Temperature-dependent dielectric functions of bcc transition metals Cr, Mo, and W from ultraviolet to infrared regions: A theoretical and experimental study

Abstract

In the bcc transition metals Cr, Mo, and W, the existence of the partially filled d bands makes interband transition occur at low photon frequencies and thus, it is difficult to differentiate it from intraband transition. Here, we present a thorough study on decomposing the intraband and interband contribution to finite temperature dielectric functions of these bcc transition metals by performing electron-phonon and electron-electron interaction calculations, as well as ellipsometry experiments. In this work, the Drude model and interband transition theory are applied to quantitatively describe the intraband and interband transition, respectively. To accurately determine intraband transition, the relevant parameters for the Drude model, such as plasma frequency and electron relaxation time, are calculated from first-principles. The electron-electron interaction within the many-body theory and electron-phonon interaction within the density functional perturbation theory are calculated to obtain the electron relaxation time and intraband dielectric function at finite temperature. As for interband transition, the spin-orbit coupling is included and it shows nontrivial influence on the interband dielectric function of Mo and W, especially at low frequencies. To verify theoretical calculations, ellipsometry experiments are performed to measure dielectric functions of Cr, Mo, and W over the temperature range of 300–700 K and energy range of 0.08–4.8 eV. The experimental results are then fitted by the Drude model, and it shows that the electron-phonon interaction rather than electron-electron interaction dominates the frequency dependence of the relaxation time for transition metals Cr, Mo, and W.