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Tailored growth of single-crystalline InP tetrapods

Abstract

Despite the technological importance of colloidal covalent III-V nanocrystals with unique optoelectronic properties, their synthetic process still has challenges originating from the complex energy landscape of the reaction. Here, we present InP tetrapod nanocrystals as a crystalline late intermediate in the synthetic pathway that warrants controlled growth. We isolate tetrapod intermediate species with well-defined surfaces of (110) and ($$\bar{1}\bar{1}\bar{1}$$) via the suppression of further growth. An additional precursor supply at low temperature induces $$[\bar{1}\bar{1}\bar{1}]$$-specific growth, whereas the [110]-directional growth occurs over the activation barrier of 65.7 kJ/mol at a higher temperature, thus finalizes into the (111)-faceted tetrahedron nanocrystals. We address the use of late intermediates with well-defined facets at the sub-10 nm scale for the tailored growth of covalent III-V nanocrystals and highlight the potential for the directed approach of nanocrystal synthesis.

Introduction

Chemistry lies at the core of modern industry and technology owing to its precise atomic and molecular control of reaction pathways1,2. This has been particularly successful in the precise control of molecular structures for their specific purpose. The comprehensive resolution of such reaction pathways in terms of the reactants, intermediates, transition states, and products enables the development of new methods to create appropriate organic structures and materials2. On the other hand, colloidal semiconductor nanocrystals (NCs) have been exploited in academic and industrial sectors for more than 30 years, mainly via trial-and-error basis synthetic development owing to their unresolved reaction kinetics and thermodynamics3,4,5,6,7,8,9,10,11. Due to the co-existence of metastable states with similar energy, unraveling the reaction pathways in full detail has been difficult12,13,14,15,16.

Recently, a group of researchers revealed atomic information of II–VI, IV–VI, and III–V NCs through analytic methodologies and computational simulations17,18,19,20,21,22,23,24,25. To ultimately create a targeted structure at the sub-10-nm scale, one must identify, understand, and precisely control its reaction pathways with complete information on all possible intermediates. This is why research on molecule-like reaction intermediates of covalent III–V NCs has recently emerged and attracted considerable attention in the scientific community26,27,28.

The reaction pathway of colloidal NCs is complicated as shown in Fig. 1, because various factors, such as the number of atoms, the composition, and the types and coverage of surface ligands change their energy landscape with a variety of intermediate species14. Here, we classify the intermediates as follows; the early intermediate is more similar to the reactants, and thus possesses a molecule-like amorphous structure; the late intermediate resembles products with a crystalline feature and well-defined facets, as marked in Fig. 1.

Recently, some early intermediates of III–V NCs such as magic-sized clusters have been isolated with full atomic information22,28,29. By bypassing the complicated monomer conversion steps, the use of early intermediates as reactants can be attempted to enhance the homogeneity of the products in III–V NC synthesis28,30,31. In contrast, product-like late intermediates, if identified, could serve as growth platform for targeted III–V NC structures.

Here, we firstly unravel the growth pathways of (111)-rich InP nanocrystals by identifying a key reaction intermediate, tetrapod, in the reaction. We then develop a synthetic route for mono-dispersed tetrapod intermediates with over 90% shape yield by catalyzing the nucleation, and thus suppressing further growth. The InP tetrapod reaction intermediates, with a single-crystalline zinc-blende structure have the well-defined atomic-scale surface information. Therefore, they can serve as the late intermediates for the directed growth to (111)-faceted tetrahedron-shaped NCs or other tetrapod NCs with thick or long arms by controlling the specific growth fronts of [110] and [$$\bar{1}\bar{1}\bar{1}$$] directions. Our late-intermediate strategy for the surface energy driven tailored growth of III–V NCs will certainly benefit to other NC synthesis that has unexplored reaction pathways.

Results and discussion

Observation of the tetrapod shape in early reaction stage of InP nanocrystal synthesis

Tetrahedron InP NCs are considered a suitable model for the surface study of colloidal III–V nanocrystals owing to their well-defined surfaces of only (111) facets passivated by chloride and oleylamine19. We discovered variously shaped nanostructures that co-exist in the synthesis of InP tetrahedron NCs, especially at the early stage of the reaction, as shown in Fig. 2a. Various thin and thick tetrapod-like InP NCs were observed in a transmission electron microscopy (TEM) image of the aliquot taken within 5 s after injection of the aminophosphine precursor at 300 °C. After 1 h under the same conditions, all of the particles were the tetrahedron shape, as shown in Fig. 2b. Tetrapod-like InP NCs were consistently observed at an early reaction stage at various reaction temperatures ranging from 170 to 300 °C (Supplementary Figs. 12). The early stage tetrapod grew into the tetrahedron as the reaction proceeded, except at 170 °C, where the tetrapod shape was retained until the end. Therefore, if they can be isolated from the reaction and stable in room temperature, the tetrapod-shaped InP NCs can be considered a reaction intermediate to the tetrahedron-shaped NCs.

The tetrahedral nanostructures can be classified into three types: thin tetrapods, thick tetrapods, and tetrahedrons (marked with yellow, pink, and sky-blue circles in Fig. 2a, respectively). More evidently, annular dark-field scanning TEM (ADF-STEM) images confirmed the shapes of the tetrapods and tetrahedrons based on the brighter contrast in the middle part of the InP NCs (Supplementary Fig. 3). High-resolution (HR) TEM images were obtained for the three types of intermediates, as shown in Fig. 2c–e. All of the HR-TEM images with fast Fourier transform (FFT) patterns clearly show {110} and {111}/{110} zinc-blende crystal lattice planes at the [111] zone axis (inset of Fig. 2c–e) and the [112] zone axis, respectively (Supplementary Figs. 45). Therefore, we propose that the thin tetrapod has arms exposed with {110} facets in the width direction and terminate with the {111} facet in the length direction and that the tetrahedron is enclosed by four {111} facets (Insets of Fig. 2f). In the In-rich crystal growth condition, the tetrahedron surface is known to be (111) terminated, which is exposed only by In atoms with one dangling bond19. As the (111) and ($$\bar{1}\bar{1}\bar{1}$$) surfaces are opposite in the zinc-blende crystal structure, the tetrapod end would be ($$\bar{1}\bar{1}\bar{1}$$), which is terminated with P atoms with one dangling bond or In atoms with three dangling bonds. Based on these findings, we speculate that the tetrapod grows into a tetrahedron such that the (111) facets emerge by filling the open space between the tetrapod arms, as schematically shown in Fig. 2f.

Synthesis of InP tetrapods

Based on the collected atomic information for the tetrapod nanostructures, we hypothesized that (1) metastable tetrapod intermediates could be isolated by the growth suppression of a tetrahedron formation, and (2) the isolated tetrapod intermediates could be a novel platform for atomically controlled growth of III–V NCs based on surface energies of the (111) and (110) facets.

To suppress the continued growth of InP tetrahedrons, we additionally injected lithium bis(trimethylsilyl)amide (LiHMDS) to accelerate their precursor-conversion. LiHMDS is a well-known strong base (pKa of 30), allowing metal precursors to react with long-chain primary amines, which rapidly deprotonate RNH2 into RNHLi32. Similarly, we anticipate that InCl3 will turn to more reactive metal-amide complexes, as evidenced by the observation of In metal (XRD data for the reaction residue shown in Supplementary Fig. 6)32,33,34,35. Supplementary Fig. 7 depicts the UV-Vis spectra of the InP NCs synthesized at 250 °C under different LiHMDS concentrations. At a wavelength of λ = 413 nm, the intrinsic absorption coefficient of the InP NCs is independent of their size, and absorption from InP clusters smaller than [InP]20 is excluded36,37,38. As the amount of LiHMDS increases, the absorbance at λ = 413 nm increases and excitonic peaks show a blue shift. This indicates that LiHMDS increases the number of NCs via burst nucleation with a fast nucleation rate, which eventually leads to growth suppression through the rapid depletion of monomers. The suppression of the tetrapod-to-tetrahedron growth with the addition of LiHMDS is also confirmed by the decreased shape yield of tetrahedron from 81 to 20% (Supplementary Fig. 8b, c).

As a result, we successfully synthesized tetrapod NCs with a near-unity shape yield (92.1%) that have a narrow size distribution of 2.2 ± 0.3 nm for the arm width and 6.8 ± 1.1 nm for the arm length (Fig. 3a and Supplementary Fig. 9). As the tetrapod shape could appear differently depending on the viewing angle, we take into account the view-angle dependent shapes (Fig. 3b) in the measurement of the size and the shape yield (see details in Supplementary Note 1). Notably, the InP tetrapod NCs in this study have a single-crystalline zinc-blende phase similar to the InP tetrahedron NCs as shown in the inset of Fig. 3a. Previously-reported tetrapod NCs typically have more than one crystal phase. For example, typical II–VI tetrapod NCs consist of a tetrahedral zinc-blend core and four wurtzite arms39,40,41. Furthermore, our InP tetrapods did not require further size-selective precipitation to enhance the uniformity, unlike the previous cases of III–V NCs with mixed shapes42,43. To generalize our idea for reaction intermediate isolation by catalyzing the monomer conversion that leads to the rapid depletion of the monomers, we used another precursor-conversion accelerator, that is, diisobutylaluminum hydride44 in our reaction. The shape conversion from tetrapod to tetrahedron again decreased to less than 14% (Supplementary Fig. 8d). Moreover, InAs tetrapod NCs were synthesized using the same reaction process with the precursor-conversion accelerator of LiHMDS (Supplementary Fig. 10).

To understand the formation mechanism of the sub-10-nm sized single-crystalline tetrapods, we calculated the surface formation energies of the (111), (110), and ($$\bar{1}\bar{1}\bar{1}$$) surfaces with and without surface passivation ligands as a function of the chlorine chemical potential using density functional theory (DFT), as shown in Fig. 4a, b and listed in Supplementary Tables 12. For bare surfaces without any passivation, the (110) surface has the lowest surface energy of 36.6 meV/Å2. This is because the stoichiometric surface cation and anion atoms form a self-passivated reconstructed (110) surface. We found that the (110) surface could be further stabilized by the adsorption of the precursor molecule, InCl3 or its derivative, InCl2NHR. In case of InCl3, two Cl atoms passivate two surface In atoms, and the remaining InCl complex passivates two surface P atoms while it binds to a single P atom. In the presence of Cl and methylamine (MA), the (111) surface is appreciably stabilized by Cl and Cl/MA passivation while the ($$\bar{1}\bar{1}\bar{1}$$) surface shows a relatively high surface energy despite InCl passivation. Under our reaction conditions, InCl could be generated from InCl3 reduction by reducing agents such as aminosphosphine or amines32,45,46,47 (more details can be found in Supplementary Figs. 11 and 12). Our DFT results indicate that the tetrapod consisting of {110} and ($$\bar{1}\bar{1}\bar{1}$$) is a metastable intermediate, and the tetrahedron, consisting of (111):Cl or (111):MA,Cl, is thermodynamically the most stable one, as schematically drawn in Fig. 4c.

Estimation of the activation energy barrier of [110] growth

To estimate the kinetic energy barrier of the transformation reaction from the intermediate tetrapod to the lowest-energy tetrahedron, we assumed that the [110] growth of tetrapod finally terminated into tetrahedrons though more complex chemistry may exist on tetrapod to tetrahedron transition. We reacted the isolated InP tetrapods with additional precursors at various reaction temperatures from 180 to 260 °C to particularly monitor the [110] growth of tetrapods. Assuming that the excitonic peaks in the absorbance spectra are predominantly determined by the width, rather than the length of the arms, a rate constant of the width growth was extracted and then fitted to the Arrhenius equation to obtain the energy barrier (see Methods section, Supplementary Figs. 1314, and Supplementary Note 2 for details). The energy barrier was estimated to be 65.7 ± 6.2 kJ/mol, as shown in the inset of Fig. 4c. We surmise that this energy barrier may be associated with the chlorine activation from tetra(oleylamino)-phosphonium chloride, which is a key byproduct during amino-phosphine based InP NC synthesis48.

Tailored growth from InP tetrapod late-intermediate

As we clearly identified the kinetic energy barrier in the tetrapod-to-tetrahedron reaction pathway, we were able to atomically control the growth reaction using the tetrapod as a late intermediate, e.g., to a more anisotropic InP NC with facet-specific growth control. Consequently, we realized tetrapods with long arms by further growing the [$$\bar{1}\bar{1}\bar{1}$$] facets from 8.3 ± 1.5 to 15.4 ± 3.1 nm (Supplementary Fig. 15). To do this, we slowly added the P precursor into the tetrapod intermediates and In precursors dispersed in oleylamine solution at a low reaction temperature of 170 °C, not to exceed the activation barrier (see Methods section). When the arm length becomes longer, a smaller shape yield of tetrapods was often observed (Supplementary Fig. 15). At higher temperatures, we obtained tetrahedron-shaped InP NCs (Supplementary Fig. 16) by overcoming the energy barrier and forming the (111) facets. Furthermore, we were able to tune the width of the InP tetrapod NCs from 2.3 to 2.9 nm, selectively growing the (110) facets from the long-arm tetrapod intermediates, by adjusting the reaction temperature without introducing additional precursors (see Methods section and Supplementary Fig. 17).

Our elemental analyses based on X-ray photoelectron spectroscopy measurements indicate that the In/P ratio of the representative short- and long-arm tetrapods is 1.3 and 1.2, respectively, which is smaller than that of the InP tetrahedron NCs 1.5 (Supplementary Table 3). The adsorption of InCl3 and InClx(NHR)y﻿ on stoichiometric (110) may be responsible for the higher In/P ratio and relatively high Cl and N contents in the tetrapods from XPS analysis in Supplementary Table 3.

Width- and length-tailored InP tetrapods

Figure 5a shows the changes in first excitonic peaks of the various length- and width-controlled InP tetrapod NCs. We found that the optical bandgaps of the tetrapods were mainly determined by the width rather than the length of the arms (Fig. 5a and Supplementary Figs. 1719). We note that the first excitonic peaks from the short- and long-arm tetrapods almost overlap whereas the exciton peak continually red-shifts up to 100 nm from thick-arm tetrapods when heated to 300 °C because of the selective (110) width growth.

Figure 5b shows the HR-TEM image of a tetrapod with a length of 10.3 nm with atomic resolution. The (111) lattice plane was clearly visible, likely due to the three arms attached to the TEM grid. Accordingly, the FFT pattern in the inset of Fig. 5b shows six {111} diffraction spots. The measured distance of the (111) plane was 3.3 Å, which is very close to that of the zinc-blende InP single-crystalline structure. We confirmed that, regardless of the arm lengths and widths of the InP tetrapod NCs, the X-ray diffraction (XRD) patterns matched those of the InP zinc-blende structure (Supplementary Fig. 20).

As we suppressed the inhomogeneity of InP crystals, our pure tetrapods may benefit optoelectronic characteristics, distinct from previously prevalent mixed-crystalline II–VI tetrapod NCs39,49,50. HF treatment with UV irradiation on as-synthesized tetrapods resulted in a dramatic increase in photoluminescence (PL) emission51,52,53,54 (Supplementary Fig. 21) while retaining their structure as a zinc blende seen in HR-TEM image (Fig. 5d and Supplementary Fig. 22) and XRD spectra (Supplementary Fig. 23). XPS analyses show that In 3d binding energy shifted to a higher energy indicating the formation of In–F or In–O. The increased F 1s peak in XPS indicates the F passivation of InP surfaces (Supplementary Fig. 24)51. Indeed, our DFT calculations show that the F passivation of the (110) surface clears the surface states, which can serve as trap states in the quantum-confinement regime (Supplementary Fig. 25). Thickness-controlled tetrapods with HF treatment (see Methods section)51,52 show PL emissions ranging from 608 to 654 nm with 36–42 nm PL FWHM, while the tetrahedrons show PL of up to 730 nm with 55 nm FWHM (Fig. 5c). We achieved as low as 36 nm (0.10 eV) of FWHM at the maximum PL of 646 nm (Supplementary Fig. 26). This is comparable to the narrowest PL FWHM of 35.9 nm at 630 nm in the InP NCs11.

A shape-dependent electronic structure at the confinement regime has long been of interest in obtaining superior or tailored optical properties for NCs, but is severely limited by the synthetic availability of various well-defined shapes at the nanoscale55,56,57,58. Our III–V single-crystalline tetrapods could be a testbed for studying complex exciton structures with complex geometries.

In conclusion, we isolated late intermediate single-crystalline tetrapods with well-defined faceting in the complex reaction pathways in III–V nanomaterial synthesis. The late intermediate tetrapods can be transformed into thermodynamically stable tetrahedron NCs by overcoming the reaction energy barrier. By controlling the reaction temperature and the amount of precursors, we were able to selectively grow ($$\bar{1}\bar{1}\bar{1}$$) and (110) facets. Based on the atomic information of the late intermediate, we could predict and realize the designed growth during wet synthesis of III–V NCs, which had been largely limited owing to the lack of a well-defined growth platform. We suggest that this finding will bring insights in the field of the intermediate-involved directed approach of nanocrystal synthesis.

Methods

Chemicals

Indium chloride (InCl3, 98%), tris(dimethylamino)phosphine ((Me2N)3P), 97%), oleylamine (70%), lithium bis(trimethylsilyl)amide (or lithium hexamethyldisilazide, LiHMDS, 97%), diisobutylaluminum hydride (DIBAL-H, 1.0 M in toluene), and hydrofluoric acid (HF, 48 wt% in H2O) were purchased from Sigma-Aldrich. Tris(dimethylamino)arsine ((Me2N)3As), 99%) was purchased from Strem. Unless otherwise stated, all chemicals were used without further purification. Degassed oleylamine (D-OLA) was prepared by degassing under vacuum (~1.0 Torr) at 90 °C for 60 min.

Synthesis of InP tetrahedron nanocrystals

InCl3 (0.2257 g, 1 mmol) and oleylamine (5 mL) were degassed at 90 °C under vacuum (~1.0 Torr) for 1 h. The solution was heated to the injection temperature (170–300 °C) under an N2 gas atmosphere. Separately, a mixed solution of 0.187 mL (1 mmol) of (Me2N)3P and 0.5 mL of D-OLA was prepared for P injection in the glove box. The prepared solution was rapidly injected into the mixed solution of InCl3 and oleylamine at temperature ranging from 170 to 300 °C, depending on the target size of the NCs, and the reaction temperature was maintained for 60 min. As-grown InP NCs were isolated by precipitation once with acetone and once with methyl acetate and redispersed in hexane for further analysis.

Synthesis of InP tetrapod NCs with LiHMDS

The degassing process of InCl3 and oleylamine was the same as the synthesis of the InP tetrahedron nanocrystals. The degassed solution was heated to an injection temperature of 170 °C under an N2 atmosphere. The injection solution was prepared by mixing 0.016 g (0.1 mmol) of LiHMDS in 0.5 mL of oleylamine and 0.187 mL (1 mmol) of (Me2N)3P in a glovebox. The prepared solution was injected into InCl3 in oleylamine at 170 °C (Fig. 3a) and maintained for 60 min. For the precipitation, the reaction mixture was transfered from flask to 50 ml of conical tube, followed by centrifuged 6000 rpm for 5 min. Supernatant and precipitates were separated, then isolated supernatant is washed same as for the InP tetrahedron NCs washing process. To confirm the role of LiHMDS, we varied the amount of LiHMDS from 0.0 to 0.4 mmol per 1.0 mmol of InCl3 at reaction temperature of 250 °C, and measured its absorption spectrum and TEM (Supplementary Figs. 7 and 8a–c).

Synthesis of InP tetrapod NCs with DIBAL-H

InP tetrapod NCs with DIBAL-H were prepared following the same procedure for the InP tetrapod NCs with 0.4 mmol of DIBAL-H at 250 °C.

Synthesis of InAs tetrapod NCs

All the experimental processes are the same as the InP tetrapod NCs with LiHMDS, except for the preparation of As injection solution and reaction temperature. The injection solution was prepared with 0.092 mL of (Me2N)3As (0.5 mmol) and 0.016 g (0.1 mmol) of LiHMDS in 0.5 mL of D-OLA. The solution was heated to 40 °C for 10 min to remove gases from transamination. Prepared As solution was rapidly injected into the InCl3 in OLA at 220 °C, and the temperature was maintained for 60 min.

Determination of the activation energy barrier for the [110] growth

Preparation of InP tetrapod (solution A): InP tetrapods were synthesized at 170 °C using LiHMDS with 10-fold scale-up; besides this, the synthesis was the same as the InP tetrapod synthesis. This was followed by precipitation and re-dispersion in hexane to 0.07 g/mL. No LiHMDS remained in the solution.

Preparation of In precursor solution (solution B): InCl3 (0.1354 g, 0.6 mmol) in 20 mL of oleylamine was degassed at 90 °C under vacuum (~1.0 Torr) for 60 min.

Growth of [110] from isolated InP tetrapod: As-prepared InP tetrapod (0.14 g, solution A) was injected into the solution B at 90 °C, and heated to the target reaction temperature from 180 to 260 °C under N2. At the elevated temperature, 0.281 mL (1.5 mmol) of (Me2N)3P solution was injected. The aliquots were taken to extract the reaction rate depending on the reaction temperature.

Atomically controlled [$$\bar{{{{\bf{1}}}}}\bar{{{{\bf{1}}}}}\bar{{{{\bf{1}}}}}$$]/[110] growth of InP tetrapods

All the experimental processes are similar to the “Determination of the activation energy barrier for [110] growth” except the concentration of In and P sources, and the injection method. In the “Determination of the activation energy barrier for [110] growth”, we used a highly diluted In and P precursors with the hot injection method to obtain the activation energy by preventing additional nucleation. Here we used a sufficient precursors for [$$\bar{1}\bar{1}\bar{1}$$]/[110] growth.

InP tetrapods were synthesized at 170 °C using LiHMDS with 10-fold scale-up; besides this, the synthesis was the same as the InP tetrapod synthesis. This was followed by precipitation and re-dispersion in hexane to 0.07 g/mL. No LiHMDS remained in the solution. Separately, 0.2257 g (1.0 mmol) of InCl3 in 5 mL of oleylamine was loaded into a three-neck flask, and the solution was degassed at 90 °C under vacuum (~1.0 Torr). Then, 0.14 g of InP tetrapods in hexane was injected into the InCl3 solution at 90 °C and heated to 170 °C under N2 atmosphere. (Me2N)3P (0.937 mL, 5 mmol) in 3.063 mL of oleylamine was slowly injected at the rate of 0.05 mL/min (for the tetrahedron InP, we used 250 °C, Supplementary Fig. 16). The reaction solution was additionally heated for 40 min at the same temperature after the complete introduction of the P precursor solution. TEM analysis showed that the obtained tetrapods had long arms via selective [$$\bar{1}\bar{1}\bar{1}$$] growth (Supplementary Figs. 15 and 19). For further growth along the [110] direction, the reaction solution was heated to various temperatures of 220, 250, 270, and 300 °C, and maintained for 60 min (Fig. 5a and Supplementary Figs. 1718). The precipitation process was the same as that followed for the InP tetrahedral NCs.

HF-treated InP tetrapod NCs

The [$$\bar{1}\bar{1}\bar{1}$$]/[110] grown InP tetrapod NCs (described above) were treated with the HF solution as previously described with slight modifications51,53. Diluted HF solution was prepared by mixing with 5 mL of butanol, 0.565 mL of 48 wt% HF solution, and 0.065 mL of deionized water. Separately, 0.07 g of [$$\bar{1}\bar{1}\bar{1}$$]/[110] grown InP tetrapod NCs was dispersed in a mixed solution of 7 mL of hexane, 5 mL of butanol, and 0.05 g of TOPO. The mixed solution was stirred vigorously. Subsequently, 0.3 mL of the diluted HF solution was added to the tetrapod solution and irradiated with UV light. After 190 min, the reaction was stopped, and the solution was precipitated using butanol.

Optical spectra

Absorption spectra were measured using a UV-Vis spectrometer (Evolution 201, Thermo Scientific). Room-temperature photoluminescence quantum yields were measured using an absolute photoluminescence quantum yield spectrometer (C9920-02, Hamamatsu).

Structural analysis

X-ray diffraction (XRD, Empyrean, PANalytical) was used to study the crystal structure of the InP NCs. The size and shape of the NCs were determined by spherical aberration-corrected TEM (JEOL, JEM-ARM 200 F) with an acceleration voltage of 200 kV at the National NanoFab Center, Republic of Korea. High-resolution TEM images (Figs. 2c–e and 5b, d and Supplementary Figs. 35) were taken by spherical aberration-corrected TEM (FEI Titan3 G2 60–300) with an acceleration voltage of 80 kV at Ulsan National Institute of Science and Technology (UNIST). To obtain high signal-to-noise ratio images, we used a single layer of graphene as a supporting film for TEM imaging. As the NCs could be damaged by the e-beam during TEM measurement at high magnification, we evaluated the arm length and width of the tetrapods with low-magnification images59.

Elemental analysis

X-ray photoemission spectroscopy was performed using the Sigma Probe model (Thermo VG Scientific).

Computational details

We performed first-principles density functional theory (DFT) calculations by employing all-electron-like projector-augmented wave potentials60 and Perdew–Burke–Ernzerhof (PBE) exchange-correlation functionals61 as implemented in the Vienna Ab Initio Simulation Package (VASP)62,63. A plane-wave energy cutoff of 550 eV was used, and all the atoms were fully relaxed until the atomic forces and electronic energies were <0.02 eV/Å and 10−4 eV, respectively.

For the non-polar (110) surface, with the same atomic structure as the front and back surfaces in the atomic slab model, as shown in Supplementary Fig. 27a, the absolute surface energy is simply the average of the total surface energy:

$$\gamma =\frac{1}{2}\frac{{E}_{{{{\rm{slab}}}}}-{E}_{{{{\rm{bulk}}}}}}{A}$$
(1)

where Eslab and Ebulk are the DFT total energies of the slab model and the corresponding bulk system, respectively, and A is the surface area of the front surface.

In contrast, when the compositions of the front and back surfaces are different, e.g., in the (111)/($$\bar{1}\bar{1}\bar{1}$$) surface slab model, the surface energy obtained from Eq. (1) is the average of the front (111) and back ($$\bar{1}\bar{1}\bar{1}$$) surfaces; therefore, the average is not the exact absolute value of each surface. Accordingly, to obtain the absolute surface energy of the polar facet, we used different-sized wedge models passivated by pseudohydrogen atoms based on the electron-counting rule (Supplementary Fig. 27b, c)64. First, to obtain the absolute energy of (100) surface, we designed the wedge models exposing (100) and (110) surfaces (Supplementary Fig. 27b) with 9–10 atoms on the (100) surface. Then, we constructed the wedge models corresponding to Fig. 27c with 6–10 atoms in the (111) surface. Using the non-polar (110) surface energy from the slab calculation (Supplementary Fig. 27a), we were able to calculate the absolute surface energies of (100) and (111) from the wedge model (Supplementary Fig. 27b, c). The calculated absolute surface energies of the (111) and ($$\bar{111}$$) surfaces converged to within approximately 0.4 meV/Å2. We employed (1 × 1) surface slab models with the (12 × 12 × 1) k-points sampling, except for the chlorine-amine co-passivated (2 × 2) surface. The wedge model with (1 × 1 × 12) k-points sampling had a triangle-shaped cross-section and infinitely periodicity along the z-direction.

To determine the surface stability, we calculated the surface formation energy with ligand coordination as a function of the chlorine chemical potential. The formation energy was defined as follow:

$${E}_{{{{\rm{Formation}}}}}=E({{{\rm{surface}}}}/{{{\rm{ligand}}}})-E\left({{{\rm{surface}}}}\right)-E({{{\rm{ligand}}}})$$
(2)

where E is the DFT total energy of each system. The chlorine chemical potential was referenced to a free chlorine gas molecule.

Data availability

The data related with this paper is available through the corresponding author upon reasonable request.

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Acknowledgements

This research was supported by the Creative Materials Discovery Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science and ICT (NRF-2019M3D1A1078299, 2019M3D1A1078302) and by NRF programs (grant numbers: 2019R1A2B5B03070407, 2018R1A2A2A14079326, 2020M3H4A3081815). H.Y.J. is supported by 2016M3D1A1900035.

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Y.-H.K., H.Y.J. and S.J. conceived the idea and designed the research. Y.K. and H.C., performed and analyzed the experiments. Y.L. and Y.-H.K. performed the calculations. W.-k.K., E.C., T.K., and H.K. analyzed activation energy barrier. H.Y.J. conducted HR-TEM and HAADF-STEM analyses. Y.K., H.C., Y.-H.K., and S.J. wrote the manuscript. All the authors have commented on the manuscript.

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Correspondence to Yong-Hyun Kim or Hu Young Jeong or Sohee Jeong.

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Kim, Y., Choi, H., Lee, Y. et al. Tailored growth of single-crystalline InP tetrapods. Nat Commun 12, 4454 (2021). https://doi.org/10.1038/s41467-021-24765-7

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