Polarizabilities of Isolated Silicon Clusters

Abstract

The static electric polarizabilities a of silicon clusters with up to 60 atoms have been measured employing a mass selective molecular beam deflection method. The polarizability per atom αN = α/N of the SiN-clusters has been investigated for Si11 and the size ranges N = 14-28, 22-34, 28-44, 34-50, 41 -58, and 42-68. The results show that the polarizability per atom decreases from N = 11 until a minimum at N≥28 is reached. The polarizability per atom increases for N > 28, passes through a maximum at N≈36 and finally converges between N≈50-70 against the value αN =1.9Å3. If the model of a homogeneous dielectric sphere is applied to the larger clusters one calculates that the value αN =1.9Å3 corresponds to a dielectric constant of ε = 3.2. This value is significantly smaller than the dielectric constant of bulk silicon εb = 11.8. The present paper focuses on the maximum in the polarizability at N≈36. This effect is discussed with special emphasis to recent Car-Parinello calculations which have predicted cage-like silicon structures that enclose a core of several highly coordinated atoms. This structure suggests an improved dielectric sphere model where the core is represented by a smaller sphere with its own dielectric constant εc. It is shown within this model that the observed maximum in polarizability is due to a significant enhancement of the core dielectric constant to a value of εc ≈50. This enhancement is related by means of a simple model to the effect that silicon becomes metallic under high pressure