Infrared spectroscopy of solids

Abstract

For materials like small gap semiconductors or intercalated layered compounds the general form of the complex dielectric function is: ϵ(ω) = ϵ x + Δϵ inter + Δϵ intra + Δϵ ph, where ϵ ∞is the high frequency dielectric constant due to all interband transitions except the uppermost valence band and the lowest conduction band, Δϵ inter is the contribution to the dielectric constant due to this two bands in particular, Δϵ intra is the contribution due to intraband free carrier transitions and Δϵ ph is the contribution due to lattice vibrations. The contribution from transitions between valence and conduction bands to the imaginary part of the dielectric function Δϵ inter(ω, T) for a narrow gap material can be readily calculated in the random phase approximation (RPA) formalism. The real part Δϵ inter is obtained by performing the Kramers-Kronig inversion on the expression Δϵ inter. Dielectric function of HgTe between 8 and 300 K is discussed. The interband contribution to the complex dielectric function in a layered intercalation compound is also examined. Pure graphite, first and second stage compounds are treated as an example. Reflectivity and magnetoreflectivity spectra simultaneously determining the plasma and the cyclotron frequencies, allow one to measure the free carrier density, hence the Fermi level, and the effective mass of the carriers. The variation of the effective mass as a function of the position of the Fermi level traces the energy bands dispersion relation. An example of such investigations is given for PbSe layered materials like Bi 2Se 3 are also studied by infrared reflectivity spectroscopy. Intercalation of such materials increases the free carrier population which consequently moves the Fermi level up in the conduction band. Analysis of reflectivity spectra allows an accurate determination of the free carrier concentration and gives a useful tool for the investigation of atom insertion in layered materials. Recent experiments on the intercalation of Li in a certain number of layered materials will be presented. In the frame of the classical theory of independent harmonic oscillators, the phonon contribution to the dielectric function is given by the sum of transverse modes for each oscillator with the corresponding damping parameters and oscillator strength. The complex dielectric function can then be written as a set of separate equations for the real and imaginary parts of the wave-number-dependent dielectric function. In the spectral region when phonon and plasmon frequencies may coincide a strong plasmon-phonon coupling will be experienced. In a simple model with one LO and one TO frequency, one expects two singularities at the two maxima of the function 1m −ϵ −1; representing longitudinal modes. The frequencies generally labeled ω + and ω - correspond to longitudinal oscillations with the lattice and electron plasma vibrating, respectively, in phase and 180° out of phase. In small gap materials the situation is more complex. Because of the particular band structure, the contribution Δϵ inter(ω) must be included. In some cases it also becomes necessary to include additional oscillators with strong polar character corresponding to a particular defect or to additional vibrations. The implications of all these fundamental concepts in the investigation of high Tc materials is discussed and examples given.