Nanocrystal Arrays: Self-Assembly and Physical Properties Part 1 (Nanotechnology)

INTRODUCTION

Over the last few years, research in the area of nano-science has blossomed into an independent and highly interdisciplinary area.[1] Materials in the nanometer scale (size range 10 A to 1 mm) are typically referred to as nanoparticles, nanocrystals, nanorods, or nanowires, depending on their crystallinity and shape. Here we refer to them simply all as nanocrystals, without distinguishing the differences. The unique material properties in this size range come from several sources: 1) quantum size effects,[2] where confinement of charge carriers in a small space leads to discrete energy levels; 2) classical charging effects,[3] which originate from the discrete nature of the electrical charge; and 3) surface/interface effects,[4] where the properties of surface or interface atoms become much more significant, as the surface-to-volume ratio increases with decreasing of particle size. Many novel properties of single, isolated nanocrystal have been investigated during the past two decades, such as size-dependent optical absorption and luminescence in semiconductors,1-5,6-1 coulomb blockade phenomena in charge transfer,1-7-1 or enhanced surface magnetic moments in magnetic nano-crystals.1-8-1

By comparison, assemblies of nanocrystals have only begun to be studied in a systematic fashion in recent years. The exciting aspect of nanocrystal arrays is that they form a truly new class of materials, where the basic building blocks are nanocrystals instead of atoms.[9] The properties of these materials not only depend on which chemical elements are used to form the building blocks, but also depend on how many atoms are in each building block and how strongly coupled these building blocks are. Traditional materials can be either crystalline or amorphous, depending on the arrangement of the constituent atoms. Similarly, nanocrystal arrays can also be ordered or disordered. In the former case, they are referred to as nanocrystal superlattices (NCSs).

The purpose of this article is to introduce several recent developments in the field, focusing on the experimental point of view. In ”Formation of Nanocrystal Arrays,” experimental issues regarding the formation of nanocrystal arrays will be discussed and, in particular, the conditions for controlled formation by self-assembly. In ”Electronic Transport” and ”Optical Properties,” we consider electronic and optical transport properties of nanocrystal arrays, with the main theme being the collective phenomena in these systems, rather than behavior related to the individual nanocrystal. ”Conclusion” contains a brief discussion of outstanding issues and concluding remarks. Because of the limited space, we will focus our article on arrays formed by chemically synthesized nanocrystals only. Therefore lithographically patterned quantum dot arrays will not be discussed. For aspect not covered here and for additional, in depth information on nanocrystal arrays, we refer the reader to Refs. [9-12].

FORMATION OF NANOCRYSTAL ARRAYS

The ultimate goal of nanocrystal self-assembly is the fabrication of highly ordered two-dimensional (2-D) or three-dimensional (3-D) superlattices or other well-defined structures.1-12,13-1 One of the earliest research efforts in this direction can be found in the work of Bentzon et al.[14] who observed uniformly sized Fe2O3 particles to spontaneously form hexagonal arrays. The discovery of high-temperature routes for high-quality semiconductor nanocrystals synthesis further stimulated the development of this field.[15- By now, nanocrys-tals made of metals,[16-20] semiconductors,1-21,22-1 and oxides[14,23,24- have been shown to form ordered NCSs under proper experimental conditions, although the degree of ordering can still vary rather significantly.

In general, the spontaneous formation of nanocrystal superlattices via self-assembly requires the following: 1) a high degree of monodispersity in nanocrystal diameter (typically a relative size deviation in nanocrystal core diameters of less than 5%); 2) a complete coating of core surface with ligand molecules; and 3) suitable physical mechanisms to promote ordered packing. In the following, we discuss the relevant issues associated with the nanocrystal cores, the ligand shells surrounding the cores, and the self-assembly mechanisms.

Nanocrystal Core

There are several different techniques to obtain mono-disperse nanocrystals. High-temperature synthesis is the most widely used since Murray et al.[15] in 1993 obtained high-quality semiconductor nanocrystals by this method. The basic principle behind this kinetically controlled process was actually proposed quite some time earlier.[25] The idea is to oversaturate the nucleating species in a very short period of time, so that there is a burst of nucleation sites at the beginning of the chemical reaction (Fig. 1A). If the concentration of the nucleating species is kept below the saturation level afterward, there will be no new nu-cleation sites. Subsequently, only the existing nucleation sites can grow. By monitoring the growth of particles, different sizes of nanocrystals can be synthesized with high monodispersity. Sugimoto[26] used this idea to synthesize uniform micron-sized spheres. Murray et al. extended this technique to semiconductor nanocrystals by using a high boiling point solvent (mixture of long chain alkylphosphines, alkylphosphine oxides, and alkyla-mines). High reaction temperature, necessary to decompose the organometallic precursor, also results in high crystallinity of the final product (Fig. 1B). The relative size distribution of nanocrystals can, furthermore, be ”focused” in situ by adjusting the concentration of reaction species during the growth.[27]

Fig. 1 Schematic diagrams of various approaches to synthesize monodisperse colloidal nanocrystals. A) Nucleation rate diagram of high-temperature synthesis.[9] B) Experimental setup of high-temperature synthesis.[9] C) Size-selective precipitation technique through solvent replacement.’20-1 D) Digestive ripening process[30] (Parts A and B are reprinted with permission from Ref. [9].

The second technique that is frequently used is the size-selective precipitation method (Fig. 1C).[28,29] This method exploits the fact that the solubility of nanocrystals in a solvent-nonsolvent mixture is highly size-dependent. By slowly adding a nonsolvent into a polydisperse colloid, large particles typically become destabilized and are the first to precipitate out from the solution, which can be separated and redissolved into the original solvent. Increasing the concentration of nonsolvent gradually causes smaller particles to precipitate. By repeating this process, different fractions become increasingly more monodisperse. Whetten et al.[20,29] have coupled this process with mass spectroscopy to obtain nanocrystals of highly precise mass.

Different from the above two methods is a recently developed process called digestive ripening which can transform a polydisperse colloid directly into a more monodisperse colloid through a thermodynamic pathway (Fig. 1D). Lin et al.[30] first demonstrated this process by heating a polydisperse gold colloid in an environment of excess dodecanethiol molecules. The large particles break up into smaller ones upon heating, and the initially polydisperse colloid evolves into a much more uniform system. This is in sharp contrast to the Ostwald ripening process, which favors large particles because of their lower surface energy. Stoeva et al.[31] recently showed that this process is not limited to the gold colloid synthesized by the inverse micelle technique, but works as well for gold colloid prepared by the solvate metal atom dispersion (SMAD) method. This ripening process explains why thiolated gold colloid typically gives particle sizes in the range of 4-6 nm. Although it has been reported that different thiol-gold ratios can be used to adjust the particle sizes,[32] they may be formed in kinetically trapped metastable sizes at room temperature. Reflux heating would eventually drive these particles into thermodynamically favored size ranges.[33- Although the detailed mechanism behind digestive ripening is still under investigation, it has been speculated that inter-molecular interaction and molecular surface interaction might induce a specific ligand packing curvature on the nanocrystal surface, which, in turn, determines the particle size.[31:l

Ligand Shell

In aqueous solution, nanocrystals are typically stabilized by double layers of ions absorbed on the surface.[34-Nanocrystals in the organic solvent generally require coating with an organic ligand shell. There has been quite a variety of ligand molecules used in the literature, such as alkanethiol,[35,36- amine/37- and carboxylic acid.[38- Li-gand shells have several functions. First, and most importantly, they prevent nanocrystals from sintering upon colliding in the solution or on the substrate. The resulting steric repulsive force between ligand molecules is essential to the ordered packing of nanocrystals into arrays.1-34 Molecular dynamics simulation by Luedtke and Land-man[39- showed that ligand molecules interdigitate and even bundle together to form a robust structure that separates nanocrystals in the array. Subsequent high-resolution transmission electron microscopy experiments supported this claim.1-40-

An important point is that the array packing order will depend not only on the particle size dispersion, but also on the integrity of the ligand shells. Adsorption of ligand molecules in the solution is a reversible process, and there is frequent exchange between molecules adsorbed on the nanocrystal surface and molecules in the solution. Therefore repeated precipitation and washing can remove some ligand molecules from nanocrystal surface, which causes incomplete coating of ligand molecules on the surface. Depending on the number of attached ligands and their interactions with those of neighboring nanocrystals, the interparticle spacings will vary when nanocrystals self-assemble on the surface. As a result, for incomplete ligand coating, the average interparticle spacing is typically smaller and has a wider distribution. As shown in Fig. 2, arrays formed by nanocrystals surrounded by an incomplete ligand shell exhibit a much reduced long-range ordering as compared with arrays formed by nanocrystals that have their surface saturated with ligands.[41-

Ligand molecules can also affect the nanocrystal solubility and induce specific interaction with complimentary molecules adsorbed on other nanocrystals or surface. Al-kanethiol with carboxylic acid group on one end can replace straight alkanethiol molecules, therefore allowing nanocrystals synthesized in the organic phase be transferred to aqueous solution.[38- DNA-labeled nanocrystals can form aggregates when complimentary strands of DNA are added and result in a color change that is easy to detect.1-42- Streptavidin-labeled nanocrystals can form a large array through biotin-streptavidin linkage.1-43-

The physical properties of nanocrystals can also be changed by the ligand molecules. For example, electron-donating ligand such as pyridine or CO can change the unpaired electron density of a magnetic nanocrystal, quenching the magnetic moment of surface atoms at-tached.[44- On the other hand, enhanced surface moments were observed for nanocrystals formed in the gas phase without electron-donating ligands on the surface.[45-

Fig. 2 Interparticle spacings for a highly ordered array formed by monodisperse 5-nm Au nanocrystals with complete ligand shell and for a disordered array formed by the same nanocrystals but with incomplete ligand shells. (Image analysis based on transmission electron micrographs was done by N. Mueggenburg.)

Self-Assembly Mechanism

The driving forces for self-assembly of nanocrystals in solution and on surfaces have been extensively studied in a variety of systems.[46-51] The mechanisms are, however, quite complicated, depending on the specific materials, the size and shape of the particles, the charges on their surfaces, and on the physical environment during the self-assembly process. They can be roughly categorized into the following types.

1. Entropy-driven systems. Colloidal particles with strong repulsive interaction can crystallize when the concentration of particles exceeds a critical li-mit.[46-48] This is because the entropy gain associated with local motions around the regular lattice point compared with motion around random sites is sufficient to compensate the entropy loss arising from long-range ordering. In some cases, the structure of colloidal crystals grown from the surface can also be controlled by prefabricated patterns on the surface.[49]

2. Attraction-driven systems. For neutral, uncharged particles of sufficiently large size, van der Waals interaction can be strong enough to induce aggregation. At large distance, the attraction force varies as – AR6/D6, where A is the Hamaker constant, R is the particle radius, and D is the interparticle distance. At small distance, the functional form changes into — AR/D.[50-52] If the attraction force is the only force that acts upon the particles or it is significantly stronger than any other interaction that is present, it will cause irreversible, diffusion-limited aggregation. Ligand coating on nanocrystal surfaces can act as a ”bumper” or buffer layer to prevent such irrevers-ibility. Diffusion of nanocrystals under the influence of the attractive force can lead to formation of large ordered arrays.[16] Care must be taken to minimize the disruptive effect of solvent dewetting to obtain high-quality arrays (Fig. 3).[16] Temperature also plays an important role to anneal out some defect sites during the self-assembly process. For a pair of 6-nm gold particles separated by a gap of 1.7 nm (dodecanethiol chain length), a simple calculation shows that the interparticle van der Waals force is roughly 46 meV, which is comparable to the thermal energy at room temperature. Fig. 4 shows the edge of a self-assembled gold nanocrystal array. Particle sizes are more polydisperse at the edge than in the interior of the domain, presumably because of the thermal annealing effect during the assembly process.

3. Other physically driven systems. Assembly of micron spheres and nanocrystals can also be accomplished by electrophoretic deposition.[53,54] The assembly of particles on the electrode surface is a result of elec-trohydrodynamic fluid flow arising from an ionic current flowing through the solution. By adjusting the electric field strength or frequency, the lateral attraction force between particles can be modulated. This facilitates the reversible formation of two-dimensional fluid and crystalline states on the surface.

Fig. 3 Long-range-ordered gold nanocrystal superlattices formed on silicon nitride substrate by controlling solvent dewetting. Each individual nanocrystal is about 5 nm in diameter.[16] Inset shows the Fourier transformation of a small portion of the image.

Fig. 4 (A) The edge of self-assembled gold nanocrystal superlattices shows a sharp boundary, indicating that diffusion under the influence of interparticle van der Waals forces is responsible for the assembly process. (B-C) The edge of the domain exhibits a large-size polydispersity in size than the interior of the domain, indicating thermal annealing effect during the assembly process.

ELECTRONIC TRANSPORT

Charge transfer through nanocrystal arrays is of great importance not only because of the fundamental new physics involved in such highly correlated system, but also because the modern electronic components are approaching the size limit of standard photolithography techniques.[55- Self-assembled structures based on chemically synthesized nanocrystals have the potential to circumvent such limitations and thus be used as alternative future electronic components.1-56-

The transport through individual nanocrystals has been well-studied both theoretically and experimentally (by both scanning tunneling microscopy[57,58- and two-terminal measurements1-59-). For metal nanocrystal, its main feature is the Coulomb blockade effect, in which transfer of a single electron on or off a nanocrystal is strongly affected by electrostatic interaction with the nanocrystal's charge. Because of the large number of free electrons in metal nanocrystals, the discrete level spacing as a result of quantum confinement effects is small and becomes significant only at very low temperatures, typically ^ 1 K. For semiconductor nanocrystals, the number of free carriers is much smaller and quantum confinement effects, together with the Coulomb blockade, determine transport properties.

Many-particle systems, on the other hand, are not as well understood and are more complex because of the intricacies of coupling between constituent nanocrystals, effects of structural order and disorder, and charge transfer between nanocrystal cores and ligands. A variety of phenomena have been reported in different systems, including spin-dependent tunneling in magnetic particle assem-blies,[18- hopping-type transport in dithiol linked arrays,1-60-and metal-insulator-like transitions in silver nanocrystal monolayers.1-61-63- Arrays of semiconductor particles exhibit interesting time- and illumination-dependent transport which, furthermore, shows striking slow relaxation behavior, reminiscent of glasses.

Our own work has focused on weakly coupled metallic nanocrystal system—monolayers of 5 nm diameter 1-dodecanethiol-ligated gold nanocrystals, self-assembled on silicon nitride substrates—and we will begin our discussion with these arrays as our focus.[65,66- By ''weakly coupled'' we mean that the Coulomb blockade energy, associated with the transfer of individual electrons between individual nanocrystals, dominates transport—the Coulomb or single electron charging energies are large compared with kBT, and the electron wavefunctions, consequently, are localized on the scale of single nano-crystals. A typical current-voltage (/-V) curve at 12 K, from an array of length N~ 50 particles separating the electrodes and width Mk 270 particles, is shown in Fig. 5. There is a significant voltage threshold (VT=4.2 V) below which no current flows. The voltage threshold is the direct consequence of the Coulomb blockade. For each particle, an energetic cost V0 ~ e/er = e/C0, where r is the particle radius, e is the dielectric constant of the medium surrounding the metal core, and C0 is the self-capacitance of the metal sphere, must be paid to transport a single electron onto the charged nanocrystal. For the particles in Fig. 5, V0 is around 100 mV, and VT arises as the sum of this single electron charging energy over all nanocrystals traversed in crossing from one electrode to the other. VT grows linearly with array length: VT = aN(e/C0), where the parameter a (a <1) accounts for interparticle capacitive coupling and the randomness of the offset charges in the underlying substrate that give rise to the Coulomb blockade repulsion.[65-68]

Fig. 5 Current-voltage (/-V) characteristic for a weakly coupled gold nanocrystal superlattice array at low temperature (12 K). The distance between the in-plane electrodes was 330 nm and the array width was 2 mm. The lower inset shows a schematic /-V curve for a single nanocrystal.

Current can flow when the voltage threshold is ex-ceeded—but how, microscopically, do electrons move from nanocrystal to nanocrystal? This can be answered by detailed measurements of the nonlinear current-voltage characteristics as a function of temperature. In the following, we start with a discussion of the low-temperature limit, in which thermal energies can effectively be neglected, and then consider the influence of finite temperatures.