Hole energy levels and intersubband absorption in modulation-doped Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ multiple quantum wells

A theoretical and experimental study of intersubband transitions in modulation-doped p-type Si/SiGe quantum wells is presented for SiGe wells with widths between 26 and 65 Å and Ge contents in the range from 19% to 50%. The SiGe multiple quantum wells are pseudomorphically strained with an in-plane lattice constant equal to the lattice constant of the Si substrate. Calculations of the in-plane dispersion of the quantum-well states are performed within the envelope-function approach, with full inclusion of the degeneracy and warping of the three topmost bulk valence bands described by the strain-dependent Luttinger-Kohn Hamiltonian. Many-body effects such as the Hartree potential and the exchange-correlation interaction are taken into account in a self-consistent manner. The transmission spectra are finally calculated with a dielectric simulation for the multilayer stack. Using the structural parameters determined by high-resolution triple-axis x-ray diffraction, the results of the calculation are in excellent agreement with the observed intersubband absorption that occurs between 480 and 1830 ${\mathrm{cm}}^{\mathrm{-}1}$ for the different samples. As long as the excited states are confined to the SiGe wells, the full widths of the absorption lines are only 20 meV. This value represents the narrowest absorption line so far observed in p-type SiGe quantum wells.