Dielectric function for free electron gas: comparison between Drude and Lindhard models

Abstract

The interaction between light and metals or heavily doped semiconductors is largely determined by their free conduction electrons. The frequency and wave vector dependent complex dielectric function is an essential ingredient of the description of its optical and transport properties. The aim of this paper is to give a didactic introduction how the conduction electrons in solids responds to an external time dependent electric field and to make a comparison between Drude and Lindhard dielectric function models for the electron gas. In within framework of Lindhard model we derived an expression for dielectric function that is similar to the familiar Drudes's formula. In particular, the differences and similarities between the complex conductivity obtained from the two models are analyzed.