Optical transition energies for lead-salt semiconductor quantum wells

The quantized states for electrons and holes confined in lead-salt semiconductor quantum wells (QW’s) grown on (100) and (111) substrates and the corresponding electric-dipole optical transition energies are calculated analytically, within the envelope function approximation and with the Dimmock two-band $\overrightarrow{k}\cdot \overrightarrow{p}$ model for the bulk. The solution takes into account nonparabolicity, anisotropy, and break of valley and spin degeneracy, due to quantum confinement. Transition energies for different PbTe QW’s, calculated as a function of temperature and well width, are shown to give a fair description of the observations of the quantum size effect reported in the literature. Limitations of the spherical and of the parabolic approximations to the electronic structure of the lead-salt QW’s are made clear and the Rashba spin-orbit term in the effective Hamiltonian is derived.