energy barrier can be increased by using Lewis-based additives [52, 133]. Increasing $\Delta {E_i}$ also exists in the formation of perovskite film from solid-state films dominated by a Lewis acid–base adduct, as will be introduced below.

In a special case, when the energy barrier $\Delta {E_i}$ is ignorable, the growth of the crystal is found to be limited by the diffusion of monomers from the solution to the crystal surface with a diffusion coefficient of D. In this situation, the flux of the solute is driven by the concentration gradient between the crystal surface and the bulk of the solution (blue line in figure 10(c)). In the case of diffusion-limited growth, the growth rate is linear with the supersaturation (S − 1) of the solution. However, in most cases, $\Delta {E_i}$ is not ignorable in the solution because the energy barrier for desolvation is comparable with the equivalent activation energy (E_d) for the monomer to diffuse in solution (i.e. $D \propto {\text{exp}}\left( { - {E_{\text{d}}}/{k_{\text{B}}}T} \right)$). In this case, the driving force $\left( {C - {C_{\text{s}}}} \right)$ is shared by the diffusion process and the $\Delta {E_i}$ overcoming process (see the red line in figure 10(c)) with the C in equation (4) replaced by the concentration around the phase boundary region (C_i ).

In both diffusion-limited growth and surface-reaction-limited growth, the growth rate (or velocity) is supposed to be linear with the supersaturation of solution (i.e. the dashed line shown in figure 10(d)). However, in the case of surface-reaction-limited growth, the growth rate departs from this rule in the low-S region with a modulated relationship of $V \propto {\left( {S{\text{ }} - {\text{ 1}}} \right)^2}$ (figure 10(d)). According to the BCF model, this departure mainly originates from the difficulty of forming an isolated 2D nucleus in a kink-free crystal surface when the supersaturation is low [127].

Precisely controlling the crystal growth speed is always desirable for the formation of high-quality, low-defect-density crystals. Tuning the supersaturation ratio of the wet film via the solvent removal rate and temperature are two feasible ways to adjust the crystal growth rate. However, these methods also induce broad impacts on the nucleation, mass transport and heat transport processes in the solution. The crystal growth itself competes with the nucleation process by influencing the mass transport and heat transport. The LaMer mechanism (also known as the self-seeding crystal growth mechanism) provides a straightforward frame to clarify the relationship between these two processes.

As shown in figure 11(a), there are three different stages in the LaMer diagram [3, 41, 84, 134–136]: (I) pre-nucleation; (II) burst nucleation; (III) growth by diffusion. At stage I, with the evaporation of the solvent, the concentration of the solution increases up to the solubility limit (C_S). Further evaporation of the solvent makes the solution supersaturated but no nucleation occurs until the concentration of the solution reaches the minimum supersaturation limit ($C_{{\text{min}}}^{\text{*}}$). At stage II, nucleation begins to precipitate when the concentration is larger than $C_{{\text{min}}}^{\text{*}}$, which is in accordance with equation (1) and figure 11(a) where the nucleation energy barrier is surpassed and the nuclei size is larger than the critical radius r*. The formed nuclei grow with the continuous supply of solute by diffusion (i.e. named as self-seeding crystal growth), and new nuclei simultaneously precipitate. As the crystal nucleation and growth proceed, the solute is continuously consumed, which in turn suppresses the nucleation rate. At stage III, since the present crystal radius is larger than the critical radius r* and the solution is still supersaturated but below the critical concentration for nucleation ($C_{{\text{min}}}^{\text{*}}$ > C> C_S), only crystal growth occurs. This mechanism can further verify the phenomenon observed in figure 8(d). When the nucleation site is introduced, the supersaturation of the system decreases and the nucleation density is lowered, which further increases the grain size. The LaMer mechanism indicates that the solution supersaturation is the primary factor in regulating the perovskite nucleation and growth and film morphology [84].

Zoom In Zoom Out Reset image size

To control the reaching time of supersaturation, antisolvent [21, 87, 96], gas quenching methods [21, 103], low atmospheric pressure [104, 139], hot casting [56, 140] and flash infrared annealing [141] were applied to remove the solvent quickly. In order to control the duration time of supersaturation, additives were applied by changing the solubility of the solute [68, 142] and the colloid size [43], where $C_{{\text{min}}}^*$ may be enhanced. Figure 11(b) presents the LaMer diagram changed by the gas quenching method with varied gas flow rates. When high-velocity gas flow was applied, the solvent evaporation was accelerated, which shortened the time to reach supersaturation and resulted in a high density of nucleation sites. The resulting film was compact but consisted of grains with extra-small crystal sizes. In contrast, with a mediate-velocity gas flow, the nucleation density is relatively smaller and the resulting crystals are larger in size [84, 137]. Therefore, the window period of the second stage of the LaMer mechanism can be adjusted by controlling the dynamic process of liquid film drying, largely determining the final film morphology. As another example of gas quenching, figure 11(c) presents the effect of the starting time of air-knife assisted nitrogen blowing on nucleation and crystal growth of perovskite via a meniscus-coating method [138]. When nitrogen blowing started before the natural nucleation process, fast supersaturation resulted in a high density of nuclei and compact perovskite films (shown as a red line). However, when nitrogen blowing started after the natural nucleation process, the system reached another supersaturation state leading to a new nucleation process, which resulted in the formation of small grains accompanying the preformed large domains (shown as a blue line). The time window for applying nitrogen blowing was evaluated by in situ measurement of absorption spectra [138]. For a similar reason, the dripping time of the antisolvent is also crucial and it requires careful refinement of processing parameters in order to yield high performance [143].

Generally, slow crystal growth is essential in the formation of high-quality perovskite. Retarded crystal growth of perovskite in solution has been widely reported [144–147]. A commonly used strategy is the incorporation of additives into precursor solutions. Most additives, such as 1,8-diiodooctane (DIO), hydroiodic, and hydrobromic, can form chelation with Pb²⁺ [8, 55, 148]. Figure 12(a) exhibits the schematic diagram for the transient chelation of Pb²⁺ with DIO [148]. The temporary coplanar chelation of Pb²⁺ with DIO as Cl⁻ ligands happened, resulting in improved solubility of PbCl₂, as shown in figure 12(b). In addition to these usual additives, the growth speeds of quasi-2D PEA₂MA_{n −1}Pb_n I_3n+1 (n = 3, 4, 5) perovskite were gradually reduced by adding increasing amounts of Rb⁺ ions into the precursor solution [132]. As shown in figure 12(c), the added Rb⁺ ions prefer to accumulate at the crystal growth front and form a Rb⁺-ion-rich region, which functions as a mild crystal growth inhibitor to retard the diffusion of organic cations at the growth front and hence regulates the crystal growth rate. This retarded crystal growth speed does not necessarily influence the average grain size, but offered an improved crystallinity characterized as narrowed XRD diffraction peaks (full width at half maximum (FWHM) reduced from 0.24° to 0.18°) and prolonged carrier recombination lifetimes (from 235 ns to 500 ns). Similarly, the retarded crystal growth of 3D perovskite in solution has been reported by using Lewis-based additives, which process the binding effect with PbI₂-based complexes or organic cations, such as MA molecules [52] and N-doped graphene [133].

Zoom In Zoom Out Reset image size

On the other hand, retarded crystallization is also available in the formation of perovskite film from solid-state films dominated by Lewis acid-base adducts. Lewis-base molecules containing S, N and O atoms with lone pair electrons can form adducts with PbX₂, which further modulate the perovskite nucleation and crystallization. Recently, a sulfonyl fluoride-functionalized phenethylammonium salt (SF-PEA) was used to form Lewis acid-base adducts with PbI₂ in the precursor. This further slowed down the crystallization of FAPbI₃ during thermal annealing, leading to increasing crystal size (shown in figure 12(d)). As a result, the average grain size for the pristine, w/PEA, and w/SF-PEA samples were calculated to be 315, 444, and 704 nm, respectively, indicating the increasing crystal size by the introduction of bulky cations. The interaction between Lewis acid-base adducts can be enhanced by molecule tailoring. Xu et al compared a group of S-atom contained Lewis bases with different densities of electron clouds located on S atoms, which offered gradually increased S–Pb interaction. In that study, the best-performing 4-PT additive did not enter the lattice but was attached onto the grain surface by S–Pb interaction, which significantly retarded the crystallization process and promoted high-quality black-phase CsPbI₃ formation [22].

As discussed in section 2, the presence of solvated phase is important for the purpose of retarding the crystallization process of 3D perovskite. The solvent phase is actually formed by the interaction between the Lewis-base solvent and weak Lewis acid PbX₂. The reported Lewis-base solvents used to retard the crystal growth are shown in figure 13(a) [23]. Among them, DMSO has been extensively employed [66, 73, 150, 151]. Due to the stronger Lewis basicity of DMSO compared to other solvents, a solvated phase of PbI₂–DMSO-MAI was formed before the conversion of perovskite precursors to perovskite crystalline structures [66]. As shown in figure 13(b), the addition of DMSO was able to highly regulate the film morphology by retarding the crystal growth, which thus resulted in high-quality pinhole-free perovskite films.

Zoom In Zoom Out Reset image size

Single crystals of perovskites have shown remarkably low trap density and excellent charge transport properties; however, the growth of such high-quality semiconductors is a time-consuming process [67, 152]. Herein, some methods were used to accelerate the growth speed in single crystal growth. A top-seeded solution growth method was developed by Dong et al to prepare single-crystalline perovskite on a piece of silicon substrate. In this process, smaller perovskite crystals synthesized in advance separately were used as the seed to grow into larger single crystals [153]. Bakr et al reported an antisolvent vapor-assisted crystallization approach to create sizable crack-free MAPbI₃ and MAPbBr₃ single crystals [154]. Liu's group reported the growth of high quality single-crystal MAPbX₃ (X = Cl, Br, I) by using an inverse temperature crystallization method [67, 152]. In addition to the 3D single crystals, the researchers from the same group also developed 2D perovskite single crystals [155]. As shown in figure 14, large 2D (PEA)₂PbI₄ perovskite single crystals were prepared using a surface-tension-controlled crystallization method. Due to the net force of the surface tension and the buoyant force, the small single crystallite could be held on the solution surface for a period of time until it grew large enough to overcome the upward force to sink to the bottom of the solution. A step-by-step cooling procedure was designed to grow (PEA)₂PbI₄ perovskite single crystals. Using this technique, some inch-sized 2D (PEA)₂PbI₄ single crystals were obtained, with the largest one reaching 36 mm in length, resulting in extraordinary device performance.

Zoom In Zoom Out Reset image size

The solute dissolved in solution is redistributed during the drying process in the forms of self-diffusion and solution flows, which often impacts on the uniformity of finalized films in complex ways because it could be a combination of different flows or form complicated convective cells. Here we briefly introduce three kinds of basic liquid flow that can influence the lateral transport of the solute.

5.1.1. Capillary flow.

Capillary motion is the ability of a liquid to flow along a solid interface driven by the tendency of forming a contact line with constant contacting angle ($\alpha$; see the example in figure 15(a)) with the local tangential direction of the solid phase. This effect leads to formation of a steady, locally bent liquid surface around the suspended particle against the leveling effect induced by gravity. When two suspended particles are close, the locally bent liquid surface induced by the capillary effect, together with the liquid surface tension, forces these two particles to approach each other and finally form a minimized total area of the liquid surface, as schematically shown in figure 15(a) [124]. This mechanism hence forms attracting effects between suspended particles (solvated phase or perovskite microcrystals) and the existing polycrystalline films, leading to reduced uniformity or even pinholes in the final films.

Zoom In Zoom Out Reset image size

5.1.2. Bénard flow.

5.1.3. Marangoni flow.

For fabricating perovskite films on a large scale with a lower solvent removal rate than that in spin coating, the lateral diffusion of the solute has sufficient time to occur and sometimes plays a quaint role in the nucleation and crystal growth. As shown in figure 16(a), polygonal perovskite domains filled with periodic concentric rings via a slot-die printing method were occasionally observed by different groups [125, 157], which is actually assembled by many smaller grains as verified from the cross-sectional SEM image by Deng et al. The difference in height was in the region of a few hundred nanometers. Another characterization of this observation is the clear domain centers and domain edges that can be recognized from each domain. Two mechanisms have been proposed to explain this amazing phenomenon: Deng et al assigned the round dot located in the center of each domain as the center of a convective cell (figure 16(b)), the size of the convective cell reduced gradually during the drying process and the edge of the convective cell was pinned and de-pinned repeatedly with the reduced volume of the solution, leading to a periodic self-seeding region as shown in figure 16(c) [125]. In another investigation, a periodic precipitation was proposed for explanation by Hu et al (figures 16(d) and (e)) [157]. The formation of the periodic concentric rings was a dynamic process featured as the liquid convection formed around the growth front, which led to a separated part of the solution located in front of the growth front, which finally left a new perovskite ring after dying [157]. This mechanism was sensitive to the temperature and the spacing between the blader and substrate, e.g. when the solution temperature was lower than 100 °C, many isolated perovskite islands were formed; and when the temperature was 180 °C (together with hot air blowing), the rapid self-seeding process dominated the formation process and resulted in compact film with small grains (figure 16(d)).

Zoom In Zoom Out Reset image size

Although there were different understandings of the formation of the very rough concentric rings, it is clear that the lateral solution flow and solute diffusion is undesirable for fabricating uniform, pinhole-free perovskites. Fortunately, the nonuniform problem mentioned above can be eliminated since it is quite sensitive to the removal rate of the solvent. A high-speed blading method with high film quality was successfully developed by Deng et al [158]. To give a clear understanding of film deposition mode, the perovskite film thickness as a function of blade-coating speed was measured and is shown in figure 17(a) [158]. Two distinct regimes of the film deposition mode were found. When the blading speed is below 4 mm s⁻¹, the decrease in thickness with increasing coating speed (with a slope of −0.99) indicates the coating falls in the evaporation regime, where solution coating and crystallization occur simultaneously. When the blading speed is above 20 mm s⁻¹, the increase in thickness with increasing coating speed (with a slope of 0.66) indicates the coating falls in the Landau–Levich regime, where crystallization occurs after the formation of wet thin film [158]. The theoretical models were proposed by Berre et al to describe the thickness dependences of the blade-coating speed (figure 17(b)) [159]. The dominant forces are different in these two modes. While surface tension dominates the fluid characteristics for meniscus coating, fluid viscosity dominates over the surface tension for fast blade coating [160]. Though the viscosity and surface tension of some precursor solutions were measured [161, 162], the relation between these two factors and perovskite crystallization and crystal growth is still not clear. Empirically, high viscosity impedes the colloid movement [163] and improves the compactness of perovskite films [164–166].

Zoom In Zoom Out Reset image size

Although the rough concentric rings disappeared in the films bladed in the Landau–Levich regime with optimized parameters, the presence of lateral liquid flow still hindered the formation of compact perovskite films [158]. During the evaporation of the solvent, microscale fluid flows moving toward perovskite islands was observed, as shown in figure 17(c), which caused a surface tension gradient. By adding a tiny amount (at the level of ∼20 parts per million) of surfactant additive, the surface tension was reduced and uniform large-scale perovskite films were obtained [158].

Besides reducing lateral liquid flow with surfactants, solvent engineering also proved important in large-area fabrication with high uniformity and high throughput since the lateral redistribution of the solute is essentially a competing process with the drying of wet film. Highly volatile solvents were employed for rapid drying and overpassed the lateral solution redistribution. Han et al developed a solvent- and vacuum-free method for scalable fabrication of perovskites. The perovskite precursor was prepared by reacting MAI or PbI₂ with methylamine gas (MAI:MA = 1:3 molar ratio; PbI₂:MA = 1:1 molar ratio) to form the amine complex liquid, which could be converted into perovskite film after MA gas release. The amine complex precursor was first added to the center of the substrate, then covered by a polyimide film, and finally pressed by a squeezing board at elevated temperature for a specific time to generate a uniform liquid solution film. After peeling off the PI film at a constant speed, a dense and large-grained perovskite film was formed, realizing a highly efficient perovskite module (a certified PCE of 12.1% with an aperture area of 36.1 cm²). For another example, as mentioned before, the mixed solvent of ACN:2-ME:DMSO was employed in blade coating for high solvent removal rate and hence formed uniform solid films at room temperature [74].

Since the GBs possess a large amount of defects that degrade the performance and induce instability of PSCs, large perovskite grains are desirable [32]. It was found that the growth quality of perovskite crystals could be improved effectively by using a grain-coarsening strategy. Solid-state grain growth and liquid-mediated Ostwald ripening are the two main classical mechanisms of grain coarsening of halide perovskite [3, 82]. As shown in figure 18(a), the curvatures of grains, the drag forces from the substrates and the orientation of the crystal affect the grain coarsening in solid-state cases [3, 82]. The differences in curvature are the thermodynamic driving force for both solid-state grain growth and Ostwald ripening mechanisms. For solid-state grain growth, grains with fewer than six sides have concave GBs (dihedral angle φ < 120°) and shrink at the expense of the growth of neighboring grains with more than six sides (φ > 120°), which makes the convex curvature even sharper. As a result, large grains coarsen at the expense of small grains [82]. Besides curvature, while the drag force from substrates stagnates the grain coarsening when the average grain size reaches approximately the film thickness, the coarsening is more favorable for the oriented grains whose surfaces and interfaces with the substrate are constituted of low-energy crystallographic planes [3, 82]. For Ostwald ripening, the higher chemical potential by curvature virtue of small grains promotes their dissolution in liquid, as shown in figure 18(b) [167]. The higher concentration of solution around small grains leads to solute transportation from the small grains to the large grains. As a result, large gains coarsen after the transporting liquid evaporates.

Zoom In Zoom Out Reset image size

Solid-state perovskite grain growth can be achieved by high-temperature annealing. However, high-temperature annealing (>100 °C) decomposes the organic–inorganic perovskite [170]. In order to avoid decomposition, the ripening temperature is expected to be as low as possible, so Ostwald ripening is an effective alternative to enlarge grain size at lower temperature. Solvent annealing, as shown in figure 18(c), where solvent vapor is introduced during the thermal annealing process, can introduce Ostwald ripening of perovskite grain [168]. The common applied vapor for Ostwald ripening is the solvents of perovskites, like DMF and DMSO [168, 171, 172]. Another typical Ostwald ripening example of solvent annealing is that the perovskite film is ripened with aminobutanol vapor [172]. Aminobutanol molecules aggregate on smaller perovskite particles and then attach to the larger particles through the interaction of amino and hydroxyl groups, which results in large-grain-size and high-quality perovskite films. Besides the common applied solvents, annealing in a humid atmosphere has also been reported to increase grain size [173, 174]. Moreover, the I–Br anion exchange reaction when spin-coating MABr/IPA on MAPbI₃ films [175] and the byproduct MA gas when adding guanidinium thiocyanate [176] have been reported to assist the Ostwald ripening. For two-step methods of fabrication on mesoporous substrates, Ostwald ripening transports the perovskite formed in mesoporous TiO₂ to the capping layer, as shown in figure 18(d) [177]. For compact substrates, while the hydrophilic substrates promote the heterogenous nucleation due to the small contact angle as discussed in section 3.1, which influences both nucleation location and density, the surface tension dragging force induced by the wetting substrates pins the GBs [169]. As shown in figure 18(e), larger grains were formed on nonwetting substrates than on wetting ones, which was attributed to the low density of nucleation and the diminished dragging force for crystal growth [169].

The introduction of a vacuum in the annealing process of perovskite precursor films can provide the power of chemical transformation and obtain excellent perovskite thin film. Xie et al found that the method of vacuum-assisted thermal annealing could effectively remove the residual MACl, which is produced from the 3MAI:PbCl₂ [178]. Therefore, the pores caused by MACl aggregation can be eliminated to produce pure, pore-free and high-crystallinity triiodide perovskite films (figure 19(a)). Similarly, Li et al reported a simple vacuum flash-assisted solution treatment method for the preparation of PSCs over 1 cm², with a certified efficiency of 19.6% [104]. As shown in figure 6(a), a perovskite precursor that consisted of FA_0.81MA_0.15PbI_2.51Br_0.45 and DMSO mixture (1:1) was spin-coated on a mesoporous TiO₂ thin film surface, the solvent was removed in a vacuum-flash tank, and the perovskite crystal was formed and finally treated by thermal annealing. The resultant large-area perovskite thin film with high electronic quality was smooth and shiny. The VASP method yielded perovskite grains with sizes between 400 and 1000 nm, which greatly exceeded the grain size of films prepared by the conventional process method. The most important step is vacuum flash, which is able to change the boiling point of substances by adjusting the pressure, so that it quickly vaporizes the liquid phase while precipitating crystal. Therefore, the speed of crystal precipitation depends on the pressure, which is the key factor in controlling the crystallinity of perovskite films. Hu et al first reported the preparation of all-inorganic perovskite films by a vacuum-assisted film-drying process at room temperature [179]. Specifically, this vacuum-assisted drying approach produced a stable black phase α-CsPb_0.96Bi_0.04I₃ without the need for an additional annealing process for flexible solar cells. In addition, the application of the vacuum-assisted film-drying technique in two-dimensional perovskite can also produce an unexpected effect. The (PEA₂MA_{n −1}PbnI_3n+1) perovskite precursor films were treated with vacuum polarization before the thermal annealing process, eventually resulting in a record-high fill factor of 82.4% with PCE of 18.04% [180]. The vacuum polarization treatment can enhance nucleation in the crystallization process, thus forming gradual junctions with different n-value nanocrystals arranged in an orderly way along the vertical direction, as shown in figures 19(b)–(d).

Zoom In Zoom Out Reset image size

CH₃NH₃ (MA) gas can induce the phase transition phenomena of liquefaction and recrystallization, which can heal the defects in the perovskite film, thus forming a dense film with high crystallinity. With respect to the application of MA gas in perovskite film fabrication, Pang et al did pioneering work [181]. In their research, it was found that organic lead halide perovskite can react directly with MA gas to produce a flowing liquid. The methylamine in the liquid can be quickly removed at room temperature when withdrawing the external MA gas, thus making the perovskite regenerate. As shown in figure 19(e), the reaction mechanism is that the strong interaction between MA molecules and iodine in perovskite makes the arrangement of PbI₆ in perovskite change from a three-dimensional to low-dimensional structure. The excess methylamine molecules in the material are spontaneously released when the concentration of external methylamine gas becomes low, and the PbI₆ is reconstructed in a three-dimensional arrangement structure. This novel phenomenon applied to the preparation process of perovskite film can realize fast repair of defects and the crystal structure reconstruction process in only a few seconds. More importantly, the crystallinity and crystal orientation are improved obviously after reconstruction. Moreover, the MA gas treatment can also cause cation substitution. Zong et al first realized the transformation of NH₄PbI₃ non-perovskite into MAPbI₃ perovskite by adopting the MA gas treatment [182]. Their research proposed the mechanism of thin-film transformation via the MA-induced conversion process, as shown in figure 19(f). When NH₄PbI₃ non-perovskite is placed in the MA gas environment, an intermediate liquid MAPbI₃·xCH₃NH₂ is formed, and further contact with the MA gas leads to the escape of the pores. After removing the film from the MA gas, the rough perovskite film becomes dense and smooth.

In addition to providing a gas atmosphere in the annealing process, Lee et al introduced a superhydrophobic perfluorodecalin two-dimensional liquid cage with superhydrophobicity during the thermal annealing process, which prevented the evaporation of DMSO physically and played the role of delaying crystallization and increasing grain size [183]. Excellent results can also be achieved by adjusting the annealing conditions, including time and temperature, without introducing additional auxiliary annealing methods (figure 6(b)). Kim et al developed a high-temperature-short-time annealing process of 400 °C, 4 s to quickly remove the residual solvent in the precursor film and obtain a smooth and uniform film with an average domain size of 1 μm [105].