Evolution of Local Structural Motifs in Colloidal Quantum Dot Semiconductor Nanocrystals Leading to Nanofaceting

Colloidal nanocrystals (NCs) have shown remarkable promise for optoelectronics, energy harvesting, photonics, and biomedical imaging. In addition to optimizing quantum confinement, the current challenge is to obtain a better understanding of the critical processing steps and their influence on the evolution of structural motifs. Computational simulations and electron microscopy presented in this work show that nanofaceting can occur during nanocrystal synthesis from a Pb-poor environment in a polar solvent. This could explain the curved interfaces and the olivelike-shaped NCs observed experimentally when these conditions are employed. Furthermore, the wettability of the PbS NCs solid film can be further modified via stoichiometry control, which impacts the interface band bending and, therefore, processes such as multiple junction deposition and interparticle epitaxial growth. Our results suggest that nanofaceting in NCs can become an inherent advantage when used to modulate band structures beyond what is traditionally possible in bulk crystals.

C ompared with conventional semiconductor manufacturing approaches, solution-processed compound semiconductors combine cost-effective processing, scalable fabrication, and compatibility with flexible substrates, which suggests that they are promising building blocks for nextgeneration semiconductor technologies. 1,2 Much progress has been made toward the goal of solution-processed solid films based on multilayer deposition processing and heteroepitaxial growth in the area of colloidal semiconductors technologies, such as the recently commercialized passive-mode photoluminescence colloidal quantum dot semiconductor nanocrystals (NCs) display and lighting products. 3,4 However, the performance of the corresponding active-mode devices, such as electroluminescence, field effect transistors, and photovoltaic devices, needs further improvement to meet the stringent requirements of industrial applications. 5,6 The limited understanding of NC processing parameters affecting active-mode device performance remains a challenge in developing further advanced solution-processable technologies. 4−6 Because of the large surface-area-to-volume ratios and solution-processability of NCs, stoichiometry and solvent effects are considered to be the key internal and external parameters, respectively, that define the unique physicochemical properties of the NCs. To complement the quantum confinement band gap engineering, one can manipulate the electronic and crystal structure properties of NCs by changing the surface bonding states, the solvent, and the overall composition. 7,8 Carrier mobility can be affected by changing the interparticle dielectric environment and the charge transfer distance. 9 Additionally, through appropriate surface states and stoichiometry, one can also modulate the electronic trap sites, alter the carrier/exciton lifetimes, and even improve the solubility of NCs. 2,7 Surface ligands are one of the commonly used stabilizers for preventing oxidation of the NCs surfaces and reducing the agglomeration of nanoparticles. 10 In particular, mediated by either a polar or nonpolar solvent, the cascaded surface capping ligand exchange can result in atomic-resolution deposition of multiple layers of NCs to form solid films. This process has attracted significant attention in colloidal epitaxial growth for optoelectronic devices. 11−16 Thus, rationally selected ligands can exchange the "native" ligands through their electrostatic or nucleophilic interactions toward the NCs, and this can provide lattice anchoring sites for new layers of NCs during the deposition process. 17,18 However, the understanding of the fundamental evolution process of the structural motifs from these nanoscale building blocks is still unclear, and the primary steps and mechanism that determines the solvent wettability of the NCs and the variation in the band structure for different solvents and stoichiometry have been barely explored to date. 19 Herein, on the basis of density functional theory (DFT) models and electron microscopy studies of a typical rock-salt cubic binary lead sulfide (PbS) model, we reveal that the nanofaceting process is the key step that underpins stoichiometry and solvent effects on the modulation of the surface energy and morphology of individual NCs. The nanofaceting process enables the evolution of local structural motifs, which reflects the changes in their physicochemical and optical−electronic properties. The DFT calculation of the surface energies enables the prediction of the thermodynamically stable morphology. In order to predict the shape of the NCs, the surface energy of the NCs was minimized using a Wulff construction, 20 as implemented in Wulffpack. 21 We have taken into consideration not only the low-index {100}, {111}, and {110} facets but also higher-index surfaces, such as the {311} family, that are observed infrequently. The low-index nonpolar {100} family of surfaces is the most stable one in vacuum and results in a near-cubic morphology for the nanocrystal. When solvent polarity is taken into account, polar surfaces become more stable relative to nonpolar ones, and the shape of the nanocrystals changes from a cube to a truncated octahedron.
Once the surface energies have been calculated, we produce a surface phase-diagram, which is shown in Table 1 and Figure   1. The nonpolar {100} surface is shown as a solid black line, while the nonpolar {110} surface is shown as a dotted line. We have considered both terminations of the {111} polar surface: the surface energy of the Pb-terminated facets is shown as a blue dashed-dotted line, and an orange dashed line is used for the S-terminated facet. The (2 × 1) reconstructions ("Wood's notation") of the corresponding {111} surfaces are shown as green dashed-dotted lines (Pb-terminated) and red dashed lines (S-terminated). Similarly, {311} polar surfaces are shown as purple dashed-dotted lines (Pb-terminated) and brown dotted lines (S-terminated).
In vacuum, surface energies are dominated by the nonpolar {100} facets and the appearance of polar {111} facets, which is similar to previous studies. 22 In order to capture the solvent effects, we have used an implicit solvation model, as implemented in the VASPsol package. 22,23 When solvent screening is taken into account (Figure 1b,c), the energy of the nonpolar facets increases, whereas that of the polar facets decreases. These effects increase with the solvent polarity, which validates the materials and device processing protocols that are normally used. 24 Figure 1d shows detailed local motif variation as a function of stoichiometry. The nonpolar {100} family of surfaces is the most stable in vacuum, which results in a near-cubic morphology for the nanocrystal (Figure 1). In vacuum and Pb-poor conditions, the preferred shape is close to a cube, and Pb-rich conditions result in an increased area of {111} (Pbterminated) facets. When solvent screening is taken into account (ODE and methanol), the faceting becomes more pronounced. In particular, Pb-rich conditions now result in a truncated octahedron nanocrystal shape that is dominated by {111} (Pb-terminated) facets, while Pb-poor NC models display significant {110} facets that play a role in the experimentally observed self-assembly, which will be further discussed in the microscopy and diffraction analysis.
We prepared different stoichiometric PbS NCs in ODE according to our previous works with slight modifications [Supporting Information (SI), Tables S1 and S2, and Figure  S1]. 12,25,26 As shown in Figure 2a, the symmetrically ordered Pb-rich PbS NCs form a superstructure with a standard hexagonal close-packing (hcp) arrangement. This is apparent from the transmission electron microscope (TEM) image and the corresponding Fast Fourier transform (FFT) pattern (e.g., intersection angle = 61.42 ± 1.54°). Nonetheless, this periodicity of the superstructure is absent for the S-rich PbS NCs ( Figure 2b). Instead, a textured crystal structure with a high packing density is identified, as shown in the selected area electron diffraction (SAED) pattern in Figure 2b (inset image). Powder X-ray diffraction (XRD) analysis ( Figure 2c) and highresolution TEM (HRTEM) analysis ( Figure 2d) suggest that these textural crystal features arise from a [110] directional attachment, which breaks the symmetry of the NC arrangement. 27,28 The surface phase diagrams (Figure 1a−c) and Wulff constructions (Figure 1d) show that polar {311} facets can be very low in energy when solvent effects are taken into account. This corroborates previous observations of nanofaceting effects observed in PbSe nanocrystals. 29,30 The S-terminated {311} facets are also lower in energy in Pb-poor conditions when compared with their Pb-terminated counterparts in Pb-rich conditions. This, in turn, might explain the observed olive shape of PbS nanoparticles synthesized in Pb-poor conditions (HRTEM, Figure 2b) and in a polar solvent (methanol, Figure  2e), as nanofaceting will result in more curved interfaces. A Wulff construction (overlay of atomic models) including these high-index polar facets for a nanocrystal synthesized in Pb-poor conditions and a polar solvent (methanol) is shown in the insets of Figure 2a  Nano Letters pubs.acs.org/NanoLett Letter ically. 28,31,32 It is worth mentioning that {311} facets have been found to be quite rare in the microscopy results (Figure 2e), but they can be difficult to resolve and to differentiate experimentally from the other facets, in particular the {111} facets.
Interestingly, through statistical analysis of HRTEM images (Figure 3a), we found that the Pb-rich NCs (synthesized in ODE) are mainly terminated by {111} planes ({111} population = 56%). However, when we enriched the amount of sulfur in the PbS NCs (synthesized in ODE), the ratio of {200} planes dramatically increased and made the ratio between the {111} and {200} facets change from 8:6 to 8:9 ({200} population = 53%). Because the carboxyl moiety preferentially binds to the Pb atom, a change in the local facet motif of NCs will inevitably affect the population of the surface bonding states and the surface polarity. 33,34 For all measurements, we have used a cryostat holder to minimize beam damage and reduce the possibility of reorientation, though we cannot completely exclude that NCs may reorient under the electron beam.
As expected, we found that the Pb/S ratio can control the wettability of the PbS@OA films. We show in Figure 3b that the contact angle of the 1.3 eV band gap Pb-rich PbS@OA film is 107.3 ± 4.81°, which is much larger (Δ = ∼25°) than the Srich PbS@OA film (82.01 ± 2.91°). The solid phase with good wettability can induce a larger volume of the liquid to disperse into the grain boundaries, and it can subsequently enhance ligand exchange efficiency. 35,36 A methanol-dispersed TBAI ligand solution was selected to replace the long-chain aliphatic ligands on the surface of the NCs in order to investigate the variation of wettability (PbS@TBAI, SI). 25, 26,37,38 The smaller the contact angle is, the better the wettability of the hydrophilic ligand solution (i.e., methanol + TBAI). 35 Indeed, quantized X-ray photoelectron spectroscopy (XPS) analysis reveals that, after TBAI ligand exchange, the S-rich NCs film has more iodine(I) intercalation than the Pb-rich NCs ( Figure  3c). This indicates that an S-rich PbS@OA film can provide a favorable wetting because iodide ions are able to replace more of the carboxyl moieties from the surface of PbS NCs. An important difference between the Pb-rich and Pb-poor NC assemblies is that the Pb-rich conditions favor a more ordered packing arrangement, while Pb-poor conditions result in a disordered assembly of particles. However, for 3D stacking multiple layers of NC films, the NC assemblies seem to be randomly ordered, which may be due to a nonequilibrium dynamical spin coating and ligand exchange process ( Figure  S4).
In Figure 3d, for those of the same film thickness (SI, Figure  S5, Table S3), FTIR and nuclear magnetic resonance (NMR, Figure S6−S7) analysis reveal that Pb-rich PbS NCs films have more OA molecules bonded surface than an S-rich film. This surface deficiency of OA ligands is due to the lack of Pbterminated sites on the S-rich NCs. 34 This bonding state variation can subsequently affect the packing arrangement of the NCs. 11 We believe that the augmented population of {200} planes not only leads to the attachment along the {110} direction of the assembly of the NCs and to the shape changing (e.g., ellipsoidal shape Figure 2b) but it also affects   11,34 As exemplified in Figure 3e, the deprotonated OA and hydroxide moieties are identified to be coordinate-bonded on the {111} planes, which are difficult to eliminate during the solid-state ligand exchange process. 34,39,40 However, in the case of the {200} planes, the OA was determined to be weakly adsorbed on their surface, which can be easily removed by applying an acidic ligand solution (e.g., methanol + TBAI). 11,26,39,40 Therefore, through deliberate enrichment of the populations of the {200} planes (i.e., S-rich NCs), we can manipulate the surface wettability of the PbS@OA NCs and, hence, enhance the inorganic (i.e., NCs) and organic (i.e., ligands) interface reaction for improving NC film ligand exchange efficiency and potentially colloidal epitaxy growth.
The NC models for the Pb-rich and Pb-poor NCs of ∼2.4 nm in diameter were generated using the Wulff construction shapes previously obtained and shown in Figure 1. Both NC models are close to a 1:1 Pb:S ratio and have a similar cubic shape that exposes either Pb-terminated or S-terminated polar {111} facets, as shown in Figure 4a,b. In order to passivate these polar facets, counterion ligands were added, namely I atoms were placed on the Pb-terminated {111} facets, following previous work. 41 In the case of the S-terminated {111} facets, H atoms were used in order to obtain passivation. The electronic structure of these NC models was evaluated, and a partial density of states (DOS) is shown in Figure 4c for the Pb-poor NC model and in Figure 4d for the Pb-rich NC model. Given the structural similarity of the two models, their partial electronic DOS are also quite similar. In both cases, the top of the valence band is dominated by S-p and Pb-s states, while the bottom of the conduction band is dominated by Pb-p states. It is known that DFT calculations can significantly underestimate the band gap. 42 In order to correct for this, we used the GLLB-SC calculation, including the derivative discontinuity. 43 The DFT calculation finds that the Pb-poor NC has a bandgap of 1.471 eV compared with 1.604 eV for the Pb-rich. Rather than the absolute values, we focus on the reduction of the band gap (0.13 eV) in Pb-poor conditions, which appears to be caused by the changes in the valence band of the material because of the stoichiometric excess of S. The absolute values of the band gaps of both models are slightly larger than those observed experimentally but are reasonable given the model size (∼2.4 nm) and the approximations made. Most importantly, the DFT estimation, including the derivative discontinuity of the Kohn−Sham potential, is able to reasonably capture the magnitude of the band gap reduction in Pb-poor conditions that was observed experimentally  Figure 4e,f, red-shifted exciton absorption (0.03 eV) and PLs (0.06 eV) were observed. The band gap reduction trend from the Pb-rich to S-rich also correlates well with the increased packing densities, as observed in Figure 2. 9,44 The variation of the Pb/S ratio can also effectively modulate the Fermi levels and DOS in the as-prepared PbS NCs film, which were identified to originate from the charge carrier density alternations. 8 The variation in the binding energies from PbS NCs of different wettability (e.g., band gap equal to 1.3 eV) was exemplified from ultraviolet photoelectron

Nano Letters
pubs.acs.org/NanoLett Letter spectroscopy analysis (UPS, Figure 5a and Figure S8). 12 As summarized in Figure 5b, when the NC is Pb-rich (hydrophobic), the electron concentration increases, and the Fermi level shifts toward the conduction band (CB). As the NC becomes S-rich (hydrophilic), the hole concentration increases, and the Fermi level drops toward the intrinsic midband gap level. It should be mentioned that a DOS variation (e.g., band edge shifting) with the enrichment of either S or Pb content was also observed from our UPS analysis ( Figure S8), which is consistent with previous DFT simulation results. 7,13,27,28,33,40 This ca. 0.17 eV DOS variation can be attributed to the cation or anion adsorption/desorption on the surface of a NC, which changes the strength of the NC−ligand surface dipole and chemical electronegativity. 7,40 As shown in Figure 5c, the hydrophilic NC films also display a much shorter PL decay in the time-resolved photoluminescence (TRPL) measurement. For the PL measurement, we employed a ZnO quenching layer, which is the typical electron transport layer in PbS NC-based diode junction devices (Figure 5c, inset). The dynamics of the exciton are complex because they include charge transfer and transport within the ZnO interfaces as the presence of the ZnO layer facilitates carrier extraction, which adds another nonradiative pathway that competes with radiative and trap-assisted recombination. 45,46 To quantify and compare the photogenerated charge carrier lifetimes, we fit the TRPL decay with a stretched exponential model to obtain lifetime. 47 The use of this model has been previously suggested to take into account a distribution of monomolecular (e.g., exponential decay) and bimolecular recombination (e.g., biexponential decay) processes, which provide an accepted way of rationalizing complicated exciton dynamics. 47−49 As shown in Figure 5c, the mean lifetime of a charge carrier reduced from 55.93 ± 0.33 ns to 13.65 ± 0.39 ns as the NCs were modified from being hydrophobic to hydrophilic. A shorter lifetime and decreased PL intensity are indicators of the exciton dissociation having been effectively enhanced. 47 It proves that the hydrophilic PbS@TBAI NCs can lead to an efficient charge transfer to ZnO NCs by producing a charge-separated state that decays nonradiatively. 45,46 In Figure   The improved ligand exchange reaction and a steep band bending are beneficial to exciton dissociation and charge collection. 50,51 The as-prepared NC solar cell (NCSC) power conversion efficiency (PCE) unambiguously shows enhancement because of the S-enrichment. The solar cell structure was similar to our TRPL measurement that employed TBAI as the only ligand (Figure 5c inset, 12 layers of NC@TBAI in total; Figure S5, Table S3) and gold as the anode. As rationalized in Figure 5e, the NCSC PCE performance can be improved more than two times when the NCs are altered from being hydrophobic (PCE = ∼2%) to hydrophilic (PCE = ∼5%). The J sc values of the NCSC can be enhanced from 8.98 ± 0.82 mA/cm 2 to 15.39 ± 0.80 mA/cm 2 , which results from the improved ligand exchange efficiency and the enlarged band bending ( Figure S9). Figure 5f,g show the semilog dark current J-V curves and ideality factor (n) as a function of the Pb/S ratio. Benefiting from the large band bending from the S-rich NCs, the charge carrier pathways are largely suppressed under forward bias, which reflects the larger shunt resistance (R sh ), as indicated in Figure 5f. However, the enhanced ligand exchange efficiency also promotes the reduction of Ohmic losses from the series resistance (R s ). The IR drops and minimizes recombination, tunnelling, and inhomogeneity at the junction interface (i.e., decreasing the leakage currents). 52 Furthermore, the n values were estimated by correlating results from both the fitting of the simple diode equation (eq 1) 53,54 and the solution of the diode equation through conductance derivative methods (eq 2). 55 In Figure 5g, the n values are reduced from 2.04 to 1.82 by enriching the S components in the PbS NCs (Figures S10−S12, and Tables S4−S6), which indicates that the charge recombination across the junction was sufficiently reduced. 38  In conclusion, our findings indicate that stoichiometric and solvent control can be used in tandem to stabilize polar surfaces. This nanofaceting process determines the solutionprocessed NC morphology and the change in optoelectronic properties of devices. The simulation framework deployed here could be further extended to study the stability of NCs further away from a Pb/S ratio of 1:1, as well as the effects of ligand exchange, and work is underway on these topics. Moreover, we believe the nanofaceting is not only limited to PbS NCs but can also apply to other compound semiconductors, such as ternary metal chalcogenides, metal phosphides, and perovskite metal halides. ■ ASSOCIATED CONTENT