Magnetoreflectivity ofPb1−xEuxTe epilayers and PbTe/Pb1−xEuxTe multiple quantum wells

Abstract

Molecular-beam epitaxy grown n-type ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te epilayers (x\ensuremath{\leqslant}0.034) and PbTe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te (x\ensuremath{\leqslant}0.039) multiple-quantum-well (MQW) samples were studied by magnetoreflectivity in the Faraday configuration (B\ensuremath{\Vert}[111]) for magnetic fields up to 6 T at 4.2 K. Since the IV-VI lead salt compounds are quite polar semiconductors, resonant electron-longitudinal-optic- (LO-) phonon coupling (Fr\"ohlich coupling) modifies the cyclotron resonance (CR) energies in the ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te single epilayers for the three-dimensional (3D) case. Due to the many-valley band structure two different Fr\"ohlich coupling constants are relevant. However, the CR energies of quasi-two-dimensional (2D) carriers in PbTe wells [${\mathrm{n}}^{2\mathrm{D}}$=(1.5-3)\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$] of PbTe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te MQW samples do not exhibit a significant resonant electron-LO-phonon interaction. This observation is attributed to finite-electron concentration effects, in particular, to a partial filling of the lowest 2D Landau spin level. The static and dynamic screening of the polar interaction are considered as well, but are ruled out as an explanation for the absence of any remarkable polaron correction to the CR energies of electrons in the PbTe quantum wells for the range of carrier concentrations investigated. The magnetoreflectivity spectra of ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te single layers and PbTe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te quantum well samples are simulated numerically, using a model for the dielectric response of IV-VI compounds in a magnetic field, which also includes the electron-LO-phonon interaction. The transverse and longitudinal masses, and thus also the interband momentum matrix elements are determined for ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Eu}}_{\mathrm{x}}$Te as a function of the composition up to x0.034. It is found that the transverse mass increases with Eu content, whereas the longitudinal one nearly stays constant. The 2D CR masses of electrons in the PbTe wells increase with decreasing well width, i.e., with increasing quantum-well interband energies, a behavior which results from the strong band nonparabolicity.