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

Dielectric mismatch and central-cell corrections in doped silicon nanodots

The effect of the central-cell corrections on the shallow donor states in Si spherical quantum dot is studied within the effective mass approximation. Finite step-like spatial confining potential, Coulomb and image charge potentials arising from the dielectric mismatch at the interface of the media are taken into account. We found that it is possible to tune the impurity energies by varying the dot radius and dielectric constant of the barrier material. In the strong confinement regime, due to the enhanced weight of the donor wave functions on the impurity atoms, large values of the chemical shifts for typical donors in Si compared to the ones in bulk are obtained. The calculated size-dependence of the effective Bohr radius in donor doped nanocrystals is in reasonable accord with electron spin resonance measurements on Si quantum dots embedded in insulating glass matrices. We conclude that both the dielectric mismatch and central-cell corrections must be considered in the study of these systems in order to obtain satisfactory agreement with experimental data