Design of Heterogeneous Chalcogenide Nanostructures with

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Design of heterogeneous chalcogenide nanostructures with pressure-tunable gaps and without electronic trap states Federico Giberti, Márton Vörös, and Giulia Galli Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00283 • Publication Date (Web): 13 Mar 2017 Downloaded from http://pubs.acs.org on March 14, 2017

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Design of heterogeneous chalcogenide nanostructures with pressure-tunable gaps and without electronic trap states Federico Giberti,∗,† Marton Vörös,†,‡ and Giulia Galli†,‡ †Institute for Molecular Engineering, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA ‡Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA E-mail: [email protected]

Abstract Heterogeneous nanostructures, such as quantum dots (QDs) embedded in solid matrices or core-shell nanoparticles, are promising platforms for a wide variety of applications, including phosphors with increased quantum yield, photocatalysis and solar energy conversion. However characterizing and controlling their interfacial morphology and defects, which greatly influence their electronic properties, have proven difficult in numerous cases. Here we carried out atomistic calculations on chalcogenides nanostructured materials, i.e. PbSe QDs in CdSe matrices and CdSe embedded in PbSe, and we established how interfacial and core structures affect their electronic properties. In particular, we showed that defects present at interfaces of PbSe nanoparticles and CdSe matrices give rise to detrimental intra-gap states, degrading the performance of photovoltaic devices. Instead, the electronic gaps of the inverted system (CdSe dots in PbSe) are clean, indicating that this material has superior electronic properties for solar applications. In addition, our calculations predicted that the core structure of

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CdSe and in turn its band gap may be tuned by applying pressure to the PbSe matrix, providing a means to engineering the properties of new functional materials.

The search for innovative technologies for solar energy conversion constitutes an active field of fundamental and applied research. Commercial solar cells are usually made of silicon, with average efficiency around 20% and maximum efficiency limited to 33%, the ShockleyQueisser limit. 1 Several materials have been considered to overcome this limit and to build more cost-efficient solar cells, for example, perovskites, 2 organic polymers 3 and colloidal quantum dots (QDs). The latter show great promise due to multi-exciton generation, enhanced by quantum confinement, 4–14 which may be exploited to improve the photoconversion efficiency. The photoconversion efficiency of QD solar cells has steadily increased in the past few years 14–17 and it has recently reached 12%, 18 however, the path towards even higher efficiencies is yet unclear. Colloidal dots can be synthesized in solution or via gas deposition, and then deposited on a film or embedded in a solid matrix. 19 Recently, heterostructured Janus and core-shell QDs, 20 have been successfully synthesized, with both nanostructures showing promise for further enhancing the efficiency of existing colloidal solar cells. 21 For example, their optoelectronic properties may be manipulated by varying the shell thickness or interlacing different shells. 19 However, the photophysical properties of these heterostructured QDs are not well understood. In particular, interfaces between the core and the shell are usually poorly characterized, and their role in determining the electronic properties of the dots is yet unclear. Recently, atomistic and electronic structure studies of core-shell nanostructures were reported, including CdSe(S)/ZnSe(S) QDs and CdSe/CdS nanorods, 22–24 where a sharp coreshell interface was easily obtained, since both materials have the same equilibrium lattice structure in the bulk. Several other interesting heterogeneous QDs, e.g. PbS/CdS and PbSe/CdSe, are instead lattice mismatched, making it challenging to define a structural model for the interface. Lattice mismatch has also been responsible for experimental dif2


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ficulties in synthesizing PbX/CdX (X=S, Se) heterostructures, which were partially solved in the work of Pietryga et al., 25 who utilized cation exchange techniques developed by Son et al.; 26 these techniques are now adopted by many groups. 10,27–44 In addition to cation exchange, synthesis procedures based on successive ionic layer adsorption and reaction (SILAR) were also developed. 38,39 It is generally accepted that the growth of a CdSe/CdS shell over a PbSe/PbS core enhances the quantum yield of the near-IR photoluminescence originating from the core. 10,25,29,32–35,37–40,43,44 Such enhancement is likely related to a better core surface passivation, compared to that obtained in ligand-terminated PbSe/PbS QDs, 41 and to a favorable alignement between the frontier orbitals of the core and shell. 10,29 However, in the absence of atomistic structural models, band alignements could only be estimated by using either bulk properties or simple models of quantum confined structures at zero temperature, with no defects, and adopting effective mass approximations. 10 Here we investigated heterogenous nanostructured materials composed of dots embedded in matrices, which offer simpler morphologies for charge extraction, than core-shell nanoparticles capped with ligands. We focused on lead selenide (cadmium selenide) nanoparticles embedded in cadmium selenide (lead selenide), which are promising platforms for solar energy conversion and thin film transistors. 41,45,46 We call these heterostructures PbSe@CdSe and CdSe@PbSe, respectively. We developed a hierarchical computational method by combining semi-grand canonical Monte Carlo, classical molecular dynamics (MD) and enhanced sampling techniques to build atomistic models, and techniques based on density functional theory (DFT) to investigate optoelectronic properties. Below we present predictions and design rules to obtain nanostructured chalcogenides without detrimental electronic gap states and with pressure-tunable band gaps. We start by briefly describing the framework used to create the models of embedded QDs. In most of previous works, the structure of QDs was optimized using DFT-based methods to obtain stable local minima. 12,47 Hence thermal effects were neglected, and structural

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defects were either not included or introduced ad-hoc after structural optimizations. 48–52 In order to include defects and thermal effects we used classical MD and enhanced sampling techniques, i.e. well-tempered metadynamics, with a force-field recently developed for mixed composition chalcogenides similar to those studied here. 53,54 We built the initial atomistic models of PbSe@CdSe and CdSe@PbSe (with PbSe and CdSe in the rocksalt and zincblende structure, respectively) by using Semi-Grand-Canonical Monte Carlo (SGCMC) simulations coupled with MD. 55 This process allowed us to exchange Pb with Cd cations and vice-versa, while enabling for structural relaxations as substitutions proceeded (see Method section for additional details). During the SGCMC procedure, all the CdSe@PbSe models retained the rocksalt (RS) structure, i.e. the same as that of the matrix surrounding the QDs. Instead, the PbSe@CdSe models retained the zincblende (ZB) structure only for a diameter smaller than 1.7 nm, while at larger sizes they adopted the RS structure. Analyses of the nanocomposite simulated in our work, which contained a PbSe nanoparticle of 2.4 nm diameter), showed that although the roughness of core-matrix interfaces is only ≈ 1-3 atomic layers, these interfaces do include coordination defects that may affect the electronic properties of the QDs. These are shown in Fig. 1. In the PbSe@CdSe case, the core has a RS structure in which most of the cations are sixfold coordinated within an octahedral geometry. However, at the core-matrix interface, a few Pb cations are undercoordinated, and Cd ions are overcoordinated. The amount of undercoordinated Pb is rather small, approximately 5 % of the total number in the core. For CdSe@PbSe the core has a ZB structure in which most of the cations are in a fourfold coordinated environment. In this case the concentration of coordination defects (all Cd) at the interface is higher than that of PbSe@CdSe, however their effect on the electronic properties will turn out to be negligible. The majority of the Cd cations are sixfold coordinated, and they assume a distorted octahedral geometry. Interestingly, no Pb coordination defects were observed. We estimated the roughness of the interfaces by using the spread of the distributions

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Figure 1: Probability (Pc (r)) (lower panels) of finding a cation with a coordination number of 4, 5 or 6 as a function of the distance from the center of mass of the nanoparticle core.The cutoff radii for the calculation of the coordination numbers were chosen as the first minimum of the Pb-Se and Cd-Se radial distribution functions, which corresponds to a distance of 4.1 ˚ A for Pb-Se and 4.3 ˚ A for Cd-Se, respectively. The results for Pc (r) were obtained by averaging 4 independent runs per quantum dot size, for both CdSe@PbSe and PbSe@CdSe. For PbSe embedded quantum dots, the majority of the Pb cations are 6-fold coordinated, with a small concentration of 4 and 5-fold coordinated cations present at the core-matrix interface. For embedded CdSe quantum dots, the majority of the core has a zincblende structure with a considerable amount of 6-fold coordinated Cd ions at the interface. Ball and stick representations of interfacial structures are shown in the upper panels. Cd, Pb and Se atoms are represented as green, purple and beige spheres, respectively. In both the left and right hand side panels, we reported the results for the two largest nanocomposites simulated in this work, corresponding to embedded nanoparticles Pb1 35Se1 35, with a a diameter of 2.4 nm. of defects, as well as the overlap of the total sixfold Pb and fourfold Cd distributions. All interfaces were found to be rather sharp, consistent with the observation of AFM and TEM experiments. 28,56 However the presence of coordination defects was not detected experimentally in this kind of core-shell QDs, to the best of our knowledge.

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First principles electronic structure calculations of the models obtained with the classical framework illustrated above, are unfortunately rather demanding. We thus constructed six additional models, which have the same core size as those investigated in the classical calculations, but a smaller surrounding matrix. Although reduced in size, these models are still rather challenging since they contains more than 16000 electrons. (See SI). Below we describe the results obtained for nanocomposites with 1728 atoms, for both PbSe@CdSe and CdSe@PbSe. Using DFT and the PBE 57 exchange correlation functional, we found that PbSe@CdSe exhibit a quasi Type-II band alignement, while CdSe@PbSe has a Type-I band alignement . In the former case defects which are present at the interface are responsible for the presence of electronic states in the gap. Instead, the gap of CdSe@PbSe is clean, in spite of a high proportion of overcoordinated Cd atoms at the interface. Note that the gaps computed here at the DFT level are smaller than in experiments, as expected as we used semilocal functionals (in addition, the energy smearing used to represent the states decreases the computed gap at T=0). Fig. 2 shows the radial density of states (RDOS), averaged over five different configurations extracted from MD trajectories of the rocksalt PbSe nanoparticles embedded in the zincblende CdSe matrix:

RDOS(ǫ, r) = 2

X

|ψi (~r)|2 (r)δ(ǫi − ǫ),

(1)

i

where ψi is the single particle wave function of state i with energy ǫi and the overline represents a spherical average. A quasi-Type-II alignement is shown in Fig. 2, with the highest occupied state (HOMO) having a core character, and the lowest unoccupied state (LUMO) a matrix character. To verify the robustness of our results, we estimated the effect of spin-orbit coupling (SOC, not included in the results shown in Fig. 2), on the LUMO of isolated stoichiometric QDs of cubic and spherical shape, and we assumed that such effect would remain similar upon embedding. We found that the core states were lowered in energy by about 0.2 eV by SOC, leaving the quasi-Type-II band alignement unchanged. 6


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These findings apply to all PbSe@CdSe models, for different configurations extracted from the MD simulations, regardless of whether the structure is ZB or RS.

A

B

C

D

Figure 2: Upper panel: radial density of states of a rocksalt PbSe quantum dot embedded in a zincblende CdSe matrix as a function of distance from the quantum dot center, obtained by averaging five different configurations extracted from the classical MD simulation. The black dashed horizontal lines show the Fermi level, while the vertical blue lines represent the position of the core-matrix interface. Black arrows indicate the band-gap in the core and the matrix. Panel A to D reports the single particle wavefunction of four electronic states. Panel A illustrates the (HOMO-4) state, which is delocalized over the embedded core; panel B reports the HOMO state, which is mostly localized on the four-fold coordinated Pb defect; panel C represents the state pinning the Fermi level, where the wavefunction is delocalized at the core-matrix interface; panel D illustrates the LUMO+1. Fig. 2 also shows that the Fermi-level of the system is pinned to the HOMO of the core-matrix dot by the first unoccupied state which has a strong interface character (see Fig. 2 C). The same result was found for all of our PbSe@CdSe models, regardless of the structure of the core. These findings have substantial implications for the usability of this type of interface in photovoltaic devices. For example, the band gap states observed here and 7


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the concomitant Fermi-level pinning may give rise to efficient non-radiative recombination in solar cells. 49 In addition, we found that the highest occupied state is localized around an interfacial 4-fold coordinated Pb atom (see Fig. 2 B). Such a state may jeopardize hole transport in FETs and solar cells. Deeper occupied and higher unoccupied states (see Fig. 2 A for (HOMO-4) and D for (LUMO+1)) are instead delocalized over the nanoparticle and the matrix, respectively. Fig. 3 displays the radial density of states of the inverted CdSe@PbSe nanostructure averaged over five different configurations, showing a Type-I band alignement: the highest occupied states have a dominant matrix character, while the lowest unoccupied states have predominantly QD character. Our results indicate that the type of band alignement between NP and matrix is dependent on the distance between nanoparticles. Indeed we found a typeI for the sample with 1728 atoms (with a distance of 4 nm between nanoparticles), but type II for a smaller sample where the NP are at a distance of 3 nm (see SI). In contrast to the PbSe@CdSe nanocomposite, we did not find any Fermi-level pinning nor localization of the single-particle wavefunctions on the coordination defects present at the interface, in spite of a higher defect concentration. The inverted structure has a clean gap, one of the most important factors for high-performing solar cells, and hence appears to have superior electronic properties to PbSe@CdSe. We also investigated the effect of SOC on the electronic states of an isolated CdSe NP, namely Cd33 Se33 . We found that the introduction of SOC does not appreciably change the position (within 0.02 eV) of the HOMO and LUMO states, and we assumed that a similar small change would occur in the case of embedded nanoparticles. Finally we addressed the occurrence of metastable configurations in which the QDs assume the structure of the matrix. We computed the free energy difference between RS and ZB structures as a function of size and pressure using well-tempered metadynamics. 58–60 Our findings are summarized in two stability diagrams, presented in Fig. 4. (See SI for details of free energy calculations)

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A

B

Figure 3: Panel A illustrates the radial density of states (DOS) of a zincblende CdSe quantum dot embedded in a rocksalt PbSe matrix as a function of distance r from the quantum dot center. Panel B reports the radial density of states of a rocksalt CdSe quantum dot embedded in a rocksalt PbSe matrix as a function of the distance. The black dashed horizontal lines show the Fermi-level, while the vertical blue lines represent the position of the core-matrix interface. Black arrows indicate the band-gap in the core and in the matrix. In both panels the DOS has been obtained by averaging five different configurations extracted from classical MD simulations. To describe the transformation between the RS and ZB structures, we employed the average coordination number (C) of the embedded cations in the cell (see Methods). This collective variable takes a value of 4 (6) for a perfect ZB (RS) structure, and intermediate values if defects are present. For embedded PbSe, we found that the stability of the ZB phase, could be increased by decreasing the external pressure. On the contrary, since RS is a high-pressure phase for CdSe, its stability could be increased by increasing the external pressure. As expected, increasing the pressure in the CdSe case helps stabilize larger dots with rocksalt structure. Surprisingly, RS quantum dots with a diameter of 2 nm can be obtained 9


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Figure 4: Region of stability of CdSe (panel A) and PbSe(panel B) nanoparticles embedded in matrices (see text), as a function of the applied pressure to the matrix (P) and nanoparticle diameter (d). ZB and RS indicate zincblende and rocksalt structures, respectively. already at 1.5 GPa which is roughly half of the bulk transition pressure for CdSe. 53 A similar effect was observed for embedded PbSe QDs, where a tension of -1.5 GPa was sufficient to stabilize a PbSe ZB structure. To understand the effect of these structural transformations on the electronic structure of PbSe@CdSe and CdSe@PbSe, we computed band alignements as a function of pressure. For strained PbSe@CdSe, the position of the band edges remained qualitatively similar to the low pressure phase; likewise the same pinning of the Fermi level was observed for the ZB structure. The reasons likely stems from the fact that the state pinning the Fermi level is localized at the interface between the core and the matrix, and it is simply related to a point defect that might have been healed by the applied tensile strain. For the CdSe@PbSe QDs, the structural transformation ZB→RS is accompanied by a lowering of the band gap of the nanoparticle, similar to what was observed in the bulk. This band gap lowering is accompanied by a change in the band alignment from Type-I to quasi-Type-II. The band gap lowering is especially important for solar cells exploiting MEG. The lower the gap, the lower the onset of MEG. 12,61,62 We also note that the ideal band gap for concentrated solar cells can be as low as 0.1 eV, but no material was yet found to 10


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achieve this target. 63 Compressed CdSe@PbSe core-matrix heterostructures may be a viable platform to obtain small band gaps for concentrated solar cells. In summary, we analyzed the relationship between structure and electronic properties of chalcogenide embedded nanoparticles, using atomistic calculations, and we proposed strategies to optimize their electronic properties for solar energy conversion, as a function of size and pressure. In particular, we designed a computational approach to generate atomistic models, by combining Monte Carlo techniques, with molecular dynamics and enhanced sampling methods; we then investigated the electronic properties of these models using density functional theory calculations. To the best of our knowledge, our calculations are the first ab initio study of atomistic models of embedded nanoparticles inclusive of defects and thermal effects. We focused on CdSe and PbSe nanoparticles embedded in PbSe and CdSe solid matrices, respectively, and for both classes of systems we observed the formation of sharp interfaces, with a quasi-Type-II band aligment for PbSe@CdSe and Type-I for CdSe@PbSe (for NP spaced 4 nm), consistent with existing experiments on core-shell nanoparticles. 19,29 The band alignement for the CdSe@PbSe system resulted to be sensitive to the thickness of the matrix representing the shell, varying from Type-I to Type-II as the NP distance is decreased from 4 to 3 nm. We found that defects were always present at interfaces, however their effect on the electronic properties of the heterogeneous composites turned out to be substantially different for CdSe@PbSe and PbSe@CdSe, an effect probably due to the difference in curvature between the PbSe and CdSe in the two nanocomposites. In the latter case, in spite of a low concentration of defects, we found electronic states in the gap that may act as traps for electrons, thus possibly decreasing the efficiency of solar energy conversion. However these intra-gap states pin the Fermi level and are optically active, hence they may be engineered to increase the quantum yield of the QDs, e.g. in IR detectors. For CdSe@PbSe we found instead no electronic defects in the gap, indicating that these heterostructures have superior electronic properties to their PbSe@CdSe counterparts. In addition, using extensive simulations of the stability of quantum dots in zinclende and

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rocksalt structures, we predicted that by applying pressure to a PbSe matrix, it is possible to stabilize embedded CdSe nanoparticles in a rocksalt structure, when their diameter is smaller than 2 nm. Pressure on the order of 5-10 GPa were applied in previous experiments to colloidal quantum dots using diamond anvil cell; similar pressures might be applicable to colloidal core-shell quantum dots as well as to embedded nanocomposites. 64,65 The transition from ZB to RS is accompanied by a decrease of the CdSe band gap to values which may be beneficial to increase the yield of PV devices based on these compounds. In addition, our calculations also showed that small QDs may be stabilized in a high-pressure structure even at ambient conditions, which is of course key for building energy conversion devices and may be beneficial for increasing the efficiency of MEG, as suggested by recent theoretical papers. 61,62 Experimental efforts to synthesize CdSe/PbSe core-shell QDs have not yet been successful; only Janus QDs have been reported. 66 Our findings suggest it is worth revisiting these experiments and seek a parameter space where CdSe@PbSe QDs may grow or form after cation exchange, by tuning, e.g. the pressure or strain applied to the matrix. Recently it has been reported that external pressure may be used to increase the mobility of the charge carriers in PV devices, and the combination of increased mobilities and smaller gaps could increase the efficiency of QDs based solar cells. 65 In a similar way, embedding PbSe in a matrix with a larger lattice constant (such as CdTe) may create the necessary tensile strain to stabilize the ZB structure. We finally note that synthesizing PbSe/CdSe QDs embedded in CdSe/PbSe matrices may be an interesting avenue to achieve heterogeneous nanostructured materials with optimal charge extraction properties, since charges generated in the QDs upon light absorption, are not required to tunnel through any ligands. Furthermore, it would be easier to apply pressure to nanoparticles embedded in a solid matrix than to ligand-terminated QD films. Several strategies exist to synthesize embedded QDs: for example, recent experiments reported that ligand stripping leads to the fusion of nanoparticles, 67 indicating that fusing core-shell nanoparticles, may be a viable strategy, possibly coupled to heat treatment. 68 It was also

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found that certain short ligands, called molecular solders, may replace native long ligands on the surface thus “gluing” the QDs together; 69 other techniques based on SILAR or atomic layer deposition might then be used to infill the inter-QD space. 70 In conclusion we presented predictions, based on atomistic models, of the structural and electronic properties of embedded chalcogenide quantum dots, which may be further extended to core shell nanoparticles and used to engineer optimal materials for solar energy conversion. Our hierarchical modeling provides an excellent foundation for future efforts to understand the optical and transport properties of related heterogeneous nanostructured materials. 52,71 Work is in progress to extend our study to other chalcogenide and group IV materials. Methods The creation of the embedded nanostructures was obtained by substituting cations in a spherical region by employing SGCMC. Cation exchanges occurred every 2 ps , i.e. at a rate many orders of magnitude higher than what observed in experiments. Hence no kinetic properties were inferred from our calculations. The initial structures were always chosen so that the matrix is in the stable ambient phase of the parent bulk material: we embedded PbSe QDs into zincblende CdSe matrices, and CdSe QDs in rocksalt PbSe matrices. A total of 6 different structures for each core-matrix system with increasing size were considered. (see Si for additional details). We performed well-tempered metadynamics calculations for all the embedded QDs reported in Table S1 but the largest one, at different pressures. Since welltempered metadynamics requires a continuous and differentiable collective variable, a contact between cations and anions was defined with the aid of a continuos switching function s(rij ) P c (see supplementary information).The atomic coordination number of cations C = N1c N i ci , where ci is the sum of the number of contacts between the i cation and all the j anions Na P a was defined using: ci = N j s(rij ). Additional details are reported in the SI.

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Acknowledgement Work by F.G. was supported by MICCoM as part of the Computational Materials Sciences Program funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division with grant number DOE/BES 5J30161-0010A. The electronic structure part of the work was supported by the Center for Advanced Solar Photophysics, an Energy Frontier Research Center funded by the U.S. DOE, Office of Science, Office of Basic Energy Sciences (M.V.). The computational time was provided by the National Energy Research Scientific Computing Center (NERSC). NERSC is supported by the Office of Science of the U.S. DOE under Contract No. DE-AC0205CH11231.

Supporting Information Available This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Shockley, W.; Queisser, H. J. J. Appl. Phys. 1961, 32, 510–519. (2) Snaith, H. J. J. Phys. Chem. Lett. 2013, 4, 3623–3630. (3) Goldey, M. B.; Reid, D.; de Pablo, J.; Galli, G. Phys. Chem. Chem. Phys. 2016, 18, 31388–31399. (4) Klimov, V. I. Annual Review of Condens. Matter Phys. 2014, 5, 285–316. (5) Nair, G.; Chang, L.-Y.; Geyer, S. M.; Bawendi, M. G. Nano Lett. 2011, 11, 2145–2151. (6) Beard, M. C.; Luther, J. M.; Semonin, O. E.; Nozik, A. J. Acc. Chem. Res. 2013, 46, 1252–1260. 14


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(7) Padilha, L. A.; Stewart, J. T.; Sandberg, R. L.; Bae, W. K.; Koh, W.-K.; Pietryga, J. M.; Klimov, V. I. Acc. Chem. Res. 2013, 46, 1261–1269. (8) Shabaev, A.; Hellberg, C. S.; Efros, A. L. Acc. Chem. Res. 2013, 46, 1242–1251. (9) Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510. (10) Cirloganu, C. M.; Padilha, L. A.; Lin, Q.; Makarov, N. S.; Velizhanin, K. A.; Luo, H.; Robel, I.; Pietryga, J. M.; Klimov, V. I. Nat. Commun. 2014, 5. (11) Zhao, H.; Sirigu, G.; Parisini, A.; Camellini, A.; Nicotra, G.; Rosei, F.; Morandi, V.; Zavelani-Rossi, M.; Vomiero, A. Nanoscale 2016, 8, 4217–4226. (12) Vörös, M.; Rocca, D.; Galli, G.; Zimanyi, G. T.; Gali, A. Phys. Rev. B 2013, 87, 155402. (13) Govoni, M.; Marri, I.; Ossicini, S. Nat. Photon. 2012, 6, 672–679. (14) Semonin, O. E.; Luther, J. M.; Choi, S.; Chen, H.-Y.; Gao, J.; Nozik, A. J.; Beard, M. C. Science 2011, 334, 1530–1533. (15) Chuang, C.-H. M.; Brown, P. R.; Bulović, V.; Bawendi, M. G. Nat Mater 2014, 13, 796801. (16) Liu, M.; de Arquer, F. P. G.; Li, Y.; Lan, X.; Kim, G.-H.; Voznyy, O.; Jagadamma, L. K.; Abbas, A. S.; Hoogland, S.; Lu, Z.; Kim, J. Y.; Amassian, A.; Sargent, E. H. Adv. Mater. 2016, 28, 4142–4148. (17) Lan, X.; Voznyy, O.; de Arquer, F. P. G.; Liu, M.; Xu, J.; Proppe, A. H.; Walters, G.; Fan, F.; Tan, H.; Liu, M.; Yang, Z.; Hoogland, S.; Sargent, E. H. Nano Lett. 2016, 16, 4630–4634. (18) National Renewable Energy Laboratory. 2017; https://www.nrel.gov/pv/assets/ images/efficiency-chart.png, [Online; accessed 2017-03-11]. 15


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(19) De Trizio, L.; Manna, L. Chem. Rev. 2016, 116, 10852–10887. (20) Reiss, P.; Protiere, M.; Li, L. Small 2009, 5, 154–168. (21) Zhang, J.; Chernomordik, B. D.; Crisp, R. W.; Kroupa, D. M.; Luther, J. M.; Miller, E. M.; Gao, J.; Beard, M. C. ACS Nano 2015, 9, 7151–7163. (22) Gr¨ unwald, M.; Lutker, K.; Alivisatos, A. P.; Rabani, E.; Geissler, P. L. Nano Lett. 2012, 13, 1367–1372. (23) Eshet, H.; Gr¨ unwald, M.; Rabani, E. Nano Lett. 2013, 13, 5880–5885. (24) Azpiroz, J. M.; Infante, I.; Angelis, F. D. J. Phys. Chem. C 2015, 119, 12739–12748. (25) Pietryga, J. M.; Werder, D. J.; Williams, D. J.; Casson, J. L.; Schaller, R. D.; Klimov, V. I.; Hollingsworth, J. A. J. Am. Chem. Soc. 2008, 130, 4879–4885. (26) Son, D. H.; Hughes, S. M.; Yin, Y.; Paul Alivisatos, A. Science 2004, 306, 1009–1012. (27) Abel, K. A.; FitzGerald, P. A.; Wang, T.-Y.; Regier, T. Z.; Raudsepp, M.; Ringer, S. P.; Warr, G. G.; van Veggel, F. C. J. M. J. Phys. Chem. C 2012, 116, 3968–3978. (28) van Veggel, F. C. J. M. Chem. Mater. 2014, 26, 111–122. (29) Lin, Q.; Makarov, N. S.; kyu Koh, W.; Velizhanin, K. A.; Cirloganu, C. M.; Luo, H.; Klimov, V. I.; Pietryga, J. M. ACS Nano 2015, 9, 539–547. (30) De Geyter, B.; Hens, Z. Appl. Phys. Lett. 2010, 97, 161908. (31) De Geyter, B.; Justo, Y.; Moreels, I.; Lambert, K.; Smet, P. F.; Van Thourhout, D.; Houtepen, A. J.; Grodzinska, D.; de Mello Donega, C.; Meijerink, A.; Vanmaekelbergh, D.; Hens, Z. ACS Nano 2011, 5, 58–66. (32) Justo, Y.; Goris, B.; Kamal, J. S.; Geiregat, P.; Bals, S.; Hens, Z. J. Am. Chem. Soc. 2012, 134, 5484–5487. 16


Page 16 of 20

Page 17 of 20

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(33) Justo, Y.; Geiregat, P.; Hoecke, K. V.; Vanhaecke, F.; De Mello Donega, C.; Hens, Z. J. Phys. Chem. C 2013, 117, 20171–20177. (34) Zaiats, G.; Yanover, D.; Vaxenburg, R.; Tilchin, J.; Sashchiuk, A.; Lifshitz, E. Materials 2014, 7, 7243. (35) Zaiats, G.; Yanover, D.; Vaxenburg, R.; Shapiro, A.; Safran, A.; Hesseg, I.; ur Physikalische Chemie 2015, 229, 3–21. Sashchiuk, A.; Lifshitz, E. Zeitschrift f¨ (36) Zaiats, G.; Shapiro, A.; Yanover, D.; Kauffmann, Y.; Sashchiuk, A.; Lifshitz, E. J. Phys. Chem. Lett. 2015, 6, 2444–2448. (37) Zhao, H.; Liang, H.; Vidal, F.; Rosei, F.; Vomiero, A.; Ma, D. J. Phys. Chem. C 2014, 118, 20585–20593. (38) Fang, H.-H.; Balazs, D. M.; Protesescu, L.; Kovalenko, M. V.; Loi, M. A. J. Phys. Chem. C 2015, 119, 17480–17486. (39) Zhang, Y.; Dai, Q.; Li, X.; Liang, J.; Colvin, V. L.; Wang, Y.; Yu, W. W. Langmuir 2011, 27, 9583–9587. (40) Treml, B.; Yang, J.; Wise, F.; Hanrath, T. Chem. Phys. 2016, 471, 69 – 74. (41) Neo, D. C. J.; Cheng, C.; Stranks, S. D.; Fairclough, S. M.; Kim, J. S.; Kirkland, A. I.; Smith, J. M.; Snaith, H. J.; Assender, H. E.; Watt, A. A. R. Chem. Mater. 2014, 26, 4004–4013. (42) Neo, M. S.; Venkatram, N.; Li, G. S.; Chin, W. S.; Ji, W. J. Phys. Chem. C 2010, 114, 18037–18044. (43) Binetti, E.; Striccoli, M.; Sibillano, T.; Giannini, C.; Brescia, R.; Falqui, A.; Comparelli, R.; Corricelli, M.; Tommasi, R.; Agostiano, A.; Curri, M. L. Science and Technology of Adv. Mater. 2015, 16, 055007. 17


Nano Letters

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(44) Grodziska, D.; Evers, W. H.; Dorland, R.; van Rijssel, J.; van Huis, M. A.; Meijerink, A.; de Mello Doneg, C.; Vanmaekelbergh, D. Small 2011, 7, 3493–3501. (45) Talapin, D. V.; Murray, C. B. Science 2005, 310, 86–89. (46) Gan, F.; Shih, I. IEEE Transactions on Electron Devices 2002, 49, 15–18. (47) Vörös, M.; Galli, G.; Zimanyi, G. T. ACS Nano 2015, 9, 6882–6890. (48) Long, R.; English, N. J.; Prezhdo, O. V. J. Am. Chem. Soc. 2013, 135, 18892–18900. (49) Brawand, N. P.; Vörös, M.; Galli, G. Nanoscale 2015, 7, 3737–3744. (50) Zherebetskyy, D.; Zhang, Y.; Salmeron, M.; Wang, L.-W. J. Phys. Chem. Lett. 2015, 6, 4711–4716. (51) Vörös, M.; Brawand, N. P.; Galli, G. Chem. Mater. Article ASAP. (52) Brawand, N. P.; Goldey, M. B.; Vörös, M.; Galli, G. Chem. Mater. 2017, 29, 1255–1262. (53) Fan, Z.; Koster, R. S.; Wang, S.; Fang, C.; Yalcin, A. O.; Tichelaar, F. D.; Zandbergen, H. W.; van Huis, M. A.; Vlugt, T. J. The J. Chem. Phys. 2014, 141, 244503. (54) Fan, Z. Mol. Simul.s of Nanoscale Transformations in Ionic Semiconductor Nanocrystals. Ph.D. thesis, TU Delft, Delft University of Technology, 2016. (55) Frenkel, D.; Smit, B. Understanding Mol. Simul.: from algorithms to applications; Academic press, 2001; Vol. 1. (56) Bals, S.; Casavola, M.; van Huis, M. A.; Van Aert, S.; Batenburg, K. J.; Van Tendeloo, G.; Vanmaekelbergh, D. Nano Lett. 2011, 11, 3420–3424. (57) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (58) Laio, A.; Parrinello, M. Proceedings of the National Academy of Sciences 2002, 99, 12562–12566. 18


Page 18 of 20

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Nano Letters

(59) Barducci, A.; Bussi, G.; Parrinello, M. Phys. Rev. Lett. 2008, 100, 020603. (60) Dama, J. F.; Parrinello, M.; Voth, G. A. Phys. Rev. Lett. 2014, 112, 240602. (61) Vörös, M.; Wippermann, S.; Somogyi, B.; Gali, A.; Rocca, D.; Galli, G.; Zimanyi, G. T. J. Mater. Chem. A 2014, 2, 9820–9827. (62) Wippermann, S.; Vörös, M.; Gali, A.; Gygi, F.; Zimanyi, G. T.; Galli, G. Phys. Rev. Lett. 2014, 112, 106801. (63) Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510. (64) Wickham, J. N.; Herhold, A. B.; Alivisatos, A. P. Phys. Rev. Lett. 2000, 84, 923–926. (65) Kim, J.; Jeong, B. G.; Roh, H.; Song, J.; Park, M.; Lee, D. C.; Bae, W. K.; Lee, C. ACS Applied Materials & Interfaces 2016, 8, 23947–23952. (66) Zhang, J.; Chernomordik, B. D.; Crisp, R. W.; Kroupa, D. M.; Luther, J. M.; Miller, E. M.; Gao, J.; Beard, M. C. ACS Nano 2015, 9, 7151–7163. (67) Baumgardner, W. J.; Whitham, K.; Hanrath, T. Nano Lett. 2013, 13, 3225–3231. (68) Law, M.; Luther, J. M.; Song, Q.; Hughes, B. K.; Perkins, C. L.; Nozik, A. J. J. Am. Chem. Soc. 2008, 130, 5974–5985. (69) Dolzhnikov, D. S.; Zhang, H.; Jang, J.; Son, J. S.; Panthani, M. G.; Shibata, T.; Chattopadhyay, S.; Talapin, D. V. Science 2015, 347, 425–428. (70) Liu, Y.; Tolentino, J.; Gibbs, M.; Ihly, R.; Perkins, C. L.; Liu, Y.; Crawford, N.; Hemminger, J. C.; Law, M. Nano Lett. 2013, 13, 1578–1587. (71) Brawand, N. P.; Vörös, M.; Govoni, M.; Galli, G. Phys. Rev. X 2016, 6, 041002.

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Design of Heterogeneous Chalcogenide Nanostructures with

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