Growth Synchronization and Size Control in Magic-Sized Semiconductor Nanocrystals.

"Magic-sized" nanocrystals (MSNCs) grow in discrete jumps between a series of specific sizes. Consequently, MSNCs have been explored as an alternative route to uniform semiconductor particles, potentially with atomic precision. However, because the growth mechanism has been poorly understood, the best strategies to control MSNC syntheses and obtain desired sizes are unknown. Experiments have found that common parameters, such as growth time and temperature, have limited utility. Here, we theoretically and experimentally investigate reactant supersaturation as a tool to control MSNC growth. We compare direct synthesis of CdSe MSNCs with ripening of isolated MSNCs or their mixtures. Surprisingly, we find that MSNCs readily synchronize to the same growth trajectory, even starting from distinct initial conditions, explaining the robustness of MSNC growth. Further, by understanding the synchronization mechanism, we demonstrate methods to control the final MSNC size. These results deepen our knowledge of MSNCs and indicate strategies to tailor their growth.

Understanding Discrete Growth in Semiconductor Nanocrystals: Nanoplatelets and Magic-Sized Clusters.

ConspectusSemiconductor nanocrystals (NCs) fluoresce with a color that strongly depends on their size and shape. Thus, to obtain homogeneous optical properties, researchers have strived to synthesize particles that are uniform. However, because NCs typically grow through continuous, incremental addition of material, slight differences in the growth process between individual crystallites yield statistical distributions in size and shape, leading to inhomogeneities in their optical characteristics. Much work has focused on improving synthetic protocols to control these distributions and enhance performance. Interestingly, during these efforts, several syntheses were discovered that exhibit a different type of growth process. The NCs jump from one discrete size to the next. Through purification methods, one of these sizes can then be isolated, providing a different approach to uniform NCs. Unfortunately, the fundamental mechanism behind such discrete growth and how it differs from the conventional continuous process have remained poorly understood.Discrete growth has been observed in two major classes of NCs: semiconductor nanoplatelets (NPLs) and magic-sized clusters (MSCs). NPLs are quasi-two-dimensional crystallites that exhibit a precise thickness of only a few atomic layers but much larger lateral dimensions. During growth, NPLs slowly appear with an increasing number of monolayers. By halting this process at a specific time, NPLs with a desired thickness can then be isolated (e.g., four monolayers). Because the optical properties are primarily governed by this thickness, which is uniform, NPLs exhibit improved optical properties such as narrower fluorescence line widths.While NPLs have highly anisotropic shapes and show discrete growth only in one dimension (thickness), MSCs are isotropic particles. The name "magic" arose because a specific set of NC sizes appear during synthesis. They have been believed to represent special atomic arrangements that possess enhanced structural stability. Historically, they were very small, hence molecular-scale "clusters." Isolation of one of the MSC sizes can then, in principle, provide a uniform sample of NCs. More recently, MSC growth has been extended to larger sizes, beyond what is commonly considered to be the "cluster" regime, challenging the conventional explanation for these materials.This Account summarizes recent work by our group to understand the mechanism that governs discrete growth in semiconductor NCs. We begin by describing the synthesis of NPLs. Next, we discuss the mechanism behind the highly anisotropic shape of NPLs. We build on this by examining the ripening process in NPLs. We show that NPLs slowly appear with increasing thickness, counterintuitively through lateral growth. Then, we turn to the synthesis of MSCs, in particular focusing on their growth mechanism. Our findings indicate a strong connection between NPLs and MSCs. Finally, we review several remaining challenges for the growth of NPLs and MSCs and give a brief outlook on the future of discrete growth. By understanding the underlying process, we believe that it can be exploited more broadly, potentially moving us toward more uniform nanomaterials.

Unraveling the Growth Mechanism of Magic-Sized Semiconductor Nanocrystals.

Magic-sized clusters (MSCs) of semiconductor are typically defined as specific molecular-scale arrangements of atoms that exhibit enhanced stability. They often grow in discrete jumps, creating a series of crystallites, without the appearance of intermediate sizes. However, despite their long history, the mechanism behind their special stability and growth remains poorly understood. It is particularly difficult to explain experiments that have shown discrete evolution of MSCs to larger sizes well beyond the "cluster" regime and into the size range of colloidal quantum dots. Here, we study the growth of MSCs, including these larger magic-sized CdSe nanocrystals, to unravel the underlying growth mechanism. We first introduce a synthetic protocol that yields a series of nine magic-sized nanocrystals of increasing size. By investigating these crystallites, we obtain important clues about the mechanism. We then develop a microscopic model that uses classical nucleation theory to determine kinetic barriers and simulate the growth. We show that magic-sized nanocrystals are consistent with a series of zinc-blende crystallites that grow layer by layer under surface-reaction-limited conditions. They have a tetrahedral shape, which is preserved when a monolayer is added to any of its four identical facets, leading to a series of discrete nanocrystals with special stability. Our analysis also identifies strong similarities with the growth of semiconductor nanoplatelets, which we then exploit to further increase the size range of our magic-sized nanocrystals. Although we focus here on CdSe, these results reveal a fundamental growth mechanism that can provide a different approach to nearly monodisperse nanocrystals.

Determining the Structure-Property Relationships of Quasi-Two-Dimensional Semiconductor Nanoplatelets.

We report a theoretical study of CdSe nanoplatelets aimed at identifying the main factors determining their photophysical properties. Using atomic configurations optimized with density functional theory calculations, we computed quasiparticle and exciton binding energies of nanoplatelets with two to seven monolayers. We employed many body perturbation theory at the GW level and solved the Bethe-Salpeter equation to obtain absorption spectra and excitonic properties. Our results, which agree well with recent experiments, were then used to design a model that allows us to disentangle the effects of quantum confinement, strain induced by passivating ligands, and dielectric environment on the electronic properties of nanoplatelets. We found that, for the model to accurately reproduce our first principle results, it is critical to account for surface stress and consider a finite potential barrier and energy-dependent effective masses when describing quantum confinement. Our findings call into question previous assumptions on the validity of an infinite barrier to describe carrier confinement in nanoplatelets, suggesting that it may be possible to optimize interfacial charge transfer and extraction by appropriately choosing passivating ligands. The model developed here is generalizable to core-shell platelets and enables the description of system sizes not yet directly treatable by first-principles calculations.

Modeling Superlattices of Dipolar and Polarizable Semiconducting Nanoparticles.

We present an analytical model to describe the stability of arbitrary semiconducting nanoparticle (NP) superlattices as a function of the dipole and polarizability of their constituents. We first validate our model by comparison with density functional theory calculations of simple cubic superlattices of small CdSe NPs, and we show the existence of a regime, relevant to experiments, where NP interactions are predominantly dipole-like. We then apply our model to binary superlattices and find striking differences between the stable geometries of lattices composed of polarizable and nonpolarizable NPs. Finally, we discuss the interplay of dipolar and ligand-ligand interactions in determining the stability of NP superlattices.

An intrinsic growth instability in isotropic materials leads to quasi-two-dimensional nanoplatelets.

Colloidal nanoplatelets are atomically flat, quasi-two-dimensional sheets of semiconductor that can exhibit efficient, spectrally pure fluorescence. Despite intense interest in their properties, the mechanism behind their highly anisotropic shape and precise atomic-scale thickness remains unclear, and even counter-intuitive for commonly studied nanoplatelets that arise from isotropic crystal structures (such as zincblende CdSe and lead halide perovskites). Here we show that an intrinsic instability in growth kinetics can lead to such highly anisotropic shapes. By combining experimental results on the synthesis of CdSe nanoplatelets with theory predicting enhanced growth on narrow surface facets, we develop a model that explains nanoplatelet formation as well as observed dependencies on time and temperature. Based on standard concepts of volume, surface and edge energies, the resulting growth instability criterion can be directly applied to other crystalline materials. Thus, knowledge of this previously unknown mechanism for controlling shape at the nanoscale can lead to broader libraries of quasi-two-dimensional materials.

Mixing with herringbone-inspired microstructures: overcoming the diffusion limit in co-laminar microfluidic devices.

Enhancing mixing is of uttermost importance in many laminar microfluidic devices, aiming at overcoming the severe performance limitation of species transport by diffusion alone. Here we focus on the significant category of microscale co-laminar flows encountered in membraneless redox flow cells for power delivery. The grand challenge is to achieve simultaneously convective mixing within each individual reactant, to thin the reaction depletion boundary layers, while maintaining separation of the co-flowing reactants, despite the absence of a membrane. The concept presented here achieves this goal with the help of optimized herringbone flow promoting microstructures with an integrated separation zone. Our electrochemical experiments using a model redox couple show that symmetric flow promoter designs exhibit laminar to turbulent flow behavior, the latter at elevated flow rates. This change in flow regime is accompanied by a significant change in scaling of the Sherwood number with respect to the Reynolds number from Sh ~ Re(0.29) to Sh ~ Re(0.58). The stabilized continuous laminar flow zone along the centerline of the channel allows operation in a co-laminar flow regime up to Re ~325 as we demonstrate by micro laser-induced fluorescence (µLIF) measurements. Micro particle image velocimetry (µPIV) proves the maintenance of a stratified flow along the centerline, mitigating reactant cross-over effectively. The present work paves the way toward improved performance in membraneless microfluidic flow cells for electrochemical energy conversion.