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

A V Andrade-Neto

doi:10.1590/1806-9126-rbef-2016-0206

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.

Highlights

In some solids, namely metals and doped semiconductors, a few loosely bound valence electrons are assumed to be completely detached from their atoms and move around throughout the material forming an electron gas
The optical response of these materials can be described by means of a frequency and wave vector dependent complex dielectric function (q, ω) of the electron gas, which is an essential ingredient of the description of the transport and optical properties of solids [1]
2 - In the Drude model the imaginary part of the conductivity is always positive, while in the Lindhard model the imaginary part of the conductivity is negative for values in the range 0 < ω < γL

Summary

Introduction

Namely metals and doped semiconductors, a few loosely bound valence electrons are assumed to be completely detached from their atoms and move around throughout the material forming an electron gas In this model, we consider that the positive ions core form a uniform positive background. Where P (r, t) is the macroscopic polarization (dipole moment per unit volume) that represents the response of the medium to an external electric field. This response for linear media that exhibit temporal and spatial dispersion, i.e., the response at position r and time t to an electric field E(r , t ) at position r and time t is given by Copyright by Sociedade Brasileira de Fısica.

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