Prospects of Colloidal Nanocrystals for Electronic - Computer Science

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398 Chemical Reviews, 2010, Vol. 110, No. 1 Talapin et al. 3.3. Multicomponent Nanoparticle Superstructures Mixing two colloidal solutions of NCs with different size and functionality (e.g., transition metals, semiconductors, oxides, etc.) can lead to the formation of ordered binary nanoparticle superlattices (BNSLs) (Figures 9-11). 215,220-224 Multicomponent nanoparticle superlattices naturally provide a much broader range of compositions and structures as compared to the assemblies of one type of NCs. When particles of different sizes and types are brought together, they must adjust themselves to space constrains in a certain way. Many efforts were made to predict the formation of various ordered binary structures and evaluate their stability. 225-231 In the simplest mechanistic approach based on space filling, the formation of a binary assembly of hard (noninteracting) spheres is expected only if its packing density exceeds the packing density of single-component crystals in fcc or in hcp structure (∼0.7405). 232 According to this principle, the key factors determining the structure of superlattices are particle size ratio (γ ) Rsmall/Rlarge) and relative concentrations. Each structure has its own γ range of stability. 232 Taking into account geometrical considerations only, we can expect the formation of superlattices isostructural with NaCl, NaZn13, and AlB2. Indeed, NaZn13- and AlB2-type assemblies of silica particles were first found in natural Brazilian opals 233 and later grown from latex spheres. 234,235 Packing density in the stable γ range usually exceeds 0.7405, the packing density for fcc single component lattices. In other words, the higher is the packing density, the larger is the entropy gain achieved during crystallization of the NC superlattice. 233 Detailed computer simulations showed that the formation of NaCl-, AlB2-, and NaZn13-type structures of hard spheres can be driven by entropy alone without any specific energetic interactions between the particles. 228-230 However, the intrinsic entropy of binary superlattice also affects its stability. For example, the maximum packing density of NaZn13-type superlattice is slightly below 0.74, whereas the detailed entropy calculations predict the stability of this structure in a rather broad range of γ. 230 Self-assembly of two types of nanoparticles gives rise to amazing diversity of binary superlattices (Figure 10). Superlattices with AB, AB2, AB3, AB4, AB5, AB6, and AB13 particle stoichiometry with cubic, hexagonal, tetragonal, and Figure 9. TEM image of (100) projection of a binary superlattice isostructural with AuCu intermetallic compound, self-assembled from 5.8 nm PbSe and 3.4 nm Ag nanoparticles; inset shows the same structure under higher magnification. Figure 10. TEM images of binary nanoparticle superlattices (BNSLs) self-assembled from various semiconductor, metallic, and magnetic nanocrystals. The bottom-left corner insets show the unit cells of corresponding structures. (a) (001) projection of AuCutype BNSL formed by 7.6 nm PbSe and 5.0 nm Au NCs. (b) (001) projection of AlB2-type BNSL assembled from 13.4 nm Fe2O3 and 5.8 nm PbSe NCs. The top-left corner inset shows small-angle electron diffraction pattern. (c) (001) projection of Laves phase MgZn2-type BNSL formed by 6.2 nm PbSe and 3.0 nm Pd nanocrystals. (d) (001) projection of CaCu5 type BNSL formed by 3.4 nm CdSe and 7.3 nm PbSe nm NCs. (e) (100) plane of cub- AB13 type BNSL formed by 8.1 nm CdTe and 4.4 nm CdSe nanocrystals. (f) BNSL self-assembled from LaF3 triangular nanoplates (9.0 nm side) and 5.0 nm spherical Au NCs. (a,b,c,f) Reprinted with permission from ref 182. Copyright 2006 Nature Publishing Group. (d) Reprinted with permission from ref 215. Copyright 2007 American Chemical Society. (e) Reprinted with permission from ref 224. Copyright 2008 American Chemical Society. orthorhombic symmetries have been identified. 182,215,220-224 Assemblies with the same stoichiometry can be produced in several polymorphous forms by tailoring the particle size and deposition conditions. Thus, BNSLs isostructural with NaCl, NiAs, CuAu, AlB2, MgZn2, MgNi2, Cu3Au, Fe4C, CaCu5, CaB6, NaZn13, and cub-AB13 compounds were made using various nanoparticle combinations. 182,220 The observed structural diversity is rather challenging to understand. Currently, the structural diversity of BNSLs is explained by the interplay of multiple factors such as entropy, Coulombic, van der Waals, charge-dipole, dipole-dipole, and other interactions, which all contribute to stabilization of BNSL’s in a rather complex way, allowing the superlattice formation to be dependent on a number of tunable parameters. Even
Colloidal Nanocrystals in Electronic Applications Chemical Reviews, 2010, Vol. 110, No. 1 399 Figure 11. Binary superlattices combining different functional building blocks (magnetic, semiconducting, metallic). (a-e) TEM micrographs of (001) planes of binary superlattices isostructural with AlB2 compound. (f) Sketch of AlB2 unit cell. (g,h) Depictions of the front and side views of the superlattice (001) plane, correspondingly. Reprinted with permission from ref 220. Copyright 2006 American Chemical Society. though the complex nature of particle-particle and particlesubstrate interactions slows the progress in control of nanoparticle self-assembly, it also provides an amazing platform to synthesize structures fascinating our imagination. It should probably be possible to coassemble more than two nanoparticle components, forming ternary and quaternary superlattices. However, even preliminary studies show that the phase analysis of such structures will be very challenging. Using multicomponent (e.g., core-shell or dumbbell) NCs as BNSL building blocks is an alternative way to combine more than two inorganic components in a long-range ordered superlattice. 236 Different types of BNSLs can form simultaneously on the same substrate, 220 and, as a result, a smooth “epitaxial” transition between two BNSL phases can form a “super-heterostructure”. 220 As compared to atomic solids, the nanoparticle superlattices can possess extra degrees of freedom such as adjustable particle size and shape. The ability to mix and match different nanoparticles and assemble them systematically into ordered binary superlattices, with precisely controlled stoichiometry and symmetry, can provide a general and inexpensive path to a large variety of novel materials with precisely controlled chemical composition and tight placement of the components. In perspective, BNSLs could make possible a modular approach to create multifunctional materials by combining independently tailored functional components. 3.4. Theoretical Insight into the Electronic Structure of Nanocrystal Solids: From Insulated Dots to Three-Dimensional Minibands Unlike atomic and molecular crystals where atoms, lattice geometry, and interatomic distances are fixed entities, the NC solids represent ensembles of designer atoms with potential for tuning their transport and optical properties. Generally speaking, NC assemblies can be considered as a novel type of condensed matter, whose behavior depend both on the properties of the individual building blocks and on the many-body exchange interactions. The presence of long- range translational order in nanoparticle superlattices can make them fundamentally different from amorphous and polycrystalline solids. The coupling among ordered quantum dots can lead to a splitting of the quantized carrier energy levels of single particles and result in the formation of threedimensional collective states, minibands. 237,238 Although different types of long-range ordered single- and multicomponent NC superlattices had already been self-assembled from colloidal NCs, very little attention has been paid to the theoretical description of electronic structure, carrier, and phonon transport in such structures. To the best of our knowledge, no electronic structure calculations for fcc or BNSL structures have been reported. At the same time, a reasonably good description of the extended states has been developed for one-dimensional quantum well superlattices239-243 and quantum dot crystals grown by molecular beam epitaxy. 237,244-246 In the latter case, the analysis was based on the effective mass or envelope function approach. 247 The one-electron Schrödinger equation was used in the form of an effective mass equation involving the envelope of the electron wave functions. The effect of the background atomic potential was accommodated as an effective mass for the electron moving under the influence of macroscopic potential perturbations. For simplicity, the theory was developed for simple cubic and tetragonal lattices (Figure 12). The motion of a single carrier in such a system can be described by the Schrödinger equation: [ -p2 2 ∇ 1 rm*(r) ∇r + V(r)] �(r) ) E�(r) (4) The atomic structure of the quantum dot crystal enters the analysis as an effective mass m*. This parameter assumes different values in the quantum dot and the barriers. The potential V(r) corresponds to an infinite sequence of quantum dots of size Lx, Ly, and Lz separated by the barriers of thickness Hx, Hy, and Hz (Figure 12). For simplicity, it was assumed that V(r) can be written as a sum of three
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