Size-Dependent Evolution of Conduction-Electron Excitations in Small Spherical Particles

Summary

We report on the size-dependent evolution of conduction-electron excitations in small spherical particles over a broad range of sizes. This evolution is investigated by analysing these excitations into their constituent electronic transition processes. We first make this transition-level analysis for dipole surface plasmons in an electron system confined within a small spherical particle. It is then made for multipole excitations in an electron gas constrained on a spherical surface (SSEG). The multipole-excitation modes in the SSEG are compared with normal-excitation modes in a two-dimensional electron gas (2DEG) confined to a flat plane. As for the above surface plasmon mode, we find that a series of transition processes satisfying specific selection rules plays the leading role in forming this mode. As the number of these leading transition processes becomes larger with increase in size, the mode gradually acquires a more definite character of a collective excitation, and evolves into a more complete surface excitation. Because of the two-dimensionality common to the SSEG and 2DEG, the size dependence of multipole-mode energies of the SSEG bears obvious similarities to the energy dispersion of normal modes in the 2DEG. With increase in size, each multipole mode gains a more definite character of either a collective excitation or a single-particle excitation. This gradual character evolution stems from the finite size of the SSEG.