Localized states of an excess electron in ionic clusters

TL;DR

This paper develops a theoretical model for electron localization in ionic clusters, analyzing how cluster size influences polaron formation, binding energy, and autolocalization radius, with implications for electron affinity in nanostructures.

Contribution

It introduces a combined quasiclassical and quantum approach to describe electron states in ionic clusters, including size-dependent polaron properties and a perturbation method for critical size determination.

Findings

Electron binding energy depends on cluster radius.

Electron autolocalization radius equals the polaron radius in an infinite crystal.

Bound states form only if cluster radius exceeds the polaron radius.

Abstract

A theory for an electron affinity of ionic clusters is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. An interaction of an electron with longitudinal optical phonons in an ionic cluster is described. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of an energy and a radius of a polaron on a cluster's size are obtained by a variational method. It has been found that a binding energy of the electron in a cluster depends on a cluster's radius but the radius of electron's autolocalization does not depend on cluster's radius and equals to the polaron radius in a corresponding infinity crystal, moreover the bound state of the electron in a cluster is possible if the cluster's radius is more then the polaron radius. A perturbation method for finding of the critical parameters is proposed, where an dependence of the critical size on a momentum of an electron in a conduction band is observed.