镶嵌于基质中的金属超微粒子特性研究(Ⅰ) 超微粒子的量子阱点模型

STUDY OF THE CHARACTERISTICS OF METALLIC ULTRA-FINE PARTICLES EMBEDDED IN HOST MEDIUM (I) QUANTUM WELL DOT MODEL OF VLTRA-FINE PARTICLES

提出超微粒子(UFP)的量子阱点模型。模型假定UFP的主要特性由其非定域电子(简称电子)决定,电子被束缚在三维有限深势阱内。电子的行为由二部分组成:单电子的和集体化的。电子能谱主要由单电子行为决定。模型反映了UFP的一些重要特性,例如块体材料逸出功,UFP原子半径和第一电离能,而忽略UFP更精细的结构。这种近似被证明是合理的。一系列有用的公式和预言被导出。(1)主要的UFP特性,量子尺寸效应和电子能谱的壳层结构。(2)UFP的逸出功和费密能级公式,这对于其他模型是困难的。导出的UFP逸出功随尺寸变化的公式很好地解释了实验结果:逸出功随UFP尺寸的增大先增大然后逐渐减至同种原子块体材料的逸出功。(3)费密能级附近的平均能级间隙(AES)及AES与电子间相互作用强度的关系,证明著名的Kubo模型是量子阱点模型的特例。(4)预言UFP电子能谱亚能带的存在和金属UFP在某些尺寸下可能呈半导体特性,当粒子尺寸增大时,亚能带将无法辨别并最终消失,此时粒子完全呈块体材料特性。

A quantum well dot model of ultra-fine particles (UFP) is presented in this paper. It is assumed that principal UFP characteristics are determined by non-localized electrons, which are restricted within a three-demensional potential well with finite depth (quantum well dot). Electronic characteristics are contributed by both of single-electron behavior and collective be-haviors. The electron energy spectrum is mainly determined by single-electron behavior. The model reflects the atomic properties, such as bulk work funtion, atomic radius and first ioni-zing energy value, and ignores the finer UFP structures. The approximation is proved rea-sonable. A number of useful formulae and predictions are derived. (1) The famous UFP cha-racteristics, quantum size effect and shell structures of electron energy spectrum, are derived from the quantum well dot model. (2) The UFP work function and Fermi-energy level, which is diffi-cult to be obtained by other models, are calculated. The formula that expresses the work func tion xarying with UFP size variation is derived, which explains well the experiments. The work function increases at first and then decreases gradually to bulk one with UFP size in-creasing. (3) The average energy space (AES) near Fermi- energy and the relationship bet-ween AES and electron interaction are derived. And the famous Kubo formula can be derived from quantum well dot model. (4) Finally, the model predicts the existence of electron energy subbands in UFP and semiconductor behavior of metallic UFP in some size. When particle size increases the sub-bands can not be discriminated and finally disappears, the particle shows complete bulk characteristics.