P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 Annu. Rev. Mater. Sci. 2000. 30:545���610 Copyright c by Annual Reviews. All rights reserved SYNTHESIS AND CHARACTERIZATION OF MONODISPERSE NANOCRYSTALS AND CLOSE-PACKED NANOCRYSTAL ASSEMBLIES C. B. Murray and C. R. Kagan IBM T. J. Watson Research Center, Yorktown Heights, NewYork 10598 e-mail: cbmurray@us.ibm.com cheriek@us.ibm.com M. G. Bawendi Massachusetts Institute of Technology, Department of Chemistry, Cambridge, Massachusetts 02139 e-mail: mgb@mit.edu Key Words quantum dot, nanoparticle, superlattice, colloidal crystal, supercrystal ������ Abstract Solution phase syntheses and size-selective separation methods to pre- pare semiconductor and metal nanocrystals, tunable in size from ���1 to 20 nm and monodisperse to ���5%, are presented. Preparation of monodisperse samples enables systematic characterization of the structural, electronic, and optical properties of ma- terials as they evolve from molecular to bulk in the nanometer size range. Sample uniformity makes it possible to manipulate nanocrystals into close-packed, glassy, and ordered nanocrystal assemblies (superlattices, colloidal crystals, supercrystals). Rigorous structural characterization is critical to understanding the electronic and op- tical properties of both nanocrystals and their assemblies. At inter-particle separa- tions 5���100 �� A, dipole-dipole interactions lead to energy transfer between neighboring nanocrystals, and electronic tunneling between proximal nanocrystals gives rise to dark and photoconductivity. At separations 5 �� A, exchange interactions cause oth- erwise insulating assemblies to become semiconducting, metallic, or superconducting depending on nanocrystal composition. Tailoring the size and composition of the nanocrystals and the length and electronic structure of the matrix may tune the prop- erties of nanocrystal solid-state materials. INTRODUCTION Many physical phenomena in both organic and inorganic materials have natural length scales between 1 and 100 nm (102 to 107 atoms). Controlling the physi- cal size of materials can be used to tune materials properties. In the nanometer size regime, new mesoscopic phenomena characteristic of this intermediate state of matter, found in neither bulk nor molecular systems, develop. For example, 0084-6600/00/0801-0545$14.00 545

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 546 MURRAY �� KAGAN �� BAWENDI the electronic and optical properties of metals (1���4) and semiconductors (5���9) strongly depend on crystallite size in the nanometer size regime. Efforts to ex- plore structures on the nanometer length scale unite the frontiers of materials chemistry, physics, and engineering. It is in the design and characterization of advanced materials that the importance of new interdisciplinary studies may be realized. Uncovering and mapping size-dependent materials properties requires synthetic routes to prepare homologous size series of monodisperse nanometer size crystals, known as nanocrystals (NCs). NC samples must be monodisperse in terms of size, shape, internal structure, and surface chemistry. A diverse set of structural probes is combined to characterize and develop consistent structural models of NC samples. Optical, electrical, and magnetic studies of well-defined NC samples reveal the unique size-dependent properties of materials in this intermediate, nanometer size regime between molecular species and bulk solid. When atoms or molecules organize into condensed systems, new collective phenomena develop. Cooperative interactions produce the physical properties we recognize as characteristic of bulk materials. Like atoms or molecules, but in the next level of hierarchy, NCs may also be used as the building blocks of con- densed matter. Routes enabling controlled manipulation of NCs into the glassy and ordered states of matter lead to the preparation of close-packed NC solids. Assembling NCs into solids opens up the possibilities of fabricating new solid- state materials and devices with novel physical properties, as interactions between proximal NCs give rise to new collective phenomena. Building upon rigorous un- derstanding of the physical properties of individual NCs, the properties of coupled NCs in the solids are uncovered. Engineering the size and composition of the NCs and the length and chemical functionality of the matrix may be used to tune the unique properties of the individual NC building blocks and those arising from coupling between proximal NCs. Although many of the concepts presented in this review are general to a range of monodisperse NC systems, we often use studies of CdSe NCs to illustrate the preparation and characterization of NCs and their assemblies (10, 11). PREPARATION OF MONODISPERSE NANOCRYSTALS (NCS) Introduction The preparation of nearly monodisperse organically passivated NC samples is es- sential to permit studies that distinguish truly novel properties inherent to nanoscale structures from those associated with structural heterogeneities or polydispersity. Although the strict definition of monodisperse requires that particles be identi- cal or indistinguishable, a relaxed definition is used here (12). Samples with standard deviations �� ��� 5% in diameter are referred to as monodisperse. This

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 547 corresponds to �� one lattice constant throughout the 1���15-nm size range. NCs must be uniform not only in size and shape, but they must also have well-formed crystalline cores and controlled surface chemistry. We reserve the term nanocrys- tals (NCs) for structures with well-characterized crystalline cores and use the more general term, nanoparticles, to denote amorphous or inherently multidomain inor- ganic cores. Although non-crystalline and multidomain nanoparticles can display a wealth of interesting size-dependent phenomena, this review emphasizes crys- talline systems. We restrict our discussion to procedures that can reproducibly prepare a homologous size series of NC samples with rational adjustments of the experimental conditions and focus on NCs that have been employed as nanoscale building blocks in assembling new designer solids. General Synthesis and Processing of Monodisperse NCs Classic studies by La Mer & Dinegar show that the production of monodisperse colloids requires a temporally discrete nucleation event followed by slower con- trolled growth on the existing nuclei (Figure 1A) (13). Rapid addition of reagents to the reaction vessel raises the precursor concentration above the nucleation thresh- old. A short nucleation burst partially relieves the supersaturation. As long as the consumption of feedstock by the growing colloidal NCs is not exceeded by the rate Figure 1 (A) Cartoon depicting the stages of nucleation and growth for the preparation of monodisperse NCs in the framework of the La Mer model. As NCs grow with time, a size series of NCs may be isolated by periodically removing aliquots from the reaction vessel. (B) Representation of the simple synthetic apparatus employed in the preparation of monodisperse NC samples.

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 548 MURRAY �� KAGAN �� BAWENDI of precursor addition to solution, no new nuclei form. Since the growth of any one NC is similar to all others, the initial size distribution is largely determined by the time over which the nuclei are formed and begin to grow. If the percentage of NC growth during the nucleation period is small compared with subsequent growth, the NCs can become more uniform over time (14). This phenomenon has been referred to as focusing of the size distribution. Many systems exhibit a second, distinct, growth phase called Ostwald ripening (15, 16). In this process the high surface energy of the small NCs promotes their dissolution, whereas material is redeposited on the larger NCs. The average NC size increases over time with a compensating decrease in NC number. Exploiting Ostwald ripening can greatly simplify the preparation of a size series of NCs (17). Portions of the reaction mixture can be removed at increments in time, as depicted in Figure 1A. Raw material can often be extracted with initial distributions of 10 �� 15% in diameter, which are then narrowed to ���5% through size-selective processing. Preparation of Monodisperse Semiconductor NCs In the growth of compound semiconductor NCs, the requisite supersaturation and subsequent nucleation can be triggered by rapid injection of metal-organic precursors into a vigorously stirred flask containing a hot (���150���350���C) coordinating solvent. The solvents usually used are mixtures of long-chain alkylphosphines R3P, alkylphosphine oxides R3PO (R = butyl or octyl), alkylamines, etc (17). A representation of the synthetic pro- cess is shown in Figure 1B. In the synthesis of II-VI NCs (ME where M = Zn, Cd, Hg E = S, Se, Te), metal alkyls (dimethylcadmium, diethylcadmium, diethyl- zinc, dibenzylmercury) are generally selected as the group II sources. The group VI sources are often organophosphine chalcogenides (R3PE) or bistrimethylsi- lylchalcogenides TMS2E (TMS, trimethylsilyl) (where E = S, Se, and Te). The R3PE class of reagents is usually preferred as Se and Te sources because they are easy to prepare TMS2S is selected as the S source because it is more reactive than R3PS and is commercially available. The use of mixed precursors, for example a combination of Se and S precursors, leads to the straightforward production of al- loys, although the NCs��� stoichiometry does not directly reflect the precursor ratio, but rather the differential rate of precursor incorporation. Growth of II-VI NCs is not limited to the use of R3P and R3PO as high boiling coordinating solvents. Injection of reagents into hot alkylphosphites, alkylphosphates, pyridines, alkylamines, and furans all produce NCs. Mikulec recently demonstrated that using alkylphosphoramide-tellurium precursors, in lieu of R3PTe, produces CdTe NCs with much higher luminescence efficiencies (18). The strong interaction of R3PO with Zn precursors unduly retards the growth of ZnE NCs. Although R3P may still be employed, Guyot-Sionnest and co-workers found that using alkylamines as the coordinating solvent greatly enhances the growth rate of ZnE NCs (19). Similarly, synthesis of high-quality InP and InAs NCs has been achieved by rapidly mixing and heating of III and V precursors in high boiling, coordinating sol- vents. Preparations of InP and InAs NCs are now capable of yielding samples with

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 549 �� ��� 10%. Typically InCl(C2O4) is employed as an In source with TMS3P or TMS3As in R3P/R3PO solvents (20���22). In these III-V preparations the In precur- sor is present in the hot solvent prior to the injection of TMS3P or TMS3As. Growth of the NCs is slow since Ostwald ripening over 1 to 6 days is required to reach the desired NC size. A wealth of other potential organometallic precursors and high-boiling coordinating solvents remain untested, thus providing opportunities for continued expansion to new NC systems. Preparation of Monodisperse Metal NCs The synthesis of metal colloids has been studied for over a century and yet the number of preparations yielding a size series of monodisperse metal NC samples is surprisingly small. The most established methods involve aqueous reduction of metal salts (notably Au or Ag) in the presence of citrate anions (23). These colloids are electrostatically stabilized by the adsorption of ions to the NCs��� surfaces during growth. These samples have long been referred to as monodisperse, although in general 10 �� 15%. Flocculation of these colloids is irreversible, preventing further processing to achieve the desired �� ��� 5%. Chemisorption of organic ligands on the surface of metal NCs is essential to permit further handling. Schmid provides an excellent overview of the advances in metal colloid synthesis (24, 25). A two-phase reduction method, described by Brust, Schiffrin, and co-workers, when coupled with size-selective processing produces capped Au and Ag NCs with �� ��� 5% (26). In general, aqueous metal salts (e.g. HAuCl4, AgNO3, AgClO4) are mixed in a toluene solution containing long-chain alkylammonium surfactants to form a two-phase system. Vigorous stirring for 1 to 3 h transfers the metal salt into the organic phase, which is then separated. A measured quantity of capping agent, typically a long-chain thiol, is added to the solution while stirring, and then a reducing agent (e.g. NaBH4 or hydrazine) is rapidly added to nucleate NCs. The average NC size is coarsely tunable by adjusting the ratio of capping groups to metal salt, whereas size-selective precipitation is employed to narrow the initial size distribution. Several studies have refined the preparation of thiol capped Ag and Au NCs (27, 28). The preparation of metal NCs in inverse micelles warrants mention. The inverse micelle method has been employed since the late 1980s for the preparation of both semiconductor and metal NCs. Although it is widely adopted, samples approach- ing the desired �� ��� 5% are rarely observed. However, Pileni and co-workers provide a notable exception by coupling the initial synthesis with extensive use of size-selective precipitation to yield high quality Ag (29), AgS (30), and more recently Co NCs (31). Higher temperature reduction of metal salts in the presence of stabilizing agents can also be employed to produce monodisperse transition metal (e.g. Co and Ni) NCs that do not crystallize well at room temperature (RT) (32). In this general scheme metal halides or acetates are dissolved in high-boiling inert sol- vents (e.g. octylether, phenylether) along with a combination of R3P and long- chain carboxylic acids (e.g. oleic acid). The solution of metal salts and stabi- lizers is vigorously stirred and heated to ���200���250���C at which time a solution

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 550 MURRAY �� KAGAN �� BAWENDI containing a strong reducing agent [e.g. LiHB(CH2CH3)3, Na naphthalide, etc] is injected. Metal NCs nucleate and grow until the reagent is consumed. Although no Ostwald ripening is observed, NC size is coarsely tunable by the ratio of capping groups to metal salt. Size-selective precipitation yields NC samples with �� ��� 5%. Progress has also been made in the preparation of monodisperse bimetallic NCs. For example, see the work by Bradley and co-workers (33). Figure 2A���D shows high-resolution transmission electron microscopy (HRTEM) images of some of the NC materials that can currently be prepared and isolated. NC Core/Shell Structures Techniques to overcoat NCs with an inorganic shell are remarkably general with only a few modest constraints: (a) The existing NC Figure 2 Collection of high resolution TEM images for typical NC materials such as (A) h100i-oriented CdSe (scale bar = 15 �� A), (B) h001i-oriented CdSe (scale bar = 15 �� A), (C) CdTe (scale bar = 20 �� A), and (D) Co (scale bar = 25 �� A) (31) [CdSe images courtesy of Kadavanich (62) CdTe courtesy of F Mikulec].

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 551 seeds must withstand the conditions under which the second phase is deposited, (b) the surface energies of the two phases must be sufficiently similar so that the barrier for heterogeneous nucleation of the second phase is lower than that for homogeneous nucleation, and (c) the seed NC and the overcoat material must not readily interdiffuse under the deposition conditions. Typically seed NCs are prepared and isolated by one of the standard procedures outlined above, size- selected, and then redispersed in a fresh solution of solvent and stabilizers. The solution is then heated while precursors for the inorganic shell are gradually added to allow the material to heterogeneously nucleate on the seed NCs. If the rate of precursor addition does not exceed the rate of deposition on the seeds, the precursor concentration never reaches the threshold for homogeneous nucleation of a second inorganic phase. Methods for overcoating a semiconductor NC with a second semiconductor material of wider bandgap are well developed. For example, CdSe nanocrystals have been overcoated with ZnS (34���36), ZnSe (37), and CdS (38), which resulted in dramatic improvements in luminescence efficiency, exemplified by the work on CdSe/ZnS by Guyot-Sionnest and co-workers (35). Mews, Weller, and co-workers have overcoated CdS NCs with lower bandgap materials such as HgS (39), while others have coated CdTe cores with HgTe shells (40). The HgS shell in CdS/HgS systems has in turn been buried by the deposition of new CdS material to produce a shell of low-bandgap HgS nested in a wider bandgap NC structure (41). Peng and co-workers showed that steady secondary addition of reagents, com- mon for overcoating NCs, could also dramatically improve the synthesis of single component systems (42). By following the initial nucleation of II-VI and III-V NCs with a calculated secondary addition of the original precursors, NC growth is accelerated and the size distribution is focused, as predicted by Reiss (14). This modified synthesis often yields samples where 5% �� 10% in the reaction flask, thus minimizing the need for size-selective processing. Cap (Ligand) Exchange Stabilizing agents must be present during growth to prevent aggregation and pre- cipitation of the NCs. When the stabilizing molecules are attached to the NC surface as a monolayer through covalent, dative, or ionic bonds, they are referred to as capping groups (43). These capping groups serve to mediate NC growth, sterically stabilize NCs in solution, and passivate surface electronic states in semi- conductor NCs. This surface capping is analogous to the binding of ligands in more traditional coordination chemistry. Synthetic organic techniques allow the tail and head groups to be independently tailored through well-established chem- ical substitutions. NC surface derivatization can be modified by ligand exchange: repeated exposure of the NCs to an excess of a competing capping group, followed by precipitation to isolate the partially exchanged NCs (10, 17, 44). Repeating this cycle allows more complete exchange. This recursive approach can cap NCs with a wide range of chemical functionalities, even if the binding of the new cap is less

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 552 MURRAY �� KAGAN �� BAWENDI favorable than the original. The cap exchange process has been used extensively to adjust the dimensions of the organic layer surrounding the NCs and thus the minimum inter-particle spacing in NC assemblies (45). Isolation and Purification of NCs NCs are stable with respect to aggregation only if the capping groups provide a repulsive force of sufficient strength and range to counteract the inherent van der Waals attraction between NCs. The energetic barrier to aggregation provided by the capping groups is strongly dependent on the energy of mixing between the tethered capping groups and the solvent. Introduction of a nonsolvent, miscible with the original dispersing solvent, destabilizes the NC dispersions. The NCs then aggregate and precipitate leaving many of the synthetic by-products in solu- tion. If the capping groups are well bound to the surface of the NCs, the resulting powders are redispersible in a variety of solvents: alkanes, aromatics, long-chain alcohols, chlorinated solvents, and organic bases (e.g. amines, pyridines, furans, phosphines). Repeated flocculation and redispersion of the NCs in fresh solvents allow the isolation of powders composed of the desired NCs and their intimate or- ganic capping layer (17). A straightforward extension of this precipitation process allows the isolation of size-selected fractions of NCs (46). Size-selective precipitation involves either the titration of a nonsolvent into the dispersion (17) or the preferential evaporation of solvent from a mixed sol- vent/nonsolvent system to bring about gradual flocculation (47). Since the largest NCs in the size distribution exhibit the greatest attractive van der Waals forces, they tend to aggregate before the smaller NCs. As aggregates of larger NCs form, there is a natural tendency to exclude smaller NCs (48, 49). If the disper- sion is allowed to only partially flocculate, filtering or centrifuging the suspension isolates a precipitate enriched in the larger NCs and leaves the smaller NCs dis- persed in the supernatant. The precipitate can be redispersed in a solvent and subjected recursively to this gentle flocculation procedure to further narrow the size distribution. Similarly, gradual addition of more nonsolvent to the decanted supernatant brings about a precipitation of a second size fraction. Size-selective precipitation is analogous to purification by fractional crystallization (50) or long- standing methods to fractionate polymers on the basis of molecular weight. Nar- rower initial size distributions allow the desired �� value to be attained with fewer stages of size-selective precipitation and thus higher yield. Slower destabilization leads to more efficient separation of the sizes, yet even well-practiced separations of NCs with an initial �� ��� 10%, yields ���30% of the initial NC sample with �� ��� 5%. Gel permeation (size exclusion) chromatography can also be employed to nar- row an initially broad size distribution, although once again the yield is limited and the process is slow (51). Wilcoxon and co-workers provide some current examples of efforts to separate NCs using chromatographic techniques (52).

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 553 CHARACTERIZATION OF THE NC CORE AND SURFACE Introduction Many studies have investigated the structure and chemical composition of NCs in an effort to reveal the structure/property relationships as the crystals grow from molecular species toward bulk solids. This is a tremendous interdisciplinary chal- lenge because the smallest NCs ( 1 nm) are nearly molecular ( 100 atoms) and the largest NCs ( 20 nm) contain 100,000 atoms. In this size range the percent- age of surface atoms goes from 75% to 0.5%. Standard chemical and surface sensitive probes are well suited for studies of the smallest species whereas physical probes, which exploit the periodicity of the internal NC lattice, are better suited for the largest species. Chemical Analysis of NCs Detailed elemental analysis is the first essential step in developing a model of NC structure. Techniques as diverse as atomic absorption and emission, neutron acti- vation, X-ray fluorescence, and mass spectroscopy (53) can be employed to reveal the composition of the average NC. The use of specific chemical spectroscopies, including infrared absorption and solution phase and H1 and C13 nuclear magnetic resonance (NMR) (54���55), photoelectron spectroscopy (56), and electron energy loss spectroscopy (EELS) (57), often aid in determining not only what species are present but how the components are distributed between NC surface and core. In addition, solid-state Se77 (58) and P31 (59) NMR have been used to investigate the inorganic species at the NC/organic interface of CdSe and InP, respectively. When these studies are combined, rational descriptions of the organic capping layer and the near surface region of the NCs emerge. Structural probes such as transmission electron microscopy (TEM), extended X-ray absorption fine structure (EXAFS) spectroscopy, small-angle X-ray scat- tering (SAXS), and wide-angle X-ray scattering (WAXS) are powerful probes of NC shape and internal structure. If the results of these diverse techniques can be made consistent with a single atomistic model of average NC structure, a coherent description of the system is possible. Transmission Electron Microscopy of NCs TEM is arguably the single most powerful technique for characterizing NCs and their assemblies. Routine low-resolution TEM studies image ensembles of NCs, permitting a statistical description of the size and shape of NCs in a sample to be developed. HRTEM imaging reveals the individual NC shape and internal structure. TEM studies of small metal NCs have been reviewed (60, 61). The methods developed for metal NCs are equally applicable to the study of dielectric and semiconducting NCs.

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 554 MURRAY �� KAGAN �� BAWENDI Examples of HRTEM images for CdSe (62), CdTe (18), and Co NCs (32) are seen in Figure 2. The relationship between the observed interference fringes and the underlying crystal lattice can be complex, and care must be taken when using real-space images as evidence for subtle lattice reconstructions or precise measures of lattice constants (63, 64). However, it is useful to develop a list of the observed structural motifs and their relative probabilities. Evidence of new structural phases of metals may also be observed in TEM of small NCs. Figure 2D shows an image of a well-formed 80 �� A diameter Co NC with a cubic lattice structure that does not correspond to the known hcp or fcc phases of cobalt. The NC structure is that of the beta phase of manganese and the label ��-Co has been proposed (65) for this new form of Co metal. A number of studies also indicate that multiply twinned structures may in fact be the lowest energy configurations for many metal NC systems (60, 61). These rough statistics are used to form an initial set of parameters for simulations of NC structure. Extensive surveys of NC samples ranging from ���25 to 150 �� A in diameter yield some general qualitative and quantitative results regarding NC size, shape, and structure. In an effort to provide accurate measurements of size, the lattice fringes of the NCs are used as an internal standard. Counting the number of lattice planes or atom columns in each NC is used to determine NC size and calibrate the magnification of the image. Measurement of several hundred NCs in a series of images, like those shown in Figure 3, are employed to develop a statistical model of NC size and shape, while 10 to 20 HRTEM images, of the type shown in Figure 2A���D, are used to develop a description of internal NC structure. These limited observations must be compared with X-ray scattering studies, which simultaneously probe statistically large ensembles of NCs. Small-Angle X-Ray Scattering of NCs SAXS studies of monodisperse NC samples reveal scattering structure previously cloaked by polydispersity and have greatly simplified the analysis (10, 66���69). The SAXS intensity, I(q), scattered from a collection of N, non-interacting particles, of rigorously uniform electron density, ��, in a homogeneous medium of density, ��o, is given by I(q) = IoN(�� - ��o)2F2(q). 1. F(q) is the form factor���the Fourier transform of the shape of the scattering object. For spheres of radius R, the form factor is expressed by (70, 71) F(q) = 4 3 ��R3 ��� 3 sin(qR) - qR cos(qR) (qR)3 ��� . 2. Figure 4A curve (a) shows the calculated pattern for a collection of 62 �� A monodis- perse spheres of rigorously uniform electron density. Real objects are not of uniform electron density. Each atom in the structure provides a local modulation

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 555 Figure 3 Large-field TEM images are employed to develop statistics on NC size and shape. A collection of 48 �� A CdSe NCs at (A) low magnification (scale bar = 200 �� A) and (B) higher magnification (scale bar = 80 �� A) (45) monolayer of 80 �� A Co NCs at (C ) low magnification (scale bar = 500 �� A) at (D) higher magnification (scale bar = 65 �� A) (32). that introduces a broad scattering background. Curve (b) shows the scattering pattern for a 4500-atom spherical fragment (���62 �� A) of the bulk CdSe wurtzite lattice. The signal is the sum of the scattering from atomic sites (the broad back- ground) as well as the coherent scattering from all discrete distances within the NC. Scattering from atomic sites scales like the volume (���R3), while the inten- sity of the oscillations from NC shape scales like the square of the volume (���R6). In large particles, such as micron size latex and silica, the contribution from atomic scattering becomes negligible. Neglecting this contribution in NC systems,

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 556 MURRAY �� KAGAN �� BAWENDI Figure 4 (A) SAXS patterns for model structures having 4500 atoms, comparable to a 62 �� A diameter CdSe NC (symbols). The curves are models for (a) 62 �� A spheres of uniform electron density (b) monodisperse, 4500 atom spherical fragments of the bulk CdSe lattice (c) monodisperse, 4500 atom ellipsoidal fragments of the bulk CdSe lattice, having a 1.2 aspect ratio and (d) fit to SAXS data (dots) assuming a Gaussian distribution of ellipsoids (as in curve c), yielding the NC sample size and size distribution. (B) SAXS patterns for CdSe NC samples ranging from 30 to 75 �� A in diameter (dots). Fits are used to devise the NC sample size, reported in equivalent diameters, and size distributions, ranging from 3.5 to 4.5% for the samples shown.

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 557 however, would result in an overestimation of the size distribution. TEM stud- ies indicate that many NC systems are better described as ellipsoids than spheres (17, 62). The scattering from elliptical particles has been dealt with extensively elsewhere (72, 73). We use an atomistic model, discussed below, to calculate SAXS scattering. The model system is essentially a collection of ellipsoidal frag- ments of the bulk lattice of the respective NCs. Although the detail of the internal structure has little effect of the SAXS pattern, the atomistic model also reproduces the wide-angle scattering as well. Small variations in NC size and shape quickly wash out the oscillations in SAXS. The amplitude of the oscillations allows deter- mination of NC size and size distribution with greater confidence than any other structural technique. Curve (c) shows the predicted pattern for a monodisperse ensemble of prolate (aspect ratio 1.2 as determined by TEM) fragments of the bulk CdSe lattice containing 4500 atoms. Curve (d) (dots) shows the experimental re- sults and fit (solid line) to an atomistic model of SAXS scattering created from the statistical observations of TEM. Experimental SAXS patterns (dots) and computer simulations (solid lines) are used to measure size and size distribution for a size series of CdSe NCs (Figure 4B). Korgel & Fitzmaurice have recently published a detailed study of monodisperse Ag NCs using SAXS (68, 69). Wide-Angle X-Ray Scattering of NCs WAXS like SAXS probes a statistically large number of NCs. WAXS reveals the internal structure of the average NC core and permits measurement of NC size and shape (17, 74, 75). Experimental WAXS patterns for CdSe NCs ranging from 17 to 90 �� A in diameter (Figure 5A) show evidence of finite size broadening in all reflections. The diffraction feature centered at ���25��� 2�� is a convolution of several crystallographic reflections, and thus its average position and width are not appro- priate for simple estimates of lattice parameters or NC size. Excessive attenuation and broadening of (102) and (103) reflections are signatures of stacking faults along the h002i axis, as observed in HRTEM. Experimental and computational WAXS studies of NC ensembles demonstrate the sensitivity of diffraction to NC size, shape, and planar disorder and to thermal effects (17, 74). These studies are extended to probe the evolution of NC structure with size and address the importance of NC shape and the possibility of lattice contractions. The intensity of X-ray scattering, I(q), is described by the Debye equation: I(q) = I0 XX m n FmFn sin(qrmn) qrmn , 3. where Io is the incident intensity, q = 4��sin(��)/2�� is the scattering parameter for X-rays of wavelength �� diffracted through the angle ��, rmn is the distance between atoms m and n, with atomic form factors Fm and Fn, respectively (75). A discrete form of the Debye equation is given by I(q) = Io f2(q) q X k ��(rk) rk sin(qr), 4.

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 558 MURRAY �� KAGAN �� BAWENDI Figure 5 (A) WAXS patterns for CdSe NC samples ranging from 17 to 90 �� A in di- ameter. (B) Three-dimensional representation of a CdSe NC, as developed from TEM studies, exemplifies the atomistic structure employed in SAXS and WAXS modeling (62). (C ) SAXS and WAXS pattern for an ���4500 atom (62 �� A) CdSe NC samples (dots). Simul- taneous fitting, using nonlinear least squares methods, to the SAXS and WAXS patterns fits the sample average NC size to ���4500 atoms, aspect ratio to 1.2 (prolate), and size distribution to 4.2%. where the summation is taken over all inter-atomic distances rk, which occur with the number ��(rk) times in a given NC (75). Since the number of unique inter- atomic distances in an ordered structure grows much more slowly than the total number of distances, using the discrete form of the equation is significantly more efficient in simulating scattering from large NCs. Atomic coordinates for the simulated NCs are obtained by systematically gen- erating positions for atoms in a bulk crystalline lattice falling within a defined ellipsoid. Approximate NC size and shape measured by TEM are used to initially define the dimensions of the model ellipsoids that are then refined in simulations by simultaneous fitting of the WAXS and SAXS patterns (10). In the case of CdSe, planar disorder along the h002i axis is extracted by fitting WAXS patterns to atomic coordinates for a set of model structures having n randomly distributed stacking faults, where n = 1, 2, or 3. Thermal effects are simulated by introducing

P1: FUI June 9, 2000 14:25 Annual Reviews AR101-18 MONODISPERSE NANOCRYSTAL ASSEMBLIES 559 a Debye-Waller factor. A schematic of such an atomistic model is shown in Figure 5B. Figure 5C shows a representative simultaneous fit of a SAXS pattern, collected from NCs dispersed at 1% by weight in polymer, and a WAXS pattern, collected from a NC powder, of the same 64 �� A CdSe NC sample with ���4.2% size distribution. Simultaneous fitting of the SAXS and WAXS patterns using parameters con- sistent with TEM observations and EXAFS studies (discussed below) unites the results of these diverse structural probes to yield a description of average NC struc- ture. The small NCs are often referred to as clusters because they possess too few atoms to define a core crystal structure and thus distinguish between structural motfis. This is observed in diffraction patterns of the smallest members of the CdSe series (Figure 5A), 17 to 22 �� A in diameter, as an abrupt transition in the WAXS patterns. This transition in the diffraction features indicates a significant surface reconstruction or change in NC shape. In 17 �� A NCs, all the atoms in the cluster are less than two bond lengths from the surface, and thus a local structural probe of bond length, such as EXAFS, is better suited to their characterization. EXAFS refers to the complex, oscillatory character of the X-ray absorption of a material at energies between 40 and 1000 eV above its characteristic absorp- tion edge. This oscillatory behavior depends on the environment of the absorbing species and provides a measurement of bond length (76). Studies, for example on 15 and 35 �� A CdE (E = S, Se, and Te) NCs (77), can be fit with atomistic models of NC structure and are consistent with NC structural models developed from WAXS, SAXS, and TEM measurements. EXAFS has also been used to study the local structure of bimetallic NCs (78). The smallest species of CdS have been isolated as molecular crystals, permit- ting unambiguous determination of the internal NC structure using single-crystal diffraction techniques (79, 80). In an elegant series of experiments, Weller and co- workers made direct comparisons between EXAFS and single-crystal diffraction results (81). The application of a diverse array of common chemical and structural probes to a homologous size series of monodisperse samples yields self-consistent models of the average NC structure in many materials systems. OPTICAL AND ELECTRONIC PROPERTIES OF DISPERSED NANOCRYSTALS Optical Properties Nanometer size semiconductor NCs smaller than the Bohr radius of the bulk exciton strongly confine electronic excitations in all three dimensions (82, 83). Photoexcitation of the NC creates an electron-hole pair that is confined to and delocalized over the volume of the NC. The photophysical properties of the NC are analogous to those of a large molecule. In the strong confinement regime, the electron and hole can be treated independently, and the electronic structure of the NC can be modeled using simple effective mass theory (see the review by Efros