Donor states in modulation-doped Si/SiGe heterostructures

We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The results obtained from calculations for Si/Si$_{1-x}$Ge$_x$ quantum wells allow us to present the general behavior of the impurity states, as the donor position is varied from the center of the well to deep inside the barrier. The influence on the donor ground state from both the central-cell effect and the strain arising from the lattice mismatch is carefully considered.Comment: 17 pages, 10 figure

Infrared Transitions between Shallow Acceptor States in Gaas-Ga1-Xalxas Quantum-Wells

We calculate energies and oscillator strengths of infrared transitions between ground and excited shallow acceptor states in quantum wells (QW's) for varying well width. The impurity states are calculated within a four-band effective-mass theory, which accounts for the valence-band mixing as well as for the mismatch of the band parameters and the dielectric constants between well and barrier materials. The envelope function is expanded into a basis set consisting of products of two-dimensional hydrogeniclike functions and impurity-free QW eigenfunctions at k parallel-to = 0. The present method is suited for s-type ground states as well as for p-type excited states. We obtain the absorption spectra for well widths ranging from 50 to 200 angstrom. We find an overall increase of the transition energies for decreasing well widths. For polarization in the layer planes, the oscillator strengths of the lines corresponding to the bulk G and D lines maintain their oscillator strengths for decreasing well widths, whereas the lines corresponding to the bulk C line are very weak for small well widths. On the other hand, in the case of polarization along the QW axis, the oscillator strengths of the main lines decrease considerably as the well width decreases. We compare our results with absorption spectra of a recent experiment, and find a fairly good agreement

Binding energies of ground and excited states of shallow acceptors in GaAs/Ga1-xAlxAs quantum wells

We calculate binding energies of shallow acceptors in GaAs/Ga1-xAlxAs quantum wells (QWs) for varying well widths. Variational calculations are performed in the framework of a multiband effective-mass theory, which accounts for the mixing between heavy and light holes. The Hamiltonian also takes into account the mismatch between the band parameters and the dielectric constants of well and barrier materials. The envelope function is expanded into a basis set consisting of products of two-dimensional hydrogeniclike functions and impurity-free QW eigenfunctions at k?=0. QW eigenfunctions of the continuum are included till convergence of the acceptor energies is reached. The present method is suited for ground as well as excited acceptor states of 6 and 7 symmetry. We do not include central-cell effects, but give the dependence of the on-center density as a function of the well width in order to estimate these corrections. Comparison with recent experiments, which determine the 1s-2s energy separation, shows very good agreement. © 1990 The American Physical Society

Shallow Impurities in Gaas-Ga1-Xalxas Quantum-Wells

A comprehensive theory of shallow impurities in quantum wells (QW's) is presented. The energy levels of donor and acceptor impurities are calculated within the effective mass theory including the mismatch of the band parameters and of the dielectric constants between well and barrier materials. The theory also accounts for Coulomb coupling between different subbands and, in the case of acceptors, for valence-band mixing. The method is based on an expansion of the envelope functions into a basis set consisting of products of two-dimensional hydrogenic-like functions and impurity-free QW eigen-functions at k parallel-to = 0. The present method is suited for the ground as well as for the excited impurity states and thus enables us to obtain the oscillator strengths of infrared transitions between these states. The results show a good agreement with recent experiments on both donor and acceptor impurities