Electronic and optical properties of PbTe/Pb1-xEuxTe multiple-quantum-well structures.

Abstract

The frequency dependence of the absorption constant \ensuremath{\alpha}(\ensuremath{\omega}) and the enhancement of the refractive index n(\ensuremath{\omega}) in the region of interband transitions between confined quasi-two-dimensional states of the valence and conduction bands of PbTe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te multiple-quantum-well (MQW) structures is studied experimentally as well as theoretically. Transmission, reflectivity, and photoconductivity spectra of several MQW's with PbTe well widths from 62 to 118 \AA{} and ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Eu}}_{\mathit{x}}$Te barrier widths from 486 to 621 \AA{} (x\ensuremath{\approxeq}3%) are compared with calculated spectra. The experimental data are compared to calculations of the transmission and reflectivity of the multilayer structures based on frequency-dependent dielectric functions \ensuremath{\epsilon}(\ensuremath{\omega}) of the buffer and MQW layers. For the buffer layer experimentally determined values for \ensuremath{\epsilon}(\ensuremath{\omega}) are used, whereas for the MQW system the sum of a background dielectric function and an additional term, which takes into account the electronic contribution due to interband transitions between electric subbands in the valence band (VB) and conduction band (CB), are used.For calculating the second term two approaches were followed. The conventional approach is based on treating these interband transitions as originating from confined states within the PbTe wells only. The second, more realistic, approach is based on a complete calculation of the band structure of the MQW systems using a k\ensuremath{\cdot}p envelope function approximation which yields proper energy eigenstates, eigenfunctions, and oscillator strengths. The absorption constant \ensuremath{\alpha}(\ensuremath{\omega}) is then obtained from an integration in k space. The electronic contribution \ensuremath{\delta}${\mathrm{\ensuremath{\epsilon}}}^{\mathrm{VB}\mathrm{\ensuremath{-}}\mathrm{CB}}$(\ensuremath{\omega}) to the total dielectric function is independent of the position z along the growth direction in the MQW structure, i.e., in this respect the MQW is treated as being optically homogeneous. The calculated transmission and reflectivity data fit the experimental data very well. The steplike changes in \ensuremath{\alpha}(\ensuremath{\omega}) result in cusplike changes of the refractive index n(\ensuremath{\omega}). From a comparison of the experimentally determined interband transition energies with the calculated values on several samples, the conduction-band offset is determined to be \ensuremath{\Delta}${\mathit{E}}_{\mathit{c}}$/\ensuremath{\Delta}${\mathit{E}}_{\mathit{g}}$=0.55\ifmmode\pm\else\textpm\fi{}0.2.