Collective optical properties of silver nanoparticles organized in two-dimensional superlattices A. Taleb, V. Russier, A. Courty, and M. P. Pileni* Laboratoire SRSI, URA 1662, Universite ´ Pierre et Marie Curie (Paris VI), Boı ˆte Postale 52, 4 Place Jussieu, F.75231 Paris Cedex 05, France and CEA-Saclay, DRECAM-SCM, F.911 91 Gif-sur-Yvette, France Received 20 April 1998; revised manuscript received 6 October 1998 In this paper we describe collective properties of silver nanoparticles organized in two-dimensional super- lattices. Our aim is to show that we can control the state of organization of the silver particles deposited on the substrate. Then the particles are found in the form of either a well-organized two-dimensional array of isolated particles or disordered and coalesced particles distributed more or less randomly on the surface. The optical spectra are compared with both polarized and unpolarized light. When particles are arranged in a hexagonal array, an asymmetrical and broad peak is observed. Under p-polarized light, a new high-energy peak appears that is interpreted as a collective effect, resulting from the mutual interactions between particles. We support this conclusion from numerical calculations performed on finite-size clusters of silver spheres, where only the electrodynamic interactions between the spheres are taken into account. With disordered and coalesced system the high-energy peak disappears whereas a peak toward low energy is observed. This is attributed to coalesced particles. S0163-18299912415-9 I. INTRODUCTION Well-defined, ordered solids prepared from tailored nanocrystallite building blocks provide opportunities for op- timizing properties of materials and offer possibilities for observing interesting, new, and potentially useful collective physical phenomena. In the past few years, several tech- niques have been developed for directing the self-assembly of nanocrystals into ordered aggregates or quantum dots superlattices. 1–11 These assemblies present some very excit- ing possibilities. In principle, interparticle separations, par- ticle size, and particle stoichiometry may be individually controlled to produce a macroscopic solid with a tailored band structure. This is similar to the well-known case of a one-dimensional quantum dot superlattice that might be en- gineered to provide unique physical properties. Such materi- als could be important constituents of tunnel resonance resistors 12 in microelectronic devices. Large classes of material can be produced by using re- verse micelles as templates. 1–3 Several years ago, by using this technique, we demonstrated that nanosized silver metal particles can be obtained. 13 The particle size was controlled from 2 to 8 nm and the optical properties of these clusters confirm predictions based on simulations. To decrease the size distribution, a size selection precipitation method was used. 14 Particles were arranged either in monolayers orga- nized in a hexagonal network, or in three-dimensional 3D superlattices with a face-centered-cubic fcc structure. 14 Similar arrangements were obtained a few years ago with silver sulfide nanoparticles. 15–17 By using different prepara- tion modes, several groups have succeeded in forming pat- terns with gold and silver nanosized particles. 18–24 We pre- viously compared the optical properties of nanosized silver particles dispersed in hexane solution and self-assembled in 2D or 3D networks. 25 In this paper, the optical properties of silver particles de- posited on a cleaved graphite substrate organized or not in 2D superlattices are presented. A peak toward high energy compared to that of isolated particles is observed. It disap- pears when particles are either disordered and coalesced. In order to explain qualitatively this optical response numerical calculations of the extinction cross section for finite-size clusters of spherical silver particles are presented. II. EXPERIMENT A. Products AOT was purchased from Sigma. Isooctane, hexane, and pyridine were from Fluka. Hydrazine and dodecanethiol were obtained from Prolabo France and Janssen chemi- cals, respectively. The materials were not purified any fur- ther. Silver di2-ethyl-hexyl sulfosuccinate, AgAOT, was prepared as described previously. 26 The graphite substrate highly oriented pyrolytic graphite HOPG were obtained from Carbon Loraine France. B. Optical measurements and characterization Measurement of the optical spectra have been performed on a conventional Varian Cary I spectrophotometer equipped with rotational stages for angular measurement in the energy interval 1.9E 4.9 eV. The polarization of the light can be perpendicular s or parallel p to the plane of incidence and the angle of incidence can range from 15° to 60° with respect to the surface normal. For particles in solution, absorption spectra were recorded in 2-mm cuvettes. For particles depos- ited on a cleaved carbon graphite substrate, the difference reflectance  R between the substrate with the particles on its surface and the clean substrate has been measured. The band- width have been measured at half-maximum by taking the minimum at low energy approximately 2 eV as a reference for the zero of the spectra. The transmission electron mi- croscope JEOL 100CX operates at 100 kV. The mean di- PHYSICAL REVIEW B 15 MAY 1999-II VOLUME 59, NUMBER 20 PRB 59 0163-1829/99/5920/133509/$15.00 13 350 ©1999 The American Physical Society