Diffusion-Limited Kinetics of Isovalent Cation Exchange in III-V Nanocrystals Dispersed in Molten Salt Reaction Media.

The goal of this work is to determine the kinetic factors that govern isovalent cation exchange in III-V colloidal quantum dots using molten salts as the solvent and cation source. We focus on the reactions of InP + GaI3→ In1-xGaxP and InAs + GaI3→ In1-xGaxAs to create technologically important ternary III-V phases. We find that the molten salt reaction medium causes the transformation of nearly spherical InP nanocrystals to tetrahedron-shaped In1-xGaxP nanocrystals. Furthermore, we determine that the activation energy for the cation exchange reaction is 0.9 eV for incorporation of Ga into InP and 1.2 eV for incorporation of Ga into InAs, both much lower than the measured values in bulk semiconductors. Next, we use powder XRD simulations to constrain our understanding of the structure of the In1-xGaxP nanocrystals. Together our results reveal several important features of molten salt-mediated cation exchange and provide guidance for future development of these materials.

Colloidal quantum dots (QDs) constitute an important class of optoelectronic materials widely explored for display applications[1−3] To date, colloidal quantum dots made of II–VI materials have shown the best optical performance in terms of near-unity photoluminescence quantum yield and narrow emission line width.[4−6] The same level of performance has not been universally achieved for III–V colloidal nanocrystals. There are several reasons, however, to develop colloidal routes to III–V nanocrystals including lower toxicity[7] and impressive optoelectronic performance achieved for nanostructures grown by CVD and MBE methods.[8−11] Synthetic efforts to improve solution-synthesized III–V materials face several challenges. For example, typical precursors are very reactive,[12,13] making it difficult to control nucleation and growth.[13−16] III–V chemical bonds are predominantly covalent,[12,17,18] making high-temperature processing necessary. In addition, Ga and Al are extremely oxophilic,[19,20] making colloidal preparation of their pnictide phases difficult. Thus far, only the In–V (V = P, As, Sb) phases have been synthesized via traditional colloidal routes with reasonable material quality.[21−27]

In recent works, our group has addressed key challenges related to III–V semiconductors by introducing high-temperature molten salt annealing (>400 °C) and molten salt-mediated cation exchange to prepare ternary III–V phases. Initially, we used InP(As) nanocrystals capped with sulfide ligands and processed them in a mixture of LiBr/KBr/CsBr + GaI3 forming In1–GaP(As).[28] We recently explored the role of nanocrystal surface chemistry and gallium halide additives on the reactivity of InP nanocrystals in LiBr/KBr/CsBr and LiI/KI eutectic mixtures. These observations indicate that in the absence of added GaI3, chalcogenide surface ligands ((NH4)2S, Li2Se, (DDA)2S, etc.) were key to suppressing undesirable ripening at elevated temperatures.[29] In addition, we found that nanocrystals capped with Lewis acid ligands[30] (GaCl3, InCl3, etc.) were stable against undesirable ripening or decomposition only in the presence of excess GaI3. This procedural modification avoids concerns regarding the presence of chalcogenide atoms, which may deleteriously affect their optical performance.[31]

In this work, we build upon our success using Z-type inorganic gallium halide ligands for molten salt-mediated cation exchange.[29] We replace the Lewis basic alkali halide salts with Lewis acidic salts consisting of GaI3 and KI mixtures, resulting in qualitatively better colloidal stability of the nanocrystals. Next, we use this chalcogenide-free molten salt system to systematically study the effect of cation exchange on particle morphology and the kinetics of the In-to-Ga replacement.[32] We find that the activation energy of the rate-determining step in the cation exchange process is considerably lower (∼1 eV) compared to the activation energy measured for self-diffusion in the corresponding bulk systems.[33−35] Finally, we use powder X-ray diffraction simulations of model nanocrystal structures to further constrain our understanding of the structure, composition, and heterogeneity of the In1–GaP nanocrystal systems and show that X-ray diffraction methods have significant limitations in their ability to discern important classes of defects. We thus propose an approach for the analysis of compositional variation using high-resolution transmission electron microscopy as an alternative tool of structural interrogation.

We synthesized InP QDs using two distinct synthetic methods to prepare sphere- and tetrahedron-shaped InP. Sphere-shaped InP QDs were synthesized from InCl3 and (TMS)3P in trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO) by an adaptation of the method developed by Mićić et al.[36,37] Tetrahedron-shaped InP QDs were synthesized from InCl3 and (NMe2)3P in oleylamine following the methods developed by Hens et al.[38,39] After size selective precipitation, we obtained sphere-shaped particles (Figure S1A,B) and tetrahedron-shaped particles with relatively narrow size distributions (Figure S1C,D). The distinct morphologies of the sphere- and tetrahedron-shaped nanocrystals provide an opportunity to explore the effect the molten salt annealing has on the shape and surface termination of the particles, as the reaction scheme in Figure A suggests. The photographs in Figure B show well-dispersed particles in the solidified molten salt matrix, consistent with our previously determined principles for colloidal stability.[40,41] TEM images of the sphere-shaped InP QDs show little evidence of particle faceting (Figure C), whereas amine/chloride passivated InP QDs show faceted particles with triangular projections consistent with a tetrahedron shape (Figure F). Following cation exchange, the In1–GaP QDs produced from either sphere- or tetrahedron-shaped nanocrystals both show faceted, triangular shapes in TEM images (Figures D and 1G, respectively). This suggests that the QD surface can recrystallize under the molten salt cation exchange conditions at ∼400 °C. The preference for tetrahedral morphology in the molten iodide matrix is supported by calculations that indicate favorable interactions between halide ions and the InP (111) surface facets, suggesting tetrahedral particles are the thermodynamically favored shapes of III–V nanocrystals in molten halide salts.[42] Evidently, the reaction zone of the pertinent molten salt cation exchange process extends beyond the dimension of these InP nanocrystals.[43−45] The change in morphology for initially spherical particles also suggests the phosphide sublattice is mobile, which may have important consequences related to the kinetics of the In-to-Ga cation exchange discussed below. This demonstrates that the process is not a simple replacement of In by Ga within a rigid phosphide lattice. Instead, the phosphide lattice reconfigures during the reaction as well, setting it apart from the low-temperature exchange reactions of ionic nanocrystals in which cations replace each other in a rigid anion lattice. Cation exchange in both sphere- and tetrahedron-shaped InP QD samples yields In1–GaP QDs, as evidenced by a shift of the XRD peaks to higher angles, indicating a decreased lattice constant (Figure E,H) and a corresponding blue-shift in the absorbance onset (Figure S2). We note that the sphere-to-tetrahedron shape change is not expected to drastically alter XRD peak intensity ratios (Figure S13). Based on the lattice constants measured with XRD, we estimate the QD composition to be In0.66Ga0.34P for the initially spherical particles and In0.58Ga0.42P for the initially tetrahedron-shaped particles.

Figure 1

(A) Reaction scheme outlining the transformation of sphere- and tetrahedron-shaped InP nanocrystals into tetrahedron-shaped In1–GaP nanocrystals. (B) Representative photographs of InP nanocrystals dispersed in GaI3/KI [65:35 mol %] eutectic molten salt (top) and the resulting In1–GaP after annealing (bottom). (C–E) TEM images of sphere-shaped InP nanocrystals before (C) and after (D) annealing in the molten salt reaction medium with corresponding powder X-ray diffraction patterns (E). (F–H) TEM images of tetrahedron-shaped InP nanocrystals before (F) and after (G) annealing in the molten salt reaction medium with corresponding powder X-ray diffraction patterns (H).

The chemical bonding in III–V semiconductors is predominantly covalent.[12,17,18] As a result, cation diffusion in bulk InP or GaP crystals is slow, characterized by a large activation energy and small diffusion coefficients. Studies on the diffusion of Ga3+ into bulk InP at the temperature ranges considered here are unavailable, so instead we extrapolate the reported self-diffusion coefficients to our working temperatures.[33,34] Based on this, the self-diffusion coefficient would be on the order of 10–24 cm2/s for InP at our working temperature,[29] requiring ∼32 years to incorporate 50% Ga into a 6.25 nm particle at 400 °C. This would indicate that Fickian diffusion for In-to-Ga cation exchange would be extremely slow at present reaction conditions. Yet we observe substantial alloying even at low temperatures, indicating that the pertinent mode of mass transport during molten salt mediated cation exchange in III–V nanocrystals has much lower barriers to Ga incorporation than in bulk systems. Previously, we hypothesized that three distinct steps exist in isovalent cation exchange processes in InP nanocrystals,[29] the final step being the introduction of Ga3+ cations into the lattice with simultaneous expulsion of In3+ cations. This step is likely the slowest and rate-determining step. Modeling this final phase within the analytical framework of the solution to Fick’s second law of diffusion for spherical particles allows us to gain crucial insight into the mechanistic pathways of In-to-Ga cation exchange occurring under diffusion-limited control.

We start with spherical InP nanocrystals with ∼6.25 nm average diameter. After GaI3 ligand exchange, the particles were dispersed in a eutectic GaI3/KI molten salt matrix at 240 °C for 1 h, sealed inside a quartz ampule under vacuum, and annealed at different combinations of time and temperature by using a custom-built shaking furnace (Figure S3). After cation exchange, alloyed In1–GaP nanocrystals were recovered with oleic acid and oleylamine ligands (OA/OAm) in toluene. The resulting colloidal solutions of nanocrystals in nonpolar solvents were characterized by using PXRD (Figure A,B). As expected, we observe the shift of diffraction peaks to higher momentum transfers (Q = 4π sin(θ)/λ, where 2θ is the Bragg angle and λ is the X-ray wavelength for the conventional 2θ axis; see Figure S4) for longer reaction times and higher reaction temperatures, consistent with the decrease in lattice parameter expected for higher gallium incorporation. We performed Le Bail refinement on each diffraction pattern[46] to estimate lattice constants and calculated the gallium composition by linear interpolation from the pure bulk phases. An additional sample was prepared without the high-temperature annealing step, allowing us to estimate the contribution of the intermediate surface exchange step toward alloying at about ∼5%. We found that annealing spherical InP nanocrystals at 393 °C resulted in nanocrystals with gallium content ranging from 25% to 60%, with increasing time resulting in increased gallium incorporation (Figure A,B). This trend occurs simultaneously with a continuous blue-shift of the excitonic absorption feature with increasing gallium content (Figure S5). TEM images of these samples show increasingly distinct faceting with longer annealing durations (Figure S6). In addition, the faceting develops even within the shortest (3 min) annealing time, indicating that the disruption and subsequent recrystallization of the phosphide sublattice happens rather rapidly at 393 °C. Notably, the average Scherrer sizes of these nanocrystals are smaller than the corresponding SAXS and TEM estimates (Figure S1A,B). The tetrahedron-shaped In1–GaP nanocrystals prepared with 1 h of annealing time have an average edge length of ∼8.5 nm via TEM (Figure S6), whereas the Scherrer estimate of the effective radius is 3.4–3.6 nm. We attribute this discrepancy to the presence of stacking faults and crystal twinning, as discussed in a later section. An annealing temperature of 362 °C yields similar trends (Figure S7) where an initially quick increase in gallium content is followed by slower incorporation at long times.

Figure 2

Powder XRD patterns for ∼6.25 nm InP nanocrystals annealed in GaI3/KI [65:35 mol %] for different times (A) and temperatures (B). Extracted gallium content (circles) and Scherrer size (squares) for the time (C) and temperature (D) series. Arrhenius plot of the apparent diffusion coefficient measured as a function of temperature with the extracted activation energy (E).

Next, we explored the temperature dependence of gallium incorporation by annealing the samples for a fixed duration at different temperatures (Figure B). From this, we extract an effective interdiffusion coefficient D̃ at each of these annealing temperatures for a reaction duration of t and extent of conversion x by utilizing the analytical solution to Fick’s second law of diffusion for a spherical particle of radius R (see Annexure, Supporting Information).[47]The gallium content increases monotonically with longer durations of annealing and increasing temperatures according to Figure C,D. As hypothesized previously, all the apparent interdiffusion coefficients extracted from the temperature series data are many orders of magnitude larger than their self-diffusion counterpart extrapolated from the available bulk data. Assuming an Arrhenius dependence of the apparent diffusion coefficients on temperature, we were able to estimate the activation barrier toward cation exchange, Ea ∼ 0.9 eV (∼87 kJ/mol), as noted in Figure E. These numbers are significantly lower than the activation barrier for self-diffusion previously reported in bulk III–V semiconductors, e.g., 3.85 eV for In in bulk InP,[33,34] but similar in magnitude to prior reports across different II–VI and IV–VI nanocrystalline systems.[45,48,49] Several high-diffusivity pathways could be invoked to explain this deviation. As noted previously, reorganization of the phosphide sublattice into a thermodynamically favored morphology is expected to generate defects and thus accelerate gallium diffusion. Additionally, these nanocrystals have stacking faults and twin defects (discussed later) which are known to be important low-temperature diffusion pathways.[50]

To test the generality of these observations, we repeated annealing experiments on smaller InP nanocrystals with an average diameter of 4 nm (Figure S8). The particles were processed similarly. The time and temperature series data under different annealing conditions are given in Figure S9A–C. We observe qualitatively similar trends, in that longer reaction times and higher temperatures result in higher gallium concentration. The resulting Arrhenius plot deviates significantly from linearity, suggesting competing pathways at different temperatures (Figure S9D). These smaller InP particles have a ∼60% higher surface-to-volume ratio relative to the ∼6.25 nm particles described before. Consequently, the surface exchange or surface recrystallization processes are expected to contribute more to the kinetics in these systems.[48]

Next, we explore the kinetics of cation exchange in InAs nanocrystals upon annealing in a KI/GaI3-based molten salt. Figure A and B shows the resulting powder X-ray diffraction patterns for InAs nanocrystals after high-temperature annealing under different conditions. Increased time and temperature led to greater shifts of the XRD peak positions to higher Q values, consistent with increased gallium incorporation. We quantified the particles’ composition and size by fitting the peaks to pseudo-Voigt functions and used extracted peak position and width to calculate the composition and Scherrer crystallite size, respectively (Figure C,D). Again, we find a monotonic increase in gallium content with both time and temperature. With regards to domain size, we see a slight increase in size as samples are annealed for a longer time (Figure C). Notably, treating InAs nanocrystals for 16 h at 400 °C results in the incorporation of over 80% Ga, suggesting cation exchange may be a viable route to nearly pure GaAs, a material which has been difficult to prepare by direct colloidal synthesis.[17]

Figure 3

Powder XRD patterns for ∼4 nm InAs nanocrystals annealed in 1:1 KI/GaI3 for different times (A) and temperatures (B). Extracted gallium content (circles) and Scherrer size (squares) for the time (C) and temperature (D) series. Arrhenius plot of the apparent diffusion coefficients measured as a function of temperature with the extracted activation energy (E).

We measured the apparent diffusion coefficients as a function of temperature (Figure E), which followed an Arrhenius relationship with an associated activation energy of 1.2 eV. The larger activation energy leads to a stronger temperature dependence for gallium incorporation in InAs compared to InP. Again, the measured activation energy is much lower than the corresponding value measured for self-diffusion of Ga in either bulk GaAs (4.24 eV[35] to 5.60 eV[33]) or bulk GaP (4.5 eV).[35] These results indicate that significantly lowered activation energies for cation exchange in III–V nanocrystals using molten salts may be quite general.

Thus far, we have used the shift of the PXRD peak positions to determine the average lattice parameter of the nanocrystal sample and a subsequent linear interpolation of the lattice parameter/composition relationship (Vegard’s law) to determine the gallium content. For colloidal nanocrystals, other factors can also affect the observed lattice parameter, such as strain resulting from the radial variation of particle composition, as observed in a core/shell morphology.[51−53] To this end, we aim to elucidate additional information from powder XRD to better constrain our understanding of the structure of these materials. We begin by simulating the powder XRD pattern (using the Debye formula) for a series of ideal zinc blende In1–GaP nanocrystals (Figure A). Expectedly, we see shifts of the XRD peak positions to larger Q values according to the variation of the composition. In addition, we observe a slight decrease in the ratio of the (200) and (111) peak intensities (i.e., I(200)/I(111) decreases) (see Figure S11 for quantification). This is expected based on the structure factor (F) for the (200) peak of a zinc blende material: F(200) = 4(fP – fGa/In). Because the peak intensity, proportional to |F|2, is determined by the difference of the atomic scattering factors (f) of the anion and cation, the relative intensity of the (002) peak may provide an independent check of the gallium content. For In1–GaAs nanocrystals, the scattering factor of As is closer in magnitude to that of In and Ga, so the ratio of the (200) and (111) peak intensities changes to a smaller extent when x varies from 0 to 1 (Figure S12). For this reason, we focus on analyzing the In1–GaP system for the remaining discussion.

Figure 4

Simulated powder XRD patterns for (A) pristine zinc blende In1–GaP nanocrystals and (B) In1–GaP nanocrystals with stacking disorder (mixture of twins and stacking faults). Comparison of the (111) and (200) peak intensities without the peak shifts due to lattice parameter change, by normalizing the scattering vector to 1 for the (111) peak position: for the simulated pristine InP (C), including stacking fault + twin (D) and the experimental diffraction (E). The color scheme used in (C) and (D) corresponds to the same color scheme used in (A) and (B), respectively. For the experimental data in (E), the color scheme used is the same as in Figure B. The reference stick pattern is for pristine InP. (F) Simulated powder XRD patterns for an ensemble of In0.50Ga0.50P nanocrystals with increasing gallium content distribution in the ensemble.

To visualize changes to the relative intensity of the (002) peak more easily, we normalized the scattering vector at the (111) peak center and the (111) peak intensity in the simulated XRD patterns to 1 (Figure C). Performing the same normalization on the experimental data for the 6.25 nm InP nanocrystals (Figure E) shows that the (002) peak is considerably less intense than expected when compared to the reference intensity in red and the simulations for a pristine In1–GaP nanocrystal (Figure C), suggesting we are not fully capturing the structure of our samples with the pristine zinc blende models. In Figure B, we calculated the powder diffraction patterns for an ensemble of In1–GaP nanocrystals with included stacking faults and twin defects, which are well-known defects in these materials systems.[54] We find that the intensity of the (002) peak decreases as planar defects are incorporated. The normalized (111) peak (Figure D) shows much better agreement with the experimental patterns, indicating our samples have considerable stacking disorder in the initial InP samples, and this disorder is maintained in the resulting In1–GaP samples. These defects are also observable with HRTEM (Figure S10). The (200)/(111) peak intensity ratio can only be used to determine the gallium content in nanocrystals that have a pristine zinc blende lattice. The attenuation of the (200) peak in the experimental samples indicates that there is a considerable stacking fault density in these samples which may have important implications for their optoelectronic properties. Finally, we discuss several additional structural parameters including strain, shape, and inhomogeneous element distribution of In1–GaP nanocrystals which PXRD is insensitive to in the Supporting Information (Figures S13–S15). Together these XRD simulations better refine our understanding of the structure of alloyed III–V colloidal nanocrystals.

The particle-to-particle compositional variation is another important source of heterogeneity we aim to understand. To do this, we first simulate the powder XRD patterns of a series of closely spaced particle compositions. Next, we weight the contribution of the scattering intensity for each composition by using a normal distribution to generate XRD patterns for an ensemble of particles with a given average composition and deviation. In Figure F, we show the simulated PXRD for In0.50±σGa0.50±σP nanocrystals with composition standard deviations ranging from σ = 0.01 to σ = 0.20. We find that increasing the composition distribution causes a minute increase in the width of the diffraction peaks. This can be understood considering the composition-dependent lattice parameter leading to an increase in the peak width. However, this small effect is convoluted with the peak broadening due to Scherrer broadening, and in any experimental system even minuscule changes in crystallite size will almost certainly obscure any observable broadening related to composition distribution. Our simulations, therefore, demonstrate that PXRD alone is rather insensitive to compositional variations and provides important context for evaluating potential composition variation in many alloyed colloidal nanocrystal systems which have been synthesized and characterized by PXRD. Importantly, composition variations do not appear to affect the average composition measured by XRD for a given ensemble, indicating our measured diffusion coefficients represent averages for the ensemble. We attempt to directly investigate the gallium content distribution by measuring the lattice parameter from an ensemble of individual particles using HRTEM (Figures S16–S19) and find a small increase in lattice parameter variation with gallium incorporation. Unfortunately, at present, limitations in data collection and analysis requirements limit our current analysis to qualitative conclusions. We hope our initial investigations inspire future inquiry into compositional variation which may have important consequences for designing particles with narrow ensemble emission line widths.

In this work we have carefully studied several aspects of the InP→ In1–GaP and InAs→ In1–GaAs cation exchange reactions on nanocrystals in molten KI/GaI3-based molten salts. We find that initially spherical InP nanocrystals are converted to faceted tetrahedron-shaped nanocrystals upon high-temperature annealing in molten salts. Furthermore, we measured the activation energy for gallium incorporation into InP and InAs nanocrystals and found it was much lower compared to related activation energies for bulk self-diffusion. We evaluated the structure of our In1–GaP nanocrystals using powder XRD simulations and determined that these materials contain considerable stacking disorder present in the original InP nanocrystals which persist after the molten salt annealing. Together, our results highlight the substantial difference that exists between kinetic parameters pertaining to cation exchange in bulk and nanocrystalline III–V phases as well as the implications of cation exchange on the morphology of III–V nanocrystals.