Optical properties of PbSe/${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se multiple-quantum-well structures

The electronic structure and optical properties of narrow-gap PbSe/${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se quantum-well structures are investigated experimentally and theoretically. The samples were grown by molecular-beam epitaxy along the (111) growth direction and were characterized by high-resolution x-ray diffraction, using triple-axis diffractometry. Their optical properties were investigated by transmission and photoconductivity experiments in the midinfrared range using Fourier-transform spectroscopy. The experimental data show that PbSe/${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se has a staggered band lineup which is in agreement with recent data on coherent anti-Stokes Raman-scattering experiments (Geist et al.), from which it was concluded that holes are confined in the PbSe and electrons in the ${\mathrm{Pb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se layers. The experimental absorption data are compared with calculated data based on a k⋅p envelope-function approach for the type-II superlattice band structure which yields the energy eigenstates, eigenfunctions, and oscillator strengths. The absorption constant is obtained from an integration over k space, and the refractive index from a Kramers-Kronig transformation. The calculated fundamental absorption coefficients are in good agreement with the experimental data. Agreement between experimental and theoretical results is best for a normalized conduction-band-offset range of Δ${\mathit{E}}_{\mathit{c}}$/Δ${\mathit{E}}_{\mathit{g}}$=-0.4 to -0.6 (±0.2).