Optical spectra of $\mathrm{Pb}\mathrm{Te}/{\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ quantum wells

The optical absorption spectrum of PbTe quantum wells is revisited. A series of ${\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{e}/\mathrm{P}\mathrm{b}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ multiple quantum well (MQW) samples with x between 0.05 and 0.07 was grown by molecular-beam epitaxy on $\mathrm{}\left(111\right)\mathrm{}{\mathrm{BaF}}_2$ substrates. The PbTe well width was varied from 2.3 to 20.6 nm, while the barrier was kept thicker than 44.2 nm. The transmission spectra were measured at varying temperature (5–300 K) and the energy of the different optical transitions between quantized electron and hole states was obtained from the corresponding absorption steps. Several transitions, from both longitudinal and oblique valleys, are clearly observed. Contrary to what is commonly believed, an overall agreement (i.e., for different transitions, temperatures, and PbTe well widths) is found between the experimental results and the electric-dipole optical transition energies calculated analytically, within the envelope function approximation and the perfect square well model. The effects of the strain inside the thin PbTe layers on the optical transition energies are included in the calculations and studied as a function of well width and temperature. The amount of tensile strain was measured with high-resolution x-ray diffraction at room temperature. From the fit to the experiment, we evaluate the PbTe deformation potentials. At low temperatures, a blueshift is observed in the energy of the longitudinal transitions of the narrow wells, which is attributed to the mismatch in the thermal expansion coefficient between the MQW structure and the ${\mathrm{BaF}}_2$ substrate.