Nanocrystalline structures of compound semiconductors, such as the II-VI compounds ZnS, CdSe, and ZnSe, etc., exhibit size-dependent optoelectronic properties, and form the basis for a new generation of highly-integrated nano-electronic and photovoltaic devices. Nanocrystalline grains of these materials (also called quantum dots) exhibit size-dependent luminescence due to quantum confinement of optically excited electron-hole pairs (excitons) by the grain boundary. There has been strong interest from the research community on developing synthesis techniques that allow precise control of the size of these nanocrystals and, as a result, precise tuning of their optoelectronic properties.

Recently, stoichiometric II-VI nanoparticles with structures that are very different than the bulk crystalline structure of these materials have been identified by mass spectroscopy. The mass spectroscopy studies indicate that ultra-stable stoichiometric clusters containing 13, 33, or 34 atoms of each element can be formed. These are referred to as “magic-size clusters” (MSCs) and are believed to have a closed-cage structure that eliminates surface dangling bonds. Our objective is to analyze the relative stability of such II-VI clusters and to gain a fundamental understanding of the structure, energetics, and morphology of these intersting nanoparticles.

In this work, we focus on a detailed analysis of the stability, structure, and formation energetics of (ZnSe)_n and (CdSe)_n (n = 1-30) clusters. In our study, we have employed a variant of simulated annealing based on first-principles density functional theory (DFT) calculations for the corresponding energy computations. The simulated annealing variant uses a standard Metropolis Monte Carlo (MC) algorithm for geometry optimization in search of global energy minima. The DFT calculations are carried out within the generalized gradient approximation and employ plane-wave basis sets, ultra-soft pseudopotentials, and supercell models; our calculational scheme was thoroughly tested in computations of bulk ZnSe and CdSe structures.

Following this computational method, we have obtained the lowest-energy clusters for both (ZnSe)_n and (CdSe)_n nanostructures, with a size “n” varying over the range 1-30. Based on the formation energetics of these clusters, we have analyzed their relative stability and investigated the existence and exceptional stability of MSCs. Our calculations reveal that MSCs are cage-like structures, analogous to fullerenes, and that they correspond to the most stable (ZnSe)_n and (CdSe)_n nanostructures. Clusters of smaller sizes (n = 1-4) are found to have planar geometries and may serve as building blocks for larger-size clusters.

In addition to studying the stability of the MSCs, we have analyzed cluster-cluster interactions and cluster coalescence. Our theoretical analysis reveals that smaller clusters, owing to a large surface-to-volume ratio, can coalesce and form an MSC through an exothermic reaction. The energy released during the reaction is due to the minimization of the unsaturated surface bonds. A better understanding of the structure and stability of MSCs can allow the development of synthesis techniques for preparing these materials. A new class of cluster-based materials is also envisioned with II-VI MSCs as the bulding blocks. Such materials are expected to have unique optoelectronic and mechanical properties.